Simplify the expression below.<br> 4(52x−5)+12x−9

You work at Initech for a year. Your annual salary income is $38,000. You received a 3% salary increase. What is your NEW salary

sdas [7]

$49,400. If you multiply the income (38,000) by the salary increase (3%=0.3), then you get 49,400. Good Luck!

4 0

3 years ago

Geometry Question attached below

Soloha48 [4]

I'm sure there's an easier way to do this, but this method does work:

First, AB = CD = CG + GF + FD, so FG = 2.

By the Pythagorean theorem, in triangle AFD we get

$1^2+3^2=A F^2\implies A F=\sqrt{10}$

and in triangle BCG,

$2^2+3^2=BG^2\implies BG=\sqrt{13}$

Angles AFD and EFG form a vertical pair, so they are congruent and have measure

$m\angle EFG=\tan^{-1}3$

Similarly, angles BGC and FGE are congruent and have measure

$m\angle FGE=\tan^{-1}\dfrac32$

Then the remaining angle in triangle EFG has measure

$m\angle FEG=\pi-\tan^{-1}3-\tan^{-1}\dfrac32$

We can solve for the lengths of FE and GE exactly by applying the law of sines:

$\dfrac{\sin\left(\pi-\tan^{-1}3-\tan^{-1}\frac 32\right)}2=\dfrac{\sin\left(\tan^{-1}3\right)}{GE}=\dfrac{\sin\left(\tan^{-1}\frac32\right)}{FE}$

$\implies GE=\dfrac{2\sqrt{13}}3,FE=\dfrac{2\sqrt{10}}3$

Let $s$ be the semiperimeter of triangle ABE, so that

$s=\dfrac{AB+BE+EA}2$

Then according to Heron's formula, the area of triangle ABE is

$\sqrt{s(s-AB)(s-BE)(s-EA)}=\dfrac{25}2$

5 0

4 years ago

if Santiago is 5 feet tall and 11 inches tall and Michael is 5 feet tall and 2 inches tall, what is their total height in centim

Masteriza [31]

Answer:

337.82 cm

Step-by-step explanation:

Santiago is 5 feet tall and 11 inches tall and Michael is 5 feet tall and 2 inches tall.

We need to find total height in cm.

1 inch = 2.54 cm

1 feet = 30.48 cm

5 feet 11 inches = 5(30.48) + 11(2.54)

= 180.34 cm

5 feet 2 inches = 5(30.48) + 2(2.54)

= 157.48 cm

Total height = Santiago's height + Michael's height

= 180.34 cm + 157.48 cm

= 337.82 cm

Hence, their total height is 337.82 cm.

7 0

3 years ago

The mother of a young child reaches into her daughter’s bag of Halloween candy to find a snack. She plans to reach into the bag

Molodets [167]

Answer:

B. determined

Step-by-step explanation:

Because she is reminding her self at the same time to return the candy she does not want

7 0

2 years ago

CosA + cosB - cosC = -1 + 4cosA/2 cosB/2 sinC/2

Lubov Fominskaja [6]

Answer:

Step-by-step explanation:

(cos A+ cos B)-cos C

$=2cos \frac{A+B}{2}cos \frac{A-B}{2}-cos C~~~...(1)\\A+B+C=180\\A+B=180-C\\\frac{A+B}{2}=90-\frac{C}{2}\\cos \frac{A+B}{2}=cos(90-\frac{C}{2})=sin \frac{C}{2}\\cos C=1-2sin^2\frac{C}{2}\\(1)=2 sin \frac{C}{2} cos \frac{A-B}{2}-1+2sin^2\frac{C}2}\\=2sin\frac{C}{2}[cos \frac{A-B}{2}+sin \frac{C}{2}]-1~~~...(2)\\\\now~again~A+B+C=180\\C=180-(A+B)\\sin\frac{C}{2}=sin(90-\frac{A+B}{2})=cos \frac{A+B}{2}\\(2)=2sin\frac {C}{2}[cos \frac{A-B}{2}+cos \frac{A+B}{2}]-1\\$

$=-1+2sin\frac{C}{2}*2cos \frac{\frac{A-B}{2} +\frac{A+B}{2} }{2} cos \frac{\frac{A-B}{2} -\frac{A+B}{2} }{2} \\=-1+4sin\frac{C}{2} cos \frac{A}{2} cos\frac{-B}{2} \\=-1+4 cos \frac{A}{2} cos \frac{B}{2} sin \frac{C}{2}\\(cos(-B)=cos B)$

8 0

4 years ago

Simplify the expression below. 4(52x−5)+12x−9