instructions: state what additional information is required in order to know that the triangle in the image below are congruent for the reason given

***I need help before it’s due**

Step-by-step explanation:

Hi there!

Please see the answer in the picture.

Hope it helps!

1. Approach

One is given a trigonometric equation with and one is asked to prove that it is true. Using the attached image, combined with the knowledge of trigonometry, one can evaluate each trigonometric function. Then one can simplify each ratio to solve. To yield the most accurate result, one has to each of the ratios in a fractional form, rather than simplifying it into a decimal form. Remember the right angle trigonometric ratios, these ratios describe the relationship between the sides and angles in a right triangle. Such ratios are as follows,

[tex]sin(\theta)=\frac{opposite}{hypotenuse}\\\\cos(\theta)=\frac{adjacent}{hypotenuse}\\\\tan(\theta)=\frac{opposite}{adjacent}\\\\csc(\theta)=\frac{hypotenuse}{opposite}\\\\sec(\theta)=\frac{hypotenuse}{adjacent}\\\\cot(\theta)=\frac{adjacent}{opposite}[/tex]

Please note that the terms (opposite) and (adjacent) are relative to the angle uses in the ratio, however the term (hypotenuse) refers to the side opposite the right angle, this side never changes its name. Use these ratios to evaluate the trigonometric functions. Then simplify to prove the identity.

2. Problem (9)

[tex]\frac{sin(60)+cos(30)}{1+sin(30)+cos(60)}=sin(60)[/tex]

As per the attached image, the following statements regarding the value of each ratio can be made:

[tex]sin(60)=\frac{\sqrt{3}}{2}\\\\cos(30)=\frac{\sqrt{3}}{2}\\\\sin(30)=\frac{1}{2}\\\\cos(60)=\frac{1}{2}[/tex]

Substitute,

[tex]\frac{sin(60)+cos(30)}{1+sin(30)+cos(60)}=sin(60)[/tex]

[tex]\frac{\frac{\sqrt{3}}{2}+\frac{\sqrt{3}}{2}}{1+\frac{1}{2}+\frac{1}{2}}=\frac{\sqrt{3}}{2}[/tex]

Simplify,

[tex]\frac{\frac{\sqrt{3}}{2}+\frac{\sqrt{3}}{2}}{1+\frac{1}{2}+\frac{1}{2}}=\frac{\sqrt{3}}{2}[/tex]

[tex]\frac{\frac{2\sqrt{3}}{2}}{1+\frac{1}{2}+\frac{1}{2}}=\frac{\sqrt{3}}{2}[/tex]

[tex]\frac{\frac{2\sqrt{3}}{2}}{1+1}=\frac{\sqrt{3}}{2}[/tex]

[tex]\frac{\sqrt{3}}{1+1}=\frac{\sqrt{3}}{2}[/tex]

[tex]\frac{\sqrt{3}}{2}=\frac{\sqrt{3}}{2}[/tex]

Thus, this equation is true.

2. Problem (10)

Use a similar strategy to evaluate this equation,

[tex]\frac{1-cos(30)}{sin(30)}=\frac{1-cot(60)}{1+cot(60)}[/tex]

Use the attached image to evaluate the ratios.

[tex]cos(30)=\frac{\sqrt{3}}{2}\\\\sin(30)=\frac{1}{2}\\\\cot(60)=\frac{1}{\sqrt{3}}[/tex]

Substitute,

[tex]\frac{1-cos(30)}{sin(30)}=\frac{1-cot(60)}{1+cot(60)}[/tex]

[tex]\frac{1-\frac{\sqrt{3}}{2}}{\frac{1}{2}}=\frac{1-\frac{1}{\sqrt{3}}}{1+\frac{1}{\sqrt{3}}}[/tex]

Simplify,

[tex]\frac{1-\frac{\sqrt{3}}{2}}{\frac{1}{2}}=\frac{1-\frac{1}{\sqrt{3}}}{1+\frac{1}{\sqrt{3}}}[/tex]

[tex]\frac{\frac{2-\sqrt{3}}{2}}{\frac{1}{2}}=\frac{1-\frac{1}{\sqrt{3}}}{1+\frac{1}{\sqrt{3}}}[/tex]

[tex]\frac{\frac{2-\sqrt{3}}{2}}{\frac{1}{2}}=\frac{\frac{\sqrt{3}-1}{\sqrt{3}}}{1+\frac{1}{\sqrt{3}}}[/tex]

[tex]\frac{\frac{2-\sqrt{3}}{2}}{\frac{1}{2}}=\frac{\frac{\sqrt{3}-1}{\sqrt{3}}}{\frac{\sqrt{3}+1}{\sqrt{3}}}[/tex]

[tex]2-\sqrt{3}=\frac{\frac{\sqrt{3}-1}{\sqrt{3}}}{\frac{\sqrt{3}+1}{\sqrt{3}}}[/tex]

[tex]2-\sqrt{3}=\frac{\sqrt{3}-1}{\sqrt{3}}*\frac{\sqrt{3}}{\sqrt{3}+1}}[/tex]

[tex]2-\sqrt{3}=\frac{\sqrt{3}-1}{\sqrt{3}+1}[/tex]

Rationalize the denominator,

[tex]2-\sqrt{3}=\frac{\sqrt{3}-1}{\sqrt{3}+1}[/tex]

[tex]2-\sqrt{3}=\frac{\sqrt{3}-1}{\sqrt{3}+1}*\frac{\sqrt{3}-1}{\sqrt{3}-1}[/tex]

[tex]2-\sqrt{3}=\frac{(\sqrt{3}-1)^2}{3-1}[/tex]

[tex]2-\sqrt{3}=\frac{3-2\sqrt{3}+1}{2}[/tex]

[tex]2-\sqrt{3}=\frac{4-2\sqrt{3}}{2}[/tex]

[tex]2-\sqrt{3}=2-\sqrt{3}[/tex]

Therefore, this equation is also true.

Answer:

Step-by-step explanation:

3x° + 60° = 360°

3x = 360 - 60

3x = 300

x° = 100°

Answer:

Infinite solutions

Step-by-step explanation:

x + 4y = 7 --------------(I)

8y = 14 - 2x

⇒ 2x + 8y = 14 -----------(II)

[tex]\frac{a_{1}}{a_{2}}=\frac{1}{2}\\\\\frac{b_{1}}{b_{2}}=\frac{4}{8}=\frac{1}{2}\\\\\frac{c_{1}}{c_{2}}=\frac{7}{14}=\frac{1}{2}\\\\\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}=\frac{1}{2}[/tex]

So, infinite solutions

Answer:

G

Step-by-step explanation:

Given the 2 equations

x + 4y = 7 → (1)

8y = 14 - 2x → (2)

make x the subject of (1) by subtracting 4y from both sides

x = 7 - 4y

Substitute x = 7 - 4y into (2)

8y = 14 - 2(7 - 4y) ← distribute

8y = 14 - 14 + 8y

8y = 8y

Since both sides are equal this indicates the system has infinite solutions

Answer:

A " (1,-2)

B " (4,0)

C " (6,-3)

Step-by-step explanation:

Hope it helped.

° ° °

Answer:

11 4-passenger cars

Step-by-step explanation:

let 'x' represent the number of 4-passenger cars,then 'x-3' represent the number of 6-passenger cars.

92=4x+6(x-3)

92=4x+6x-18

92=10x-18

92+18=10x

110=10x

x=110/10

x=11

Therefore there are 11 4-passenger cars

Answer:

8.80

Step-by-step explanation:

(S. D.)^2=summation(x-mean)^2/(n-1)

S. D.=sqrt(388/5)

S. D.=8.80

Answer:

68

Step-by-step explanation:

17x8 = 136

136/2 = 68

Answer:

1≤f(x)≤5

Step-by-step explanation:

-1≤x≤1

-2≤2x≤2 (Multiplied by 2 both side)

-2+3≤2x+3≤2+3 (Adding three both sides)

1≤f(x)≤5

Answer:

its 1,2,4,5

Step-by-step explanation:

Answer:

A, B, D, E

Step-by-step explanation:

Arc PQ is congruent to arc SR. TRUE

The measure of arc QR is 150°. TRUE

The circumference of circle C is 20π cm. FALSE

Arc PS measures about 13.1 cm. TRUE

Arc QS measures about 15.7 cm. TRUE

Answer:

1/2

Step-by-step explanation:

The radius is 1/2 of the diameter

a radius is 1/2 the diameter

Answer:

Each car should get 1.7, 17/10 or 1 7/10

Step-by-step explanation:

Answer:

[tex]1\frac{3}{4} \ liters[/tex]

Step-by-step explanation:

7 liters of gasoline is shared between 4 cars. So 7÷ 4

[tex]\frac{7}{4}=1\frac{3}{4} \ liters[/tex]

5y=-2x-10

y=-2/5x-2

Rewriting the equation to slope intercept form, you get that the slope is -2/5 and the y intercept is -2. The graph that matches that is line d.

Answer:

Line D (-5,-2)

Step-by-step explanation:

I usually just use the website, demos graphing calculator.

[tex]\\ \sf\longmapsto 2x^2+3x^2+3(-1)=5x.x+5x.1[/tex]

[tex]\\ \sf\longmapsto 5x^2-3=5x^2+5x[/tex]

[tex]\\ \sf\longmapsto 5x^2-5x^2-3=5x[/tex]

[tex]\\ \sf\longmapsto 5x=-3[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{-3}{5}[/tex]

Answer:

4, yes through the middle    5, yes through the middle 6, yes through the middle  all of them reflect from the center

Step-by-step explanation:

Answer:

$687.5

Step-by-step explanation:

Cost of the rug per square foot = $22

Length of the rug = 31.25 feet

Total amount Mrs brown will pay = Cost of the rug per square foot × Length of the rug

= 31.25 × 22

= $687.5

Total amount Mrs brown will pay = $687.5

Answer:

No, they cannot. Some polynomials are different than others and can be factored in different ways. Some can't even be factored at all.

Perfect Square Trinomials have a pattern with factoring and can be written as one binomial squared.

Difference of Squares has a pattern of (x - y)(x + y).

Difference/Sum of Cubes have formulas for their patterns.

Prime Polynomials simply cannot be factored.

Step-by-step explanation:

Brainliest, please! (Almost an Ace)

Answer:

5, 2

Step-by-step explanation:

hope u got it.........

Answer:

y = 5x + 2

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Given

- 5x + y = 2 ( add 5x to both sides )

y = 5x + 2 ← in slope- intercept form

Mark Brainliest if correct:

x = 36

Step-by-step explanation:

x + 2x + 3x + 4x + 5x = 540 (Sum of interior angles in pentagon)

15x = 540

x = 36

Answer:

37

Step-by-step explanation:

tan(theta)=perpendicular/base

tan(theta)=3/4

theta=arctan(3/4)=37

Answer:

37°

Step-by-step explanation:

for this question you have to use the tan ratio since the opposite of that angle has been given as 3 and the adjacent has also been given which is 4..I will represent the unknown angle using x so,

tan x=opposite/adjacent

tanx=3/4

tanx=0.75

x=tan inverse of 0.75

x=36.9 or 37°

I hope this helps

Answer:

575 minutes

Step-by-step explanation:

this is  a systems of equations problem

2 plans, 2 equations

Scenario 1:

$23 is a mandatory fee, 11 cents per minute

x=23+0.11m (x= total cost, m= minutes called)

Scenario 2:

There is no mandatory fee, but there is a higer 15 cents per minute

x=0.15m (y=total cost, m=minutes called)

Set them equal to each other because you want to know when they become equal

23+0.11m=0.15m

23=0.04m

m=575

Answer:

Plan 1: 65 minutes, Plan 2: 201 minutes

Step-by-step explanation:

Not sure if this is the answer that you need but here is the math that i did..

Plan 1: $23 + $0.11/min

$0.11 x 65 minutes will give you a total of $7.15 + the inital $23 = $30.15

Plan 2: $0 + $0.15/min

$0.15 × 201 minutes will give you a total of $30.15

I hope this helps!

Answer:

-117 is irrational number

Answer:

Irrational

Step-by-step explanation:

Irrational number can't be written as a faction, -11pie can't be written as a fraction. Therefore it is a irrational number.

Answer:

54

Step-by-step explanation:

162 divided by 3 is 54

Answer:

54 words per minute

Step-by-step explanation:

in 3 minute Rachel types 162 words

so, in 1 minute Rachel types 162words÷ 3 minutes

= 54 words per minute

Answer:

{1, 0, 16}

Step-by-step explanation:

given..

j(x) = x^2-2x+1

put all given values of domain (1,0 and 5 ) in the equation..

the values you get are range of the function

Answer: 1

Step-by-step explanation

0(2)-2(0)+1=0+0+1= 1

1(1)-(2)(1)+1=1-2+1= 1

(5)(2)-(2)(5)+1=10-10+1= 1

the answer is

A. 28, 25, 22

Answer:

O D. 3x2 + 2x-3

Answer:

A.7x2-5x questions 2of 20

Answer:

I found x for you, right there.

Answer:  x is 12 and y is 5

Step-by-step explanation:

Answer:

(2,-2.5)

Step-by-step explanation:

(2,4) and (2,-9)

((2+2)/2,(4+(-9))/2)

or, (4/2,-5/2)

or, (2,-2.5)

The midpoint of the  vertical line segment in the graph is (2, -5/2), option D is correct.

A coordinate geometry is a branch of geometry where the position of the points on the plane is defined with the help of an ordered pair of numbers also known as coordinates.

We have to find the midpoint of the line joining the two points (2, 4) and (2, -9)

Midpoint = (x₁+x₂/2, y₁+y₂/2)

x₁ = 2, y₁=4, x₂ =2 and y₂ = -9

We have to plug in the values in the above formula

Midpoint = (2+2/2, 4-9/2)

Midpoint = (6/2, -5/2)

=(2, -5/2)

Hence, the midpoint of the  vertical line segment in the graph is (2, -5/2)

To learn more on Coordinate Geometry click:

brainly.com/question/27326241

#SPJ7

Given:

The equation for the linearized regression line is:

[tex]\log y=0.30x+0.296[/tex]

where x represents number of weeks and y be the customer's stock.

To find:

The number of weeks that will pass before the value of the stock reaches $200.

Solution:

We have,

[tex]\log y=0.30x+0.296[/tex]

Substituting y=200, we get

[tex]\log (200)=0.30x+0.296[/tex]

[tex]2.301=0.30x+0.296[/tex]

[tex]2.301-0.296=0.30x[/tex]

[tex]2.005=0.30x[/tex]

Divide both sides by 0.30.

[tex]\dfrac{2.005}{0.30}=x[/tex]

[tex]6.6833333=x[/tex]

[tex]x\approx 6.7[/tex]

Therefore, the correct option is C.

Answer:

33/14

Step-by-step explanation:

[tex] - 10 \frac{2}{7} + ( - 4 \frac{4}{11} )[/tex]

[tex] = - \frac{72}{7} \div - ( \frac{48}{11} )[/tex]

[tex] = \frac{72}{7} \times \frac{11}{48} [/tex]

[tex] = \frac{3}{7} \times \frac{11}{2} [/tex]

[tex] = \frac{33}{14} [/tex]

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