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3 years ago

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a homeowner measured her rectangle backyard is having a length of 40 yards and a width of 25 yard. Her measurements were accurat

e to the nearest yard. What is the range of possible values for an eight. The actual area in square yards of her backyard

1 answer:

svp [43]3 years ago

6 0

Answer:

A. 936 ≤ A < 1066

Step-by-step explanation:

It is given that:

w = width of lawn accurate to nearest yard = 25 yards

L = length of lawn accurate to nearest yard = 40 yards

Now, for the lower bound value of the area ( $A_l$ ) can be given as follows:

$A_l = (L-Uncertainty)(w-Uncertainty)\\A_l = (40\ yards-1\ yard)(25\ yards - 1\ yard)\\A_l = 936\ sq.\ yard$

Now, for the upper bound value of the area ( $A_u$ ) can be given as follows:

$A_u = (L+Uncertainty)(w+Uncertainty)\\A_u = (40\ yards+1\ yard)(25\ yards + 1\ yard)\\A_u = 1066\ sq.\ yard$

Therefore, the correct option is:

<u>A. 936 ≤ A < 1066</u>

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Hello, I am currently very stuck with this problem and I am unsure as to how I would solve it.

borishaifa [10]

We have the equation

$20y=x^2-10-15$

Let's complete the square, to do it let's add and subtract 25 on the right side

$\begin{gathered} 20y=x^2-10-15+25-25 \\ \\ 20y=(x-5)^2-15-25_{} \\ \\ 20y=(x-5)^2-40 \\ \\ \end{gathered}$

Now we can have y in function of x

$\begin{gathered} y=\frac{1}{20}(x-5)^2-2 \\ \\ \end{gathered}$

Now we can already identify the vertex because it's in the vertex form:

$y=a(x-h)+k$

Where the vertex is

$(h,k)$

As we can see, h = 5 and k = -2, then the vertex is

$(5,-2)$

Now we can continue and find the focus, the focus is

$\mleft(h,k+\frac{1}{4a}\mright)$

We have a = 1/20, therefore

$\begin{gathered} \mleft(5,-2+5\mright) \\ \\ (5,3) \end{gathered}$

The focus is

$(5,3)$

And the last one, the directrix, it's

$y=k-\frac{1}{4a}$

Then

$\begin{gathered} y=-2-5 \\ \\ y=-7 \end{gathered}$

Hence the correct answer is: vertex (5, -2); focus (5, 3); directrix y = -7

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1 year ago

Can someone check my answers please? :)

zhannawk [14.2K]

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4 years ago

For any positive number b not equal to 1 and any number or variable n, evaluate the following expression.

kirza4 [7]

Answer:

$log_{b} b^{n}$ = n.

Step-by-step explanation:

Given : $log_{b} b^{n}$ , b is any positive number not equal to 1 and n is any number.

To find : Evaluate the expression $log_{b} b^{n}$ .

Formula used : $log_{b} x^{y}$ . = y ∙ $log_{b}$ (x) and

$log_{b}(b) = 1.Solution : We have [tex]log_{b} b^{n}$ .

By logarithm rule : $log_{b} x^{y}$ . = y ∙ $log_{b}$ (x).

Then $log_{b} b^{n}$ = n∙ $log_{b}$ (b).

By logarithm rule : $log_{b}(b) = 1.Now, n∙ [tex]log_{b}$ (b) = n.

Therefore, $log_{b} b^{n}$ = n.

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3 years ago

Read 2 more answers

Help me please solve the circled question show your work

Rasek [7]

<u>Part 1)</u> Use the fact that there are 12 inches in a foot

a) How many inches tall is a 7 foot basketball player?

we know that

1 foot=12 inches

so by proportion

$\frac{12}{1} \frac{inches}{foot} =\frac{x}{7} \frac{inches}{feet} \\ \\x=12*7\\ \\x=84\ inches$

therefore

<u>the answer Part 1a) is</u>

$84\ inches$

Part b) If a yard is a 3 feet long, how many inches are in a yard?

we know that

1 yard=3 feet

1 foot=12 inches

so

Convert 3 feet to inches

by proportion

$\frac{12}{1} \frac{inches}{foot} =\frac{x}{3} \frac{inches}{feet} \\ \\x=12*3\\ \\x=36\ inches$

therefore

<u>the answer Part 1b) is</u>

$36\ inches$

<u>Part 2) </u>At the farmer's market two pounds of peaches cost $4.20 How much will five pounds cost?

by proportion

$\frac{4.20}{2} \frac{\$}{pounds} =\frac{x}{5} \frac{\$}{pounds} \\ \\2*x=4.2*5\\ \\x=4.2*5/2=\$10.5$

therefore

<u>the answer Part 2) is</u>

$\$10.5$

<u>Part 3) </u>Janice mother gave her a ten dollars bill to buy five pounds each of bananas and apples at the grocery store. When she got there she found that bananas were 80 c per pound and apples were $1.40 per pound.

Did Janice's mother give her enough money? If so, should she receive any change? If not, how much more money does she need?

we know that

<u>Find the cost of the bananas</u>

$5\ pounds*0.80\frac{\$}{pounds}=\$4$

<u>Find the cost of the apples</u>

$5\ pounds*1.40\frac{\$}{pounds}=\$7$

Sum the cost of the bananas and the cost of the apples

$\$4+\$7=\$11$

$\$11 > \$10$ ------> Janice's mother didn't give her enough money

She needs more money

She needs-------> $\$11-\$10=\$1$

therefore

<u>the answer part 3) is</u>

She needs $\$1$ more

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3 years ago

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Alisiya [41]

Answer:5

Step-by-step explanation:

Add 4 and 1

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3 years ago

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