Mathematics, 22.12.2020 17:10 Robinlynn228

One - step adding/ subtraction equation / multiplication/ division problems The height of the water in an above ground pool is 36 inches. The pool needs to be drained. As the water drains, the height of the water changes at a rate of -1/2 inch per minute. Write and solve and equation to find out how many minutes it will take to drain the pool.

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Answer from: AkramMasoud

It would take x = 72 minutes to drain the pool.

Step-by-step explanation:

We know that the slope-intercept form of the line equation is

y = mx+b

where m is the rate of change or slope and b is the y-intercept

Let 'y' be the height of the water poolLet 'x' be the time in the minute of the water pool

As the height of the water of the pool is 36 inches, meaning the basic condition of the pool states that the ground pool is 36 inches.

Thus,

y-intercept = b = 36

As the water drains, the height of the water changes at a rate of -1/2 inch per minute.

Thus, the rate of change or slope = m = -1/2

Thus, using the equation

y = mx+b

substituting m = -1/2 and b = 36

$y\:=\:-\frac{1}{2}x+36$

We know that when the pool drains, the height of water reduces to zero.

Thus, substituting y = 0 in the equation

$0=-\frac{1}{2}x+36$

switching sides

$-\frac{1}{2}x+36=0$

subtract 36 from both sides

$-\frac{1}{2}x+36-36=0-36$

$-\frac{1}{2}x=-36$

Multiplying both sides by -2

$\left(-\frac{1}{2}x\right)\left(-2\right)=\left(-36\right)\left(-2\right)$

x=72

Therefore, it would take x = 72 minutes to drain the pool.

Answer from: Quest

∠lno ≅ ∠lnm

∠oln ≅ ∠mln

step-by-step explanation:

given that triangle lno is congruent to triangle lnm.

we have to fill up the blanks in the given question.

according to above order of congruency kept in mind we can say that

∠lno ≅ ∠lnm

∠oln ≅ ∠mln

ln ≅ ln due to common in both.

hence, by sas congruency,

the side angle side rule states that if two sides and the included angle of one triangle are congruent to another triangle, then these two triangles are congruent.

Answer from: Quest

Answer

1 number

explanation

if we use a graphing calculator, there is only one such number $c\in[0.5,0.75]$ that satisfies the conclusion of the mean value theorem, that is, a number $c\in[0.5,0.75]$ such that

$f'(c) = \dfrac{f(0.75) - f(0.5)}{0.75-0.5},$

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.

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One - step adding/ subtraction equation / multiplication/ division problems The height of the water...