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Pie
4 years ago
12

A garden has four sides that are all the same length. Each side measures x + 5 units. The garden’s perimeter is 144 units. What

is the value of x?
Mathematics
1 answer:
Aliun [14]4 years ago
4 0

Answer:

31

Step-by-step explanation:

Each side=L=x+5

Since the garden has four equal sides, it seems to look like a square.

So perimeter of square=4L

So

4L=144

4(x+5)=144

4x+20=144

4x=144-20

4x=124

x=31 (dividing both sides by 4)

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Circular tracts of land with diameters 900 meters, 700 meters and 600 meters are tangent to each other externally. There are hou
Rudik [331]

Answer:

\alpha=69.28^o

\beta=61.26^o

\gamma=49.46^o

<em />A=227980.26\ m^2<em />

Step-by-step explanation:

<u>Triangle Solving</u>

If we had a triangle will its three sides of known length, we can solve for the rest of the parameters of the triangle, i.e. the area, perimeter and internal angles.

The three circles have diameters 900 m, 700 m and 600 m and are tangent to each other externally. The distances from their centers (where houses are located) are the sum of each pair of the radius of the circles. Thus, the sides of the triangle are

x=450+350=800

y=450+300=750

z=350+300=650

The internal angles can be computed by using the cosine's law

x^2=y^2+z^2-2yzcos\alpha

y^2=x^2+z^2-2xzcos\beta

z^2=x^2+y^2-2xycos\gamma

Where \alpha, \beta and \gamma are the opposite angles to x, y and z respectively. Solving for each one of them:

\displaystyle cos\alpha=\frac{y^2+z^2-x^2}{2yz}

\displaystyle cos\alpha=\frac{750^2+650^2-800^2}{2\cdot 750\cdot 650}

cos\alpha=0.3538

\alpha=69.28^o

Similarly

\displaystyle cos\beta=\frac{x^2+z^2-y^2}{2xz}

\displaystyle cos\beta=\frac{800^2+650^2-750^2}{2\cdot 800\cdot 650}

cos\beta=0.4808

\beta=61.26^o

The other angle is computed now

\displaystyle cos\gamma=\frac{x^2+y^2-z^2}{2xy}

\displaystyle cos\gamma=\frac{800^2+750^2-650^2}{2\cdot 800\cdot 750}

cos\gamma=0.65

\gamma=49.46^o

The area can be found by

\displaystyle A=\frac{1}{2}x.y.sin\gamma

\displaystyle A=\frac{1}{2}\cdot 800\cdot 750\cdot sin49.46^o

A=227980.26\ m^2

8 0
3 years ago
How far will the car have traveled after 10 hours
Alecsey [184]
The answer is C. 650
8 0
3 years ago
Joe wants to rent an apartment with an initial monthly rent of $1,400. He has been told that the landlord raises the rent 1.25%
nadya68 [22]

Answer: his pay for the 4th year is $1453.16

Step-by-step explanation:

The landlord raises the rent 1.25% each year. It means that the rent is increasing in geometric progression.

The formula for determining the nth term of a geometric progression is expressed as

Tn = ar^(n - 1)

Where

a represents the first term of the sequence.

r represents the common ratio.

n represents the number of terms.

From the information given,

a = $1,400

r = 1 + 1.25/100 = 1.0125

n = 4 years

The 4th term(year), T4 is

T4 = 1400 × 1.0125^(4 - 1)

T4 = 1400 × 1.0125^3

T4 = $1453.16

8 0
3 years ago
Please help me!! thank you.
LUCKY_DIMON [66]
Break the problem down and replace the x with the given number when you do that it’ll show you the answer to the question you just need to use key details in it to get the exact answer
3 0
3 years ago
What is the fraction 2/5 divided by 3/35?
muminat
(2/5)/(3/35)= 14/3. Any questions please ask!
7 0
3 years ago
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