Find the GCF of 45 and 75 using the prime factorization. (You can leave your answers in the prime factorization form.)

Answer:

72

Step-by-step explanation:

[tex]\bf \begin{array}{cll} \stackrel{ordinal}{position}&\stackrel{term}{value}\\ \cline{1-2} 1&12\\ 2&12+d\\ 3&12+d+d\\ 4&12+d+d+d\\ &12+3d \end{array}\qquad \implies ~\hfill \begin{array}{llll} \stackrel{\textit{4th term}}{12+3d}~~=~~\stackrel{\textit{4th value}}{3}\\\\ 3d=-9\implies d = \cfrac{-9}{3}\\\\ \stackrel{\textit{common difference}}{d = -3} \end{array}[/tex]

well, we know the common difference is -3, to go from the 4th term to the 8th term, we need to add "d" 4 times or namely 3+4(-3), likewise to go from the 13th term to the 19th term we have to add "d" 6 times, or namely -24 + 6(-3).

[tex]\bf \stackrel{\textit{8th term}}{3+4(-3)}\implies 3-12\implies -9 \\\\\\ \stackrel{\textit{19th term}}{-24 + 6(-3)}\implies -24-18\implies -42[/tex]

Answer:

0.04

Step-by-step explanation:

0.0398

when rounding if its over 5 you round up if its under you round down

The number 0.0398 rounded to the nearest cent; is 0.04.

According to the question;

To round off to the nearest cent;

We must know that cents is synonym for Hundredths;

Consequently; 0.0398 rounded to the nearest cent is 0.4

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Answer:

About 9.5 meters tall. Make sure to include the meters and the wiggly equal sign indicating about

Step-by-step explanation:

This is just a ratio

1.66:3.5 = 4.5:x

Cross multiply

1.66x = 15.75

Divide by 1.66 on both sides

x = about 9.5

Answer:

70 would be the answer to this question....apparently.

Step-by-step explanation:

Answer:

70

Step-by-step explanation:

25 divided by 1750 = 70

subtract 1750 to 175 =

00 subtract 00 = 00

overall 70 is your answer in long division

Answer:

D

Step-by-step explanation:

Quadratic has a general form of:

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

The quadratic given here is:

[tex]y = x^2 + 3x + 1[/tex]

Matching it with the general form, we can see that:

a = 1 [coefficient of x^2]

b = 3

c = 1

Now, if we look at the formula for axis of symmetry, we can easily solve this out. The axis of symmetry is given by:

Axis of Symmetry is  [tex]x=-\frac{b}{2a}[/tex]

We know a = 1 and b = 3, so we have:

[tex]x=-\frac{b}{2a}\\x=-\frac{3}{2(1)}\\x=-\frac{3}{2}[/tex]

Hence,

D is the correct answer.

Answer:

is D

Step-by-step explanation:

The total number of boxes will be 60 that the girls have sold in one hour.

The ratio is defined as a relationship between two quantities, it is expressed as one divided by the other.

We have to determine the total number of boxes will the girls have sold in one hour

Let Kate sold x boxes in 60 minutes

As per the given situation, we can write the ratio would be as:

27 boxes : 45 minutes = x boxes :  60 minutes

⇒ 27/45 = x/60

Apply the cross-multiplication operation,

⇒ x = (60×27)/45

⇒ x = 36

Let Miley sold y boxes in 60 minutes

⇒ 12/30= y/60

Apply the cross-multiplication operation,

⇒ y = (12×60)/30

⇒ y = 24

So, the total number of boxes = x + y = 36 + 24 = 60

Thus, the total number of boxes will be 60 that the girls have sold in one hour.

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Final answer:

Kate sells 36 boxes and Miley sells 24 boxes in one hour. So, they will have sold a total of 60 boxes in one hour.

Explanation:

To find the total number of boxes sold by both Kate and Miley in one hour, we need to calculate the rate at which each of them sells boxes. Kate sells 27 boxes in 45 minutes, which can be converted to 0.6 boxes per minute (27 boxes / 45 minutes = 0.6 boxes per minute). Miley sells 12 boxes in 30 minutes, which can be converted to 0.4 boxes per minute (12 boxes / 30 minutes = 0.4 boxes per minute).

To find the total number of boxes sold in one hour, we add the number of boxes each of them sells in one minute and multiply it by 60 (the number of minutes in an hour). Kate sells 0.6 boxes per minute, so in one hour she would sell 0.6 boxes/minute * 60 minutes = 36 boxes. Miley sells 0.4 boxes per minute, so in one hour she would sell 0.4 boxes/minute * 60 minutes = 24 boxes. Therefore, the total number of boxes sold by both Kate and Miley in one hour would be 36 + 24 = 60 boxes.

Answer:

d=50

Step-by-step explanation:

-d+100=-3d+200

Subtract 100 from both sides

-d+100-100=-3d+200-100

Simplify

-d=-3d+100

Add 3d to both sides

-d+3d=-3d+100+3d

Simplify

2d=100

Divide both sides by 2

\frac{2d}{2}=\frac{100}{2}

Simplify

d=50

Answer:

In 50days

Step-by-step explanation:

Since the equation below can be used to find the number of days (d) until they will have the same number of pages left in their journals −d + 100 = −3d + 200, this equations will be solved to get 'd'

Given the equation;

−d + 100 = −3d + 200

Collecting like terms we will have;

-d+3d = 200-100

2d = 100

d = 50

This shows that Max and Pat will have the same number of pages left in their journals in 50days.

Answer:57

Step-by-step explanation:

Conversion factor is

1 US bushel = 4 US pecks

76 rows x 3 pecks= 228 pecks

228 pecks / 4 = 57

To plant 76 rows of seed potatoes, with 3 pecks per row, we would need a total of 57 bushels, as there are 0.75 bushels per row and this is multiplied by the number of rows.

To answer this question, we first need to understand the relationship between bushels and pecks. There are 4 pecks in one bushel. If 3 pecks are planted per row, then each row requires 0.75 bushels (because 3/4 = 0.75). So, to find the number of bushels needed for 76 rows, we multiply 76 by 0.75.

The final calculation is: 0.75 bushels/row * 76 rows = 57 bushels.

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Answer:

$18.50

Step-by-step explanation:

.37×50 = 18.5

$18.50

Answer:

$18.50

Step-by-step explanation:

GIven

1 stamp ----> $0.37

50 stamps ------> $0.37 x 50 = $18.50

Answer: 1/30

Step-by-step explanation:

Answer:

3+(axb)

Step-by-step explanation:

The algebraic representation of the expression The sum of 3 times a and b is 3a + b

From the question, we have the following parameters that can be used in our computation:

The sum of 3 times a and b

By definiton:

sum means plus

Using the above as a guide, we have the following:

3 * a + b

When solved, we have

3a + b

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Question

Translate the sentence into an algebraic expression

The sum of 3 times a and b

Answer:

9261

Step-by-step explanation:

the problem is payed out like this formula

x² = 441

you take the square root of 441 to find x which is 21 and then you just take cubic of 21 which is 9261

Answer:

9261

Step-by-step explanation:

x² = 441  

you take the square root of 441 to find x which is 21 and then you just take cubic of 21 which is 9261

C. 3.16 is the right answer

Step-by-step explanation:

The distance formula used in coordinate geometry is derived from the Pythagorean theorem.

The distance formula is give by:

[tex]d=\sqrt{(x_2-x_2)^2+(y_2-y_1)^2}[/tex]

Here (x1,y1) are the coordinates of first point and (y1,y2) are the coordinates of second point

Here,

(x1,y1) = (5,-3)

(x2,y2) = (6,0)

Putting the values in the formula

[tex]AB = \sqrt{(6-5)^2+(0-(-3))^2}\\=\sqrt{(1)^2+(0+3)^2}\\=\sqrt{(1)^2+(3)^2}\\=\sqrt{1+9}\\=\sqrt{10}\\=3.16\ units[/tex]

The distance between two points is 3.16 units.

Hence,

C. 3.16 is the right answer

Keywords: Coordinate geometry, Pythagorean Theorem

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Answer:

The number of blocks in the nth figure will be (3n + 1).

Step-by-step explanation:

See the attached figure where few arrangements are there.

The number of blocks in the first arrangement is (3 + 1)

Now, the number of blocks in the second arrangement is (3 × 2 + 1)

Again, the number of blocks in the third arrangement is (3 × 3 + 1)

So, the pattern says that the number of blocks in the nth arrangement will be (3 × n + 1) = (3n + 1) (Answer)

The product of 576 and 684 is a rational number since it results in an integer, which is a subset of rational numbers.

The product of 576 and 684 is asked to be classified as rational or irrational. The multiplication of two integers will always produce another integer, as is the case with 576 multiplied by 684. Since all integers are rational numbers (they can be expressed as the ratio of two integers), the product, in this case, is also a rational number.

Therefore, the product of 576 and 684 is rational because it can be expressed as a ratio of the two integers (the product itself over 1), fitting the definition of a rational number which includes integers, fractions, finite decimals, and repeating decimals.

Final answer:

The product of 576 and 684 is a rational number because the multiplication of two integers always results in another integer.

Explanation:

The question asks whether the product of 576 and 684 is rational or irrational. A rational number is a number that can be expressed as a ratio of two integers. Since both 576 and 684 are integers, their product will also be an integer, as the multiplication of two integers always results in another integer. Therefore, this product is definitely a rational number. An irrational number, by contrast, cannot be expressed as such a ratio, and is typically found with non-repeating, non-terminating decimal expansions or with numbers like the square root of a non-square number. However, as there is no square root or any other irrational operation involved in multiplying 576 and 684, the result is rational.

Answer:

y= 12x+5 and It would be 10 days.

Step-by-step explanation:

Y= total

+5 = each rental

X= # of days

125= 12x+5; x=10

The equation to determine the cost of renting a chainsaw for x days is y = 12x + 5. For a cost of $125, one can rent the chainsaw for 10 days.

To write an equation for the number of dollars (y) that must be paid to rent a chainsaw for x days, take into account the daily rental fee and the one-time sharpening fee. The daily rental fee is $12, and there is an additional one-time sharpening fee of $5 for each rental. The total cost y is therefore the sum of the daily rental fees for x days and the sharpening fee.

The equation is:

y = 12x + 5

To find out how many days one can rent a chainsaw for a cost of $125, we can set y equal to $125 and solve for x:

125 = 12x + 5

Subtract 5 from both sides to get:

120 = 12x

Divide both sides by 12 to solve for x:

x = 10

Therefore, one can rent a chainsaw for 10 days at a cost of $125.

Answer:

1.  [tex]2 \times 10^{- 4} = 2 \div 10^{4}[/tex]

2. [tex](- 10)^{2} = 100[/tex] and [tex]- 10^{2} = - 100[/tex]

3. [tex](a.b.c. ........)^{n} = a^{n}.b^{n}.c^{n}. ..........[/tex]

Example:  [tex](30)^{4} = (2 \times 3 \times 5)^{4} = 2^{4} \times  3^{4} \times 5^{4}[/tex]

Step-by-step explanation:

1. We have [tex]2 \times 10^{- 4}[/tex], and we have to prove that this term is equivalent to [tex]2 \div 10^{4}[/tex].

Now, [tex]2 \times 10^{- 4}[/tex]

= [tex]2 \times \frac{1}{10^{4} }[/tex]  

{Since we know the property of exponent as [tex]a^{- b} = \frac{1}{a^{b} }[/tex] }

= [tex]\frac{2}{10^{4} }[/tex]

= [tex]2 \div 10^{4}[/tex]

2. [tex](- 10)^{2} = (- 10) \times (- 10) = 100[/tex] and  

[tex]- 10^{2} = - [(10) \times (10)] = - 100[/tex]

3. The power of products property gives

[tex](a.b.c. ........)^{n} = a^{n}.b^{n}.c^{n}. ..........[/tex] ........ (1)

For example, we can write, [tex](30)^{4} = (2 \times 3 \times 5)^{4} = 2^{4} \times  3^{4} \times 5^{4} = 810000[/tex]

Answer:

constant

It is the unchanging value, and the coefficiant is the numbers with the variables because the variable changes the number. The variable is the letter that is either alone or with a number.

Answer:

He will order 72 pairs of high tops

Explanation:

Given the store owner sells two pairs of running shoes for each pair of high tops

For every pair of high tops, he sells 2 pairs of running shoes

1 high top = 2 running shoes

He has planned to order 144 pairs of shoes

Therefore, 144 pair of running shoes = 144/2 = 72 pairs of high tops

Therefore, he will order 72 pairs of high tops

Answer:

$5.89

Step-by-step explanation:

29.45/5=5.89

Answer:

$5.89

Step-by-step explanation:

I divided 29.45 and 5 and got the product+cost of a single pair of the gloves; $5.89

Answer:

50%

Step-by-step explanation:

cause 50% is 1/2 and 1/2 of 20 is 10

Answer: 50%

Step-by-step explanation:

10 is half of 20.

Half converted to a percent is 50%

Answer:

1

Step-by-step explanation:

Greatest Common Factor is the highest number that divides exactly into two or more numbers. It is the "greatest" thing for simplifying fractions.

No number (except 1) is divisible by both 35, 15, and 3. Therefore, the GCF is 1.

Answer:

35: 5×7               GCF: 5×3=15

15:  5×3

 3:  1×3

Step-by-step explanation:

 35               15              3

/     \            /    \           /    \

5 × 7         3  ×  5        1  ×  3

Answer:

19

Step-by-step explanation:

8+4=12 +7=19

The solution to the linear equation d – 10 – 2d + 7 = 8 + d – 10 – 3d is d = 1.

An equation is an expression that shows the relationship between two or more numbers and variables.

Given the equation:

d – 10 – 2d + 7 = 8 + d – 10 – 3d

Simplifying:

-d - 3 = -2d - 2

Collecting like terms:

-d + 2d = -2 + 3

d = 1

The solution to the linear equation d – 10 – 2d + 7 = 8 + d – 10 – 3d is d = 1.

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Answer:

simplify the expression:  2x+2

Step-by-step explanation:

The equivalent expression of the given expression is is 2 + 2x

To solve this expression, we should simply proceed to multiply the value outside the bracket and simplify.

steps required;

This is done to add up or subtract similar or like values with each other.

[tex]\frac{1}{5}(15+10x-5)=\frac{1}{5}(15-5+10x)=\frac{1}{5}(10+10x)\\[/tex]

Multiply the entire value inside the bracket by 1/5.

[tex]\frac{1}{5}(10+10x)=2+2x[/tex]

This is the simplified expression of what we are given.

The equivalent expression is 2 + 2x.

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Answer:

The correct answer is A. Draw a graph that joins the points (100, 120) and (50, 95) and has a slope = 0.50

Step-by-step explanation:

1. Let's review the information given to us for solving the question:

Total of megabytes of date used = x

Total monthly charges = y

x₁ = 50 Megabytes, x₂ = 100 Megabytes

y₁ = US$ 95, y₂ = US$ 120

2. Let's find out the best description of the steps to draw the graph and the slope.

Slope = (y₂ - y₁)/ (x ₂- x₁)

Slope = 120 - 95/ 100 - 50

Slope = 25/50 = 1/2 = 0.50

Remember that the coordinates of the points in the line are written this way:

(x, y) ⇒ (Total of megabytes of date used, Total monthly charges)

The correct answer is A. Draw a graph that joins the points (100, 120) and (50, 95) and has a slope = 0.50

Answer:

a

Step-by-step explanation:

100% on test

Answer:

$4.86

Step-by-step explanation:

2.97/11 =.27                 .27 x 18= 4.86

Answer:

4.86

Step-by-step explanation

Answer:

9/5

Step-by-step explanation:

1 2/3=5/3

3/(5/3)=(3/1)(3/5)=9/5

Answer:

80in^3

Step-by-step explanation:

Answer:

80 in^3

Step-by-step explanation:

I just did this