Joshua used two wood beams, PC and QA, to support the roof of a model house. The beams intersect each other to form two similar triangles QRP and ARC as shown in the figure below. The length of segment PR is 4.8 inches and the length of segment CR is 7.2 inches. The distance between A and C is 9.6 inches.
What is the distance between the endpoints of the beams P and Q?
7.2 inches
3.6 inches
6.4 inches
12.0 inches
Answers
since triangle PRQ and ARC are similar
PR = QR = PQ
AR CR AC
so we can use
PR = PQ
AR AC
but AR = CR finally, PQ = AC x PR / CR
PQ = 9.6 x 4.8 / 7.2 = 6.4
the true answer is 6.4 inches
Answer:
The answer is C, 6.4 inches
Step-by-step explanation:
Related Questions
K-X=V-W solve for the letter x
Answers
Mul -1 X = -(V-W) + K
X = -V + W + K
To solve for 'x' in the equation 'K - X = V - W', we rearrange the equation to isolate 'x', resulting in 'X = K - V + W'.
Explanation:To solve the equation for the letter x, you need to isolate x on one side of the equation. It's a simple process of rearranging the equation.
Here we start with the original equation:
K - X = V - W
First, to separate your desired variable, or in this case 'x', we add 'X' to both sides to cancel 'X' from the left hand side:
K = X + V - W
Finally, to isolate 'x', we just need to subtract 'V' and add 'W' to both sides
X = K - V + W
So, the solution to the equation when solved for the letter 'x' is X = K - V + W.
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What is the inverse of the conditional statement " If a number is divisible by 6, then it is divisible by 3"?
A) If a number is divisible by 3, then it is divisible by 6.
B)If a number is not divisible by 6, then it is not divisible by 3.
C)If a number is not divisible by 3, then it is not divisible by 6.
D)If a number is not divisible by 6, then it is divisible by 3.
...?
Answers
"If a number is divisible by 3, then it is divisible by 6." is the inverse of the conditional statement " If a number is divisible by 6, then it is divisible by 3".
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Answer: I think its A.
using the quadratic formula 3x2 – 13x + 4 = 0
Answers
So your two answers here are x=4 and x=0.3333 (:
What is the 8th term in the sequence?
Note: Use the explicit rule.
an=25−3n
Enter your answer in the box.
a8=
Answers
a8=25-24=1
car salesman sells cars with prices ranging from $5,000 to $45,000. The histogram shows the distribution of the numbers of cars he expects to sell over the next
10 years.
The salesman has observed that many students are looking for cars that cost less
than $5,000. If he decides to also deal in cars that cost less than $5,000 and projects selling 200 of them over the next 10 years, how will the distribution be affected?
The mean will shift to the right.
The mean and the median will be the same.
The median will shift to the right.
The mean will shift to the left.
I think it's B
Answers
Answer:
The mean will shift to the left.
Step-by-step explanation:
Find the discriminant of the following equation.
4x2 + 12x + 9 = 0
Answers
ax^2+bx+c=0
discriminatn is b^2-4ac
a=4
b=12
c=9
discriinat is
12^2-4(4)(9)=
144-144
0
the discrminat is 0
what is 4/12 simplest form
Answers
the smaller of two containers has a capacity of 150 gallons. When it is 4/5 full, its contents are emptied into a larger container, filling exactly 2/3 of it. What is the capacity, in gallons, of the larger container?
Answers
x= capacity, in gallons, of the larger container.
We can suggest this equation:
(4/5)150+(2/3)x=x
120+2x/3=x
360+2x=3x
3x-2x=360
x=360
Answer: the capacity, of the larger container is 360 gallons.
Answer: the ca
What is the expression in simplest radical form?
√384
Answers
= 8√6
Hope this helps!
On level ground, a 60-foot-tall vertical building casts a 10-foot shadow. at the same time, another vertical building casts a 25-foot shadow. how many feet tall is the second building?
Answers
Using the concept of similar triangles, the height of the second building is calculated to be 150 feet, since its 25-foot shadow corresponds proportionally to the 60-foot building's 10-foot shadow.
Explanation:To find the height of the second building given that a 60-foot-tall building casts a 10-foot shadow, and another building casts a 25-foot shadow, we can use the concept of similar triangles. The idea behind similar triangles is that corresponding sides of similar triangles are proportional. Therefore, if one building is 60 feet tall and casts a 10-foot shadow, the ratios of the height to shadow length will be the same for the second building.
To set up the proportion, we have:
We can write the proportion as:
h1/s1 = h2/s2
Substituting the known values into the proportion gives us:
60/10 = x/25
Now we solve for x:
x = (60/10) * 25
x = 6 * 25
x = 150
Therefore, the height of the second building is 150 feet.
In order to avoid heavy traffic, Antonio can drive home after working less than 7 hours (h < 7) or after working more than 9 hours (h >9). How can these inequalities be written as one statement?
a. 7 < h < 9
b. 7 > h > 9
c. h < 7 or h > 9
d. h > 7 or h < 9
Answers
B is not correct. h cannot be both larger than 9 and less than 7. I would say that answer isnt correct
C conditions are correct and written exactly as they should be. sepparated. unlike ones in B
D is oposite from C so it is not correct.
Will give brainlyiest answer if explained.
In the figure below, lines g and h are parallel and are cut by transversal j to form the angles shown. If the measure of <8 is 82, what is the measure of <1?
A. 180.
B. 98.
C. 82.
D. 8.
Answers
math plzz I got turn it in Monday she just barely sent me it
Answers
Remember, the hypotenuse is the side opposite the right angle of the triangle.
A parabola has the equation –5x^2 + 30x – y – 34 = 0. Which equation is that of the parabola in vertex form? ...?
Answers
-5x^2 + 30x - y - 34 = 0
y = -5x^2 + 30x - 34
y = -5(x^2 - 6x) - 34
y = -5(x^2 - 6x + 9 - 9) - 34, by completing the square
y = -5(x^2 - 6x + 9) + 45 - 34
y = -5(x - 3)^2 + 11
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can -2/5 be simplified
Answers
What is the value of ∑n=13(17n−15)?
Answers
the value of [tex]\( \sum_{n=1}^{13} (17n - 15) \)[/tex] is indeed 1352.
To find the value of [tex]\( \sum_{n=1}^{13} (17n - 15) \)[/tex], we need to compute the sum of the expression 17n - 15 for n ranging from 1 to 13.
Using the formula for the sum of an arithmetic series, we can express this sum as:
[tex]\[ \sum_{n=1}^{13} (17n - 15) = \sum_{n=1}^{13} 17n - \sum_{n=1}^{13} 15 \][/tex]
We know that the sum of the first \(n\) natural numbers can be expressed as [tex]\( \sum_{n=1}^{N} n = \frac{N(N+1)}{2} \).[/tex]
So, the sum of [tex]\(17n\) from \(n=1\) to \(n=13\)[/tex] is:
[tex]\[ \sum_{n=1}^{13} 17n = 17 \sum_{n=1}^{13} n = 17 \cdot \frac{13 \cdot (13 + 1)}{2} \][/tex]
[tex]\[ = 17 \cdot \frac{13 \cdot 14}{2} = 17 \cdot 91 = 1547 \][/tex]
And the sum of 15, 13 times (since there are 13 terms) is[tex]\(15 \cdot 13 = 195\).[/tex]
Now, we can find the value of the given expression:
[tex]\[ \sum_{n=1}^{13} (17n - 15) = 1547 - 195 = 1352 \][/tex]
So, the value of [tex]\( \sum_{n=1}^{13} (17n - 15) \)[/tex] is indeed 1352.
Divide. Express your answer in lowest terms
=15/16 + (-3/4)
please tell me how you got your answer after
Answers
You need to know the number of different arrangements possible for five distinct letters. You decide to use the permutations rule, but your friends tells you to use 5!. Who is correct? Explain.
Both methods are correct, since you are counting all possible arrangements of 5 items taken 5 at a time.
Your friend is correct because applying the permutations rule in this setting would be inappropriate.
Neither method is correct. The combinations rule should be applied in this setting.
Your method is correct because you are applying the permutations rule in the appropriate setting.
Answers
Both methods are correct, since you are counting all possible arrangements of 5 items taken 5 at a time.
Answer:
Option A
Step-by-step explanation:
Whenever we want to arrange a number of objects or letters or numbers n then we must check whether
i) repitition is allowed
If repitition is allowed then total number of ways = n!
ii) repitition not allowed.
In this case again we have to check whether order matters or not.
If order matters then no of ways nPn.
Here n =5
We find that nPn = 5!
Thus both are correct.
Hence option A
Shape 1 and shape 2 are plotted on a coordinate plane. Which rigid transformation can you perform on shape 2 to show that shape 2 is congruent to shape 1?
a 45° rotation clockwise about the origin
a translation 6 units to the left and 8 units up
a reflection across the x-axis
a translation 3 units to the left and 6 units up
Answers
So, option B is your answer.
Hope this helps!
Two translation rigid transformations are required to transform shape 1 to shape 2
The rigid transformation that can be performed on shape 2 to show that shape 2 is congruent to shape 1 is the option
A transformation of 6 units to the left and 8Reasons:
The coordinates of the three points on shape 1 are; (2, 12), (4, 14), (6, 14)
The coordinates of the three points shape 2 are; (8, 4), (10, 6), (12, 6)
The difference in the coordinates are;
Difference in x-coordinate are;
Point 1 = 8 - 2 = 6
Point 2 = 10 - 6 = 6
Point 3 = 12 - 6 = 6
Therefore;
To get the x-value of shape 1 from the shape 2, the transform that is to be performed on shape 2 is a transformation of -6 units or 6 units left
Difference in y-coordinate are;
Point 1 = 4 - 12 = -8
Point 2 = 6 - 14 = -8
Point 3 = 6 - 14 = -8
Therefore;
To get the y-value of shape 1 from the shape 2, the transform that is to be performed on shape 2 is a transformation of 8 units or 8 units up
The composite transformation is therefore;
A transformation of 6 units to the left and 8 units upLearn more here:
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if x=t^2-1 and y=t^4-2t^3, then when t=1 what's d^2y/dx^2? if x=t^2-1 and y=t^4-2t^3, then when t=1 what's d^2y/dx^2?
Answers
d^2y/dx^2 = d/dt(dy/dx) * dt/dx
= d/dt (2t^2 - 3t) * dt/dx
= ( 4t-3) * 1 / 2t = (4t-3)/2t
when t = 1 d^2y/dx^2 = 1/2
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To find d^2y/dx^2 when t = 1, we need to first express y in terms of x. Then, differentiate y with respect to x to find dy/dx. Finally, differentiate dy/dx to find d^2y/dx^2 and substitute t = 1.
Explanation:Given the equations x = t^2 - 1 and y = t^4 - 2t^3, we can find d^2y/dx^2 when t = 1.
First, we need to express y in terms of x. From the equation x = t^2 - 1, we can solve for t as t = sqrt(x + 1). Substituting this into the equation y = t^4 - 2t^3, we get y = (sqrt(x + 1))^4 - 2(sqrt(x + 1))^3.
Next, we need to find the first derivative of y with respect to x: dy/dx. Then, we can find the second derivative d^2y/dx^2 by differentiating dy/dx. Finally, substitute t = 1 into d^2y/dx^2 to find the value.
Lucia bought a table and some chairs at a furniture store. The equation that models this situation is y = 40x + 55, where y is the amount of money she spent and x is the number of chairs she bought. What does the y-intercept mean in this situation?
A. She paid $40 for each chair.
B. She paid $55 for the table.
C. She paid $40 for the table.
D. She paid $55 for each chair.
Answers
Answer: C. She paid $40 for each chair.
Step-by-step explanation:
find g'(4) given that f(4)=3 and f'(4) = -5. g(x) = f(x)/x
Answers
g' (x) = [f(x)/x ]' = f'(x) x - f(x) / x2
g' (4) = [f(4)/4]' = f'(4) 4 - f(4) / 4² = -5x4) +5 /16= -15/16
so g' (4) = -15/16
Calculate the average rate of change for the function f(x) = −x4 + 4x3 − 2x2 + x + 1, from x = 0 to x = 1.
0
1
2
7
Answers
just calculate the slope
slope is (y2-y1)/(x2-x1)
for x=0, y=1
for x=1, y=3
slope=(y1-y1)/(x-x1)=(3-1)/(1-0)=2/1=2
answer is 2
Answer:
C) 2
Step-by-step explanation:
I took the quiz and got a 100%.
On the cube in the figure above, each of the following points is the same distance from
P as it is from Q
EXCEPT
(A) A (B) B (C) C (D) D (E) E
Answers
Suppose the length of the edge of a cube is 1.
CQ = 1 and [tex]PQ= \sqrt{2} [/tex]
What is 6 1/2 as a decimal?
Answers
What is the gcf for 36, 54 and 135?
Answers
36=2*2*3*3
54=2*3*3*3
135=3*3*3*5
gcf=3*3=9
Are 8:5 and 4:19 equivalent
Answers
A restaurant manager recorded the number of people in different age groups who attended her food festival. She then created the following histogram:
Histogram with title Food Festival Participants, horizontal axis labeled Age Group (year) with bins 0 to 19, 20 to 39, 40 to 59, and 60 to 79 and vertical axis labeled Number of People with values from 0 to 60 at intervals of 10. The first bin goes to 20, the second goes to 40, the third goes to 60, and the last goes to 50.
Which of the following statements best compares the height of the bars of the histogram?
There are twice as many participants in the 60–79 age group than in the 0–19 age group.
There are 3 times as many participants in the 40–59 age group than in the 0–19 age group.
There are more participants in the 40–59 age group than in the 0–19 and 60–79 groups combined.
There are more participants in the 60–79 age group than in the 0–19 and 20–39 groups combined.
Answers
Answer:
Option: B
There are three times as many participants in the 40-59 age group than in the 0-19 age group.
Step-by-step explanation:
From the histogram we have following observations:
Number of people in the age group 0-19= 20
Number of people in the age group 20-39=40
Number of people in the age group 40-59=60
Number of people in the age group 60-79=50
Hence, from the data we could say that there are three times as many participants in the 40-59 age group( which is 60) than in the 0-19 age group(which is 20).
Hence, option B is correct.
make a conjecture about the next item in the sequence.
6,8,-32,-30,120
answer choices....... a.122 b.-480 c. -488 d. 116 ...?
Answers
Previous number + 2
The sequence alternates between adding 2 and multiplying by -4. Starting with 6, the sequence progresses by these operations to reach 120. Following this pattern, the next term after 120 is a) 122 by adding 2.
The student has asked to make a conjecture about the next item in the sequence 6, 8, -32, -30, 120. To determine the pattern, let's look at the differences between each pair of numbers.
From 6 to 8, we add 2.
From 8 to -32, we multiply 8 by -4.
From -32 to -30, we add 2.
From -30 to 120, we multiply -30 by -4.
It appears that the sequence alternates between adding 2 and multiplying by -4. Following this pattern, after 120 the next operation should be adding 2.
Therefore, the next number in the sequence would be 120 + 2 = 122. Hence, the answer is option a. 122.
What are the x and y intercept of c = 0.75m + 2.25?