The width of the desk is 7 in. The perimeter of the desk is 63 in. What is
the length of the desk?

[tex]\textit{sum of a finite arithmetic sequence} \\\\ S_n=\cfrac{n(a_1+a_n)}{2}\qquad \begin{cases} a_n=n^{th}\ term\\ n=\textit{last term's}\\ \qquad position\\ a_1=\textit{first term}\\[-0.5em] \hrulefill\\ a_1=3\\ n=5\\ S_5=75 \end{cases} \implies \begin{array}{llll} S_5=\cfrac{5(a_1+a_5)}{2} \\\\\\ 75=\cfrac{5(3+a_5)}{2} \end{array} \\\\\\ 150=5(3+a_5)\implies \cfrac{150}{5}=3+a_5\implies 30=3+a_5\implies \boxed{27=a_5} \\\\[-0.35em] ~\dotfill[/tex]

[tex]n^{th}\textit{ term of an arithmetic sequence} \\\\ a_n=a_1+(n-1)d\qquad \begin{cases} a_n=n^{th}\ term\\ n=\textit{term position}\\ a_1=\textit{first term}\\ d=\textit{common difference}\\[-0.5em] \hrulefill\\ n=5\\ a_5=27\\ a_1=3 \end{cases}\implies 27=3+(5-1)d \\\\\\ 24=(5-1)d\implies 24=4d\implies \cfrac{24}{4}=d\implies \boxed{6=d} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \stackrel{\textit{\LARGE Terms}}{3~~,~~\stackrel{3+6}{9}~~,~~\stackrel{9+6}{15}~~,~~\stackrel{15+6}{21}}~\hfill[/tex]

Answer:

[tex]\frac{1}{125}[/tex]cm³

Step-by-step explanation:

volume of cube= (side)³

0.2³ = [tex]\frac{1}{125}[/tex]

A function assigns the values. The value of (r+s)(-2) is equal to 9.

A function assigns the value of each element of one set to the other specific element of another set.

Given the function r(x)=3x+5, while s(x)=4x, therefore, the expressions can be written as,

(r-s)(x) =r(x)-s(x) = 3x+5 - 4x = -x+5

(r*s)(x) = r(x)·s(x) = (3x+5)·(4x) = 12x² + 20x

The expression for (r+s)(x) can be written as,

(r+s)(x) = r(x)+s(x) = 3x+5+4x = 7x+5

(r+s)(-2) = 7(-2)+5 = -14+5 = 9

Hence, the value of (r+s)(-2) is equal to 9.

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Answer: Cost is minimized at the levels of capital and labor such that the marginal product of labor divided by the wage (w) is equal to the marginal product of capital divided by the rental price of capital (r)

Step-by-step explanation:

The answer is 8.06.

Answer:

(a) √25 rational

(b) √30 irrational

Step-by-step explanation:

Note : only perfect squares have rational roots

25 = 5² then 25 is a perfect square

            therefore √25 = 5 is a rational number

30 cannot be written in the form a² where ‘a’ I start a natural number then 30 is not a perfect square

           Therefore √30 is irrational.

The probability of selecting a turkey sandwich and a bag of pretzels is 3/8.

Probability determines the likelihood that an event would happen. The odds the event occurs is 1 and the odds that the event does not occur is 0.

The probability of selecting a turkey sandwich and a bag of pretzels = number of turkey sandwiches / total number of sandwiches x number of pretziel bags / total number of bags

12/20 x 10/16 = 3/8

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Answer:

A = x² - 5x - 8

Step-by-step explanation:

Finding x

Answer:

25 pages

Step-by-step explanation:

60 minutes in 1 hour. 60/12=5  5 x 5 =25

Answer:

2 , 3 , 5 , 5

Step-by-step explanation:

Prime numbers are numbers that are only divisible by itself and 1.

Divide 150 by primes:

150/2 = 75

75/3 = 25

25/5 = 5

Your prime factorization will be: 2 , 3 , 5 , 5.

Check:

2 * 3 * 5 * 5

= 6 * 25

= 150

~

Step-by-step explanation:

G(x) = - x^2 + 10x

a + G(a) = a - a^2 + 10a = - a^2 + 11a or 11a - a^2 or a(11 - a)

1/G(a) = 1/(10a - a^2) = 1/a(10 - a)

Answer: 2,4

Step-by-step explanation:

Step-by-step explanation:

I think 1 is correct..

all positive numbers are greater than negative. 7.11 is greater that -7.1

Answer:

7.11 > -7.1

Step-by-step explanation:

» Concept

Negative numbers will always be less than positive numbers. Negative numbers will always have the (-) sign to indicate its value.

» Solution

The only correct inequality is A. 7.11 > -7.1 because it displays that the positive number, 7.11, is greater than the negative number, -7.1.

Answer:

5/10

Step-by-step explanation:

To solve this problem we find equivalent fractions with the same denominator:

The LCM of 10,100 and 1000 is 1000. So we make all the denominators 1000:

5/100 = 50/1000

5/10 = 500/1000

24/1000 = 24/1000

Now we compare the numerators and see which is the largest number.

24 < 50 < 500

So 5/10 must be the greatest.

Hope this helped and brainliest please

Hi! :)

Answer:

B) 32 Square Units

Step-by-step explanation:

I counted the squares. <3

Answer:

Step-by-step explanation:

14÷2+3²×(7-2) pemdas order

14 : 2 + 3^2 * (7 - 2) =

14 : 2 + 3^2 * 5 =

14 : 2 + 9 * 5 =

7 + 9 * 5 =

7 + 45 =

52

Mean=Sum of data/No of data

#a

Mean

#b

Mean:-

#c

Mean

#d

Mean

Answer:

See below ~

Step-by-step explanation:

a)

b)

c)

d)

[tex]\begin{array}{llll} \textit{Logarithm of rationals} \\\\ \log_a\left( \frac{x}{y}\right)\implies \log_a(x)-\log_a(y) \end{array}~\hfill \begin{array}{llll} \textit{Logarithm Cancellation Rules} \\\\ log_a a^x = x\qquad \qquad \underset{\stackrel{\uparrow }{\textit{let's use this one}}}{a^{log_a x}=x} \end{array} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\log_4(x+10)-\log_4(x-2)=\log_4(x)\implies \log_4\left( \cfrac{x+10}{x-2} \right)=\log_4(x) \\\\\\ \stackrel{\textit{exponentializing both sides}}{4^{\log_4\left( \frac{x+10}{x-2} \right)}=4^{\log_4(x)}}\implies \cfrac{x+10}{x-2}=x\implies x+10=x^2-2x \\\\\\ 10=x^2-3x\implies 0=x^2-3x-10 \\\\\\ 0=(x-5)(x+2)\implies x= \begin{cases} 5~~\checkmark\\ -2 \end{cases}[/tex]

notice, -2 is a valid value for the quadratic, however, the argument value for a logarithm can never 0 or less, it has to be always greater than 0, so for the logarithmic expression with (x-2), using x = -2 will give us a negative value, so -2 is no dice.

Answer:

Yes

Step-by-step explanation:

You need the formula to solve area.

You must plug in / subsitute numbers in order to find the area.

Solids or three-dimensional forms are shapes or figures that have three (or more) dimensions. The solid could be a Triangular prism or a pyramid.

Solids or three-dimensional forms are shapes or figures that have three (or more) dimensions. Solid Geometry is the study of the characteristics, volume, and surface area of three-dimensional forms.

Given a solid is cut by a plane that is perpendicular to its base, forming a two-dimensional cross-section in the shape of a triangle. Therefore, the solid could be a Triangular prism or a pyramid.

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Answer: right cone because if you use a right cone and cut it perpendicular to the base you get a triangle making cone triangle the answer.

Answer:

1

Step-by-step explanation:

[tex]F =\cos 0^{\circ} = 1[/tex]

Answer:

15 1/8"

Step-by-step explanation:

Adding the values

⇒ 9 3/4" + 2 1/8" + 3 1/4"

⇒ 13 + 2 1/8"

⇒ 15 1/8"

[tex]~~~~~~11|x+1| < 44\\\\\implies |x+1| < \dfrac{44}{11}\\\\\implies |x+1| < 4\\\\\implies x +1 > -4~~~ \text{and}~~~ x+1 < 4\\\\\implies x > -4-1~~~ \text{and}~~~~ x < 4-1\\\\\implies x > -5~~~~~~~~ \text{and}~~~~~ x < 3\\\\\text{Hence,}~~ -5 < x < 3[/tex]

Answer:

$11.13

Step-by-step explanation:

24 cans = $38.16

divide both sides by 24 to find the cost per can, as this leaves us with 1 can on one side

24 cans / 24 = $38.16 / 24

1 can = $1.59

multiply both sides by 7 to get 7 cans of soup on one side, which is what we want

1 can * 7 = $1.59 * 7

7 cans = $11.13

Answer:

E. 40

Step-by-step explanation:

First, we can start out by stating that this is a right triangle, since it has a right angle, shown by the marker square in the corner of the triangle. The x part, is called the hypotenuse. When finding the value of the hypotenuse, we use a thing called the Pythagorean Theorem. This theorem is :

a^2 + b^2 = c^2

a is one side length, and b is the other. c is the hypotenuse. To find x, the hypotenuse, we simply plug in the values, and solve.

24^2+32^2 = c^2

576 + 1024 = c^2

1600 = c^2

40 = c

The answer is E. 40.

Answer: 1 4/5 pounds is equal to 28.8 ounces

Step-by-step explanation:

1 pound is equal to 16 ounces.

Answer:

81

Step-by-step explanation:

Multiply 90/100 with 90 = (90/100)*90 = (90*90)/100 = 81.

i got 100. not sure how the other guy got 81, but what i did is compare it to a test score or a discount. if you have a total of 100 possible points on the test with every question worth 10 points and i got 9 questions right, i got a 90 percent.

let's say a shopping discount. If you got a 90% discount for a item with original price of $100, it costs $10 with "90" being the amount you took off

if 100 isn't right, i honestly have no clue lol. good luck though

The radical form of   [tex]5^{\frac{2}{3}}[/tex] is   [tex]\sqrt[3]{25}[/tex].

If n is a positive integer that is greater than 1 and a is a real number then, n√a = [tex]a^{1/n}[/tex]. where n is called the index, a is called the radicand, and the symbol √ is called the radical.

Here, given value =  [tex]5^{\frac{2}{3}}[/tex]

                              =   [tex](5^2)^{1/3}[/tex]

                             = [tex](25)^{1/3}[/tex]

                             = [tex]\sqrt[3]{25}[/tex]

Thus, the radical form of [tex]5^{\frac{2}{3}}[/tex] is [tex]\sqrt[3]{25}[/tex].

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