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2 years ago

A water pipe is 4 7/12 feet beneath the surface of the road. What is the elevation of the pipe, in feet, expressed as a decimal?

Mathematics

1 answer:

Furkat [3]2 years ago

3 0

Answer:

4.5833feet

Step-by-step explanation:

Given the elevation of a water pipe as 4 7/12 feet

Expressing as decimal

4 7/12

= 4 + 7/12

= 4 + 0.5833

= 4.5833

Hence the elevation of the pipe expressed as a decimal is 4.5833feet

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Kath starts with a number. she adds 3 to her number then double the result. finally, she subtracts 7. if she ended with 9, what

Dimas [21]

The answer is 5. Work backwards: first add 7 to 9, then divide by 2, then subtract 3.

9+7=16
16/2=8
8-3=5

Cross Check:
5+3=8
8*2=16
16-7=9

Final Answer: 5

4 0

3 years ago

Given points A(-1, -2) and B(2, 4) where AP: BP=1:2, find the locus of point P.

koban [17]

Answer:

$x^2 + 4x + y^2 +8y = 0$

Step-by-step explanation:

Given

$A = (-1,-2)$

$B = (2,4)$

$AP:BP = 1 : 2$

Required

The locus of P

$AP:BP = 1 : 2$

Express as fraction

$\frac{AP}{BP} = \frac{1}{2}$

Cross multiply

$2AP = BP$

Calculate AP and BP using the following distance formula:

$d = \sqrt{(x - x_1)^2 + (y - y_1)^2}$

So, we have:

$2 * \sqrt{(x - -1)^2 + (y - -2)^2} = \sqrt{(x - 2)^2 + (y - 4)^2}$

$2 * \sqrt{(x +1)^2 + (y +2)^2} = \sqrt{(x - 2)^2 + (y - 4)^2}$

Take square of both sides

$4 * [(x +1)^2 + (y +2)^2] = (x - 2)^2 + (y - 4)^2$

Evaluate all squares

$4 * [x^2 + 2x + 1 + y^2 +4y + 4] = x^2 - 4x + 4 + y^2 - 8y + 16$

Collect and evaluate like terms

$4 * [x^2 + 2x + y^2 +4y + 5] = x^2 - 4x + y^2 - 8y + 20$

Open brackets

$4x^2 + 8x + 4y^2 +16y + 20 = x^2 - 4x + y^2 - 8y + 20$

Collect like terms

$4x^2 - x^2 + 8x + 4x + 4y^2 -y^2 +16y + 8y + 20 - 20 = 0$

$3x^2 + 12x + 3y^2 +24y = 0$

Divide through by 3

$x^2 + 4x + y^2 +8y = 0$

3 0

2 years ago

Which ratios of side lengths are equal to tan (a) ?

Eddi Din [679]

Answer:

$tan(\alpha)=\frac{opposite}{adjacent}$

Step-by-step explanation:

$tan(\alpha)=\frac{opposite}{adjacent}$

4 0

1 year ago

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The average income, I, in dollars, of a lawyer with an age of x years is modeled with the following function:

Alinara [238K]

The answer is 37 years old.

I = -425x² + 45500x -650000
I = 450000

-425x² + 45500x -650000 = 450000
-425x² + 45500x - 650000 - 450000 = 0
-425x² + 45500x - 1100000 = 0

Divide all factors by 25:
- 17x² + 1820x - 44000 = 0

This is quadratic equation (ax² + bx + c = 0)
$x_{1,2} = \frac{-b+/- \sqrt{ b^{2}-4ac } }{2a} = \frac{-1820+/- \sqrt{ 1820^{2}-4*(-17)*(-44000) } }{2*(-17)} = \\ \\ = \frac{-1820+/- \sqrt{3312400-2992000 } }{-34} = \frac{-1820+/- \sqrt{320400} }{-34} =\frac{-1820+/- 566}{-34} \\ \\ 
x_1= \frac{-1820+ 566}{-34}= -37 \\ \\ 
x_2 = \frac{-1820- 566}{-34}=70$

Since, the youngest age is needed, the correct answer is x = 37

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3 years ago

Solve for m. m=-(4+m)+2

pishuonlain [190]

Answer:

m= -1

Step-by-step explanation:

Order summands

Apply negation to the value inside parentheses

Add the numbers

Add

to both sides of the equation

Simplify

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2 years ago

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