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2 years ago

Find the exact length of side a

Mathematics

1 answer:

pantera1 [17]2 years ago

5 0

The figure is a scalene triangle, and the exact length of side a is √13

<h3>How to determine the exact length of side a?</h3>

To calculate the length of a, we make use of the following law of cosine

a² = b² + c² - 2bc * cos(A)

Using the values in the figure, we have:

a² = 3√2² + 5² - 2 * 3√2 * 5 * cos(45)

Evaluate the expression

a² = 18 + 25 - 30

Evaluate the sum and the difference

a² = 13

Take the square root of both sides

a = √13

Hence, the exact length of side a is √13

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Working together, it takes 2 computers 12 minutes to send out emails. If it takes the slower 30 minutes to the job on its own, h

artcher [175]

Answer:

The faster computer can do the job in 20 mins on it own.

Step-by-step explanation:

Given:

Time taken by slower computer to do job on its own =30 minutes.

Time taken by both the computers to do the job = 12 mins.

We need to find the Time taken by faster computer to do job on its own.

Solution:

Let the the Time taken by faster computer to do job on its own be 'x'.

Now we know that;

Rate to complete the job is equal to number of jobs divided by time taken to complete the job.

Rate of faster computer = $\frac1x$

Rate of slower computer = $\frac{1}{30}$

Rate of both the computers = $\frac{1}{12}$

Now we can say that;

Rate of both the computers is equal to sum of Rate of faster computer and Rate of slower computer.

framing in equation form we get;

$\frac{1}{12}=\frac{1}{30}+\frac{1}{x}\\\\\frac{1}{x} = \frac{1}{12}-\frac{1}{30}$

Now we will take the LCM to make the denominator common we get;

$\frac{1}{x}=\frac{5}{12\times5}-\frac{2}{30\times2}\\\\\frac1x=\frac{5}{60}-\frac{2}{60}$

Now denominator are same so we will solve the numerator.

$\frac1x=\frac{5-2}{60}\\\\\frac1x=\frac{3}{60}\\\\\frac1x=\frac{1}{20}\\\\x=20\ mins$

Hence The faster computer can do the job in 20 mins on it own.

4 0

3 years ago

The softball team stopped for ice cream after a big game. five 2-scoop cones cost the same as three sundaes. If they bought nine

Savatey [412]

<span>Let the cost of 2-scoop cones be x, and the cost of sundaes be y.
The first statement tells us that 5x = 3y
The second statement tells us that 9x + 6y = 19.95
Then we need to calculate the value of y (the cost of a sundae).
From our first equation, y = 5x/3. Substituting this into the second equation:
9x + 6(5x/3) = 19.95
9x + 10x = 19.95
19x = 19.95
x = 1.05
Substituting back into the first equation: 5(1.05) = 3y
5.25 = 3y
y = 1.75
Therefore the cost of a sundae is $1.75.
</span>

3 0

3 years ago

What are the two point plz help me

evablogger [386]

Your first point should always be shown in the y-intercept following the standard form for slope-intercept form

Y = mx + b

b = y - intercept

In this case your first point would be (0,1)

You next point would be following the slope which is -2x. When you graph a equation always know that it is rise over run. For this line, it would be going from left to right since it is a negative line.

Your second point would go down 2 points from your starting point (0,1) and run 1 to the right in the x-axis, which is also called, (1,-3)

5 0

3 years ago

How many zeros are there at the end of 100!?

frutty [35]

Well, at the END of 100, none excluding post decimal zeroes, including them there are infinite. If you meant how many zeroes inside 100, 2 then.

4 0

3 years ago

The Lopez family and the Russell family each used their sprinklers last summer. The water output rate for the Lopez family's spr

grin007 [14]

L = hours used by the Lopez's sprinkler

R = hours used by the Russell's sprinkler

so, we know the Lopez's sprinkler uses 15 Liters per hour, so say after 1 hour it has used 15(1), after 2 hours it has used 15(2), after 3 hours it has used 15(3) liters and after L hours it has used then 15(L) or 15L.

likewise, the Russell's sprinkler, after R hours it has used 40R, since it uses 40 Liters per hour.

we know that both sprinklers combined went on and on for 45 hours, therefore whatever L and R are, L + R = 45.

we also know that the output on those 45 hours was 1050 Liters, therefore, we know that 15L + 40R = 1050.

$\bf \begin{cases}
L+R=45\implies \boxed{L}=45-R\\
15L+40R=1050\\
----------\\
15\left(\boxed{45-R} \right)+40R=1050
\end{cases}
\\\\\\
675-15R+40R=1050\implies 25R=375\implies R=\cfrac{375}{25}\\\\\\ R=15$

how long was the Lopez's on for? well, L = 45 - R.

7 0

4 years ago