5. What is the range of the graph?8all real numbers{y 1-1 sys1)(XI-15x51){x | xs-1 or x 21)

EXPLANATION

Using a composite figure to approximate the area of the figure will give us the needed surface,

The area of the composite is approximately the area of the squares:

Area of square:

A= base * height = 1.0*1.0 = 1 cm^2

Since we have approximately 22 squares inside the figure, the approximate area will be as follows:

Therefore, the solution is approximately 22 square units.

$ 142.5

Explanation

to solve this we can use the formula:

where i is the interest, P is the principal, r is the rate ( in decimals) and t is the time

then

Step 1

Let

replace in the formula

hence, the answer is

$ 142.5

I hope this helps you

Given:

After coming from school to home,

He played video games for 45 minutes.

Then he took 30 minutes to finish his homework.

When John finished his homework, it was 4:25 PM.

To find:

The time at which John got home from school

Explanation:

According to the problem,

Total time to play video games and do homework is,

So, the time he got home from school will be,

Final answer:

The time he got home from school is 3:10 P.M.

f(x) = 37x + 20

Answer:

Option D, $20 is the membership beause it is a fixed cost, it does not depend on the amount of months

The trail map having a trail length of 7 1/2 in has an actual distance of 3 miles

The amount Kepler paid for the tool not including tax is $120

34% of 850 is 289

Given that

5 in ⇒ 2 miles

7 1/2 in ⇒ ?

The question is about scaling a map, the scale is 2miles is represented by 5 inches. This information is used to calculate the actual length when a measure of 7 1/2 inch is taken from the drawing

5 * ? = 7 1/2 * 2

? = 7 1/2 * 2 / 5

? = 3 miles

Hence 7 1/2 inch in the drawing represent an actual distance of 3 miles

Given that:

with a discount of 40% off the regular price

The regular price was $200

A discount of 40% is given to Mr Kepler. Discount represents amount less the total amount. At a 40% discount Mr Kepler paid 60%  

40% = 0.4

40% discount = 1 - 0.4 = 0.6 (equivalent to 60%)

The amount Kepler paid

= 0.6 * 200

= $120

Knowledge of percentage is used here and the amount Mr Kepler paid is $120 not including tax

34% of 850

The statement 34% of 850 means 34 divided by 100 multiplied by 850. The division by hundred takes care of the percent, then "of" means multiplication

34% = 0.34

0.34 * 850 = 289

Hence, we conclude that the concept of percentage and division is used to solve 34% of 850 to get 289

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The number of brownies left in the refrigerator is 4.

It's important to note that 1 dozen = 12

In this case, Abby baked 2-dozen brownies, she took 1 dozen to her scout meeting and her family ate 8, and she put the rest in a container in the refrigerator.

Therefore, the remaining amount will be:

= 2 dozens - 1. dozen - 8

= (2 × 12) - 12 - 8

= 24 - 12 - 8

= 4

There'll be 4 left. This illustrates the concept of subtraction.

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To be able to determine the distance that the skier travels, let's first determine its constant rate (speed).

A skier travels for 4 seconds and covers 72 meters.

Constant Rate (Speed):

Determining the distance covered in 2 minutes:

Step 1: Convert the time in minutes into seconds.

Step 2: Multiply the time by the constant rate (speed) of the skier.

Therefore, in 2 minutes, the skier travels 2,160 meters.

She will make 16 boxes.

To answer this question we simply have to divide the number of cookies (132) by the number of cookies that each box can contain.

Mathematically speaking:

Since we can´t have half boxes, we have to round the number to 16.

16 boxes.

In order to find possible dimensions for the scaled rectangle, the proportion between the dimensions of the rectangles must be the same.

So first let's find this proportion for rectangle R:

Now, let's find the proportion of the possible options of rectangle S:

So the correct options are the first, second and fourth options.

We want to find the percentage of students that scored between 70-90 points on the examn. Also, we know that there are a total of 71 students, so we have to count the number of students who got between 70-90 points.

We see them represented on the histogram as the two largest bars, and we obtain:

So, the total of students that scored between 70-90 points is 21+22=43.

For finding the percentage, we make the quotient between the number of students with a score of 70-90 and the total of the students in the class.

This means that approximately a 60.6% of the class students scored between 70 and 90 points.

Let p be the number of balloons required to make one balloon poodle and g the number of balloons required to make one balloon giraffe.

Then we have:

I) 5p + g = 15

II) p + g = 7

Subtracting equation II from equation I, we have:

5p - p + g - g = 15 - 7

4p = 8

p = 8/4

p = 2

Replacing p with 2 in equation II we have:

2 + g = 7

g = 7 - 2

g = 5

Answer: Each poodle requires 2 balloons and each giraffe requires 5 balloons.

The equation of the line that is perpendicular with y = 4 · x - 3 and passes through the point (- 12, 7) is y = - (1 / 4) · x + 4.

In this problem we find the case of a line that is perpendicular to another line and that passes through a given point. The equation of the line in slope-intercept form is described below:

y = m · x + b

Where:

In accordance with analytical geometry, the relationship between the two slopes of the lines are:

m · m' = - 1

Where:

If we know that m = 4 and (x, y) = (- 12, 7), then the equation of the perpendicular line is:

m' = - 1 / 4

b = 7 - (- 1 / 4) · (- 12)

b = 7 + (1 / 4) · (- 12)

b = 7 - 3

b = 4

And the equation of the line is y = - (1 / 4) · x + 4.

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The average rate of change of the function from t=1 to t=2.5 is given by:

It is given that:

Substitute the values to get:

Hence the rate of change is -22.6667.

The midpoint between two points can be found by averaging their coordinates. This is done below:

Using the above expressions we can apply the coordinates of the points we want to find, A(2,13) and O(-4,3).

The coordinates of the midpoint are (-1,8).

Given:

There are two equation given in the question.

Required:

We have to find the lowest common denominator of both equation.

Explanation:

are given equations

first of all we need to factorization both denominator

so here (p+2) is common in both so take (p+2) for one time only

so now the lowest common denominator is

Final answer:

The lowest common denominator for given two equations is

we know that

the formula to calculate teh slope between two points is equal to

where

(x1,y1) is one point

and

(x2,y2) is the other point

substitute the values in the formula and solve for m

Example

you have the points

(1,4) and (3,2)

so

(x1,y1)=(1,4)

(x2,y2)=(3,2)

substitute in te formula

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

m=-2/2

m=-1

the slope is -1

The discounted price of the computer was $486.50.

An electronic store discounted a tablet computer by 30%.

So, the original price was

So, the original price of the tablet computer was $632.45.

Answer:

(8.5, - 2 )

Step-by-step explanation:

given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is

( [tex]\frac{x_{1}+x_{2} }{2}[/tex] , [tex]\frac{y_{1}+y_{2} }{2}[/tex] )

here (x₁, y₁ ) = (- 6, - 10 ) and (x₂, y₂ ) = (23, 6 ) , then

midpoint = ( [tex]\frac{-6+23}{2}[/tex] , [tex]\frac{-10+6}{2}[/tex] ) = ( [tex]\frac{17}{2}[/tex] , [tex]\frac{-4}{2}[/tex] ) = (8.5, - 2 )

The Solution.

By formula, the volume of the planet (sphere) is given as below:

In this case,

Substitting these given values into the formula above, we can solve for r, the radius of the planet.

Dividing both sides by

We get

Taking the cube root of both sides, we have

Thus, the correct answer is 1060784.418km.

The Solution:

Given the numbers below:

12, 18 and 36.

We are asked to find the greatest common factor of the above numbers.

Note:

Greatest Common Factor means Highest Common Factor (HCF).

Recall:

The Greatest common factor of 12, 18 and 36 is the highest number that can divide 12, 18 and 36 without any remainder.

Thus, the correct answer is 6.

After solving the system of equations we get the values as:

Given the equations are as follows, we need to solve them using multiplication method:

take c+3t=7

rearrange the terms.

c = 7-3t

substitute c value in other equation.

3(7-3t)-2t=-12

21-9t-2t=-12

21-11t=-12

-11t = -12-21

-11t=-33

t=33/11

t=3

now substitute t value in c = 7-3t

c = 7-3(3)

c=7-9

c=-2

hence t and c values are 3 and -2.

take 5x – 4z = 15

5x = 15+4z

x=15+4z/5

substitute x value in other equation.

-3(15+4z/5)+2z=21

-45-12z+10z=105

-45-2z=105

-2z=105+45

z=-75

substitute z value in x=15+4z/5

x=15+4(-75)/5

x=-57

hence x and z values are -57 and -75.

consider, -4m+3n=50

3n = 50+4m

n=50+4m/3

substitute n value in other equation.

2m+n=10

2m+50+4m/3 = 10

6m+50+4m=30

10m=30-50

10m=-20

m=-2

substitute m value in n=50+4m/3

n = 50+4(-2)/3

n = 50-8/3

n = 42/3

n = 14

hence m and n values are -2 and 14.

consider 2p - 4q = 18

2p = 18+4q

p = 9+2q

substitute p value in other equation.

-3p+5q=22

-3(9+2q)+5q=22

-27-6q+5q=22

-27-q=22

-q = 22+27

q = -49

now p = 9+2q

p = 9+2(-49)

p = 9-98

p=-89

hence p and q values are -89 and -49.

consider 3a + 4b = 51

3a = 51-4b

a=51-4b/3

substitute a value in other equation.

2(51-4b/3)+3b=37

102-8b+9b=111

102+b=111

b=111-102

b=9

now, a=51-4(9)/3

a = 51-36/3

a = 15/3

a = 5

hence a and b value are 5 and 9.

Therefore, we solved the required system of equations.

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Let x = value of the bond when Tyler’s mom purchased it.

After one year, this value increased by 4%. This new value is calculated as follows:

The new value is $156.00, then

The value of the bond was $150.00 when Tyler’s mom purchased

Answer:

4 3/4

Step-by-step explanation:

The problem is;

-2(x-1) - 2 > 8 - 5x +4+ x

open the parenthesis

-2x + 2 -2 > 8- 5x + 4+ x

collect the like-term

-2x+5x-x > 8+4

2x > 12

divide both-side of the inequality by 2

x>6

The first mistake that was made is adding of the x-variables

It is 2x and not -6x

Given:

To prepare a pancake that serves 4 people, we need 6 eggs and 2 bananas.

Required:

The number of eggs and bananas that serves 6 people

By comparison,

If we need 6 eggs to prepare a pancake that serves 4 people, the number of people that 1 egg would serve is:

Similarly, If we need 2 bananas to prepare a pancake that serves 4 people, the number of people that 1 banana would serve is:

The number of eggs that serves 6 people:

The number of bananas that serves 6 people:

Answer:

9 eggs are needed

3 bananas are needed

Ok, we are going to use the midpoint formula

M = ( (x1 + x2) / 2 , (y1 + y2) / 2 )

(-7,-21)=((x1-13)/2 , (y1-15)/2 )

Break up this formula into two equations.

(x1-13)/2=-7 and (y1-15)/2=-21

Solve for x1 and y1 from the equations. So:

x1=(-7*2)+13

x1=(-14)+13=-1

y1=(-21*2)+15=(-42)+15=-27

So the other endpoint is (-1, -27).

Answer:

That is true but still remember that playing the knight at the start can be very useful.

Answer:

Step-by-Step explanation:

We are given the following equation: