Elena wants to make a scale drawing of her bedroom. Her bedroom is a rectangle with length 500 cm and width 300 cm. She decides on a scale of 1 to 50.

b. Elena's bedroom door is 80 cm wide. How wide should the door be on the scale drawing? Explain your reasoning.

(*Hint #1* a good explanation uses Words, Numbers, or Pictures to justify your thinking).

4b = 5b - 3a # Starting equation, solve for 'a'

-b = -3a # Subtract 5b from both sides

\(\frac{b}{3}\)  = a # Divide both sides by -3.

a = \(\frac{b}{3}\) # Use the reflexive property of equality

Hope this answers your question!

My recommendation to Carlos and Clarita would be to prepare for 3 cats and 3 dogs. This combination offers the highest profit potential based on the given prices and costs.

In order to maximize their profit, Carlos and Clarita should choose the combination of cats and dogs that yields the highest total profit.

In order to make a reasonable recommendation, we can create a profit table based on different values of x and y:

x y Total Profit

0 0 0

1 0 6

0 1 15

1 1 21

2 1 27

1 2 30

2 2 36

3 2 42

2 3 45

3 3 51

From the table, we can see that the highest total profit is achieved when they accommodate 3 cats and 3 dogs. This combination would result in a daily profit of $51.

Therefore, my recommendation to Carlos and Clarita would be to prepare for 3 cats and 3 dogs.

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a. It will take 7 months to pay off the credit card.

b. it will take 4 months to pay off the credit card.

Since, APR stands for Annual Percentage Rate. It is the interest rate charged on a loan or credit card, expressed as a yearly percentage rate. The APR takes into account not only the interest rate, but also any fees or charges associated with the loan or credit card.

a. If you put half of the available money each month toward the credit card, then you are paying $150.00 per month towards the credit card balance.

We can use the formula for the present value of an annuity to find how many months it will take to pay off the credit card:

PV = PMT × ((1 - (1 + r)⁻ⁿ) / r)

where:

PV is the present value of the debt

PMT is the payment amount per period

r is the monthly interest rate

n is the number of periods

Substituting the values, we get:

754.43 = 150 × ((1 - (1 + 0.011333)⁻ⁿ) / 0.011333)

Simplifying and solving for n, we get:

n = log(1 + (PV ×r / PMT)) / log(1 + r)

n = log(1 + (754.43×0.011333 / 150)) / log(1 + 0.011333)

n = 6.18

Therefore, it will take 7 months to pay off the credit card if you put half of the available money each month toward the credit card.

b. If you put all of the available money each month toward the credit card, then you are paying $300.00 per month towards the credit card balance.

754.43 = 300 ×((1 - (1 + 0.011333)⁻ⁿ) / 0.011333)

Simplifying and solving for n, we get:

n = log(1 + (PV × r / PMT)) / log(1 + r)

n = log(1 + (754.43× 0.011333 / 300)) / log(1 + 0.011333)

n = 3.43

Therefore, it will take 4 months to pay off the credit card if you put all of the available money each month toward the credit card.

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The amount that the taxpayer is owing in taxes is $2,691.05.

We have,

Income tax payable refers to a business organization's tax liability to the government in the jurisdiction in which it operates. The amount of liability will be determined by the company's profitability over a given time period and the applicable tax rates. Tax payable is considered a current liability rather than a long-term liability because it must be settled within the next 12 months.

Based on the table, we are using the tax rate of 15% for the taxable income of $11,757.

The tax payable will equals to:

= 15%*$11,757 + $927.50

= $1,763.55 + $927.50

= $2,691.05

Hence, The amount that the taxpayer is owing in taxes is $2,691.05.

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complete question:

Based on this table, if someone had a taxable income of $11,757, how much would they owe in taxes?

Answer:

h = 14 units

Step-by-step explanation:

area of parallelogram = bh

plug everything in: 84 = (6)h

h = 84/6 = 14

Answer:

171 > 117

Step-by-step explanation:

171 is greater than 117 meaning the alligator is eating the bigger number, 171.

Answer:

s≤ -2, and s≥ 2

Step-by-step explanation:

The domain means all possible values, so we need to find all possible values for which \(\sqrt{s^2-4}\) is true. It would not be true if the expression under the square root equals to 0 or is less a negative number, so we need to find the numbers that would make the square root 0, and go from there. Why can't the expression under the square root be less than zero? Because you cannot find the square root of a negative value.

In this case, if s was 2 or -2, then the expression under the root would equal 0. This also means that any number between 2 and -2 would make the expression negative.

If s was 0, the expression would be \(\sqrt{0^2-4} = \sqrt{-4}\), it goes the same for any number between 2 and -2.

The domain, which is all possible values for this equation, would be that

\(s\leq -2\) or \(s\geq 2\). These inequalities would show that s would have to be greater or less than those numbers for the equation to be true.

The graph of \(y = 2 - \sqrt x\) is (c) a curved line that passes through points (0,2) and (3,0.3)

The function is given as:

\(y = 2 - \sqrt x\)

The above function is a square root function.

This means that the domain is \(x \ge 0\)

The domain implies that options (a) and (b) are false, because they include negative x values

For option (c); set x= 0 and 3

\(y = 2 - \sqrt 0 = 2\)

\(y = 2 - \sqrt 3 = 0.3\)

This means that the graph of \(y = 2 - \sqrt x\) is a curved line that passes through points (0,2) and (3,0.3)

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Answer: 18

Step-by-step explanation:

taking a looksie at the picture above, we can see the parabola has zeros/solutions at x = -2 and x = 1, we can also see that it passes through (0 , 2) as well, so

\(\begin{cases} x = -2 &\implies x +2=0\\ x = 1 &\implies x -1=0\\ \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{original~polynomial}{a( x +2 )( x -1 ) = \stackrel{0}{y}}\hspace{5em}\textit{we also know that} \begin{cases} x=0\\ y=2 \end{cases} \\\\\\ a ( 0 +2 )( 0 -1 ) = 2\implies -2a=2\implies a=\cfrac{2}{-2}\implies \boxed{a=-1} \\\\[-0.35em] ~\dotfill\\\\ -(x+2)(x-1)=y\implies -(x^2+x-2)=y\implies {\Large \begin{array}{llll} -x^2-x+2=y \end{array}}\)

Check the picture below.

Answer:

Step-by-step explanation:

To rewrite the equation x² + 18x + 7 = 4 in the form (x - p)² = q, we need to complete the square by adding and subtracting a constant term.

First, we subtract 4 from both sides of the equation:

x² + 18x + 7 - 4 = 0

Simplifying, we get:

x² + 18x + 3 = 0

To complete the square, we need to add and subtract the square of half the coefficient of x, which is (18/2)^2 = 81:

x² + 18x + 81 - 81 + 3 = 0

Simplifying, we get:

(x + 9)² - 78 = 0

Now, we can rewrite the equation in the desired form by adding 78 to both sides:

(x + 9)² = 78

Therefore, the values to be entered in the boxes are:

1: (x + 9)

2: 78

The rate of change of the function that is defined by the table:

X: 2 4 6 8 10

Y: 4 8 12 16 20

is r = 2

For a function with two known points (x₁, y₁) and (x₂, y₂), the rate of change between these two points is written as:

r = ( y₂ - y₁)/(x₂ - x₁)

Here we have the table that defines a function:

X: 2 4 6 8 10

Y: 4 8 12 16 20

Here we can use any pair of two points on the table, for example, if we use the first pair and last pair:

(2, 4) and (10, 20)

The rate is:

r = (20 - 4)/(10 - 2) = 16/8 = 2

If we use the first two pairs (2, 4) and (4, 8) we get:

r = (8 - 4)/(4 - 2) = 4/2 = 2

So the rate of change of the function is r = 2.

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To draw a tree diagram for randomly choosing a letter from the word "bell" and another letter from the word "beep," follow these steps:

Step 1: Start by drawing a horizontal line. This line represents the first letter selection.

Step 2: Label the branches of the first letter selection with the letters from the word "bell": b, e, l, and l. Each branch represents one of these letters being selected.

Step 3: Extend each branch from Step 2 by drawing vertical lines. These lines represent the second letter selection.

Step 4: Label the branches of the second letter selection with the letters from the word "beep": b, e, e, and p. Each branch represents one of these letters being selected.

Step 5: Connect each branch of the first letter selection (from Step 2) to the corresponding branches of the second letter selection (from Step 4). This creates the complete tree diagram.

Thus, this way, one can create tree diagram.

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Answer:

34 total students.

25 are not 7th graders

27/35

The graph which represents the polar curve r = -4 sin ( 3θ ) is plotted

Polar coordinates describe the position of a point P in the plane by its separation from the origin, r, and the angle formed between the positive x-axis and the line segment leading to P.

To graph the polar curve, we make use of the following representations:

r represents the y-axis

θ represents the x-axis

Polar coordinates can also be extended into three dimensions using the coordinates (ρ, φ, θ), where ρ is the distance from the pole, φ is the angle from the z-axis ( called the co-latitude or zenith and measured from 0 to 180° ) and θ is the angle from the x-axis ( as in the polar coordinates ).

Given data ,

Let the polar curve be represented as A

Now , the polar coordinates is given as

r = -4 sin ( 3θ )

And , To graph the polar curve, we make use of the following representations:

r represents the y-axis

θ represents the x-axis

So , on simplifying , we get

The graph which represents the polar curve r = -4 sin ( 3θ ) is plotted

Hence , the polar curve is r = -4 sin ( 3θ )

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Answer:

D

Step-by-step explanation:

The slope of the line tangent to the graph of h(x) = 1/x + 3 at the point when x is -6 is -1/36.

To determine the slope of the line tangent to the graph of the given function when x = -6;

Using alternative form of the definition of derivative.

f'(a) = lim (h->0) [f(a+h) - f(a)] / h

Using this formula for the given function;

h'(a) = lim (h->0) [h(a+h) - h(a)] / h

Now, substitute a = -6 into the formula:

h'(-6) = lim (h->0) [h(-6+h) - h(-6)] / h

Next, simplify the expression by plugging in the values:

h'(-6) = lim (h->0) [1/(-6+h) + 3 - (1/-6 + 3)] / h

Simplifying further:

h'(-6) = lim (h->0) [1/(-6+h) - 1/-6] / h

Now, let's combine the fractions with a common denominator:

h'(-6) = lim (h->0) [(-6 - (-6+h))/((-6+h)(-6))] / h

Simplifying the numerator:

h'(-6) = lim (h->0) [-h / ((-6+h)(-6))] / h

Canceling out the h's:

h'(-6) = lim (h->0) [-1 / ((-6+h)(-6))]

Taking the limit as h approaches 0:

h'(-6) = -1 / ((-6)(-6))

Simplifying further:

h'(-6) = -1 / 36

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the interval over which the graph of f(x) = -(x + 3) - 1 is decreasing is (-∞, +∞).

What is a function?

A unique kind of relation called a function is one in which each input has precisely one output. In other words, the function produces exactly one value for each input value. The graphic above shows a relation rather than a function because one is mapped to two different values. The relation above would turn into a function, though, if one were instead mapped to a single value. Additionally, output values can be equal to input values.

The given function is:

f(x) = -(x + 3) - 1

To find the interval over which the function is decreasing, we need to find the values of x where the function's derivative is negative.

The derivative of the function is:

f'(x) = -1

The derivative is a constant, which means the function has a constant slope of -1. Since the slope is negative, the function is decreasing over its entire domain.

Therefore, the interval over which the graph of f(x) = -(x + 3) - 1 is decreasing is (-∞, +∞).

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Answer:

\(\frac{9344}{45}\)

Step-by-step explanation:

\(\frac{74752}{360}\)

Simplify by 8, and we get

\(\frac{9344}{45}\)

We can't simplify any more, so the answer is  \(\frac{9344}{45}\)

The required answer is the simplified fraction of the given problem 74752/360 is the whole fraction 9344/45, where 9344 represents the whole number part and 45 represents the fractional part.

To simplify the fraction 74752/360 as a whole fraction, we need to find the greatest common divisor (GCD) of the numerator and the denominator and divide both of them by it.

Step 1: Find the GCD of 74752 and 360. The GCD can be calculated using various methods, such as prime factorization or the Euclidean algorithm. In this case,  use the Euclidean algorithm.

Let's find the GCD using the Euclidean algorithm:

Divide 74752 by 360:

74752 ÷ 360 = 207 R 272

Divide 360 by 272:

360 ÷ 272 = 1 R 88

Divide 272 by 88:

272 ÷ 88 = 3 R 8

Divide 88 by 8:

88 ÷ 8 = 11 R 0

Since the remainder is 0, the GCD is the last non-zero remainder, which is 8.

Step 2: Divide both the numerator and denominator of the fraction by the GCD.

74752 ÷ 8 = 9344

360 ÷ 8 = 45

The simplified whole fraction is 9344/45.

A whole fraction refers to a fraction in which the numerator is equal to or greater than the denominator. It represents a whole number and a fraction together. For example, 3 1/4 is a whole fraction where the whole number part is 3 and the fractional part is 1/4.

Hence, the simplified fraction of the given problem 74752/360 is the whole fraction 9344/45, where 9344 represents the whole number part and 45 represents the fractional part.

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The flour and sugar coral that will be use to make the cookies is 2 1/4 cups.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.

In this situation, Tucker is making cookies the recipe called for 1/3/4 cups of flour and 1/2cup of sugar.

The flour and sugar coral that will be use to make the cookies will be:

= 1 3/4 + 1/2

= 2 1/4

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Answer:

Lower quartile = 65

Upper quartile = 95

Median = 80

Step-by-step explanation:

✔️Lower quartile = the value at the beginning of the edge of the rectangular box = 65

✔️Upper quartile = the value at the end of the edge of the rectangular box = 95

✔️Median = the value indicated by the vertical line that divides the box into two = 80

Answer:

Step-by-step explanation:

The slope is the change in y divided by the change in x

If (x₁, y₁) and (x₂, y₂) are points on the line

slope m = (y₂ - y₁) / (x₂ - x₁)

or

         m = (y₁ - y₂) / (x₁ - x₂)

Answer:

x + x - 45 = 90

2x - 45 = 90

2x = 135

x = 67.5, so x - 45 = 22.5

The other two angles measure 22.5° and 67.5°.

The sale price of the shoe is given as follows:

P3,436.

The sale price of the shoe is obtained applying the proportions in the context of the problem.

The initial price is of:

P 4,295.

The shoe is sold at a discount of 20%, meaning that the sale price is 80% of the initial price, and the value is given as follows:

0.8 x 4295 = P3,436.

The problem asks for the selling price of the shoe.

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The maximum number of pieces of drywall that can be installed before running out of screws is 0.

To determine the number of pounds of drywall that can be installed before running out of screws, we need to consider the weight of both the drywall and the screws.

Given:

12 screws are required per piece of drywall.

Each piece of drywall weighs 30 lbs.

Each screw weighs 0.011 lbs.

The company received a bulk order of 100 lbs of screws.

Let's denote the number of pieces of drywall as "x".

The weight of the screws can be calculated as:

Weight of screws = Number of screws × Weight per screw

Weight of screws = 12 screws × 0.011 lbs/screw

Weight of screws = 0.132 lbs

Now, we can calculate the maximum number of pieces of drywall that can be installed based on the weight of the screws:

Maximum number of pieces of drywall = Weight of screws / Weight per drywall piece

Maximum number of pieces of drywall = 0.132 lbs / 30 lbs

Maximum number of pieces of drywall ≈ 0.0044 pieces

Since it doesn't make sense to have a fraction of a drywall piece, we can round down the result. Therefore, the maximum number of pieces of drywall that can be installed before running out of screws is 0.

In conclusion, with the given bulk order of 100 lbs of screws, the company cannot install any drywall before running out of screws.

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Answer:

see below

Step-by-step explanation:

We want where  both inequalities are true

y > -3

-2 >-3  this is true

y ≥ 2/3x -4

-2≥ 2/3*3 -4

-2 ≥ 2 -4

-2≥ -2

This is true

This is is the graph

Answer:

\(\boxed{\sf Option \ 3}\)

Step-by-step explanation:

\(\sf The \ values \ must \ be \ true \ for \ both \ inequalities.\)

\(x = 3\\y = -2\)

\(y>-3\\-2>-3\\ \sf True\)

\(y\geq \frac{2}{3}x-4 \\ -2\geq \frac{2}{3}(3)-4\\2\geq 2-4\\-2\geq-2 \\ \sf True\)

Answer:

Step-by-step explanation:

\(\tt -33=x+1\)

First of all, let's flip the equation:-

\(\tt x+1=-33\)

Subtract 1 from both sides:-

\(\tt x+1-1=-33-1\)

Simplify:-

\(\tt x=-34\)

_________________

Hope this is what you're looking for!

Have a great day!

Answer:

-34

Step-by-step explanation:

Answer:

4(2 on top) + 3(2 on top) + 2(2 on top)

Step-by-step explanation:

The value of the expression (c² - d²) / (d² + cd - 2c²) in the simplified form will be negative (c + d) / (d + 2c).

When the relevant components and basic processes of a numerical method are given values, the expression's result is the result of the computation it depicts.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The expression is given below.

⇒ (c² - d²) / (d² + cd - 2c²)

Factorize the numerator and denominator, then we have

⇒ (c² - d²) / (d² + cd - 2c²)

⇒ (c² + cd - cd - d²) / (d² + 2cd - cd - 2c²)

⇒ [c(c + d) - d(c + d)] / [d(d + 2c) - c(d + 2c)]

⇒ [(c + d)(c - d)] / [(d - c)(d + 2c)]

⇒ - [(c + d)(d - c)] / [(d - c)(d + 2c)]

⇒ - (c + d) / (d + 2c)

The value of the expression (c² - d²) / (d² + cd - 2c²) in the simplified form will be negative (c + d) / (d + 2c).

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The formula to find the volume of a cylinder is:

In this case, we have:

Therefore, the volume of the cylinder is approximately 189