Which expression uses the greatest common factor and the distributive property to rewrite the sum 60 + 24?

6(10+4) ​

10(6+4) ​

6(10+24)

12(5+2) ​

Answer:

Sphere Volume = (4/3) * PI * radius^3

Sphere Volume = (4/3) * PI * radius^3

11,488 = ((4/3) * 3.14) * radius^3

radius^3 = 11,488 / 4.1866666667

radius^3 = 2,743.9490445641

radius = 14 cm

diameter = 28 cm

Step-by-step explanation:

Answer:

∠DOF = 49°

Step-by-step explanation:

note that ∠DOF = ∠DOE + ∠EOF = 27° + 22° = 49°

The formula for the side length of 3 inches is P = 5s; 15 inches. So option (a) is correct.

To find the perimeter of a regular pentagon, we can use the formula:  P = 5s , where  P  is the perimeter and  s  is the length of a side.

Let's evaluate this formula for a side length of 3 inches:

P = 5s

P = 5 x 3

P = 15

So, the perimeter of the pentagon with a side length of 3 inches is 15 inches.

The correct option is (a) ( P = 5s; 15)  inches.

To find the perimeter of a regular pentagon, multiply the number of sides (5) by the length of one side.

To find the formula for the perimeter of a regular pentagon in terms of the length of a side, let's first understand the properties of a regular pentagon. A regular pentagon is a polygon with five equal sides and five equal angles.

The perimeter of any polygon is the sum of the lengths of all its sides. Since a regular pentagon has five equal sides, we can express its perimeter as the product of the number of sides (5) and the length of one side (s). Therefore, the formula for the perimeter [tex](\( P \)) of a regular pentagon in terms of the length of a side (\( s \)) is \( P = 5s \).[/tex]

Now, to evaluate the formula for a side length of 3 inches, we substitute  [tex]\( s = 3 \) into the formula:[/tex]

[tex]\[ P = 5 \times 3 = 15 \text{ inches} \][/tex]

This means that the perimeter of the regular pentagon with a side length of 3 inches is 15 inches.

Therefore, the correct answer is option a: [tex]\( P = 5s; 15 \text{ inches} \).[/tex]

This solution provides a clear explanation of how to derive the formula for the perimeter of a regular pentagon and how to evaluate it for a specific side length.

Answer:

For minimum cost  the number of speedboats produced would be 4,000.

Step-by-step explanation:

That would be the value of x which minimises the cost C(x).

You can find this by converting the function to vertex form.

C(x) = 3x^2 - 24x + 144

= 3(x^2 - 8x) + 144

= 3[ (x - 4)^2 - 16] + 144

= 3(x - 4)^2 -48 + 144

= 3(x - 4)^2 + 96

For this to be a minimum x must be = 4.

That is 4,000 speedboats.

The actual minimum cost of producing theses is  is  96 million dollars.

Answer:

4 thousand speedboats

Step-by-step explanation:

The minimum/maximum point on a parabola is just another name for that parabola's vertex. A parabola can be defined in a few different ways, but one is as the curve described by a quadratic function, a function of the form [tex]y=ax^2+bx+c[/tex] where a, b, and c ≠ 0. To see how we can get a vertex out of this, we can start with the simpler function [tex]y=ax^2[/tex]. Here, the vertex is simply the origin, (0, 0). If we shift the graph horizontally by h units, replacing x with (x - h), we get the function [tex]y = a(x-h)^2[/tex] and the vertex (h, 0), and if we shift it vertically by k units, we get the equation [tex]y-k=a(x-h)^2[/tex] and the vertex (h, k). We can, of course, add k to either side to obtain the function [tex]y=a(x-h)^2+k[/tex], also known as the general vertex form of a quadratic function.

This problem asks us to find a value for x which would minimize the C(x) in the function [tex]C(x)=3x^2-24x+144[/tex]. This essentially boils down to getting C(x) in vertex form and finding the x coordinate of the vertex from there. To do this, we can utilize an algebraic technique called completing the square to transform the expression on the right side into the form we want. Our task then is to somehow manipulate [tex]3x^2-24x+144[/tex] so that it resembles the form [tex]a(x-h)^2+k[/tex], where a, h, and k are constants, and (h, k) is the vertex of the parabola.

The first thing we can do with our expression is pull out a 3 from all three terms:

[tex]3x^2-24x+144\rightarrow3(x^2-8x+48)[/tex]

What we'd like now is to somehow turn that expression in the parentheses into something resembling [tex](x-h)^2[/tex]. To do this, we can recall that

[tex](x-y)^2=x^2-2xy+y^2[/tex].

If we rewrite [tex](x^2-8x+48)[/tex] as [tex](x^2-2\cdot4\cdot x+48)[/tex], we can see that this almost resembles [tex](x-4)^2=x^2-2\cdot4\cdot x+4^2=x^2-8x+16[/tex]. The only difference is between the 48 and the 16. To fix this, we can subtract 32 from the 48:

[tex]3(x^2-8x+48-32)[/tex]

However, to balance this subtraction out, we'll need to add 96 (which is 32 × 3) on to the end:

[tex]3(x^2-8x+16)+96[/tex]

Finally, we can rewrite our function C(x) as

[tex]C(x)=3(x-4)^2+96[/tex]

This gives us a vertex/minimum point of (4, 96), which means we need to produce 4 thousand speedboats to minimize its costs.

Answer:

4500

Step-by-step explanation:

you just need to see where the line stops at the price and drag your finger across to see how many people :}

Answer:

$4500

Step-by-step explanation:

Bellas line is the purple colored line.  She wants a banquet for 150 people.  That is along the x axis or across the bottom.  Go up from 150 until you hit the purple line and then go left until you hit the y axis.  That is the cost of a banquet for 150 people for Bella

Answer:

>

Step-by-step explanation:

7 x 60 = 420

So...

420 > 400

(420 is greater than 400)

Answer:

420>400

Step-by-step explanation:

7×60 is it <,> or = 400

First we multiply the left side

7*6 = 42  so

7*60 = 420

420>400

Answer:

5m-50

Step-by-step explanation:

Let Diego current age be x,

Given that Diego’s current age is five times Martina’s age ten years ago

Martina current age = m years

10 years ago Martina's age = m-10

Hence we have

x = 5(m-10) = 5m-50

So we find that Diego's current age can be expressed in terms of m as

Deigo's current age= 5m-50

Verify:

Deigo current age = 5m-50

Hence Martina age 10 years ago = 5m-50 divided by 5 = m-10

Martina current age = m-10+10 = m

Verified.

The current age of Diego in terms of m is expressed as:  [tex]5m - 50[/tex]

You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically. For example if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4. If something is for example, doubled, then you can multiply that thing by 2 and so on methods can be used to convert description to mathematical expressions.

For the given condition, we can take Diego's current age represented by a symbol.

Then, converting the statement "Diego’s current age is five times Martina’s age ten years ago." in mathematical terms,

Diego's current age = 5 times (Martina's age 10 years ago)

[tex]D = 5 \times (m - 10)\\\\or\\\\D = 5m - 50[/tex]

( sign of multiplication is often hidden if there are non numeric symbols and numbers being multiplied are written together)

Therefore, The current age of Diego in terms of m is expressed as:  [tex]5m - 50[/tex]

Learn more about forming equations here:

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Answer:

50

Step-by-step explanation:

12*5=60---------------1 hour

5*2=10

10*5=50

In 2 hours 50 City blocks will be covered.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

Five city blocks covered = 12 minutes

So, in one minutes the blocks covered = 5/12

Then, to walk 2 hours the number of block covered

= 120 x 5 /12

= 5 x  10

= 50 blocks

Learn more about Unitary Method here:

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For a $100 purchase, 10% off plus $8 off results in a final price of $82, which is better than 15% off resulting in a final price of $85.

1. 15% off on a $100 purchase:

- Discount amount =  0.15 × 100 = 15

- Final price =  100 - 15 = 85

2. 10% off plus $8 off on a $100 purchase:

- 10% off discount amount =  0.10 × 100 = 10

- Price after 10% discount =  100 - 10 = 90

- Then apply $8 off:  90 - 8 = 82

So, for a $100 purchase:

- The final price with 15% off is $85.

- The final price with 10% off plus $8 off is $82.

Answer:

The required inequality is [tex](x-82)\geq 420[/tex].

Step-by-step explanation:

Let the total number of points scored = x

It is given that the team has already scored 82 points.

So, the points left to score are (x-82).

As, the team needs to score at least 420 points.

The inequality representing the situation is given by,

Points to score ≥ 420

i.e. [tex](x-82)\geq 420[/tex].

Hence, the required inequality is [tex](x-82)\geq 420[/tex].

Answer:

420≤x -82

Step-by-step explanation:

We need to score at least 420 points.

420≤  x

where x is the score we need to set the record

We have 82 points so far

420≤x -82

We still need to score x-82 points this season

Answer:

Option A is correct.

An inequality:  [tex]7+5>6+2[/tex]

Step-by-step explanation:

Given the sentence: Seven plus five is greater than six plus two.

"Seven" means 7

"Plus" means +

"Five" means 5

"Greater than" means >

"six" means 6

"two" means 2

Then, the inequality for the given sentences is;  

[tex]7+5>6+2[/tex]

Answer:

Band A:  

Linear equation: y = 600  

Band B:  

Linear equation: y = 1.25x + 350  

The cost will be equal at 200 tickets.  

The cost when they are equal is $600.

use desmos copy and paste the graph

It's an isosceles triangle 45° - 45° - 90°, therefore y = 5.

In that triangle, sides are in proportion 1 : 1 : √2.

Therefore we have x = 5√2.

Other method.

You can use the Pythagorean theorem:

x² = 5² + 5²

x² = 25 + 25

x² = 2 · 25

x = √(25 · 2)

x = √25 · √2

x = 5√2

Answer: Hello there!

You can see that this is a triangle rectangle, where one of the catheti is equal to 5, and we know all the angles (you can see that both lower angles are equal to 45°, then is safe to assume that both catheti are equal in length, but let's do the math):

we need to find the length of the other cathetus and the length of the hypotenuse.

A very useful thing to remember when you are working with a triangle rectangle is:

So-Ca -Toa

this means:

sin(a) = (opposite cathetus)/(hipotenuse)

cos(a) = (adjacent cathetus)/(hipotenuse)

tan(a) = (opposite cathetus)/(adjacent cathetus)

now, we can find y using the third relation:

tan(45°) = 5/x

y= 5/tan(45°) = 5

because tan(45°) = 1

and this has a lot of sence, because you can see that both cathetus are symetric.

Now we can find the value of x with the next Pythagorean theorem:

the square hypotenuse is equal to the sum of the squares of the cathetus:

x^2 = 5^2 + 5^2 = 2*(5^2)

x= (√2)*5

then the right answer is option B:

x =  (√2)*5 and y = 5

Answer:

9

Step-by-step explanation:

average = [tex]\frac{sum of patients}{number of assistants}[/tex]

             =  [tex]\frac{7+8+5+9+10+10+14}{7}[/tex] = [tex]\frac{63}{7}[/tex] = 9

To get this answer you need to find the average. To find the average, you need to add the number of patients for each assistant together.

7 + 8 + 5 + 9 + 10 + 10 + 14 = 63

Then divide the answer by the number of assistants.

63 / 7 = 9

So, the answer is 9. There are an average of 9 patients per nurse.

Answer:

  exponential growth

Step-by-step explanation:

The function type is identified by where the variables are, and what their exponents are.

When the variable is in the exponent of an expression, the function is called an exponential function.

When the base of an exponential function has a magnitude greater than 1, the function is a growth function. When it is less than 1, the function is a decay function.

Here, the base is 4, which is greater than 1.

The function is an exponential growth function.

Answer:

4 = y

Step-by-step explanation:

2y+16=4y+8

The first step is to subtract 2y from each side.

2y-2y+16=4y-2y+8

16 = 2y+8

Now subtract 8 from each side

16-8 = 2y+8-8

8 = 2y

Now divide each side by 2

8/2 = 2y/2

4 = y

Find the GCF (Greatest Common Factor)

GCF = 8

Factor out the GCF (Write the GCF first and then in parentheses, divide each term by the GCF)

8(16bc/8 + 8am/8)

Simplify each term in parentheses

8(2bc + am)

Answer:

8(2bc + am)

Step-by-step explanation:

Factor out common factors from both terms. Note that each variable (the letters) are different, but that the numbers have factors.

Factors of:

16: 1, 2, 4, 8, 16

8: 1, 2, 4, 8

Note that the greatest factor is 8 in both numbers. Divide 8 from both terms

(16bc + 8am)/8 = 2bc + am

Add the factor to the front and parenthesis the leftover factors.

8(2bc + am) is your new answer.

~

Answer: The scale factor is 1.3  .

Step-by-step explanation:

Given: The first hexagon is dilated to form the second hexagon.

The side length of first hexagon=5 units.

The side-length of second hexagon= 6.25 units

When a shape having measure x is dilated by using a scalar factor of k, then the side measure (y) of the image is given by:-

[tex]y=kx[/tex]

Substitute, y=6.5 and x=5  to find the value of k we get

[tex]6.5=5k\\\Rightarrow\ k=\frac{6.5}{5}=1.3[/tex]

Hence, the scale factor is 1.3

Answer:

-5

Step-by-step explanation:

What you do to one side of the equation, you  do to the other side of the equations.

If you add -5 to the left side of the equation, you add -5 to the right side of the equation.

5 + x = 12

-5 +5 + x = 12-5

x = 7

Answer:

5+x=12-5

x=2

Step-by-step explanation:

Add 5 to both sides of the equation

The equation becomes 10+x=12

Then subtract 10 from both sides of the equation

The equation becomes x=2

And now that x is by itself, you've gotten your answer

Answer:

the answer is 10.26

Step-by-step explanation:

If 3 gallons cost 15.39 you would have to divide 15.39 into 3. Once you find out how much one gallon costs (which is 5.13) you multiply it by 2.

The price for a 2-gallon container of paint would be $10.26, based on the provided price for 3-gallon containers.

The subject of your question deals with cost and volume, which is a topic in mathematics, specifically ratios and unit rate. In this scenario, we are given that 3-gallon containers of paint are sold for $15.39. To find the price per gallon, we divide the total price by the number of gallons. This gives us a unit price of $15.39 / 3 = $5.13 per gallon.

If we want to find the price for a 2-gallon container, we would multiply this unit price by 2. So, the cost for a 2-gallon container would be $5.13 * 2 = $10.26.

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Answer:

62 cm  

Step-by-step explanation:

P = 2(5x - 2) + 2(3x + 1)         Insert the value of x

P = 2(5×4 - 2) + 2(3×4 + 1)

P = 2(20 - 2) + 2(12 + 1)

P = 2×18 + 2×13

P = 36 +26

P = 62 cm

Zohar must cut 62 cm with the scissors.

Answer:

y=3x+26

Step-by-step explanation:

Make sure they have the same slope.

Answer:

[tex]\frac{45y}{56x}[/tex]

Step-by-step explanation:

[tex]\frac{5}{-7x} times \frac{-9y}{8}[/tex]

When we multiply two fractions we multiply numerator with numerator and denominator with denominator

5 times -9y is -45y

Then -7x  times 8 is -56x

So the fraction becomes [tex]\frac{-45y}{-56x}[/tex]

we have negative at the top and bottom so it becomes positive

[tex]\frac{45y}{56x}[/tex]

We cannot simplify further

Answer:

8 1/2

Step-by-step explanation:

Given:

Looks like you already know what PEMDAS is.

Substitute the values of m and n into the underlined equation-- make sure you include parentheses around the numbers you substitute as this helps you easily see what you are doing.

(2 1/2)^2 + ((4 1/4) - 2)

Start inside the parentheses and subtract 2 from 4 1/4, then rewrite your equation.

(2 1/2)^2 + (2 1/4)

Next evaluate the exponent.

(6 1/4) + (2 1/4)

Since the fractions already have common denominators, you can add the whole numbers and the fractions together.

8 2/4

2/4 can be simplified by dividing both sides by 2/2.

8 1/2 is the final, fully simplified answer.

Answer:

D) {12, 7, 6, 8, 9, 9, 7, 11, 14}

Step-by-step explanation:

The box plot for Set D (below) has  

maximum    = 14

3rd quartile = 11.5

IQR              =  4.5

=====

Your box plot has

maximum    = 12

3rd quartile = 10

IQR              =  3

=====

Sets A, B, and C all fit your box plot.

Answer:

D) {12, 7, 6, 8, 9, 9, 7, 11, 14}

Step-by-step explanation:

Write the data in numerical order. Find the first quartile, the median, the third quartile, the minimum (smallest value) and the maximum (largest value).

{6, 7, 7, 8, 9, 9, 11, 12, 14}

Thus,

low -- 6

1st quartile -- 7

median -- 9

3rd quartile -- 11.5

high -- 14

Therefore, this data does not match the graph.

Answer:

x = 2.5

Step-by-step explanation:

Multiply 2.5 to remove the denominator

x/2.5 * 2.5 = 1

Multiply 2.5 on the other side.

2.5 * 1

x = 2.5

Answer:

x = 2.5

Step-by-step explanation:

x/2.5=1

To solve this equation, multiply both sides by 2.5

x/2.5* 2.5=1 * 2.5

x = 2.5

Answer:

i think your answer is 90

Answer:

Step-by-step explanation:

I am assuming this is meant to say 9/10 and 36/40.

If so 9/10=36/40.

Because 10 x 4 = 40

and 9 x 4 = 36.

Hope this helps! :)