Kayla pays her plumber $22 per hour to replace her drain pipe. She ends up paying him $99. Which equation can you use to find h, the number of hours the plumber worked?

Answers

Answer 1

Answer: Simple....

so, if she payed him $99 in total and she payed him $22 dollars per hour...

just make it...

99=22h
and...

$(99)/(22)= (22h)/(22)$

4.5=h

Thus, the plumber worked 4.5 hours. (4 and a half hours)

Answer 2

Answer: Let's see...
.
FORMULAS!! Or equations too...
.
Sorry, we just have to, even if you don't want to.
.
$22x = $99, where x is the numbers of hours the plumber worked.
.
Now this is REALLY easy.
.
Divide 22 on both sides!!
.
22x/22 = 99/22.
.
So... what's 99/22?
.
4.5.
.
The plumber worked 4.5 hours.
.
Hope I helped!!

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Answers

$2.)\n \n n^2 - 9n +14 = 0 \n \n a=1 , \ b = -9, \ c = 14 \n \n\Delta =b^2-4ac = (-9)^2 -4\cdot1\cdot 14 = 81 -56 = 25 \n \nn_(1)=(-b-√(\Delta) )/(2a)=(9-√(25))/(2 )=( 9-5)/(2)=(4)/(2)= 2$

$n_(2)=(-b+√(\Delta) )/(2a)=(9+√(25))/(2 )=( 9+5)/(2)=(14)/(2)= 7 \n \n Answer : \ n^2 - 9n +14 =(n-2)(n-7)$

$3.)\n \n n^2 + 4n - 12 =0 \n \n a=1 , \ b = 4, \ c = -12 \n \n\Delta =b^2-4ac = 4^2 -4\cdot1\cdot (-12) = 16+48=64 \n \nn_(1)=(-b-√(\Delta) )/(2a)=(-4-√(64))/(2 )=( -4-8)/(2)=(-12)/(2)= -6$

$n_(2)=(-b+√(\Delta) )/(2a)= (-4+√(64))/(2 )=( -4+8)/(2)=(4)/(2)=2\n \n Answer : \ n^2 +4n -12 =(n+6)(n-2)$

second way :

$2.)\n \n n^2 - 9n +14 = n^2 - 9n+2n -2n +14 = n^2 - 7x -2n +14 =\n \n = n(n-7)-2(n-7)=(n-7)(n- 2)\n \n \n Answer : \ n^2 - 9n +14 =(n-2)(n-7)$

$3.)\n \n n^2 + 4n - 12 = n^2 + 4n +2n - 2n - 12 = n^2 + 6n - 2n - 12 =\n \n = n(n+6) -2(n+6)=(n+6)(n-2) \n \n \n Answer : \ n^2 +4n -12 =(n+6)(n-2)$

n^2-9n +14
n^2-7n-2n+14
n(n-7) -2(n-7)
(n-2)(n-7)

Anna wrote this equation to represent the total number of fish she owns. 34 = 11 t

Answers

Answer:

Step-by-step explanation:

Eleven (11) plus t equals thirty-four (34)

Sarah invested $2,500 in an account paying an interest rate of 2.1% compounded continuously. Assuming no deposits or withdrawals are made, how much money, to the nearest hundred dollars, would be in the account after 14 years?

Answers

Answer:3400

Step-by-step explanation:

Final answer:

To find the amount of money in the account after 14 years with continuous compound interest, we can use the formula A = P * e^(rt), where P is the principal amount, e is Euler's number, r is the interest rate per year, and t is the number of years. Substituting the values into the formula, we find that the final amount in the account is approximately $3831.

Explanation:

To find the amount of money in the account after 14 years, we can use the formula for continuous compound interest, which is given by the formula:

A = P * e^(rt)

A is the final amount in the account (what we're trying to find)

P is the principal amount (the initial investment of $2,500)

e is Euler's number (approximately 2.71828)

r is the interest rate per year (2.1% or 0.021)

t is the number of years (14)

Substituting the values into the formula:

A = $2500 * e^(0.021 * 14)

Using a calculator, we can find that the final amount in the account is approximately $3831.

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A radio tower is located on a coordinate system measured in miles. The range of a signal in a particular direction is modeled by a quadratic function where the boundary of the signal starts at the vertex at (4, 2). It passes through the point (5, 4). A linear road connects points (–3, 7) and (8, 2). Which system of equations can be used to determine whether the road intersects the boundary of the tower’s signal?

Answers

Given that the range of the signal is a quadratic function: (x-h)^2 = 4a (y - k) (5-4)^2 = 4a (4 - 2) 4a =1/2 therefore, (x -4)^2 = (1/2)(y – 2) The road is a line. Slope of the road is (7 -2)/(-3 -8) =-5/11 Therefore the equation of the line: 5x + 11y = 5(8) + 11(2) 5x + 11y = 62

The system of equations can be used to determine whether the road intersects the boundary of the tower’s signal; y = 2( x - 4 )² + 2 and 5 x + 11 y = 62.

What is the vertex form of a quadratic equation?

If a quadratic equation is written in the form

y = a(x-h)^2 + k

then it is called to be in vertex form.

It is called so because when you plot this equation's graph, you will see the vertex point is on (h,k).

To determine a quadratic function in vertex form:

y = a ( x - 4 )² + 2

4 = a ( 5 - 4 )² + 2

4 = a + 2

a = 2

y = 2 ( x - 4 )² + 2

Then we will determine a linear function in standard form, that passes through the points ( -3, 7 ) and ( 8, 2 ).

7 = -3 m + b

2 = 8 m + b / ·(-1)

7 = - 3 m + b

- 2 = - 8 m - b

5 = - 11 m

m = -5/11,

2 = -5/11 · 8 + b,

b= 2 + 40/11,

b = 62/11

Substitue,

y = - 5/11 x + 62/11 / ·11

11 y = - 5 x + 62

5 x + 11 y = 62

Finally the system of equations is:

y = 2( x - 4 )² + 2

5 x + 11 y = 62

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Y varies directly as x , y= 25 when x=5. Determine y when x= 13

Answers

Answer:

y = 65 when x = 13

Step-by-step explanation:

Here we have a proportion problem.

Y varies directly as x means that y equals the product of x and a constant

Let’s say our constant is k

Thus;

y = kx

now, k = y/x

Using the initial values;

k = 25/5 = 5

Now we want to get y when x = 13

Recall; y = kx

Thus using the value of k earlier calculated;

y = 13 * 5

y = 65

Solve for X.

A. 10
B. 12
C. 15
D. 22

Answers

Answer:

B. 12

Step-by-step explanation:

Since Z is midpoint of SR and Y is midpoint of QR, so as per triangle midpoint theorem ZY is parallel to SQ and measures half of its value:

SQ = 2ZY
3x - 8 = 2(x + 2)
3x - 8 = 2x + 4
3x - 2x = 4 + 8
x = 12

Correct answer choice is B

Answer:

the answer is B.12 ......

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