Samuel can do 120 jumping jacks in two minutes.
What is the ratio?
What is the unit rate?
What is the rate?

Answer:21/7

Step-by-step explanation:

The main fact that helps you solve 2,100 ÷ 7 is understanding that division is splitting into equal parts. Doing this with 2,100 split into 7 gives you a result of 300.

The fact that's most helpful in finding the result of 2,100 ÷ 7 is understanding the basic operation of division. Division is splitting into equal parts or groups. It is the result of 'fair sharing'. So, if you have 2,100 and you divide it into 7 equal groups, how much is in each group? We do this by taking 2,100 and divvying it up 7 times. The result will be 300. So, 2,100 ÷ 7 = 300.

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Answer:

21x - 16y

Step-by-step explanation:

First you need to multiply 5 with the numbers inside the brackets ( -5 x 4y= -20y and -5 x -3x = 15x ) so you will get 6x - 20y + 15x + 4y now you just add 15x plus 6x to get 21x and add 4y to -20y to get -16y so your answer should look like 21x - 16y.

Hope this helps!

Answer:

2 is a co-efficient to the variable, x. 4 is a constant.

Step-by-step explanation:

Don't know exactly what you're asking here.

Answer:

693 sq. m.

Step-by-step explanation:

The figure consists of a triangular prism (Bottom Part) and a Triangular Pyramid (Top Part). We will find the volume of each and add it up to get volume of total figure.

1. Volume of Triangular Prism = Area of Triangular Base * Height

Area of Triangular Base = (1/2)*base*height

Given that the triangle is a right triangle, we find the unknown side by using Pythagorean Theorem, which tells us:

Leg^2 + Another Leg^2 = Hypotenuse^2

8.8^2 + Another Leg^2 = 13.7^2

77.44+ Another Leg^2 = 187.69

Another Leg (unknown side, or the base of the triangle) = Sqrt(187.69-77.44) = 10.5 (this is base of triangle)

So, we have:

Area of Triangular Base = [tex]\frac{1}{2}*10.5*8.8=46.2[/tex]

Thus,

Volume of Triangular Prism = 46.2 * 10(given) = 462 sq.m.

2. Volume of Triangular Pyramid = (1/3) * area of triangular base * height

Here, area of triangular pyramid is 46.2 (already found)

the height of the pyramid is 25 - 10 = 15

SO, we have:

Volume of Triangular Pyramid = [tex]\frac{1}{3}*46.2*15=231[/tex] sq. m.

Now we sum them up and get total volume of the figure:

Total Volume of Figure = 462+ 231 = 693 sq. m.

Answer:

$81.60

Step-by-step explanation:

A 20% markdown means that the chairs were sold at 80% of the original cost.

Original cost = $102

markdown = 20%

Cost after markdown = original cost* (1-markdown)

Cost after markdown = 102 *(1 - 0.20)

= 102*0.80

= 81.6

Therefore, the 4 chairs were sold at a total cost of $81.60

Answer:

22

Step-by-step explanation:

The number of male friends : 200 ÷100 × 45 = 90

The number of female friends : 200 - 90 = 110

Joan likes 20% of her female friends and there are total of 110 female friends

20% 110 would be➡ 110 ÷ 100 × 20 = 22

Answer:

0,12 grams

Step-by-step explanation:

0,96:8=0,12

Each serving will contain 0.12 grams of sodium.

In order to find out how many grams of sodium each serving contains in the bag of potato chips, we can divide the total amount of sodium in the bag by the number of servings. Given that the bag contains 0.96 grams of sodium and is split into 8 equal servings, we can divide 0.96 by 8 to find the sodium content per serving.

Step 1: Divide 0.96 by 8: 0.96 ÷ 8 = 0.12

Step 2: Each serving will contain 0.12 grams of sodium.

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Set up the polynomials to be divided. If there is not a term for every exponent, insert one with a value of

0

.

2

x

-

3

2

x

2

-

3

x

+

5

Divide the highest order term in the dividend

2

x

2

by the highest order term in divisor

2

x

.

x

2

x

-

3

2

x

2

-

3

x

+

5

Multiply the new quotient term by the divisor.

x

2

x

-

3

2

x

2

-

3

x

+

5

+

2

x

2

-

3

x

The expression needs to be subtracted from the dividend, so change all the signs in

2

x

2

−

3

x

x

2

x

-

3

2

x

2

-

3

x

+

5

-

2

x

2

+

3

x

After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.

x

2

x

-

3

2

x

2

-

3

x

+

5

-

2

x

2

+

3

x

0

Pull the next term from the original dividend down into the current dividend.

x

2

x

-

3

2

x

2

-

3

x

+

5

-

2

x

2

+

3

x

0

+

5

The final answer is the quotient plus the remainder over the divisor.

x

+

5

2

x

−

3

Answer:

110

Step-by-step explanation:

A bump is 180 degrees as well as a triangle. So 90+20=110 and 180-110=70. Meaning 180-70 =110

Answer:

110

Step-by-step explanation:

Solve for the angle in the triangle

solve for the "?"

Answer:

$73

Step-by-step explanation:

Multiply 7 and 7 to get 49. Next, multiply 6 and 4 to get 24. The museum is free for the 3 children so you do not have to do anything. Add 49 and 24 to get 73, which is the price for the Baker Family.

Answer:

4

Step-by-step explanation:

x-y

14-8=6

so x is 6 more than y

y+6=x

y= -2. -2 + 6 = 4

Answer:4

Step-by-step explanation:

i don’t know

Answer:

y + 3 = (1/2)(x -6)

Step-by-step explanation:

When we have the slope m of the line and a point (a,b) which the line passes through, the point-slope form is

y - b = m (x -a)

Since the slope is 1/2 and the line passes through (6, -3), the point-slope equation is

y -(-3) = (1/2)(x -6)

or

y + 3 = (1/2)(x -6)

Answer:

Original point (1,2) and the image is (1,-2).

Step-by-step explanation:

If a point on the coordinate plane reflects across the x-axis then the x-coordinates of the original point and that of the image point will remain the same and the y-coordinates of the original point and that of the image point will only change their signs.

So, a point having coordinates (a,b) when reflected across the x-axis then the point generated after reflection will have coordinates (a,-b).

This is true for any real values of a and b.

So, for example, if (1,2) is a point reflected across the x-axis will generate an image point with coordinates (1,-2). (Answer)

Answer:

First one is D.

Second one is A.

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]x\div9=157\\\\\dfrac{x}{9}=157\qquad\text{multiply both sides by 9}\\\\9\!\!\!\!\diagup^1\cdot\dfrac{x}{9\!\!\!\!\diagup_1}=(9)(157)\\\\x=1413[/tex]

Answer:

84 pumpkins; less than she expected

Step-by-step explanation:

Find 20% of 100 and add the percent to 100. That is 120.Then find 30% of 120, which is 36. Then do 100-36 to get 84 pumpkins. That is less than 100 so she got less than she hoped.

The final number of pumpkins less than she ​hoped is 84 pumpkins.

A percentage is a number or ratio expressed as a fraction of 100.

A percentage is a dimensionless number, it has no unit of measurement.

Brianna hoped to get = 100 pumpkins

percentage of increased yield = 20%

∴ number of pumpkins = 100*20/100

                                      = 20 pumpkins more.

      total pumpkins yield = 100 + 20 = 120.

percentage of pumpkins animals eat = 30%

          ∴ number of pumpkins = 120*30/100

                                      = 36 pumpkins more.

total number of pumpkins she left = 120 - 36

                                                       = 84.  answer.

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Answer:

a)6,7,8,9 and 10th term is 15.

b)1,3,5,7 and 10th term is 19.

Step-by-step explanation:

Given a) n+5

b)2n-1

Solution for  a) n+5

Taking the value of n is 1 we get the first term of the sequence;

[tex]n+5=1+5=6[/tex]

Similarly taking the value of n 2,3,4 we get;

[tex]2+5=7\\3+5=8\\4+5=9[/tex]

And for 10th term we take the value of n is 10 and get;

[tex]n+5=10+5=15[/tex]

So the solution for 1st sequence is 6,7,8,9 and 10th term is 15.

Solution for  b)2n-1

Taking the value of n is 1 we get the first term of the sequence;

[tex]2n-1=2\times1-1=2-1=1[/tex]

Similarly taking the value of n 2,3,4 we get;

[tex]2n-1=2\times2-1=4-1=3\\2\times3-1=6-1=5\\2\times4-1=8-1=7[/tex]

And for 10th term we take the value of n is 10 and get;

[tex]2n-1=2\times10-1=20-1=19[/tex]

So the solution for 2nd sequence is 1,3,5,7 and 10th term is 19.

Final answer:

The first 4 terms and the 10th term of sequence (a) n + 5 are 6, 7, 8, 9, and 15, respectively. For sequence (b) 2n - 1, they are 1, 3, 5, 7, and 19, respectively.

Explanation:

For each sequence, we need to find the first 4 terms and the 10th term. The sequences are given by (a) n + 5 and (b) 2n - 1.

Let's start with sequence (a) n + 5. The first 4 terms, where n starts at 1, will be:

The 10th term can be found by substituting n = 10 into the expression, so the 10th term is:

10 + 5 = 15

Moving on to sequence (b) 2n - 1. The first 4 terms are:

The 10th term is calculated as:

2(10) - 1 = 19

Answer:y=mx+b

Step-by-step explanation:

Final answer:

To calculate the savings of 25% off a $500 stove, you multiply 500 by 0.25 to get a savings of $125.

Explanation:

The question asks us to calculate how much money will be saved on a stove that is on sale for 25% off its regular $500 price. To find the amount of savings, we need to calculate 25% of $500. This is done by multiplying the original price by the percentage discount in decimal form.

The percentage in decimal form is 0.25 (since 25% is 25 per hundred, or 25/100), hence, we multiply 500 by 0.25 to find the savings:

500 × 0.25 = $125.

Therefore, the amount of savings from the original price during the sale is $125.

Answer:

2.9%

Step-by-step explanation:

Given:

Total earnings : $1,825

Electricity : $53.20

% of earnings spent on electricity,

= (53.2 / 1825) x 100%

= 0.2915 x 100%

= 2.915%

= 2.9% (nearest tenth)

Answer:

a.3/4 b.2/3

Step-by-step explanation:

Answer:

a) 3/4

b) 2/3

Step-by-step explanation:

a)    15    ÷    5           3

     _________ =  ____

      20   ÷    5           4

b)     8     ÷    4           2

      _________ =  ____

       12    ÷    4           3  

Hope this helps OwO!

Answer:

1.5, 3, 6, 12, 24, 48

Explanation:

multiply all of the numbers by 2

1.5*2=3

3*2=6

6*2=12

12*2=24

24*2=48

Answer:

- 5/6 is the answer

Step-by-step explanation:

The number which when multiplied by 1/2 is -5/12 is -5/6

Let

The unknown number = x

So,

x × 1/2 = -5/12

1/2x = -5/12

Divide both sides 1/2

x = -5/12 ÷ 1/2

= -5/12 × 2/1

= -10 / 12

= -5/6

Hence, -5/6 id the number need-

-5/6

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Answer:

David took 32 more steps

Step-by-step explanation:

first we need to find out how many steps each person takes every one mile to find that out we divide the steps by how many miles .

megan: 9780÷5= 1956 steps in one mile

David: 11928÷6= 1988 steps in one mile

then you subtract to find by how many more steps .

1988-1956 =32

david took 32 more steps

f(x) + c -> up by c

f(x) - c -> down by c

f(x + c) -> left by c

f(x - c) -> right by c

For y = f(x + c), the y value of x now takes the y value of the function of x + c, or the one c to the right of x, shifting the entire graph left by c.

The function y=f(x+c) signifies a horizontal shift of the graph y=f(x). The graph shifts left if 'c' is positive and right if 'c' is negative.

In mathematics, y=f(x+c) represents a transformation of the graph y=f(x). Specifically, the addition of the constant 'c' in the function results in a horizontal shift of the graph. If 'c' is positive, then the graph moves to the left by 'c' units. If 'c' is negative, then the graph moves to the right by 'c' units.

Let's look at an example to illustrate this. Consider the function y = f(x) where f(x) = x^2, the graph is a parabola centered on the origin (0,0). If we transform this function into y = f(x+c), where c = 2, the resulting graph y = (x+2)^2 would be a parabola shifted 2 units to the left of the origin.

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Answer:

A) y^3+27

Step-by-step explanation:

(y+3)(y^2-3y+9)

y^3-3y^2+9y+3y^2-9y+27

y^3+27

The product of the polynomial is A = y³ + 27

Polynomials are mathematical expressions involving variables raised with non-negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication and non-negative exponentiation of variables involved.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

To find the product of (y+3)(y^2 - 3y + 9), we can use the distributive property of multiplication:

(y+3)(y² - 3y + 9) = y(y² - 3y + 9) + 3(y² - 3y + 9)

Now we can simplify each term:

y(y² - 3y + 9) = y³ - 3y² + 9y

3(y² - 3y + 9) = 3y² - 9y + 27

Adding these two simplified polynomial terms, we get:

(y+3)(y² - 3y + 9) = y³ - 3y² + 9y + 3y² - 9y + 27

Simplifying further, we get:

(y+3)(y² - 3y + 9) = y³ + 27

Hence , the product is A = y³ + 27

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Answer:

1. k = 3

2. k = 5

Step-by-step explanation:

1. The graph shows two parallel lines intersecting y-axis:

The graph of the function g(x) is translated 5 - 2 = 3 units up graph of the function f(x). Thus, k = 3.

2.  The graph shows two parallel lines intersecting y-axis:

The graph of the function g(x) is translated 3 - (-2) = 5 units up graph of the function f(x). Thus, k = 5.

Final answer:

The sum of the two weights, 13 lb 7 oz and 10 lb 2 oz, is 23 lb 9 oz. You add the ounces first, which don't need conversion, and then add the pounds.

Explanation:

Adding Pounds and Ounces

The question involves adding two weights together that are given in pounds and ounces. To do this, we need to add the ounces together first and then the pounds. The sum of 7 ounces and 2 ounces is 9 ounces. Since there are 16 ounces in one pound, we have no need to convert these ounces to pounds. The sum of 13 pounds and 10 pounds is 23 pounds. Therefore, when we combine these two sums, we arrive at the total weight of 23 pounds and 9 ounces.