factor the expression completely. 8y - 36

Answer: ? = x + 1

Step-by-step explanation:

The perimeter of the garden is x + 3x + 1 + x + ?

The perimeter of the garden is also (6x + 2)

Therfore:

x + 3x + 1 + x + ? = 6x + 2

Collect like terms:

5x + 1 + ? = 6x + 2

Subtract 5x from both sides:

1 + ? = x + 2

Subtract 1 from both sides:

? = x + 1

You cannot find ? as a number, only in terms of x.

The original price of the three video games before the discount was $200.

Sam purchased 3 video games for a total of $140 after receiving a 30% discount. To find the original price of the games before the discount, we need to divide the sale price by the percentage that Sam actually paid (100% - discount percentage).

The discount percentage is 30%, so Sam paid 100% - 30% = 70% of the original price. Since 70% is the same as 0.70 in decimal form, we can set up the equation:

$140 = original price * 0.70

To determine the original price, divide $140 by 0.70:

Original price = $140 / 0.70

Original price = $200

Therefore, the original price of the three video games before the discount was $200.

At the same rate, it would take Marisa 6/4 of an hour to paint the entire room. This is a ratio problem, specifically dealing with rates and proportional relationships.

Since Marisa painted 1/2 of her room in 3/4 of an hour, to paint the entire room would take double that time. When you double 3/4, you get 6/4. Therefore, at the same rate, Marisa would need 6/4 of an hour to paint the entire room.

This problem is a basic ratio problem related to rates and proportional relationships, common topics in middle school math. The rate in this case is painting speed, half a room per 3/4 of an hour. Thus, when we double the room space to be painted (from half a room to a full room) we should also double the required time.

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Answer:

20 lbs

Step-by-step explanation:

Answer:

100/7 miles

Step-by-step explanation:

So 3 1/3 can be written as 10/3 and 4 2/7 can be written as 30/7. So multiplying, we get 300/21 which can be simplified to 100/7.

Hey there!

Good luck on your assignment and enjoy your day!

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1) All three are right A.K.A 4

4) The answer is also 4).

2xty=5 is not linear.

Answer: n = -6

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

12= −1/3n +10

Step 2: Flip the equation.

−1/3n +10=12

Step 3: Subtract 10 from both sides.

−1/3n +10−10=12−10

−1/3n =2

Step 4: Multiply both sides by 3/(-1).

(3/−1) x (-1/3n) = (3/-1) x (2)

n=−6

Answer:

2x + 7 = 3x - 5

Step-by-step explanation:

Since triangle RTS is isosceles, RT is congruent to RS. So you can set up the equation 2x + 7 = 3x - 5 to find x. Then you can input the value of x into 2x +7 or 3x - 5 to find the measure of the congruent sides.

Answer:

[tex]a_{15}[/tex] = 5

Step-by-step explanation:

to find the 15th term substitute n = 15 into the nth term formula

[tex]a_{15}[/tex] = (- 3 × 15 ) + 50 = - 45 + 50 = 5

To find the 15th term, enter n = 15 into the nth term formula.

A list of numbers in a specific order is called a sequence. A term is the name given to each number in a sequence. A sequence has a place for each phrase (first, second, third and so on). Consider the sequence 5, 15, 25, 35, for instance. Each number in the series is referred to as a word. You should be familiar with the following four main categories of sequences: arithmetic sequences, geometric sequences, quadratic sequences, and special sequences.

Sets of numbers that adhere to a pattern or norm are known as number sequences. It is referred to as an arithmetic sequence if the rule is to add or remove a number each time. It is referred to as a geometric sequence if the rule is to multiply or divide by the same integer each time.

A term is the name given to each number in a series. A sequence is a list of objects that is in order in mathematics (or events). Similar to a set, it has members (also called elements, or terms). The length of the sequence is the number of ordered elements (potentially infinite)

Detailed explanation:

Substitute n = 15 into the nth term formula to discover the 15th term.

a15= (- 3 × 15 ) + 50 = - 45 + 50 = 5

a15= 5

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Answer:

x=24 in

Step-by-step explanation:

We can use proportions to solve this problem

5                15

------ =  -------------

8              x

Using cross products

5 * x = 8 *15

Divide by 5

5x/5 = 8*15/5

x = 8*3

x =24

Answer:

Step-by-step explanation:

On Monday: $2 on lunch.

On Tuesday: $1 on a snack.

On Wednesday: her siter gave her $3.

Now, before we graph the integers, first you need to think about those number and their meaning. If the number represents debt or expenses, then it must be a negative number. But, if the number represents money received, then it must be a positive number.

So, we have the following integer: -2, -1, 3.

If we graph these integers, it would be like the images attached shows.

Answer:

The correct answer is option (C).

Coconut oil freezes at a higher temperature than cottonseed oil because 24.8 > -48.1

Step-by-step explanation:

We have been given the freezing temperatures of cottonseed oil and coconut oil. The freezing temperature of cottonseed oil is -48.1 degree celsius and the same for coconut oil is 24.8 degree celsius.

We are supposed to compare the two freezing temperatures. We know that 24.8 is higher than -48.1, therefore, we can conclude that freezing temperature of coconut oil is higher than the freezing temperature of cottonseed oil because 24.8 is more than -48.1. Thus, correct answer is option (C).

Answer:

C

Step-by-step explanation:

Answer:

18

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

All circles are similar and therefore proportional. C/C' is the ratio of Circle C to Circle C'. Since it is 0.75, this means that C is 75% of C'. We know that radius of C will also be 75% of the radiuc of C'. We can the radius because we know the diameter of Circle C is 6. The radius is therefore 3. 3 is 75% of 4. So r/r' or 3/4=0.75. r/ must be 4.

Answer: B) 4

Step-by-step explanation:

Got this right on USA test prep

Answer: 100/1220*792= 64.9 have cell phones.

Step-by-step explanation:

Answer:

The percentage of students with cell phone is 64.92%

Step-by-step explanation:

Given

Sample Size = 1,220

Number of student with cell phones = 792

Required

Percentage of students with cell phone

To calculate the percentage of students with cell phone, we take a ratio of the number of students with cell phone to the sample size.

Mathematically, this is represented as

[tex]Percentage = \frac{Students-with-cell-phone}{Sample Size}[/tex]

By Substitution,

[tex]Percentage = \frac{792}{1220}[/tex]

[tex]Percentage = 0.64918032786[/tex]

[tex]Percentage = 64.918032786[/tex]%

[tex]Percentage = 64.92[/tex]% Approximated to nearest hundredth

Hence, the percentage of students with cell phone is 64.92%

Answer:

300 teenagers

Step-by-step explanation:

6a + 5t + 4c = 5300

a + t + c = 1200

(8/3)*t = c

6a+4c+5t = 5300

a+c+t = 1200

3c-8t = 0

a = 100

c = 800

t = 300

Answer: c is the right answer

Step-by-step explanation:

Answer:

14/6

Step-by-step explanation:

To find the slope, we can put it into slope intercept form. So 6y=14x+5. So y=14/6+5/6.

To find the fraction of candies that are either grape or lemon flavored, we add the fractions representing each flavor: 2/5 for grape and 3/10 for lemon. After finding a common denominator, we get 4/10 + 3/10, yielding 7/10 of the candies being either grape or lemon-flavored.

To find the fraction of candies that are either grape-flavored or lemon-flavored, we need to add the fractions that represent each flavor. We are told that 2/5 of the candies are grape-flavored and 3/10 are lemon-flavored.

First, we need a common denominator to add these two fractions. The least common denominator for 5 and 10 is 10. We can convert 2/5 to a fraction with a denominator of 10 by multiplying both the numerator and denominator by 2. This gives us 4/10. Now we can add:

4/10 (grape flavored)

+ 3/10 (lemon flavored)

= 7/10 (either grape or lemon flavored)

Hence, the fraction of the candies that are either grape-flavored or lemon-flavored is 7/10.

Answer:

m = 1

Step-by-step explanation:

distribute and simplify the left side of the equation

m + 8m - 12 = - 3

9m - 12 = - 3 ( add 12 to both sides )

9m = 9 ( divide both sides by 9 )

m = 1

Step-by-step explanation:

a. Given => m∠5 = 40°

b. Given => m∠2 = 140°

c. Same Side Interior Angle Theorem => The same side interior angles must add up to 180°, which in this case, it does. m∠4 and m∠2 are alternate interior angles, and so there measurements are the same. 180 - 140 = 40

d. Both angles are part of the "same-side interior angles", which means that there measurements should add up to 180°. Note that m∠5 = 40°, and m∠2 = 140° (Given). Set the equation

m∠5 + m∠2 = 180

Plug in the number for each angle

40 + 140 = 180

180 = 180 (True).

e. It is proven that the above measurements are congruent with their corresponding parts. This means that a || b through Converse of Same Side Interior angle Theorem.

~

[tex]\left\{\begin{array}{ccc}5x+7y=-1&\text{multiply both sides by 2}\\4x-2y=22&|\text{multiply both sides by 7}\end{array}\right\\\underline{+\left\{\begin{array}{ccc}10x+14y=-2\\28x-14y=154\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad38x=152\qquad\text{divide both sides by 38}\\.\qquad \boxed{x=4}\\\\\text{Put the value of x to the first equation:}\\\\5(4)+7y=-1\\20+7y=-1\qquad\text{substract 20 from both sides}\\7y=-21\qquad\text{divide both sides by 7}\\\boxed{y=-3}\\\\Answer:\ \boxed{x=4\ and\ y=-3\to(4,\ -3)}[/tex]

Answer:

D. triglyceride:

Step-by-step explanation:

lipids are a groups of organic molecules, that are insoluble, that contain fatty acids, triglyceride, phospholipids, and sterols.

Answer:

1. The angle ladder makes with the wall is 11.54°

2. The height above the ground at which the upper end of the ladder touches the wall is 9.80 m

Step-by-step explanation:

We see that the side opposite of ∠A and the hypotenuse (side opposite of 90 degree angle) of the triangle are known. The ratio that relates these two sides are SINE.

We know,

[tex]sin(angle)=\frac{opposite}{hypotenuse}[/tex]

Thus we can write:

[tex]sin(A)=\frac{2}{10}\\sin(A)=\frac{1}{5}[/tex]

To find ∠A, we take the inverse sine of [tex]\frac{1}{5}[/tex]. Our answer is:

[tex]sin(A)=\frac{1}{5}\\A=sin^{-1}(\frac{1}{5})\\A=11.54[/tex]

Thus the angle ladder makes with the wall is 11.54°

Second part of the question asks for the height above the ground at which the upper end of the ladder touches the wall, this is the length of AC.

Given the angle we found, we see that the side AC is adjacent of the angle and we also know the hypotenuse. The ratio that relates these 2 sides is COSINE.

We know,

[tex]cos(angle)=\frac{adjacent}{hypotenuse}[/tex]

Thus, we can write:

[tex]cos(11.54)=\frac{AC}{10}[/tex]

Cross multiplying and solving for AC, gives us:

[tex]cos(11.54)=\frac{AC}{10}\\AC=10*cos(11.54)\\A=9.80[/tex]

Thus, the height above the ground at which the upper end of the ladder touches the wall is 9.80 m

Answer:

P= -2 NEGATIVE 2

Step-by-step explanation:

Answer:

B. -2

Step-by-step explanation:

Answer:

Option B is correct

36 pizzas were topped with vegetables

Step-by-step explanation:

Let x be the number.

As per the statement:

At a pizzeria, the ratio of pizzas topped with meat to pizzas topped with vegetables was 4:3 on Saturday.

The ratio of pizza topped with meat to pizzas topped with vegetables = 4 : 3

then;

the number of pizza topped with meat = 4x

and

the number pizza topped with vegetables  = 3x

It is also given that the pizzeria made a total of 84 pizzas that day.

[tex]\text{Total Pizzas} = \text{Number of pizzas topped with meat}+ \text{Number of pizzas topped with vegetables}[/tex]

Substitute the given values we get;

[tex]84 = 4x+3x[/tex]

Combine like terms;

[tex]84= 7x[/tex]

Divide both sides by 7 we get;

12 = x

The pizza were topped with vegetables = 3x = 3(12) = 36

therefore, 36 pizzas were topped with vegetables

Answer:

The correct answer is option B.

Step-by-step explanation:

The ratio of pizzas topped with meat to pizzas topped with vegetables was 4:3 on Saturday.

Let the pizza's topped with meat be 4x

Let the pizza's topped with vegetable be 3x

Total pizzeria made a Saturday = 84

4x + 3x = 84

7x = 84

x = [tex]\frac{84}{7}=12[/tex]

Pizza's topped with meat = 4x = 4 × 12 = 48

Pizza's topped with vegetable = 3x = 3 × 12 = 36

12 pizzas were topped with vegetables.

A

E

And

F

They all add up to under 32.