solve for x: -1/2x + 15=-3
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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:

cosec45° = [tex]\sqrt{2}[/tex]

Step-by-step explanation:

Using the identity

cosec x = [tex]\frac{1}{sinx}[/tex] and the exact value

sin45° = [tex]\frac{1}{\sqrt{2} }[/tex]

Then

cosec45° = [tex]\frac{1}{\frac{1}{\sqrt{2} } }[/tex] = [tex]\sqrt{2}[/tex]

Answer:

E

Step-by-step explanation:

i dont know at this point

Answer:

angle E

Step-by-step explanation:

Hello There!

We need to find an angle that is a pair with angle D and they have to be alternate interior angles

alternate interior angle properties:

In the image below; represents a pair of alternate interior angles

These properties match angle D with angle E

Why? they are both on the inside of the parallels

They also happen to be congruent

Answer: A

Step-by-step explanation:

Answer:

60

Step-by-step explanation:

Answer:

y=4

Step-by-step explanation:

3(9) +4y= 43

27+4y=43

4y=16

y=4

Answer:

[tex]y = 2(0.5) {}^{x} [/tex]

Step-by-step explanation:

Use the general formula of exponential equation

[tex]y = ab {}^{x} [/tex]

Plug 0,2 into the function

[tex] - 2 = ab {}^{0} [/tex]

[tex] - 2 = a \times 1[/tex]

[tex]a = - 2[/tex]

[tex]y = - 2b {}^{x} [/tex]

[tex] - 4 = - 2b {}^{ - 1} [/tex]

[tex]2 = b {}^{ - 1} [/tex]

[tex] {2}^{ \frac{ 1}{ - 1} } [/tex]

[tex]2 {}^{ - 1} = 0.5[/tex]

B=0.5

[tex]y = 2(0.5) {}^{x} [/tex]

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:

120

Step-by-step explanation:

TQR = 180 - (35+25) = 120

TQP= 180-120=60

TNP=TQP =60

MNT= 180-60=120

Answer:

Hhhhhhhhnnnnnnnnnn

Step-by-step explanation:

Bbb

Answer:

true

Step-by-step explanation:

Answer:

y=1/2x-7/2

Step-by-step explanation:

Since the line is parallel, we know that the slope is the same as the equation given: 1/2. So you just plug in the coordinates for x and y. So it would be -2=1/2(3)+b because we don't know what the intercept is for this line. If you simplify the equation you'll get -2=1.5+b. Then, you must isolate B, so you would get -3.5=b or -7/2.

Answer:

I have made it in above picture

Answer:

the ratio of 6 kg 400 gram is 1:662

Answer:

18

Step-by-step explanation:

Here is my answer. I hope this is helpful.

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:

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

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:

4

Step-by-step explanation:

volume is equal to a x a x a

This means that [tex]a^{3}[/tex] = V

Therefore, a = cube root of V, which is 4

Answer:

x y

12 100

13 70

14 40

Step-by-step explanation:

Answer:

the answer is 1,1 1/2 os c

Step-by-step explanation:

Step-by-step explanation:

Given

[tex] \sqrt{4} \times (2) \\ \sqrt{ {2}^{2} } \times 2 \\ = 2 \times 2 \\ = 4

Hope it will help :)❤

Look at the explanation to understand.

Step-by-step explanation:

Step 1.

Apply the rule. (a) = a

For this expression, (2) = 2

[tex]\sqrt{4}\times2[/tex]

Step 2.

Multiply 4 by 2.

4 × 2 = 8

Step 3.

Prime factorization of 8: 2³

[tex]\sqrt{2^3}[/tex]

Step 4.

Apply the exponent rule. [tex](a^b^+^c=a^b\times a^c)[/tex]

2³ = 2² × 2

[tex]\sqrt{2^2\times2}[/tex]

Step 5.

Apply the radical rule. [tex]\sqrt{ab}=\sqrt{a}\sqrt{b}, a\geq 0, b\geq 0[/tex]

[tex]\sqrt{2^2}\sqrt{2}[/tex]

Step 6.

Apply the radical rule again. [tex]\sqrt{a^2}=a, a\geq 0[/tex]

[tex]2\sqrt{2}=4[/tex]

Hence, 4 is the answer.

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:

The answer is 2

Step-by-step explanation:

5x² = 20

x² = 4

x = 2

Answer:36

Step-by-step explanation:it just is

Answer: 34

Hope this helps :)