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3 years ago

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Shameka is tossing acorns into a hole. She started with 800 acorns in the hole. On average, she gets 75 acorns per hour in the h

ole. Write an equation that represents the amount of acorns, A, in the hole, where h is the number of hours.

2 answers:

gulaghasi [49]3 years ago

4 0

$A=75h$
$75h \leq 800$
$A \leq 800$

SIZIF [17.4K]3 years ago

3 0

(800÷75=10.7) A=H10.7

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Fynjy0 [20]

Gina saw 25 monkeys
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3 years ago

Which equation is equivalent to √x^2+81 = x+10

jeka57 [31]

Keywords:

<em>equation, operations, equivalent, binomial, square root </em>

For this case we have an equation in which we must apply operations to rewrite it in an equivalent way. We must start by raising both sides of the equation to the square. Thus, we eliminate the square root of the left side of equality and finally solve the binomial of the right side of equality.

So we have:

$\sqrt {x ^ 2 + 81} = x + 10\\(\sqrt {x ^ 2 + 81}) ^ 2 = (x + 10) ^ 2\\x ^ 2 + 81 = (x + 10) ^ 2$

By definition: $(a + b) ^ 2 = a ^ 2 + 2ab + b ^ 2$

$x ^ 2 + 81 = x ^ 2 + 2 (x) (10) + (10) ^ 2\\x ^ 2 + 81 = x ^ 2 + 20x +100$

Thus, $x ^ 2 + 81 = x ^ 2 + 20x +100$ is equivalent to $\sqrt {x ^ 2 + 81} = x + 10$

Answer:

$x ^ 2 + 81 = x ^ 2 + 20x +100$

Option D

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4 years ago

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3 years ago

The perimeter of a rectangular baking sheet is 58 inches and its area is 201.25 in.2. What are the length and width of the bakin

anzhelika [568]

Answer:

$Length=17.5\ in\\\\Width=11.5\ in$

Step-by-step explanation:

The formula for calculate the Area of a rectangle is:

$A=lw$

Where "l" is the lenght and "w" is the width.

And the formula for calculate the peimeter of a rectangle is:

$P=2l+2w$

Where "l" is the lenght and "w" is the width.

We know that the perimeter of the rectangular baking sheet is 58 inches and its area is 201.25 in². Then:

$A=201.25\ in^2\\\\P=58\ in$

<u>The steps are:</u>

1. Solve for the "l" from the formula $A=lw$ :

$A=lw\\\\l=\frac{A}{w}\\\\\l=\frac{201.25}{w}$

2. Substitute $l=\frac{201.25}{w}$ into the formula $P=2l+2w$ and solve for "w":

$58=2(\frac{201.25}{w})+2w\\\\58=\frac{402.5}{w}+2w\\\\58=\frac{402.5+2w^2}{w}\\\\58w=402.5+2w^2\\\\2w^2-58w+402.5=0$

Applying the Quadratic formula $x=\frac{-b\±\sqrt{b^2-4ac}}{2a}$ , we get:

$x=w=\frac{-(-58)\±\sqrt{(-58)^2-4(2)(402.5)}}{2(2)}\\\\w_1=17.5\\\\w_2=11.5$

3. Substitute $w_1=17.5$ into $l=\frac{201.25}{w}$ :

$l=\frac{201.25}{17.5}=11.5$

4. Substitute $w_2=11.5$ into $l=\frac{201.25}{w}$ :

$l=\frac{201.25}{11.5}=17.5$

Therefore, since the value of the lenght of a rectangle must be greater that the value of the width, we can conclude that the lenght and the width of the rectangular baking sheet are:

$l=17.5\ in\\\\w=11.5\ in$

8 0

3 years ago