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3 years ago

9

An executive in an engineering firm earns a monthly salary plus a Christmas bonus of $9300. If she earns a total of $78,900 per

year, what is her morthly salary?

1 answer:

polet [3.4K]3 years ago

3 0

12x+9300=78900
12x=69600
x=5800
x being her monthly salary

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Please help me with question 3

JulsSmile [24]

Set up a proportion.
24/x=9/15
24(15)=9x
360=9x
40=x

x=40

This is because if side one of the smaller triangle is 9 and side two of the smaller triangle is 15, and if side one of the larger triangle is 24 then side two of the larger triangle has to be 40 because they are proportional.

I hope this helps!
Best wishes :)

8 0

3 years ago

Write the equation of the line that passes through<br> the given points.<br> (0, 1) and (2, 2)

Rasek [7]

Answer:

y = 1/2x + 1

General Formulas and Concepts:

<u>Pre-Alg</u>

Order of Operations: BPEMDAS
Equality Properties

<u>Alg I</u>

Slope-Intercept Form: y = mx + b

m - slope

b - y-intercept

Slope Formula: $m=\frac{y_2-y_1}{x_2-x_1}$

Step-by-step explanation:

<u>Step 1: Define</u>

y-intercept (0, 1)

Point (2, 2)

<u>Step 2: Find slope </u><em><u>m</u></em>

Substitute: $m=\frac{2-1}{2-0}$
Subtract: $m=\frac{1}{2}$

<u>Step 3: Write equation</u>

y = 1/2x + 1

7 0

3 years ago

4x-3+x=7x-3 solve x and show work easy to undertand please. Really appreciate it ^^

nalin [4]

Answer: x = 0

Step-by-step explanation:

4x − 3 + x = 7x − 3

Step 1: Simplify both sides of the equation.

4x − 3 + x = 7x − 3

4x + −3 + x = 7x + −3

(4x + x) + (−3) = 7x − 3(Combine Like Terms)

5x + −3 = 7x − 3

5x − 3 = 7x − 3

Step 2: Subtract 7x from both sides.

5x − 3 − 7x = 7x − 3 − 7x

−2x − 3 = −3

Step 3: Add 3 to both sides.

−2x − 3 + 3 = −3 + 3

−2x = 0

Step 4: Divide both sides by -2.

-2x/-2 = 0/-2

x = 0

3 0

3 years ago

Read 2 more answers

What is the slope of the line shown below (-4, 3) (3, 1)

motikmotik

slope of line passing through (-4,3) (3,1)

= (3-1)/(-4-3)

= -2/7

3 0

3 years ago

Let $A = (4,-1)$, $B = (6,2)$, and $C = (-1,2)$. There exists a point $X$ and a constant $k$ such that for any point $P$,

goldfiish [28.3K]

Answer:

k=32

Step-by-step explanation:

Given the points:

$A = (4,-1)$, $B = (6,2)$, and $C = (-1,2)$.$

The first step is to find the <u>Centroid</u> of the triangle.

Centroid, X

$=\left(\dfrac{x_1+x_2+x_3}{3} ,\dfrac{y_1+y_2+y_3}{3} \right)\\=\left(\dfrac{4+6+(-1)}{3} ,\dfrac{-1+2+2}{3} \right)\\=\left(\dfrac{9}{3} ,\dfrac{3}{3} \right)=(3,1)$

Next, let P be a point (x,y)

Using the <u>distance formula, </u> $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$ <u />

<u /> $PA^2=(x-4)^2+(y-(-1))^2\\PB^2=(x-6)^2+(y-2)^2\\PC^2=(x-(-1))^2+(y-2)^2\\PX^2=(x-3)^2+(y-1)^2\\$ <u />

On Substitution into: $PA^2 + PB^2 + PC^2 = 3PX^2 + k$

$(x-4)^2+(y-(-1))^2+(x-6)^2+(y-2)^2+(x-(-1))^2+(y-2)^2=3[(x-3)^2+(y-1)^2]+k$

Let us simplify the LHS first

$\\LHS: x^2-8x+16+y^2+2y+1+x^2-12x+36+y^2\\-4y+4+x^2+2x+1+y^2-4y+4\\=3x^2-18x+3y^2-6y+62$

Also, the Right Hand Side

$RHS:3[(x-3)^2+(y-1)^2]+k\\=3[x^2-6x+9+y^2-2y+1]+k\\=3x^2-18x+27+3y^2-6y+3+k\\=3x^2+3y^2-18x-6y+30+k$

Therefore:

$3x^2-18x+3y^2-6y+62=3x^2+3y^2-18x-6y+30+k\\k=3x^2-18x+3y^2-6y+62-3x^2-3y^2+18x+6y-30\\k=3x^2-3x^2+3y^2-3y^2-18x+18x+62-30\\k=32$

7 0

3 years ago