9
Step-by-step explanation:
let 2nd proportion be x
6:x=24:36
6÷x=24÷36
x=6×36÷24
x=9
II. Solve the problems involving variations. Show your complete solution. (3 points each) 1. If y varies directly as the square of x, and y = 32 when x = 2, find y when x = 5. 2. The force of attraction (F) between two opposite electrical charges varies inversely as the square of the distance (d) between them. If F = 18 when d = 10, find F when d = 15. 3. If y varies jointly as x and z, find y if x = 3, k = 6 and z = 9
Answer:
see explanation
Step-by-step explanation:
(1)
y varies directly as x² then the equation relating them is
y = kx² ← k is the constant of variation
To find k use the condition y = 32 when x = 2
32 = k × 2² = 4k ( divide both sides by 4 )
8 = k
y = 8x² ← equation of variation
When x = 5 , then
y = 8 × 5² = 8 × 25 = 200
(2)
Given F varies inversely as d² then the equation relating them is
F = [tex]\frac{k}{d^2}[/tex] ← k is the constant of variation
To find k use the condition F = 18 when d = 10
18 = [tex]\frac{k}{10^2}[/tex] = [tex]\frac{k}{100}[/tex] ( multiply both sides by 100 )
1800 = k
F = [tex]\frac{1800}{d^2}[/tex] ← equation of variation
When d = 15 , then
F = [tex]\frac{1800}{15^2}[/tex] = [tex]\frac{1800}{225}[/tex] = 8
(3)
y varies jointly as x and z then the equation relating them is
y = kxz ← k is the constant of variation
when x = 3, y = 6, z = 9 ,then
y = 6 × 3 × 9 = 162
HELP ASAP!!!!hgghfuygkjb,
Answer:
120$
Step-by-step explanation:
With words, describe the translation:
(x, y)—(x+2, y-4)
o Move 2 to the left and 4 up
o Move 6 diagonally
o Move 4 left and 2 up
o Move 2 to the right and 4 down
Describe the location of point (4,2) on a coordinate plane. Enter a number in each box to complete the sentence.
The point is
units up from the origin on the y-axis and
units to the right of the origin on the x-axis.
Answer:
2 units up and 4 units to the right.
Step-by-step explanation:
It is 2 units up and 4 units to the right because since the x-coordinate is positive, that means the point is to the right of the origin and since the y-coordinate is positive, that means the point is above the origin.
Solve -(2x + 4) = 18.
7
-11
11
-7
Answer:
x=7
Step-by-step explanation:
Hope this helps!
solve y=f(x) for x. Then find the input when the output is -3. f(x)=3x^3
x=___
The input is____when the output is-3
[tex]f(x) =-3\\\\\implies 3x^3= -3\\\\\implies x^3 = -1\\\\\implies x = \sqrt[3]{-1} ~~\text{or}~~ x= \sqrt[3]{-1} \left(\dfrac{-1 \pm i\sqrt 3}2\right)\\[/tex]
[tex]\text{For x} \in \mathbb{R}, ~\text{the answer is x} = \sqrt[3]{-1} = -1[/tex]
coaches take people to a festival.
Each coach can take 50 people.
From one city there are 820 people.
How many coaches are needed?
Answer:
17 coaches
Step-by-step explanation:
820 divided by 50 is 16.4 but you can't have part of a coach so you round up it 17
Answer:
17 coaches
Step-by-step explanation:
820 divided by 50 is 16.4 but you can't have part of a coach so you round up it 17
A function is described by the equation f(x) = x² +5. The replacement set for the independent
variable is {1, 5, 7, 12}. Which of the following is contained in the corresponding set for the
dependent variable?
Answer:
5
Step-by-step explanation:
5 =5 +5+5=5+5
The distance of AB = [?]
Round to the nearest tenth.
No links and actual help plz!
Answer:
AB ≈ 5.7
Step-by-step explanation:
Calculate AB using the distance formula
d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = (- 2, - 2 ) and (x₂, y₂ ) = (2, 2 )
AB = [tex]\sqrt{(2-(-2))^2+(2-(-2))^2}[/tex]
= [tex]\sqrt{(2+2)^2+(2+2)^2}[/tex]
= [tex]\sqrt{4^2+4^2}[/tex]
= [tex]\sqrt{16+16}[/tex]
= [tex]\sqrt{32}[/tex]
≈ 5.7 ( to the nearest tenth )
Quick! I need an answer now! Please!
Linear or nonlinear:
y=x y=x/2 - 3 3x + y =12 y= 6/x - 2 y=3x^3+5
this equation is a non linear equation
What is the slope of the line that passes through the points (10, 2) and (19, 14)?
Write your answer in simplest form.
Answer:
The slope of this line is 4/3.
Step-by-step explanation:
(x1, y1) = (10, 2)
(x2, y2) = (19, 14)
First, find the slope using the slope formula:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
All this is doing is finding the distance between the y-coordinates and dividing it by the distance between the x-coordinates. I marked these two as points 1 and 2 above, so you can plug in all 4 values and solve:
[tex]m=\frac{14-2}{19-10}\\\\m=\frac{12}{9}\\\\m=\frac{4}{3}[/tex]
The slope of this line is 4/3.
3.9 as a improper fraction
Answer:
18/5
Step-by-step explanation:
simple division mm m m k l k obkbono
Answer:
39/10
Step-by-step explanation:
I promise you correct answer ur welcome
of the 400 employees,5% of them managers.How many managers does the zoo employ?
Answer:
20 of them are managers
Step-by-step explanation:
Basically All you gotta do is convert that 5 percent to a decimal, so 5% = 0.05
400 x 0.05 (multiplying it will just increase your answer) and you will get 20
To check it
20/5% or 0.05 = 400
Question 5 of 10
What is the solution to this equation?
6x + 10 - 2x = 7 + 23
A. X = 15
B. X= 4
C. X= 5
D. X= 2
Answer:
x=5
Step-by-step explanation:
First you combine the like terms. next you add 7+23. After that you subtract 10 from both sides. You're left with 4x=20. divide the equation by 4 on each term. Then you're left with x=5.
Which equation choice could represent the graph shown below?
1308 evaluated khan academy
Answer: what? What’s the question?
Today, everything at the store is on sale. The store offers a 20% discount
If the regular price of an item is x dollars, what is the discount price in dollars?
Answer:
.8x dollars
Step-by-step explanation:
Twenty percent off means you are paying 80 percent of every dollar, and 80 percent translates to .8 to 1 as a proportion.
Answer:
$.80x
Step-by-step explanation:
0.80x
It is 5:15 pm now. What time will it be in 40 minutes?
Answer:
5:55 pm
Step-by-step explanation:
Answer:
5:55pm
Mark brainlest if correct
Step-by-step explanation:
1) 2x – 3y - z = 7
3x + 5y - 3z = -2
4x – y + 2z = 17
When this system of equations is solved, what is the value of x?
Answer:
x = 3
Step-by-step explanation:
2x - 3y - z = 7 (equation 1)
3x + 5y - 3z = -2 (equation 2)
4x – y + 2z = 17 (equation 3)
(1) * 3 : 6x - 9y - 3z = 21 (1)'
(1)' - (2) : 3x - 14 y = 23 (equation 4)
(1) * 2 : 4x - 6y - 2z = 14 (1)"
(1)" + (3) : 8x - 7y = 31 (equation 5)
(5)*2 : 16x - 14y = 62 (5)'
(5)' - (4) : 13x = 39
x = 3
So thus, x = 3 in this system of equations, you can plug x back into equation 4 or 5 to find y and then plug x and y back into equations 1, 2, or 3 to find z
The ratio of cookies to muffins made at The Berry Bakery is 3 : 4. If they make 12 cookies on Monday, how many muffins did they make?
Answer:
13
Step-by-step explanation:
The proportion is solved and the number of muffins is M = 16
What is Proportion?The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.
The proportional equation is given as y ∝ x
And , y = kx where k is the proportionality constant
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Given data ,
Let the proportion be represented as A
Now , the value of A is
The ratio of cookies to muffins made at The Berry Bakery is 3 : 4
Now , the number of cookies is = 12
So , the proportion is
3 / 4 = 12 / M
Multiply by M on both sides , we get
( 3/4 )M = 12
Divide by 3/4 on both sides , we get
M = 16 muffins
Hence , the number of muffins is 16
To learn more about proportion click :
https://brainly.com/question/7096655
#SPJ2
what will be the total surface area of a cylinder if
h = 22cm
and
r = 3cm
TSA = ?
Please give me the answer plssss??
Answer:
total surface area of a cylinder is 471 cm²
A ramp for a loading truck is 13 long and covers 12 feet along the level ground. How many feet high is the highest point on the ramp?
Answer:
5 feet
Step-by-step explanation:
Using pythagoras' theorem a^2 = b^2 + c^2
13^2 = 12^2 + c^2
c^2 = 25
c = 5 feet
Answer:5
Step-by-step explanation:
e: x10+x15+x30=3
⇒3x+2x+x30=30
∴x=15
a: 1.5t+2.5t+3.5t=70+0.5t
⇒7.5t−0.5t=70
⇒7t=70⇒t=707=10
b: Let the number be x.
Given that, 2x3−x6=10
⇒4x−x6=10
x=20
d: 3x+5>25−x
⇒3x+x>25−5
⇒4x>20⇒x>204⇒x>5.
Which point is located at (Negative 1, 1 and one-fourth)? A B C D
Answer:
Point A
Step-by-step explanation:
Look along the x axis (horizontal) and find -1. Then look on the y axis and find 1 and 1/4. Finally, find where the two coordinates meet and that's your point - A.
Hope this helps!
Staci pays $32.70 for 5 cell phone cases. Each case costs the same amount. How much does eachcase cost?
Answer: Each phone case costs $6.54.
Explanation:
$32.70 ÷ 5 = cost per cell phone
$32.70 ÷ 5 = $6.54
PLEASE HELP QUESTION IN PIC.
Answer:
21.8
Step-by-step explanation:
Item 3 Martin is a chef and a caterer. When catering an event, he plans the amount of food to be prepared based on the number of people he needs to serve. The equation y = 7x represents the number of ounces of chicken required to serve x people. The equation y = 5x represents the number of ounces of fish required to serve x people. What is true of the comparison of the two graphs?
Answer:
The line representing the number of ounces of chicken required to serve x people is steeper than the line representing the number of ounces of fish required to serve x people.
Step-by-step explanation:
I took the test
Comparing the two graphs, we can conclude that: the graph representing the number of ounces of chicken required to serve x people has a steeper slope than the graph representing the number of ounces of fish that will serve x people
Recall:
The linear equation of a proportional graph is represented as y = mx, where m is the slope or gradient.The larger the value of the slope, the steeper the slope of the graph.Given the following:
Graph representing the number of ounces of chicken required to serve x people: y = 7x
The slope is 7.
Graph representing the number of ounces of fish required to serve x people: y = 5x.
The slope is 5.
Therefore, comparing the two graphs, we can conclude that: the graph representing the number of ounces of chicken required to serve x people has a steeper slope than the graph representing the number of ounces of fish that will serve x peopleLearn more about slopes on:
https://brainly.com/question/12242745
Katarina bought a package of 500 stickers. 25% of the stickers are hearts. The remaining stickers are stars. Select all the statements that are true.
Answer: 125 hearts and 375 stars
Step-by-step explanation:
25% of 100 is 25. Take 100 and x it by 5. 100 x 5 is 500 making 25 x 5 125. That being said 125 hearts and 375 stars
Answer:
125 hearts and 375 stars
Step-by-step explanation:
The price of petrol increased by 8% to Rs 540 per litre. Find the old price.
Answer:
The original price is Rs. 50
Step-by-step explanation:
Let the original price be Rs.x
x+8% of x=54
x+(8/100)*x=54
x+8x/100=54
(100x+8x)/100=54
108x/100=54
x=54* 100/108
x=50.
The original price is Rs. 50
Answer:
Rs 500 per literStep-by-step explanation:
Let the initial price be x.
We have:
x + 8% of x = 540Rewrite it as below and solve for x:
x + 0.08x = 5401.08x = 540x = 540/1.08x = 500
A television set costs $4500 cash. When bought on hire-purchase, a deposit of $450 is
required, followed by 12 monthly payments of $400. How much is saved by paying cash?
Answer:
$750
Step-by-step explanation:
did the problem
Please solve this question
Answer:
K so we want to find angle EFC
Its a much longer process
AC is a line, so its 180 degrees
ED is 32 (This also makes AB 32 degrees)
Now we need DC
Find the other side angle length
180 - 32 - 87 = 61
theta is 61+32