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3 years ago

Angle of 74° with the ground if the foot of the latter 6.5 feet from the wall, how high on the wall is the ladder?

Mathematics

1 answer:

Pie3 years ago

7 0

Tanα=h/x

h=xtanα, we are told that x=6.5ft and α=74° so

h=6.5tan74 ft

h≈22.67 ft (to nearest hundredth of a foot)

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How do you turn 12/15 and 68/80 into a decimal and into a percent

Allisa [31]

$\frac{12}{15}\\\\divide\ a\ numerator\ and\ a\ denominator\ by\ 3\\\\12:3=4;\ 15:3=5\\\\therefore\ \frac{12}{15}=\frac{4}{5}\\\\multiply\ a\ numerator\ and\ a\ denominator\ by\ 2\\\\4\cdot\ 2=8;\ 5\cdot2=10\\\\therefore\ \frac{12}{15}=\frac{4}{5}=\frac{8}{10}=\boxed{0.8}\Rightarrow0.8\cdot100\%=\boxed{80\%}$

$\frac{68}{80}\\\\divide\ a\ numerator\ and\ a\ denominator\ by\ 4\\\\68:4=17;\ 80:4=20\\\\therefore\ \frac{68}{80}=\frac{17}{20}\\\\multiply\ a\ numerator\ and\ a\ denominator\ by\ 5\\\\17\cdot\ 5=85;\ 20\cdot5=100\\\\therefore\ \frac{68}{80}=\frac{17}{20}=\frac{85}{100}=\boxed{0.85}\Rightarrow0.85\cdot100\%=\boxed{85\%}$

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2 years ago

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Tables originally priced at $70 are now on sale for $42.What is the discount, as a percentage?

d1i1m1o1n [39]

Answer:

40%

Step-by-step explanation:

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2 years ago

What is the equation of the line that is parallel to the line x = -2 and passes through the point (5.4)?

Leno4ka [110]

Lines parallel to each others only occur when two slopes of equations are same. The definition of parallel lines is:

$\large \boxed{m_1 = m_2}$

We are given the equation of a line which is x = -2. For x = a, the equation forms a verical line and has an undefined slope. These below are basic that you may need to learn when learning about the line graph:

y = a —> horizontal line; slope is 0.
x = a —> vertical line; slope is undefined.
For y = a, any a-values would have same x-values. For example, if we are given y = 2 then any domains or x-values can have the range of 2.
For x = a, any a-values would have same y-values or range.

Back to the question. We want to find the equation of a line that is parallel to the line x = -2 and passes through (5,4) point. Recall the definition of parallel line that both slopes of equations must equal. Since x = a for any a-values would give an undefined slope. That means our parallel would be x = b.

Because the line passes through (5,4) - for any a-values from x = a would give out the set of all real numbers for range. Therefore the equation of a line is x = 5.

Answer

The equation of a line that is parallel to x = -2 and passes through (5,4) is x = 5.

I hope this helps! If you have any doubts or questions, don't hestitate to ask in comment! Good luck on your assignment and have a great day!

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3 years ago

Acapulco, Mexico and Hyderabad, India both lie at 17° north latitude, and lie very nearly halfway around the world from each oth

Nataly_w [17]

In solving this problem we can consider Earth to be a sphere. When we have a circle, then we can use this formula to find arc length:
$L=2 \pi R \frac{C}{360}$
Where:
L= arc length (in this problem it is disance we need to travel)
R = radius of circle (in this problem it is equal to a radius of Earth)
C = angle we need to pass

We are told that two cities lie halfway around the world. If we fly to west this means angle is 180°.
This gives an arc length of:
$L=2* \pi *3960* \frac{180}{360} \\ \\ L=12440.71 miles$

If we want to fly to north we need to go to 90° northern latidtude and then back to 17° latitude. This means angle is:
C=2*(90-17)=2*73°=146°
This gives an arc length of:
$L=2* \pi *3960* \frac{146}{360} \\ \\ L=10090.8 miles$

We can see that flying north is shorter. It is shorter by:
12440.71 miles - 10090.8 miles = 2349.91 miles

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2 years ago

Lloyd solves the equation 24x + 18(x – 2) = 216 for x. Some of his steps are shown.

Elena-2011 [213]

Answer:

Hi there!

Your answer is:

To get from step 3 to step 4, Lloyd added 36 to both sides. On the left side, this equaled 0 due to the additive inverse property! (-36 + 36 = 0!) On the right side, 36 is added to 216! (216+36 = 252)

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3 years ago

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