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Oksi-84 [34.3K]

2 years ago

13

Pieter wrote and solved an equation that models the number of hours it takes to dig a well to a level of 72 feet below sea level

.
7h – 5(3h – 8) = –72
Which statement is true about Pieter’s solution?

2 answers:

nignag [31]2 years ago

7 0

Answer:

<h2><u>B.</u> <u>It must be a positive number since it represents a number of hours.</u></h2>

Step-by-step explanation:

I got it right on EDG.

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Simplifying

7h + -5(3h + -8) = -72

Reorder the terms:

7h + -5(-8 + 3h) = -72

7h + (-8 * -5 + 3h * -5) = -72

7h + (40 + -15h) = -72

Reorder the terms:

40 + 7h + -15h = -72

Combine like terms: 7h + -15h = -8h

40 + -8h = -72

Solving

40 + -8h = -72

Solving for variable 'h'.

Move all terms containing h to the left, all other terms to the right.

Add '-40' to each side of the equation.

40 + -40 + -8h = -72 + -40

Combine like terms: 40 + -40 = 0

0 + -8h = -72 + -40

-8h = -72 + -40

Combine like terms: -72 + -40 = -112

-8h = -112

Divide each side by '-8'.

h = 14

Simplifying

h = 14

Digiron [165]2 years ago

4 0

Answer: h=-4

Step-by-step explanation:

You might be interested in

The function h(t)=-4.87t^2+18.75t is used to model the height of an object projected in the air, where h(t) is the height in met

rodikova [14]

Looking at the graph you can see that the domain of the function is:
[0, 3.85]
To find the range of the function, we must follow the following steps:
Step 1)
Evaluate for t = 0
h (0) = - 4.87 (0) ^ 2 + 18.75 (0)
h (0) = 0
Step 2)
find the maximum of the function:
h (t) = - 4.87t ^ 2 + 18.75t
h '(t) = - 9.74 * t + 18.75
-9.74 * t + 18.75 = 0
t = 18.75 / 9.74
t = 1.925051335
We evaluate the function at its maximum point:
h (1.925051335) = - 4.87 * (1.925051335) ^ 2 + 18.75 * (1.925051335)
h (1.93) = 18.05
The range of the function is:
[0, 18.05]
Answer:
Domain: [0, 3.85]
Range: [0, 18.05]
option 1

3 0

3 years ago

Eddi Din [679]

Answer:

a) $y=\dfrac{5}{2}x$

b) yes the two lines are perpendicular

c) $y=\dfrac{5}{4}x+6$

Step-by-step explanation:

a) All this is asking if to find a line that is perpendicular to 2x + 5y = 7 AND passes through the origin.

so first we'll find the gradient(or slope) of 2x + 5y = 7, this can be done by simply rearranging this equation to the form $y = mx + c$

$5y = 7 - 2x$

$y = \dfrac{7 - 2x}{5}$

$y = \dfrac{7}{5} - \dfrac{2}{5}x$

$y = -\dfrac{2}{5}x+\dfrac{7}{5}$

this is changed into the $y = mx + c$ , and we easily see that -2/5 is in the place of m, hence $m = \frac{-2}{5}$ is the slope of the line 2x + 5y = 7.

Now, we need to find the slope of its perpendicular. We'll use:

$m_1m_2=-1$ .

here both slopes $m_1$ and $m_2$ are slopes that are perpendicular to each other, so by plugging the value -2/5 we'll find its perpendicular!

$\dfrac{-2}{5}m_2=-1$ .

$m_2=\dfrac{5}{2}$ .

Finally, we can find the equation of the line of the perpendicular using:

$(y-y_1)=m(x-x_1)$

we know that the line passes through origin(0,0) and its slope is 5/2

$(y-0)=\dfrac{5}{2}(x-0)$

$y=\dfrac{5}{2}x$ is the equation of the the line!

b) For this we need to find the slopes of both lines and see whether their product equals -1?

mathematically, we need to see whether $m_1m_2=-1$ ?

the slopes can be easily found through rearranging both equations to $y=mx+c$

Line:1

$2x + 3y =6$

$y =\dfrac{-2x+6}{3}$

$y =\dfrac{-2}{3}x+2$

Line:2

$y = \dfrac{3}{2}x + 4$

this equation is already in the form we need.

the slopes of both equations are

$m_1 = \dfrac{-2}{3}$ and $m_2 = \dfrac{3}{2}$

using

$m_1m_2=-1$

$\dfrac{-2}{3} \times \dfrac{3}{2}=-1$

$-1=-1$

since the product does equal -1, the two lines are indeed perpendicular!

c)if two perpendicular lines have the same intercept, that also means that the two lines meet at that intercept.

we can easily find the slope of the given line, y = − 4 / 5 x + 6 to be $m=\dfrac{-4}{5}$ and the y-intercept is $c=6$ the coordinate at the y-intercept will be (0,6) since this point only lies in the y-axis.

we'll first find the slope of the perpendicular using:

$m_1m_2=-1$

$\dfrac{-4}{5}m_2=-1$

$m_2=\dfrac{5}{4}$

we have all the ingredients to find the equation of the line now. i.e (0,6) and m

$(y-y_1)=m(x-x_1)$

$(y-6)=\dfrac{5}{4}(x-0)$

$y=\dfrac{5}{4}x+6$

this is the equation of the second line.

side note:

this could also have been done by simply replacing the slope(m1) of the y = − 4 / 5 x + 6 by the slope of the perpendicular(m2): y = 5 / 4 x + 6

8 0

3 years ago

I NEED SERIOUS HELP PLEASE WITH PROBABILITY

erastova [34]

Since its a six sided die the probability for rolling a single number ( like six or four) is always going to be 1/6.

and since the dice has the numbers 1, 2, 3, 4, 5 and 6 on it the probability for the even and the odd numbers are the same the even being 2, 4, 6 and odd being 1, 3, 5. the probability is 3/6 or simplified 1/2.

3 0

3 years ago

Read 2 more answers

The product of 2, and a number increased by 7, is -36

vodka [1.7K]

Here is the equation you should use.

2(x+7) = -36

4 0

3 years ago

Given the parametric equations x = 2sint and y = -3cost on 0 ≤ t ≤ π. convert to a rectangular equation and sketch the curve

Temka [501]

The rectangular equation for given parametric equations x = 2sin(t) and y = -3cos(t) on 0 ≤ t ≤ π is $\frac{x^{2} }{4} +\frac{y^2}{9} =1$ which is an ellipse.

For given question,

We have been given a pair of parametric equations x = 2sin(t) and y = -3cos(t) on 0 ≤ t ≤ π.

We need to convert given parametric equations to a rectangular equation and sketch the curve.

Given parametric equations can be written as,

x/2 = sin(t) and y/(-3) = cos(t) on 0 ≤ t ≤ π.

We know that the trigonometric identity,

sin²t + cos²t = 1

⇒ (x/2)² + (- y/3)² = 1

⇒ $\frac{x^{2} }{4} +\frac{y^2}{9} =1$

This represents an ellipse with center (0, 0), major axis 18 units and minor axis 8 units.

The rectangular equation is $\frac{x^{2} }{4} +\frac{y^2}{9} =1$

The graph of the rectangular equation $\frac{x^{2} }{4} +\frac{y^2}{9} =1$ is as shown below.

Therefore, the rectangular equation for given parametric equations x = 2sint and y = -3cost on 0 ≤ t ≤ π is $\frac{x^{2} }{4} +\frac{y^2}{9} =1$ which is an ellipse.

Learn more about the parametric equations here:

brainly.com/question/14289251

#SPJ4

7 0

1 year ago