The slope of the line is 52 and passes through the points A ( 8, -6), what is the equation of this line ?

Answer:

[tex] \huge \boxed{ \red{ \boxed{\begin{cases} \theta = {45}^{ \circ} \\ \theta= {60}^{ \circ} \end{cases} }}}[/tex]

Step-by-step explanation:

distribute tan(θ):

=>tan²(θ)-(tan(θ)+√3tan(θ))+√3=0

remove parentheses:

=>tan²(θ)-tan(θ)-√3tan(θ)+√3=0

so this equation is now in standard form i.e ax²+bx+c=0

we can solve by factoring as we solve quadratic equation

factor out tanθ:

=>tan(θ)(tan(θ)-1)-√3tan(θ)+√3=0

factor out -√3:

=>tan(θ)(tan(θ)-1)-√3(tan(θ)-1)=0

group:

=>(tan(θ)-√3)(tan(θ)-1)=0

separate it as two different equation:

[tex] \implies \begin{cases} \tan( \theta) - 1 = 0 \\ \tan( \theta) - \sqrt{3} = 0 \end{cases}[/tex]

add 1 and √3 to both sides to first and second equation respectively:

[tex] \implies \begin{cases} \tan( \theta) - 1 + 1 = 0 + 1 \\ \tan( \theta) - \sqrt{3} + \sqrt{3} = 0 + \sqrt{3} \end{cases} [/tex]

[tex] \implies \begin{cases} \tan( \theta) = 1 \\ \tan( \theta) = \sqrt{3} \end{cases} [/tex]

[tex] \therefore \begin{cases} \theta = {45}^{ \circ} \\ \theta= {60}^{ \circ} \end{cases} [/tex]

Answer:

The description of Margot as a frail girl who had lost her vibrancy shows that she was in eager anticipation of the rain.

Step-by-step explanation:

The short story, "All Summer in a Day", tells of how a girl named Margot always stood differently from her classmates because she eagerly anticipated a time when the sun will come out as the scientists projected. It had been raining in this planet, Venus for seven years non-stop.

Margot who came from planet earth some five years ago could still clearly recall how the sun looked like and despite her description of it, the children still doubted her. On the day the sun finally came, the children locked Margot in a closet and she was unable to see the sun.

Answer:

120

Step-by-step explanation:

TQR = 180 - (35+25) = 120

TQP= 180-120=60

TNP=TQP =60

MNT= 180-60=120

Answer:

the ratio of 6 kg 400 gram is 1:662

Answer:

x ≈ 8.1 units

Step-by-step explanation:

Using the tangent ratio in the right triangle

tan72° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{25}{x}[/tex] ( multiply both sides by x )

x × tan72° = 25 ( divide both sides by tan72° )

x = [tex]\frac{25}{tan72}[/tex] ≈ 8.1 ( to the nearest tenth )

Answer:

B

Step-by-step explanation:

Using the cosine ratio in the right triangle and the exact value

cos45° = [tex]\frac{1}{\sqrt{2} }[/tex] , then

cos45° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{3}{c}[/tex] = [tex]\frac{1}{\sqrt{2} }[/tex] ( cross- multiply )

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

Answer:

Usually it means to solve it. Sometimes they give you values to substitute in for variables (letters) in the math sentence/equation/expression.

Does that make sense?

Step-by-step explanation:

Answer:

C. 262 cm

Step-by-step explanation:

Use the formula for the volume of a sphere, V = [tex]\frac{4}{3}[/tex][tex]\pi[/tex]r³

Since the diameter is 10 cm, the radius will be 5 cm

Plug in the radius into the formula:

V = [tex]\frac{4}{3}[/tex][tex]\pi[/tex](5³)

V = [tex]\frac{4}{3}[/tex][tex]\pi[/tex](125)

V = 523.6

Since the bowl is a hemisphere, divide this by 2:

523.6/2

= 261.8

Rounding to the nearest cm, the volume of the bowl is 262 cubic cm.

So, the correct answer is C. 262 cm

Answer:

y=4

Step-by-step explanation:

3(9) +4y= 43

27+4y=43

4y=16

y=4

Answer:

B

Step-by-step explanation:

C = πd = 3.14 * 32 = 100.48in

Answer:

D

Step-by-step explanation:

D starts low on both sides but is highest in the middle

Answer: https://brainly.com/question/22661875?answering=true&answeringSource=feedPublic%2FhomePage%2F10

Step-by-step explanation: hope tis helps

Answer:

x=5 and y=16

Step-by-step explanation:

x = number of pants

y = number of shirts

Set up equations:

Set the equations up as a system:

25x+14.5y=357

x+y=21

Steps:

Solve the system by substitution.

(You can also solve this system by elimination.)

25x + 14.5y=  357

x + y = 21

Step 1: Solve x+y=21 for x:

(x + y) − y = (21) − y(Subtract y from both sides)

x = −y + 21

Step 2: Substitute −y + 21 for x in 25x + 14.5y = 357:

25x + 14.5y = 357

25(−y + 21) + 14.5y = 357

−10.5y + 525 = 357 (Simplify both sides of the equation)

(−10.5y + 525) − 525 = (357) − 525(Subtract 525 to both sides)

−10.5y =  −168

−10.5y / −10.5 = −168 / −10.5 (Divide both sides by -10.5)

y = 16

Step 3: Substitute 16 for y in x = −y + 21:

x = −y + 21

x = −16 + 21

x = 5 (Simplify both sides of the equation)

Answer:

x=5 and y=16

Answer: 34

Hope this helps :)

Equations:

[tex]x+6=5+x[/tex]

[tex]-2(x-3)=-2x+6[/tex]

[tex]4-4x=3x+2[/tex]

[tex]4(x+1)=3(x+2)[/tex]

[tex]5-3x=-3x+4[/tex]

Answer:

[tex]x+6=5+x[/tex]

[tex]5-3x=-3x+4[/tex]

Step-by-step explanation:

Given

[tex]x+6=5+x[/tex]

[tex]-2(x-3)=-2x+6[/tex]

[tex]4-4x=3x+2[/tex]

[tex]4(x+1)=3(x+2)[/tex]

[tex]5-3x=-3x+4[/tex]

Required:

Which have no solution

[tex]x+6=5+x[/tex]

Subtract x from both sides

[tex]x -x+6 = 5 + x - x[/tex]

[tex]6 = 5[/tex]

[tex]x+6=5+x[/tex] has no solution because [tex]6 \ne 5[/tex]

[tex]-2(x-3)=-2x+6[/tex]

Open bracket

[tex]-2x + 6 = -2x + 6[/tex]

Both sides are equal.

Hence, there is an [tex]Infinite\ Number[/tex] of Solutions

[tex]4-4x=3x+2[/tex]

Collect like terms

[tex]-3x - 4x = 2 - 4[/tex]

[tex]-7x = -2[/tex]

Solve for x

[tex]x = \frac{-2}{-7}[/tex]

[tex]x = \frac{2}{7}[/tex] --- This has a solution

[tex]4(x+1)=3(x+2)[/tex]

Open brackets

[tex]4x + 4 = 3x + 6[/tex]

Collect like terms

[tex]4x-3x = 6 - 4[/tex]

[tex]x = 2[/tex] --- This has a solution

[tex]5-3x=-3x+4[/tex]

Add 3x to both sides

[tex]5 - 3x + 3x = -3x + 3x + 4[/tex]

[tex]5 = 4[/tex]

[tex]5-3x=-3x+4[/tex] has no solution because [tex]5 \ne 4[/tex]

Answer:

$80

Step-by-step explanation:

10x + 30 = y

He wants to rent it for 5 hours, so we replace x with 5.

10(5) + 30 = 80

He should expect to pay $80 for the rental.

Answer:

a/8 = b/15

Step-by-step explanation:

a/b = 8/15  -- divide both side by 8 and multiple both side by b

a/8 = b/15

Answer:

4 ) reflexive property of congrunce

5 ) Definition of Equilateral Triangle

Step-by-step explanation:

4) the lines are equal to each other

5) if one triangle is equal to another triangle than they must be the same triangle

Answer:

m = -1, b = 5.

Step-by-step explanation:

We can find the slope, m, by plugging in our coordinates into the slope formula: [tex]\frac{y2-y1}{x2-x1} =\frac{2-7}{3-(-2)}=\frac{-5}{5}=-\frac{5}{5}=-\frac{1}{1}=-1[/tex]. That gives us the slope. Now we can fill that in the slope intercept formula: [tex]y=-1x+b[/tex]. We know one of the coordinates and the slope, which allows to find the y-intercept. We know that for every 1 unit down on the line, we move 1 unit right, and vice versa. Meaning we can just count down (or up in this case), so, (-2, 7), (-1, 6), (0, 5). Therefore, our y intercept is 5.

Answer

x + 7.

Step-by-step explanation:

The answer is X + 7 because you know, 8x + 13 and if 7x - 9 we're solded. We remove 7x at 8x so at least we have only one x and we remove 9 than 16 so we have 7. That's why the reply is x + 7. Sorry if I wasn't clear, I am not really good at english.

Answer:

true

Step-by-step explanation:

Answer:

1/52 OR 0.01923076923 (unusual)

Step-by-step explanation:

So, since it is only asking for 1 card and there is 52 cards in a deck, you have a in 52 chance to pick that card.

Hope that helps!

*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆**☆*――*☆*――*☆*――*☆

Answer: 27528 ft^3

Explanation:

24 x 31 x 37 = 27528

I hope this helped!

<!> Brainliest is appreciated! <!>

- Zack Slocum

*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆**☆*――*☆*――*☆*――*☆

Answer:

The answer is D

Answer:

0,-1

Step-by-step explanation: