A carpenter is building a rectangular table. He wants the perimeter of the tabletop to be no more than 28 feet. He also wants the length of the tabletop to be greater than or equal to the square of 2 feet less than its width.
Create a system of inequalities to model the situation, where x represents the width of the tabletop and y represents the length of the tabletop. Then, use this system of inequalities to determine the viable solutions.

A. Part of the solution region includes a negative width; therefore, not all solutions are viable for the given situation.
B. No part of the solution region is viable because the length and width cannot be negative.
C. The entire solution region is viable.
D. Part of the solution region includes a negative length; therefore, not all solutions are viable for the given situation.

here i hope this exaple helps but for the time being while i solve it heres this example

if you currently owe $500 on your credit card throughout the month and your current APR is 17.99%, you can calculate your monthly interest rate by dividing the 17.99% by 12, which is approximately 1.49%. Then multiply $500 x 0.0149 for an amount of $7.45 each month.

Solid is a substance that can be measured. The required volume of a solid is 90 cubic cm

The formula for calculating the volume of a solid ie expressed as:

V = lwh

l is the length

w is the width

h is the height

For the given figure;

Volume =  (11 * 2 * 3) + (2 * 3 * 4)
Volume = 66 + 24
Volume = 90 square cm

The required volume of a solid is 90 cubic cm

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Answer:

693.19 m^2.

Step-by-step explanation:

This consists of 2 triangles and 3 rectangles,

Surface area = 2 * 1/2 * 3 * 9 + 9*31 + 3*31 + 9.49*31

=  27 + 279 + 93 + 294.19

= 693.19 m^2

Check the picture below.

Answer:

168 [tex]cm^{3}[/tex]

Step-by-step explanation:

Start by finding the whole prism's volume. 9 x 3 x 8 = 216 Then find the volume of the missing part. 8 x 6 x 1 = 48. Subtract the missing volume from the whole volume. 216 - 48 = 168

Answer:

[tex]38.47 {m}^{2} [/tex]

Step-by-step explanation:

The formula to find the area of a circle is

[tex] a= \pi {r}^{2} [/tex]

We know that

[tex]\pi = 3.14 \: \: \: \: \: \: r = 3.5[/tex]

Therefore the area is

[tex] a= \pi {r}^{2} \\ \\ a = (3.14) {(3.5)}^{2} \\ \\ a = 3.14 \times 12.25 \\ \\ a = 38.47 {m}^{2}[/tex]

The sum of the first 14 terms of the finite geometric series 0.5+ (-1) +2+... is -2730.5

The series is given as:

0.5+ (-1) +2+...

The above series is a geometric series, with the following parameters:

The sum of the first 14 terms is calculated using:

[tex]S_n= a *(1 - r^n) \div (1 - r)[/tex]

So, we have:

[tex]S_{14}= 0.5 *(1 - (-2)^{14}) \div (1 + 2)[/tex]

Evaluate

[tex]S_{14}= -2730.5[/tex]

Hence, the sum of the series is -2730.5

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Answer:

12.

Step-by-step explanation:

There are 3 * 4 = 12 possible outcomes

for example

Walk / Red

Walk/Green

Walk/Blue

Walk/Orange

- and there are  4 similar outcomes for Run and Stop.

Taxes usually increase how much you pay from the purchase price.  To find the tax charged on the purchase, multiply the tax rate by the purchase.

$28.38 × 0.0825 = $2.34

The tax charged is $2.34

Answer:

2985 yes votes.

Explanation:

Yes : No

5x : 8x

Total Ratio: 5x + 8x = 13x

Solve for x

13(x) = 7761

divide both sides by 13

x = 597

Yes-Votes: 5(x) = 5(597) = 2985

No-Votes: 8(x) = 8(597) = 4776

Answer:

[tex]y = -6x[/tex]

Step-by-step explanation:

We can see that with every [tex]x[/tex] value that increases, the [tex]y[/tex] value decreases by [tex]-6[/tex]. Thus the slope is [tex]-6[/tex], which would make the equation: [tex]y = -6x[/tex].

Answer:

A= 3.14

Step-by-step explanation:

The formula for finding the area of a circle is A=  π r²

A= 3.14*1²

1. A reasonable price for my friend to sell the car is $13,480.

2. This price is determined as an average of the prices of similar cars.

An average is a typical value in a dataset.

An average is the mean of a set of numbers.

The average value can be computed by summing the set of numbers and dividing the result by the number of items.

Prices of similar cars:

A. 13,500

B. 12,900

C. 15,300

D. 13,700

E. 12,000

Sum = $67,400

Average = $ 13,480 ($67,400/5)

Thus, a reasonable price for my friend to sell the car is $13,480, which is the average price of similar cars.

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Answer:

(0, -12)

Step-by-step explanation:

The y-intercept of a line can be found when taking x = 0.

Therefore,

The y-intercept of the line is (0, -12)

                 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

[tex]\diamond\large\blue\textsf{\textbf{\underline{\underline{Question:-}}}}\diamond[/tex]

       ◈ What is the y-intercept of the line, [tex]\bold{y=\dfrac{x}{5} -12}\textit{?}[/tex]

[tex]\diamond\large\blue\textsf{\textbf{\underline{\underline{Answer and how to solve:-}}}}\diamond[/tex]

    ◈ Here's a shortcut to find the y-intercept.

Here's the equation:-

[tex]\large\textbf{y=x/5-12}[/tex]

         [tex]\square\!\!\!\!\!\!\triangle[/tex] The y-intercept is a negative or positive constant that's added to or subtracted from the slope.

       Constant:- A number with no variables next to it (for example, in the expression d-12, -12 is the constant)

So we conclude that

             [tex]\Huge\textit{The y-intercept is -12}[/tex].

The y-intercept is usually written as (0, -12).

                       - -- - - - - - - - - - - - - -  - - - - - - - - - - - - - - - - - - - -

Answer:

- 8.14 = m = slope

Step-by-step explanation:

We know from the diagram that  8x-7  + 5x+18  = 180    so x = 13

  so 8x -7  =  97

slope = tan 97 = -8.14

If ɑ and β are roots of 2x² - 5x + 7, then

2x² - 5x + 7 = 2 (x - ɑ) (x - β)

Expanding the right side and matching up coefficients, it follows that

2ɑβ = 7   ⇒   ɑβ = 7/2

-2 (ɑ + β) = -5   ⇒   ɑ + β = 5/2

Now consider a polynomial whose roots are 3ɑ + 4β and 4ɑ + 3β, which can be written with factorization

(x - (3ɑ + 4β)) (x - (4ɑ + 3β))

and expanded to get

x² - (7ɑ + 7β) x + (3ɑ + 4β) (4ɑ + 3β)

Expand/factor the coefficients to rewrite them in terms of the known relations above.

x² - 7 (ɑ + β) x + (12ɑ² + 25ɑβ + 12β²)

x² - 7 (ɑ + β) x + 12 (ɑ² + β²) + 25ɑβ

Recall the square of a binomial,

(x + y)² = x² + 2xy + y²

so we rewrite the latter quadratic as

x² - 7 (ɑ + β) x + 12 ((ɑ + β)² - 2ɑβ) + 25ɑβ

x² - 7 (ɑ + β) x + 12 (ɑ + β)² + ɑβ

Then substituting the expressions whose values we know, we get

x² - 7 (5/2) x + 12 (5/2)² + 7/2

= x² - 35/2 x + 157/2

which we can multiply by 2 to get integer coefficients like in the given quadratic,

= 2x² - 35x + 157

Answer:

Original price = t = $24

Expression = t + 0.05t

—-

New price = t + 0.05t = 24 + (0.05*24) = $25.20

—-

Have a nice day!!

Answer:

$25.20

Step-by-step explanation:

Original price = t = $ 24

New price = 1.05*24

                 = 25.20

Just multiply 1.05 by 24

Answer:

120h = 5 days

240h = 10 days

144h = 6 days

720m = 1/2 (half a day)

13w = 91 days

please make this brainliest

Answer:

8.2 * 10^-3 is the greatest and 5.2 * 10^-6 is the smallest.

Step-by-step explanation:

Answer:

$127.32

Step-by-step explanation:

Selling price= $139.99

Sale discount= 15% = $139.99 * 0.15 = $21

Discounted price= $139.99 - $21 = $118.99

Sales tax added= 7% = $118.99 * 0.07 = $8.33

Victoria has to pay = $118.99 + $8.33 = $127.32 so she has enough money to buy it with $2.68 left

Like terms are those terms that are having the same variables, also the variables are of the same order as well. The first step to solving an equation is to rearrange the like terms.

Like terms are those terms that are having the same variables, also the variables are of the same order as well.

for example, 25x and 5x are like terms; 30xy and 7xy are like terms, 9x³ and 4x² are not like terms, etc.

To solve an equation the first step is to rearrange the equation such that like terms are together.

Hence, the first step to solving an equation is to rearrange the like terms.

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Answer:

The to 42 x 42 is 1764

Step-by-step explanation:

22 x 22 = 484

Answer:

g(x) = f(x) - 4.

Step-by-step explanation:

4 down = -4

g(x) = f(x) - 4.

Answer:

Step-by-step explanation:

what is the mean of 10,16,14,12and 16?

Find the sum of the values by adding them all up.

Divide the sum by the number of values in the data set.

10 + 16 + 14 + 12 + 16 = 68

68 : 5 = 13.6

or

(10 + 16 + 14 + 12 + 16) : 5 = 13.6

Answer: The answer is the first option:  [tex]a > -21\frac{1}{3}[/tex]

Step-by-step explanation:

[tex]\frac{3}{4}[/tex] × [tex]a > -16[/tex]

[tex]\frac{3}{4}a\cdot \frac{4}{3} > -16\cdot \frac{4}{3}[/tex]

[tex]\frac{3}{4}\cdot \frac{4}{3}a > -16\cdot \frac{4}{3}[/tex]

[tex]a > -16\cdot \frac{4}{3}[/tex]

[tex]a > \frac{-16\cdot 4}{3}[/tex]

[tex]a > \frac{-64}{3}[/tex]

Answer:

Step-by-step explanation:

3 1/3 is 10/3. 1 1/5 is 6/5. KCF, Keep Change Flip.

10/3 divided by 6/5 becomes 10/3 multiplied by 5/6, or 50/18.

50/18 becomes 25/9, or 2 7/9.

Answer:

Length = 12 ft.

Width = 8 ft.

Step-by-step explanation:

Given :

Let :

Solving :

The dimensions are :

Length = 12 ft.

Width = 8 ft.

Hence, [tex]x=13cm[/tex].

What is the triangle?

A triangle is a two-dimensional shape, in Euclidean geometry, which is seen as three non-collinear points in a unique plane.

Here given that,

Perpendicular is [tex]12cm[/tex]

Base is [tex]5cm[/tex]

Hypotenuse is [tex]x[/tex]

As we know,

[tex]H^2=B^2+P^2[/tex]      ........[tex](1)[/tex]

Now substitue these values in equation [tex](1)[/tex], we get

[tex]H^2=(5)^2+(12)^2\\\\x^2=25+144\\\\x^2=169\\\\x=\sqrt{169}\\\\x=13cm[/tex]

Hence, [tex]x=13cm[/tex].

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