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SashulF [63]
3 years ago
15

The longer leg of a right triangle is 3 inches more than the length of the shorter leg tripled. the hypotenuse is 3 inches less

than four times the length of the shorter leg. find the length of the hypotenuse
Mathematics
1 answer:
lukranit [14]3 years ago
4 0
We have this equation.
A²+B²=C²
We have bits of information that'll help us simplify the equation so there's only one variable.
The longer leg, A, is 3 inches more than the length of the shorter leg, B, tripled.
A=3B+3
Let's plug that in.
(3b+3)²+B²=C²
The hypotenuse, C, is 3 inches less than four times the length of the shorter leg. C=4B-3
Let's plug that in.
(3b+3)²+B²=(4B-3)²
Let's solve.
9B²+18B+9+B²=16B²-24B+9
10B²+18B+9=16b²-24b+9
Let's subtract 9 from both sides.
10b²+18b=16b²-24b
Let's subtract 10b² from both sides.
18b=6b²-24b
Let's add 24b from both sides.
42b=6b²
Let's divide each side by 6.
7b=b²
With this, you can tell that b is 7 since it times 7 equal itself squared.
The shorter leg is 7 inches.
Now, let's look back at the bits of information.
The longer leg of a right triangle is 3 inches more than the length of the shorter side tripled.
3(7)+3=24
So, the longer side is 24. We can either use the other information or plug it into the equation. We can do both. 
The hypotenuse is 3 less than four times the shorter leg.
4(7)-3=25
7²+24²=
49+576=625
√625=25
So, the length of the hypotenuse is 25 inches.
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tatuchka [14]
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7 0
3 years ago
The distance (d) in meters that an ant can travel varies directly with the amount of time (t) in hours it spends walking.assume
Assoli18 [71]

Answer:  d=18t

Step-by-step explanation:

By definition, Direct proportion equations have the following form:

y=kx

Where "k" is the constant of proportionality.

In this case you know that the distance (in meters) that an ant can travel varies directly with the amount of time (in hours) the ant spends walking.

With this information you can write the following equation:

d=kt

According to the exercise, the constant of proportionality is:

k=18

Therefore, substituting the value of the constant of proportionality into the equation, you get that  the equation that represents the proportional relationship between "d" and "t" is:

d=18t

4 0
3 years ago
A sporting goods store sells right-handed and left-handed baseball gloves. In one month, 12 gloves were sold for a total of $561
Korvikt [17]

about 9 right handed gloves were sold, and about 3 left-handed gloves were sold.

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3 years ago
Luisa recieved $108 for a necklace she sold on an online auction. The auction site took a fe of 10% of selling price. What was t
Vera_Pavlovna [14]
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3 0
3 years ago
Arlene is comparing the prices of two truck rental companies. Company A charges $7 per hour and an additional $30 as service cha
Valentin [98]

Answer:

Part A: 7n + 30= -5 and 8n + 40= 16

Part B: 7(8) + 30= 86 and 8(8) + 40= 104

Part C: Company A saves you 12.

Step-by-step explanation:

Company A: 7n + 30

Company B: 8n + 40

7n + 30= -5       8n + 40= 16

7(8) +30= 86     8(8) +40= 104

7(2) + 30= 44    8(2) + 40= 56

56 - 44= 12

7 0
3 years ago
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