The table shows the height of a soccer ball that has been kicked from the ground over time. (For reference: h(t) = −16t2 + 40t) Time (seconds) Height (feet) 0 0 0.5 16 1 24 1.25 25 1.5 24 2 16 2.5 0 Which statement describes the rate of change of the height of the ball over time? The rate of change is not constant and decreases over the entire time. Between 0 and 0.5 second the ball rises 16 feet, but between 0.5 and 1 second it rises only 8 more feet. The rate of change is not constant and increases over the entire time. Between 1.5 and 2 seconds the ball falls 8 feet, but between 2 and 12.5 seconds it falls 16 more feet. The rate of change is not constant and decreases then increases over time. The ball rises by 16 in the first half second, but only 8 feet over the next one. After it reaches 25 feet in the air, the ball drops. The rate of change is not constant and increases then decreases over time. The height of the ball above ground gets larger until 1.25 seconds and then gets smaller after that time.

You haven't provided any value, but I can tell you the solution set for the inequality.

First of all, expand both sides:

[tex] -3x+12 > 6x-6 [/tex]

Add 3x to both sides:

[tex] 12 > 9x-6 [/tex]

Add 6 to both sides:

[tex] 18 > 9x [/tex]

Which is of course equivalent to

[tex] 9x < 18 [/tex]

Divide both sides by 9

[tex] x < 2 [/tex]

So, every number smaller than 2 is part of the solution of this inequality.

Answer: No.

Step-by-step explanation: No, as two of sides need to be equal.

Answer:

we cannot form a triangle using the given lengths.

Step-by-step explanation:

There are three conditions that must be satisfied in order to form a triangle.

Let's take a, b and c are the sides of a triangle.

Conditions are:

i) a + b > c

ii) b + c > a

iii) c + a > b

Here let's take a = 12.2, b = 6.0 and c = 4.2

Let's check the conditions

i) 12.2 + 6 > 4.2

18.2 > 4.2

Which is true.

ii) 6 + 4.2 > 12.2

10.2 > 12.2

Which is not true.

The condition fails.

Therefore, we cannot form a triangle using the given lengths.

Hope this will helpful.

Thank you.

You run 0.5 miles every 3 minutes => 1 mile every 6 minutes. Your friend runs 2 miles every 14 minutes => 1 mile every 7 minutes. You run a whole number of miles every number of minutes that is a multiple of 6. Your freind runs a whole number of miles every number of minutes that is a multiple of 7 Then the least possible number of miles that you both run to end at the same time is the least common factor of 7 and 6 minutes. This is 7 * 6 = 42 minutes. You will have run 42 min / (6 miles/min) = 7 miles, and your friend will have run 42 min / (7 miles/min) = 6 miles

The number of minutes would she take to run 9 miles will be 66 minutes.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

Speed is defined as the length traveled by a particle or entity in an hour. It is a scale parameter. It is the ratio of length to duration.

We know that the speed formula

Speed = Distance/Time

Rita runs 6 miles in 44 minutes. The speed is given as,

Speed = 6 / 44

Speed = 0.13636 miles per minute

The number of minutes would she take to run 9 miles will be given as,

0.13636 = 9 / T

T = 66 minutes

The number of minutes would she take to run 9 miles will be 66 minutes.

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Instead of y = g(x)^2, it should be y = g(x)+2

What this means that every point on g(x) will be shifted up 2 units. A point like (2,-1) which is the saddle point shown on the graph, will move up to (2,1) after you shift up 2 units. Every other point will follow the same path. Another example: The point (0,-5) -- which is the y intercept -- will move up to (0,-3).

Check out the attached image below for a visual of what's going on.

The graph of the translation to make it y = g(x) + 2 is added as an attachment

From the question, we have the following parameters that can be used in our computation:

The graph of y = g(x)

Translating the graph to make it y = g(x) + 2, we simply move the given up by 2 units

This means that the curves are moved up by 2 units

The graph to make it y = g(x) + 2 is added as an attachment

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We are given domain of the function: 1 ≤ x ≤ 5.

Range:  0 ≤ f(x) ≤ 15.

Also included order pairs  (1,4) and (5,15).

First order pair has domain 1, and second order pair has domain 5.

Both are included in domain of the given function.

Also, first order pair has range 4, and second order pair has range 15.

Both are included in range of the given function.

Option  C. (3,8)  has domain 3 and range 8 within the function.

But if we see option D. (5,10) also withing the function but we already given  (5,15), that is range for domain 5 is 15.

Answer:

D for plato users

Step-by-step explanation:

Answer:

125 minutes

Step-by-step explanation:

Answer:

The vertices of parallelogram ESTA  are E (10, 0), S (14, 3), T (6, 9), and A (2, 6).

As we know ,Area of parallelogram = Base × Height

As base can be determined by using distance formula because coordinates of the vertices are given.

Now to determine perpendicular, we will find the equation of line through E and perpendicular to ST.

Equation of line through S(14,3) and T(6,9) is

[tex]\frac{y-3}{x-14}=\frac{9-3}{6-14}\\\frac{y-3}{x-14} =\frac{6}{-8}[/tex]

[tex]\frac{y-3}{x-14}=\frac{-3}{4}\\4y -12=-3x+42[/tex]

⇒4y + 3x =12+42

⇒ 3 x + 4 y=54

Equation of line perpendicular to ST and passing through E(10,0) is

4 x-3 y + k=0

Put x=10, y=0 in above equation is

4×10 -3×0 +k=0

⇒ k= -40

The Equation of line through point E and perpendicular to ST is

4 x-3 y -40=0

move the decimal point 2 places to the right

note 1m = 100 cm

4450m = 4450 × 100 cm

multiplying by 100 is equivalent to moving the decimal point 2 places to the right

For a better understanding of the explanation given here please go through the two graphs provided in the two files attached.

In the first graph we have plotted all the given points from the question. The y-axis is the quantity and the x-axis is the price. As can be seen, as the price increases, the quantity decreases.

In the second graph, the line that connects all the given points is drawn. This line represents the "Demand" Line and is evaluated as follows:

We take any two points (in our case we took the first and the last points, that is, [tex](x_1,y_1)=(0,19)[/tex] and [tex](x_2,y_2)=(3,1)[/tex]) and we made use of the "point slope form" as:

[tex]\frac{y-y_1}{x-x_1}= \frac{y_2-y_1}{x_2-x_1}[/tex]

Thus, we got:

[tex]\frac{y-19}{x-0}= \frac{1-19}{3-0}= \frac{-18}{3}=-6[/tex]

[tex]y-19=-6x[/tex]

[tex]\therefore y=-6x+19[/tex]

Thus, the complete graph will be a straight line [tex]y=-6x+19[/tex] as shown in the second diagram.

If the orbital period of planet Y is twice the orbital period of Planet X, by then the factor is the mean distance increased by 4.

Given

The equation T^2 = A^3 shows the relationship between a planet’s orbital period, T, and the planet’s mean distance from the sun, A, in astronomical units, AU.

The mean is defined as the sum of all data set numbers and the total number in the data set.

If the orbital period of planet Y is twice the orbital period of Planet X,

Therefore,

If the orbital period of planet Y is twice the orbital period of Planet X, by then the factor is the mean distance increased is;

[tex]\rm Factor \of\ increase =\dfrac{2&^3}{2 }\\\\ Factor \of\ increase =4[/tex]

Hence, If the orbital period of planet Y is twice the orbital period of Planet X, by then the factor is the mean distance increased by 4.

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Answer:

D: 2^3/2

Step-by-step explanation:

Right on Edgenui test

Answer:

D: 2^3/2

Step-by-step explanation:

Right on Edgenui test

A(-3, -2) and B(3, -8)

slope m = (-2 + 8)/(-3 - 3) = 6/-6 = -1

b = y intercept = -5

Equation

y = -x - 5

Answer

y = -x - 5

The equation of the linear system will be y = - x - 5.

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

The graph is given below.

If the graph is decreasing, then the slope of the linear system will be negative.

And the y-intercept is negative 5.

Then the equation of the linear system will be y = - x - 5.

Thus, the correct option is D.

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The number of ways can a group of three students be chosen is 20 ways

The number of ways of selecting r objects from n unlike objects is given by combinations

ⁿCₓ = n! / ( ( n - x )! x! )

where

n = total number of objects

x = number of choosing objects from the set

Given data ,

Let the number of ways of selecting students be A

Now , the total number of students = 6

And , to choose 3 students out of 6 without regard to order. The formula for combinations is

n C r = n! / r!(n-r)!

where n is the total number of items, and r is the number of items to choose

6 C 3 = 6! / 3!(6-3)! = 20

Hence , there are 20 ways to choose a group of three students out of six

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The correct number of ways to choose a group of three students from six is [tex]\boxed{20}.[/tex]

To solve this problem, we can use the concept of combinations from combinatorics. A combination is a way of selecting items from a collection, such that the order of selection does not matter. In our case, we have six students and we want to choose three of them to participate in the spelling bee. The order in which we choose the students does not matter since all three will participate equally.

 The formula for calculating combinations is given by:

[tex]\[ C(n, k) = \frac{n!}{k!(n-k)!} \][/tex]

where n is the total number of items to choose from, k is the number of items to choose, and ! denotes factorial, which is the product of all positive integers up to that number.

 For our problem:

[tex]- $n = 6$[/tex] (total number of students)

[tex]- $k = 3$[/tex] (number of students to choose)

 Plugging these values into the formula, we get:

[tex]\[ C(6, 3) = \frac{6!}{3!(6-3)!} \][/tex]

 Calculating the factorials, we have:

[tex]\[ 6! = 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 720 \][/tex]

[tex]\[ 3! = 3 \times 2 \times 1 = 6 \][/tex]

[tex]\[ (6-3)! = 3! = 6 \][/tex]

 Now, we substitute these values into the combination formula:

[tex]\[ C(6, 3) = \frac{720}{6 \times 6} \][/tex]

[tex]\[ C(6, 3) = \frac{720}{36} \][/tex]

[tex]\[ C(6, 3) = 20 \][/tex]

 Therefore, there are 20 different ways to choose a group of three students from six for the spelling bee.

it is either 5 cm or its 4 cm

Answer:

The graph B.

Step-by-step explanation:

1. As you can see in the table shown in the picture attached, the correct graph must have the following points (x,y): (-1,8); (0,6), (1,4); (2,2) and (3,0).

2. To draw the graph, you must plot each point. For example, the third point is (1,4). Then, you can draw an imaginay line vertically from 1 (x axis) and an imaginary line horizontally from 4 (y axis). The intersection of this lines is the point (1,4).

Answer:

B is the right answer

Step-by-step explanation:

I just did it and it was right

Answer:

The fraction of the tank is filled with gasoline is [tex]\frac{3}{8}[/tex].

Step-by-step explanation:

Consider the provided information.

Jamal filled his gas tank and then use 7/16 of the tank for traveling to visit his grandfather.

After his first traveling the amount of gas left can be calculated as:

[tex]1-\frac{7}{16}[/tex]

[tex]\frac{16-7}{16}[/tex]

[tex]\frac{9}{16}[/tex]

He then used 1/3 of the remaining gas in the tank to run around town.

That means he left with 2/3 of gas.

[tex]\frac{9}{16}\times \frac{2}{3}[/tex]

[tex]\frac{3}{8}[/tex]

Hence, the fraction of the tank is filled with gasoline is [tex]\frac{3}{8}[/tex].

under a reflection in the x- axis

a point (x, y) → (x, - y)

P( - 1, 0 ) → P'( - 1, 0 )

R(3, 1) → R'( 3, - 1 )

D( 3, - 2 ) → D'( 3, 2 )

Q(0, - 5 ) → Q'( 0,  5 )

U (0,5) P (-1,0) R (3,-1) D (3,2)

[tex]\frac{90 + 87 + 72 + x}{4} = 88[/tex]

90 + 87 + 72 + x = 88(4)

             249 + x = 352

                        x = 103

Answer: 103

I hope the next exam has extra credit questions!

We know:

The sum of the measures of the angles of a triangle is equal 180°.

Therefore we have the equation:

[tex](3x-16)+x+(x+6)=180\\\\3x-16+x+x+6=180\\\\(3x+x+x)+(-16+6)=180\\\\4x-10=180\ \ \ \ |+10\\\\4x=190\ \ \ \ |:4\\\\x=47.5[/tex]

m∠M = (3x-16)°

Substitute:

[tex]m\angle M=(3\cdot47.5-16)^o=(142.5-16)^o=126.5^o[/tex]

Answer:

98

Step-by-step explanation:

I got it wrong when I typed in 126.5, its actually 98

Go forth and Conquer

Answer: $2.84 per pint

Step-by-step explanation:

[tex]\frac{5.68 (dollars)}{4 (cups)} *\frac{2(cups)}{1(pint)} = \frac{5.68(2)dollars}{4 pints} = \frac{2.84 dollars}{1 pint}[/tex] = $2.84 per pint

Final answer:

To find the price per pint of sour cream from a 4-cup carton costing $5.68, divide the total cost by the number of pints, resulting in $2.84 per pint.

Explanation:

The question asks to find the price per pint for a 4-cup carton of sour cream that costs $5.68. Since there are 2 cups in a pint, a 4-cup carton is equivalent to 2 pints. To find the price per pint, we simply divide the total cost by the number of pints.

Calculation:

Thus, the price per pint of sour cream is $2.84.

Easiest way for me is to convert those mixed fractions and then divide.

Sorry for some bad handwriting! Hope it helps

Answer:

Distance traveled 17.5 kilometers

Step-by-step explanation:

We can use the following equation to find the distance traveled,

Distance traveled = Speed * Time

First we need to find the total time he walked = 2.30 p.m. - 11.a.m.

                                                                             =[tex]3.5[/tex] hours

Now we can substitute the values to the equation,

Distance traveled = [tex]5[/tex] kilometers per hour * [tex]3.5[/tex] hours

                              = [tex]5*3.5[/tex] kilometers

                              = 17.5 kilometers

Answer:

y = -6x - 9

Step-by-step explanation:

Given 6x + y = 4, we borrow the form 6x + y = C to obtain a new line parallel to the given line.  Subst. -2 for x and 3 for y to find C:  6(-2) + 3 = C, or C = -9.

Thus, the desired equation is 6x + y = -9, or  y = -6x - 9.  

Check:  Does this line pass thru (-2,3)?  Is 3 = -6(-2) - 9 true?  Yes, it is.

okay the answers are

Question 1 A survey was sent to GCA students asking the question "Who is your favorite teacher?"  

What type of data was collected?

Answer) Qualitative

Question 2 ) A survey was sent to GCA students asking the question "On a scale of 1 to 5, with 1 being the lowest and 5 being the highest, how would you rate your AMDM teacher?"  

The data collected was

Answer) Quantitative

Question 3)  You decided to attend the GCA outing at Stone Mountain. Before you left for the park, you entered the park address into a GPS/Traffic app on your phone. The app told you that Stone Mountain was 47.6 miles from your house.

47.6 miles is an example of...

Answer) Quantitative, continuous data

Question 4 ) While you were at the Stone Mountain outing, you played a game of corn hole. You counted the number times you tossed the beanbag into the hole.

The number of times you were able to sink the beanbag is an example of....

Answer) Quantitative, discrete data

Question 5) You recorded the time you left Stone Mountain and the time you arrived home. You calculated time it took you get home was 57.28 minutes.

57.28 minutes is an example of....

Answer) Quantitative, continuous data

Here we are given the expression:

[tex]x^{2}+52[/tex]

Now let us equate it to zero to find x first,

[tex]x^{2}+52=0[/tex]

Now subtracting 52 from the other side,

[tex]x^{2}=-52[/tex]

taking square root on both sides,

So we will get two values of x as ,

[tex]x=+2\sqrt{-13}[/tex]

[tex]x=-2\sqrt{-13}[/tex]

Now we can write square root -1 as i,

So our factors become,

[tex]x=+2i\sqrt{13}[/tex]

[tex]x=-2i\sqrt{13}[/tex]

Answer:

The final factored form becomes,

[tex](x+2i\sqrt{13})(x-2i\sqrt{13})[/tex]

Solution

The general form of the equation is y = mx + b, where m is the slope and b is the y-intercept.

Given: m = 8/7 and b = -3

Plugin the given values into the formula.

y = 8/7x - 3

The answer is y = 8/7x - 3

Thank you :)

The correct equation representing the line with a slope of negative 8/7 and a y-intercept of negative 3 is y = -8/7x - 3. This was determined by substituting these values into the slope-intercept form of a line equation, y = mx + b.

The equation of a line in slope-intercept form is given as y = mx + b, where m is the slope of the line and b is the y-intercept. In this case, we're looking for an equation with a slope (m) of -8/7 and a y-intercept (b) of -3.

Substituting these values into the slope-intercept form, we get: y = -8/7x - 3.

So, the correct answer is y = -8/7x - 3.

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Correct answer is: A) [tex]\frac{-15F}{13hours}[/tex]

Solution:-

Given that temperature of town increased 16 Fahrenheit in 5 hours and decreases 31 Fahrenheit in the next 8 hours.

If we assume T as temperature, it became T+16 in 5 hours and (T+16-31) in next 8 hours.

That is change in temperature in (5+8) hours is 16-31 = -15 Fahrenheit.

Rate of total change in temperature = [tex]\frac{change in temperature}{time}[/tex]

                                                            = [tex]\frac{-15}{5+8}=\frac{-15}{13}[/tex]

Hence rate of total change in temperature is [tex]\frac{-15F}{13hours}[/tex]

The correct expression that shows the rate of the total change in temperature is -15 hours / 13 hours. The Option A.

The rate of change in temperature refers to the speed at which the temperature is increasing or decreasing over a given period of time.

Total change in temperature is:

= Temperature increase - Temperature decrease

= 16°F - 31°F

= -15°F

Total time for the change:

= Time for increase + Time for decrease

= 5 hours + 8 hours

= 13 hours

Rate of total change in temperature:

= Total change in temperature / Total time for the change

= -15°F / 13 hours.

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