The length of a parking lot is 4 yards more than the width. If the area of the parking lot is 117 square yards, find the dimensions of the parking lot.

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[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{2}~,~\stackrel{y_1}{\frac{7}{2}})\qquad (\stackrel{x_2}{\frac{5}{3}}~,~\stackrel{y_2}{1})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{(\frac{5}{3}-2)^2 + (1-\frac{7}{2})^2}\implies d=\sqrt{(\frac{-1}{3})^2 + (-\frac{5}{2})^2} \\\\\\ d=\sqrt{\cfrac{1}{9}~~ + ~~\cfrac{25}{4}}\implies d=\sqrt{\cfrac{229}{36}}\implies d=\cfrac{\sqrt{229}}{\sqrt{36}}\implies d=\cfrac{\sqrt{229}}{6}[/tex]

The Simple interest after three month $423.70

What is Simple Interest ?

Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan. The daily interest rate, the principle, and the number of days between payments are multiplied to calculate simple interest.

If she deposits $366 in the account and you receive interest, you must first calculate the interest for the current year before adding the sum to calculate the interest for the following month.

for instance, deposit plus interest equals the new amount for month one, month one amount plus interest equals amount for month two, and month two amount plus interest equals amount for month three.

The total would thus be $423.70 for the following month:

month 1

366+ (366*.05)=x

366+18.3=x

month 2

384.30+(384.30*.05)=x

384.30+19.22=x

month 3

403.52+(403.52*.05)=x

403.52+20.18=x

423.7 = x

Thus, total amount then would be $423.70

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Answer:

C' = (13, 4)

Dilation by a scale factor of 2 with the origin (0, 0) as the center of dilation, followed by a translation of 3 units right.

Step-by-step explanation:

Given vertices of triangle ABC:

If two triangles are said to be similar:

To keep the corresponding angles of both triangles the same and maintain similarity, dilate triangle ABC.

If we compare the coordinates of B (1, 4) and B' (5, 8), the y-value has been multiplied by 2.

Therefore, the first step of the transformation is a dilation by a scale factor 2 with the origin (0, 0) as the center of dilation.

⇒ (1 × 2, 4 × 2) = (2, 8)

After multiplying the coordinates of B by two, the difference between the x-values of the dilated point and B' is 3, so the second step of the transformation is a translation of 3 units right.

Therefore, the series of transformations is:

Mapping Rule:  (x, y) → (2x+3, 2y)

Therefore, the coordinates of point C' are:

⇒ C' = (2(5) + 3, 2(2)) = (13, 4)

Answer:   (13, 4)

Infinitely many answers are possible.

====================================================

Explanation:

See this similar question

https://brainly.com/question/28933426

because I'll be using the same steps and ideas. There are also diagrams that might help visualize what's going on.

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The translation vector from B(1,4) to C(5,2) is <4,-2> since we move to the right 4 units, and down 2 units. It's the shorthand way of writing [tex](x,y) \to (x+4,y-2)[/tex]

Double the coordinates of the translation vector <4,-2> to get <8,-4>

If we started at point B'(5,8) and followed the pathway "right 8, down 4" then we arrive at C'(13,4) as one possible answer.

We could express the steps like this

[tex](\text{x},\text{y})\to(\text{x}+8,\text{y}-4)\\\\(5,8)\to(5+8,8-4)\\\\(5,8)\to(13,4)\\\\[/tex]

As I mentioned in the link above, there are infinitely many answers because we can change the scale factor to any nonnegative real number. For instance we could triple the coordinates of <4,-2> to get <12,-6> and follow the same outline of steps to get C'(17,2) as another possible answer.

answer: 4) -10

Answer:

Write down one equation or inequality that has more than two solutions, but not infinitely many solutions

Step-by-step explanation:

From the given table, it is found that:

a. The weight function is linear, as it has a constant rate of change.

b. The equation for the linear function is: W(x) = 0.85x + 2.22.

Linear functions are modeled according to the following rule:

y = mx + b.

In which the coefficients are:

The slope is the rate of change, and it has to be constant for the relation to be a linear function.

Relating the number of cans x and the cost of the cans C(x), the slope can be calculated as follows:

Different slopes, hence the cost function is not linear.

For the weight function, the slope can be calculated as follows:

Due to the constant rate of change, the weight function is a linear function.

Considering the slope of m = 0.85, the weight function can be written as follows:

W(x) = 0.85x + b.

When x = 8, W(x) = 6.8, hence the intercept b is found as follows:

8 = 0.85(6.8) + b

b = 8 - 0.85 x 6.8

b = 2.22.

Then the function is:

W(x) = 0.85x + 2.22.

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20 miles per hour converted to feet per second is 88/3 feet per second.

It is given in the question that there are 60 minutes in one hour and 60 seconds in one minute.

We have to convert 20 miles per hour in feet per second.

We know that,

1 mile = 5280 feet

1 hour = 60 minutes

1 minute = 60 seconds

Hence, we can write,

1 hour = 60*60 = 3600 seconds

1 mile per hour = 5280/3600 feet per second = 22/15 feet per second

Using unitary method, we can write,

20 miles per hour = 20*(22/15) = 88/3 feet per second or 29.3334 feet per second.

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Answer:

2.5×10^-11

Step-by-step explanation:

Put the point in the middle of 2 and 5 and count how many times you need to get there ...

like 0.05 to put point after 5 you have to jump 2 steps so it is 5×10^-2.

An expression exists as a number, a variable, or a combination of numbers and variables, and function symbols. The speed in still water exists 4 mph.

The acronym BODMAS, which stands for brackets of, division, multiplication, addition, and subtraction, might be used to simplify the expression. It specifies how to answer a mathematical expression in a particular order.

Let x be the speed in still water

[tex]$&\frac{5}{x+1}+\frac{6}{x-1}=3[/tex]

LCD = (x + 1)(x - 1)

[tex]$&(x+1)(x-1) \cdot \frac{5}{x+1}+(x+1)(x-1) \cdot \frac{6}{x-1}=(x+1)(x-1) \cdot 3 \\[/tex]

simplifying the above equation, we get

5(x - 1) + 6(x + 1) = 3(x + 1)(x - 1)

5x - 5 + 6x + 6 = 3 x² - 3

3x² - 11x - 4 = 0

(3x + 1)(x - 4) = 0

x = -1/3 (speed is not negative);

then we get x = 4 mph

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If Scampini has no debt or preferred stock, and its WACC is 12%, and it has zero nonoperating assets in which Scampini has 40 million shares of stock outstanding, the stock's value per share is $37.50.

Next year CF = $75 millions

Growth rate of CF = 7%

WACC = 12%

Number of shares outstanding = 40 million shares

Estimated business valuation:

Valuation = Next year CF/ (WACC -growth rate)

Valuation = $75 million / (12% - 7%)

Valuation = $75 million /5%

Valuation =$1500 million

Estimated stock price:

Stock price = Valuation /Shares outstanding

Stock price = $1500 million / 40 million shares

Stock price = $37.50

Therefore the stock price is $37.50.

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Answer: 415

Step-by-step explanation:

??

We take a look at the inequalities y > 2 and x >4. This means that the solutions must have values that has x > 4 and y > 2. Letters A, C, and E are candidates to be solution since they satisfy the inequalities provided. Using the inequality y > x, this means that the y value must be greater than the x value that we have. Letter A has higher x value than y value, hence, it will be crossed out. Both C and E has higher y values compared to their x values. Hence, the points that are solution to the system of inequalities provided are C. (9, 10) and E. (5, 6).

First, find the actual number of miles per round trip in each case.

-Hyperloop

-Airplane

Then, the cost (round trip) would be related to the constant b in both cases since it is a fixed rate. Multiply it by the maximum number of passengers,

Then, multiply the rate of consumption by the fuel costs for each mean of transportation,

Notice that it is multiplied by 2 since the rate of consumption row is given in one-way unitsThus,

EXPLANATION

To solve the given equation:

Step 1:

Multiply both-side of the equation by 2 in other to eliminate the denominator.

At the right-hand side of the equation, 2 add the numerator will cancel-out 2 at the denominator.

- 8 = v+ 6

step 2:

Subtract 6 from both-side of the equation.

That is;

-8 - 6 = v + 6 - 6

-14 = v

Hence, the value of v = -14

An equation for a parabola with​ x-intercepts (-3,0) and (4,0) which passes through the point (2,-40) is 5(x+3)(x-4)

Quadratic equations are equation that has a leading degree of 2. The standard quadratic equation is given as:

y = a(x-a)(x-b)

where a and b are the x-intercepts of the function

Given the​ x-intercepts (-3,0) and (4,0), the equation will below:

y = a(x-(-3)(x-4))

y = a(x+3)(x-4)

If the curve pass through the y-intercept (2,-40)

-40= a(2+3)(2-4)

-40 = a(4)(-2)
-40 = -8a

a = 5

Substitute the value of a into the resulting function to have:

y = 5(x+3)(x-4)

This gives the required quadratic equation.

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The game's expected value is -$0.83.

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The most appropriate choice for linear equation will be given by -

Kevin is not correct

What is linear equation?

At first it is important to know about equation

Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.

A one degree equation is known as linear equation.

Here,

Let Kevin has x times as many stamps as stamp

Jackie has 9 stamps

Number of stamps Kevin has = 9x stamps

By the problem,

                          9x = 36

                            [tex]x = \frac{36}{9}[/tex]

                            x = 4

So Kevin has 4 times as many stamps as Jackie

But Kevin says  he has 5 times as many stamps as Jackie.

So Kevin is not correct.

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Step-by-step explanation:

you would take half of 15 and then square it to get to number, which is 56.25

Answer:

[tex](\frac{15}{2} )^2=\frac{225}{4}[/tex]

Step-by-step explanation:

[tex]x^2+15x-23=0\\x^2+15x+(\frac{15}{2} )^2-(\frac{15}{2})^2-23=0\\(x^2+15x+(\frac{15}{2})^2)=23+(\frac{15}{2})^2\\(x+\frac{15}{2})^2=(23*4+15^2)/4=317/4\\x+\frac{15}{2}=+\frac{\sqrt{317}}{4}\\, -\frac{\sqrt{317}}{4}\\\\x=-\frac{15}{2}-\frac{\sqrt{317}}{4}\\\\, -\frac{15}{2}+\frac{\sqrt{317}}{4}\\\\[/tex]

Answer:

see explanation

Step-by-step explanation:

(a)

the 2 angles are vertically opposite angles and are congruent

(c)

since they are congruent , then

7x + 6 = 6x + 18 ( subtract 6x from both sides )

x + 6 = 18 ( subtract 6 from both sides )

x = 12

(d)

then

7x + 6 = 7(12) + 6 = 84 + 6 = 90

6x + 18 = 6(12) + 18 = 72 + 18 = 90

The length of the rectangle is 3 times it width. The width size is given as 2 inches.

Therefore,

width = 2 inches

length = 3(2) = 6 inches

The area of the rectangle can be calculated below

The answer is B.

The linear function that gives the full-time year-round median salary for U.S. workers in t years after 2000 is given by:

S(t) = 30846 + 1097.7.

A linear function, in slope-intercept format, is modeled according to the following rule:

y = mx + b

In which:

Linear functions are used in situations when the rate of change is constant, or can be interpreted as a constant, and this rate is called the slope, as we stated above.

In this problem, we have that:

Hence the linear function that models the situation is given as follows:

S(t) = 30846 + 1097.7.

The complete problem could not be found on any search engine, hence we are going to suppose that it asks for a linear function for the median salary in t years after 2000.

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Answer:

Slope: 2

Y-intercept: -3

Step-by-step explanation:

y=2x-3

The slope is always the number(s) before the x and the y-intercept is what is added or subtracted

iven:

he fucnction is,

xplanation:

he graph fo the function cnan be obtained by graph of cube root of x.

If we shift the graph of cube root by x by one unit left then then function changed to,

If the obtained graph shrink vertically by a factor of 3/4 then graph changed to function,

This is the requied function for which we need the graph.

So graph can be obtained by horizontal shift of 1 unit to left, shrink by a factor of 3/4 and there is no vertical shift and graph will not flip over any axis.

Thus answer is, All statements are true.

Answer:

That depends on what exactly is meant by "$3 in equipment fees". Is that per hour, per day or what?

Assuming per hour, he makes $7 per hour but pays $3 for a profit of $4 per hour. So, to make at least $39, he'd have to work 39/4 or 9 3/4 hours.

Now, if his equipment fee is daily, then he would need to earn at least $42 in a day to profit at least $39. Thus, he'd have to work at least 42/7 or 6 hours to make that much profit.

Step-by-step explanation:

Step-by-step explanation:

9x + 4y is where (9,4) is the coordinates

Factor the left hand side:

Subtract 2x from both sides:

Sutract 1 from both sides:

Divide both sides by 10:

Therefore, the equation is correct for every x different from 0.

Domain = the set of possible values along the x axis.

Domain = (-5 , 3 ]

Range = the set of possible values along the y axis.

Range = (-3 , 5 ]