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vivado [14]
3 years ago
10

the perimeter of a right triangle is 30 inches. The longer leg is 2 more than twice the shorter leg. The hypotenuse is one more

than the longer leg. Find the area of the triangle?
Mathematics
1 answer:
emmasim [6.3K]3 years ago
8 0

Answer:

s represents the shorter leg

3s - 9 represents the longer leg

2s + 1 represents the hypotenuse

(2s + 1)2 = s2 + (3s - 9)2                 Pythagorean Theorem

4s2 + 4s + 1 = s2 + 9s2 - 54s + 81  square binomial

4s2 + 4s + 1 = 10s2 - 54s + 81        combine like terms

0 = 6s2 - 58s + 80                           set to 0

0 =3s2 - 29s + 40                            divide both sides by 2

0 = (3s - 5)(s - 8)                             FOIL

{5/3, 8}

5/3 is not feasible since 3(5/3) - 9 is negative.

-by-step explanation:

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The school that molly goes to is selling tickets to a choral performance. On the first day of ticket sales the school sold 6 sen
krek1111 [17]
The cost of a senior citizen ticket is $15 and the cost of a student ticket is $12.

How did I get this?
We know that 6 citizen tickets and 7 student stickers sold for $174 the first day. And 10 citizen tickets and 14 student tickets sold for $318 the second day.

1. create two equations out of this: C= citizen cost per ticket and S = student cost per ticket.

  6C + 7S = $174
10C + 14S = $318

2. Use process of elimination. Multiply the first equation by 2 because we want two variables to cancel out.

-12C - 14S = -$348
10C + 14S = $318
Combine like terms.

-2C = $30
Divide by -2 on both sides. The left side cancels out.

C = $30/-2
C = -$15 (In this case the negative doesn't matter)

C = $15 (cost of senior citizen ticket)

Plug the value of C into any of the two equations so we can get the value of S.

6($15) + 7S = $174
Distribute the 6 into the parenthesis.

$90 + 7S = $174
Subtract both sides by $90 and the left side will cancel out.

7S = $84
Divide both sides by 7.
S = $12

Student ticket: $12
Senior citizen ticket: $15




5 0
3 years ago
The length of a rectangle is 5cm more than it's width and the area is 55cm. find the length and perimeter of the rectangle
Inessa [10]

Answer:

L=10.326cm

P=31.30cm

Step-by-step explanation:

A=55=L*W

L=5+W

A = (5+W)(W) = 55

55=W^2 + 5W

0 = W^2 + 5W - 55

use quadratic formula

W = [-5 (+/-) sqrt(25-4(-55))]/2

W= 5.326 cm or W=-20.65, so W=5.326cm

L=5+5.326

=10.326cm

P=2W+2L

P=2(5.326) + 2(10.326)

=31.30 centimeters

5 0
3 years ago
The product of 2x-3 and x+4 can be expressed asA) 2x^2+5x-12B) 3x+1C) 2x^2+x-12D) 2x^2-12
DanielleElmas [232]

The given product is

(2x-3)(x+4)

We have to use the distributive property

2x\cdot x+2x\cdot4-3\cdot x-3\cdot4=2x^2+8x-3x-12

Then, we reduce like terms

2x^2+5x-12<h2>Hence, the answer is A.</h2>
5 0
1 year ago
Briana spent a total of $52 on 4 used video games what was the average cost of a game a 13 per gameb 18 per gamec 48 per game d
Hatshy [7]

Answer:

13 duh

Step-by-step explanation:

The answer is 13 per game because it is a division problem.  So you 4 games is 52. So one game is 13 when you divided it by 4. You can also set it up as a proportion 52/4= x/1.  Or, you do 52 divided by 4 to get 13. 

5 0
3 years ago
HELLP!!!! Please? HELPPP??
svet-max [94.6K]

1 - a) x^2+10=36

b)x^2=36

x=-6 OR x=6

2 - a) 2x^2-20=3x

b) 2x^2-3x-20=0

2x^2-8x+5x-20=0

(2x+5)(x-4)=0

x=-5/2 OR x=4

5 0
3 years ago
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