Antonia participated in a run-a-thon and raised $265 for her school. She received $25 in donations and an additional $8 for every lap she ran. How many laps did Antonia run?

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:

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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Answer:y=mx+b

Step-by-step explanation:

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:

- 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:

The least number is - 5 3/7.

Then in order we have - 4 5/6.

- 4 3/7

4 2/7

And the greatest is 5 1/7.

Step-by-step explanation:

1. Let's look for the least number of this set and then continue to order them until we find the greatest, this way:

The least number is - 5 3/7 because is the biggest negative number among the three given to us.

The second least number is - 4 5/6, that is < - 5 3/7 and > than - 4 3/7. Their whole number is the same but the fraction part is bigger: 5/6 > 3/7 or 0.83 > 0.42.

The third number is the only negative number remaining: - 4 3/7.

Now, the fourth term in order is 4 2/7, because it's < 5 1/7.

Finally, the greatest number of the set given to us is 5 1/7.

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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Final answer:

Similar triangles can be used to solve real-world problems by applying the concept of proportionality. By comparing corresponding sides of similar triangles, you can find the unknown measurements.

Explanation:

Similar triangles can be used to solve real-world problems by applying the concept of proportionality. In a pair of similar triangles, corresponding sides are in proportion to each other. This means that if you know the measurements of one triangle, you can use the ratios of corresponding sides to find the measurements of the other triangle.

For example, if you have a 10-meter tall tree and its shadow is 5 meters long, and you want to determine the height of a nearby building using the shadow it casts, you can set up a proportion using the tree's height and shadow length as one ratio and the building's height and its shadow length as the other ratio. By solving this proportion, you can find the height of the building.

Similar triangles can be used to solve various real-world problems involving measurements such as distances, heights, widths, and more. By identifying corresponding sides and setting up ratios, you can find the unknown measurements.

Answer:

B. A sans serif font in size 30-point

Step-by-step explanation:

18, 10 and 10 are too small therefore 30 would be the correct font size.

The best type of front to use in a slide presentation is a sans serif font in size 30-point. That is option B.

A slide presentation is a type of presentation that involves the use of typed pages or pictures that contains information which are displayed in a screen.

The best type of font used in a slide presentation goes to the sans serif font with a size of 30 point. This is because, they lack the edge strokes and they are easy to read.

Therefore, the best type of front to use in a slide presentation is a sans serif font in size 30-point.

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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:

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!

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:

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:

$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:

10 cm

Step-by-step explanation:

if he knits 2cm per hour we can times it by 3 hours and get 6cm then he already had 4cm done so we will need to add that to it and get 10cm

Hey there! :)

-3(5a - 5) + 6a = 31 - 5a

Simplify! -15a + 15 + 6a = 31 - 5a

We must get all variables to one side and everything else to the other so that we can add like terms, so we can start by subtracting 15 from both sides. Additionally, add 5a to both sides.

-15a + 6a + 5a = 31 - 15

Simplify.-4a = 16

Divide both sides by -4.

-4a ÷ -4 = 16 ÷ -4

Simplify.

a = -4

~Hope this helped! :)

Answer:

[tex]a = 4[/tex]

Step-by-step explanation:

[tex] - 3(5a - 5) + 6a = 31 - 5a[/tex]

Solve the brackets.

[tex] - 15a + 15 + 6a = 31 - 5a[/tex]

Combine like terms.

[tex]-9a + 15 = 31 - 5a[/tex]

Take -5a to left side and 15 to the right.

[tex]-9a + 5a = 31 - 15[/tex]

Combine like terms.

[tex]-4a = 16[/tex]

Divide both sides by -4.

[tex]a = -4[/tex]

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:

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:

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:

First one is D.

Second one is A.

Step-by-step explanation:

Answer:

The number of trees in each row is  21.

Step-by-step explanation:

Let us assume the number of trees in each row  = m

So, the number of rows in the orchard = Number of trees in each row + 10

or, total number of trees in each row = (10 +m)

Now, Total number of Trees = Number of Rows x Number of trees in 1 row

⇒ 651  = m (m + 10)

[tex]651 = m^2 + 10m\\\implies  m^2 + 10m - 651 =0\\or,   m^2 + 31m  21m - 651 =0\\or, m(m +31) -21(m+31) =0\\\implies (m +31) (m-21) = 0[/tex]

⇒ (m +31) = 0, or (m-21) = 0

⇒ m= -31, or m = 21

Now, as m = The number of trees in each row, so m ≠ -31

So, m =  21

Hence, the number of trees in each row is m = 21.

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

Answer:

C

Step-by-step explanation:

D=m/v

Rearranging the formula

v=m/D

V=1000/13.56

V=73.69 cm3

Answer:

v = 73.69 cm²

Step-by-step explanation:

V = m/p

Where,

v is volume

m is mass

p is density

So,

v = 1000 / 13.57

v = 73.69 cm²

I believe that this maybe a wrong answer because 1000 kg is suppose to be converted to g but since the answer (which is 73692 cm³) would not meet any of the options, I would have to go for that answer.

Answer:

9y - 0.2xy is the answer after applying Distributive property.

Step-by-step explanation:

Given:

[tex]y(9-0.2x)[/tex]

To Find:

Expression after applying Distributive property.

Solution:

Distributive property:

In Distributive property, it lets you multiply a sum by multiplying each addend separately and then add the products.

OK, that definition is not really helpful for most people. It is easier to understand the meaning if you look at the examples below.

i.e A (B + C) = A×B + A×C

On Applying Distributive property to the given expression we get,

[tex]y(9-0.2x)=y\times 9-y\times0.2\times x\\y(9-0.2x)=9y-0.2\times x\times y[/tex]

[tex]\therefore y(9-0.2x)=9y-0.2xy \ \ \ \textrm{we can write xy or yx it same as 2*3 = 3*2 = 6}[/tex]

9y - 0.2xy

is the answer after applying Distributive property.

The expression y(9-0.2x) expands to 9y - 0.2xy using the distributive property, where y is multiplied by each term inside the parentheses.

To expand the expression y(9-0.2x) using the distributive property, you multiply y by each term inside the parentheses. Applying the distributive property, we get:

y × 9 - y × 0.2x

Which simplifies to:

9y - 0.2xy

This is the expanded form of the given expression.

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:

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!

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