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3 years ago

15

The bottom end of a ramp at a warehouse is 10 feet from the base of the main dock and is 11 feet long. How high is the dock, rou

nded to the nearest hundredth? Answer the question in the box below, showing ALL the work.

1 answer:

Bas_tet [7]3 years ago

6 0

Answer:

The dock is $4.58\ ft$ high

Step-by-step explanation:

we know that

Applying the Pythagoras theorem

Let

x------> the height of the dock

$11^{2}=x^{2} +10^{2}$

Solve for x

$x^{2}=11^{2}-10^{2}$

$x^{2}=121-100$

$x^{2}=21$

$x=\sqrt{21}\ ft$

$x=4.58\ ft$

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vodomira [7]

Step-by-step explanation:

$\sqrt{ x^{2}-10x+25}+25+12\sqrt{x} =15\sqrt{x} \\ \\ \therefore \: \sqrt{ x^{2}-10x+ {5}^{2} }+25 =15\sqrt{x} - 12\sqrt{x}\\ \\ \therefore \: \sqrt{( x - 5)^{2}}+25 =3\sqrt{x} \\ \\ \therefore \: x - 5+ 25 = 3 \sqrt{x} \\ \\ \therefore \: x + 20 = 3 \sqrt{x} \\ \\ squaring \: both \: sides \\ (x + 20)^{2} = ( {3 \sqrt{x} })^{2} \\ \therefore \: {x}^{2} + 40x + 400 = 9x \\ \therefore \: {x}^{2} + 40x + 400 - 9x = 0 \\ \therefore \: {x}^{2} + 31x + 400 = 0 \\$

8 0

3 years ago

Sort the ratios listed at the right into bins so that equivalent ratios are grouped together:

cestrela7 [59]

Step $1$

<u>Find the irreducible fraction in each ratio</u>

<u>case 1)</u> $\frac{40}{64}$

Divide by $8$ boths numerator and denominator

$\frac{40}{64}=\frac{5}{8}$

<u>case 2)</u> $\frac{5}{75}$

Divide by $5$ boths numerator and denominator

$\frac{5}{75}=\frac{1}{15}$

<u>case 3)</u> $\frac{14}{35}$

Divide by $7$ boths numerator and denominator

$\frac{14}{35}=\frac{2}{5}$

<u>case 4)</u> $\frac{24}{64}$

Divide by $8$ boths numerator and denominator

$\frac{24}{64}=\frac{3}{8}$

<u>case 5)</u> $\frac{6}{15}$

Divide by $3$ boths numerator and denominator

$\frac{6}{15}=\frac{2}{5}$

<u>case 6)</u> $\frac{65}{104}$

Divide by $13$ boths numerator and denominator

$\frac{65}{104}=\frac{5}{8}$

<u>case 7)</u> $\frac{66}{176}$

Divide by $22$ boths numerator and denominator

$\frac{66}{176}=\frac{3}{8}$

<u>case 8)</u> $\frac{12}{30}$

Divide by $6$ boths numerator and denominator

$\frac{12}{30}=\frac{2}{5}$

<u>case 9)</u> $\frac{15}{225}$

Divide by $15$ boths numerator and denominator

$\frac{15}{225}=\frac{1}{15}$

<u>case 10)</u> $\frac{6}{16}$

Divide by $2$ boths numerator and denominator

$\frac{6}{16}=\frac{3}{8}$

<u>case 11)</u> $\frac{15}{24}$

Divide by $3$ boths numerator and denominator

$\frac{15}{24}=\frac{5}{8}$

<u>case 12)</u> $\frac{48}{128}$

Divide by $16$ boths numerator and denominator

$\frac{48}{128}=\frac{3}{8}$

Step $2$

<u>Sort the ratios into bins</u>

1<u>) First Bin</u>

<u> $Ratio=\frac{5}{8}$ </u>

$\frac{40}{64}$

$\frac{65}{104}$

$\frac{15}{24}$

<u>2) Second Bin </u>

<u> $Ratio=\frac{1}{15}$ </u>

$\frac{5}{75}$

$\frac{15}{225}$

<u>3) Third Bin</u>

$Ratio=\frac{2}{5}$

$\frac{14}{35}$

$\frac{6}{15}$

$\frac{12}{30}$

4<u>) Fourth Bin</u>

<u> $Ratio=\frac{3}{8}$ </u>

$\frac{24}{64}$

$\frac{66}{176}$

$\frac{6}{16}$

$\frac{48}{128}$

3 0

2 years ago

Read 2 more answers

Select the expression that could be used to determine if 96 is a factor of 8.

Svet_ta [14]

Answer:

C.

Step-by-step explanation:

To find out if it is a factor divide 96 by 8 and you will see. Hope this helped you!!

8 0

3 years ago

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65. A pizza, heated to a temperature of 400°F, is taken out of an oven and placed in a 75°F room at timet= 0 minutes. The temper

Amanda [17]

Answer:

769MIN

Step-by-step explanation:

Hello!

To solve this problem we must use the straight line equation, this equation is as follows

Y=mx+b

where

X= time

Y=Temperature

b= intercept with the y axis when x = 0, therefore y = 400

m=k= temperature decrease with respect to time=-0.325

now we replace the values in the equation of the line

Y=-0.325X+400

Now we find the time it takes for the pizza to reach 150 F replacing in the equation and finding X

150=-0.325X+400

150-400=-0.325X+

$X=\frac{150-400}{-0.325} =769MIN$

4 0

2 years ago

Someone please helppp

MArishka [77]

Answer:

you can use SSA to prove congruence. side DE and AB are congruent, and C and F are both right angles

6 0

2 years ago

Read 2 more answers