What are like terms? How do you combine them? Can you give an example?

Final answer:

The correct option is (d) 200. By using a proportion based on the sample data where 51 students (25% of the grade) chose summer, it can be predicted that approximately 204 students in total would choose summer. The closest provided option to this calculated number is 200.

Explanation:

Latricia surveyed 25% of the seventh-grade students, and out of this sample, 51 students chose summer as their favorite season. To find the total number who would choose summer, we assume that the sample is representative of the entire grade. If 51 represent 25%, then to find 100% (the whole grade), we use the following proportion:

Sample size (25%) : Number who chose summer in sample (51) = 100% : Total number who would choose summer

To solve the proportion for the total number who would choose summer, we set up a simple equation:

25% / 51 = 100% / x, where x is the total number we want to find.

To find x, we multiply both sides by x and divide by 25%:

x = (51 * 100%) / 25%

x = (51 * 4)

x = 204

Therefore, the most reasonable prediction for the number of seventh-grade students who would choose summer as their favorite season is 204. However, since 204 is not one of the options provided, we will choose the closest option, which is (d) 200.

62+x≥85 is the inequality to show how much more money Chantal must save.

a relationship between two expressions or values that are not equal to each other is called 'inequality.

Given that Chantel would like to buy a new pair of running shoes.

The shoes she likes start at $85.

Chantel has already saved $62.

We need to find the inequality to show how much more money Chantal must save.

Let x be the more money needed to purchase the shoes.

62+x≥85

Subtract 62 from both sides

x≥85-62

x≥23

Hence, 62+x≥85 is the inequality to show how much more money Chantal must save.

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Answer:

a) See the attachment (measurements are in meters).

b) x = √(12² + 16²) = √(144 + 256)

= √400 = 20

The slant height of the roof is 20

meters.

Given is (2x+1)(x−5)

We need to multiply the binomials and write the expression in standard form.

We know about distributive property that is given as "a(b+c) = ab + ac".

We have (2x+1)(x−5).

Step 1: Using Distributive property on first binomial expression (2x+1).

2x(x-5) + 1(x-5)

Step 2: Using Distributive property on second binomial expression (x-5).

2x(x) + 2x(-5) + 1(x) + 1(-5)

2x² - 10x + 1x - 5

Step 3: Combining like terms.

2x² - 9x - 5

Hence, final answer is (2x² - 9x - 5).

Final answer:

To find out how many paint cans Jim needs, calculate the area of the circular pad using the formula πr^2 and divide by the coverage area of one can. For a 50 feet diameter pad, Jim would need approximately 10 cans of paint.

Explanation:

To calculate the number of paint cans needed, we first need to find the area of the circular helicopter pad. The diameter of the pad is given as 50 feet, so the radius is half of that, which is 25 feet. The area A of a circle is calculated using the formula A = πr^2, where r is the radius.

Substituting the radius into the formula gives:

A = π(25 feet)^2

A = 3.14159 × (25 feet) × (25 feet)

A = 3.14159 × 625 feet²

A = 1963.495 feet²

Since each can covers about 200 square feet, we divide the total area by the coverage area per can:

Number of cans = 1963.495 feet² / 200 feet²/can

Number of cans ≈ 9.82 cans

Since Jim cannot buy a fraction of a can, he would need to round up, meaning he would need 10 cans of paint to cover the helicopter pad.

The equation which can be used to determine p, the cost of b cans of beans will be;

⇒ p = 9.5b

What is Equation of line?

The equation of line in point-slope form passing through the points (x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

The values on the x - axis are 0, 2, 4, 6, 8, 10.

The values on the y- axis are 0, 19, 38, 57, 76, and 95.

These points are connected by a line.

The label on the x axis is Number of Cans.

The title on the y axis is Price in dollars.

Now,

Find the equation as;

Let two points from the table are,

⇒ (0, 0) and (2, 19)

So, The equation of line passing through the points (0, 0) and (2, 19) is,

⇒ y - y₁ = (y₂ - y₁) / (x₂ - x₁) (x - x₁)

⇒ y - 0 = (19 - 0) / (2 - 0)  (x - 0)

⇒ y = 19/2x

⇒ y = 9.5x

So, The equation which can be used to determine p, the cost of b cans of beans will be;

⇒ p = 9.5b

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Answer:

1) 32 bracelets if she cuts the ribbon into a 7 and 1/2 inch.

2) 35 bracelets if she cuts the ribbon into a 6 and 3/4 inch.

Step-by-step explanation:

1) Length of the ribbon = 20 feet = 240 inches

1 foot = 12 inches

Length of the ribbon required to make a bracelet = [tex]7\frac{1}{2}=\frac{15}{2}inches[/tex]

Let the number of bracelets Sally can make from 20 feet ribbon be x.

[tex]x=\frac{240 inches}{\frac{15}{2}inches}=32[/tex]

32 bracelets if she cuts the ribbon into a 7 and 1/2 inch.

2) Length of the ribbon = 20 feet = 240 inches

1 foot = 12 inches

Length of the ribbon required to make a bracelet = [tex]6\frac{3}{4}=\frac{27}{4} inches[/tex]

Let the number of bracelets Sally can make from 20 feet ribbon be x.

[tex]x=\frac{240 inches}{\frac{27}{4}inches}=35.555\approx 35[/tex]

35 bracelets if she cuts the ribbon into a 6 and 3/4 inch.

Answer:

[tex]x=50.6cm[/tex]

Step-by-step explanation:

Triangle MAB is similar to triangle MNP

Since the triangles are similar, the corresponding ratios are in the same proportion.

Therefore we can write the relation;

[tex]\frac{|MB|}{|MP|}=\frac{|MA|}{|MN|}[/tex]

[tex]\frac{x}{72.6}=\frac{46.2-14}{46.2}[/tex]

This implies that;

[tex]\frac{x}{72.6}=\frac{32.2}{46.2}[/tex]

We multiply both sides by 72.6 to get

[tex]\frac{x}{72.6}\times 72.6=\frac{32.2}{46.2}\times72.6[/tex]

[tex]\Rightarrow x=50.6[/tex]

Hence the value of [tex]x[/tex] is 50.6 cm