What is the justification for each step in the solution of the equation?

Answer:

2.5 in  

Step-by-step explanation:

A = lw     Divide each side by w

l = A/w

A = 25 in²; w = 10 in

l = 25/10

l= 2.5 in

Answer: we need the measurements

Step-by-step explanation:

Answer:

find below

Step-by-step explanation:

-2/3 (-3 – 9x) = 2+6x

2+6x

33/4 = 8.25 per hour.

Hi there! :)

Step-by-step explanation:

[tex]SLOPE=\frac{Y_2-Y_1}{X_2-X_1}=\frac{RISE}{RUN}[/tex]

[tex]\frac{8-(-6)}{(-4)-2}=\frac{14}{-6}=\frac{14}{-6}[/tex]

Slope is 14/-6

Final answer is 14/-6

Hope this helps!

-Charlie

Have a nice day! :)

:D

Thanks!

Answer: A. (4,0)

Step-by-step explanation: It is the only ordered pairs that are on the line.

Hope this helps! :)

Answer:

Step-by-step explanation:

What is the scale of the map? Just multiply the ratio (distance on map x actual distance) by 5.

Answer:

The answer is 17/12

Step-by-step explanation:

3/4 + 2/3

= 9/12 + 8/12

= 9 + 8/12

= 17/12

We must find the common denominator.

The list of multiples of 4: 0, 4, 8, 12, 16, 20, ...

The list of multiples of 3: 0, 3, 6, 9, 12, 15, 18, ...

The common denominator is 12.

[tex]\dfrac{3}{4}=\dfrac{3\cdot3}{4\cdot3}=\dfrac{9}{12}\\\\\dfrac{2}{3}=\dfrac{2\cdot4}{3\cdot4}=\dfrac{8}{12}[/tex]

Therefore:

[tex]\dfrac{3}{4}+\dfrac{2}{3}=\dfrac{9}{12}+\dfrac{8}{12}=\dfrac{9+8}{12}=\dfrac{17}{12}=\dfrac{12+5}{12}=1\dfrac{5}{12}[/tex]

Answer:

B= 44.9506°

Step-by-step explanation:

WE apply sine angle formula

[tex]\frac{a}{sin(A)} =\frac{b}{sin(B)}=\frac{c}{sin(C)}[/tex]

Given angle C = 51, c= 11 and b = 10

[tex]\frac{b}{sin(B)}=\frac{c}{sin(C)}[/tex]

Plug in the values

[tex]\frac{10}{sin(B)}=\frac{11}{sin(51)}[/tex]

Cross multiply it

10 * sin(51) = 11* sin(B)

7.771459615 = 11 sin(B)

Now divide by 11 on both sides

0.706496328 = sin(B)

Now [tex]B = sin^{-1} (0.706496328)[/tex]

B= 44.9506°

Answer:

Step-by-step explanation:

a) y=800x+1000=800(12)+1000

b)y=1000x              (15 months)  

Answer:

Linear model is given as

Total cost of renting = 1000 + n(800)

Total cost of renting for 6 months = $5800

Step-by-step explanation:

The linear model can be represented as follows ;

The one time fee = $1000

monthly fee = $ 800

Total cost of renting = 1000 + n(800)

n  = number of month you will rent

Total cost of renting office space for 6 months can be computed using the model.

Total cost of renting = 1000 + n(800)

where n = 6 months

Total cost of renting for 6 months = 1000 + 6(800)

Total cost of renting for 6 months = 1000 + 4800

Total cost of renting for 6 months = $5800

Answer:

Part A

(5x+4)+(6x-9)=11x-5

part (B)

(5x+4)(6x-9)

30x²-45x+24x-36

30x²-21x-36

part (c)

m[n(x)]=m(6x-9)+4=30x-45+4=30x-41

Step-by-step explanation:

Answer:

The company will break even at x=1 and x=4.

Step-by-step explanation:

The given profit function is

[tex]P(x)=-x^4-2x^3+21x^2+22x-40[/tex]

Where, x is number of commercials.

Use synthetic division or long division to find the factors of the function.

[tex]P(x)=(x-1)(x^3+3x^2-18x-40)[/tex]

[tex]P(x)=(x-1)(x+2)(x^2+x-20)[/tex]

[tex]P(x) = -(x - 4) (x - 1) (x + 2) (x + 5)[/tex]

Equate P(x)=0, to find the break even points.

[tex]-(x - 4) (x - 1) (x + 2) (x + 5)=0[/tex]

Use zero product property and equate each factor equal to zero.

[tex]x=4,1,-2,-5[/tex]

Therefore the zeros of the function P(x) are 4, 1, -2 and -5. Since x is number of commercials, therefore the value of x must be positive. Therefore the company will break even at x=1 and x=4.

The higher degree of the function is even and the leading coefficient is negative. So,

[tex]P(x)\rightarrow -\infty \text{ as }x\rightarrow \infty[/tex]

[tex]P(x)\rightarrow -\infty \text{ as }x\rightarrow -\infty[/tex]

Since the value of x must be positive, therefore the left end point is y-intercept of the graph, i.e., (0,-40).

Therefore the company faces huge loss when the number of commercials increases unboundly.

The graph of the function is given below.

Answer:

Step-by-step explanation:

The common difference of the sequence is -5

Since the difference is -5

a_n= 7+(n-1)(-5)

a_n = 7-5n+5

a_n = 12-5n

Answer:

13

Step-by-step explanation:

To solve for any missing side of a triangle, simply use the Pythagorean Theorem.

[tex]a^2 + b^2 = c^2[/tex]

[tex]c^2=12^2+5^2\\c^2 = 144 +25\\\sqrt{c^2} = \sqrt{169} \\\text{The square root of 169 is 13}[/tex]

The length of the hypotenuse (C) in a right triangle given sides A=12 and B=5 can be calculated using the Pythagorean theorem. Substituting these values leads to a calculation of √169, resulting in C being 13.

The subject at hand pertains to the Pythagorean Theorem. This theorem states that in a right triangle, the square of the length of the hypotenuse (side C) is equal to the sum of the squares of the lengths of the other two sides (A and B). Hence, the formula is a² + b² = c².

Given that A=12 and B=5, we substitute these values into the Pythagorean theorem. Therefore, the calculation is C = √(12² + 5²). This simplifies to C = √(144 + 25), which further simplifies to C = √169. Thus, the length of the hypotenuse C is 13.

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Answer:

37.7 feet ( to 1 dec. place )

Step-by-step explanation:

arc length = circumference × fraction of circle

                 = 2π r × [tex]\frac{240}{360}[/tex]

                 = [tex]\frac{2\pi (9)(240)}{360}[/tex] ≈ 37.7 feet

Answer:

No

Step-by-step explanation:

So, you have 56 and 66. The others are 72, 346, 4132.7216, and 9. 66 can not go into 72 more than once, so therefore the answer is no.

The polynomial 5x3 + 2x + 7x5 written in descending form is 7x5 + 5x3 + 2x, organized from the highest to the lowest power of x.

To write the polynomial 5x3 + 2x + 7x5 in descending form, arrange the terms in order from the highest power of x to the lowest. The given polynomial has the terms with powers of 5, 3, and 1. Organizing the polynomial in descending order of the exponents gives us:

7x5 + 5x3 + 2x.

As we can see, the term with the highest exponent, 7x5 (degree 5), comes first, followed by 5x3 (degree 3), and lastly the term with the lowest degree, 2x (degree 1).

Answer:

I don't know I don't know I don't know I don't know

Answer:

It would be B, Both are linear because the slope is a normal number like 4&-5)

Step-by-step explanation:

They are both linear because they are straight lines.

Answer:

Equation A is nonlinear and Equation B is linear.

If its wrong please tell me and I'll see what i did wrong. Please and Thank you!

Hope this is helpful!

Answer:

x=9 y=24

Step-by-step explanation:

take the triangle with 43 Degrees and 90 degrees to get the answer for that missing angle.

which equals 133

subtract 133 from 180 and get 47

then set 5x+2 = 47 because opposite angles are equal to each other

-2 on both sides

5x=45

divide by 5

x=9

then take 3y+1=?

add 47 + 60 =107

180-107=73

3y+1=73

-1 both sides

72

divide by 3

y=24

Answer:

4

Step-by-step explanation:

To evaluate a function with certain defined values, we must substitute the values ​​in the equation, perform the indicated operations and in this way we obtain the final value.

If j = 25  and k=5

replacing in the equation

[tex]\frac{j}{k} -0.2k = \frac{25}{5} -0.2(5)  = 5 -1 = 4[/tex]

Answer:

see below

Step-by-step explanation:

1) 4

2) 1 or -1

Answer:

Step-by-step explanation:

(-3/7)*(-4/11)

12/77

Answer:

=-12/7 or -1.71429....

Step-by-step explanation:

Answer:

c) 2.082

Step-by-step explanation:

First you would add 1.567 and 2.345 together to get 3.912. If you take 3.912 and subtract 1.83 from that, it would be 2.082.

Hey there!

1.567 + 2.345 - 1.83 (5)

1.567 + 2.345 = 3.912

3.912 - 1.83(5)

1.83(5) = 9.15

3.912 - 9.15 = -5.238

Answer: -5.238 ✅

Good luck on your assignment and enjoy your day!

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[tex]\bf 200 > 4.50x+35\implies 165 > 4.50x\implies \cfrac{165}{4.50}>x\implies \cfrac{110}{3}>x[/tex]

which is about 36.67 > x.

Answer:

? = 30

Step-by-step explanation:

If the triangles are similar, then the only way I see this working is the sides measuring 63 and 54 are corresponding. The sides measuring 56 and 48 are corresponding. That leaves the sides measuring 35 and ? corresponding.

Set up a proportion.

63/54 = 35/?

63? = 54 * 35

63? = 1890

? = 30