some of the values of a linear function given in the table which of the following could be the graph of the function

Answer:

[tex]17\sqrt{3}[/tex]

Quiz Results:

The length of the longer leg in the considered 30-60-90 Special Right Triangle is given by: Option 3) 17√3yd

The right angled triangle in which, the angles are of the measure 30, 60 and 90 degrees is called 30-60-90 Special Right Triangle.

For any triangle ABC, with side measures |BC| = a. |AC| = b. |AB| = c,

we have, by law of sines,

[tex]\dfrac{sin\angle A}{a} = \dfrac{sin\angle B}{b} = \dfrac{sin\angle C}{c}[/tex]

Remember that we took

[tex]\dfrac{\sin(angle)}{\text{length of the side opposite to that angle}}[/tex]

The wider the angle is, the larger the side opposite to is.

For this right angled triangle, the side opposite to 60 degrees angle is larger leg (let it be of x yd), and the side opposite to 30 degrees angle is shorter leg (of 17 yd).

As shown in the image below, using the sine law for non right angles,  we get:

[tex]\dfrac{\sin\angle A}{a} = \dfrac{\sin\angle B}{b}\\\\\dfrac{\sin(30^\circ)}{17} = \dfrac{\sin(60^\circ)}{x}\\\\x =\dfrac{17 \times \sin(60^\circ)}{\sin(30^\circ)} = 17\sqrt{3} \: \rm yd[/tex]

Thus, the length of the longer leg in the considered 30-60-90 Special Right Triangle is given by: Option 3) 17√3yd

Learn more about law of sines here:

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Answer:

q= 49.5

Step-by-step explanation:

[tex] \frac{33}{q} = \frac{8}{12} [/tex]

Cross multiply:

8q= 33(12)

8q= 396

Divide by 8 on both sides:

q= 396 ÷8

q= 49.5

Answer:

11.1%

Step-by-step explanation:

percentage decrease is calculated as

[tex]\frac{decrease}{original}[/tex] × 100%

decrease = 18 - 16 = 2 , then

percent decrease = [tex]\frac{2}{18}[/tex] × 100% = 11.1% ( to the nearest tenth )

Answer:

see explanation

Step-by-step explanation:

(a)

Given

[tex]\frac{y}{3}[/tex] + [tex]\frac{y+3}{5}[/tex]

The common denominator is 15 ( the LCM of 3 and 5 )

Multiply numerator/ denominator of first fraction by 5

Multiply the numerator/ denominator of second fraction by 3

= [tex]\frac{5y}{15}[/tex] + [tex]\frac{3y+9}{15}[/tex] ← add numerators , leaving denominator of 15

= [tex]\frac{5y+3y+9}{15}[/tex]

= [tex]\frac{8y+9}{15}[/tex]

(b)

Given

[tex]\frac{3x}{8}[/tex] - [tex]\frac{x+5}{4}[/tex]

The common denominator is 8 ( the LCM of 8 and 4 )

Multiply numerator/ denominator of second fraction by 2

= [tex]\frac{3x}{8}[/tex] - [tex]\frac{2(x+5)}{8}[/tex] ← simplify numerators leaving denominator of 8

= [tex]\frac{3x-2x-10}{8}[/tex]

= [tex]\frac{x-10}{8}[/tex]

Answer:

a) (8y + 9)/15.

b) (5x + 10)/8.

Step-by-step explanation:

(a)  y/3 + (y + 3)/5

     The LCD of 3 and 5  is 15 so we have:

     5y/15 + 3(y + 3)/15

      = (5y + 3(y + 3)) / 15

     = (5y + 3y + 9)/15

     = (8y + 9)/15.

b)  3x/8 + (x + 5)/4

     The LCD of 4 and 8  is 8 so we have:

     3x/8 + 2(x + 5)/8

      = (3x + 2x + 10) / 8

      = (5x + 10)/8.

Answer:

B

Step-by-step explanation:

Answer:

I think the answer is B, but don't take my word for it as I'm not the best at math.

Hope this helps you anyhow! <3

| c - 7 | 《 17

- 17 《 c - 7 《 17

add sides 7

- 17 + 7 《 c - 7 + 7《 17 + 7

simplification

- 10 《 c《 24

Answer:

c - 7 ≤ 17

c ≤ 24

Step-by-step explanation:

The difference of c and 7 can be written as c - 7 or 7 - c.

Now, since c - 7 is less than or equal to 17, you need to add ≤ to imply that it's less than or equal to 17.

As always, write the 17 on the other side. Now you have an inequality.

If you just need the equation, it's c - 7 ≤ 17.

But if you want to solve for c, it would be c ≤ 24.

(bring the like terms together and isolate c.)

Answer:

4√2

Step-by-step explanation:

If a square has a perimeter of 16,  then its side lengths are 4.

Use the pythagorean theorem to find the diagonal.

√32 can be simplified to 4√2.

The length of the diagonal of the square whose perimeter is 16 is 4√2

What is diagonal of the square?

The length of a diagonal is equal to the length of a side multiplied by the square root of 2

Given data ,

Let d be the diagonal of a square

Perimeter of square = 16

Perimeter of square = 4 x A

16 = 4 x A

A = 4

Therefore , diagonal of square is = 4√2

Hence ,The length of the diagonal of the square whose perimeter is 16 is 4√2

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Answer:

2pier = A x

Step-by-step explanation:

Answer: They are related by the AAS postulate and they can be proven congruent.

Step-by-step explanation: You can see that one of the lines on each of the triangle has that little tick which means those lines are congruent. You can also see that for two of the angles one of them has one arc and the other has two arcs for BOTH triangles which makes those two angles congruent. Two angles and one side congruent makes the triangles congruent by the AAS postulate.

I hope I helped! :)

Answer:

x=-7

Step-by-step explanation:

-30=5(x+1)

6-1(x+1)

x=-1-6

=-7

The answer is [tex]x=-7[/tex]

Answer:

-4 *-4 *-4

= 16*-4

= ANWSER

-9*-9

=81

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

A polynomial is an expression with variables, and this expression does not have a variable. So, answer D is not a polynomial.

Step-by-step explanation:

a. 6 £/hr

b. 6.8 £/hr.....is this right?

Answer:

B) 1 hour = £10

Step-by-step explanation:

the higher rate starts from 20 hours and the pay is £120 if you go to 30 hours, the pay rate is £220. A raise of £100. This means the new pay rate is for every 1 hour worked, you get £10

Answer:

it would be 200 points. Lets assume that all of the apprentice magicians are 143 years old. If so, then 143 x 7 = 1001. 1001 + 200 = 1201. 1021 ÷ 8 (the number of magicians) the answer is 150. so the age of head wizard is actually 200 years.

Answer:

srry if you still need this asnwer but here you go my grades

Step-by-step explanation:

Answer:

SSS

Step-by-step explanation:

the corresponding sides of the triangles are proportional to each other

Answer:

-32

Step-by-step explanation:

-2 x -2 x -2 x -2 x -2 = -32

Answer:

y =(2/3)x + 80

Step-by-step explanation:

to get the slope.. change in y/change in x  in two points.

so use the points (0,80) and (30,100) and you get 2/3

you know the intercept, where x=0 (0,80) therefore the equation is 2/3x + 80

Answer:

12

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

Answer:

Step-by-step explanation:

actual over theoretical times 100 equals ur percentage

Answer:

Step-by-step explanation:

According to Pythagoras Theorem,

[tex]{(height)}^{2} + {(base)}^{2} = {(hypotenuse)}^{2} [/tex]

[tex] = > {12}^{2} + {5}^{2} = {x}^{2} [/tex]

[tex] = > {x}^{2} = 144 + 25[/tex]

[tex] = > {x}^{2} = 169[/tex]

[tex] = > x = \sqrt{169} [/tex]

=> x = 13 (Ans)

Answer: 73 will be your answer hope this helped

Step-by-step explanation:

Answer:

the red one is the pre image because if there is two of the same letters then there is a dash behind the second letter.

Step-by-step explanation:

PLEASE GIVE BRAINLIEST!!!!

Answer:

-9

Step-by-step explanation:

I just took the same test

Answer:

E=30H

Melissa earns $330 in 11 hours

Step-by-step explanation:

Answer:

Equation = 30h=E

Melissa's earnings for 11 hours : $363

If you need further explaination I'll be happy to help!!

~ PumpkinSpice1 ♥

Answer:

x = √3

Step-by-step explanation:

tan 30° = 1/x

x = 1.73

but to get it in radical form:

sin 30° = 1/hypotenuse

hypotenuse = 2

x² = 2²- 1² = 4 - 1 = 3

x = √3