I need help with this proof!

For the first one we divide every element by sqrt3

we get

q+2/sqrt3 =sqrt5/sqrt3

q=(sqrt5-2)/sqrt3

q=sqrt3*sqrt5-2*sqrt3/3

q=sqrt15-2sqrt3/3

which is the third option

For the second one

sqrt(2y-5) +4=8

first we move the 4 to the right

sqrt(2y-5)=4

we remove the square root by bringing to the power of two

2y-5=16

2y=21

y=21/2

y=10 1/2

third option

Step-by-step explanation:

y = kx, where k is a real constant.

When x = 6, y = -12:

(-12) = (6)k

Therefore k = -2.

Hence y = -2x.

The direct variation of Y with X is Y = -2X.

Equation: A declaration that two expressions with variables or integers are equal. In essence, equations are questions, and attempts to systematically identify the solutions to these questions have been the driving forces behind the creation of mathematics. Simple algebraic equations with merely addition or multiplication to differential equations, exponential equations with exponential expressions, and integral equations are examples of different types of equations. They are employed to represent a number of physics laws.

As per the given data:

Y varies directly with X.

Y equals -12 when X equal 6.

Let's consider the equation Y = kX:

∴ -12 = k(6)

k = -2

Y = -2X

Hence, the direct variation of Y with X is Y = -2X.

To learn more about equation, click:

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Answer:

The width of the rectangle given is equal to 3m.

Step-by-step explanation:

In order to solve this question we need to know that the areas of the rectangle is equal to [tex]A_{rectangle} = (l)(w)[/tex], where "l" is length and "w" is width. So know in order to solve this question we would have to find out the unknown width by using area and the length of the triangle. Based on the formula I wrote down earlier we can understand the following.....

[tex]A_{rectangle} = (l)(w)[/tex]

[tex]\frac{A_{rectangle} }{l} = \frac{(l)(w)}{l}[/tex]

[tex]w = \frac{A_{rectangle} }{l}[/tex]

Just now we found out the formula that we can use to solve for the width when we know the area and the length of the rectangle. Now in order to get the answer we just have to plug in the values we know, and we get........

[tex]w = \frac{A_{rectangle} }{l}[/tex]

[tex]w = \frac{11m^{2} }{(3\frac{2}{3}m )}[/tex]

[tex]w = 3m[/tex]

Answer: its b

Step-by-step explanation:

Answer:

B.

Step-by-step explanation:

Answer:

52 miles per hour

Step-by-step explanation:

The formula for Average speed is given as: Distance(miles)/Time in hours

From the question,

Distance = 117 miles

Time = 2.25 hours

Average Speed = 117 miles/2.25 hours

Average Speed = 52 miles per hour

The average speed that he was traveling is 52 miles per hour

Answer:

-543

Step-by-step explanation:

For every value of k, you substitute 9 and for every value of c, you substitute 2

-6((8x(9)+ 9(2)) - 3

so order of operations says you should do what's in the parentheses first.

8 x 9= 72     and 9 x 2 = 18

so now you have -6 ( 72 + 18) -3

Finish the calculating inside the parentheses:   -6 (90) -3

and now multiply -6   and 90 before you subtract 3

-6 x 90 = -540

-540 - 3   = -543

Answer:

The constant of proportionality = k = 2/5

Step-by-step explanation:

Also given that The number of gallons, g (/), is proportional to the number of

seconds, t (x).

i.e.

g ∝ t

g = k × t

k = g / t

as

g = 2

t = 5

Thus,

k = g / t

  = 2 / 5

Thus, the constant of proportionality = k = 2/5

Answer:

f(x) = 9x+8

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

i did the test

Given:

Initial pay rate = $8.50 per hour

Increase in pay rate = $0.75 per year

To find:

The equation that represents the relationship between years on the job and pay for hour.

Solution:

Let x be the number of years and y be the pay rate after x years.

According to the question,

Increase in pay rate in 1 year = $0.75

Increase in pay rate in x year = $0.75x

So, variable pay rate = $0.75x

Initial pay rate = $8.50

So, the total pay rate is

Total pay rate = Initial pay rate + Variable pay rate

[tex]y=8.50+0.75x[/tex]

Therefore, the required equation is [tex]y=8.50+0.75x[/tex].

Answer:

its B

Step-by-step explanation:

Answer:

i don't know if you still need a answer or not-

Step-by-step explanation:

Answer:

B because the 3 interior angles of any triangle adds up to 180 degrees.

Step-by-step explanation:

Answer:

Thus: m=14°, n=28°

Step-by-step explanation:

Angles in a Circle

Let's review some concepts about angles in a circle.

The central angle is formed between two radii and its vertex lie at the center of the circle.

The inscribed angle is formed between two chords whose vertex lies on the circumference of a circle.

The measure of a central angle x formed by the same lines that define an inscribed angle y is:

x = 2y

Following the definitions and relations above, we find that:

The first statement leads to:

98 = 2 (35+m)

Dividing by 2:

49 = 35 + m

m = 49 - 35 = 14

m = 14°

The second statement leads to:

n = 2m = 28°

Thus: m=14°, n=28°

Answer:

82.8

Step-by-step explanation:

24/.29

=82.75862

but you want it rounded so 82.8 is your answer

I hope this helps

Answer:

82.8

Step-by-step explanation:

Step 1: If 29% of a number is 24, then what is 100% of that number? Set up the equation.

24 over 29% = Y over 100%

Step 2: Solve for Y

Using cross multiplication of two fractions, we get

29Y = 24 x 100

29Y = 2400

Y = 2400 over 100 = 82.76

If you round 82.76 to the nearest tenth you get 82.8.

Answer:

True. 3:4 is the same as 30:40 because they both times 10

Step-by-step explanation:

Answer:

A. y>x−9y is greater than x minus 9

Answer:

This is the answer...And can I get the Brainliest

Answer:

180

Step-by-step explanation:

To solve we must first plug 31 into each expression for x.

2(31)+5= 67

3(31)-9= 84

31-2= 29

Then, remember that the perimeter is the sum of all of the sides. So add all of the previous sums, 67+84+29. Therefore, the answer is 180.

Answer:

$45

Step-by-step explanation:

so where the line intercepts the 2 hours is $45, and to find the .25 hours we take the $20 for working one hour and divide that by four, because .25 is 1/4 of an hour. so 20/4 is five. then you add 5 to 40 and we get $45 for work 2.25 hours. hope that helped

Answer:

$172.46

Step-by-step explanation:

Discount = 229.95 × 25/100

Discount = 229.95 x 0.25

= $57.49

Final Price = 229.95 - 57.4875

= $172.46

Answer:

Step-by-step explanation:

Temperature is the abiotic factor that is changing the ecosystem. Both the top layer temperature and the overall temperature of the lake are increasing. The warmer temperatures have delayed the yearly springtime mixing of warm and cold water in the lake.

Answer:

infinite

Step-by-step explanation:

plz give brainliest

Answer:

infinite

it has infinite solutions because the numbers on both sides of the equal sign are exactly the same

Step-by-step explanation:

Answer:

his faucet will leak 6/4 cup of water every hour, its c, you are correct good job, good luck

Step-by-step explanation:

Since it leaks 3/4 cups every 1/2 hour, in a whole hour it will leak twice as much:

[tex]\dfrac{3}{4}\cdot 2=\dfrac{6}{4}[/tex]

Answer:

x=2

Step-by-step explanation:

first distribute the 1/2

1/2x - 5=-4

then add 5 to both sides

1/2x=1

multiple by 2 on both sides

x=2