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gregori [183]
3 years ago
11

A flower bed is in the shape of a triangle with one side twice the length of the shortest​ side, and the third side is 18 feet m

ore than the length of the shortest side. Find the dimensions if the perimeter is 174 feet.
Mathematics
1 answer:
Marysya12 [62]3 years ago
8 0

Answer: The dimensions of the flower bed are,

39 ft, 57 ft and 78 ft.

Step-by-step explanation: Of the three sides, one side is twice the length of the shortest. Let the shortest side be labelled as b. That means one of the sides of the flower bed measures twice b, that is, 2b.

Also we are told that the third side measures 18 feet more than the shortest side, b. The third side can now be represented by b + 18.

So the triangle has sides

b, 2b and b + 18

If the perimeter is 174, then

b + 2b + (b + 18) = 174

b + 2b + b + 18 = 174

4b + 18 = 174

Subtract 18 from both sides of the equation

4b = 156

Divide both sides of the equation by 4

b = 39.

Therefore the shortest side of the triangle measures 39 ft while the other two sides measure 78 ft (twice the length of b) and 57 ft (18 ft more than the shortest side)

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Answer:

FGHI is a Parallelogram

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How do I solve (|x-3|+5|x|) ?
11111nata11111 [884]

Answer:

x≤0 ⇒|x-3|+5|x| = -6x + 3

0≤x≤3 ⇒ |x-3|+5|x| = 4x + 3

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Step-by-step explanation:

Check the picture below.

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3 years ago
Last time, one out of every 4 students in our class was absent. This time, after Jen came back, only one out of every 5 students
VMariaS [17]

Answer: There are 20 students and 4 students are not here today.

Step-by-step explanation:

If the number of students = 4

Let the number of students be 'x'.

Fraction of students absent = \dfrac{x}{4}

If the number of students = 5

Fraction of students absent = \dfrac{x}{5}

And Jen came back,

So, the fraction of student absent is also written as

\dfrac{x}{4}-1

According to question, it becomes,

\dfrac{x}{5}=\dfrac{x}{4}-1\\\\\dfrac{x}{5}=\dfrac{x-4}{4}\\\\4x=5(x-4)\\\\4x=5x-20\\\\4x-5x=-20\\\\-x=-20\\\\x=20

Hence, there are 20 students in our school.

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3 0
3 years ago
3. You want to have $4000 in your savings account after 2 years. Find the amount you should deposit for each of the situations d
pychu [463]

Answer:

Part A)

About $3767.34.

Part B)

About $3692.47.

Step-by-step explanation:

Part A)

Recall that compound interest is given by the formula:
\displaystyle A = P\left(1+\frac{r}{n}\right)^{nt}

Where <em>A</em> is the final amount, <em>P</em> is the initial amount, <em>r</em> is the interest rate, <em>n</em> is the number of times compounded per year, and <em>t</em> is the number of years.

To obtain $4000 after two years, let <em>A</em> = 4000 and<em> t</em> = 2.

Because the account pays 3% interest compounded monthly, <em>r</em> = 0.03 and <em>n</em> = 12.

Substitute and solve for <em>P: </em>

<em />\displaystyle \begin{aligned} (4000) & = P\left(1+\frac{(0.03)}{(12)}\right)^{(12)(2)} \\ \\ P & = \frac{4000}{\left(1+\dfrac{(0.03)}{(12)}\right)^{(12)(2)}} \\ \\ & \approx \$3767.34\end{aligned}

In concluion, about $3767.34 should be deposited.

Part B)

Recall the formula for continuous compound:

\displaystyle A = Pe^{rt}

Where <em>e</em> is Euler's number.

Hence, let <em>A</em> = 4000, <em>r</em> = 0.04 and <em>t</em> = 2. Substitute and solve for <em>P: </em>

<em />\displaystyle \begin{aligned}(4000) & = Pe^{(0.04)(2)} \\ \\ P & = \frac{4000}{e^{(0.02)(4)}} \\ \\ & \approx \$3692.47 \end{aligned}

In conclusion, about $3692.47 should be deposited.

8 0
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Answer:

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Given :

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Add 2 on both sides :

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Divide both sides by -4 (remember the sign changes direction when divided by a negative number) :

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7 0
2 years ago
Read 2 more answers
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