The table below represents the height of a bird above the ground during flight, with p(t) representing height in feet and t representing time in seconds

calculate the average rate of change from 3 to 9 seconds

Answer:

C, Plus or minus 3

Step-by-step explanation:

to solve 3x² - 27 = 0, we want to get the x by itself, so lets add 27 to both sides.

3x² = 27 < divide both sides by 3 to get x alone

3x²/2 =x²

27/3 = 9

x² = 9 < we can use the square-root property and square both sides of the equation to get x alone. we use the ± because there are 2 possible solutions to a square rooted number

√x² = x

√9 = 3

x = ±3

looking at our answer choices, the correct answer is C

Answer:

C. Plus or minus 3

Step-by-step explanation:

Take a GCF of 3 out of both terms in the binomial. You'll get 3*(x^2-9)=0. Then use FOIL to get the binomials (x+3) and (x-3). You're answers will  be -3 and 3

The question involves calculating the volume of a right rectangular prism and dividing it by the volume of a unit cube to find out how many such cubes can fit inside the prism.

The question is about finding how many unit cubes, each with edge lengths of 1/2 meter, can fit inside a right rectangular prism whose edge lengths are 4/5 meter, 3/4 meter, and 5/8 meter. To solve this, we first calculate the volume of the prism and then divide it by the volume of a unit cube to determine how many such cubes can fit inside the prism.

Step-by-step Solution:

By applying the above steps, we'll know the exact number of unit cubes that can fit inside the given right rectangular prism.

40square +30square

which is2500

2500 square root is 50

so answer is 50

The transformed equation results in [tex]f(x) = 3(x - 2)^2 - 3 = 3x^2-12x+9[/tex].

Let's start with the function[tex]f(x) = x^2[/tex]. We need to apply the following transformations:

Let's break down each transformation step-by-step.

Therefore, the equation of the transformed function is [tex]f(x) = 3(x - 2)^2 - 3[/tex].

Answer:

You're correct

The slope is -2/5; and the y-intercept is  -1/3

Step-by-step explanation:

Slope = (-13/30 + 1/30) / (1/4 + 3/4)

= (-12/30) / ( 4/4)

= - 2/5

Slope intercept form: y = mx + b, where b = y-intercept

b = y - mx

b = (-3/5) - (-2/5)(2/3)

b = -3/5 + 4/15

b = -9/15 + 4/15

b = -5/15

b = -1/3

Answer

Slope = -2/5; y-intercept = -1/3

The slope and the y-intercept of the linear function is;

Option A; slope is -2/5 and y-intercept is -1/3

      m = (y2 - y1)/(x2 - x1)

Let's make use of the first 2 coordinates to get the slope;

x1 = -3/4

x2 = -1/2

y1 = -1/30

y2 = -2/15

m = (-2/15 + 1/30)/(-1/2 + 3/4)

m = (-1/10)/(1/4)

m = -2/5

We know equation of a line in slope intercept form is;

y = mx + c

where m is slope and c is y-intercept

-1/30 = (-2/5)(-3/4) + c

-1/30 - 3/10 = c

c = -1/3

Thus, y-intercept is -1/3 and slope is -2/5

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Answer:

[tex]f^{-1} (x)=\frac{x+6}{7}[/tex]

Step-by-step explanation:

To find the inverse of a function, we must substitute in y for f(x), swap the locations of y and x, and then solve for y

[tex]y=7x-6\\\\x=7y-6\\\\x+6=7y\\\\y=\frac{x+6}{7} \\\\f^{-1} (x)=\frac{x+6}{7}[/tex]

The inverse of the given function [tex]f^{-1}(x)=\frac{x+6}{7}[/tex].

We have given that,F(x) = 7x - 6

We have to determine the value of the inverse function.

An inverse is a function that serves to undo another function.

That is, if f(x) produces y, then putting y into the inverse of f produces the output x.

To find the inverse of a function,

we must substitute in y for f(x), swap the locations of y and x, and then solve for y,

[tex]y=7x-6\\x=7y-6\\x+6=7y\\y=\frac{x+6}{7}[/tex]

We get the value of [tex]y=(x+6)/7.[/tex]

Taking inverse on both sides so we get,[tex]f^{-1}(x)=\frac{x+6}{7}[/tex]

Therefore the inverse of the given function [tex]f^{-1}(x)=\frac{x+6}{7}[/tex].

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Answer:

About 23 in

Step-by-step explanation:

2908.33/7=415.475

415.475/[tex]\pi[/tex]=132.31

132.31 sqr rt = r = 11.5

2r=d

d=23 aprox

The diameter of the cylinder is approximately 22.94 inches.

To find the diameter of the cylinder, we can use the formula for the volume of a cylinder:

Volume [tex]= \pi \times r^2 \times h,[/tex]

where π is a mathematical constant (approximately 3.14159), r is the radius of the cylinder, and h is the height of the cylinder.

Given that the height of the cylinder is 7 inches and the volume is 2,908.33 cubic inches, we can rearrange the formula to solve for the radius:

Volume [tex]= \pi \times r^2 \times h[/tex]

[tex]2,908.33 = \pi \times r^2 \times 7[/tex]

Dividing both sides of the equation by 7π, we have:

[tex]r^2[/tex] = 2,908.33 / (7π)

[tex]r^2[/tex] ≈ 131.50

Taking the square root of both sides, we get:

r ≈ √131.50

r ≈ 11.47.

The radius of the cylinder is approximately 11.47 inches.

To find the diameter, we multiply the radius by 2:

d = 2 [tex]\times[/tex] r

d ≈ 2 [tex]\times[/tex] 11.47

d ≈ 22.94

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Answer:

Step-by-step explanation:

First, you can reduce it

4(n^2-11n+30)

This should make it easier to work with. But remember, keep the 4 there. You cannot just get rid of it because it would change the value of the equation

Now find factors of 30 that have a difference or ad up to 11.

Factors of 30:

1, 30

2, 15

3, 10

5, 6

Ahh  yes, 5 and 6 add to 11

4(n-5)(n-6)

[tex]\bf \stackrel{\textit{perpendicular lines have \underline{negative reciprocal} slopes}} {\stackrel{slope}{-\cfrac{3}{2}}\qquad \qquad \qquad \stackrel{reciprocal}{-\cfrac{2}{3}}\qquad \stackrel{negative~reciprocal}{+\cfrac{2}{3}\implies \cfrac{2}{3}}}[/tex]

Since it’s a square all sides are even. Meaning you multiply 7/12 by 4. Giving you 7/3 or 2 ⅓. Hope this helps!

The perimeter of a square piece of cardboard with each side measuring 7/12 meter is found by using the formula P = 4a. After calculation, the perimeter is 2 1/3 meters.

The question asks us to calculate the perimeter of a square piece of cardboard with each side measuring 7/12 meter. To find the perimeter of a square, we use the formula P = 4a, where 'P' is the perimeter and 'a' is the length of one side. Since all sides of a square are equal, we simply multiply the length of one side by 4.

In this case, the length of one side (a) is 7/12 meter, so the perimeter (P) would be:

P = 4 × (7/12 meter)
P = (4 × 7/12) meter
P = 28/12 meter
P = 7/3 meter (after simplifying)
P = 2 1/3 meters (in mixed numbers)

Therefore, the perimeter of the square piece of cardboard is 2 1/3 meters.

Answer:

log3 81 = 4

Step-by-step explanation:

Convert the exponential equation to a logarithmic equation using the logarithm base (3)(3) of the right side (81)(81) equals the exponent (4)(4).

log3(81)=4

or

you can remember this

loga Y= X

so, a^x =y

The logarithmic form of the equation 81=3^4 is log3 81 = 4. It uses the base number 3 (which is being raised to a power), the result of the multiplication (81), and the number of times 3 is multiplied by itself (4).

The logarithmic form of the equation 81=3^4 can be found by applying the basic principles of logarithms. Remember, a logarithm is another way to express exponentiation, in a format that involves the base number, the exponent, and the result. Therefore, the logarithmic form of 81=3^4 is written as log3 81 = 4.

To understand this, consider the logarithmic expression log3 81 = 4. The base number (3 in this case) is the number being multiplied repeatedly (the number being raised to a power). The number 81 is the result of this multiplication, and 4 is the number of times base number, 3, is multiplied by itself to get 81. So, in this case, 3 to the power of 4 (3*3*3*3) equals 81.

So, in short, for the equation 81=3^4, the logarithmic form will be log3 81 = 4. This equation reads as "log base 3 of 81 equals 4".

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Answer:

504

Step-by-step explanation:

144X3.5=504

There are [tex]\( \boxed{504} \)[/tex] square inches in 3.5 square feet.

To convert square feet to square inches, we can use the given conversion factor that there are 144 square inches in 1 square foot. We need to determine how many square inches are in 3.5 square feet.

Here is the step-by-step calculation:

1. Start with the given conversion factor:

 [tex]\[ 1 \, \text{square foot} = 144 \, \text{square inches} \][/tex]

2. Multiply the number of square feet by the conversion factor to get the number of square inches:

 [tex]\[ 3.5 \, \text{square feet} \times 144 \, \text{square inches per square foot} \][/tex]

3. Perform the multiplication:

 [tex]\[ 3.5 \times 144 = 504 \][/tex]

I would say an equation would look roughly as such:

y = - | x - 800 | + 50

If you want me to explain how I got to this conclusion just comment on my answer, If you were only looking for the answer then we are good. Brainliest is encouraged but not required :)

The absolute value equation representing the word count for the scholarship essay is |w - 800| <= 50, ensuring that the essay will be between 750 and 850 words long.

To represent the word count requirements for the scholarship essay using an absolute value equation, you can consider the midpoint of the word limit, which is the average between the minimum and maximum word count. This midpoint is at 800 words since (750 + 850) / 2 equals 800. Now, you can state the absolute difference from this midpoint that is allowed on either side of 800, which is 50 words, since 850 - 800 equals 50 and 800 - 750 equals 50. Therefore, the absolute value equation that represents the number of words (w) the scholarship essay should be is |w - 800| <= 50. This equation tells us that the word count can be 50 words fewer or 50 words greater than 800, perfectly capturing the range of 750 to 850 words.

Answer: Multiplying and Dividing are inverse operations

Multiplying by a number is the same as dividing by its reciprocal

Step-by-step explanation:

Answer:

Multiply and divide are inverse operations.

Multiply by a number is the same as divide by its reciprocal.

Step-by-step explanation:

To divide by a fraction, you can multiply by its inverse.

If a number is defined as a/b, then the reciprocal of the number is b/a.

The given equation is

[tex]\frac{5}{8}\div \frac{2}{3}=\frac{5}{8}\times \frac{3}{2}[/tex]

Here, [tex]\frac{3}{2}[/tex] and [tex]\frac{2}{3}[/tex] are inverse of each other.

Reason 1:

Multiply and divide are inverse operations.

Reason 2:

Multiply by a number is the same as divide by its reciprocal.

Answer:

It only counts as a zero when the y-intercept is (0,0).

Step-by-step explanation:

The zeros of a quadratic function are always written as (x,0), while the y-intercept is always written as (0,y). Therefore, in order for a y-intercept to be a zero, it must be (0,0), because the y-coordinate in any zero is 0. At any other time, the y-intercept is not a zero.

Final answer:

The y-intercept represents the starting value of the relationship when x is zero, but it is not considered a zero itself.

Explanation:

The y-intercept, also represented as 'b' in the equation y = mx + b, is the point where the line intersects the y-axis. It indicates the starting value of the relationship when x is zero. However, the y-intercept does not count as a zero because it represents a specific value on the y-axis, rather than being a zero value on the x-axis. For example, if the y-intercept is 5, it means that the line starts at the point (0, 5) on the coordinate plane.

Answers:

1.) Each person gets half a bar. (1/2) (4 is half of 8. As such, breaking each bar in half and distributing it that way would make it so that everyone gets the same amount.)

Answer: 1/2

2.) Each person gets 2 packages.

Answer: 2/1 or 2

3.) Each rabbit gets 10/17 ths of a carrot.

10/17 cannot be simplified any further than it already is, as 17 is a prime number. This means that every rabbit simply gets 10/17ths of a carrot.

Answer:

2

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

Answer:

y=3.15

Step-by-step explanation:

I am assuming you meant 2.8y in your equation.

Plug in for x

6.4(3)+2.8y=44.4

6.4*3=19.2

So now 19.2 + 2.8y = 44.4

44.4-19.2=25.2

25.2/2.8=3.15

Meaning Y=3.15

Answer:

The monthly cost would be equivalent to [tex]=0.37x+5[/tex]

Answer:

25x^2-40x+16

Step-by-step explanation:

(5x-4)(5x-4)

= 25x^2-20x-20x+16

=25x^2-40x+16

Final answer:

None of the given points A (-1, -9), B (1, 9), and C (1/2, 3) lie on the graph of y=32x, as the calculated y values using the equation do not match the given y values of the points.

Explanation:

The question asks which of the following points does not lie on the graph of y=32x. To determine this, we need to substitute the x value of each point into the equation y=32x and see if the resulting y value matches the y value of the point.

For point A (-1, -9), substituting x = -1 gives y = 32(-1) = -32, which does not match the y value of point A, so A does not lie on the graph.

For point B (1, 9), substituting x = 1 gives y = 32(1) = 32, which does not match the y value of point B, so B also does not lie on the graph.

For point C (1/2, 3), substituting x = 1/2 gives y = 32(1/2) = 16, which does not match the y value of point C, so C also does not lie on the graph.

All given options A, B, and C do not lie on the graph of y=32x because the calculated y values do not match the provided y values of the points.

Answer: i think the answer is B for number 1

Step-by-step explanation:

Answer:

1.

The slope is : [tex]\frac{8.4-4.2}{2-1}[/tex] = 4.2

[tex]\frac{12.6-8.4}{3-2}[/tex] = 4.2

We can see that the distance is same each time.

Hence, the equation that represents the relationship between the distance traveled and the elapsed time is [tex]f=4.2p[/tex]

2.

Let the amount of money needed be = z

Total bags purchased = n

Cost of 1 bag = $1.58

So, the required equation is :

[tex]z=1.58n[/tex]

3.

When rainfall increases, the water level in the lake goes up. Rainfall is the independent variable in this situation. This is True.

Here the water level is dependent on the amount of rainfall so water level is dependent and rainfall is independent. Rainfall is not dependent on the water level in a lake.

4.

Let y represents the distance the plane has traveled.

Let z represents the time it has spent traveling.

distance = speed x time

So, [tex]y=600z[/tex]

5.

Diana can earn money for the tickets she sells. Here tickets are independent and money earned is dependent on the number of tickets sold. The more tickets sold, the more money Diana can earn.

So, the answer is : C: The number of tickets sold is the independent variable because it affects the amount of money earned.

Answer:

per 100 pencils he looses $75

Step-by-step explanation:

If he sells 100 pencils at $1.75 he will make $175 which is less than the $250 he spent for the 100 pencils. So per 100 pencils he looses $75

Answer:

4.1 =y

Step-by-step explanation:

This is a problem involving trig.

sin of a angle is equal to opposite side divided by hypotenuse

sin 36 = y / 7

Multiply each side by 7

7 sin 36 = y/7 * 7

7 sin 36 = y

4.1144 = y

To 1 decimal place

4.1 =y

When multiplying exponents, they actually get added.

You can see that the x^9 and the x^2 become x^11.

This means for y to end u p at y^20, with one of them y^10, the other one would also need to be y^10.

n = 10.

Answer:

The correct answer is 10.

Step-by-step explanation:

If you have a product of numbers with the same base, by definition you can add the exponents.

So you have:

yⁿ2x⁹yⁿ4x²y¹⁰=8x¹¹y²⁰

Using the rule of product for x you have:

8x¹¹yⁿy¹⁰=8x¹¹y²⁰

Simplifly 8x¹¹ in both sides of the equation.

yⁿy¹⁰=y²⁰

Using the rule of product for y you have:

yⁿ⁺¹⁰=y²⁰

Divide by y on both sides:

n+10=20

Subtract 10 on both sides:

n=10

Answer:

The mean will stay the same.

The standard deviation will decrease.

Step-by-step explanation:

For the 5 cards, she has received, the mean will be:

μ=(∑x)/n

=125/5

=25

The mean is 25 and the standard deviation is 10.  

σ=10

If a new card is received with $25, then the sum will be $150  

So the new mean will be:

μ'=(∑x)/n

=150/6

=25

And the new standard deviation will be:  

σ'= 9.12

We can clearly see that  

μ= μ'

and

σ> σ'

So the mean will remain the same and standard deviation will decrease. .

Answer:

0

Step-by-step explanation:

Look at x = -2 on the graph (on the x-axis).  Draw a vertical line through x = -2.  If this line passes through a dark dot (which indicates that a y-value is associated with that x-value), we have evaluated the function.  The dot in question is (-2, 0) (dark dot).  The same vertical line passes through (-2, -2), but this is not the correct y value for x = -2 (it's an open circle).

The value of [tex]f(-2)[/tex] is [tex]0[/tex].

Given:

The graph of the function [tex]f(x)[/tex].

To find:

The value of [tex]f(-2)[/tex].

Explanation:

In the given graph there is an open circle at [tex](-2,-2)[/tex] and a closed circle at [tex](-2,0)[/tex]. It means the point [tex](-2,0)[/tex] is included in the function but the points [tex](-2,-2)[/tex] does not included in the function.

[tex]f(-2)=0[/tex]

Therefore, the value of [tex]f(-2)[/tex] is [tex]0[/tex].

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Answer:

x = 7

Step-by-step explanation:

Subtract 7.2 from both sides of 11.3x + 7.2 = 86.3, obtaining:

11.3x = 79.1

Then x = 79.1 / 11.3 = 7

The answer is x = 7.

Please, when you list possible answers, separate them from one another using commas, semicolons or new entry lines.  Thank you.

Answer:

-5, -3, -2

Step-by-step explanation:

This is correct because you are adding each by -2. The inputs are -3, -2,-1, 0,-1

the outputs become -5,-4,-3,-2,-1

Hopefully I helped

For this case we must propose a function of the form[tex]y = f (x)[/tex]that complies with the given relation:

We have the values of "x", that is, the entry is given by:

-3, -2, -1,0,1

If we propose:

[tex]f (x) = x-2[/tex]

We have the values of "and", that is, the output will be given by:

[tex]f (-3) = - 3-2 = -5\\f (-2) = - 2-2 = -4\\f (-1) = - 1-2 = -3\\f (0) = 0-2 = -2\\f (1) = 1-2 = -1[/tex]

The relationship is fulfilled.

Then, the function is f (x) = x-2

Answer:

[tex]-5, -4, -3, -2, -1\\f (x) = x-2[/tex]

Answer:

I think A i think

Step-by-step explanation: