Find the value of y for a given value of x, if y varies directly with x. If y = –96 when x = 32, what is y when x = 58?
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Related Questions
If you horizontally stretch the quadratic parent function, f(x) = x2, by a factor of 4, what is the equation of the new function?
A. g(x) =1/4 x2
B. g(x) = (1/4x)2
C. g(x) = 4x2
D. g(x) = (4x)2
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Answer:
B is your answer
Step-by-step explanation:
g(x)=(1/4x)^2
does the set of numbers form a pythagorean triple explain 24 , 10 ,26
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10^2 + 24^2 = 26^2
100 + 576 = 676
That is true
So take 4,5,6 for example
4² + 5² = 6²
16 + 25 = 36
41 = 36
A car travels 95 miles on 5 gallons of gas. give the ratio of miles to gallons as a rate in miles per gallon.
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In sakura's garden for every 5 red flowers, there are 10 yellow flowers. There are a total of 75 yellow and red flowers in her garden. How maNY red flowers are in sakura'sgarden?
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Let y = the number of red flowers.
There are a total of 75 flowers, therefore
x + y = 75 (1)
For every 5 red flowers, there are 10 yellow flowers, therefore
x = 2y (2)
Substitute (2) into (1).
2y + y = 75
3y = 75
y = 25
x = 2*y = 50
Answer: 25 red flowers.
Answer:
25 red flowers
Step-by-step explanation:
yeah
Really need help with this GeoMETry qUIz
The following is an incomplete paragraph proving that ∠WRS ≅ ∠VQT, given the information in the figure where segment UV is parallel to segment WZ. :
(picture attached)
According to the given information, segment UV is parallel to segment WZ while angles SQU and VQT are vertical angles. Angle VQT is congruent to angle SQU by the Vertical Angles Theorem. Because angles SQU and WRS are _____________ angles, they are congruent according to the ____________ Angles Postulate. Finally, angle VQT is congruent to angle WRS by the Transitive Property of Equality.
Which term accurately completes the proof?
1Same-side interior
2Corresponding
3Alternate interior
4Vertical
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vertical angle postulate
Find the absolute value and the opposite of the integer.
–989,006
A rectangle has a length of n units its width is 6 unit less its length what is the area of the rectangle
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Answer:
Step-by-step explanation:
The steps to do it. It says "solve for x. Each figure is a parallelogram. Show your work.
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The value of x is 4.
To solve for x, we'll use the property of parallelograms that opposite angles are supplementary.
Given that one angle is [tex]\(140^\circ\)[/tex], we can set up the equation:
140 + 10x = 180
Now let's solve for x:
10x = 180 - 140
10x = 40
[tex]x = \frac{40}{10}[/tex]
x = 4
Therefore, the value of x is 4. Adjacent angles in a parallelogram are indeed supplementary.
Suppose you drop a ball from a window 10 meters above the ground. The ball bounces to 80% of its previous height with each bounce. What is the total number of meters (rounded to the nearest tenth) the ball travels between the time it is dropped and the 10th bounce?
79.3 meters
73.2 meters
89.3 meters
77.5 meters
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Drops 10 m
1st bounce = 0.8*10 = 8 m up
+ 8 m down
2nd bounce = 0.8*8 = 6.4 m up
+ 6.4 m down
3rd bounce = 0.8*6.4 = 5.12 m up
+ 5.12 m down
....
9th bounce = 10(0.8)^9 = 1.34 m up
+ 1.34 m down
See the pattern? each bounce multiplies another 0.8 ; count the distance twice for returning to the ground
10, 8, 6.4, 5.12, ... 1.34
term in sequence = 10(0.8)^(n-1)
where n = {1,2,3,...10}
Total meters traveled
= ∑ 10(0.8)^0 + 2[10(0.8)^1 + 10(0.8)^2 + ..... 10(0.8)^9]
multiply sum by 2 then subtract the extra 10 m
Sum of a geometric sequence for the bounces
where n in (n-1) [tex]S = a( \frac{1- r^{n} }{1-r} ) \\ \\ S = 10 ( \frac{1- 0.8^{10} }{1-0.8} ) \\ \\ S = 44.63 \\ \\ 2*44.63 = 89.26 \\ \\ 89.26 - 10 = 79.3 m [/tex]would be 10 for the number of bounces before 10th bounce, "a" is 10.
Consider the equation below. f(x) = 4x3 + 6x2 − 24x + 3 (a) find the intervals on which f is increasing. (enter your answer using interval notation.)
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The function f(x) = 4x^3 + 6x^2 - 24x + 3 is increasing on the interval (-2/3, 1.5), where the derivative of the function is positive.
Explanation:To find the intervals on which the function f(x) = 4x^3 + 6x^2 − 24x + 3 is increasing, we first need to calculate its derivative, which will give us the slope of the tangent line to the function at any point x. The function is increasing wherever its derivative is positive.
The derivative of f with respect to x is:
f'(x) = 12x^2 + 12x - 24.
To find where the function is increasing, set the derivative greater than zero:
12x^2 + 12x - 24 > 0
Solve this inequality to find the intervals for x. Factoring the quadratic, we get:
(2x - 3)(6x + 4) > 0
The zeros of this equation are x = 1.5 and x = -2/3. These values divide the real number line into intervals. Test a value from each interval to see where the function is increasing:
If x < -2/3, for example x = -1, the derivative becomes negative, indicating the function is decreasing.If -2/3 < x < 1.5, for example x = 0, the derivative is positive, indicating the function is increasing.If x > 1.5, for example x = 2, the derivative is again negative, indicating the function is decreasing.Thus, the function f(x) is increasing in the interval (-2/3, 1.5).
I made a clay snake 9 5/8 inches long, but a section 1 7/8 inches long broke off. How long is the snake now?
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R
9 5/8 = 8x9+5= 77/8
1 7/8 = 8x1+7 = 15/8
Now subtract since your denominators are equal.
77/8 - 15/8 = 62/8
Now change back to a mixed number, 8 × 7 = 56 with a remainder of 6.
7 6/8 , simplify 6/8 to 3/4.
Your final answer is 7 3/4. Hope this helps you!
The parent function of a graph is f(x) = x2. The graph shifts a units to the left and down b units. Which function models the transformed function?
A) y = x2 - a + b
B) y = (x - a)2 - b
C) y = (x + a)2 - b
D) y = (x - b)2 - a
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Answer:
Option c
Step-by-step explanation:
A parent function is given by f(x) = x²
If the graph of the parent quadratic function is shifted a units to the left then new function will become
f'(x) = (x+a)²
Now the new function f'(n) is shifted b units down then the shifted function will be
f" (x) = (x + a)² - b
Therefore, Option c. is the answer.
11/12+(−7/12). Write your answer as a fraction in simplest form.
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The result of the operation 11/12 + (-7/12) simplifies to 1/3, because the sum of the numerators is 4, and we keep the same denominator of 12, giving us 4/12. In simplest form, this fraction is 1/3.
Explanation:The question is asking us to perform an addition operation on two fractions. Specifically, we are asked to add 11/12 and -7/12. When adding or subtracting fractions, the most important thing is that they have the same denominator, which our fractions do. Here's how you perform the operation:
Add the numerators of the fractions: 11 + (-7) = 4.
You keep the same denominator: 12.
So, 11/12 + (-7/12) = 4/12.
To simplify this fraction, we find the greatest common divisor of 4 and 12, which is 4, and divide both the numerator and denominator by it. So, 4/12 simplifies to 1/3.
Learn more about Fraction Addition here:https://brainly.com/question/34291287
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Pqr is a right angle. If pq=8 what is equivalent
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1/2=RQ/8
So RQ= 4
please help me with my math homework??
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Find the value of x, please
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x^2 = 360 - 311
x^2 = 49
so
x = √49
x = 7
4 inside angles = 360 degrees
131 + 75 + 105 = 311
360 - 311 = 49
x^2 = 49
x = sqrt(49) = 7
x = 7
A hockey team played 81 games in a season. they won one fewer games than three times the number of ties, and lost eight fewer games than they won. how many games did they win? lose? tie?
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Final answer:
The hockey team won 38 games, lost 30 games, and tied 13 games in the season.
Explanation:
Let's define the variables for the different outcomes in the hockey team's season:
T = number of games tiedW = number of games won = 3T - 1L = number of games lost = W - 8The total number of games is the sum of wins, losses, and ties, and we know this number is 81. This gives us the equation:
W + L + T = 81
Substituting W and L gives:
(3T - 1) + (3T - 1 - 8) + T = 81
Combining like terms and solving for T:
7T - 10 = 81
7T = 91
T = 13 (number of ties)
We then calculate W and L as:
W = 3T - 1 = 3(13) - 1 = 38 (number of wins)
L = W - 8 = 38 - 8 = 30 (number of losses)
Can someone help me with this question?
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[tex]8x+16y[/tex]≥[tex]20[/tex]
[tex]8(6)+16(1)[/tex]≥[tex]20[/tex]
[tex]48+16[/tex]≥[tex]20[/tex]
[tex]64[/tex]≥[tex]20[/tex]
The price of a bookcase, including 8% sales tax, is $378. What is the price of the bookcase, before sales tax?
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Hope this Helps
Then you subtract: 378-30.24= 347.76
Two numbers are between 20 and 30. their greatest common factor is 4.Which two numbers could they be?
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These are the only two numbers (other than 20 itself) that have a factor of 4. And if you were to find all of their common factors, 4 would be the greatest!
-3(m-2n) = 5m
solve for m
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it should be that.
Answer:
n=3n/4
Step-by-step explanation:
Brandon has 7/1/2gallon of paint. He plans on using 1/1/2 gallon on each room. How many rooms will he be able to paint.
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The rate of change is constant in each table. Find the rate of change. Explain what the rate of change means for the situation. time (hours) 4, 6, 8, 10 distance (miles) 212, 318, 424, 530
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[tex]\bf \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ 6}}\quad ,&{{ 318}})\quad % (c,d) &({{ 10}}\quad ,&{{ 530}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{530-318}{10-6}\implies \cfrac{212}{4} \\\\\\ \stackrel{\textit{average rate of change}}{\cfrac{53}{1}}[/tex]
recall the top is distance, and the bottom is hours, so 53 miles for every 1 hour. So the object or vehicle is moving at 53 mph on average.
Answer:
The car travels 53 miles per hour.
Step-by-step explanation:
time (hours) 4 6 8 10
distance (miles) 212 318 424 530
The rate of change can be given as:
[tex]\frac{318-212}{6-4}[/tex] = [tex]\frac{106}{2}[/tex] = 53 mph
[tex]\frac{424-318}{8-6}[/tex] = [tex]\frac{106}{2}[/tex] = 53 mph
Hence, the rate of change is 53 mph or we can say the car travels 53 miles per hour.
The sum of 4 consecutive even integers is 36, what is the 3rd largest integer in the set?
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The sum of four consecutive even integers that equal 36 is broken down to find the smallest integer. Once the smallest integer is found (6), we can determine that the third largest integer in the sequence is 8.
Explanation:To solve for the third largest integer in a set of four consecutive even integers that sum to 36, we can define the smallest integer as x. The next integers would be x + 2, x + 4, and x + 6. Setting up the equation:
x + (x + 2) + (x + 4) + (x + 6) = 36
Combining like terms, we get:
4x + 12 = 36
Subtracting 12 from both sides:
4x = 24
Dividing by 4:
x = 6
Now we have our integers: 6, 8, 10, 12. The third largest integer, which is the second smallest, is 8.
In a triangle, the measure of the first angle is three timesthree times the measure of the second angle. the measure of the third angle is 80 degrees80° more than the measure of the second angle. use the fact that the sum of the measures of the three angles of a triangle is 180degrees° to find the measure of each angle.
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The total of all the angles in a triangle is 180 degrees.
1x +3x +x - 35 = 180.
5x = 215.
Write the ratio as a fraction in simplest form a/b. What is the ratio of baseballs to basketballs?
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baseball: basketballs, or
baseballs/basketballs
if you give me the numbers i can plug it in
hope this helps
Answer: 5/8 im pretty sure i hope it helps :) i took it on freckle so i know but i think this is right
A local civic group is selling t-shirts to raise funds for Relay to Life. They plan to sell
2500 t-shirts for $10. They consider raising the t-shirt price in order to earn more
profit. For each $1 increase, they will sell 100 fewer t-shirts. Let x represent the
number of $1 increases.
a. Write a function,
Write a function, c(x), to represent the cost of one t-shirt based on the number
of increases.
b. Write a function, t(x), to represent the number of t-shirts sold based on the
number of increases.
c. Write a revenue function, r(x), for the t-shirt sell that could be used to maximize
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a. Let us say that c(x) is the cost of one t shirt based on the number of increases therefore:
c = 10 + x
b. Say that t(x) is the number of t shirts sold based on the number of increases so:
t = 2500 – 100 x
b. The revenue is simply the product:
r(x) = (10 + x) (2500 – 100 x)
Combining:
r(x) = 25000 – 1000 x + 2500 x – 100 x^2
r(x) = 25000 + 1500 x – 100 x^2
Taking the 1st derivative and setting dr / dx = 0 to get the maxima:
dr / dx = 1500 – 200 x
1500 = 200 x
x = 7.5
t = 2500 – 100 x = 2500 – 100 (7.5) = 1750
Hence 1750 shirts should be sold.
A car travels 100 meters in 5 seconds. What is the speed of the car/7281023/14f0e74f?utm_source=registration
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What is the sum of the first five terms of the geometric series 3 − 6 + 12 − . . . ?
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3,−6,12,−24,...
You can rewrite this as:
(−1)n3⋅(1,2,4,8,...)
If we focus on 1,2,4,8...
an+1=2an
with a0=1.
This can be written out as a nice sum:
N∑n=02n=20+21+22+23+...
=1+2+4+8+...
Thus, now we can recombine everything to get:
3N∑n=0(−1)n2n
Find the GCF of the given polynomial.
16a⁴b⁴ + 32a³b⁵ - 48a²b⁶
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The GCF of this polynomial would be:
[tex]16a^2b^4[/tex]
[tex](16a^2b^4)(a^2+2ab+3b^2)[/tex]
Hope this helps.
-Benjamin
Rectangle EFGH is graphed on a coordinate plane with vertices at E(-3,5), F(6,2), G(4,-4), and H(-5,-1). Find the slopes of each side. What do you notice about the slopes of opposite sides? What do you notice about the slopes of adjacent sides?
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Slope of Side FG- 2/-6
Slope of Side GH- 3
Slope of Side HE- 2/6