Problem: A piece of farmland is a watering plot of land in a circular pattern. A sewer line needs to be installed from a new housing project to a processing plant The city does not want the sewer line to cross the farm land. Can a direct line be installed?
● Let 1 unit = 100 feet.
● The entry to the sewer plant is at (2,3)
● The sewage exit from the housing project is at (12,6)
● The sprinkler system extends 200 ft and the center of the land is at (8,3)
Questions: (1) Will the sewer line cross the farmland? If so then at what points?
(2) If the farmer wants to maximize the farming area and does not want to cross the sewer line, what is the longest sprinkler system that could be installed?
Answers
The entry and exit points of (2, 3), and (12, 6), and 200 ft. extension of the sprinkler system gives;
(1) The sewer line crosses the farmland at (6.53, 4.36), and (8.48, 4.9)
(2) The longest installable sprinkler system is approximately 172.4 feet
How can the points where the line crosses the farmland be found?1. The slope of the sewer line is found as follows;
m = (6 - 3)/(12 - 2) = 3/10 = 0.3The equation of the sewer line can be expressed in point and slope form as follows;
(y - 3) = 0.3×(x - 2)y = 0.3•x - 0.6 + 3
y = 0.3•x + 2.4
The equation of the circumference of the sprinkler can be expressed as follows;
(x - 8)² + (y - 3)² = 2²Therefore;
(x - 8)² + (0.3•x + 2.4 - 3)² = 2²
Solving gives;
x= 6.53, or x = 8.48
y = 0.3×6.53 + 2.4 = 4.36
y = 0.3×8.48 + 2.4 = 4.9
Therefore;
The sewer line crosses the farmland at (6.53, 4.36), and (8.48, 4.9)2. When the farmland does not cross the sewer line, we have;
sewer line is tangent to circumference of farmland
Slope of radial line from center of the land is therefore;
m1 = -1/0.3
Equation of the radial line to the point the sewer line is tangent to the circumference is therefore;
y - 3 = (-1/0.3)×(x - 8)
Which gives;
y = (-1/0.3)×(x - 8) + 3
The x-coordinate is therefore;
0.3•x + 2.4 = (-1/0.3)×(x - 8) + 3
x ≈ 7.5y = 0.3 × 7.5 + 2.4 ≈ 4.65The longest sprinkler system is therefore;
d = √((7.5 - 8)² + (4.65 - 3)²) ≈ 1.724
Which gives;
The longest sprinkler system is 1.724 × 100 ft. ≈ 172.4 ft.Learn more about the equation of a circle here:
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Related Questions
search for research that has utilized analytical tools mentioned in the readings (i.e., single-sample ztest, t tests) and identify why that analysis was appropriate for the data.
Answers
The given analytical tools:
a. The single sample z-test analysis is appropriate for the data where the sample size is large and all data points are independent. Where the standard deviation is given(known).
b. The single sample t-test analysis is appropriate for the data where the sample size is small and the population variation or standard deviation is unknown.
What is single sample z-test analysis?This is a type of hypothesis test where the sample means and the population means are compared when the population variance or the standard deviation are given(known).
z = (X - μ)/(σ/√n)
Where X - sample mean, μ - population mean, σ - population standard deviation, and n - sample size.
Here the sample size is large and all data points are independent.
What is single sample t-test analysis?This is a type of parametric hypothesis test where the sample means and the population means are compared when the population variance or the standard deviation are not given(unknown).
t = (X - μ)/(s/√n)
Where X - sample mean, μ - population mean, s - sample standard deviation, and n - sample size.
Here the sample size is small.
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The functions f(x) and g(x) are graphed.
On a coordinate plane, a curved red line with an upward arc, labeled g of x, crosses the y-axis at (0, 4) and the x-axis at (2, 0). A straight blue line with a negative slope, labeled f of x, crosses the y-axis at (0, 4) and the x-axis at (2, 0).
Which represents where f(x) = g(x)?
f(0) = g(0) and f(2) = g(2)
f(2) = g(0) and f(0) = g(4)
f(2) = g(0) and f(4) = g(2)
f(2) = g(4) and f(1) = g(1)
Answers
The function equality that represents the point where f(x) = g(x) is; A: f(0) = g(0) and f(2) = g(2)
How to interpret Graphed Functions?From the question, the curved red line represents g(x) while the straight blue line represents f(x).
Now, the equality of functions f(x) = g(x) is represented as a common function between their curves. Thus, we will just need to find a common point for both. This is;
f(x) has points (0, 4) and (2, 0).
g(x) has points (0,4) and (2,0).
It is pertinent to note that both functions have the same y-value for x=0 and x = 2. Thus, we can say that;
f(2) = g(2) and f(0) = g(0)
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A circle with a diameter of 10 cm and a central angle of 30° is drawn below.
what is the area, to the nearest tenth of a square centimeter, of the sector formed by the 30° angle?
(A) 5.2 (B) 6.5 (C) 13.1 (D) 26.2
Answers
Answer:
B 6.5
Step-by-step explanation:
The area of a whole circle is
a = [tex]\pi[/tex][tex]r^{2}[/tex] A whole circle is 360 degrees. We only have part of a circle. We were also given the diameter and we need the radius. The radius is half of the diameter.
a = [tex]\frac{30}{360} \pi 5^{2}[/tex]
a= 6.5 rounded.
A whole circle exists 360 degrees. The radius exists half of the diameter.
[tex]$$a = (30/360) $\pi 5^2[/tex]
a = 6.5 rounded.
The area to the nearest tenth of a square centimeter, of the sector formed by the 30° angle exists at 6.5 rounded.
How to calculate the area of a circle with diameter?The diameter of the circle exists double the radius of the circle. Therefore the area of the circle formula utilizing the diameter exists equivalent to π/4 times the square of the diameter of the circle. The formula for the area of the circle, utilizing the diameter of the circle
π/4 × [tex]$$diameter^2[/tex].
Given: diameter of the circle = 10 cm
then the radius of the circle is half of the diameter
Radius of the circle = 10/2 = 5 cm
Area of circle = [tex]$$\pi $r^2[/tex]
Where r be the radius of the circle
A whole circle exists 360 degrees. The radius exists half of the diameter.
[tex]$$a = (30/360) $\pi 5^2[/tex]
simplifying the above equation we get
[tex]$$a = 25$\pi$ /$12[/tex]
a = 6.5 rounded.
The area to the nearest tenth of a square centimeter, of the sector formed by the 30° angle exists at 6.5 rounded.
Therefore, the correct answer is option (B) 6.5
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Paul flips a fair coin five times. In how many ways can he flip at least three tails?
Answers
Answer:
16
Step-by-step explanation:
We can use the binomial distribution formula to find the probability of flipping three coins tails, four coins tails, and five coins tails. This is because the probability of P(x=3) is going to give the same result if we had defined the entire set, counted how many had 3, and then divided that by the entire set. So we can use this to find how much % of the data set is going to have at least 3.
So the binomial distribution formula is defined as: [tex]P_x=(^n_x)p^x(1-p)^{n-x}[/tex], where n=number of trials, x=how many successes (in this case it will be 3, 4, and 5) and p=probability of success.
The binomial coefficient is defined as: [tex](^n_x)=\frac{n!}{k!(n-x)!}[/tex].
So let's define the variables.
x = 3, 4, 5 since we want to find the probability of getting at least 3. This means we want the probability of getting 3, 4, or 5 tails, and then we simply add up these probabilities.
n = 5, since Paul is flipping the coin 5 times
p = 0.5 since the probability of flipping tails is 0.50
So let's plug the information in!
[tex]P_{x\ge3} = P_3 + P_4 + P_5[/tex]
[tex]P_3=\frac{5!}{3!2!}*0.5^30.5^2 = 0.3125[/tex]
[tex]P_4=\frac{5!}{4!1!}*0.5^4*0.5^1=0.15625[/tex]
[tex]P_5 = \frac{5!}{5!0!}0.5^50.5^0 = 0.03125[/tex]
Now let's add up all these probabilities to get:
[tex]0.3125 + 0.15625 + 0.03125 = 0.5[/tex]
This means 50% of the time Paul will flip three or more tails.
To translate this to the number of ways, we need to find how many combinations there are which can generally be defined as: [tex]options^{length}[/tex] and in this case options = tails and heads so 2, and the length is 5. So we get: [tex]2^5 = 32[/tex]
Now multiply the 32 by the 0.5 and you get 16, which is the amount of ways he can flip at least three tails
Answer:
16
Step-by-step explanation:
Select the correct answer. which equation could possibly represent the graphed function?
Answers
The function for the given graph is f(x) = (x - 4)(x + 2)(x + 4).
How to represent a graph by an equation?A graph can be represented by the equation y = f(x).In the equation, the variable x is called the independent variable and the variable y is called the dependent variable.Calculation:In the given graph,
The points that lie on the x-axis are (-4, 0), (-2, 0), and (4, 0) where y-coordinate is 0 and the x coordinates are -4, -2, and 4.
On solving the given functions,
Option A:
f(x) = (x - 4)(x + 2)(x + 4)
Since y = 0 consider f(x) becomes 0
So,
(x - 4)(x + 2)(x + 4) = 0
According to the zero product rule,
x - 4 = 0, x + 2 = 0, and x + 4 = 0
⇒ x = 4, x = -2 and x = -4.
Thus, option A represents the function of the given graph.
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Disclaimer: The question given on the portal was incomplete. Here is the complete question.
Question:
Select the correct answer. which equation could represent the graphed function (given in the figure below)?
Yolanda paid for her movie ticket using 28 coins, all nickels and quarters. the ticket cost $4. which system of linear equations can be used to find the number of nickels, n, and the number of quarters, q, yolanda used? n q = 28 0.05n 0.25q = 4 n q = 4 5n 25q = 28 n q = 28 5n 25q = 4 n q = 4 0.05n 0.25q = 28
Answers
The system of linear equations can be used to find the number of nickels, n, and the number of quarters, q, yolanda used is n + q = 28
n + q = 280.05n + 0.25q = 4
Simultaneous equationn + q = 28
0.05n + 0.25q = 4
n = 28 - q
substitute n = 28 - q0.05n + 0.25q = 4
0.05(28 - q) + 0.25q = 4
1.4 - 0.05q + 0.25q = 4
- 0.05q + 0.25q = 4 - 1.4
0.20q = 2.6
q = 2.6 / 0.20
q = 13
Substitute into
n + q = 28
n + 13 = 28
n = 28 - 13
n = 15
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A flat rectangular piece of aluminum has a perimeter of 60 inches. The length is 12 inches longer than the width. Find the width.
Answers
Answer:
width = 9 inches
Step-by-step explanation:
let width be w then length is w + 12
the perimeter ( P) is calculated as
P = 2( width + length )
here P = 60 , then
2(w + w + 12) = 60 ( divide both sides by 2 )
2w + 12 = 30 ( subtract 12 from both sides )
2w = 18 ( divide both sides by 2 )
w = 9
that is the width of the rectangle is 9 inches
explian GOLDEN RATION singinficane
Answers
[tex]\large\bold\blue{ANSWER:-}[/tex]
Golden ratio, also known as the golden section, golden mean, or divine proportion, in mathematics, the irrational number (1 + Square root of√5)/2, often denoted by the Greek letter ϕ or τ, which is approximately equal to 1.618.
need help don’t know what to do
Answers
Freddie has 2 times as many comic books as David. The ratio of the number of comic books David has to the number of comic books Gary has is 5 : 3. Freddie has 110 comic books. How many comic books do David and Gary have in total?
Answers
Answer:
88
Step-by-step explanation: make me brainliest if it is correct
Write an equation in the form y = m x + b for the following table:
x y
-6 -42
-4 -26
-2 -10
0 6
2 22
4 38
6 54
8 70
y= ?
Answers
Answer: y=8x+6
Step-by-step explanation:
The slope is
[tex]\frac{70-54}{8-6}=\frac{16}{2}=8[/tex]
So, the slope is 8.
Since the y-intercept is 6, the equation is y=8x+6.
You want to prove that FHG is similar to RXS by the SSS Similarity Theorem. Complete the proportion that is needed to use this theorem.
Answers
Answer:
[tex]\frac{FH}{RX} =\frac{HG}{XS} =\frac{FG}{RS}[/tex]
Step-by-step explanation:
The order of the letters matters in any similarity theorem.
When triangle FHG is similar to triangle RXS, the lengths of FH must be similar to RX.
When 2 similar lines are divided, that number is the factor by which one triangle can be dilated to match the other.
That being said, each of these proportion statements can be read as individual division expressions that equal the next division expression.
This means [tex]FH\div RX = HG\div XS = FG\div RS[/tex].
If you look at it this way, you can see that the sides you need to fill in must be the corresponding similar sides, so that you end up with the factor for the dilation of the 2 triangles.
Which problem could be solved with the expression 5 x ( 2 + 4 ) ÷ 6 ?
1. Hayden made 222 bracelets before school and 444 after school each day for 555 days. Then he split the bracelets into 666 equal groups. How many bracelets did Hayden have in each group?
2. Khai, the dog, ate 222 bones on Monday, 444 bones on Tuesday and 666 bones on Wednesday. On Thursday, she ate 555 times more bones than the other days combined. How many bones did Khai eat on Thursday?
3. Shadi is building a new back deck. He puts 222 nails and 444 screws in each board. He did this to 555 boards. How many total screws and nails did he use?
PLEASE ANSWER AS SOON AS POSSIBLE!
I know its a lot to read but I would REALLY appreciate if you could answer this with the problem numbers 1, 2, and 3. THANK YOU!
Answers
Answer:
1
Step-by-step explanation:
This is the only problem that could be answered with this equation, because you would add the bracelets he made (2+4) then times that number by the days he made them, 5, then divide by the number of groups, 6. Which equals 5 x ( 2 + 4 ) divided by 6.
I hope this helps!
A pot contains 3/4 gallon of soup.A serving is 1/16 gallon.How many servings does the pot contain?
Answers
by taking the quotient between the volume in the pot and the volume of each serving, we conclude that there are 12 servings.
How many servings does the pot contain?
The number of servings is given by the quotient between the volume in the pot and the volume of each serving, so we have:
Volume in the pot = 3/4 gallon.Volume of each serving = 1/16 gallon.N = (3/4)*/(1/16) = 12
So there are 12 servings in the pot.
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A prism with volume 244 cm³ is dilated with a factor of 4
What is the volume of the image?
Enter your exact answer, as a decimal, in the box.
cm³
Answers
Step-by-step explanation:
the volume of a 3D object is always calculated in some way by multiplying the 3 dimensions with each other.
so, if every dimension is then changed by a factor f (4 in our case), then the volume changes by f×f×f = f³, as the factor has to be included in the calculation for each dimension. and as they are multiplied with each other, so are the scaling factors in each case.
in our case the prism is dilated by the factor 4.
that means that every side length, every height, ..., each dimension is increased by the factor 4.
and therefore, the volume increases by the factor 4³ = 64.
so, the volume of the new image is
244 × 64 = 15,616 cm³
Volume changes by f × f × f = f³
Volume increases by the factor of 4³ = 64
The volume of the new image exists 244 × 64 = 15616 cm³.
What is the volume of the prism?The volume of a 3D object exists always computed in some form by multiplying the 3 dimensions by each other.
The volume changes by f × f × f = f³, as the factor, contains to be included in the calculation for each dimension and as they exist multiplied with each other, so exist the scaling factors in each case.
Here, the prism exists dilated by factor 4 which indicates that every side length, every height and each dimension exists increased by factor 4.
Volume increases by the factor of 4³ = 64
The volume of the new image exists 244 × 64 = 15,616 cm³.
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Five guys walk into a bar, how many ways can they sit so as to be arranged from oldest to youngest?
Answers
There are 24 ways in which 5 guys can sit if arranged from oldest to youngest.
We have,
Five guys.
Now,
We know that,
Total number of ways to arranged around a table (n) = (n-1)!
So,
For n = 5,
I.e.
(n - 1)! = (5 - 1)! = 4!
So,
Total number of ways to arranged Five guys rom oldest to youngest (n) = (n-1)!
i.e.
= (5 - 1)! = 4!
We get,
= 4 × 3 × 2 × 1
i.e.
Total number of ways to arranged Five guys rom oldest to youngest (n) = 24.
Hence we can say that there are 24 ways in which 5 guys can sit if arranged from oldest to youngest.
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An advertising company charges $60 per half-page advertisement and $100 per full-page advertisement. michael has a budget of $1340 to purchase 15 advertisements. define a variable for each unknown. write a system of equations to represent the situation. how many half-page advertisements does michael purchase? show your work. how many full-page advertisements does michael purchase? show your work.4
Answers
The number of half page advertisements that Michael purchased is 4 while the full page advertisements is 11.
What is elimination method?The elimination approach involves taking one variable out of the system of linear equations by utilising addition or subtraction together with multiplication or division of the variable coefficients.
Let the number of half page ads be represented by h
Let the number of full page ads be represented by f.
Total number of advertisements = 15
h + f = 15 ....... (i)
h = 15 - f
Therefore, the system of equations to represent the situation will be:
60h + 100f = 1340 ........ (ii)
Put the value of h into equation (ii)
60(15 - f) + 100f = 1340
[tex]\Rightarrow[/tex] 900 - 60f + 100f = 1340
Collect like terms
100f-60f = 1340-900
[tex]\Rightarrow[/tex] 40f = 440
[tex]\Rightarrow[/tex] f = 11
The number of full-page advertisements that Michael purchased is 11.
Since h + f = 15
[tex]\Rightarrow[/tex] h + 11 = 15
[tex]\Rightarrow[/tex] h = 15 - 11
[tex]\Rightarrow[/tex] h = 4
The number of half page advertisements that Michael purchased is 5.
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Which expresses the correct factorization
of….? look at pic
Answers
Answer:
Option 1
Step-by-step explanation:
Find 2 numbers that multiply to give 16 and sum to give +8 :
These numbers are 4 and 4
Now split +8x into +4x and +4x and factor each part :
x²+4x+4x+16 = 0
x(x+4)+4(x+4) = 0
Keep 1 bracket and the terms outside the brackets make their own :
(x+4)(x+4) = 0
(x+4)² = 0
Therefore answer will be Option 1
Hope this helped and have a good day
(a+b)^2 = a^2 + 2ab + b^2
(x+4)^2 = x^2 + 8x + 4
help please much appreciated if you attempt to help
Answers
196 36 correct answer is 232
Answer:
728 cm²
Step-by-step explanation:
the surface area is the area of the 6 faces.
the opposite rectangular faces are congruent , then
SA = front/ back + sides + top/ bottom
= 2(14 × 14) + 2(6 × 14) + 2(14 × 6)
= 2 × 196 + 2 × 84 + 2 × 84
= 392 + 168 + 168
= 728 cm²
What is the area of the trapezoid above?
A. 188 cm²
B. 196 cm²
C. 392 cm²
D. 5,236 cm²
Answers
Answer:
B. 196cm²Step-by-step explanation:
Area = h/2 (b_1+b_2)
[tex]\sf\cfrac{7}{2}\:(22+34)[/tex]
Add 22 and 34 = 56
[tex]\sf \cfrac{7}{2} \times 56[/tex]
Let's express 7/2 * 56 as a single fraction:-
[tex]\sf \cfrac{7\times 56}{2}[/tex]
Multiply 7 and 56 = 392
[tex]\sf \cfrac{392}{2}[/tex]
Divide
[tex]\sf 196[/tex]
Therefore, the area of the trapezoid is 196cm².
_______________________
how much greater is 9 hundredths than 8 thousandths
Answers
9 hundredths is greater than 8 thousandths by 82 thousandths
Place valueFrom the question, we are to determine how much greater 9 hundredths is than 8 thousandths
9 hundredths = 9/100 = 0.09
8 thousandths = 8/1000 = 0.008
Then,
0.09 - 0.008 = 0.082
= 82/1000
≡ 82 thousandths
Hence, 9 hundredths is greater than 8 thousandths by 82 thousandths
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13.222.. - 1.3222.. = ??
Answers
Answer:
Answer
Answer in decimal
11.8998
Suppose you have a box with 3 blue marbles, 2 red marbles, and 4 yellow marbles. You are going to pull out one marble, record its color, remove it from the box and draw another marble. What is the probability of pulling out a red marble followed by a blue marble? The multiplication rule says to use P(red) P(blue).
Describe the probability of finding a red marble?
Describe the probability of finding a blue marble?
Describe the process of finding the probability of finding a red marble followed by a blue marble if the first marble was permanently removed?
What affect did removing the first marble from the box have on the problem?
Describe the probability of finding a red marble followed by the blue marble if the first marble is removed?
Answers
The probability of randomly getting first a red marble and then a blue marble is:
P = 0.083
How to find the probability?
There are:
3 blue marbles2 red marbles4 yellow marbles.For a total of 9 marbles.
The probability of getting a red marble is equal to the quotient between the number of red marbles and the total, so:
P(red) = 2/9
Then the probability of getting a blue marble is equal to the quotient between the number of blue marbles and the total, but because we already took one marble, now the total is 8.
P(blue) = 3/8
The joint probability is given by the product:
P = (2/9)*(3/8) = 0.083
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Zhang is constructing a loading ramp (BA) that is 4-feet high (AC). The back of the base (BC) must be 12.8 ft. How long must the entire base (BD) be?
Proportion : __________________
Front of base: __________
Total base: __________
Answers
Answer:
Step-by-step explanation:
This is a geometric means problem where the height (length AC of 4) is the geometric mean between the base BC and the base DC. The proportion is
[tex]\frac{12.8}{4} =\frac{4}{CD}[/tex] . Cross multiply to get
12.8CD = 16 and divide both sides by 12.8 to get that
CD = 1.25
That means that the length of the whole thing, BD, is
12.8 + 1.25 = 14.05
Complete the system that models the heights of the ball and the receiver’s hands over time. h = -16t² 14t h = -16t² t
Answers
Answer: The height of the ball at time t is given as h = -16t² + 14t + 6 while the height of the receiver hand at time t is given as h = -16t² + 10t + 8
What is an equation?
An equation is an expression that shows the relationship between two or more variables and numbers.
A quarterback throws a football toward a receiver from a height of 6 ft. The initial vertical velocity of the ball is 14 ft/s. At the same time that the ball is thrown, the receiver raises his hands to a height of 8 ft and jumps up with an initial vertical velocity of 10 ft/s.
The height of the ball at time t is given as h = -16t² + 14t + 6 while the height of the receiver hand at time t is given as h = -16t² + 10t + 8
Answer:
6
10
8
Step-by-step explanation:
Can someone help me out on these 2 geometry questions pls? ASAP!!!
Write formal proofs using the HL Theorem
Answers
Question 2
1) [tex]\overline{PR} \perp\overline{QS}, \overline{PQ} \cong \overline{PS}[/tex] (given)
2) [tex]\overline{PR} \cong \overline{PR}[/tex] (reflexive property)
3) [tex]\angle PRQ, \angle PRS[/tex] are right angles (perpendicular lines form right angles)
4) [tex]\triangle PRQ, \triangle PRS[/tex] are right triangles (a triangle with a right angle is a right triangle)
5) [tex]\triangle PRQ \cong \triangle PRS[/tex] (HL)
Question 3
1) [tex]\angle C[/tex] is a right angle, [tex]\overline{AC} \cong \overline{AE}, \overline{DE} \perp \overline{AB}[/tex] (given)
2) [tex]\angle DEA[/tex] is a right angle (perpendicular lines form right angles)
3) [tex]\triangle ACD, \triangle DAE[/tex] are right triangles (a triangle with a right triangle is a right angle)
4) [tex]\overline{AD} \cong \overline{AD}[/tex] (reflexive property)
5) [tex]\triangle ACD \cong \triangle AED[/tex] (HL)
6) [tex]\angle CAD \cong \angle DAE[/tex] (CPCTC)
7) [tex]\overline{AD}[/tex] bisects [tex]\angle BAC[/tex] (if a segment splits an angle into two congruent parts, it is an angle bisector)
what inequality is shown on the graph ?
Answers
The inequality of the graph that is given is: y < 2x - 3.
How to Write the Inequality of a Graph?First find the slope (m) = rise / run of the line.
Rise = 2 units
Run = 1 unit
Slope (m) = 2/1 = 2
Y-intercept (b) = -3.
Since the shaded side is at the left, we are going to use the ">" sign. Substitute m = 2 and b = -3 into y < mx + b.
y < 2x - 3
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Each side of a square is increasing at a rate of 5 cm/s. At what rate (in cm2/s) is the area of the square increasing when the area of the square is 9 cm2
Answers
The area of the square increasing at 30 [tex]\frac{cm^{2} }{sec}[/tex]
The rate of change function is defined as the rate at which one quantity is changing with respect to another quantity. In simple terms, in the rate of change, the amount of change in one item is divided by the corresponding amount of change in another
Let the side of a square be x.
So,
Area of square = [tex]x^{2}[/tex]
A =[tex]x^{2}[/tex]
Differentiating with respect to time we get,
dA/dt = 2x dx/dt
When area = 9 [tex]cm^{2}[/tex] the side becomes 3 cm
At x = 3cm and dx/dt = 5 cm/s (Given)
dA/dt = 2.3.5 = 30 [tex]\frac{cm^{2} }{sec}[/tex]
Thus the area of the square increasing at 30 [tex]\frac{cm^{2} }{sec}[/tex]
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4(3) / 4(8) +.9(7.8 x 7.45)
Answers
The value is 52. 674
How to determine the valueWe have;
4(3) / 4(8) +.9(7.8 x 7.45)
From BODMAS, we have that we must must open up the bracket
= [tex]\frac{12}{32} + 0. 9 (58. 11)[/tex]
Divide the fraction to get decimals
= [tex]0. 375 + 52. 299[/tex]
Add the decimals
= [tex]52. 674[/tex]
Thus, the value is 52. 674
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There are 120 students in class 7. it is known that 2 3 out of them like maths, out of which 35 are girls. also, out of total students, 3 5 are boys. (3) (a) what is the number of girls in the class? (b) how many students like maths? (c) how many boys like maths?
Answers
maths questions can be solved using unitary method.
Answer:
(a) The total number of girls in the class are 48
(b) The total number of students that like maths are 80
(c) The total number of boys like maths are 45
Solution:
According to the question, [tex]\frac{3}{5}[/tex] of total students are boys
number of boys = [tex]\frac{3}{5}[/tex] × 120 = 72
Also, According to the question, [tex]\frac{2}{3}[/tex] of total students like maths
number of students = [tex]\frac{2}{3}[/tex] × 120 =80
(a) The total number of girls in the class = total number of students - total number of boys
total number of girls in the class = 120 - 72 = 48
(b) The total number of students that like maths are 80
(c) The total number of boys like maths = total number of students that like maths - total number of girls that like maths
total number of boys like maths = 80 - 35 = 45
What is unitary method?
The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.
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