the function of (x) varies directly with x^2, and f(x)=96 when x=4 what is the value of f(2)

Answers

Answer 1

[tex]\bf \qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array}\\\\ -------------------------------[/tex]

[tex]\bf \textit{f(x) varies directly with }x^2\qquad f(x)=kx^2 \\\\\\ \textit{we also know that } \begin{cases} f(x)=96\\ x=4 \end{cases}\implies 96=k(4)^2\implies 96=16k \\\\\\ \cfrac{96}{16}=k\implies 6=k\qquad therefore\qquad \boxed{f(x)=6x^2} \\\\\\ \textit{now, when }\stackrel{f(2)}{x=2}\textit{ what is \underline{f(x)}?}\qquad f(2)=6(2)^2[/tex]

Related Questions

John made $20 for 2 hours of work. Sally made $50 for 4 hours of work. How do John and Sally's hourly pay rate compare?

Answers

John make 20 dollars an hour because 20/2 is 10 nd sally makes 12.50 dollars an hour because 50/4 is 12.50

Answer:

sally makes more

Step-by-step explanation:

john makes 20 per 2 hours

20/2= 10

sally makes 50$ per 4 hours

50/4= 12.5

so Sally makes more

the / is division

A line intersects the points (6, -12) and (15, -3). What is the slope intercept equation for this line?
y = 1x - [?]

Answers

Let's say that the unknown value here is c. Although we are given two points on the line, it is only necessary to use one as there is only one unknown value, so let's say we choose the point (6, -12) and substitute this into the equation:

-12 = 1(6) - c
-12 - 6 = -c
-18 = -c
c = 18

Thus the equation for the line is y = 1x - 18

Q # 7.Write a congruence statement for the pair of triangles

Answers

Answer: Fourth option:
Triangle ZYB is congruent with triangle OWR, by SSS
SSS: Side Side Side, because the three sides are given, and they are congruent

Which describes the difference between the graph of f(x) = 2x3 - 8x + 3 and g(x) = x3 - 4x?
A) The graph of g(x) is obtained by shifting f(x) up 3 units and stretching vertically by a factor of 2.
B) The graph of f(x) is obtained by shifting g(x) up 3 units and stretching vertically by a factor of 2.
C) The graph of g(x) is obtained by shifting f(x) right 3 units and compressing vertically by a factor of 2.
D) The graph of f(x) is obtained by shifting g(x) right 3 units and compressing vertically by a factor of 2.

Answers

The difference between the graph of f(x)=2x^3-8x+3 and g(x)=x^3-4x will be described as follows:
The graph of f(x)=2x^3-8x+3 is the first one
The graph of g(x)=x^3-4x is the second one
From the two graphs we see that:

B) The graph of f(x) is obtained by shifting g(x) up 3 units and stretching vertically by a factor of 2.

B) The graph of f(x) is obtained by shifting g(x) up 3 units and stretching vertically by a factor of 2.

Which description best fits the distribution of the data shown in the histogram?

skewed right

uniform

approximately bell-shaped

skewed left
Histogram with vertical axis ranging from 0 to 14 labeled Frequency. For 0 to 49, the bar height is 2. For 50 to 99, the bar height is 6. For 100 to 149, the bar height is 12. For 150 to 199, the bar height is 5. For 200 to 249, the bar height is 1.

Answers

This is an approximately bell-shaped distribution. The highest bar is in the center, with height = 12. Just to its left and right are bars of heights 6 and 5. At the extremes are bars of heights 2 and 1.

If the highest bar was on the left, it would be skewed left (and if it was on the right, skewed right). A uniform distribution would more or less have the same height level over all the bars.

Answer with explanation:

The Description about the Histogram is

Vertical Axis = 0-14

Horizontal Axis Bar Height

0-49 2

50-99 6

100-149 12

150-199 5

200-249 1

Plotting the Histogram

→Class interval 150-199 has frequency =5, and class interval 50-99, has frequency equal to 6.

→The curve is not uniform on both sides.

→The interval in which mean , median lies has 6+2=8 frequency on the left of that interval , and 5+1=6, values on the right of class interval [100-149].We can conclude that,the histogram is left Skewed.

→But when we join ,mid points of histogram,the curve obtained resembles with a normal distribution curve called bell curve.It is not exactly bell shaped,as not uniform on both sides explained above.

Option C: Approximately bell Shaped

hey can you please help me posted picture of question

Answers

The correct answer for the problem shown in the figure atttached is the last option (option D), which is shown below:

D. (-3x+6i)(x+2i)
It is impotant to know that if you want to verify that the option D. (-3x+6i)(x+2i) is the correct answer, you can apply the distributive property to (-3x+6i)(x+2i).
Therefore, when you apply the distributive property, you obtain that the result is:
-3x²-12

Which is correct

Therefore, you can be sure that the correct answer is the option D. (-3x+6i)(x+2i).

hey can you please help me posted picture of question

Answers

The solutions to the given quadratic equation can be determined using quadratic formula.

[tex]x= \frac{-b+- \sqrt{ b^{2} -4ac} }{2a} [/tex]

b =coefficient of x term = -3
a = coefficient of squared term = 1
c = constant term = 3

Using the values in the above formula we get:

[tex]x= \frac{3+- \sqrt{9-4(1)(3)} }{2(1)} \\ \\ x= \frac{3+- \sqrt{-3} }{2} \\ \\ x= \frac{3+- \sqrt{3}i }{2} [/tex]

Thus, option A gives the correct solution

To which sets of numbers does 0.0202002000200002 . . . belong? A. Irrational B.Rational only C.Rational and natural D.Rational and integer

Answers

It does not repeat and it does not terminate, so that would make it irrational.

Can adjacent angles be supplementary complementary or neither

Answers

They can be and supplementary and complementary but they do not have to be. Did I Help?

Answer:

Supplementary angles are two angles whose sum is 180 degrees while complementary angles are two angles whose sum is 90 degrees. Supplementary and complementary angles do not have to be adjacent

Step-by-step explanation:

Jamelia estimates the square root of 72 in the following way: √72=2√36= 2*6=12 Explain why her reasoning is incorrect. Estimate the square root of 72 to the nearest tenth without using your calculator. Show your work.

Answers

We are going to review the following procedure:
√72 = 2√36 = 2 * 6 = 12
The next step is incorrect:
√72 = 2√36
The correct step is:
√72 = √2 * (36).
Let's now calculate √72. We have the following steps:
Step 1:
√72 = √ (2 * (36))
Step 2:
√72 = √ (2 * (6) ^ 2)
Step 3:
√72 = 6√2
Step 4:
√72 = 6 * 1.41
Step 5:
√72 = 8.46
Step 6:
√72 = 8.5
Answer:
√72 = 8.5

how is this solved? graph and explanation would be helpful

Answers

As a rule, you plot the lines as though the equations had an equal sign. Because both are strict inequalities (no "or equal to"), the lines are dashed, indicating the (x, y) values on the line are NOT part of the solution.

The solution space will be above the first line (y > ...) and below the second line (y < ...). As a rule, you indicate the solution space by shading the portion of hte plane that satisfies the inequality.* The solution is the portion of the plane that is in both solution regions (that is, doubly-shaded).

_____
* Sometimes, it may actually work better to shade the portion of the plane that does NOT satisfy the inequality. That way, the remaining unshaded area is the solution space. If you do it that way, make sure the graph is clearly marked indicating that is the case. The usual expectation is that the shaded area is the solution, so you don't want to get your answer marked wrong or misinterpreted.

hey can you please help me posted picture of question

Answers

Two transformations are applied to F(x) to obtain G(x)

1) F(x) is multiplied by 2.
Multiplying a function by a magnitude greater than 1 results vertical stretch.
So, F(x) is stretched by a factor of 2.

2) 5 is subtracted from the function value.
Subtraction of a number indicates downward shift.

So, G(x) is obtained from F(x) by stretching it vertically by a factor of 2 and shifting down by 5 units

Thus, option D is the correct answer

F(x) = x^2
G(x) = 2x^2 - 5

the graph G(x) is the graph of F(x) stretched vertically by factor of 2 and shifted 5 units down

Answer.
D
The graph G(x) is the graph of F(x) stretched vertically and shifted 5 units down

Hugo is a veterinarian. He knows the following information about his 41 patrons: 20 patrons in total do not have a dog. 17 patrons in total have a cat. 7 patrons have neither a dog nor a cat. Can you help Hugo organize the results into a two-way frequency table?

Answers

Answer:

4,17,13,7

Step-by-step explanation:

i got it right :)

Final answer:

To assist Hugo in organizing patron pet ownership into a two-way frequency table, calculations were made to determine the number of patrons with both a dog and a cat, leading to a complete frequency table illustrating pet ownership among 41 patrons.

Explanation:

Hugo, the veterinarian, is attempting to organize patron pet ownership information into a two-way frequency table. First, let's establish the total number of patrons which is 41. Since 20 patrons do not have a dog, it implies that 41 - 20 = 21 patrons have a dog. Of the 41 patrons, we know that 17 have a cat. Also, 7 patrons have neither a dog nor a cat. To create the two-way frequency table, we need to figure out how many patrons have both a dog and a cat.

To find the number of patrons with both pets, we add the number of patrons without pets to those with dogs and then subtract from the total number of patrons, which gives us 41 - 20 + 7 = 28. However, since this number includes all dog owners, we need to subtract those who only have dogs and no cats, which gives us 28 - (41 - 17) = 28 - 24 = 4 patrons with both a dog and a cat.

With these calculations, we can now fill out the two-way frequency table:

Patron\PetDogNo DogTotalCat41317No Cat17724Total212041

Note: The sum of the numbers for dog owners and non-dog owners must equal the total number of patrons, and the same applies for cat ownership.

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21 ÷ 7 + 20 • 100 • 2 – 3

PLEASE SOLVE

Answers

Do the multiplication and division first.

21 / 7 = 3

20 * 100 * 2 = 4000.

Now for the addition and subtraction. The 3 and - 3 cancel each other out.

3 + 4000 - 3 = 4000

The first step for solving this expression is to divide 21 by 7.
3 + 20 × 100 × 2 - 3
Eliminate the opposites in the expression.
20 × 100 × 2
Multiply 20 by 100.
2000 × 2
Lastly,, multiply the two numbers together to get your final answer.
4000
Let me know if you have any further questions.
:)

what are some types of quadrilaterals

Answers

Quadrilaterals include all regular 4 sides shapes.
Such as, square, rectangle, trapezoid, and parallelogram

I hope this helped!

Functions f(x) and g(x) are described as follows: f(x) = −5x2 + 9 x g(x) 0 0 1 4 2 8 3 4 4 0 Which statement best compares the maximum value of the two functions?

Answers

Let's look at the description for g(x) first. On the left we have the input (like the horizontal axis on a graph) and on the right is the output, or the value of the function (the vertical axis on a graph). If you look on that right list, the highest number is 8. This is the maximum value of g(x). Now we have to compare this to f(x). Looking at f(x), it's an upside-down parabola (like a frown), with starts at 9 on the vertical axis and goes down from there. You can see this if you think about plugging in x=0. Then f(0)=9. If you plug in any other number for x, it gets squared, then multiplied by -5, o you have 9 + [negative number], which will be less than 9. So the maximum value for f(x) is 9. Since 9 is 1 unit larger than 8 (the max for g(x))

To compare the maximum values of function, which is a discrete function with given values, we find that C ) It is 3 units lower for f ( x ) than g ( x )

To compare the maximum values of functions f(x) and g(x), we first analyze each function separately. The quadratic function f(x) = -4x2 + 5x has a vertex form which reveals its maximum value at x = 1/3, and since g(x) is a discrete function defined by its values at certain points, we look directly at the given values to find its maximum.

Function g(x) reaches its maximum at g(2) = 8. Comparing this to f(x), whose vertex form shows that its maximum is f(1/3), we need to compute f(1/3) = -4(1/3)2 + 5(1/3) to find its specific value. After calculation, f(1/3) is found to be higher than 8, which is the maximum of g(x).

Thus,

g ( x ) maximum value = 8

f ( x ) maximum value = 5

g ( x ) max - f ( x ) max = 8 - 5 = 3

Complete Question:

Functions f(x) and g(x) are described as follows:

f(x) = -4x2 + 5

x g(x)

0 0

1 4

2 8

3 4

4 0

Which statement best compares the maximum value of the two functions? A. It is equal for both functions. B. It is 3 units higher for f(x) than g(x). C. It is 3 units lower for f(x) than g(x). D. It is 4 units lower for f(x) than g(x).

Lana is trying to find an equation for a line that passes through (5, 2) and is parallel to 3x + 2y = 15. explain the steps that lana could take to determine the equation.

Answers

We have the following equation:
3x + 2y = 15

Step 1:
Rewrite given equation:
2y = 15 - 3x
y = 15/2 - (3/2) x

Step 2:
Parallel lines have the same slope:
y = mx + b
m = -3 / 2
y = (- 3/2) x + b

Step 3:
Find b, for this we evaluate the point (5, 2) in the equation:
2 = (- 3/2) (5) + b
2 = (- 15/2) + b
2 + 15/2 = b
19/2

Step 4:
The parallel line is:
y = (- 3/2) x + 19/2

What is the Least common denominator for -3/x -6/8x^2

Answers

Assuming your second fraction is -6/(8x^2), the denominator of the second fraction already includes the first denominator as a factor, so it is the lowest common denominator.

The Least Common Denominator is 8x^2 for the fractions as written.

_____
You can reduce the second fraction to -3/(4x^2), which would make the Least Common Denominator be 4x^2.

If r = -6, s = -2, v = 10, and w = 3; then vs(r - s) ÷ 2 + rw =

Answers

vs(r - s) ÷ 2 + rw =

= (10)(-2)[-6 - (-2)] ÷ 2 + (-6)(3)

= -20(-4) ÷ 2 -18

= 80 ÷ 2 - 18

= 40 - 18

= 22

Mrs.Alvarado gets a raise that increases their income to $6,500 a month. Their mortgage stays the same. What percent of their monthly income do they now spend on the mortgage?

Answers

Less than what they used to, if you would let me know what the mortgage is per month, I could calculate it.

Determine whether quantities vary directly or inversely and find the constant of variation.
A teacher grades 25 students essays in 4 hours. Assuming he grades at the same speed, how long will it take him to grade 35 essays?

Answers

Divide 25/4 to figure out how many essays the teacher grades in 1 hour.

The time take him to grade 35 essays is, 5.6 hours.

What is Proportional?

Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.

Given that;

A teacher grades 25 students essays in 4 hours.

And, To find the time take him to grade 35 essays.

Now, Let us assume that,

Time take him to grade 35 essays is, x

Hence, We get;

25 / 4 = 35 / x

Solve for x;

x = 35 × 4 / 25

x = 5.6 hours

Thus, the time take him to grade 35 essays is, 5.6 hours.

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What is the sum of the first 35 terms in the series 7 + 9 + 11 + ...?

a.

29

c.

1645

b.

1399

d.

1435

Answers

The answer is d
Hope this helps :)

First find the 35th number in the series using the formula:
an = a1 + (n - 1)d
a1 = first number in the series
d = difference between successive number
n = number of terms
a35 = 7 + (35 - 1)2
a35 = 7 + (34)2
a35 = 7 + 68 = 75.
Therefore, the 35th term is 75.
To find the sum of the first 35 numbers, use the formula:
Sn = n(a1 + an) / 2
Sn = 35(7 + 75) / 2
Sn = 2870 / 2 = 1,435.
Therefore, the sum of the first 35th term is 1,435.
The correct answer is D.

Solve by using the quadratic formula. 9x2 + 24x + 32 = 0

Answers

The quadratic formula is:

[tex]x= \frac{-b+- \sqrt{ b^{2} -4ac} }{2a} [/tex]

b =coefficient of x term = 24
a = coefficient of squared term = 9
c = constant term = 32

Using the values, we get:

[tex]x= \frac{-24+- \sqrt{576-4(9)(32)} }{2(9)} \\ \\ x= \frac{-24+- \sqrt{-576} }{18} \\ \\ x= \frac{-24+-24i}{18} \\ \\ x= \frac{-4+-4i}{3} \\ \\ x= \frac{-4+4i}{3}, x \frac{-4-4i}{2} [/tex]

The first step for solving this equation is to multiply the first two numbers together.
18 + 24x + 32 = 0
Add together 18 and 32.
50 + 24x = 0
Now move the constant to the right side of the equation and change its sign.
24x = -50
Lastly,, divide both sides of the equation by 24.
x = [tex]- \frac{25}{12} [/tex]
This means that the correct answer to your question is going to be x = [tex]- \frac{25}{12} [/tex] or x = [tex]-2 \frac{1}{12} [/tex] simplified.
Let me know if you have any further questions.
:)

Ben writes the number 74,443. The value of the digit 4 in the hundreds place is 10 times the value of the digit 4 is what place vakue

Answers

Place Value Going to Left of Decimal:

Decimal
Ones
Tens
Hundreds
Thousands
Ten-Thousands

The middle 4 in 74,443 is in the hundreds place. The 4 next to the 3 is in the tens place.

The 4 in the tens place is worth 40. 40 * 10 would equal the 400 in the hundreds place.

ANSWER: tens place

Hope this helps! :)

what are the common factors of 24 and 48

Answers

The common factors of 24 and 48 are 1, 2, 3, 4, 6, 8, 12, and 24.

Factors are the numbers that can be multiplied with another number, to equal the product stated. Common factors are the factors that both stated products have.
Factors of 24: 1, 2, 3, 4, 6, 8, 12, and 24.
Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48.

Finding all the shared factors, will give you a final answer of 1, 2, 3, 4, 6, 8, 12, and 24.

I hope this helps!

seven and thirty twp hundreths plus two and one tenth times two and seven tenths minus 18a

Answers

Answer: Write the expression as:

" 70 [tex] \frac{32}{100} [/tex] +
2[tex] \frac{1}{10} [/tex] * 2[tex] \frac{7}{10[/tex] − 18a " ;
______________________________________________________
or; write as:
______________________________________________________
" 70.32 + (2.1) * (2.7) − 18a " ;
______________________________________________________

To simplify:
______________________________________________________

Using "PEDMAS" (the "order of operations") ;

the "multiplication" comes first;

So: → "(2.1) * (2.7) = 5.67 " .

And rewrite:
______________________________________________________
" 70.32 + 5.67 − 18a " .

Now: " 70.32 + 5.67 = 75.99 " ;

So, we can the final simplified expression as:
______________________________________________________
" 75.99 − 18a " ;

or; write as: " 75[tex] \frac{99}{100} [/tex] − 18a " .
______________________________________________________

Engineers are analyzing the performance of windshield wiper blades. At the end of one swipe, the tip of a blade is at (−5, 7) when represented graphically. What is the sine value of this function? (2 points) negative 7 square root 74 divided by 74 negative 5 times square root of 74 over 74 7 times square root of 74 over 74 square root 74

Answers

The correct answer to this question is "7 times square root of 74 over 74."

First, we need to get for the "r."r^2 = (−5)^2 + 7^2r^2 = 25 + 49r^2 = 74r = square root of 74

Then, after that, we need to formulate the equation of a sin:sin x = 7 / rsin x = 7 / sqrt(74)sin x = 7 * sqrt (74) / 74

hope this helpsss

Answer:

Option C. [tex]7.\frac{\sqrt{74}}{74}[/tex]

Step-by-step explanation:

At the end of one swipe the tip of one blade is at (-5, 7). We have to find sine value of this function.

As shown in the figure coordinates of the tip of the wiper blade are (-5, 7)

So [tex]sin a = \frac{Height}{Hypotenuse}[/tex]

Here Height of the triangle = 7

and Hypotenuse = x = [tex]\sqrt{(-5)^{2}+7^{2}}=\sqrt{25+49}=\sqrt{74}[/tex]

By putting these values in the expression

[tex]sina=\frac{7}{x}=\frac{7}{\sqrt{74}}=7.\frac{\sqrt{74}}{74}[/tex]

Answer is option C.[tex]7.\frac{\sqrt{74}}{74}[/tex]

A local am radio station broadcasts at a frequency of 764 khz. calculate the energy of the frequency at which it is broadcasting. energy = kj/photon

Answers

The frequency of the emitted radio waves is:
[tex]f=764 kHz = 7.64 \cdot 10^5 Hz[/tex]

The energy of a photon is given by:
[tex]E=hf[/tex]
where h is the Planck constant and f is the photon frequency. Using the frequency given by the problem, we can find the energy of each photon of this radiation:
[tex]E=hf=(6.6 \cdot 10^{-34} Js)(7.64 \cdot 10^5 Hz)=5.04 \cdot 10^{-28} J=5.04 \cdot 10^{-31} kJ[/tex]

the graph below shows the amount of snowfall in a 6-hour period

Between which hours did the least amount of snow fall?

Answers

The amount of snow per given time is calculated by its height. From the graph shown the least amount of ice was between 0 hours and 4 hours. This is because between these times the amount the amount of snow was lower than 5 inches.

Answer=(4,5)

Step-by-step explanation:

A square garden has side lengths of 8 inches. Jackie makes a rectangular garden with the same area as the square garden .which of these could be the dimensions of the rectangular garden. a-10 inches by 6 inches, b7 inches by 9 inches, c 8 inches by 12,d 16 inches by 4 inches.

Answers

D.

When you multiply 16 by 4 you get 64. 8 times 8 is also 64.

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