7. Is it proportional?
8. If so, what is the constant of
proportionality? (unit rate)
9. Write an equation that
expresses the table in the
form
Y= KX
Answers
Answer:
A unit rate is the rate of change in a relationship where the rate is per 1.
The rate of change is the ratio between the x and y (or input and output) values in a relationship. Another term for the rate of change for proportional relationships is the constant of proportionality.
If the rate of change is yx, then so is the constant of proportionality. To simplify things, we set yx=k, where k represents the constant of proportionality.
If you solve a yx=k equation for y, (like this: y=kx), it is called a direct variation equation. In a direct variation equation, y varies directly with x. When x increases or decreases, y also increases or decreases by the same proportion.
To find y in a direct variation equation, multiply x by the constant of proportionality, k.
For example: Given the relationship y=7x, the constant of proportionality k=7, so if x=3, then y=3×7 or 21.
Given the same relationship, if x=7, then y=7×7, or 49.
Step-by-step explanation:
Answer:
Yes it is. Y=2.5x
Step-by-step explanation:
So, lets start with bthe first values of the table and work our way down:
2x=5y
Lets just divide both sides by the 2:
x=5/2y
This means that for every 1 x, there should be 5/2y's.
Or, for every 1 x, there should be 2.5ys.
Lets check the next few to see if thats correct:
3x=7.5y
Divide both sides by 3:
x=7.5/3
This means for every one x, there are again, 2.5ys.
Lets check one more just to be sure:
4x=10y
Divide both sides by 4:
x=10/4
This means for everyone one x, y equals 2.5ys, yet again,
So we can conclude that the poprotional relationship between x and y is:
When x equals 1, y=2.5
Or
Y=2.5x
Hope this helps!
Related Questions
In the first quarter of the game,the giants gained 5 yards,lost 13 yards,gained 2 yards,gained 6 yards and,unfortunately,lost 12 yards in their final play.
1.Use a number line to depict the Giants' activity in the first quarter.
2.Use addition only to illustrate the Giants' activity in the first quarter.
3.What was the net yardage for the Giants in the first quarter.
Answers
Answer:
5 + (-13) + 2 + 6 + (-12) ;
-12 yards
Step-by-step explanation:
5 yards gain = + 5
13 yard loss = - 13
2 yards gain = + 2
6 yards gain = + 6
12 yards loss = - 12
Using addition Rule :
5 + (-13) + 2 + 6 + (-12)
The net yardage :
5 - 13 + 2 + 6 - 12 = - 12
Net yardage = - 12 yards
Extra Credit:
8 congruent spheres are packed into a cube with
edge length x so that each sphere is tangent to 3
faces of the cube and 3 other spheres as shown.
what is the ratio of the total volume of the
spheres of the volume of the cube?
Answers
Answer:
Ratio of the volumes of the spheres and cube = 0.523
Step-by-step explanation:
From the figure attached,
Diameter of one sphere = Half of the measure of one side of the cube
= [tex]\frac{x}{2}[/tex]
Radius of the sphere = [tex]\frac{\frac{x}{2}}{2}[/tex]
= [tex]\frac{x}{4}[/tex]
Volume of a cube is given by the formula,
V = [tex]\frac{4}{3}\pi r^{3}[/tex]
Therefore, volume of one sphere = [tex]\frac{4}{3}\pi (\frac{x}{4})^{3}[/tex]
= [tex]\frac{x^3\pi}{48}[/tex]
Volume of 8 spheres = [tex]8\times \frac{x^3\pi}{48}[/tex]
= [tex]\frac{x^3\pi}{6}[/tex]
Volume of a cube = (side)³
= [tex]x^3[/tex]
Ratio of the volumes of the sphere and cube = [tex]\frac{\frac{\pi x^3}{6} }{x^3}[/tex]
= [tex]\frac{\pi}{6}[/tex]
≈ 0.523
Use the properties of logarithms to determine the value of logb 1. Explain your reasoning.
Answers
Answer:
[tex]log_b 1 = 0[/tex]
Step-by-step explanation:
Given
[tex]log_b 1[/tex]
Required
Solve
[tex]log_b 1[/tex]
Express 1 as [tex]b^0[/tex]
[tex]log_b 1 = log_b b^0[/tex]
Apply power rule of logarithms
[tex]log_b 1 = 0 * log_b b[/tex]
Multiply by 0
[tex]log_b 1 = 0[/tex]
Answer:
logb 1 = 0
Step-by-step explanation:
Suppose that logb 1 = x.
Using the definition of a logarithm, bx = 1.
The only way a number that’s not equal to 1 can be raised to a power and equal 1 is if the exponent is 0. So, x = 0.
Therefore, logb 1 = 0.
You and two of your friends go to eat pizza
together. There are two deals:
1. 10% off of 1 pizza )
2. 30% off of 3 pizzas
Do you want to each pay separately and get
10% off of your bill, or do you want to split the
bill 3 ways and get 30% off of 3 pizzas?
Write a response that convinces your teacher
Answers
Answer:
The second deal offers a lower cost for the three friends.
Step-by-step explanation:
Let consider that each pizza has a price [tex]c_{o}[/tex]. Now, we proceed to check the total cost for each case, the better choice is whose total cost after discounts is the lowest.
Case 1 - 10 % off of 1 pizza (Split costs and buy 3 pizzas separately)
[tex]C = 0.9\cdot C_{o} + 0.9\cdot C_{o} + 0.9\cdot C_{o}[/tex]
[tex]C = 2.7\cdot C_{o}[/tex]
The cost for each person is:
[tex]c = \frac{C}{3}[/tex]
[tex]c = 0.9\cdot C_{o}[/tex]
Case 2 - 30 % off of 3 pizzas (Split costs and buy 3 pizzas in a row)
[tex]C = 0.7\cdot (3\cdot C_{o})[/tex]
[tex]C_{o} = 2.1\cdot C_{o}[/tex]
The cost for each person is:
[tex]c = \frac{C}{3}[/tex]
[tex]c = 0.7\cdot C_{o}[/tex]
The second deal offers a lower cost for the three friends.
3. Solve triangle ABC if a = 4, b = 6, and c = 5.
Show work
Answers
Answer:
4 x 6 x 5= 120 divided by 2 equals 60 because 4 x 6 = 24 x 5 = 120 and u divide by 2 when its a triangle. :) hope this helps
Step-by-step explanation:
https://socratic.org/questions/in-triangle-abc-a-4-b-6-c-8-how-do-you-find-the-cosine-of-each-of-the-angles
PLEASE HELP!!!!
Given f(x).... what is lim f(x)?
Answers
Answer:
[tex] \pi[/tex]
Step-by-step explanation:
[tex] Lim_{x \to\pi} f(x) [/tex]
[tex] =Lim_{x \to\pi} \pi [/tex]
([tex] \because for\: x =\pi, \: f(x) = \pi[/tex])
[tex] = \pi [/tex] (Applying limit)
Two partners are starting a new business. The total investment is $52,000.
Their investments are in the ratio 3:7. How much does each investor contribute?
Answers
Answer:
One partner will pay $15600 and the other would pay $36400
Step-by-step explanation:
52000 ÷ (3 + 7) =
52000 ÷ 10 =
5200
5200 x 3 = 15600
5200 x 7 = 36400
8. The bottom part of this block is a rectangular prism. The top part is a square pyramid. You want to
cover the block entirely with paper. How much paper do you need? Show ALL steps to find the
amount of paper. Do not use units in your answer. Enter the number only.
7 cm
5 cm
<
6 cm
6 cm
(The figure is not to scale)
Amount of paper:
Answers
Answer:
Amount of paper need = 140 cm²
Step-by-step explanation:
Given:
Length of rectangular prism = 5 cm
Width of rectangular prism = 5 cm
Height of rectangular prism = 4 cm
Base of triangular side = 5cm
Height of triangular side = 6 cm
Find:
Amount of paper need
Computation:
Amount of paper need = Curved surface area of rectangular prism + Curved surface area of square pyramid
Amount of paper need = 2h(l + b) + 4[Area of triangle]
Amount of paper need = 2h(l + b) + 4[(1/2)(b)(h)]
Amount of paper need = (2)(4)(5 + 5) + 2[(5)(6)]
Amount of paper need = (8)(10) + 2[30]
Amount of paper need = 80 + 60
Amount of paper need = 140 cm²
What is the correct answer?
Answers
Answer:
yellow
Step-by-step explanation:
this is how I solved it....
have a great day!
PLEASE I NEED SOME HELP WITH MATH
Answers
Answer:
28 cm area
Step-by-step explanation:
If the equation of a circle is (x + 4)2 + (y - 612 = 25, its center point is
(4,6)
(4,6)
(4,-6)
Answers
Answer:
Center point: [tex](-4,6)[/tex]
Radius: [tex]r=5[/tex]
Step-by-step explanation:
The equation of a circle is [tex](x-h)^2+(y-k)^2=r^2[/tex] where [tex](h,k)[/tex] is the center point of the circle and [tex]r[/tex] is the radius of the circle.
Given our equation [tex](x+4)^2+(y-6)^2=25[/tex], we can see that [tex](h,k)[/tex] is [tex](-4,6)[/tex] and since [tex]r^2=25[/tex], our radius is [tex]r=\sqrt{r^{2} } =\sqrt{25} = 5[/tex]
Therefore, the center point is [tex](-4,6)[/tex] and the radius is [tex]r=5[/tex]
Select all ratios equivalent to 3:5.
A) 24:40
B) 33:55
C) 4:6
Answers
Answer:
A and B
Step-by-step explanation:
Answer: B and A
Step-by-step explanation:
B, because if you divide 33:55 by 11 it equals 3/5
A, becuase 14:40 divded by 8 equals 3:5
using the formula 1 =PxRxT what is the interest on a $500 tv at 2% rate for 2 years
Answers
Answer:
$20.
Step-by-step explanation:
2% = 0.02.
Interest = 500*0.02*2
= $20.
I need to know what X solves for
Answers
Answer:
x= 30
Step-by-step explanation:
triangle is equal to 180 n we know c=90 so now we're just looking for the other 90 so 3x=90 n solve for x
sorry im bad at explaining
Answer:
X = 30
Step-by-step explanation:
Renee can sew a 25-square-foot quilt in 16 hours. Genera can sew the same size quilt in 12 hours. How long would it take them to sew the quilt working together? Rate (Quilts per Hour) Time (Hours) Fraction Completed Renee One-sixteenth x Genera One-twelfth x 6 hours 6 and six-sevenths hours 8 and six-sevenths hours 28 hours
Answers
Answer:
Step-by-step explanation:
Renee can sew a 25-square-foot quilt in 16 hours. Genera can sew the same size quilt in 12 hours. How long would it take them to sew the quilt working together? Rate (Quilts per Hour) Time (Hours) Fraction Completed Renee One-sixteenth x Genera One-twelfth x 6 hours 6 and six-sevenths hours 8 and six-sevenths hours 28 hours
This is calculated as:
1/ number of hours for Renee + 1/ number of hours for Geneva = 1/ Total number of hours that they can do it together
= 1/16 + 1/12 = 1/T
Lowest common denominator = 192
= 12 + 16/192 = 1/T
= 28/192 = 1/T
Cross Multiply
28T = 192 × 1
T = 192/28
T = 6 24/192 hours
Answer:
its b
Step-by-step explanation:
i just took the test :)
Name two pairs of adjacent angles and two pairs of vertical angles in
the figure.
Answers
Answer:
choice 2
Step-by-step explanation:
NEED HELP ASAP TAKING TEST-On average, a person’s body temperature should be approximately 98.6°F. A doctor would like to test the hypotheses H Subscript 0 Baseline: mu = 98.6 versus H Subscript alpha Baseline: mu not-equals98.6 where μ = the true mean body temperature of all adults. Before conducting the test, the doctor determines that the power of the test to reject the null hypothesis when μ = 98 using α = 0.01 and n = 10 is 0.2474. What combination of sample size and significance level would increase the power of this test the most?
use n = 5, alpha = 0.05
use n = 5, alpha = 0.10
use n = 20, alpha = 0.05
use n = 20, alpha = 0.10
Answers
Answer:
D I think,
Step-by-step explanation:
Classify the function as linear or quadratic and identify the quadratic, linear, and constant terms.
f(x) = 6x2 + x − 12
A. quadratic function; quadratic term: −12x2; linear term: −6x; constant term: −12
B. linear function; linear term: x; constant term: −12
C. linear function; linear term: 6x2; constant term: −12
D. quadratic function; quadratic term: 6x2; linear term: x; constant term: −12
Answers
Answer:
D
Step-by-step explanation:
The function f(x) = 6x2 +x -12 is a quadratic since the highest degree polynomial term is 2. So that eliminates B and C. Option A is incorrect because the quadratic term is 6 not double the constant. There for the correct choice is D because the function is a quadratic and the quadratic term is 6x2, the linear term is x and the constant term is -12.
A figure has 4 sides with two sets of parallel sides
Answers
Answer:
It can be a square!
Step-by-step explanation:
Answer:Parallelogram
Step-by-step explanation: Parallelogram: A quadrilateral with 2 pairs of parallel sides
Parts for an automobile repair cost $173. The mechanic charges $32 per hour. If a person receives an estimate for at least $253 and at most $285 for fixing the car, what is the time interval that the mechanic will be working on the job?
Answers
Answer:
58
Step-by-step explanation:
The time interval for the mechanic for this job is at least 2 hours and 30 minutes or at most 3 hours and 30 minutes.
What is at least and at most concept ?At least means lower limit of a given contrast and at most means higher limit of a given contrast.
According to the given question parts for an automobile repair cost 173 dollars and the mechanic charges 32 dollars per hour.
Given the person receives a cost of at least 253 dollars.
∴ The mechanic's total rate is ( 253 - 173 ) dollars which is = 80 dollars.
Also given the mechanic charges 32 dollars per hour so the time mechanic work for is at least (80/32) hours which is = 2.5 hours or 2 hours and 30 minutes.
In the later case when the owner receives a bill of 285 dollars the total rate of mechanic is
= ( 285 - 173 ) dollars.
= 112 dollars.
So, the mechanic have worked for (112/32) hours which is
= 3.5 hours or 3 hours and 30 minutes.
learn more about at least and at most here :
https://brainly.com/question/13015019
#SPJ2
whats the answers??????????????
Answers
the arrows pointing to 36
A) 37
B) 6.4
C) 8.58
Use the vertical line test to determine whether y is a function of x
Answers
Answer:
Not a function of x
Step-by-step explanation:
A vertical line intersects the graph twice, which immediately tells us that y is not a function of x here. If y were a function, the vertical line would intersect the graph in only one place.
No, A vertical line intersects the graph doubled, which instantly tells us that y exists not a function of x here. If y existed a function, the vertical line would intersect the graph in just one area.
What is Vertical line test?If a vertical line can be drawn to connect the graph of a function in more than one place, then stands NOT a function. If it exists not feasible to draw a vertical line to touch the graph of a function in more than one place, then y exists as a function of x.
No, A vertical line intersects the graph doubled, which instantly tells us that y exists not a function of x here. If y existed a function, the vertical line would intersect the graph in just one area.
Therefore, the correct answer is option B. No.
To learn more about vertical line test
https://brainly.com/question/1821791
#SPJ2
- A school is using 12 passenger vans to transport
students on a field trip. Write an expression
represent the number of vans needed for (s)
students
Answers
Answer: s/12 = v
Step-by-step explanation:
Tan C=
Help help help
Answers
Answer:
I believe the ans is (B) 40/9
Answer:
The answer is B. 40/9.
Step-by-step explanation:
We know, tan= opposite/adjacent
so, tan C = 40/9
The bus left Little Rock at 3:10pm and arrived at Dallas at 7:40pm. How long did it take to get from one town to the other?
Answers
Answer:
4 hrs 30 mins
Step-by-step explanation:
Need help ASAP please
Answers
Answer:
C
Step-by-step explanation:
Given
x² - 36 = 0 ( add 36 to both sides )
x² = 36 ( take the square root of both sides )
x = ± [tex]\sqrt{36}[/tex] = ± 6
That is x = - 6, x = 6 → C
What type of model does the data suggest?
Answers
X désigne un nombre quelconque. Exprimer à l'aide d'une expression littérale : a. La somme de x et de 12 b. Le produit de x par 5 c. La différence entre 17 et x d. Le quotient de x par 9
Answers
Answer:
L'expression littérale est la suivante
a) La somme de x et 12 b
Solution
X + 12b
b) Le produit de x par 5
Solution
X * 5
c) La différence entre 17 et x
Solution
17-X
d) Le quotient de x par 9
X / 9
Step-by-step explanation:
L'expression littérale est la suivante
a) La somme de x et 12 b
Solution
X + 12b
b) Le produit de x par 5
Solution
X * 5
c) La différence entre 17 et x
Solution
17-X
d) Le quotient de x par 9
X / 9
Can someone help me? Don’t put a link I will report links
Answers
Answer:
3.5
Step-by-step explanation:
Find the area of the circle. Use 3.14
42 mm
Answers
Answer:
A = 5538.96mm
Step-by-step explanation:
A = πr2
A = π × 422
A = 1764π
A = 5538.96
Please mark as brainliest if answer is right
Have a great day, be safe and healthy
Thank u
XD