9 Ron's family plans to add a new room to their house. They initially planned the width and the length of the room to be 10 feet and 25 feet. Now they want to add to the width. The amount they want to add to the width is shown by the variable I. 25 101 + Ron thinks that the area of the room will be 250 + 257. Is he correct? Why or why not? Select all that apply. A Yes, because the area of the room is the sum of 25.10 and 25r. No, because the area of the room is the sum of 25 . 10 and I. No, because the area of the room is the product of 25 + 10 and 25.1. D Yes, because the area of the room is the product of 25 and 10+ I.

Hello

we are given a function and asked to find the reminder when it is divided by a binomial

According to the remainder theorem, f(a) would be the remainder from dividing f(x) by x -a

but our f(x) is given as

From the calculation above, the answer to this question is 31

Answer:

(2y+5)x(5y-2)

Step-by-step explanation:

For a polynomial of the form ax² - bx + c rewrite the middle term as a sum of two terms whose product is a·c=10·-10 = -100 and whose sum is b= 21.

We factor 21 out of 21y.

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{10y^{2}+21(y)-10 } \end{gathered}$}}[/tex]

Rewrite 21 as −4 plus 25.

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{10y^{2}+(-4+25)y-10 } \end{gathered}$}}[/tex]

Apply the distributive property.

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{10y^{2}-4y+25y-10 } \end{gathered}$}}[/tex]

Factor the highest common denominator of each group. Group the first two terms and the last two.

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{(10y^{2}-4y)+25y-10 } \end{gathered}$}}[/tex]

Factor the highest common denominator (GCF) of each group.

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{2y(5y-2)+5(5y-2) } \end{gathered}$}}[/tex]

Factor the polynomial by factoring the greatest common denominator, 5y-2.

[tex]\boxed{\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{(5y-2)(2y+5) } \end{gathered}$}}}[/tex]

ANSWER:

Option c

STEP-BY-STEP EXPLANATION:

The function given in the statement is the following:

If D(h) = 383, we substitute and solve for h, just like this:

Therefore, the correct answer is option c.

The solution of the given system of equation will have infinite many solutions.

In the above question, the following equations are given

4x + 6y = 24

2x + 3y = 8

Now, we need to find the number of solutions that this system of equation will have

We know that,

a1 x + b1 y = c1

a2 x + b2 y = c2

is the general system of equation, and

[tex]\frac{a1}{a2} \neq \frac{b1}{b2}[/tex] then unique solution, or

[tex]\frac{a1}{a2} = \frac{b1}{b2} = \frac{c1}{c2}[/tex] then there will be infinite solutions or,

[tex]\frac{a1}{a2} = \frac{b1}{b2} \neq \frac{c1}{c2}[/tex] then there will be no solution

Now, we'll check for the given system of equations

a1 = 4, b1 = 6 , c1 = 24

a2 = 2, b2 = 3 , c2 = 8

[tex]\frac{a1}{a2} = \frac{b1}{b2} \neq \frac{c1}{c2}[/tex] = 2 = 2 [tex]\neq[/tex] 3

As this condition satisfies the third condition, the solution of the given system of equation will have infinite many solutions.

Now as we multiply the first equation 4x + 6=24 by 3 we get we have 12x+18y=72, the system will still have same solutions as only the equations are multiplied by a constant k = 3 which does not affect the solution.

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The equation to represent this situation is given by 0.65x = 282.75 .

In the various mathematical formulas that are used, the equals sign is used to show that two expressions on either side of the equal sign are equal.  The meaning of the word equation and its cognates might vary slightly depending on the language.

Finding the exact values of the unknown variables that result in the given equality is the very first step in the solving of a variable equation. The values of the unknown variables that fulfil the equality are the equation's solutions, also known as the variables for which the equation must be solved. There are two sorts of equations.

Le t the original cost of the bike be x dollars.

After 35% reduction the new cost is x - (35% of x) = 0.65 x

Therefore 0.65 x = 282.75

or, x = 435

Therefore the cost of the bike is $435.

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Given the line which passes through the points (2, 3) and (5,8) and the line that passes through the points (-7, 5) and (-12, 8).

To determine the relationship which best describes the line, the first thing we do is find the gradients of the lines.

For point A and B with coordinates:

For points (2, 3) and (5,8)

For the points (-7, 5) and (-12, 8)

• Two lines are said to be ,parallel, ,if their gradients are the same.

• Two lines are said to be ,perpendicular ,if the ,product of the gradients is -1.

Product of the two gradients

Since the product of the gradients is -1, the two lines are said to be perpendicular.

The correct option is D

Kali needs to work between 10 to 22 hours to earn an income between 200 and 400

Flat fee earned by Kali = 50

Earning per hour of Kali = 15.75

Required income is between 200 and 400

Inequality: Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

Inequality represents the equation:

200<=15.75x + 50<=400

200<= 15.75x + 50

150<= 15.75x

x = 9.52

So, she needs to work a minimum of 10 hours

15.75x+50<=400

15.75x <=350

x <= 22.22

So, she can work a maximum of 22 hours

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One rational number between -0.45 and -0.46 is -0.451, such that:

-0.45 > -0.451 > -0.46

So we want to find a rational number between -0.45 and -0.46. Remember that any decimal number with a finite number of digits after the decimal point (like the above numbers) is a rational number.

So:

3.16436

2.21412

1.4

All of these are rational numbers.

Then a rational number on the interval -0.45 and -0.46 could be -0.451, which is smaller than -0.45 and larger than -0.46

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Answer: 10%

Step-by-step explanation:

2 out of 20 people are willing to pay a maximum of 4.01 to 5 which is 0.10 which equals 10%

The overall percentage reduction in the price of the radio is 40%.

Percentage is the fraction of an amount expressed as a number out of hundred. Percentage is a measure of frequency. The sign that is used to represent percentages is %.

Let's assume that that initial price of the radio is 100.

Price of the radio after the 20% decline in price = (1 - 0.2) x 100

0.8 x 100 = 80

Price of the radio after the 25% decline in price = (1 - 0.25) x 80

0.75 x 80 = 60

The percentage decline in price = (initial price / final price) - 1

(60 / 100) - 1 = 0.4 = 40%

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Given the Subtraction:

You can identify that the denominators are different, then, you need to follow these steps in order to find the Difference (the result of the Subtraction):

1. Find the Least Common Denominator (LCD):

- Decompose the denominators into their Prime Factors:

- Multiply the common and non-common factors with the largest exponents:

2. Divide the LCD by each original denominator and multiply the Quotient by the corresponding numerator:

3. Subtract the whole number parts and then subtract the fractions. You get:

Hence, the answer is:

The z-score values for the given quantile are found.

For the given question;

The given normal quantile plot are-

-1.28, -0.52, 0.00, 0.52, 1.28

The corresponding z-score taken from the positive and negative z table are-

The z-score values for the given quantile are found.

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Question on Compound Interest.

The formula below can be used to calculate the compound interest;

Where A= ? , P =$2000, r =2.5% and n = 10 years

Substituting these values into the formula above, we get

Note that: Amount = Principal + Interest, though not needed in this question.

Thus, the correct answer is $2560.17

To solve this problem, we will use the formula for compound interest:

Where:

• Pₙ = principal amount after N years,

• P₀ = initial principal amount,

• r = interest ratio in decimals,

• k = compound periods per year.

From the statement, we know that:

• N = 3.4 years,

• P₀ = $56,000,

• Pₙ = P₀ + interest = $56,000 + $1,400 = $57,400,

• r = ?,

• k = 4 (the interest is compounded quarterly.

Replacing these values in the formula above, we get:

The annual interest must be 0.73%.

Answer:

  zero

Step-by-step explanation:

You want Amy Van's average velocity when she swims 50 m to the end of the pool and back.

Average velocity is the ratio of the change in position to the amount of time over which that change occurs. When Amy ends up where she started, she has not changed position at all, so her average velocity is ...

  Vave = (change in position)/time = 0/time = 0

Her average velocity is zero.

Given the function:

The end behaviour of the function f(x) describes the behaviour of the function as x approaches +∞ and -∞.

When x approaches +∞,

Thus, as x approaches +∞, the function f(x) approaches zero.

When x approaches -∞,

Thus, as x approaches -∞, the function f(x) approaches zero.

x-value of the hole:

For a rational function f(x) given as

Provided that p(x) and q(x) have a common factor (x-a), the function f(x) will have a hole at x=a.

Thus, from the function f(x)

by expansion, we have

The expression (x-1) is a common factor of the numerator and the denominator.

Thus,

Hence, the x-value of the hole is 1.

[tex] { 3 }^{ - 1} \times {3}^{x + 1} - { 3}^{x - 2} + {3}^{ - 2} \times { 3}^{x + 3} = 35 \\ {3}^{ - 1 + x + 1} - {3}^{x - 2} + {3}^{ - 2 + x + 3} = 35 \\ {3}^{x} - {3}^{x - 2} + { 3}^{ - 2 + 3 + x} = 35 \\ { 3 }^{x} - {3}^{x - 2} + {3}^{x + 1} = 35 \\ {3}^{x} - {3}^{x} \times {3}^{ - 2} + {3}^{x} \times {3}^{1} = 35 \\ {3}^{x} (1 - {3}^{ - 2} + 3) = 35 \\ {3}^{x} (3 + 1 - \frac{1}{9}) = 35 \\ \\ {3}^{x} (4 - \frac{1}{9} ) = 35 \\ {3}^{x} ( \frac{35}{9} ) = 35 \\ \frac{ {3}^{x}( \frac{35}{ 9 } )}{ \frac{35}{9} } = 35 \div ( \frac{35}{9} ) \\ {3}^{x} = 9 \\ {3}^{x} = { 3 }^{2} \\ x = 2[/tex]

ATTACHED IS THE SOLUTION.

I USED THE LAWS OF EXPONENTS.

GOODLUCK.

We know that the angle terminates in the fourth quadrant and that the tangent of it is -3/4.

Angles that are on the fourth quadrant have a negative sine and a positive cosine.

We can start with the cot():

We can relate the cosine with the tangent as:

We can now calculate the sine of the angle as:

We can now calculate the sec() and csc() as:

Answer:

sin() = -3/5

cos() = 4/5

cot() = -4/3

sec() = 5/4

csc() = -5/3

We can see that if we rotate P 90° counterclockwise it would be located in the first quadrant. So it can be A or B. But A forms a 90° with the position of point P. So, the answer is A.

we have that the figure of a rectangle and a triangle. So the area of this figure is:

so the answer is 68 in^2

1. it has infinite solutions because since the equations are equal it is a line equation and a line has infinite points

2. It will have only one solutions, because the lines aren't parallel or the same line (we know that because there won't be a number that you can multiply by one of the equations and obtain the other one)

3.it has infinite solutions because since the equations are equal it is a line equation and a line has infinite points

Answer:

1. 6 units

2. 13 units

3. 5 units

Step-by-step explanation:

The Solution.

The correct answer is y = 0.34x - 0.9 (option A ).

Step 1:

First, we shall determine the slope of the line by picking two coordinates from the table.

Answer:

y = 3x+3

Step-by-step explanation:

The rate of change, or slope, in this case, is 3, as we can either count the increase in y-values or perform the Δy/Δx (slope equation: [tex]\frac{9-3\\}{2-0}[/tex])to yield three, meaning that the (3x) in this equation would be the slope. Since the y-intercept is the constant in the equation and the y-intercept is always when x=0 (when the graph crosses the y-axis) on the XY plane, we can just subtract 3 from the x=1 coordinate, meaning that the y-intercept/x=0 coordinate would be (0, 3), leaving 3 as the constant.

Therefore,

the equation is y = 3x+3.

Answer:

6:20 - 2:4 (simplified)

Step-by-step explanation:

20 total slips

6 red slips

Answer: A relation is just a relationship between x and y-coordinates. It maps inputs to outputs. A function is just a special kind of relation: any input has exactly one output.

Step-by-step explanation:

Answer:A rate of change is a rate that describes how one quantity changes in relation to another quantity. Constant rate is also called as uniform rate which involves something travelling at fixed and steady pace or else moving at some average speed. For example, A car travels 3 hours.

Step-by-step explanation:

Answer:

The correct answers are below, if you want a more in depth explanation let me know and I will provide

Step-by-step explanation:

- The Diver surfaced 3 min before the Watcher

- When the noticed was received, the Diver was 20 ft deeper than the watcher

- 3 Min after receiving the notice, the diver and the watcher are at the same depth

Based on the sequence given of 3,5,8,12,17, it would be incorrect to say that the sequence is arithmetic. The sequence is not arithmetic.

In an arithmetic sequence, one would find that the number that separates each of the figures in the sequence is the same. In other words, the common difference between each figure is the same.

For instance, 2, 5, 8, 11, 14 has the common difference of 3 so this is an arithmetic sequence.

The sequence given of 3,5,8,12,17 is not arithmetic because the difference between each number is not common and instead increases.

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