the water level in Noah's water tank is 72 inches high. Noah begins to drain a water tank by opening a valve. the water drains at the speed of 5 inches per minute.​ what is the slope?

Answer:

Please check the explanation.

Step-by-step explanation:

Given the equation

[tex]x^2\:-16x\:+\:39\:=\:0[/tex]

Subtract 39 from both sides

[tex]x^2-16x+39-39=0-39[/tex]

Simplify

[tex]x^2-16x=-39[/tex]

Rewrite in the form x² + 2ax + a²

solve for a, 2ax = -16x

2ax = -16x

divide both sides by 2a

2ax/2x = -16x/2x

a = -8

Add a² = (-8)² to both sides

[tex]x^2-16x+\left(-8\right)^2=-39+\left(-8\right)^2[/tex]

simplify

[tex]x^2-16x+\left(-8\right)^2=25[/tex]

Apply perfect square formula:  (a-b)² = a² - 2ab + b²

[tex]\left(x-8\right)^2=25[/tex]           ∵ [tex]x^2-16x+\left(-8\right)^2=\left(x-8\right)^2[/tex]

Thus,

[tex]\left(x-8\right)^2=25[/tex]

BONUS! EXTENDED SOLUTION!

We can further solve for x such as

[tex]\mathrm{For\:}f^2\left(x\right)=a\mathrm{\:the\:solutions\:are\:}f\left(x\right)=\sqrt{a},\:-\sqrt{a}[/tex]

solve

[tex]x-8=\sqrt{25}[/tex]

[tex]x-8=\sqrt{5^2}[/tex]

[tex]x-8=5[/tex]        

[tex]x=13[/tex]

similarly,

[tex]x-8=-\sqrt{25}[/tex]

[tex]x-8=-5[/tex]

[tex]x=3[/tex]

Therefore,

[tex]x=13,\:x=3[/tex]

Answer:

Concept: Algebraic Function

Answer:

-4m-3s-2

Step-by-step explanation:

Answer:

(1, 0.5)

Step-by-step explanation:

From the graph attached,

x-values are representing the number of games downloaded,

y - values are representing the total cost.

Unit rate means rate of 1 game downloaded.

If we represent this in terms of coordinates,

x- value (game downloaded) = 1

y - value (price of one game download) = $0.5

Therefore, point (1, 0.5) will represent the unit rate.

Option (2) on the top row will be the answer.

Answer:

sin30: 1/2   cos30: (sqrt3)/2    tan60: (sqrt3)

Step-by-step explanation:

Answer:

65

Step-by-step explanation:

0.50(80)+25

40+25 =60

Answer:

65°

Step-by-step explanation:

They are corresponding angles if M and N are parallel

Answer:

m∠b = 65°

Step-by-step explanation:

∠b and the 65° angle are known as corresponding angles meaning they are equivalent. Therefore, m∠b is 65°.

Answer:

-21p - 7c

Step-by-step explanation:

Answer:

Equation for question number 1:

y = -6x -1

Equation for question number 2:

y = 6x

OR

y = 6x + 0

btw, if you want to know how to solve the equations by urself, the equation is y = mx + b

m = slope

b = starting point / intercept

hope this helps!

Answer:

y= -1/3x + 1

Step-by-step explanation:

The slope is going down 1  and 3 to the right so its -1/3 and the y intercept is 1 so b=1

Hope it helps !

Answer:

5

Step-by-step explanation:

the answer is 5.75, but when rounded off, it will become 5

ask me

what help needed

I can help uhh

Answer:

you got this I believe in u and your talents

Step-by-step explanation

JESUS LOVES YOU BRO

Answer:

5% of the cars has a standard transmission.

Step-by-step explanation:

20 out of 400 is equal to 5 out of 100, which would be 5%

therefore 20 is 5% of 400

Answer: 390

Step-by-step explanation:

32 ÷ 6 = 5 1/3

2080 ÷ 5 1/3 = 390

Answer:

a^4b^2

Step-by-step explanation:

s represents one side, or a^2b

so if s^2=A and s=a^2b then A=(a^2b)^2 or a^4b^2

Answer:

D

C

Step-by-step explanation:

Answer:

I tried solving it and I got an answer of 86c

Hope I helped!! :)

Step-by-step explanation:

Answer:

k = - 3.8

k = 3.4 - 7.2

k = -3.8

Answer:

k = -3.8

Step-by-step explanation:

Equation Solving

We are given the equation:

k + 7.2 = 3.4

To solve the equation we must make k the subject, that is, isolate the letter k at the left side of the equation.

Since the number 7.2 is adding with k, we subtract 7.2 on both sides:

k + 7.2 - 7.2 = 3.4 - 7.2

Simplifying the left side, the numbers cancel:

k = 3.4 - 7.2

Now calculate the subtraction 3.4-7.2=-3.8

k = -3.8

Answer:

c = 70°

Step-by-step explanation:

The sum of the angles of a triangle is always 180°.

We can use the other two to solve for c:

57 + 53 + c = 180

110 + c = 180

c = 70

Therefore, angle c is 70°.

Answer:

x > 6

Step-by-step explanation:

Given

3(x + 4) - 5(x - 1) < 5 ← distribute and simplify left side

3x + 12 - 5x + 5 < 5

- 2x + 17 < 5 ( subtract 17 from both sides )

- 2x < - 12

Divide both sides by - 2, reversing the symbol as a result of dividing by a negative value.

x > 6

Answer:

First Question: 75 x [tex]10^{3}[/tex] and 7.5 x [tex]10^{4}[/tex]

Second Question:

A = bh (parallelogram)

A = 1/2bh (triangles)

Step-by-step explanation:

First Question: It's multiplied by [tex]10^{3}[/tex] because 75,000 has 3 zeros.

It's also multiplied by [tex]10^{4}[/tex] because you move the decimal place 4 times on the right at 7.5 which leads to 75,000.

Second Question: Well there aren't specific numbers to solve the areas of the parallelogram or triangle, so I gave the formulas instead. "b" stands for base and "h" stands for height

Hope this helped! <3

Answer:

A

Step-by-step explanation:

Its a positive slope and you go up 2 and to the right 5

Answer:

The probability is 1/10.

Step-by-step explanation:

Without loss of generality, the first card is blue. Then choose a red one with probability 3/5, a blue one with probability 2/4=1/2, a red one with probability 2/3, and the last blue one with probability 1/2, followed by the last red one.

The result is 2/5⋅(1/2)^2=1/10.

OR

There are actually 6!/(3!3!)=720/36=20 ways, so the probability is 2/20=1/10.

Answer:

[tex] \frac{k}{5} = 7 \\ k = 5 \times 7 \\ \boxed{k = 35}[/tex]

k=35 is the right answer.

Answer:

whats the rest?

Step-by-step explanation:

Answer: The answer is C) y= 2/3x-3

Step-by-step explanation:

i figure it out

Answer:

C

Step-by-step explanation:

so obviously your slop is 2/3. so it starts with y=2/3. so B is out of the question. since the slope is x in the equation, you still have to add the x in the equation; y=2/3x

Answer:

DF = 10 units

[tex]m\angle DFG = 28^\circ[/tex]

EG = 5.04

Step-by-step explanation:

Properties of Rhombus es

The image contains a rhombus with the following data (assume the center as point O):

DO = 5 units

GF = 5.6 units

[tex]m\angle FEO = 62^\circ[/tex]

4. Calculate DF

Applying property 4, diagonals bisect each other, thus the length of DF is double the length of DO, i.e. DF=2*5 = 10:

DF = 10 units

5. Calculate [tex]m\angle DFG[/tex]

Applying property 4 in triangle EFO, the center angle is 90°, thus angle EFO has a measure of 90°-62°=28°.

Applying property 5, this angle is half of the measure of angle EFG and angle DFG has the same measure of 28°.

[tex]m\angle DFG = 28^\circ[/tex]

6. FG is the hypotenuse of triangle OFG, thus:

[tex]OG^2=FG^2-OF^2[/tex]

[tex]OG^2=5.6^2-5^2[/tex]

[tex]OG^2=6.36[/tex]

[tex]OG=\sqrt{6.36}=2.52[/tex]

EG is double OG: OG=2*2.52=5.04

EG = 5.04

Answer:

length = 8

width = 4

Step-by-step explanation:

Area = length x breadth

Let x represent the width

length = x + 4

32 = x × (x + 4)

32 = x² + 4x

x² + 4x  - 32  = 0

solving using quadratic equation =

(x² - 4x) -32 + 8x

x = 4 or -8

since width cannot be a negative number, we would use 4

Answer:

5/16

Step-by-step explanation:

Answer:

a.y=6

b.-1/8

c.1/2

d.2800

e.-8

f.7.71

Step-by-step explanation: