MATHEMATICS MIDDLE SCHOOL

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Answers

Answer 1

Answer:

Answer:

1. $(√(13) )/(3)$

2. 3.2362

3. $(60)/(11)$

Step-by-step explanation:

Cot is the trigonometric ratio defined by "adjacent" over "opposite". So, adjacent = 2 and opposite = 3.

By pythagorean theorem, we have the "hypotenuse" as $√(2^2+3^2)=√(13)$

Csc is defined as the trig ratio "hypotenuse" over "opposite". We know the sides, so Csc $\theta$ = $(√(13) )/(3)$

First answer choice is right.

By definition, Csc $\theta$ is the inverse of Sine $\theta$ . If given the value of sin theta, to find value of csc theta, we take the reciprocal of it. Hence:

$Csc\theta=(1)/(0.3090)\n=3.2362$

Third answer choice is right.

By definition tan and cot are inverse of each other. So the value of tan is the reciprocal of the value of cot. We can simply "flip" the value of tan theta to get the value of cot theta. Hence:

$Cot\theta=(60)/(11)$

Third answer is right.

Answer 2

Answer:

Answer:

1). First option √13/3

2). Third option 3.2362

3). Third option 60/11

Step-by-step explanation:

1). To find cosec θ

It is given cot θ = 2/3

We have cotθ = adjacent side /Opposite side

Hypotenuse = √(adjacent side² + opposite side²) =√(2² + 3²) = √13

Cosec θ = Hypotenuse/opposite side = √13/3

2). To find cosec θ

It is given that,

Sinθ = 0.3090

Cosec θ = 1/Sinθ = 1/0.3090 = 3.2362

3). To find cot θ

It is given that,

Tanθ = 11/60

Cot θ = 1/tan θ = 1/(11/60) = 60/11

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carol makes 9 1/3 cups of snack mix. she puts 2/3 cupof the snack mix into plastic bags does carol need?

Answers

9 1/3 is the same as 28/3. 2/3 can go into 28/3 14 times (14*2=28), so she needs 14 plastic bags.

2-1. , expression H +2.

Answers

Fourteen divided by two

Simplify 24 ÷ (-2)(3) + 7Simplify 24 ÷ (-2)(3) + 7

Answers

Answer:

The answer is 3

Step-by-step explanation:

Step 1: 24 ÷ -6 + 7

Step 2: -4 + 7

Step 3: 3

Write the equation of the line parallel to the given line and passing through the given point. y=6 through (3,4)

Answers

If the given line's equation is y = 6, then it is a horizontal line. Therefore, the parallel line must also be horizontal, and pass through (3, 4). In order for the line to pass through (3, 4), the y needs to be at 4, so the equation of the parallel line would be y = 4.

Hope this helps! :)

What times what equals 49

Answers

seven times seven equals forty nine

A convex pentagon has the following measurements for its interior angles: (x-8), (3x-11), (x+8), (x), and (2x+7). Which of the following could be measurements for interior angles of the pentagon? Select all that apply.A: 60

B: 68

C: 76

D: 108

E: 193

F: 540

Answers

Answer: A, B, C, E

Explanation:

The sum of the interior angles of a polygon can be determined by the formula: (n - 2)180 ; where n represents the number of sides. Since a pentagon has 5 sides, then (5 - 2)180 = 540

x - 8

3x - 11

x + 8

2x + 7

8x - 4 = 540

+4 +4

8x = 544

÷8 ÷8

x = 68

**********************

x - 8 ⇒ 68 - 8 = 60 (A)

3x - 11 ⇒ 3(68) - 11 = 193 (E)

x + 8 ⇒ (68) + 8 = 76 (C)

x ⇒ (68) (B)

2x + 7 ⇒ 2(68) + 7 = 143

The sumof the pentagon's interior angles is: 540°

According to the Question, we have: (x-8)+(3x-1)+(x+8)+x+(2x+7)=540

x-8+3x-11+x+8+x+2x+7=540

x+3x+x+x+2x=540+8+11-8-7

8x=544

x=544/8=68

(x-8)=68-8=60 (choose letter A)

(3x-11)=3*68-11=193 (choose letter E)

(x+8)=68+8=76 (choose letter C)

(x)=68 (choose letter B)

(2x+7)=2*68+7=143 (cannot select any letter)

In short, we choose letter A, B, C and E.