Consider these scenarios. 1. A piano weighs 5.5 × 102 units.   2. A grain of salt weighs 1.02 × 10-3 units.   3. A tractor trailer weighs 8.8 × 101 units. Determine the unit of measurement that best represents each scenario. 1.   2.   3.

Step-by-step explanation:

2) Slope can be written as rise over run:

[tex]a) Slope=-1\ over\ 1\quad \rightarrow \quad (11 + 1, -8 - 1)\implies (12, -9)\\b) Slope=7\ over\ 2\quad \rightarrow \quad (2+2,2+7)\implies (4, 9)\\c) Slope=9\ over\ 4\quad \rightarrow \quad (-5+4,-2+9)\implies (-1, 7)[/tex]

3) Slope formula is: [tex]\dfrac{y_2-y_1}{x_2-x_1}[/tex]

[tex]slope=\dfrac{15-3}{5-1}=\dfrac{12}{4}=\boxed{3}[/tex]

4) Average rate of change is the slope of the given interval:

a) when x = 0, y = 0 and when x = 1, y = -3

   [tex]Slope=\dfrac{-3-0}{1-0}=\dfrac{-3}{1}=-3[/tex]

b) when x = -2, y = 0 and when x = -1, y = 3

   [tex]Slope=\dfrac{3-0}{-1+2}=\dfrac{3}{1}=3[/tex]

c) when x = 0, y = 0 and when x = 2, y = 0

   [tex]Slope=\dfrac{0-0}{2-0}=\dfrac{0}{2}=0[/tex]

Answer:

This is an independent event, as the marble is put back into the bag. If it were removed completely, it would be dependent.

Answer:

The right answer is dependent events

Step-by-step explanation:

Answer: The answer is D

Step-by-step explanation:

Each point on the house was divided by 2.

Answer:

D: (x,y) -> (2x, 2y)

Step-by-step explanation:

Take a look at the top of the roof, in the small house it is at (6,4) and in the big house it is at (12, 8).

To get from (6,4) to (12,8) you have to multiply x and y by 2.

You can test this with multiple points. Only the  (x,y) -> (2x, 2y) mapping works for all of them.

Answer:

$1,953

Step-by-step explanation:

So, we need to figure out how many times the big warehouse is actually bigger than the small one, in order to calculate the air conditioner cost for the large warehouse.

Let's say x represents the dimensions of the small warehouse, and y represents the dimensions of the large warehouse.

We have y = 2.5x, for every dimension (length, width, height)

The formula to calculate the volume of a cubic space is the following:

volume = length * width * height

Now, we don't know the exact measurements involved, but we know the large warehouse is 2.5 times bigger in every dimension, so...

volume = 2.5x * 2.5x * 2.5x = 2.5³x³ = 15.625 x³

So, the larger warehouse is 15.625 times larger than the small one.  We then multiply that by the cost of cooling down the small warehouse:

cost for large warehouse = 15.625 * $125/month = $1,953.25

Rounded to the nearest dollar: $1,953

Answer:

y = -3,-4

Step-by-step explanation:

Factor the equation, which gives you (y+3)(y+4)=0

Then, all you do is find the values that give the equation an answer of 0.

Since anything times 0 is 0, all you have to do is make one of the (y+x) values equal 0.

Since -3 and -4 added to 3 and 4 make 0 the answers are -3 and -4.

You can check by plugging it back into the equation or graphing it.

Answer:

7/8 or 0.875 units^3

Step-by-step explanation:

The volume for a rectangular prism is l*w*h. What you must remember is that l*w can be rewritten as the base of the prism. Thusly, the volume formula can be reduced to B*h, where B is the area of the base. You are given the area of the base as 1/2, so just multiply 1/2 by 1&3/4 (I rewrote it as 7/4) to get 7/8.

Answer:

The answer is the second option.

B.

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

Answer:

V = \pi r^2h

When the radius is doubled, then

V=\pi (2r)^2h=4\pi r^2h

Therefore, when the radius is doubled, it volume will be four times as much.

Step-by-step explanation:

Answer: four times as much

Step-by-step explanation:

The volume of a cylinder is given by :-

[tex]V=\pi r^2h[/tex], where r is the radius and h is the height of the cylinder.

If the radius of this cylinder is doubled, then the radius of the new cylinedr will be:

R=2r

Now, the volume of the new cylinder is given by :-

[tex]V_1=\pi (2r)^2h\\\\\Rightarrow\ V_1=\pi(4r^2)h\\\\\Rightarrow\ V_1=4\pi r^2h\\\\\Rightarrow\ V_1=4(\pi r^h)\\\\\Rightarrow\ V_1=4(V)[/tex]

Hence, If the radius of cylinder is doubled, its volume will be four times as much.

The answer is 192 square inches.

Answer:

192 square inches.

Step-by-step explanation:

Answer:

The answer is 30.044 Hope this Helps!

Step-by-step explanation:

You have to line up the decimal points when adding decimals.

Answer:

The answer is 30.044.

Step-by-step explanation:

When ever adding decimals you always have to line them up.  

 24.566

+   5.478  This is how it's written.

Hope this helps.

Answer:

A: y = 4x + 7

Step-by-step explanation:

Step 1:  Our line is parallel to this line, so it has the same slope, but a different  y-intercept, so set up the equation...

  y = 4x + b      

We are given a  point (x, y) of (2, 15), so plug that in and solve for b.  

 15 = 4(2) + b

    15 = 8 + b      (simplify)

        7 = b      (subtract 8 from both sides to isolate b)

So the equation of our line is  y = 4x + 7

Step-by-step explanation:

the answers is A. y=4x+7

Answer:

School A gave 12 correct and 12 incorrect answers. School B gave 12 correct answers and the competition was tied.

Step-by-step explanation:

We are given the following information:

School A points = 174

School B points = 102

Every correct answer is awarded 10 points and every incorrect answer reduces 6 points.

Let x be the number of correct answer given by school A and thus x is the number of  incorrect answer given by school A. The, school B also gives x number of correct answer.

Thus, the scored can be modeled with the following equations:

School A: [tex]174 + 10x - 6x = 174 + 4x[/tex]

School  B: [tex]102 + 10x[/tex]

Since, both the schools tied, equating both the equations:

[tex]174 + 4x = 102 + 10x\\\Rightarrow 10x - 4x = 174 -102\\\Rightarrow 6x = 72\\\Rightarrow x= 12[/tex]

Thus, school A gave 12 correct and 12 incorrect answers. School B gave 12 correct answers and the competition was tied.

Answer:

x < 5

Step-by-step explanation:

Solve the inequality by using the distributive property and inverse operations.

4(x + 5) > 10(x - 1)

4x + 20 > 10x - 10

20 > 10x - 4x - 10

20 > 6x - 10

20 + 10 > 6x

30 > 6x

5 > x

Step-by-step explanation:

if you put in the numbers twice ill just ignore that.

If 149 is 35less than the original cost, add 35 for the original cost

The original cost was 184 dollars

Answer:

184

Step-by-step explanation:

Answer:

The length of its diagonal is [tex]27.01\ m[/tex]

Step-by-step explanation:

Let

b------> the length side of the square

d-----> the diagonal of the square

we know that

The perimeter of the square is

[tex]P=4b[/tex]

[tex]P=76.4\ m[/tex]

Find the value of b

[tex]4b=76.4[/tex]

[tex]b=76.4/4=19.1\ m[/tex]

Applying the Pythagoras theorem find the length of the diagonal

[tex]d^{2}=19.1^{2}+19.1^{2}\\ \\d^{2}=729.62\\ \\ d=27.01\ m[/tex]

The length of the diagonal of a square is approximately 27.02m.

The perimeter of a square is the total length of all four sides of the square. Since we know that the perimeter is 76.4 meters, we can calculate the length of one side by dividing the perimeter by 4.

Length of one side = Perimeter ÷ 4 = 76.4m ÷ 4 = 19.1m.

To find the length of the diagonal, we can use the Pythagorean theorem for a square, which is a² + a² = diagonal². Here, a is the length of one side of the square. Thus, diagonal² = 2 × (19.1m)².

Diagonal = √(2 × (19.1m)²) = √(2 × 364.81m²) = √729.62m² = 27.02m (rounded to two decimal places).

Therefore, the length of the diagonal of the square is approximately 27.02 meters.

The scale factor of two means you need to multiply the original length by 2:

9 x 2 = 18

The new length would be 18 cm.

Answer:

2000+600+9+.75 maybe?

Step-by-step explanation:

✧･ﾟ: *✧･ﾟ:*    *:･ﾟ✧*:･ﾟ✧

                  Hello!

✧･ﾟ: *✧･ﾟ:*    *:･ﾟ✧*:･ﾟ✧

❖ The ratios in SIMPLEST FORM are:

1:3

3:55

55:1

~ ʜᴏᴘᴇ ᴛʜɪꜱ ʜᴇʟᴘꜱ! :) ♡

~ ᴄʟᴏᴜᴛᴀɴꜱᴡᴇʀꜱ

To write the ratios in simplest form, find the greatest common divisor (GCD) of the two numbers in each ratio and divide both numbers by the GCD.

The ratios we need to write in simplest form are:

1. Students to teachers = 550:30

2. Students to aids = 550:10

To write these ratios in simplest form, we need to find the greatest common divisor (GCD) of the two numbers in each ratio and divide both numbers by the GCD.

1. Students to teachers = 55:3

2. Students to aids = 55:1

Final answer:

The input value for an output of -4 for the function g(x) = 28/x - 7 is x = 28/3.

Explanation:

To find the input value for a given output value of a function, we need to set the function equal to the output value and solve for the variable. The student is asking for the input value that results in an output of -4 for the function g(x) = 28/x - 7. To solve for x, we follow these steps:

Set the function g(x) equal to -4: g(x) = -4.

Substitute g(x) with the function definition: -4 = 28/x - 7.

Isolate the term with x by adding 7 to both sides: -4 + 7 = 28/x.

Simplify the left side of the equation: 3 = 28/x.

To find x, multiply both sides by x and then divide by 3: x = 28/3.

Therefore, the input value for an output value of -4 for the function g(x) = 28/x - 7 is x = 28/3.

Answer:

The solution in point form is (9,7) and the equation would be x+9, y=7

Step-by-step explanation:

By using moving the -4y to the right side and by flipping the signs you can turn the equation -x-4y=-37 into x=37-4y.

With this new equation you can use the substitution method and replace the x in -2x-5y=-53 with 37-4y, making it look like this: -2(37-4y)-5y=-53.

Then you solve for y getting y=7.

With the value of y, you can plug that into the equation x=37-4y so it will look like x=37-4(7)

Then you solve for x getting x=9

And with that you get the point (9,7)

Answer:

B

Step-by-step explanation:

Answer:

One

Step-by-step explanation:

The graphs of these two equations intersect at one point.  This means there will only be one solution to the system.

The count of point of intersection of a graphed system of equation is the number of its solution.

The number of solution is (b) one

From the attached graph, we observe that:

The system equations on the graph have just one point of intersection.

This means that the number of solution of the system of equations is one.

Hence, the correct option is (b) one.

Read more about system of equations at:

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Answer:

D (3,1)

Step-by-step explanation:

solving simultaneous equations

Arrange equations

2x+y=7

3x-4y=5

make y side cancell by addition by multiplying by 4 and 1 as shown

4{2x+y=7}

1{3x-4y=5}

8x+4y=28

3x-4y=5

11x=33

x=33/11=3

substitute for x=3 in 3x-4y=5

9-4y=5

4=4y

y=1

Answer:

D(3,1)

Step-by-step explanation:

The given equations are:

[tex]2x+y=7...(1)[/tex]

and

[tex]3x-4y=5...(2)[/tex]

Multiply equation (1) by 4.

[tex]\Rightarrow 8x+4y=28...(3)[/tex]

Add equation (2) and (3)

[tex]\Rightarrow 11x=33[/tex]

Divide through by 11.

[tex]\Rightarrow x=3[/tex]

Put x=3 into equation (1)

[tex]2(3)+y=7[/tex]

[tex]6+y=7[/tex]

[tex]y=7-6[/tex]

[tex]y=1[/tex]

The solution is (3,1)

The correct choice is D

Answer:

There are 6 possible combinations

Step-by-step explanation:

the number of numbers (3)  times the other numbers (2)

The surface area of a rectangular prism can be found using the formula A = Ph + 2B. This utilizes the perimeter, P, and area, B, of the base, as well as the height, h, of the prism.

The surface area (A) of a rectangular prism can be given as: A = Ph + 2B, where P is the perimeter of the base, h is the height of the prism, and B is the area of the base. This formula is derived by adding the areas of all six sides of the prism, two of which have area B and the other four having an area of Ph/2. Therefore, to calculate the surface area, simply substitute the known values for P, h, and B into the formula and perform the arithmetic operation.

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The formula for the surface area of a rectangular prism using the height, perimeter of the base, and area of the base is 2B + Ph.

The formula for the surface area of a rectangular prism can be expressed using the given variables:

Surface Area = 2B + Ph

Where:

For example, if the area of the base is 10 square units, the perimeter of the base is 20 units, and the height of the prism is 5 units, the surface area would be:

Surface Area = 2(10) + (20)(5) = 20 + 100

= 120 square units

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Answer:

75 minutes

Step-by-step explanation:

The number of minutes for Mia to finish her homework is A = 30 minutes

The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.

The proportional equation is given as y ∝ x

And , y = kx where k is the proportionality constant

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Given data ,

Let the proportion be represented as A

Now , the value of A is

If Mia finished 60% of her homework in 45 minutes, that means she has 40% of her homework left to complete.

Let x be the number of minutes it takes Mia to complete all of her homework:

So , the proportion is

60% completed / 45 minutes = 40% left / A minutes

To solve for A , we can cross-multiply:

60% completed x A minutes = 45 minutes x 40% left

0.6A = 18

Dividing both sides by 0.6 , we get

A = 30

Hence , it will take Mia 30 minutes to complete all of her homework

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Answer:

Step-by-step explanation:

1. 6(7) +5

= 6x7 + 5

=  47

2. A =1/2 bh

= 1/2 x 18 x 6

= 54 squared inches

3. V = l x w x h

= 6 x 3 x 4

72 cubic inches

4. C

The solution is done on your page

Answer:

D

Step-by-step explanation:

1. When a number is divisible by 2 it must end with even digit 0, 2, 4, 6 or 8.

So the number 24,515 is not divisible by 2.

2. When a number is divisible by 5 it must end with  digit 0,  or 5.

The number 24,515 ends with 5 so it is divisible by 5.

3. When a number is divisible by 3, the sum of all digits must be divisible by 3.

The sum of all digits of the number 24,515 is 2+4+5+1+5=17. 17 is not divisible by 3, so the number 24,515 is not divisible by 3.

4. When a number is divisible by 9, the sum of all digits must be divisible by 9.

The sum of all digits of the number 24,515 is 2+4+5+1+5=17. 17 is not divisible by 9, so the number 24,515 is not divisible by 9.

5. When a number is divisible by 10 it must end with  digit 0.

The number 24,515 ends with 5 so it is not divisible by 10.

Answer:84 degrees

Step-by-step explanation:

so if a triangle is 180 degrees in total you need to find how much you need to equal that so you add 59+37=96 degrees so then you will subtract 180-96=84 degrees

Your welcome!

Answer:

C

Step-by-step explanation:

Let's break down the definitions.

Supplementary = degrees add up to 180

Vertical = share a common vertex

Complementary = degrees add up to 90

Adjacent = share a common side and vertex

Since the degrees add up to 90 and don't share a common side/vertex, the angles are complementary.