Find b, given that a = 18.2, B = 62°, and C = 48°. Round answers to the nearest whole number. Do not use a decimal point or extra spaces in the answer or it will be marked incorrect.

Answers

Answer 1

Answer:

Answer:

Step-by-step explanation:

We have been given that in triangle ABC, measure of angle B is 62 degrees and measure of angle C is 48 degrees. The length of side opposite to angle a is 18.2. We are asked to find length of side b.

We will use law of sines to solve for side b.

$\frac{a}{\text{sin}(A)}=\frac{b}{\text{sin}(B)}=\frac{c}{\text{sin}(C)}$

$m\angle A+m\angle B+m\angle C=180^(\circ)\n\nm\angle A+62^(\circ)+48^(\circ)=180^(\circ)$

$m\angle A+110^(\circ)=180^(\circ)$

$m\angle A+110^(\circ)-110^(\circ)=180^(\circ)-110^(\circ)$

$m\angle A=70^(\circ)$

Upon substituting our given values, we will get:

$\frac{18.2}{\text{sin}(70^(\circ))}=\frac{b}{\text{sin}(62^(\circ))}$

$\frac{18.2}{\text{sin}(70^(\circ))}*\text{sin}(62^(\circ))=\frac{b}{\text{sin}(62^(\circ))}*\text{sin}(62^(\circ))$

$\frac{18.2}{\text{sin}(70^(\circ))}*\text{sin}(62^(\circ))=b$

$b=\frac{18.2}{\text{sin}(70^(\circ))}*\text{sin}(62^(\circ))$

$b=(18.2)/(0.939692620786)*0.882947592859$

$b=19.1551999*0.882947592859$

$b=16.9130376$

$b\approx 17$

Therefore, the length of side b is 17 units.

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An equivalent fraction for 2/3 is 1. 2/6 2. 1/3 3. 8/15 4. 10/15

Negative X Plus 2y equals 6

Answers

plus x on bot sides. then divide both sides by 2 to get y by itself.

Stir-fry is tony's favorite food to cook, but it always makes a lot of smoke! Tony needs to know the volume of his kitchen so he can buy a fan that is the right size. Tony's kitchen has a floor area of 85 square feet. The height of the ceiling is 8 feet. What is the volume of tony's kitchen?

Answers

Answer:

Volume = 680 ft³

Step-by-step explanation:

Given

Floor Area = 85 ft²

Height = 8 ft

Required

Volume of the Kitchen

To solve this, it'll be assumed that Tony's kitchen has a regular shape.

Having said that, the volume of Tony's kitchen is calculated as thus.

Volume = Floor Area * Height.

Substitute the values of floor area and height

Volume = 85ft² * 8ft

Volume = 680 ft³

Hence, the volume of Tony's kitchen is 680ft³

What is the equation of the line, in general form, that passes through the point (1, 1) and has a y-intercept of 2

Answers

$The\ slope-intercept\ form:y=mx+b\n\ny-intercept\ is\ 2\ then\ y=mx+2\n\nThe\ point\ (1;\ 1)\to substitute\ x=1\ and\ y=1:\n\nm\cdot1+2=1\nm+2=1\nm=1-2\nm=-1\n\nFinish:y=-1x+2\to y=-x+2\n\nGeneral\ form:x+y-2=0$

HELP ); Match each function formula with the corresponding transformation of the parent function y = - (x + 2)2.

1. y = - (x + 4)2
2. y = - (x + 2)2 - 2
3. y = (x - 2)2
4. y = 2 - (x + 2)2
5. y = -x2
6. y = (x + 2)2

A. Reflected across the x-axis and the y-axis

B. Translated right by 2 units

C. Translated up by 2 units

D. Reflected across the x-axis

E. Translated left by 2 units

F. Translated down by 2 units

Answers

Always remember general rules of transformation.

1) Vertical Shift:

y= f(x)+k ; shifts the graph of f up k units if k>0, shifts it down |k| units if k<0.

2) Horizontal Shift:

y=f(x+h) ; shifts the graph of f left h units if h>0, shifts it right |h| units if h<0.

3) Reflection across x-axis

y= - f(x) ; reflect the graph of f across the x-axis.

Now,

The parent function is y= -(x+2)²

1. y= -(x+4)²

In this question +2 is added with x+2 and becomes y= -(x+2+2)²=-(x+4)²

So, according to rule 2 it will shift the parent function to the left by 2 units.

E is the correct option.

2. y = - (x + 2)² - 2

In this question, -2 is added to the parent function and we get y= - (x + 2)² - 2

So, according to rule 1, it will shift the graph down by 2 units.

F is the correct option.

3. y=(x - 2)²

In this question, two operations are performed on the parent function.

First one, -4 is added with x+2 so we get x+2-4= x-2

Second one, -1 is multiplied with parent function.

By performing the two operations at a time we get a new function which is

y=-(-(x+2-4)²)=(x-2)²

The first operation will translate the parent function 4 units right (according to rule 2).

The second operation will reflect the graph across x-axis(according to rule 3).

D and translation 4 units to right is correct option.

4. y= 2 -(x+2)²

In this question, we add +2 to the parent function so according to rule 1 it will shift the graph up by 2 units.

C is the correct option.

5. y= -x²

In this question, we add -2 to x+2 so we get a new function y= -(x+2-2)²=-x²

So, according to rule 2 it will shift the graph right by 2 units.

B is the correct option.

6. y= (x+2)²

In this question, -1 is multiplied with parent function and we get

y= -(-(x+2)²)= (x+2)²

So, according to rule 3 , graph is reflected across x-axis.

D is the correct answer.

The graph of parent function and question no. 1,2,3 are attached separately, while question no. 4,5,6 are attached in combined form(due to space limit).

Write the inverse of the given conditional statement

Answers

Answer:

If I live in South Carolina then I live in Charleston

Step-by-step explanation:

Just switch them

A phone store employee earns a salary of $450 per week plus 10% commission on her weekly sales.what function rule models the employers weekly earnings?

if the employee earned $570 in a week, what was the amount of her sales for that week?

Answers

Answer:

Weekly earning of employee, E(w) is given by 450+0.1w, where w is the weekly sales.

Weekly sales for that week = 1200 $

Step-by-step explanation:

A phone store employee earns a salary of $450 per week plus 10% commission on her weekly sales.

Let w be the weekly sales, the weekly earning of employee, E(w) is given by

$E(w)=450+(10)/(100)* w=450+0.1w$

Weekly earning of employee, E(w) is given by 450+0.1w, where w is the weekly sales.

Now we need to find what was the amount of her sales for that week, if she earned 570 $

That is

570 = 450+0.1w

0.1 w = 570 - 450 = 120

w = 1200 $

Weekly sales = 1200 $

If w = earnings that week, and s = sales, w - 450 = s/10, or 10(w - 450) = s, simplified as 10w - 4,500 = s If the employee made $570 in one week, then w = 570. 10(570) - 4,500 = s, simplified as 5,700 - 4,500 = s, simplified as 1,200 = s. So the employee made 1,200 sales that week.

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