9. The maximum horizontal range of a projectile is given by the formula R= u2/g where u is the initial velocity and g is the acceleration due to gravity. Find the velocity with which a ball can be thrown to have a maximum range of 20 meters when the acceleration due to gravity is equal to 9.8 m/s.
(SHOW WORK)

ANSWER

The correct answer is A

EXPLANATION

The parent function is

[tex]f(x) = {x}^{3} [/tex]

The function g(x) is obtained by shifting the graph of the parent function, 4 units left and 6 units up.

Therefore the transformation is of the form:

[tex]g(x) = f(x + 4) + 6[/tex]

Hence the transformed function has equation:

[tex]g(x) = {(x + 4)}^{3} + 6[/tex]

The correct answer is A

The resulting function g(x) after the translation will be g(x) = (x+4)³ + 6

Translation is a way of changing the position of an object on an xy plane. According to the graph shown, the parent function of the graph is f(x) = x^3.

The translates function shows an upward translation by 4 units and horizontal translation to the left by 6 units. The resulting function g(x) after the translation will be g(x) = (x+4)³ + 6

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Answer:

The correct answer is C

Step-by-step explanation:

If a straight line passes through [tex](x_1,y_1)[/tex] and has a slope of [tex]m[/tex] , its equation is;

[tex]y-y_1=m(x-x_1)[/tex]

In this case, we have [tex](x_1,y_1)=(5,1)[/tex] and [tex]m=\frac{1}{2}[/tex].

To find the required equation: you have to substitute [tex]x_1=5,y_1=1[/tex] and [tex]m=\frac{1}{2}[/tex] into the equation to obtain:

[tex]y-1=\frac{1}{2}(x-5)[/tex]

The correct answer is C

Answer: 0.35

Step-by-step explanation:

Answer: 11

Step-by-step explanation:

You can set up a ratio.

8/456 = x/627

Cross multiply and divide

8 • 627 = 5016

5016 / 456 = 11

Final answer:

It takes 11 hours to drive 627 miles when the rate is 57 miles per hour, which is derived from the given information that 456 miles are driven in 8 hours.

Explanation:

To determine the travel time for 627 miles when we know that 456 miles were driven in 8 hours, we can use the concept of direct variation. With direct variation, if two variables vary directly, as one increases, the other also increases by a constant multiplier known as the constant of variation (k). In this case, the distance traveled varies directly with the time spent driving.

First, we need to determine the rate of driving based on the information provided:

Now we can use the rate to calculate the time required to drive 627 miles:

It would take 11 hours to drive 627 miles at that rate.

Answer:

The correct answer option is B. [tex] 5 1 2 x ^ 6 [/tex].

Step-by-step explanation:

We are given the following expression and we are to choose its correct simplification from the given answer options:

[tex] ( 8 x ^ 2 ) ^ 3 [/tex]

Applying the power to the terms inside the bracket to get:

[tex]8^3 \times x^{2.3[/tex]

Solving it further by applying the power property of exponent to get:

[tex] 5 1 2 x ^ 6 [/tex]

The expression to represent the number of items this online company sold n hours after 6am is 120 + 30n. Since the company had already sold 120 items at 6am, and then sells an average of 30 items every hour, the overall quantity of items sold is expressed by this linear formula.

This is a problem related to linear functions, as the company's rate of sales is constant throughout the day. We are given the company sold 120 items at 6 am, which is our starting condition or 'y-intercept'. Then, we know the company sells an average of 30 items per hour, our rate or 'slope', for the rest of the day.

Therefore, the expression to represent the number of items sold n hours after 6 am is 120 + 30n. Here, 120 represents the number of items sold by 6 am, 30 is the average rate at which items are sold per hour, and n is the number of hours after 6 am.

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The expression to represent the total number of items sold n hours after 6 am is 120 + 30n, where 120 is the initial amount at 6 am, and 30n is the number of items sold per hour after 6 am.

The question involves a linear equation to find the number of items sold by a company n hours after 6 am. Given that the company has sold 120 items by 6 am, and that it sells an average of 30 items per hour for the rest of the day, we represent this scenario with an expression. This can be expressed as 120 + 30n, where n represents the number of hours passed after 6 am.

This equation is made up of two parts: 120 represents the initial number of items sold by the company by 6 am, and 30n represents the number of items the company sells per hour (30) multiplied by the number of hours passed after 6 am (n). Hence, the total number of items sold after n hours will be the sum of these two values.

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okay l gonna give you stright answer it B okay

Answer:

(2,0)

Step-by-step explanation:

For given line AB:

y-intercept = b = -2

slope = m = y₂-y₁/x₂-x₁

= -3/2-(-4) = -3/6 = -1/2

Equation of line AB:

y = (-1/2)x - 2

Finding equation of line that is parallel to line AB and passes through the point C(2,2):

Substituting the slope from line AB into the equation of the line

y = (-1/2)x + b.

Substituting the given point (-2,2) into the x and y values 2 = (-1/2)-2 + b.

Solving for b (the y-intercept) , we get b = 1

Substitute this value for 'b' in the slope intercept form equation y = (-1/2)x + 1.

For x-intercept of the line, we let y = 0

0 = (-1/2)x + 1

x = -1(-2/1)

x = +2

So, the point on the x-axis that lies on the line that passes

through point C and is parallel to line AB is (2,0).

A proper fraction must have a denominator that is greater then the numerator.

If the numerator is the same as the denominator is the same then it can be simplified to 1.

If the numerator is greater than the denominator then the fraction is improper.

This means that the answer must be D) 3/4

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

d

Step-by-step explanation:

A proper fraction is when the numerator is less than the denominator

example is 2/3, 100/200 etc.

The linear graph y = 2x + 3 represents the relationship between the data provided.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have input and output in the table:

From the points:

(3, 9) and (6, 15)

[tex]\rm \left(y-9\right)=\dfrac{\left(15-9\right)}{6-3}\left(x-3\right)[/tex]

(y - 9) = 2(x - 3)

y = 2x + 3

Thus, the linear graph y = 2x + 3 represents the relationship between the data provided.

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Answer:

[tex]\frac{5x-12}{x-1}[/tex]

Step-by-step explanation:

[tex]\frac{8x-5}{x-1}[/tex]-[tex]\frac{3x+7}{x-1}[/tex]

= [tex]\frac{8x-5-3x-7}{x-1}[/tex]

= [tex]\frac{5x-12}{x-1}[/tex]

The Fraction that is between 0 and 1/2 is 2/10

The fraction 1/2 can also be written as 5/10. If you were to make a number line, you would be able to see that 2/10 is between. Here, let me order them from least to greatest:

< - 0 - - 2/10- - - 1/2- - 7/10- 3/4 - 8/10 - >

As you can see, 2/10 is between 0 and 1/2 (5/10).

Answer:

answer is a

Step-by-step explanation:

Answer:

(0, 1)

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Given

y - 4x = 1 ( add 4x to both sides )

y = 4x + 1 ← in slope- intercept form

with y- intercept c = 1 ⇒ (0, 1) ← coordinates of y- intercept

The coordinates of the point where y-4x=1 crosses the y axis is (0, 1)

The following information should be considered:

Therefore we can conclude that The coordinates of the point where y-4x=1 crosses the y axis is (0, 1)

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Answer:

140

Step-by-step explanation:

if you are rounding you round if 5 or over go up and if 4 or lower go down

The area of the given parallelogram is 24 square units.

The area of a parallelogram is the product of the height and the base of the  parallelogram.

The height of the given parallelogram is

[tex]= (5-2)[/tex] units

[tex]= 3[/tex] units

The base of the given parallelogram is

[tex]= [7-(-1)][/tex] units

[tex]= 8[/tex] units

Therefore, the area of the given parallelogram is

[tex]= (8)(3)[/tex] square units

[tex]= 24[/tex] square units

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you have a 1/12.5 chance of getting a white egg. so the theoretical possibility of getting only two white eggs is 1/156.25. so it is very unlikely to get two white eggs

Answer:

0.029

Step-by-step explanation:

Last year, the porgs laid 30 dotted eggs, 40 grey eggs, and 15 white eggs.

Total eggs = 30+40+15 = 85 eggs

White eggs = 15

So, probability of getting 1 white egg = [tex]\frac{\text{No. of white eggs}}{\text{Total no. of eggs}}[/tex]

                                                              = [tex]\frac{15}{85}[/tex]

Remaining white eggs = 14

Total eggs remaining = 84

Probability of getting 1 white egg on second draw   = [tex]\frac{14}{84}[/tex]

So, the probability that you would only collect 2 white eggs =[tex]\frac{15}{85} \times \frac{14}{84}[/tex]

                                                                                                   =0.029

Hence the probability that you would only collect 2 white eggs is 0.029.

Answer:

3^x-8=8 then x=log_3(16)

3^(x-8)=8 then log_3(8)+8

Step-by-step explanation:

So if it is 3^x-8=8

then 3^x=16

and then convert to logarithmic form you write it as log_3(16)=x

_3 means the subscript (the base) is 3

So if it is 3^(x-8)=8

then the log form is log_3(8)=x-8

add 8 on both sides log_3(8)+8=x

The value of x that satisfies the given equation is 9.8929

From the question, we are to solve [tex]3^{x-8} =8[/tex] for x, using the change of base formula [tex]\log _{b} y = \frac{log _{} y}{log _{} b}[/tex]

From the given equation,

[tex]3^{x-8} =8[/tex]

Take [tex]log_3[/tex] of both sides,

That is,

[tex]\log _{3} 3^{x-8} = \log _{3} 8[/tex]

This becomes,

[tex](x-8)\log _{3} 3= \log _{3} 8[/tex]

Since [tex]\log _{x} x =1[/tex],

∴ [tex]\log _{3} 3 =1[/tex]

[tex](x-8)(1)= \log _{3} 8[/tex]

[tex]x-8= \log _{3} 8[/tex]

Using the change of base formula [tex]\log _{b} y = \frac{log _{} y}{log _{} b}[/tex]

[tex]\log _{3} 8=\frac{\log 8}{\log 3}[/tex]

Then,

[tex]x-8=\frac{\log 8}{\log 3}[/tex]

[tex]x-8=\frac{0.9031}{0.4771}[/tex]

x - 8 = 1.8929

x = 8 + 1.8929

x = 9.8929

Hence, the value of x that satisfies the given equation is 9.8929

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Answer:

True

Step-by-step explanation:

Every rectangle is a parallelogram.

Answer:  Graph (-4, -2) and (-2, 1)

Step-by-step explanation:

[tex]\text{The given equation is: }y+2=\dfrac{3}{2}(x+4)\\\\\text{which is of the form: }y-y_1=m(x-x_1)\\\implies(x_1, y_1)=(-4, -2)\quad and \quad m=\dfrac{3}{2}\implies (x+2, y+3)\\\\.\qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad (-4+2, -2+3)=(-2, 1)[/tex]

So, two possible points are (-4, -2) and (-2, 1).

Plot those two coordinates and draw a line through them.

Answer:

Got it right on the test, here is the answer.

Step-by-step explanation:

Answer:

The slope - intercept equation for this line is y = 17x - 55

Step-by-step explanation:

The general form of the slope-intercept form is

y = mx +b

where m is the slope and b is the y-intercept.

We are given slope m = 17

we need to find b the y-intercept.

To find y-intercept we would use point(3,-4) and formula

y = -4

x = 3

m = 17

b=?

y = mx + b

-4 = (17)(3) + b

-4 = 51 + b

b = -4 -51

b = -55

So, y-intercept is -55

The slope - intercept equation for this line is y = 17x - 55

Answer:

5

Step-by-step explanation:

First we need to find the slope

m = (y2-y1)/ (x2-x1)

   = (-3-3)/(4-1)

  =-6/3

  = -2

Then we can use point slope form to make the equation

y-y1 = m(x-x1)

y-3 = -2(x-1)

Distribute

y-3 = -2x+2

Add 3 to each side

y-3+3 = -2x+2+3

y = -2x+5

Since this is in slope intercept form, y = mx +b, the y intercept is 5

Answer: D. 5

Step-by-step explanation: First we need to find the slope

m = (y2-y1)/ (x2-x1)

  = (-3-3)/(4-1)

 =-6/3

 = -2

Then we can use point slope form to make the equation

y-y1 = m(x-x1)

y-3 = -2(x-1)

Distribute

y-3 = -2x+2

Add 3 to each side

y-3+3 = -2x+2+3

y = -2x+5

Since this is in slope intercept form, y = mx +b, the y intercept is 5

9514 1404 393

Answer:

  $5611

Step-by-step explanation:

We can't make use of your calculator, but we know the formula.

__

The future value of the investment is ...

  FV = P(1 +r)^t

  FV = $4300(1.03^9) ≈ $5611

The investment will be worth about $5611 after 9 years.

Answer:

Step-by-step explanation:

If the solution of the system of equations is {(x, y): x - y = 4} - infinitely many solutions, then this system is consistent and dependent.

x - 3y = 4            multiply both sides by 2

2x - 6y = 8

Therefore Q = -6

Answer:

Say that the price at the whole for a bottle is some x

We know that the Snack Bar sold them at 33% profit which is in dollars $0.28

i.e 33% x=0.28

so now its a matter of finding what x is 

writing this in algebraic form

0.33x=0.28

divide both sides of the equation by 0.33

0.33x/0.33=0.28/0.33

Therefore x=0.85 roughly

so the price per bottle at the whole sell is 85 cent

the snack bar is selling it for 1.13 dollars

assuming no tax applied 

Step-by-step explanation:

Answer:

0.84 (B)

Step-by-step explanation:

Answer:

X= All real Numbers

Step-by-step explanation:

Answer:

All real numbers

Step-by-step explanation:

The domain is the set of x values that we can plug into the function and it will have a y value.

The domain is the "allowed" x values of a function.

Exponential functions of the form  [tex]y=a^x[/tex], where a is a constant have domain of "all real numbers".

The function in this problem is of this form with a "-5" at the end, which shifts the function vertically 5 units down. This doesn't affect x values (or domain)

Hence, the domain is the set of all real numbers.

Answer:

-9

Step-by-step explanation:

Answer:

slope = - 9

Step-by-step explanation:

Calculate the slope m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (5, - 6) and (x₂, y₂ ) = (4, 3)

m = [tex]\frac{3+6}{4-5}[/tex] = [tex]\frac{9}{-1}[/tex] = - 9

Answer:

Ashrita

Step-by-step explanation:

The mean of any set of data is found by finding the summation of all the values in the set of data then dividing it by the number of entries in the data.

Mean=Σfx/Σf

Σf=26+31+39+30+16+16+18+38= 214

Σf= 8= the number of entries.

Mean=214/8=26.75

Ashrita's work was correct.

Answer:

Ashrita

Step-by-step explanation:

When you are finding the mean of some numbers you are meant to add all the numbers then divide by the amount of numbers

Answer:

doubles every 10 years

20 years, so it has doubled 2 times

1700 times 4=6800

it is worth $6800