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3 years ago

Which numbers below belong to the solution set of the equation? Check all that apply. x+9=26

Mathematics

1 answer:

aleksandrvk [35]3 years ago

7 0

Subtract x=26-9, Simplify 26-9 to 17, So x=17

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Suppose that θ is an acute angle of a right triangle and that sec(θ)=52. Find cos(θ) and csc(θ).

insens350 [35]

Answer:

$\cos{\theta} = \dfrac{1}{52}$

$\csc{\theta} = \dfrac{52}{\sqrt{2703}}$

Step-by-step explanation:

To solve this question we're going to use trigonometric identities and good ol' Pythagoras theorem.

a) Firstly, sec(θ)=52. we're gonna convert this to cos(θ) using:

$\sec{\theta} = \dfrac{1}{\cos{\theta}}$

we can substitute the value of sec(θ) in this equation:

$52 = \dfrac{1}{\cos{\theta}}$

and solve for for cos(θ)

$\cos{\theta} = \dfrac{1}{52}$

side note: just to confirm we can find the value of θ and verify that is indeed an acute angle by $\theta = \arccos{\left(\dfrac{1}{52}\right)} = 88.8^\circ$

b) since right triangle is mentioned in the question. We can use:

$\cos{\theta} = \dfrac{\text{adj}}{\text{hyp}}$

we know the value of cos(θ)=1\52. and by comparing the two. we can say that:

length of the adjacent side = 1
length of the hypotenuse = 52

we can find the third side using the Pythagoras theorem.

$(\text{hyp})^2=(\text{adj})^2+(\text{opp})^2$

$(52)^2=(1)^2+(\text{opp})^2$

$\text{opp}=\sqrt{(52)^2-1}$

$\text{opp}=\sqrt{2703}$

length of the opposite side = √(2703) ≈ 51.9904

we can find the sin(θ) using this side:

$\sin{\theta} = \dfrac{\text{opp}}{\text{hyp}}$

$\sin{\theta} = \dfrac{\sqrt{2703}}{52}}$

and since $\csc{\theta} = \dfrac{1}{\sin{\theta}}$

$\csc{\theta} = \dfrac{52}{\sqrt{2703}}$

4 0

3 years ago

Helppppppp??????!!!!!!!!!!

zzz [600]

I think the answer would be C. (btw, you should charge your phone/tablet, lol)

7 0

3 years ago

Joseph is creating a dilation through point B with a scale factor of 2. Which statements about the dilation are correct? Check a

swat32

Answer:

Options (1), (2) and (4).

Step-by-step explanation:

Given question is incomplete; Find the complete question in the attachment.

Triangle ABC is a right triangle.

ΔABC has been dilated by a scale factor of 2 forming ΔA'B'C'.

These are the observations,

1). A and A' will be co-linear.

2). Since the given triangle has been dilated about a point B therefore, after dilation vertex B and B' will at be same location.

3). Length of B'C' = 2BC

4). AB and BC are the segments which will lie on the sides BA' and BC'.

5). Pre-image ABC will be inside the image A'B'C'.

Therefore, Options (1), (2) and (4) will be the answer.

4 0

3 years ago

Read 2 more answers

Jerome is painting a rectangular toolbox that is 20 inches by 10 inches by 8 inches. A tube of paint covers 300 square inches. W

Valentin [98]

Answer:

880 in³

Step-by-step explanation:

L = 20, W = 10, H = 8

2(h × W) + 2(h × L) + 2(W × L)

= 2(8*10) + 2(8*20) + 2(10*20)

= 2(80) + 2(160) + 2(200)

= 160 + 320 + 400

= 880 in³

8 0

3 years ago

Help on my quiz i’m so confused

DerKrebs [107]

Answer:

Step-by-step explanation:

6 0

3 years ago