The ratios that have the same constant of proportionality as Hilary's observation are 4:6 and 8:12.
Hilary's observation states that he needs 2 cups of glue for every 3 cups of water. This can be represented as the ratio 2:3.
Now, let's compare this ratio to the given options:
4:6 = 2:3
Same ratio, same constant of proportionality.
3:6 = 1:2
Different ratio, not the same constant of proportionality.
3:12 = 1:4
Different ratio, not the same constant of proportionality.
8:12 = 2:3
Same ratio, same constant of proportionality.
So, the ratios that have the same constant of proportionality as Hilary's observation are 4:6 and 8:12.
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Mrs.Peterson dropped a ball from the top of a tower. At the same time, her son, Drake, launches a rocket from a different level of the tower.
The height of the tennis ball in feet after t seconds can be represented by the quadratic function: b(t)=-t^2-2t+26.
The height of Drakes rocket after t seconds can be represented by the linear function: p(t)=-2t+10.
What are the two solutions to this system? Show your work.
Explain which solution is not reasonable in this situation.
After how many seconds do the rocket and the ball reach the same height.
9514 1404 393
Answer:
two solutions: t = -4, t = 4t = -4 is not reasonable4 secondsStep-by-step explanation:
A graphing calculator shows the two solutions to be ...
(t, h) = (-4, 18) and (4, 2)
__
The two heights will be equal when ...
p(t) = b(t)
-2t +10 = -t^2 -2t +26
t^2 -16 = 0 . . . . subtract the right side expression
(t -4)(t +4) = 0 . . . factor the difference of squares
t = 4 or -4 . . . . values of t that make the factors zero
At these times, the heights will be ...
p(t) = -2{4, -4} +10 = {-8, 8} +10 = {2, 18}
The solutions are ...
(t, height) = (-4, 18) and (4, 2).
__
We generally discount solutions for negative time, because we start counting time when the objects are launched. t = -4 is an extraneous solution.
__
The rocket and ball reach the same height after 4 seconds.
Ben participated in a diving competition from a platform 25 feet above the
water. Ben's height above the water in feet can be modeled by the
quadratic function f(t) = - + + 5t + 25 where t represents time in
seconds. During which time interval did the height of Ben's trajectory
increase?
=
1.3.2 checkup - lessons learned
2. What is the slope of the line represented by the table of values below? How do you know?
Answer:
y=2/3x-4
Step-by-step explanation:
we can see that x goes up 1 for every 1.5y and if we start y at 0 x starts at -4 so if y is one than x has to be 2/3-4 becuase it is -4 + 2/3 for every 1 y goes up or one for every 1.5 y goes up. hope this answer was helpful.
PLEASE SHOW YOUR WORK!!!
Solve for y: 3^3 + 14 y- (25y - 13) = y + 7y - 9y
Answer:
y = 4
Step-by-step explanation:
3^3 + 14y - (25y - 13) = y + 7y - 9y
Exponents first.
27 + 14y - (25y - 13) = y + 7y - 9y
Distribute the negative sign from the parenthesis.
27 + 14y - 25y + 13 = y + 7y - 9y
Common terms.
27 + 13 = 40
14y - 25y = -11y
y + 7y - 9y = -y
40 - 11y = -y
Add 11 to both sides.
40 = 10y
Divide both sides by 10.
4 = y
Rearrange.
y = 4.
MATH
Which equation would you use to solve the following situation? If everybody on the team scores 4 points, and the team has a total of 28 points, how many people are on the team? 7 p = 28 4 p = 28 28 - p = 4 4 + p = 28
Answer:p=7
Step-by-step explanation:4x7=28
Twice the sum of a certain number and 36 is 90?
Step-by-step explanation:
Let the number be x
According to the question
2(x+36)=90
2x+72=90
2x=90-72
2x=18
x=18/2
x=9
What is the inverse of the function g(x)=
-3(x + 6)?
g-1(x) =
A jogger ran 13.5 miles in 3 hours.
What is the unit rate?
Answer:
Unit rate = 4.5 mph.
Step-by-step explanation:
Unit rate: 13.5/3
=> Unit rate: 4.5 mph.
Hoped this helped.
Cumulative GPA (CGPA) of a student is defined as the sum of the product of all grades multiplied by the credits of the corresponding class, divided by the sum of all credits. For instance consider a student took three courses with 3, 3, and 4 credits. Assume that the grades of this student from these courses are 4.0, 3.7, and 3.3.
The CGPA of this student is: __________
Answer:
probably about 3.5
Step-by-step explanation:
If a = 3 and b = 5, find a/b= option 1 = 5/3 option 2 = 3/5 option 3 = 2/5
Answer:
34
Step-by-step explanation:
yeah
Answer:
Answer is option 2 = 3/5
Step-by-step explanation:
a/b=3/5
A crate has a mass of 6kg. Using the fact that the acceleration due to gravity is g=9.8 m/s2, how much work is done in lifting the crate 3m, in Joules? Round answer to one decimal place if necessary.
Work done = force applied * distance covered
Force = mass * acceleration
Therefore, Work done = mass * acceleration * distance covered
Parameters:
mass = 6kg
acceleration = 9.8m/s2
distance = 3m
Substitution:
Work done = 6 * 9.8 * 3
Work done = 176.4J (to 1 decimal place)
What is the slope of the line between the points ( 2 , 7 ) and ( 7 , 1 )?
Answer:
slope = - [tex]\frac{6}{5}[/tex]
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (2, 7 ) and (x₂, y₂ ) = (7, 1 )
m = [tex]\frac{1-7}{7-2}[/tex] = [tex]\frac{-6}{5}[/tex] = - [tex]\frac{6}{5}[/tex]
Hello there! :)
To find the slope of the line when we are given 2 points, we use the following formula:
m=[tex]\frac{y2-y1}{x2-x1}[/tex]
m=[tex]\frac{1-7}{7-2} \\\frac{-6}{5}[/tex]
So the slope is -6/5. Hope this helps!
~Just a cheerful gal
#CarryOnLearning
[tex]MysteriousNature :)[/tex]
Identify the graph that matches the piecewise function
A coin is flipped 10 times. What is the probability of getting exactly 4 tails?
Answer: The probability is approximately 20.51%.
Step-by-step explanation:
Q1). A={1,2,3} B={2,3,4}. Find (A∩B) xA
Step-by-step explanation:
Given sets are :
A = {1, 2, 3}
B = {2, 3, 4}
AnB = {1, 2, 3} n { 2,3,4 }
AnB = {2,3}
Now
(AnB) X A
⇛ { 2,3 } X { 1 , 2, 3 }
⇛ { (2,1) , (2,2) , (2,3) , (3,1) , (3,2) , (3,3) }
(AnB) X A for the given problem is
{ (2,1) , (2,2) , (2,3) , (3,1) , (3,2) , (3,3) }
-2-(3(x+6)-9-(7-x)-3x
Answer:
- 24 - 5x
Step-by-step explanation:
1) Remove Parentheses
-2 - 3x - 6 - 9 - 7 + x - 3x
2) Collect like terms
( -2 - 6 - 9 - 7) + (-3x+x-3x)
3) Simplify
Similar Triangles
In the figure below, AB has length 6 feet, BC has length 8 feet and CD has length 7 feet.
If angles B and D are right angles, what is the length of DE rounded to the nearest tenth foot?
Answer:
5.3 ft
Step-by-step explanation:
Because CD corresponds to BC, the scale factor from triangle ABC to triangle CDE, is 7/8. Now, DE corresponds to AB, so to get DE, we must multiply the value of AB by 7/8. 6 times 7/8 is 5.25, and rounding to the nearest tenth of a foot, the value of DE is 5.3.
A circle has diameter 11 cm
Pythagoras theorem
Please answer will mark BRAINELIST:)
If f(x) = 3^{2+x}-3f(x)=3
2+x
−3, what is the value of f(-4)f(−4), to the nearest hundredth (if necessary)?
find four rational numbers between -5 and 8
Answer:
4.3, 4,5, 5.4, and 5.5
Step-by-step explanation:
Which expressions have a value of 54 when v= 6? Choose all the correct answers.
A 2(v2 – 9)
B V3 = 18 + 3
C (2v)2 – 90
-
D 13 = 3 – 18
E 2(v2 – 90)
F (v + 2)2 – 10
help with this please help
Answer:
10
Step-by-step explanation:
A. What is the formula for exponential growth?
B. What does each variable mean?
Please someone help!!! It’s for my final pleaseee!!!
Answer:
A. exponential growth or decay function is a function that grows or shrinks at a constant percent growth rate. The equation can be written in the form f(x) = a(1 + r)x or f(x) = abx where b = 1 + r. ... r is the percent growth or decay rate, written as a decimal, b is the growth factor or growth multiplier.
Which of the following is a factor of
f(x) = x - 3x² - 64x - 60?
(x - 1)
(x - 3)
(x + 10)
(x+6)
Answer:
x-1
MARK ME BRAINLIEST PLScual de estas fracciones es mayor que 2/5?explica como lo has averiguado
Answer:
33333
Step-by-step explanation:
Does this graph represent a function? Why or why not?
A. No, because it fails the vertical line test.
B. Yes, because it passes the vertical line test
C. Yes becquse it has two straight lines
D. No because it is not a straight line
Answer: A. No because it fails the vertical line test
The graph does not represent function because it fails the vertical line test.
What is Function?In mathematics, a function is an expression, rule, or law that establishes the relationship between an independent variable and a dependent variable. In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
The "function" would pass the vertical line test if the two lines meet at an angle larger than 90 degrees and the base line is horizontal.
Here, the vertical line test indicates that it is invalid.
The "vertical line test" primary consideration whenever it appears in an option. In this instance, failing the vertical line test is defined as all x values having two y values.
Thus, graph does not represent function.
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darlene has a rooftop carrier for her car. She puts 5 items in the carrier
with the following weights, in pounds: 10.4, 13, 8, 112, and 15.7.
3
10
A. Write and evaluate an expression to find the total weight of the
5 items.
Answer:
159.1
Step-by-step explanation:
The expression would be 10.4+13+8+112+15.7, which equals 159.1 which is the total weight.
ADD the given the polynomials: (x + 2) + (8x + 4)
CHOOSE THE RIGHT ANSWER:
A] 9x + 6
B] 8x + 6
C] 7x + 6
D] 9x + 8
NEED SOLUTION PLS!
Answer:
the answer is 9x + 6 ......
Answer:
[tex] = > (x + 2) + (8x + 4)[/tex]
[tex] = > x + 2 + 8x + 4[/tex]
[tex] = > x + 8x + 2 + 4[/tex]
[tex] = > 9x + 6[/tex]
x divide3=8 solve equation for x
Answer:
x = 24
Step-by-step explanation:
x ÷ 3 = 8
you multiply both sides by three
so it cancels out 3 and 8 × 3 = 24
so your answer is 24
hope this helps
which histogram helps best predict how much time until the next customer comes into the Clothes Shoppe.