a) The cosine rule can be used to find the value of x in the triangle below.
What number completes the following calculation? x² = 12² +152 - 2 x 12 x 15 x cos(?)
b) What is the value of x? Give your answer to the nearest integer.
Answers
Answer:
see explanation
Step-by-step explanation:
(a)
(the side required )² = sum of squares of other 2 sides - ( 2 × product of other 2 sides and cos(angle opposite side required ) )
x² = 12² + 15² - (2 × 12 × 15 × cos71°)
(b)
x² = 144 + 225 - 360cos71°
= 369 - 360cos71° ( take square root of both sides )
x = [tex]\sqrt{369-360cos71}[/tex]
≈ 16 cm ( to the nearest integer )
Related Questions
Juan had 4 candy bars for his 3 friends to share after lunch. But then, three other friends joined them. If Juan wants each friend to get the same amount, what part of a candy bar will each friend get?
Answers
Using proportions, it is found that the fraction of each candy bar that each friend will get is:
[tex]\frac{2}{3}[/tex].
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
Considering the three friends that were there initially and the three that arrived later, 4 candy bars will be split between 6 friends, hence the fraction that each will get is:
[tex]\frac{4}{6} = \frac{2}{3}[/tex]
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41. The Puuur Place builds customized cat trees for pet owners. The basic tree is $100 and each additional platform, perch, or toy costs $50. Meow Now also builds customized cat trees. Their basic cat tree starts at $50 and each additional piece costs $75.
[A] Write and solve a system of equations to represent the total cost, y, when x additional pieces are purchased with a basic cat tree at each store.
[B] Solve this system of equations and show your work.
[C] Reggie wants to purchase a cat tree for his pets. Based on your work, explain which store would be cheaper depending on how many add-ons he wants to purchase.
Answers
The system of equations to represent the total cost, y, when x additional pieces are purchased with a basic cat tree at each store are;
y = 50x + 100 ------(eq 1)
y = 75x + 50 ------(eq 2)
How to Solve Simultaneous Equations?A) Let the total cost of the cat tree be y
Let each additional piece added be x.
Since basic tree is $100 and each additional platform costs $50, then we can say that;
y = 50x + 100 ------(eq 1)
Now, their basic cat tree starts at $50 and each additional piece costs $75. Thus;
y = 75x + 50 ------(eq 2)
B) Subtract eq 1 from eq 2 to gte;
25x - 50 = 0
25x = 50
x = 50/25
x = 2
y = 75(2) - 50
y = $100
C) The Store that would be cheaper depending on the add - ons is Puuur Place because as x increases, it's y-value increases at a lesser rate than that of Meow.
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An equilateral triangle has a median drawn from one angle to the opposite side. What is the measure of each angle formed by the place where the median meets the vertex?
(Step by step pls)
Worth 20 points
Answers
The measure of each angle formed by the place where the median meets the vertex is 30 degrees
How to determine the angle?The median of an equilateral triangle divides the side and the angle into equal parts.
If the angle at the vertex is, the new angle would be
Angle = x/2
The angle at the vertex of an equilateral triangle is 60.
So, we have:
Angle = 60/2
Evaluate
Angle = 30
Hence, the measure of each angle formed by the place where the median meets the vertex is 30 degrees
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Determine whether the triangles can be proved similar. If they are similar, write a similarity statement. If they are not similar, explain why.
Answers
Answer: [tex]\triangle RQP \sim \triangle VPW[/tex]
Step-by-step explanation:
By the corresponding angles theorem, [tex]\angle RPQ \cong \angle VWP[/tex] and [tex]\angle RQP \cong \angle VPW[/tex].
Therefore, [tex]\triangle RQP \sim \triangle VPW[/tex] by AA.
Find the missing values
Answers
Answer:
5
Step-by-step explanation:
5×(-4)=20
5×3=15
5×0.5=2.5
5×5=25
5×0=0
5×(-2)=-10
3. You recently bought a rolled up poster at a convention and need to fit it in
your luggage. In order to pack it efficiently, we need to know the surface
area of the tube. If the radius measures out to be 0.4 inches and the height
is 25 inches, what is the full surface area? Use 3.14 for .
63.8 in²
1in²
62.8 in²
63.8 in3
Answers
Answer:
A. 63.8 in^2
Step-by-step explanation:
The surface area of a cylinder is given by:
A=2πrh+2πr^2
2πr^2 gives the area of the 2 ends, each with area πr^2.
2πrh gives the suface area of the outside of the cylinder.
r = 0.4 inches
h = 25 inches
Area = 63.8 in^2
PLEASE I NEED HELP ASAP
The question is :
Danielle reflects shape S in the line x = - 1 , and then reflects the new shape in the line y = 2
Zachary reflects shape S in the line y = 2 , and then reflects the new shape in the line x = - 1
Work out the coordinates of the vertex that A maps to after
a) Danielle's two reflections.
b) Zachary's two reflections.
.
Answers
The coordinates of the vertex that A maps to after Daniel's reflections are (3, 4) and the coordinates of the vertex that A maps to after Zachary's reflections are (3, 2)
How to determine the coordinates of the vertex that A maps to after the two reflections?From the given figure, the coordinate of the vertex A is represented as:
A = (-5, 2)
The coordinates of the vertex that A maps to after Daniel's reflections
The rule of reflection across the line x = -1 is
(x, y) ⇒ (-x - 2, y)
So, we have:
A' = (5 - 2, 2)
Evaluate the difference
A' = (3, 2)
The rule of reflection across the line y = 2 is
(x, y) ⇒ (x, -y + 4)
So, we have:
A'' = (3, -2 + 4)
Evaluate the difference
A'' = (3, 4)
Hence, the coordinates of the vertex that A maps to after Daniel's reflections are (3, 4)
The coordinates of the vertex that A maps to after Zachary's reflections
The rule of reflection across the line y = 2 is
(x, y) ⇒ (x, -y + 4)
So, we have:
A' = (-5, -2 + 4)
Evaluate the difference
A' = (-5, 2)
The rule of reflection across the line x = -1 is
(x, y) ⇒ (-x - 2, y)
So, we have:
A'' = (5 - 2, 2)
Evaluate the difference
A'' = (3, 2)
Hence, the coordinates of the vertex that A maps to after Zachary's reflections are (3, 2)
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What is the equation of the line parallel to the given line with an x-intercept of 4? y = x
Answers
Parallel lines are lines with the same slope, and the y-intercept is b in y=Mx+b.
We already know the slope, so we add the y-in.
Y=x+4
Putting the other player's king in check is always a good move. true or false subject: chess
Answers
Putting the other player's king in check is always a good move. true
What is chess?The policies of chess allow a king to take an opponent's piece whilst in check, so long as that piece isn't always being defended. At the equal time, a king in the test is usually forced to move.The standard regulations of chess, a participant may not make any pass that places or leaves their king in the test. A player may additionally pass the king, seize the threatening piece, or block the check with some other piece. A king cannot look at the opposing king, considering this will vicinity the first king in check as well.
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The taxi fare for the first two miles is $5 and for each additional mile the fare increases by $ 2. What is the taxi fare for a journey of n miles in dollars?
Answers
The taxi fare for a journey of n miles in dollars is 1 + 2n
What are linear equations?Linear equations are equations that have constant average rates of change, slope or gradient
How to determine the equation of the system?The given parameters about the taxi fares are given as
First two miles = $5
Additional mile = Increment of $2
Let the number of miles be n
So, we have:
2 miles = $5
Additional miles = (n - 2) * 2
Add the above expressions
5 + (n - 2)* 2
Represent the value with f(n)
So, we have:
f(n) = 5 + (n - 2)* 2
Expand the bracket
f(n) = 5 + 2n - 4
Collect the like terms
f(n) = 5 - 4+ 2n
Evaluate the like terns
f(n) = 1 + 2n
Hence, the taxi fare for a journey of n miles in dollars is 1 + 2n
So, the complete parameters are:
First two miles = $5
Additional mile = Increment of $2
n miles 1 + 2n
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a set of data has the values 11,14,23 and 16
Answers
The number to add to the set of data is 26
How to determine the new number?The set of data is given as:
11,14,23 and 16
Let the new number be x
So that
Mean = 18
Mean is calculated as:
Mean = Sum/Count
So, we have:
(11 + 14 + 23 + 16 + x)/5 = 18
Multiply by 5
11 + 14 + 23 + 16 + x = 90
Evaluate the like terms
x = 26
Hence, the number to add is 26
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Complete question
A set of data already has the values 11, 14, 23, and 16. What value would have to be added to the set for the mean of the five numbers to be 18?
You are investigating having business cards printed for your new game store. A local printing company charges $250 for the cardboard used and an hourly rate for labour of $40.
a. If h is the number of hours of labour required to print the cards, construct an equation for the cost
of the cards, C.
b. You have budgeted $1000 for the printing job. How many hours of labour can you afford? Give
your answer to the nearest minute.
c. The company estimates that it can print 1000 cards per hour of labour. How many cards will you
get printed with your current budget?
d. An alternative to printing is photocopying. The company charges 15 cents per side for the first 10 000 cards and then 10 cents per side for the remaining cards. Which is the cheaper option for 18 750 single-sided cards and by how much?
Answers
Answer:
See below.
Step-by-step explanation:
a. If h is the number of hours of labour required to print the cards, construct an equation for the cost of the cards, C.
C = $250 + ($40/hr)*h
b. You have budgeted $1000 for the printing job. How many hours of labour can you afford? Give your answer to the nearest minute.
$1000 = $250 + ($40/hr)*h
($40/hr)*h = $750
h = 18.75 hours
(18.75 hours)(60 min/hr) = 1125 minutes
c. The company estimates that it can print 1000 cards per hour of labour. How many cards will you get printed with your current budget?
(18.75 hr)*(1000 cards/hr) = 18,750 cards
d. An alternative to printing is photocopying. The company charges 15 cents per side for the first 10 000 cards and then 10 cents per side for the remaining cards. Which is the cheaper option for 18 750 single-sided cards and by how much?
Photocopy Cost for the first 1000 single-sided cards is:
(1000 cards)*($0.15) = $150
Photocopy Cost for the final 17,750 single-sided cards is:
(17,750)*($0.10) = $1,775
Totoal photocopy cost for 18,750 single-sided cards is $1,925. [1775+150]
The cheapest option for 18,750 cards is printing: $1,000
Printing is (1,925 - 1000) $925 cheaper than photocopying.
In a survey of 1002 people, 701 (which is 70%) said that they voted in the most recent presidentia l election (based on data from ICR Research Group). The margin of error for the survey was 3 percentage points. However, actual voting records show that only 61% of all eligible voters actually did vote. Does this necessarily imply
Answers
Based on the percentage of people who actually voted and the margin of error, the data implies that people lied when responding to the survey.
What is the evidence that people lied?The evidence that people lied about voting would bet be shown by the confidence interval. If the confidence interval of the survey does not have the actual percentage of people who voted in it, then people lied.
The confidence interval is:
= Average ± Margin of error
Solving:
= 70% + 3%
= 73%
= 70% - 3%
= 67%
Confidence interval is:
67% - 73%
The actual percentage of 61% who voted is not in this interval which means that some people lied about voting in the survey.
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PLEASE ASAP NEEDED SO BADLY PLEASEE PLEASE
Answers
Answer:
[tex]6x^{2} -24x-10[/tex] with remainder -5
Answer:
[tex]6^2-24x-10-\frac{5}{x+4}[/tex]
In other words, [tex]6x^2-24x-10[/tex] is the answer and -5 is the remainder
Step-by-step explanation:
I used long division for this, and I uploaded an image for the steps. The final answer I got was [tex]6x^2-24x-10-\frac{5}{x+4}[/tex]
Calculate the area of triangle abc with altitude bd, given a (-6,0) b (0,0) c (o,6) and d (3,-3)
Answers
The area of the triangle abc in which bd is altitude and having coordinates a(-6,0),b(0,0),c(0,6),d(3,-3) is 18 square units.
Given the coordinates of abcd are a (-6,0) b (0,0) c (o,6) and d (3,-3).
We are required to find the area of the triangle when bd is the altitude of the triangle.
When we draw the triangle we will find that that the base is ac and altitude is given bd.
ac=[tex]\sqrt{(6-0)^{2} +(0+6)^{2} }[/tex]
=[tex]\sqrt{36+36}[/tex]
=[tex]\sqrt{72}[/tex]
=6[tex]\sqrt{2}[/tex]
bd=[tex]\sqrt{(-3-0)^{2} +(3-0)^{2} }[/tex]
=[tex]\sqrt{9+9}[/tex]
=[tex]\sqrt{18}[/tex]
=3[tex]\sqrt{2}[/tex]
Area=(Base*Height)/2
=(6[tex]\sqrt{2}[/tex]*3[tex]\sqrt{2}[/tex])/2
=(18*2)/2
=18 square units.
Hence the area of the triangle abc in which bd is altitude and having coordinates a(-6,0),b(0,0),c(0,6),d(3,-3) is 18 square units.
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The equation represents an ellipse. which points are the vertices of the ellipse? (7, 1) and (7, −5) (7, −10) and (7, 6) (10, −2) and (4, −2) (15, −2) and (−1, −2)
Answers
The points which represents the vertices of the given equation are; (15, −2) and (−1, −2).
Which points among the answer choices represents the vertices of the ellipse whose equation is given?The complete question gives the equation of the ellipse as; (x-7)²/64+(y+2)²/9=1.
Since, It follows from convention that general equation of ellipse with centre as (h, k) takes the form;
(x-h)²/a² +(y-k)²/b² = 1.
Consequently, it follows from observation that the value of a and b in the given equation in the task content is; √64 = 8 and √9 = 3 respectively.
Since, 8 > 3, The vertices of the ellipse are given by; (h±a, k).
The vertices in this scenario are therefore;
(7+8, -2) and (7-8, -2).
= (15, -2) and (-1, -2).
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True or
False?
A binary predictor variable is tested for significance using a different test statistic than used for a quantitative predictor variable.
Answers
Answer:
it is False
Step-by-step explanation:
Your team decides to erect 8 tent frames that can each hold a tarp to provide shade and cover if needed. The area under each tarp is 25 feet wide and 40 feet long, and the top of the tarp will run the length of your seating area. Your tarp needs a slope of to allow runoff in case of rain. The frame will be 10 feet high around the outside.
How high does the center of the frame need to be?
Answers
The height of the frame is 15 feet.
How to calculate the height?From the information given, the following can be depicted:
b - 10/a = 2/5
2a = 5b - 50
2a - 5b = -50
Also, slope of AC:
= (b - 10(/(a - 5) = 2/5
2a - 50 = -5b + 50
2a + 5b = 100
Both equations will be solved
The height of the frame will be:
= 5 + 10
= 15 feet
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i need the answer to number 9
Answers
Answer:
502.5
Step-by-step explanation:
C = 24(12) + 5.50(39)
C = 288 + 214.5
C = $502.5
-8+(3x)
3
2
=
5834
729
Answers
Homer mowed 5 lawns in his first month and increased the number he mows by two for each month following. Which of the following is the correct interpretation of the rate of change and the initial value?
Answers
The equation which represent the interpretation of the scenario is 5 + 2x
AlgebraNumber of lawns Homer mowed = 5Additional laws mowed each month = 2Number of months = xTotal laws mowed = Number of lawns Homer mowed + (Additional laws mowed each month × Number of months)
= 5 + (2 × x)
= 5 + 2x
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This map of china is 65inches from east to west and 68 from the north to south. if 1 inch is 50 miles, how large is the actual country?
Answers
The country is 3250 miles in distance from east to west, and 3400 miles from north to south.
Given Information
It is given that,
The distance of the country on map from east to west, l = 65 inches
The distance of the country on map from north to south, b = 68 inches
As per the given scaling of map, 1 inch = 50 miles
How large is the actual country?
Thus, the actual distance from east to west, L = l × 50 miles
L = 65 × 50 miles
L = 3250 miles
The actual distance from north to south, B = b × 50 miles
B = 68 × 50 miles
B = 3400 miles
Therefore, the actual size of the country is 3250 miles in distance from east to west, and 3400 miles in distance from north to south.
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C
The graph of f(x) is shown.
O-4,0,2
For what values of x does f(x) = 0?
O-2.0.4
O-5.0.17
45
O-17.0.5
40
Answers
Answer: -4, 0, 2
Step-by-step explanation:
The graph intersects the x-axis at [tex]x=-4, x=0, x=2[/tex].
Which of the x-values are solutions to the following inequality? x < 100
help pls i need now
Answers
Answer:
A and B
Step-by-step explanation:
x < 100 means x is less than 100. Therefore, pick any x-values that are less than 100 which are x = 54 and x = 89.
Hence, A and B are the answer.
Using the sine rule, calculate the length y. Give your answer to 2 s.f.
Answers
Answer:
y = 9.84 mm
Step-by-step explanation:
Sine rule:Law of sine:
[tex]\sf \boxed{\bf \dfrac{a}{Sin \ A}=\dfrac{b}{Sin \ B}= \dfrac{c}{Sin \ C}}[/tex]
a = y
A = 31°
b = 17 mm
B = 117°
[tex]\sf \dfrac{y}{Sin \ 31^\circ}=\dfrac{17}{Sin \ 117^\circ}\\\\[/tex]
[tex]\sf y = \dfrac{17}{Sin \ 117^\circ}*Sin \ 31^\circ\\\\ y = \dfrac{17}{0.89}*0.515\\\\y = 9.84 \ mm[/tex]
How do I do C?Someone please help asap.
Answers
You have to find the slope of the line. It will give you the conversion rate from inches to centimetres or the other way around.
Looking closely at the graph, or using a ruler as reference, you can estimate that 30 cm ≈ 12 in. In terms of the graph, the line very nearly passes through the point (12, 30). It also passes through the origin, (0, 0), since 0 cm = 0 in exactly.
The slope of the line is then
[tex]\dfrac{30\,\mathrm{cm}-0\,\mathrm{cm}}{12\,\mathrm{in}-0\,\mathrm{in}} = \dfrac{30\,\rm cm}{12\,\rm in} = \dfrac{5\,\rm cm}{2\,\rm in} = 2.5\dfrac{\rm cm}{\rm in}[/tex]
which means that 1 in ≈ 2.5 cm.
So, if Sarah's height is 64 in, we convert this to cm and find her height is (approximately)
[tex]64\,\mathrm{in} \times 2.5\dfrac{\rm cm}{\rm in} = \boxed{160\,\rm cm}[/tex]
A landscaping company is covering this trapezoid-shaped yard with grass seed. A trapezoid with base lengths of 6 meters and 7 meters, and height 4 meters. How much area will they need to cover with grass seed
Answers
Area covered with grass seed = 10.4[tex]m^{2}[/tex].
What is trapezoid geometry?
A quadrilateral with one set of parallel opposite sides is referred to as a trapezoid. It can have congruent sides (isosceles) and right angles (a right trapezoid), but neither is necessary.
Area of the trapezoid ={ (a+b)/2} +h
where a and b is base and h is height of the trapezoid geometry.
In the question,
a=6m , b=7m and h=4m.
According to the formula { (a+b)/2} +h.
Area covered with grass seed = {(6+7)/2} + 4
= 10.4[tex]m^{2}[/tex].
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Answer:
26
Step-by-step explanation:
GOT IT RIGHT`
if m = 2 and n = 5 then find the value of 6m+5n
Answers
Answer:
37
Step-by-step explanation:
6m+5n
plug in your given values
6(2) + 5(5)
12+25
=37
Answer:
37
Step-by-step explanation:
6m + 5n
6*2 + 5*5 = 12 + 25
= 37
line segment connecting the vertices of a hyperbola is called the ________ ________, and the midpoint of the line segment is the ________ of the hyperbola.
Answers
line segment connecting the vertices of a hyperbola is called the transverse axis and the midpoint of the line segment is the center of the hyperbola.
What is transverse axis and center of hyperbola ?
The transverse axis is a line segment that passes through the center of the hyperbola and has vertices as its endpoints. The foci lie on the line that contains the transverse axis. The conjugate axis is perpendicular to the transverse axis and has the co-vertices as its endpoints.
And The center of a hyperbola is the midpoint of both the transverse and conjugate axes, where they intersect. Every hyperbola also has two asymptotes that pass through its center. As a hyperbola recedes from the center, its branches approach these asymptotes.
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A certain university recently calculated the number of days that its students took to complete their master's degrees. It took 100 of the students 800 days. In contrast, it took 150 of the students 600 days. What is the average number of days that these students took to complete their master's degrees? a) 620 days b) 680 days c) 700 days d) 720 days?
Answers
Answer:
c) 700
Step-by-step explanation:
Add 800 and 600, and then divide by the number of number, or in this case, two. This should give you 700.