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vekshin1
2 years ago
11

Dave rented a limousine for his wife's birthday. The hourly rate is $80. They used the limousine for 4 hours, plus Dave gave the

driver a 20% tip. How much did he spend in total for the hourly charges plus tip?
Mathematics
1 answer:
Pavel [41]2 years ago
7 0
$80 hourly used limousine
80 * .20 = $16 tip

$80 + $16 = $96 <span>he spent hourly charges plus tip

$96 * 4 = $384 total for 4 hours plus tip</span>
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A seamstress makes 2 cushions for a couch, a smaller cushion and a larger cushion. The cushions are similar rectangular prisms.
Allisa [31]
Do you need help or you just wanted the answer?
5 0
2 years ago
You want to get from a point A on the straight shore of the beach to a buoy which is 54 meters out in the water from a point B o
anyanavicka [17]

Answer:

x =\dfrac{45 \sqrt{6}}{ 2}

Step-by-step explanation:

From the given information:

The diagrammatic interpretation of what the question is all about can be seen in the diagram attached below.

Now, let V(x) be the time needed for the runner to reach the buoy;

∴ We can say that,

\mathtt{V(x) = \dfrac{70-x}{7}+\dfrac{\sqrt{54^2+x^2}}{5}}

In order to estimate the point along the shore, x meters from B, the runner should  stop running and start swimming if he want to reach the buoy in the least time possible, then we need to differentiate the function of V(x) and relate it to zero.

i.e

The differential of V(x) = V'(x) =0

=\dfrac{d}{dx}\begin {bmatrix} \dfrac{70-x}{7} + \dfrac{\sqrt{54^2+x^2}}{5} \end {bmatrix}= 0

-\dfrac{1}{7}+ \dfrac{1}{5}\times \dfrac{x}{\sqrt{54^2+x^2}}=0

\dfrac{1}{5}\times \dfrac{x}{\sqrt{54^2+x^2}}= \dfrac{1}{7}

\dfrac{5x}{\sqrt{54^2+x^2}}= \dfrac{1}{7}

\dfrac{x}{\sqrt{54^2+x^2}}= \dfrac{1}{\dfrac{7}{5}}

\dfrac{x}{\sqrt{54^2+x^2}}= \dfrac{5}{7}

squaring both sides; we get

\dfrac{x^2}{54^2+x^2}= \dfrac{5^2}{7^2}

\dfrac{x^2}{54^2+x^2}= \dfrac{25}{49}

By cross multiplying; we get

49x^2 = 25(54^2+x^2)

49x^2 = 25 \times 54^2+ 25x^2

49x^2-25x^2 = 25 \times 54^2

24x^2 = 25 \times 54^2

x^2 = \dfrac{25 \times 54^2}{24}

x =\sqrt{ \dfrac{25 \times 54^2}{24}}

x =\dfrac{5 \times 54}{\sqrt{24}}

x =\dfrac{270}{\sqrt{4 \times 6}}

x =\dfrac{45 \times 6}{ 2 \sqrt{ 6}}

x =\dfrac{45 \sqrt{6}}{ 2}

8 0
3 years ago
!SUBSTITUTION METHOD!<br><br>6y - 5z = -8 <br>3z = -6 <br>4x - 3y - 2z= 21​
hichkok12 [17]

Answer:

<h2>x = 2 </h2><h2>y = - 3</h2><h2>z = - 2</h2>

Step-by-step explanation:

6y - 5z = -8 .......... Equation 1

3z = -6 ................... Equation 2

4x - 3y - 2z= 21...... Equation 3

<u>First solve for z in Equation 2</u>

That's

3z = - 6

Divide both sides by 3

<h3>z = - 2</h3>

Next substitute the value of z into Equation 1 in order to find y

We have

6y - 5(-2) = - 8

6y + 10 = - 8

6y = - 8 - 10

6y = - 18

Divide both sides by 6

<h3>y = - 3</h3>

Finally substitute the values of y and z into Equation 3 to find the value of x

That's

4x - 3(-3) - 2(-2) = 21

4x + 9 + 4 = 21

4x + 13 = 21

4x = 21 - 13

4x = 8

Divide both sides by 4

<h3>x = 2</h3>

So the solutions are

<h3>x = 2 </h3><h3>y = - 3</h3><h3>z = - 2</h3>

Hope this helps you

3 0
3 years ago
Can someone please help me find the value of x
Nadya [2.5K]

Answer:

its approximately 55 cos you subtract 13 from 92

Step-by-step explanation:

8 0
2 years ago
the loudness, L, measured i in decibels (Db), of a sound intencity, I, measured in watts per square meter, is defined as L=10log
Jet001 [13]

Answer: D, 110 !!!

Step-by-step explanation:

8 0
3 years ago
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