Answer:
x = -18
Step-by-step explanation:
Step 1: Define
w(x) = 5/6x - 3
w(x) = -18
Step 2: Substitute and Evaluate
-18 = 5/6x - 3
-15 = 5/6x
x = -18
Among the 7th graders in a middle school, three quarters of them play at least one sport. Among the 7th graders who play sports, half of them play more than one sport. Among the 7th graders who play more than one sport, one third of them play more than two sports. Among the 7th graders who play more than two sports, one quarter of them play more than three sports. Sixteen 7th graders play more than three sports at the school. How many 7th graders are in the school
Answer:
512
Step-by-step explanation:
Let the number of 7th graders in the school is x.
As three-quarters of them play at least one sport, so, the number of 7th graders who play sport = [tex]\frac 3 4 x[/tex].
Among the 7th graders who play sports, half of them play more than one sport. So, the number of 7th graders who play more than one sport [tex]= \frac 1 2\times \frac 3 4 x=\frac 3 8 x[/tex].
Among the 7th graders who play more than one sport, one-third of them play more than two sports. So, the number of 7th graders who play more than two sport [tex]= \frac 1 3\times \frac 3 8 x=\frac 1 8 x[/tex].
Among the 7th graders who play more than two sports, one-quarter of them play more than three sports.
So, the number of 7th graders who play more than three sport [tex]= \frac 1 4\times \frac 1 8 x=\frac{1}{32} x[/tex].
7th graders play more than three sports at the school= 16
[tex]\Rightarrow \frac{1}{32} x=16[/tex]
[tex]\Rightarrow x =16 \times 32[/tex]
[tex]\Rightarrow x = 512[/tex]
Hence, the total numbers of 7th graders in the school are 512.
Solve the following system.
y + 4z = -14
x + 3z = -8
2x-3y=8
Please actually help and don’t just answer with “idk” for points
Answer:
[tex]y=-2,\:\\x=1,\:\\z=-3[/tex]
Step-by-step explanation:
[tex]\begin{bmatrix}y+4z=-14\\ x+3z=-8\\ 2x-3y=8\end{bmatrix}\\\\Isolate\:y\:for\:y+4z =-14\: : \:y=-14-4z\\\\\mathrm{Subsititute\:}y=-14-4z\\\\\begin{bmatrix}x+3z=-8\\ 2x-3\left(-14-4z\right)=8\end{bmatrix}\\\\Isolate\:x\:for\:x+3z =-8\: :\:x =-8-3z\\\mathrm{Subsititute\:}x=-8-3z\\\\\begin{bmatrix}2\left(-8-3z\right)-3\left(-14-4z\right)=8\end{bmatrix}\\\\Simplify\\\\\begin{bmatrix}6z+26=8\end{bmatrix}\\\\Isolate\:z\:for 6z+26=8 \: ;\:z =-3\\\\\mathrm{For\:}x=-8-3z\\\\[/tex]
[tex]\mathrm{Subsititute\:}z=-3\\\\x=-8-3\left(-3\right)\\\\-8-3\left(-3\right)=1\\\\x=1\\\\\mathrm{For\:}y=-14-4z\\\\\mathrm{Subsititute\:}x=1,\:z=-3\\\\y=-14-4\left(-3\right)\\\\-14-4\left(-3\right)=-2\\\\y=-2\\\\\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}\\\\y=-2,\:x=1,\:z=-3[/tex]
-4x+-3=-2x+-2
what is X?
Which statement best describes the relationship between the two figures?
Answer:
it is C
Step-by-step explanation:
it is reflected so the angles and the sides stay the same.
The statement best describes the relationship between the two figures is: figure JKL is similar to figure J'K'L'.
What are Similar Triangles?Similar triangles are defined as two triangles with the same shape, equal pair of corresponding angles, and the same ratio of the corresponding sides.
As per the given figure,
In triangles ΔJKLand ΔJ'K'L',
side JK = side J'K'
side KL= side K'L'
side JL = side J'L'
According to Side-Side-Side criterion, two triangles are similar if three sides of a triangle are equal to the corresponding sides of the other triangle.
Thus, ΔJKLand ΔJ'K'L' are similar triangles due to equal pairs of corresponding sides.
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Jenny works in a picture framing shop. She has a function f(x) equals X +2 that find the size of a square frame, given a picture of side length X in inches. She has a function p(x) equals 3X that gives the price in dollars for the frame. What is the single function that Jenny can use to give a customer a price for a picture with an edge length of X
Given:
The function for size of a square frame is
[tex]f(x)=x+2[/tex]
where, x is the side length of the picture.
The function for the price in dollars for the frame is
[tex]p(x)=3x[/tex]
To find:
The single function for the price of a picture with an edge length of x.
Solution:
We know that, for a picture with an edge length of x.
Size of a square frame = f(x)
Price in dollars for the frame = p(x)
Single function for the price of a picture with an edge length of x is
[tex](p\circ f)(x)=p(f(x))[/tex]
[tex](p\circ f)(x)=p(x+2)[/tex] [tex][\because f(x)=x+2][/tex]
[tex](p\circ f)(x)=3(x+2)[/tex] [tex][\because p(x)=3x][/tex]
Let the name of this function is c(x). So,
[tex]c(x)=3(x+2)[/tex]
Therefore, the required function is [tex]c(x)=3(x+2)[/tex].
On a coordinate plane, a curved line with a minimum value of (5.1, negative 7) and a maximum value of (0, 25), crosses the x-axis at (negative 3.4, 0), (3.9, 0), and (6, 0), and crosses the y-axis at (0, 25).
Which statement is true about the local minimum of the graphed function?
Over the interval [–4, –2], the local minimum is 0.
Over the interval [–2, –1], the local minimum is 25.
Over the interval [–1, 4], the local minimum is 0.
Over the interval [4, 7], the local minimum is -7.
Answer:
D
Step-by-step explanation:
The rest of the question is the attached figure and the statement options.
A. Over the interval [–4, –2], the local minimum is 0.
B. Over the interval [–2, –1], the local minimum is 25.
C. Over the interval [–1, 4], the local minimum is 0.
D. Over the interval [4, 7], the local minimum is -7.
============================================================
According to the graph, we will check the options:
A. Over the interval [–4, –2], the local minimum is 0. (Wrong)
Because the minimum is -12
B. Over the interval [–2, –1], the local minimum is 25. (Wrong)
Because the minimum is 18
C. Over the interval [–1, 4], the local minimum is 0. (Wrong)
Because the minimum is at x = 4 less than zero
D. Over the interval [4, 7], the local minimum is -7. (True)
Answer:
The answer would be D
Step-by-step explanation:
The difference of six times a number and seven results in 35.
Identify the steps necessary to solve the equation.
Answer:
Let the number be x
According to the question,
6x -7 = 35
=> 6x = 35 + 7
=> x = 42/6
=> x = 7
The solution to the equation is x = 7.
We have,
Let's assume the unknown number is represented by the variable 'x'.
- Translate the given information into an equation:
6x - 7 = 35.
- To isolate the variable 'x', start by adding 7 to both sides of the equation:
6x - 7 + 7 = 35 + 7.
- Simplify:
6x = 42.
- Next, divide both sides of the equation by 6 to solve for 'x':
(6x)/6 = 42/6.
x = 7
Therefore,
The solution to the equation is x = 7.
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The recipe calls for 2/3 cup of sugar and 3/4 cup of flour. What is the total amount of dry goods that the recipe calls for you to make the cake?
Answer:
17/12
Step-by-step explanation:
find a common denominator for each number so 8/12 and 9/12
a ferris wheel can accommodate 40 people in 25 minutes, how many people can people ride the ferris wheel in 5 hours? What's the rate per hour?
Answer:
480 in 5hrs
Rate is 96 per hour
Step-by-step explanation:
In 5 hours there are 300 minutes (5x60) and 300min/25min = 12. So 25 mins pass 12 times in 5 hours. Since each 25 mins its 40 ppl then 12x40 = 480.
480 in 5 hours so 480/5= 96 per hour
simplify 8/9 over 20. 8/9/20
2 over 45
Step-by-step explanation:
i divide 8over9 by 20
If a cube has a side length of 5 inches, what would be the volume of that
cube?
2 points
*
Answer:
125 inches^3
Step-by-step explanation:
To solve for cubes it is L^3 or Length Cubed. Whcih is simply L×L×L where L is Length.
Devon has 4 1/2bags of soil to put in his flower beds. Each bag of soil will cover 115.4 ft2. How many square feet will Devon be able to cover if he uses all these bags of soil?
help, please. will give brainliest.
Answer:
x =11
Step-by-step explanation:
XWY + YXZ = XWZ
5x+5 + 2x+8 = 90
Combine like terms
7x+ 13 = 90
Subtract 13 from each side
7x= 90-13
7x = 77
Divide by 7
7x/7 = 77/7
x = 11
8x + 21 ≤ 56
i need help on this
Answer:
YOU NEED TO DOWNLOAD CYMATH RIGHT NOW
Step-by-step explanation:
I got this answer one time and that is a great app seriously it WILL save your life
what is 1,935,825 in scientific notation ?
answer:1.935825×10 to the sixth power
step by step: your going to move the decimal point 6 places to the left. which became 1.935825x10 to the sixth power.
3[25-2(9+3)]=?. Pleaseeeeeeee
figure B is not a correct rotation of figure A
Not an answer. There should be a question here? I didn’t see one
What steps would you do to solve 3x-52 -12?
1. Add-12, then divide by 3
2. Divide by 3, then add 5
3. Multiply by 3, then subtract 5
4. Add 5, then divide by 3
Answer:
But you just gave us the steps-
Answer:
Step-by-step explanation:
Well for this you wouldn't necessarily solve you you simplify, to simplify you would do 56- 12 which would get you 3x - 44.
2ax - 15 = 3(x + 5) + 5(x - 1) In the equation above, a is a constant. If no value of x satisfies the equation, what is the value of a ?
NEED EXPLANATION!
Answer:
Step-by-step explanation:
Hello,
let s regroup the terms
2ax - 15 = 3(x + 5) + 5(x - 1) *** add 15 to both sides ***
<=> 2ax = 15 + 3x + 15 + 5x - 5 *** develop to remove the parentheses***
<=> 2ax = 8x + 25 *** simplify ***
<=> (2a-8)x = 25 *** subtract 8x from both sides ***
<=> (a-4)x=25/2 *** divide by 2 both sides ***
There is no solution is a-4 = 0 ,
because it would mean 0 = 25/2 and this is not possible
So it gives a = 4
Thanks
In the case when no value of x satisfies the equation so there the value of a should be 4.
Calculation of the value of a:Since
the equation is
2ax - 15 = 3(x + 5) + 5(x - 1)
2ax = 15 + 3x + 15 + 5x - 5
2ax = 8x + 25
(2a-8)x = 25
So a = 4
hence, In the case when no value of x satisfies the equation so there the value of a should be 4.
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Which is the smallest?
A) 1.2 x 10^-8
B) 1.2 x 10^-9
C) 2.1 x 10^-9
D) 5.6 x 10^-6
E) 1.2 x 10^-3
Answer:
I think the answer is B my friend
Dave uses the function P(d)=20d-20 to calculate the net profit of his dog walking business. Where P(d) is the net profit in dollars, and d the number of dogs he walks.
Interpret the meaning of the equation below using the context of the problem.
P(3)=40
Dave's profit is ____ when he walks _____dogs.
The height of the house is 28feet what is the height x of each story
preform the indicated operation 2 3/8 × 5 3/4
Answer:
It is 13 21/32 hope this helps
If 500x =500 then x equals?
Answer:
x=1
Step-by-step explanation:
On Monday Jim had -$20 in his bank account. On Tuesday Jim had -$60 in his bank account. What was the change in Jim's account?
Answer:40
Step-by-step explanation:
HELP BTAINLIEST!!!
IS 12x=15 and 4x=5 EQUIVALENT Y OR N
Answer:
Yes
Step-by-step explanation:
Answer: Yes it is equivalent
Step-by-step explanation:
If you crossed out the 12 and put it under 15, it would be 15/12=1.25.
Same for the second one cross out the 4 and put it under the 5 and it would be 5/4 is 1.25.
Tiffany wants to calculate the volume of her globe. The globe is in the shape of a sphere. She measured the circumference of the globe along the equator to be 24 inches. What is the volume of the globe? Round your answer to the nearest whole number.
Answer:
231in^3Step-by-step explanation:
We know that the volume of a sphere/globe is given as
V=4 /3πr^3
but the circumference is expressed as
C=2πr
solving for r given that C=24
24=2*3.142r
24=6.284r
r=24/6.284
r=3.8in
put r=3.6 in the expression for volume we have
V=4 /3π(3.8)^3
V=4 /3π(55
V=(220.59*3.142)/3
V=693.12/3
V=231in^3
The volume of the globe is 231in^3
The volume of the globe is 233 cubic inches.
Important information:
Circumference of the globe along the equator to be 24 inches.We need to find the volume of the globe.
Volume of sphere:Let [tex]r[/tex] be the radius of the globe.
Circumference of the globe along the equator is:
[tex]C=2\pi r[/tex]
[tex]24=2\pi r[/tex]
[tex]\dfrac{24}{2\pi }=r[/tex]
[tex]\dfrac{12}{\pi}=r[/tex]
Volume of the globe is:
[tex]V=\dfrac{4}{3}\pi r^3[/tex]
[tex]V=\dfrac{4}{3}\pi \left(\dfrac{12}{\pi}\right)^3[/tex]
[tex]V=\dfrac{4}{3}\pi \left(\dfrac{1728}{\pi^3}\right)[/tex]
[tex]V=233.444...[/tex]
[tex]V\approx 233[/tex]
Therefore, the volume of the globe is 233 cubic inches.
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10. The ratio of red marbles to purple marbles is 3:8. If there are 44
marbles, how many purple marbles are there? *
Answer:
32 purple marbles.
Step-by-step explanation:
Turn 3:8 into 3x+8x.
Equation:
3x+8x=44
x=4
Now, refer back to 3x:8x. We know that x=4, so 4*8=32.
32 purple marbles.
Answer:
There are 32 purple marbles and 12 red marbles
Step-by-step explanation:
The ratio is 3:8 and the total is 44. For 3 red marbles, they have 8 purple marbles but we don't know how many each marble we need if the total sum is 44. So we do...
3x+8x=44
11x=44
x=4
We need to know the number of purple marbles so we do,
8*4=32
7.3 times 10^22 what does it equal?
The correct answer is 7.3e +22
Plz help I don’t get what this is
Answer:
A) 98.94 sq. meters
B) 42 sq. meters
Step-by-step explanation:
A) So first we calculate the area for the square which is 15*20 = 300. Then we calculate the area of the circle which is pi*r^2 and in this case the radius is 4 which is 1/2 of 8. The area is approx. 201.06. Then we subtract that from 300. 300-201.06 = 98.94. The answer for A) is approx. 98.94
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B)First we calculate the area of the whole square which is 8*6 = 48. Then the area of the garden which is 2*3 = 6. 48-6 = 42. The answer is B) is 42 then.