A small theater had 7

rows of 26

chairs each. An extra 9

chairs have just been brought in. How many chairs are in the theater now?

ANSWER

A. {75, 145, 198, 214}

EXPLANATION

From the given information,the income is given by the function

[tex]f(x) = 2x + 54[/tex]

where f(x) is the income in dollars and x is the area in square meters of lawn mowed.

To find the area that corresponds to John's earnings, we equate the function to the earnings and solve for x.

For the area that corresponds to 204, we have

[tex]2x + 54 = 204[/tex]

[tex]2x = 204 - 54[/tex]

[tex]2x = 150[/tex]

[tex]x = 75[/tex]

For the area that corresponds to 344, we have:

[tex]2x + 54 = 344[/tex]

[tex]2x = 344 - 54[/tex]

[tex]2x=290[/tex]

[tex]x = 145[/tex]

For the area that corresponds to 450, we have

[tex]2x + 54 = 450[/tex]

[tex]2x= 450 - 54[/tex]

[tex]2x =396[/tex]

[tex]x = 198[/tex]

For the area that corresponds to 482, we have

[tex]2x + 54 = 482[/tex]

[tex]2x= 482 - 54[/tex]

[tex]2x = 428[/tex]

[tex]x = 214[/tex]

Therefore the correct answer is A.

Answer:

unit pay 10

slope  10

Step-by-step explanation:

$40/4hr = $10/1hr =10

Answer:

The Answer is D

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Equation of a circle: (x - h)² + (y - k)² = r

h is the x-coordinate of the center, and k is the y-coordinate.

Here, h is 3 and y is -2.

So, we find the circle which has the center of (3, -2).

That is D, because the center is 3 to the right and 2 down from the origin.

Answer:

x is 12

Step-by-step explanation:

Write a proportion

4:5

x:15

or you can write it as 4/5=x/15

Cross multiply and you get 12  

The value of x if the scale factor of figure A to figure B is 4:5 is; x = 12

We are given the scale factor of figure A to figure B as 4:5.

Now, looking at both triangles, we can say that;

x:15 = 4:5

Thus,we can write in fraction as;

x/15 = 4/5

x = 15 × 4/5

x = 12

In conclusion, the value of x from the given proportion between both triangles is 12.

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Answer:

4     5

8     10

20    25

5,20

Step-by-step explanation:

Answer:

Area of the parking lot = 6525 ft²

Explanation:

Since the two isosceles right-angled triangles have equal bases and heights, therefore, their areas are equal

Therefore:

Area of the parking lot = area of rectangle + 2*area of isosceles triangles

1- getting the area of the rectangle:

Area of rectangle = length * width

We are given that the dimensions of the rectangle are 45 ft and 100 ft

Therefore:

Area of rectangle = 45 * 100 = 4,500 ft²

2- getting the area of the isosceles triangle:

Area of triangle = 0.5 * base * height

From the drawing, we can note that:

base of triangle = height of triangle = smaller side of the rectangle = 45 ft

Therefore:

Area of triangle = 0.5 * 45 * 45 = 1,012.5 ft²

3- getting the total area:

Total area of parking lot = area of rectangle + 2*area of isosceles triangles

Total area of parking lot = 4500 + 2(1012.5)

Total area of parking lot = 6,525 ft²

Hope this helps :)

Answer:the anwser is B I am not 100% positive because a seems like it make sense to

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

30 divided by 4 = 7.5

75 divided by 10 = 7.5

The answer is C. Jason goes 2 miles per every 15 minutes. If Jason goes 10 miles you would multiply 15 by 5 and that is 75.

Answer:

The answer is 6.

Step-by-step explanation:

Remember,  Gloria can knit one block in 50 minutes, and they want to know how many blocks she can knit in 5 whole hours.

Which means, that is 5 squares in 4 hours, but we still have the 10 minutes from each of the 50 minutes.

So, you add up the 5 ten minutes (50 minutes) Which gives you a whole square.

Therefore, Gloria can knit 6 squares in 50 minutes.

Gloria can knit 6 blocks in 5 hours if she maintains her knitting rate of one block every 50 minutes.

Gloria can knit one block of a quilt in 50 minutes. To find out how many blocks she can knit in 5 hours, one should first convert the knitting time from hours to minutes. Since there are 60 minutes in an hour, 5 hours is equal to 300 minutes. Next, divide the total available knitting time by the time it takes to knit one block.

300 minutes / 50 minutes per block = 6 blocks
So, if Gloria knits at the same rate, she can knit 6 blocks in 5 hours.

Answer:

Step-by-step explanation:

First, you need to make these conversions:

(Remember that [tex]1m=100cm[/tex])

4,000 cm to m:

[tex](4,000cm)(\frac{1m}{100cm})=40m[/tex]

700 cm to m:

[tex](700cm)(\frac{1m}{100cm})=7m[/tex]

You can observe in the figure that it is formed by  two rectangles and a semi-circle.

To calculate the perimeter, you need to add the exterior measures of each figure.

Remember that the circumference of a circle is:

[tex]C=2\pi r[/tex]

Where "r" is the radius

Therefore, the perimeter is:

[tex]P=34m+7m+10m+40m+10m+68m+33m+\frac{(2\pi (17m)}{2}\\P=255.40m[/tex]

To find the area of the indoor sports exhibition, you need to add the areas of the rectangles and the area of the semi-circle.

The area of a rectangle can be calculated with:

[tex]A_r=lw[/tex]

Where "l" is the lenght and "w" is the width.

The area of a semi-circle can be calculated with:

[tex]A_{sc}=\frac{\pi r^2}{2}[/tex]

Where "r" is the radius.

Then, the area of the indoor sports exhibition  is:

[tex]A=(40m)(10m)+(68m)(33m)+\frac{\pi (17m)^2}{2}\\A=3,097.96m^2[/tex]

For this case we have that by definition, the coordinates of the midpoint are given by:

[tex]M = (\frac {x_ {1} + x_ {2}} {2}, \frac {y_ {1} + y_ {2}} {2})[/tex]

We have the following points:

[tex](x_ {1}, y_ {1}) :( 8, -3)\\(x_ {2}, y_ {2}): (- 5, -9)[/tex]

Substituting the values:

[tex]M = (\frac {8 + (- 5)} {2}, \frac {-3 + (- 9)} {2})\\M = (\frac {8-5} {2}, \frac {-3-9} {2})\\M = (\frac {3} {2}, \frac {-12} {2})\\M = (1.5; -6)[/tex]

Answer:

Option C

Answer:

(1.5, -6) ~apex

Step-by-step explanation:

Hey there!

First, the minus sign is equal to -1 (in this case)

Now, let's distribute -1 by multiplying it times 5 and -3v:

-5+3v

or

3v-5

Both expressions are equivalent (equal to each other)

Hence, the answer is

[tex]\boxed{\boxed{\bold{3v-5}}}[/tex]

Hope everything is clear.

Let me know if you have any other questions.

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To simplify the expression -(5-3v) using the distributive property, distribute the negative sign to each term inside the parentheses and combine like terms.

To simplify the expression -(5-3v) using the distributive property, we need to distribute the negative sign to each term inside the parentheses. This means we will multiply -1 by both 5 and -3v.

The distributive property states that for any numbers a, b, and c, a(b + c) is equal to ab + ac. Applying this property to our expression, we get -(5) - (-3v), which simplifies to -5 + 3v.

Therefore, the simplified expression is -5 + 3v.

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Answer:

The awnser is Street A

Step-by-step explanation:

Answer:

f(x) = (x + 4)² - 13

Step-by-step explanation:

You will have to "complete the square [½B]²" to figure this out. Here is how you would set it up:

(x + 4)² → x² + 8x + 16

x² + 8x + 16 - 13 → x² + 8x + 3 [TA DA!]

We know that our vertex formula is correct. Additionally, that -h gives you the OPPOSITE terms of what they really are, and k gives you the EXACT terms of what they really are. Therefore, your vertex is [-4, -13].

I am joyous to assist you anytime.

Check the picture below.

make sure your calculator is in Degree mode.

Thus, the kite is height of 400 ft above the ground.

Hence, option B is correct.

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that,

Hypotenuse of tringle = 520 ft

And inclination angle = 50.2 degree

We know that if any one of interior angle is of 90 degree then the angle is said to be right angle triangle.

Since,

sinΘ = (opposite side of Θ)/Hypotenuse

Therefore,

⇒ sin50.2 = Height/520         (since opposite side is height of triangle as shown in figure)

⇒ 0.76 = Height/520  

⇒ Height = 395.2 feet ≈ 400ft  (in nearest foot)

Hence,

Height of kite is 400 ft.

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Answer:

[tex]x>5[/tex] or [tex]x<-5[/tex]

Step-by-step explanation:

Isolate the absolute value term.

[tex]7|\frac{x}{7}|>5 \\ \\ |\frac{x}{7}|>35[/tex]

Take about the absolute value sign.

[tex]\frac{x}{7}>5[/tex] or [tex]-\frac{x}{7}>5[/tex]

Solve for each inequality.

[tex]x>5[/tex] or [tex]x<-5[/tex]

Answer:

Step-by-step explanation:

the answer is 365,412

Answer:

multiply 22.8 by 22.8

Step-by-step explanation:

If you are referring to the question in the attachment, the answer is the one I have selected!

Or "f(x) has the greater maximum."

Hope this helps

Answer:

B

Step-by-step explanation:

[tex]m+4\leq6[/tex]

We subtract 4 from each side to get [tex]m\leq2[/tex]

Let's plug in a random point such as 0.

[tex]0+4\leq6 \\ \\ 4\leq6[/tex]

Since this is true, the inequality we made is true.

The distance between the point (-3, -4) and the line 2y = -3x + 6 is 23 ÷ 13.

The distance between the point (-3, -4) and the line given by the equation 2y = -3x + 6 can be found using the point-to-line distance formula:

D = |Ax + By + C| ÷ (A^2 + B^2)

Firstly, we want to put the line equation in the standard form of Ax + By + C = 0. Let us rearrange the given equation of the line to this form:

3x + 2y - 6 = 0

Where A = 3, B = 2, and C = -6. Using the point (-3, -4), we plug the values into the point-to-line distance formula:

D = |3(-3) + 2(-4) - 6| ÷(3^2 + 2^2)

D = |-9 - 8 - 6| ÷(9 + 4)

D = | -23 | ÷ 13

D = 23 /÷ 13

Since ÷ 13 is an irrational number, we can't simplify it further. Therefore, the distance is:

D = 23 ÷ 13

Answer:

[tex]\large\boxed{1\dfrac{3}{5}\times2\dfrac{1}{7}=3\dfrac{3}{7}}[/tex]

Step-by-step explanation:

Step 1:

Convert the mixed numbers to the improper fractions:

[tex]1\dfrac{3}{5}=\dfrac{1\cdot5+3}{5}=\dfrac{8}{5}\\\\2\dfrac{1}{7}=\dfrac{2\cdot7+1}{7}=\dfrac{15}{7}[/tex]

Step 2:

We multiply the numbers remembering about simplifying:

[tex]1\dfrac{3}{5}\times2\dfrac{1}{7}=\dfrac{8}{5\!\!\!\!\diagup_1}\times\dfrac{15\!\!\!\!\!\diagup^3}{7}=\dfrac{8\times3}{1\times7}=\dfrac{24}{7}=\dfrac{21+3}{7}=\dfrac{21}{7}+\dfrac{3}{7}=3\dfrac{3}{7}[/tex]

Answer:

Median = 18

Step-by-step explanation:

The median is the middle number if the elements (prices)  are arranged from least to greatest.

let's arrange the prices of watches from least to greatest:

12, 15, 16, 16, 20, 22, 24 27

Since there are even number of numbers (8), the median is the value between 4th and 5th numbers.

4th number is 16

5th number is 20

We need the value between 16 and 20. We get that by adding these 2 and dividing by 2:

16 + 20 = 36

36/2 = 18

THus, median = 18

there are 12 inches in 1 foot, so 6 inches is really just half a foot, thus 3'6" is really just 3.5' or 3½ feet.

now, let's convert those mixed fractions to improper fractions and then subtract, bearing in mind our LCD will be 8.

[tex]\bf \stackrel{mixed}{4\frac{5}{8}}\implies \cfrac{4\cdot 8+5}{8}\implies \stackrel{improper}{\cfrac{45}{8}}~\hfill \stackrel{mixed}{3\frac{1}{2}}\implies \cfrac{3\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{7}{2}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{45}{8}-\cfrac{7}{2}\implies \stackrel{\textit{using the LCD of 8}}{\cfrac{(1)45~~-~~(4)7}{8}}\implies \cfrac{45-28}{8}\implies \cfrac{17}{8}\implies 2\frac{1}{8}[/tex]

She has 1 and 1/8 foot of wood left.

3 feet and 6 inches is equal to 3 and 1/2 feet.

3 and 1/2 feet are also equal to 3 and 4/8 feet.

Subtract 3 4/8 from 4 5/8.

4 5/8 - 3 4/8 = 1 1/8.

Hope this helps!

If it does, it would help me a lot if you could make me brainliest.

Answer:

See explanation

Step-by-step explanation:

Zeros of the function are those values of x, for which g(x)=0, so solve the equation g(x)=0:

[tex]x^3-x^2-4x+4=0\\ \\x^2(x-1)-4(x-1)=0\\ \\(x-1)(x^2-4)=0\\ \\(x-1)(x-2)(x+2)=0\\ \\x_1=-2,\ x_2=1,\ x_3=2[/tex]

Hence, the function has three zeros, x=-2, x=1 and x=2.

To find the y-intercept, substitute x=0:

[tex]y=g(0)=0^3-0^2-4\cdot 0+4=4,[/tex]

so y-intercept is at point (0,4).

The graph of the function shows that when x is infinitely small, then y is infinitely small too and if x is infinitely large, then y is infinitely large too.

Answer:

The zeros: x = 1, -2, 2

The y-intercept:  (0, 4)

The end behavior :

x  --> + ∞, f(x) --> + ∞

x  --> - ∞, f(x) --> - ∞

Step-by-step explanation:

Zero function:

x^3 - x^2 - 4x + 4 = 0

(x^3 - x^2) - (4x - 4) = 0

x^2(x - 1) - 4(x - 1) = 0

(x^2 - 4)(x - 1) = 0

(x + 2)(x - 2)(x - 1) = 0

x + 2 = 0; x = -2

x - 2 = 0; x = 2

x - 1 = 0; x = 1

The zeros: x = 1, -2, 2

The y-intercept when x = 0 so y-intercept = 4 or (0, 4)

The end behavior of a function f(x) :  the behavior of the graph of the function at the ends of the x-axis.

As x approaches + ∞, f(x) approaches + ∞

As x approaches - ∞, f(x) approaches - ∞

The perimeter of a square, if half of a diagonal is equal to 8 inches would be [tex]32\sqrt{2}[/tex] inches.

In Mathematics and Geometry, the perimeter of a square can be calculated by using the following formula;

P = 4s

Where:

In Mathematics and Geometry, the side length of a square can be calculated by using this mathematical equation (formula);

Diagonal, d = √2s

d/2 = 8

d = 16 inches.

By solving for s, we have the following side length:

s = 16/√2

s = [tex]8\sqrt{2}[/tex] inches.

Now, we can determine the perimeter of the square is given by;

P = 4 × [tex]8\sqrt{2}[/tex] inches.

P = [tex]32\sqrt{2}[/tex] inches.

Answer:

A = choosing a red marble

B = choosing a green marble

Probability of A happening = P(A) = 5/(3+5+4) = 5/12

Probability of B happening = P(B) = 4/(3+5+4) = 4/12

Probability of either happening = P(A) + P(B) = 5/12 + 4/12 = 7/12

The key word in their question is red OR green and that is why we add the two probabilities. If they ask the probability of them both happening (if they said red AND green), you would multiply P(A)*P(B).

The probability that the chosen marble is not red is [tex]\frac{7}{12}[/tex].

A probability is a number that reflects the chance or likelihood that a particular event will occur.

The formula of the probability is

[tex]P(E) = \frac{Number\ of\ favorable\ outcomes}{Total\ number\ of\ outcomes }[/tex]

Where, P(E) is the probability of an event.

According to the given question.

Number of red marbles = 5

Number of blue marbles = 4

Number of green marbles = 3

So,

The total number of marbles in a bag = 5+4+3 = 12

And, the probability that chosen marble is red = [tex]\frac{5}{12}[/tex]

Therefore,

the probability that the chosen marble is not red

[tex]=1-\frac{5}{12} \\[/tex]

[tex]= \frac{12-5}{12}[/tex]

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

Hence, the probability that the chosen marble is not red is [tex]\frac{7}{12}[/tex].

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For number 1 the answer is A because negative correlation means something decrease as times goes on and for number 2 the answer is B because it is the best fit and is not really far away if you sustract.hope this helps. please add brainlist

The answer is:

{-5<x<5}

To solve the problem, we need to remember how Absolute Value Functions behave, when we have this type of function, related to an inequality, the solution will be between two values.

We are given the inequality:

[tex]|x|<5[/tex]

So, we know that "x" will be between -5 and 5:

[tex]-5<x<5[/tex]

Hence, the solution of the given inequality will be:

(-5,5) or {-5<x<5}

Have a nice day!

Answer:

{x|-5 < x < 5}

Step-by-step explanation:

I got the answer right.

[tex]\bf \qquad \qquad \textit{joint compound proportional variation} \\\\ \begin{array}{llll} \textit{\underline{y} varies directly with \underline{x}}\\ \textit{and inversely with \underline{z}} \end{array}\implies y=\cfrac{kx}{z}\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \stackrel{\textit{W varies jointly as its width, squared heght and inversely with length}}{W=\cfrac{wh^2}{L}}[/tex]

[tex]\bf \textit{now we also know that }~~ \begin{cases} w=\frac{1}{4}\\ h=\frac{1}{3}\\ L=12\\ W=30 \end{cases}\implies 30=\cfrac{~~k\frac{1}{4}\left( \frac{1}{3} \right)^2~~}{12} \\\\\\ 360=\cfrac{k}{36}\implies 12960=k~\hfill \boxed{W=\cfrac{12960wh^2}{L}}[/tex]

[tex]\bf \textit{when } \begin{cases} w=\frac{1}{4}\\ h=\frac{1}{2}\\ L=12 \end{cases}\textit{ what is \underline{W}?}\qquad W=\cfrac{12960\left( \frac{1}{4} \right)\left(\frac{1}{2} \right)^2}{12} \\\\\\ W=1080\left( \cfrac{1}{4} \right)\left( \cfrac{1}{4} \right)\implies W=1080\cdot \cfrac{1}{16}\implies W=\cfrac{135}{2}\implies W=67\frac{1}{2}[/tex]

Using the joint variation, A similar beam can support [tex]67 \frac{1}{2}[/tex] feet if the beam is one-fourth foot wide and half a foot high, and 12 feet long.

What is Proportion

A proportion is an equation stating that two rational expressions are equal. Simple proportions can be solved by applying the cross products rule.

If [tex]\frac{a}{b} = \frac{c}{d}[/tex] then ab = bc.

What is Direct variation?

The phrase “ y varies directly as x” or “ y is directly proportional to x” means that as x gets bigger, so does y, and as x gets smaller, so does y. That concept can be translated in two ways.

[tex]\frac{y}{x} = k[/tex] for some constant k.

The k is called the constant of proportionality. This translation is used when the constant is the desired result.

What is Inverse Proportion?

According to the expressions "y varies inversely as x" and "y is inversely proportionate to x," y decreases as x increases or vice versa. There are two translations for this idea. For any constant k, referred to as the constant of proportionality, yx = k. If the constant is wanted, use this translation.

What is Joint Variation?

Joint variation is the term used to describe when one variable changes as the sum of other variables. There are two translations for the phrase "y fluctuates concurrently as x and z."

So, In the given question:

Weight that a rectangular beam can support varies jointly as its width and the square of its height and inversely as its length;

It is in joint proportion;

[tex]\begin{aligned}&\mathbf{W}=\frac{\mathbf{w h}^2}{\mathbf{L}} \\&\left\{\begin{array}{l}w=\frac{1}{4} \\h=\frac{1}{3} \\L=12 \\W=30\end{array} \quad \Longrightarrow 30=\frac{\mathbf{k} \frac{1}{4}\left(\frac{1}{3}\right)^2}{12}\right.\end{aligned}[/tex]

[tex]360=\frac{\mathrm{k}}{36} \Longrightarrow 12960=\mathrm{k}[/tex]

Now,

[tex]\text { when }\left\{\begin{array}{l}w=\frac{1}{4} \\h=\frac{1}{2} \\L=12\end{array}\right.[/tex]

[tex]W=\frac{12960\left(\frac{1}{4}\right)\left(\frac{1}{2}\right)^2}{12}[/tex]

[tex]W=1080\left(\frac{1}{4}\right)\left(\frac{1}{4}\right) \\\Longrightarrow W=1080 \cdot \frac{1}{16}[/tex]

[tex]\\\Longrightarrow\mathrm{W}=\frac{135}{2} \\\Longrightarrow \mathrm{W}=67 \frac{1}{2}[/tex]

Hence, A similar beam can support [tex]67 \frac{1}{2}[/tex] feet if the beam is one-fourth foot wide and a half a foot high, and 12 feet long.

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