(05.01 MC)

Which statement best describes the area of Triangle ABC shown below?

A triangle ABC is shown on a grid. The vertex A is on ordered pair 4 and 5, vertex B is on ordered pair 5 and 2, and the vertex C is on ordered pair 3 and 2.

It is one-half the area of a rectangle with sides 2 units × 3 units.
It is twice the area of a rectangle with sides 2 units × 3 units.
It is one-half the area of a square of side length 3 units.
It is twice the area of a square of side length 3 units.

Answer:

The length of rectangle is 14.25 inches and the width of rectangle is 8.25 inches

Step-by-step explanation:

we know that

The perimeter of rectangle is equal to

[tex]P=2(L+W)[/tex]

[tex]P=45\ in[/tex]

so

[tex]45=2(L+W)[/tex]

simplify

[tex]22.5=L+W[/tex] -----> equation A

The length of a rectangle is 6 inches more than its width

so

[tex]L=W+6[/tex] ----> equation B

Solve the system by substitution

substitute equation B in equation a

[tex]22.5=(W+6)+W[/tex]

solve for W

[tex]22.5=2W+6\\2W=22.5-6\\2W=16.5\\W=8.25\ in[/tex]

Find the value of L

[tex]L=W+6[/tex]

substitute the value of W

[tex]L=8.25+6=14.25\ in[/tex]

therefore

The length of rectangle is 14.25 inches and the width of rectangle is 8.25 inches

Answer:

5

Step-by-step explanation:

2(x+3)=4(x-1)

2x+6=4x-4

6=4x-2x-4

6=2x-4

2x=6+4

2x=10

x=10/2

x=5

Answer:

(3, 0) and (5, 0)

Step-by-step explanation:

we have

[tex]y=x^{2}-8x+15[/tex]

we know that

The x-intercepts are the values of x when the value of y is equal to zero

so

For y=0

[tex]x^{2}-8x+15=0[/tex]

The formula to solve a quadratic equation of the form

[tex]ax^{2} +bx+c=0[/tex]

is equal to

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

in this problem we have

[tex]x^{2}-8x+15=0[/tex]  

so

[tex]a=1\\b=-8\\c=15[/tex]

substitute in the formula

[tex]x=\frac{-(-8)\pm\sqrt{-8^{2}-4(1)(15)}} {2(1)}[/tex]

[tex]x=\frac{8\pm\sqrt{4}} {2}[/tex]

[tex]x=\frac{8\pm2} {2}[/tex]

[tex]x=\frac{8+2} {2}=5[/tex]

[tex]x=\frac{8-2} {2}=3[/tex]

so

x=3, x=5

therefore

The x-intercepts are (3,0) and (5,0)

Final answer:

To determine which apartment Mrs. Cooper should choose, first list all available apartments with two bedrooms and a parking space. Next, compare the monthly rents to her income, aiming to spend no more than 30% on rent, and then consider other monthly expenses before making a final decision.

Explanation:

The student's question relates to determining which apartment Mrs. Cooper should choose based on her monthly income and her specific requirements of having a two-bedroom apartment and a parking space. Unfortunately, the question does not provide a list of available apartments with their respective rents, so I can't provide a specific recommendation. However, I can guide the student on how to make the decision.

First, Mrs. Cooper should list each available apartment that meets her criteria of having two bedrooms and a parking space. Next, she should determine the monthly rent for each of these apartments. Having this, she should compare the rent prices against her monthly income of $2,960 keeping in mind that a general rule of thumb is not to spend more than 30% of one's income on rent, which in her case would be $888 per month.

It is also important for Mrs. Cooper to account for additional monthly expenses (like utilities, groceries, and any other recurring payments) when determining affordability. If there are any apartments that fit these financial parameters, Mrs. Cooper can then choose the one that best fits her other personal preferences or needs.

Answer:

3

Step-by-step explanation:

5x-2y=3  when: y=2x

1. Plug in the y-value (y=2x) into the equation (5x-2y=3). The equation should then look like 5x-2(2x)=3

2. Simplify:

5x-2(2x)=3

5x-4x=3

1x=3

x=3

Check:

5x-2(2x)=3 (plug in the x-value you solved for: 3)

5(3)-2×2(3)=3

15-2×6=3

15-12=3

3=3

Hope this helped !

Cheers, Z

Answer:

2 grams

Step-by-step explanation:

multiply by 1000

Answer:

-7

12

10.54

-8

Step-by-step explanation:

Answer:

Therefore [tex]x =\frac{1}{3}[/tex]

Step-by-step explanation:

[tex]\frac{7}{8} x+\frac{3}{4} x+\frac{7}{16} x-\frac{1}{16} =\frac{5}{8}[/tex]

[tex]\Leftrightarrow \frac{7}{8} x+\frac{3}{4} x+\frac{7}{16} x =\frac{5}{8}+\frac{1}{16}[/tex]

[tex]\Leftrightarrow \frac{14x+12x+7x}{16} =\frac{10+1}{16}[/tex]         [ L.C.M of 8,4,16 =16 and  L.C.M of 8,16 =16]

[tex]\Leftrightarrow \frac{33x}{16} =\frac{11}{16}[/tex]

[tex]\Leftrightarrow x =\frac{11\times 16}{16\times 33}[/tex]

[tex]\Leftrightarrow x =\frac{1}{3}[/tex]

Therefore [tex]x =\frac{1}{3}[/tex]

The maximum amount that can be financed is $156,250.

Minimum down payment required by the lender = 16% of the value of home

Available cash in hand = $25,000

Now,

the  maximum amount of down payment that can be paid = $25,000

let the maximum amount that can be financed is 'x'

also,

16% of x = $25,000

or

0.16 × x = $25,000

or

x = [tex]\frac{\$ 25,000}{0.16}[/tex]

or

x = $156,250.

Hence, the maximum amount that can be financed is $156,250.

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The range is the value of y in the graph so the range of the function graphed below is -∞ < y ≤ 2.

We have,

The range of a function on a graph is the y-values the graph touches.

Now,

From the graph,

There are two parts the graph touches the y-values.

- From -∞ to 0

- From 0 to 2

This can be written in an interval as:

(-∞, 2]

Thus,

The range of the function is (-∞, 2].

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Answer:

Echo can plant a maximum of 8 shrubs.

The total cost for Echo's shrubs is  = 8 [tex]\times[/tex] $15.32 = $122.56

Step-by-step explanation:

i) Garden is 36 feet wide

ii) Each shrub is 4.5 feet wide.

iii) therefore the maximum number of shrubs that can be planted are

[tex]= \frac{36}{4.5} = 8[/tex]

 Therefore Echo can plant a maximum of 8 shrubs.

Therefore the total cost for Echo's shrubs is  = 8 [tex]\times[/tex] $15.32 = $122.56

Answer:

it is C

Step-by-step explanation:

40% of 20 is 8

so 15% of 20 is 3

Answer:

18, 21

Step-by-step explanation:

There is a difference of 3 between any two consecutive term ( succeeding - preceding)

Hence 15 + 3 = 18

& 18 + 3 = 21 are the required terms.

Answer: C.) 18, 21

Step-by-step explanation:

Answer:

52 sides

Step-by-step explanation:

The only way I know how to do this is to create one fraction which is a combination of 2 steps used when 1 of the interior angles is known.

Formula

360/(180 - 9000/s ) = s

Multiply denominator and numerator on the left by s.

360 * s

=======                  = s        

s* (180 - 9000/s)

Remove the brackets on the denominator

360s

================    =s

180s - 9000

Cancel the numerators s's.

360 / (180s - 9000) = 1

Multiply both sides by 180s - 9000

360 =180s - 9000

Add 9000 to both sides

360 + 9000 = 180s

9360 = 180s

Divide by 180

9360/180 = 180/180 s

s = 52

Both the friends stayed for 2 hours. Each one paid $12.

Step-by-step explanation:

Given,

Amount paid by Ronald = $12

Amount paid by Tyler upfront = $4

Amount per hour = $4

Let,

x be the number of hours.

R(x) = 12

T(x) = 4x+4

As both the friends paid same;

T(x) = R(x)

[tex]4x+4=12\\4x=12-4\\4x=8[/tex]

Dividing both sides by 4

[tex]\frac{4x}{4}=\frac{8}{4}\\x=2[/tex]

Putting x=2 in T(x)

T(2) = 4(2) + 4 = 8+4 = 12

Both the friends stayed for 2 hours. Each one paid $12.

Keywords: function, division

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Answer:

The numbers are 6 and 9

Step-by-step explanation:

Let the two numbers be x and y.

Given :

The sum of two numbers [tex]x+y=15[/tex]  equation:1

Also the difference of x and y  [tex]x-y= -3[/tex] equation:2

On solving equation:2  

                                      [tex]x=y-3[/tex]    equation:3

Putting this value of x in equation 1.

                      [tex]x+y=15\\\\(y-3)+y=15\\2y-3=15\\2y=15+3\\2y=18\\y=18/2\\y=9[/tex]

     Putting value of y in equation:3 to find x

                     [tex]x=y-3\\x=9-3\\x=6[/tex]

Paul bought  23 / 15 pounds of bananas.

Calculate the answer using a math operator is referred to as a mathematical operation.

Basic mathematical operations are addition, multiplication, subtraction and division.

Given that,

The total quantity of bananas and apples bought by Paul = 3 ¹/₃

Also, Paul bought 1 ⁴/₅ pounds of apples.

To find the quantity of bananas that Paul bought.

Use subtraction property,

Quantity of bananas = total quantity - quantity of apples

=  3 ¹/₃ -  1 ⁴/₅

= 10 / 3 - 9 / 5

= 50 - 27 / 15

= 23 / 15

The required quantity of bananas is 23 / 15.

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The area of the figure PQRS can be found by applying the rule of areas in proportional shapes. The area of PQRS equals 32 square centimeters after rounding the calculated value.

The given problem involves the calculation of area and the application of ratios. It mentions two figures, ABCD and PQRS, along with certain dimensions and the area of the first figure. To find the area of the figure PQRS, we apply a rule of ratios used in geometry that states the areas of two similar figures is equal to the square of the ratio of their corresponding sides.

The corresponding sides here are DC and SR. So the ratio of their areas would be (DC/SR)². Plugging in the values we get = (10 centimeters/15 centimeters)² which simplifies to 0.444 (after rounding).

Then, to find the area of PQRS, we multiply the area of ABCD (which is 72 square centimeters) with the calculated square of the ratio. Therefore, the area of figure PQRS is 72 * 0.444 which equals 31.968 square centimeters (rounded to 32 square centimeters).

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Answer:

30 years old.

Step-by-step explanation:

Here's what we know.

B=5J

M+2=8J+16

M=3B

So now let's solve using substitution.

M+2=8J+16

M=8J+14

But we know that M=3B

3B=8J+14

And we know B=5J

3*5J=8J+14

15J=8J+14

7J=14

J=2

Now, we can plug it into the M+2=8J+16

M+2=2*8 +16

M+2=16+16

M+2=32

M=30

Hope you enjoyed.

Answer:

30 years old

Step-by-step explanation:

look at the person above me he is right

Answer:

9+10-1+4+1

25

Step-by-step explanation:

The second robot working alone would spend 7.5 minutes to do the task.

Equation is used to show the relationship between two or more numbers and variables.

Let y represent the rate at which the first robot work and x represent the rate that the second robot work.

Two robots can do a task in 5 min, working together. Hence:

The first robot, working alone, can for the task in 15 min. hence y = 15 min.

(1/x + 1/15)5 = 1

5/x + 1/3 = 1

x = 7.5 minutes

The second robot working alone would spend 7.5 minutes to do the task.

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The second robot working alone would spend 7.5 minutes to do the task.

To find the time it takes for the second robot to complete the task alone, we can utilize the concept of rate. Here's how:

Define rates:

Let R be the combined rate of both robots working together. We know they can complete the task in 5 minutes, so their combined rate is R = 1/5 tasks per minute (since rate = work done / time taken).

Let R1 be the rate of the first robot working alone. We know it takes him 15 minutes to complete the task, so R1 = 1/15 tasks per minute.

Relate rates:

The second robot's rate (R2) can be found by subtracting the first robot's rate from the combined rate: R2 = R - R1.

Calculate R2:

Substituting the known values: R2 = (1/5) - (1/15) = 2/15 tasks per minute.

Find time taken by second robot:

To find the time (T2) it takes for the second robot to complete the task alone, we can use the formula: T2 = 1 / R2.

Substituting the calculated rate: T2 = 1 / (2/15) = 15/2 = 7.5 minutes.

Therefore, the second robot will take 7.5 minutes to do the task alone.

Answer:

[tex]A=64.95\ in^2[/tex]

Step-by-step explanation:

we know that

A regular hexagon can be divided into six equilateral triangles

so

The area of a regular hexagon is the same that the area of six congruent equilateral triangles

The area of one equilateral triangle in the regular hexagon is equal to

[tex]A=\frac{1}{2}(b)(h)[/tex]

where

b is the base of triangle (the length of the regular hexagon)

h is the height of triangle (the apothem of the regular hexagon)

so

[tex]b=5\ in\\h=4.33\ in[/tex]

substitute

[tex]A=\frac{1}{2}(5)(4.33)=10.825\ in^2[/tex]

Multiply the area of one triangle by 6 to obtain the area of the regular hexagon

[tex]A=10.825(6)=64.95\ in^2[/tex]

Answer:49

Step-by-step explanation:

294/6

=49

Answer:

See Explanation Below

Step-by-step explanation:

Question is incomplete.

(The height of the prism is missing and no attachment is provide)

However, I'll solve on a general rule.

Given

Volume of prism, V = 294in³

The volume of a prism is calculated multiplying the base area by the height of the prism.

Let's represent the base area by B and the height by H.

Mathematically,

V = B * H.

Make B the subject of formula

B = V/H

Substitute 294 for V.

The expression becomes

B = 294/H

Now, let's assume the height is 6 inches.

The expression for base area becomes

B = 294/6

B = 49 in²

Answer:

1759

Step-by-step explanation:

multiply, then add

Answer:

1759

Step-by-step explanation:

5*354=1725

1725+34=1759

To make an educated decision between the two job offers, you need to consider factors such as the number of hours worked, additional benefits, potential for overtime, job satisfaction, career growth opportunities, and work-life balance.

To make an educated decision, there are a few factors to consider when comparing these two job offers. First, you need to know the number of hours you will be working in a year for both jobs. Second, you need to know if there are any additional benefits, such as health insurance or retirement plans, offered with each job. Third, you need to consider the potential for overtime hours and how often you would work them.

Let's assume that the first job pays $45,000 for working 40 hours a week, 52 weeks a year, with no overtime. The second job pays $15 per hour for 40 hours a week, 52 weeks a year, and you can potentially earn time and a half for any hours worked beyond the 40 hours.

If the second job offers consistent overtime hours, then it could potentially provide a higher income compared to the first job. However, if the overtime hours are not guaranteed or if you prefer the stability of a fixed salary, then the first job with a salary of $45,000 would be a better option. Other factors to consider when finding work include job satisfaction, career growth opportunities, and work-life balance.

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Answer:

the second one

Step-by-step explanation:

The system of equations is solved by setting the two equations equal to each other and solving for x followed by solving for y using the obtained x value. The solution is x = -15.6 and y = 0.2.

The student is asking to solve a system of two linear equations:

To find the solution, we need to set the two equations equal to each other since they both equal y:

47 + 3x = 8 + 0.5x

Now, let's solve for x:

Now that we have x, we can solve for y using either of the original equations:

y = 8 + 0.5(-15.6)

Calculate y:

y = 8 - 7.8

y = 0.2

Therefore, the solution to the system of equations is x = -15.6 and y = 0.2.

Answer:

n = 24 - 8.

Step-by-step explanation:

n + 8 = 24

Subtract 8 from each side:

n + 8 - 8 = 24 - 8

n = 24 - 8.