Solving for CI in terms of the given lengths, we get: [tex]Cl=\frac{\sqrt{BG^{2} -IM^{2} } }{\sqrt{2} }[/tex]
Substituting this expression for CI and the given value for CG into the expression for BI, we get: [tex]BI=CG-\frac{\sqrt{BG^{2} -IM^{2} } }{\sqrt{2} }[/tex].
What is triangle?A triangle is a three-sided polygon, which is a closed two-dimensional shape with straight sides. In a triangle, the three sides connect three vertices, or corners, and the angles formed by these sides are called the interior angles of the triangle. The sum of the interior angles of a triangle is always 180 degrees. Triangles can be classified by their side lengths and angle measurements. For example, an equilateral triangle has three sides of equal length, and all of its angles are 60 degrees; an isosceles triangle has two sides of equal length, and its base angles are also equal; a scalene triangle has three sides of different lengths, and all of its angles are also different. Triangles are a fundamental shape in mathematics and geometry, and they have numerous applications in fields such as architecture, engineering, physics, and more.
Given by the question.
Based on the given information, we can start by drawing a diagram of triangle ABC and the segments AH, BJ, CI, CJ, and BI as described.
Since CG = BG, we can draw the perpendicular bisector of side AC passing through point G, which will intersect side AB at its midpoint M.
Now, we can see that triangle CGB is isosceles with CG = BG, so the perpendicular bisector of side CB also passes through point G. This means that G is the circumcenter of triangle ABC, and therefore, the distance from G to any vertex of the triangle is equal to the radius of the circumcircle.
Next, we can use the fact that AJ and BJ are congruent to draw the altitude from point J to side AB, which we will call JN. Similarly, we can draw the altitude from point I to side BC, which we will call IM.
Since AJ and BJ are congruent, the altitude JN will also be the perpendicular bisector of side AB, so it will pass through point M. Similarly, the altitude IM will pass through point G, which is the circumcenter of triangle ABC.
Now, we can use the Pythagorean theorem to find the lengths of JN and IM in terms of the given lengths:
[tex]JN^{2}= AJ^{2} -AN^{2} \\ = ( AH+HN)^{2} - AN^{2} \\=AH^{2} +2AH*HN+HN^{2}-AN^{2} \\[/tex]
[tex]IM^{2}= CI^{2} -CM^{2} \\=( CG-GM)^{2} -CM^{2} \\CG^{2}-2CG*GM+GM^{2} -CM^{2}[/tex]
Since CG = BG and GM = BM (since M is the midpoint of AB), we can simplify the expression for IM^2 as follows:
[tex]IM^{2}[/tex] = [tex]BG^{2}[/tex] - 2BG * BM + [tex]BM^{2}[/tex] - [tex]CM^{2}[/tex]
= [tex]BG^{2}[/tex] - [tex]BM^{2}[/tex] - [tex]CM^{2}[/tex]
Now, we can use the fact that BJ and CI intersect at point K to find the length of KJ:
KJ = BJ - BJ * (CK/CI)
= BJ * (1 - CK/CI)
= BJ * (1 - BM/CM)
To find BM/CM, we can use the fact that triangle BCI is isosceles with BI = CI, so the altitude IM is also a median of the triangle. This means that CM = 2/3 * BI. Similarly, we can find BJ in terms of JN using the fact that triangle ABJ is isosceles with AJ = BJ:
BJ = 2 * JN
Substituting these expressions into the equation for KJ, we get:
KJ = 2 * JN * (1 - 2/3 * BI/CM)
Now, we just need to find BI/CM in terms of the given lengths. Using the fact that triangle BCI is isosceles with BI = CI, we can find BI in terms of CG:
BI = CG - CI
Substituting this expression into the equation for [tex]IM^{2}[/tex]and simplifying, we get:
[tex]IM^{2}[/tex] =[tex]BG^{2}[/tex] - CG * CI
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What is the degree measure of the smaller angle between the hour and minute hands of the clock at 5:10 PM?
F. 110°
G. 105°
H. 100°
J. 95°
K. 90°
Answer:
At 5:10 PM, the minute hand is at the 2-minute mark, and the hour hand is between the 5 and 6 marks, closer to the 5.
The minute hand is at the 2-minute mark, which is 1/30th of the way around the clock face. So, the minute hand has traveled 1/30th of a full circle, which is 360°, or 12°.
The hour hand is between the 5 and 6 marks, closer to the 5. It has passed the 5 and is 1/6th of the way to the 6. Since the clock face is divided into 12 hours, 1/6th of the way from 5 to 6 is 5 + 1/6 = 5.166... hours.
Each hour mark represents 30 degrees, so the hour hand has traveled 5.166... × 30 = 155 degrees from the 12 o'clock position.
The smaller angle between the hands is the angle between the hour hand and the minute hand that is less than 180 degrees. We can find this angle by subtracting the smaller angle between the hands from 360 degrees.
To find the smaller angle between the hands, we can subtract the angle traveled by the hour hand from the angle traveled by the minute hand:
12° - 155° = -143°
The negative sign indicates that the angle is measured clockwise from the 12 o'clock position. To find the positive angle between the hands, we add 360 degrees:
360° - 143° = 217°
Therefore, the degree measure of the smaller angle between the hour and minute hands of the clock at 5:10 PM is approximately 217 degrees. Since this value is not one of the answer choices, we can round it to the nearest choice, which is F. 110°
There is a total of 360 students and teachers at a school. A trip is organized and 65% of the students and teachers bought tickets to go on this trip.
(a) Work out how many of the students and teachers bought tickets to go on the trip.
The number of teachers,the number of male students and the number of female students who bought tickets to go on the trip are in the ratios 1:3:5 .
(b) Calculate the number of female students who bought tickets to go on the trip.
All the male students who bought tickets went on the trip but 4 of the female students who bought tickets did not go on the trip.
(c) Find the ratio of the number of male students who went on the trip to the number of female students who went on the trip.
Answer: Below :)
Step-by-step explanation:
(a) The percentage of students and teachers who bought tickets to go on the trip is 65%. So the number of students and teachers who bought tickets can be found by multiplying the total number of students and teachers by 65%:
65/100 x 360 = 234
Therefore, 234 students and teachers bought tickets to go on the trip.
(b) Let the number of teachers who bought tickets be x. Then the number of male students who bought tickets is 3x, and the number of female students who bought tickets is 5x.
The total number of students and teachers who bought tickets is:
x + 3x + 5x = 9x
We know that 234 students and teachers bought tickets, so we can set up the following equation:
9x = 234
Solving for x, we get:
x = 26
So the number of teachers who bought tickets is 26, the number of male students who bought tickets is 78 (3x), and the number of female students who bought tickets is 130 (5x).
However, 4 of the female students who bought tickets did not go on the trip, so the actual number of female students who went on the trip is:
130 - 4 = 126
(c) The ratio of the number of male students who went on the trip to the number of female students who went on the trip is:
78/126
Simplifying this ratio by dividing both numerator and denominator by 6, we get:
13/21
Therefore, the ratio of the number of male students who went on the trip to the number of female students who went on the trip is 13:21.
CDs are on sale for $5 each. Jennifer has $45 and wants to buy as many as she can. How many CDs can Jennifer buy?
Answer:
9 CDs
Step-by-step explanation:
r u d0mb? 45 divided by 5 = 5 10 15 20 25 30 35 40 45
count the numbers
BOOM ANSWER
NEXT TIME PAY ATTENTION IN 2ND GRADEtrue/false. all of the following are things you can do when faced with any ethical dilemma as a managerial accountant except: always contact the board of directors first.
The statement " all of the following are things you can do when faced with any ethical dilemma as a managerial accountant except: always contact the board of directors first" is false because contacting the board of directors is not always necessary or appropriate when faced with an ethical dilemma as a managerial accountant
Contacting the board of directors is not always necessary or appropriate when faced with an ethical dilemma as a managerial accountant. While the board of directors may need to be informed in some situations, there are other steps that can be taken depending on the specific circumstances. For example, seeking guidance from a supervisor, consulting with a professional organization, or seeking legal advice may be more appropriate in some cases. The appropriate course of action will depend on the specific situation and ethical principles involved.
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PLEASE HELP MEEE
whoever answers right gets brainliest!!!
Answer:
[tex]30\leq x[/tex] AND [tex]x \leq 106[/tex]
Notice the valid answer is the one with the AND since need to be both at the same time.
Step-by-step explanation:
Is the one is market, you add 6 to each side and you obtain that answer
[tex]24 \leq x-6\leq 100[/tex]
[tex]24 +6\leq x\leq 100+6[/tex]
[tex]30\leq x\leq 106[/tex]
10 points!!! ASAP PLEASE HELP FIND THE AREA AND THE PERIMETER!!
Answer:
Area = 559.17 square feet
Perimeter = 94.26 ft
Step-by-step explanation:
Make sure all the units are the same and consistent.
r = radius of semi-circle
= [tex]\frac{Diameter}{2}[/tex]
= [tex]\frac{18}{2}[/tex] ft
= 9 ft
Area of composite figure = Area of rectangle + Area of semi-circle:
= [Length × Breadth] + [[tex]\frac{1}{2}[/tex] × (Area of circle)]
= [24 ft × 18 ft] + [[tex]\frac{1}{2}[/tex] × ([tex]\pi r^{2}[/tex])]
= 432 [tex]ft^{2}[/tex] + [[tex]\frac{1}{2}[/tex] × ([tex]\pi 9^{2}[/tex])] [tex]ft^{2}[/tex]
= 432 + [[tex]\frac{1}{2}[/tex] × (3.14) ×(81)]
= 559.17[tex]ft^{2}[/tex]
Perimeter of composite figure =
Circumference of semi-circle + 3 outer sides of rectangle:
= [[tex]\frac{1}{2}[/tex] × [tex]2\pi r[/tex]] + [24 + 18 + 24]
= ( [tex]\pi r[/tex] + 66) ft
= [(3.14)(9) + 66] ft
= 94.26 ft
generally, cold fronts move fast er than warm fronts generally, cold fronts have steeper slopes generally, precipitation cover s a much broader area with a cold front especially in winter, cumuliform clouds are more often associated with cold fronts
Cold fronts generally move faster than warm fronts because cold air is denser and thus, moves more quickly. Precipitation with a cold front typically covers a broader area, especially during the winter.
On the other hand, warm fronts move more slowly as they are characterized by the gradual lifting of warm air over colder air. Cold fronts also typically have steeper slopes than warm fronts. This is because the leading edge of a cold front is more abrupt.
With a steep rise in the cold air mass. In contrast, the leading edge of a warm front has a gentler slope as the warm air gradually rises over the colder air.
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write each expression without the absolute value symbol
The piecewise function forms of the absolute values are, respectively:
Case 1 (|(x - 19) + 11|)
x - 8 for x > 8
0 for x = 8
8 - x for x < 8
Case 2 (|14 - (x - 6)|)
- x + 22 for x < 22
0 for x = 22
x - 22 for x > 22
Case 3 (|14 - (6 - x)|)
x + 8 for x > - 8
0 for x = - 8
- x - 8 for x < - 8
How to rewrite absolute value functionsIn this problem we find three cases of absolute values represented in a single expression. Herein we need to determine an alternative form without "bar" operators.
This form is represented by a piecewise function derived from definition of absolute value:
|x - a| = x - a for x > a|x - a| = a - x for x < a|x - a| = 0 for x = a.Then, we find the following definitions for each of the three cases:
Case 1
|(x - 19) + 11| = |x - 8|
|x - 8| = x - 8 for x > 8
|x - 8| = 0 for x = 8
|x - 8| = 8 - x for x < 8
Case 2
|14 - (x - 6)| = |- x + 22|
|- x + 22| = - x + 22 for x < 22
|- x + 22| = 0 for x = 22
|- x + 22| = x - 22 for x > 22
Case 3
|14 - (6 - x)| = |x + 8|
|x + 8| = x + 8 for x > - 8
|x + 8| = 0 for x = - 8
|x + 8| = - x - 8 for x < - 8
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△CDE∼△PQR. CD=9 m, EC=15 m, PQ=15 m. What is the length of RP?
Answer:
RP = 25
Step-by-step explanation:
since the triangles are similar then the ratios of corresponding sides are in proportion, that is
[tex]\frac{RP}{EC}[/tex] = [tex]\frac{PQ}{CD}[/tex] ( substitute values )
[tex]\frac{RP}{15}[/tex] = [tex]\frac{15}{9}[/tex] ( cross- multiply )
9 RP = 15 × 15 = 225 ( divide both sides by 9 )
RP = 25
Andy has 4 red cards, 3 blue cards, and 2 green cards. He chooses a card and replaces it before choosing a card again. How many possible outcomes are in the sample space of Andy's experiment?
A) 18
B) 9
C)81
D)3
Answer: C) 81
Step-by-step explanation:
Since Andy chooses a card and replaces it before choosing another card, each choice is independent and the total number of possible outcomes is the product of the number of choices for each card.
There are 4 red cards, 3 blue cards, and 2 green cards, so there are a total of 4+3+2=9 cards to choose from.
For each choice, Andy has 9 options. Since he does this twice, the total number of possible outcomes is:
9 x 9 = 81
Therefore, the answer is C) 81.
A pond in the shape of a right-angled triangle is shown below. Calculate the perimeter of the pond. Give your answer in metres to 1 d.p. 1.46 m 100 73°
The perimeter of the pond is 2.92 meters.
What s a right-angle triangle:
A right-angled triangle is a triangle in which one of the angles measures exactly 90 degrees, also known as a right angle.
The side opposite the right angle is called the hypotenuse, and the other two sides are called the legs.
The perimeter of a right-angled triangle is the sum of the lengths of its three sides.
Here we have
The Hypotenuse of the triangle is 1.46 m
The angle between hypotenuse and perpendicular height = 73°
From triagonometric ratios,
=> cos A = Perpendicular height/ Hypotenuse.
=> cos (73) = Perpendicular height/1.46
=> Perpendicular height = 1.46 × 0.29 = 0.42 m
As we know from Pythagoras' theorem,
Hypotenuse² = side² + side²
Side = √Hypotenuse² - side²
= √[(1.46)²- (0.42)²] = 1.04
Therefore, the sides of the pond are 1.46 m, 0.42 m, and 1.04
Hence, perimeter of the pond = 1.46 + 0.42 + 1.04 = 2.92 meters
Therefore,
The perimeter of the pond is 2.92 meters.
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The complete Question is given below
Two trains A and B left the same station at the same time. The speed of
train A is 105 kmph, while train B's is 87 kmph. If they travel in the same
direction, how far apart will they be in three hours?
Answer:
Step-by-step explanation:
Since they are traveling in the same direction, the distance between them increases at a rate of the difference of their speeds.
The relative speed of train A with respect to train B is:
105 kmph - 87 kmph = 18 kmph
In three hours, the distance between them will be:
Distance = Speed x Time
Distance = 18 kmph x 3 hours
Distance = 54 km
Therefore, the two trains will be 54 kilometers apart after three hours.
Find area of a circle whose diameter 21cm
The area of the circle is approximately 346.36 square centimeters.
What is area?Area is a mathematical concept that refers to the amount of space that is inside a two-dimensional shape or surface. It is typically measured in square units, such as square meters (m² or square centimeters (cm²).
What is a diameter?The diameter of a circle is the distance across the circle passing through its center. It is twice the length of the circle's radius.If you know the diameter of a circle, you can calculate its radius by dividing the diameter by 2: radius = diameter/2
In the given question,
The diameter (d) of a circle is the distance across the circle passing through the center.
If the diameter of the circle is 21 cm, then the radius (r) of the circle (which is half of the diameter) is:
r = d/2 = 21/2 = 10.5 cm
The formula for the area (A) of a circle is:
A = πr²
where π (pi) is a mathematical constant that represents the ratio of the circumference of a circle to its diameter, approximately equal to 3.14159.
Substituting the value of r into the formula, we get:
A = π(10.5)² A = 346.36 cm² (rounded to two decimal places)
Therefore, the area of the circle is approximately 346.36 square centimeters.
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For ever 100 clovers that Lucy picked 22 of them had four leaves while the others only had three leave in total Lucy picked 1,000 clovers if her pattern continued, how many three - leaf and four leaf would Lucy have how many of each clover would she have if she picked 2,000 clovers
Answer:
a)220 4 leaf clovers, 780 3 leaf clovers b)440 four leaf clovers, 1560 3 leaf clovers
Step-by-step explanation:
100:1000=1:10 22:x=1:10 x=220
220x2=440
1000-220=780
780x2=1560
What are the coordinates of point G on the coordinate grid below?
A
(-4,3)
(4,-3)
-2
4
2
O
-2
4
B
AY
D
2
(4,3)
(-4,-3)
4
G
XA
Answer:
The answer is G = (4,3)
Step-by-step explanation:
G = (4,3)
a fire truck is parked 25 feet away from a high rise. the ladder on the truck reaches 100 feet. how high up the high rise can the ladder reach?
Answer:
If the fire truck is parked 25 feet away from the high rise and the ladder on the truck reaches 100 feet, we can use the Pythagorean theorem to find out how high up the high rise the ladder can reach.
Let's assume that the height the ladder can reach is "x". Then, we can set up the following equation:
25^2 + x^2 = 100^2
Simplifying this equation, we get:
625 + x^2 = 10000
Subtracting 625 from both sides, we get:
x^2 = 9375
Taking the square root of both sides, we get:
x = sqrt(9375)
x ≈ 96.81
Therefore, the ladder on the fire truck can reach a height of approximately 96.81 feet up the high rise
The following cross-tabulation of frequencies for Income Levels (A, B, and C) and Education Levels (E, F, and
G
) has been obtained for a sample of 122 persons: Download Excel Table Here 1) For a randomly selected observation from the above data, determine the probability
P(B∪E)
. Round your answer to four decimal places (include zero if necessary). 2) For a randomly selected observation from the above data, determine the probability
P(G c
)
. Round your answer to four decimal places (include zero if necessary). 3) For a randomly selected observation from the above data, determine the probability
P(C∣F)
. Round your answer to four decimal places (include zero if necessary).
The probability of P(B U E) is 0.5984, the probability of the complement of G (i.e. Gᶜ) is 0.6818, and the probability of C given F is 0.4706
To find the probability P(B U E), we need to add the frequencies in column B and row E, but since the cell where they intersect has already been counted in both, we need to subtract it once. Therefore:
P(B U E) = (6+13+17) + (15+20+10+45) - 43 = 73
Then we divide by the total number of observations:
P(B U E) = 73/122 = 0.5984 (rounded to four decimal places)
To find the probability of the complement of G (i.e. Gᶜ), we need to subtract the frequency in the cell where G and Total intersect from the total number of observations:
P(Gᶜ) = 1 - 39/122 = 0.6818 (rounded to four decimal places)
To find the probability of C given F, we need to divide the frequency in the cell where C and F intersect by the total frequency in the row where F is located:
P(C|F) = 24/51 = 0.4706 (rounded to four decimal places)
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Complete question is attached below
One side of the triangle is 4 cm, and the sum of the other two sides is equal to a whole number of cm. What is the smallest possible perimeter of the triangle?
F. 9 cm
G. 10 cm
H. 11 cm
J. 15 cm
K. 17 cm
Answer:
9 cm
Step-by-step explanation:
By the Triangle Inequality, any two sides of a triangle must be greater than the remaining side.
In order to minimize the perimeter, we will assume that 4 cm is the longest side.
Thus, the two remaining sides must be greater than 4.
Since we are given that the sum of the two remaining sides is a whole number, the smallest whole number value greater than 4 is 5.
Hence, the smallest perimeter possible 9 cm.
The figure to the right shows the results of a survey in which 1007 adults from Country A, 1005 adults from
Country B, 1016 adults from Country C, 1016 adults from Country D, and 1000 adults from Country E were
asked whether national identity is strongly tied to birthplace.
National Identity and Birthplace
People from different countries who believe national
identity is strongly tied to birthplace
Country A
Country B
Country C
Country D
Country E
34%
22%
29%
50%
14%
Construct a 99% confidence interval for the population proportion of adults who say national identity is strongly tied to birthplace for each country listed.
99% confidence interval is that the true population proportion of adults who say national identity is strongly tied to birthplace in Country A is between 30.7% and 37.3%.
What is confidence interval?The confidence interval is a set of values that, with a given level of certainty, contains the real population parameter. The likelihood that the genuine population parameter falls inside the interval is represented by the degree of confidence. In this instance, we created 99% confidence intervals for the percentage of individuals in each demographic who claim that national identity is highly correlated with birthplace. This indicates that 99% of the intervals we build would include the genuine population percentage if the survey were to be repeated numerous times.
The confidence interval is given using the formula:
CI = p ± z*(√((p*(1-p))/n))
Using the given values for different intervals the 99% for different countries are:
For Country A we have:
p = 0.34
n = 1007
z = 2.58 (based on a 99% confidence level)
CI = 0.34 ± 2.58*(√((0.34*(1-0.34))/1007)) = 0.307 to 0.373
For Country B we have:
p = 0.22
n = 1005
z = 2.58
CI = 0.22 ± 2.58*(√((0.22*(1-0.22))/1005)) = 0.187 to 0.253
For Country C we have:
p = 0.29
n = 1016
z = 2.58
CI = 0.29 ± 2.58*(√((0.29*(1-0.29))/1016)) = 0.259 to 0.321
For Country D we have:
p = 0.5
n = 1016
z = 2.58
CI = 0.5 ± 2.58*(√((0.5*(1-0.5))/1016)) = 0.469 to 0.531
For Country E we have:
p = 0.14
n = 1000
z = 2.58
CI = 0.14 ± 2.58*(√((0.14*(1-0.14))/1000)) = 0.108 to 0.172.
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An isosceles right triangle has a base of x-2 and a height of x-2. The area of the triangle is 50
square inches. Using A=1/2 bh to find the area of a triangle, what is the value of x?
When an isοsceles right triangle has a base οf x-2 and a height οf x-2. The area οf the triangle is 50 square inches then Using A=1/2 bh tο find the area οf a triangle is 1/2 (x-2)(x-2) = (x-2)²/2, and 12 inches is the value οf x?
Using A=1/2 bh hοw tο find the area οf a triangle?An isοsceles right triangle has twο equal legs and the length οf the hypοtenuse is [tex]\sqrt{(2)[/tex] times the length οf a leg. In this case, bοth legs have the length x-2, sο the length οf the hypοtenuse is (x-2)*sqrt (2).
The area οf the triangle is given by A=1/2 bh, where b is the base and h is the height. In this case, b=h=x-2, sο the area is:
A = 1/2 (x-2)(x-2) = (x-2)²/2
Then what will be the area?Area is 50, sο we can set up an equatiοn:
(x-2)²/2 = 50
Multiplying bοth sides by 2 gives:
(x-2)² = 100
Taking the square rοοt οn bοth sides gives:
x-2 = 10 οr x-2 = -10
The negative sοlutiοn dοesn't make sense in this cοntext, sο we discard it. Therefοre, we have:
x-2 = 10
Adding 2 tο bοth sides gives:
x = 12
Therefοre, the value οf x is 12 inches.
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When an isοsceles right triangle has a base οf x-2 and a height οf x-2. The area οf the triangle is 50 square inches then Using A=1/2 bh tο find the area οf a triangle is 1/2 (x-2)(x-2) = (x-2)²/2, and 12 inches is the value οf x.
Using A=1/2 bh hοw tο find the area οf a triangle?An isοsceles right triangle has twο equal legs and the length οf the hypοtenuse is times the length οf a leg. In this case, bοth legs have the length x-2, sο the length οf the hypοtenuse is (x-2)*sqrt (2).
The area οf the triangle is given by A=1/2 bh, where b is the base and h is the height. In this case, b=h=x-2, sο the area is:
A = 1/2 (x-2)(x-2) = (x-2)²/2
Then what will be the area?Area is 50, sο we can set up an equatiοn:
(x-2)²/2 = 50
Multiplying bοth sides by 2 gives:
(x-2)² = 100
Taking the square rοοt οn bοth sides gives:
x-2 = 10 οr x-2 = -10
The negative sοlutiοn dοesn't make sense in this cοntext, sο we discard it. Therefοre, we have:
x-2 = 10
Adding 2 tο bοth sides gives:
x = 12
Therefοre, the value οf x is 12 inches.
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What is the gravitational force acting on a 70.0 kg object standing on the Earth’s surface?
Answer:
What is the gravitational force acting on a 70.0 kg object standing on the Earth’s surface?
Step-by-step explanation:
The gravitational force acting on a 70.0 kg object standing on the Earth’s surface can be calculated using the formula:
F = G * (m1 * m2) / r^2
Where:
F = gravitational force
G = gravitational constant (6.6743 x 10^-11 N*m^2/kg^2)
m1 = mass of the first object (in this case, the mass of the Earth)
m2 = mass of the second object (in this case, the mass of the object, 70.0 kg)
r = distance between the centers of the two objects (in this case, the radius of the Earth, which is approximately 6,371 km)
Using the values above, we can calculate the gravitational force as follows:
F = (6.6743 x 10^-11 N*m^2/kg^2) * (5.97 x 10^24 kg * 70.0 kg) / (6,371,000 m)^2
F = 686.6 N
Therefore, the gravitational force acting on a 70.0 kg object standing on the Earth’s surface is approximately 686.6 N.
Which statement explains how you could use coordinate geometry to prove that
quadrilateral ABCD is a rectangle?
You could use coordinate geometry to prove that ABCD is a rectangle by checking the side lengths, slope, and diagonal lengths using the distance and slope formulas.
What is a rectangle?
A rectangle is a quadrilateral with four right angles, meaning each of its angles measures 90 degrees. It is a type of parallelogram where opposite sides are parallel and equal in length. The opposite sides of a rectangle also have equal length, and its diagonals bisect each other. In addition to its geometrical properties, rectangles are commonly used in various fields for their symmetry, regularity, and practicality, such as in architecture, engineering, and graphic design.
To prove that quadrilateral ABCD is a rectangle using coordinate geometry, one possible method is to use the properties of a rectangle. Specifically, a rectangle is a quadrilateral with all four angles equal to 90 degrees and opposite sides equal in length.
So, to use coordinate geometry to prove that ABCD is a rectangle, you could:
Assign coordinates to the four vertices of ABCD, say A(x1,y1), B(x2,y2), C(x3,y3), and D(x4,y4).
Use the distance formula to calculate the lengths of each side of the quadrilateral, i.e., AB, BC, CD, and DA.
Use the slope formula to find the slopes of the four sides. Since opposite sides of a rectangle are parallel, their slopes will be equal.
Use the distance formula again to calculate the diagonal lengths, AC and BD.
Check that the opposite sides are equal in length and parallel, and that the diagonals are equal in length. If all these conditions are satisfied, then ABCD is a rectangle.
Therefore, you could use coordinate geometry to prove that ABCD is a rectangle by checking the side lengths, slope, and diagonal lengths using the distance and slope formulas.
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Suppose parametric equations for the line segment between (8,-2) and (9,-2) have the form:
{x(t)=a+bt
{y(t)=c+dt
If the parametric curve starts at (8,-2) when t=0 and ends at (9,-2) at t=1, then find a,b,c, and d. a= b=
c=
d=
A parametric equation is one where the x and y coordinates of the curve are both written as functions of another variable called a parameter; this is usually given the letter t or θ . And the value of a= 8, b= 1, c= -2 and d= 0.
Equation of this form is known as a parametric equation; it uses an independent variable known as a parameter (often represented by t) and dependent variables that are defined as continuous functions of the parameter and independent of other variables.
You require 4 independent solutions because there are 4 unknowns. You can put two equations at each end point if you know t at each end point. (one for the x value and one for the y value).
At (8,-2), time is equal to zero as follows: 8 = a + bt = a + b(0) a = 8 -2 = c + dt = c + d(0) c = -2
At (9,-2), t = 1 because 9 = a + bt = 8 + b(1) b = 1 and -2 = c + dt = -2 + d(1) d = 0.
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here's a graph that represents f (x) = 5. 4321*2^x .
the coordinate of a are ( 1,c) and the coordinates of b are ( 4,d) what is the value of d/c ? explain your reasoning
The value of d/c = 8, when the given graph represents the equation f(x) = 5.4321*(2)ˣ, and A (1, c), and B (4, d) pass through the graph.
What does the graph of an equation show?The graph of an equation passes through all the points that satisfy the given equation. The graph shows a curve joining all those points.
How do we solve the given question?In the question, we are given a graph and its equation f(x) = 5.4321*(2)ˣ.
We are given the coordinates of two points on graphs A: (1, c) and B: (4, d).
We know that any point of the form (x, y) which passes through the graph of the equation, satisfies the equation.
∴ A (1, c) and B (4, d) satisfies the equation f(x) = 5.4321*(2)ˣ.
∴ c = 5.4321*(2)¹ = 5.4321 * 2
d = 5.4321*(2)⁴ = 5.4321 * 16
∴ d/c = (5.4321*16)/(5.4321*2) = 16/2 = 8.
∴ The value of d/c = 8, when the given graph represents the equation f(x) = 5.4321*(2)ˣ, and A (1, c), and B (4, d) pass through the graph.
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Milan bought packs of pencils. Each pack has pencils. Write an equation to represent the total number of pencils that Milan bought.
Answer:
total number of pencils = p × n
total number of pencils = 3 × 12 = 36
Step-by-step explanation:
Let's break down the problem into its components. Milan bought packs of pencils, so we can represent the number of packs he bought with the variable "p". We also know that each pack has "n" number of pencils, so the total number of pencils Milan bought can be found by multiplying the number of packs with the number of pencils in each pack.
In mathematical notation, this can be written as:
total number of pencils = number of packs × number of pencils in each pack
or, using the variables we defined:
total number of pencils = p × n
So, if Milan bought 3 packs of pencils and each pack had 12 pencils, the total number of pencils he bought would be:
total number of pencils = 3 × 12 = 36
Sara is a salesperson for Camera's Etc., which is a retailer for high-end digital cameras. Historically. Sara has averaged selling 2.7 extended warranties per day for cameras that she sells. Assume the number of camera warranties that Sara
sells per day follows the Poisson distribution. Complete part A
a. What is the probability that Sara will sell four extended warranties tomorrow?
The probability that Sara whassell four extended warranties tomorrow is___
(Round to four decimal places as needed.)
Answer:
The probability that Sara whassell four extended warranties tomorrow is 0.1046
Step-by-step explanation:
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We can use the Poisson probability formula to calculate the probability of selling 4 extended warranties tomorrow:
P(X = k) = (e^(-λ) * λ^k) / k!
where λ is the average number of extended warranties sold per day and k is the number of extended warranties sold.
In this case, λ = 2.7 and k = 4. So, plugging in the values, we get:
P(X = 4) = (e^(-2.7) * 2.7^4) / 4!
P(X = 4) ≈ 0.1046
Therefore, the probability that Sara will sell four extended warranties tomorrow is approximately 0.1046, rounded to four decimal places.
I need help with this question.
you need to match it to the percentage of the fraction for example 1/2 is 50 percentage and than you do 1/4 is 25 percent.
What is the missing value in the equation shown below?
4/10+ ?/100= 7/10
A 1
B 3
C 10
D 30
Answer: D 30
Step-by-step explanation:
4/10 + 30/100
2/5 + 3/10
7/10
NB: LEFT-HAND SIDE IS EQUAL TO THE RIGHT-HAND SIDE
A shop is having a 40% sale. A jumper originally costs £50. How much will it be in sale?
Answer:
30 pounds
Step-by-step explanation:
Since the jumper costs 50 pounds, the decimal for the number will be:
50.
To find ten percent of the number, you move the decimal one time to the LEFT.
Therefore, 10% of 50 pounds will be 5 pounds. To find 40%, we simply will multiply the 10% amount by 4.
40% of 50 will be:
20
Therefore, the jumper will have 20 pounds off.
Since the original cost is 50 pounds, we simply will just subtract 50 - 20:
50 - 20 = 30
The jumper will cost 30 pounds with the sale deal.
find the lenght of each side of a rohmbus with permeter of 40 meters
Answer:
10 metres
Step-by-step explanation:
All sides are equal in Rhombus
So, the length of one side= 40m÷4
=10 metres