1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Mandarinka [93]
2 years ago
14

A triangle has a perimeter of 31. The longest side is equal to 12. The difference of the other two is 3. What is length of the s

hortest side ?
Mathematics
1 answer:
xenn [34]2 years ago
3 0

Answer:

8

Step-by-step explanation:

The perimeter is the sum of the 3 sides of the triangle.

let the other 2 sides be x and x - 3 , then

12 + x + x - 3 = 31

2x + 9 = 31 ( subtract 9 from both sides )

2x = 22 ( divide both sides by 2 )

x = 11 and x - 3 = 11 - 3 = 8

The 3 sides are 12, 11, 8

with shortest side 8

You might be interested in
Cards are drawn, one at a time, from a standard deck; each card is replaced before the next one is drawn. Let X be the number of
steposvetlana [31]

Cards are drawn, one at a time, from a standard deck; each card is replaced before the next one is drawn. Let X be the number of draws necessary to get an ace. Find E(X) is given in the following way

Step-by-step explanation:

  • From a standard deck of cards, one card is drawn. What is the probability that the card is black and a jack? P(Black and Jack)  P(Black) = 26/52 or ½ , P(Jack) is 4/52 or 1/13 so P(Black and Jack) = ½ * 1/13 = 1/26
  • A standard deck of cards is shuffled and one card is drawn. Find the probability that the card is a queen or an ace.

P(Q or A) = P(Q) = 4/52 or 1/13 + P(A) = 4/52 or 1/13 = 1/13 + 1/13 = 2/13

  • WITHOUT REPLACEMENT: If you draw two cards from the deck without replacement, what is the  probability that they will both be aces?

P(AA) = (4/52)(3/51) = 1/221.

  • WITHOUT REPLACEMENT: What is the probability that the second card will be an ace if the first card is a  king?

P(A|K) = 4/51 since there are four aces in the deck but only 51 cards left after the king has been  removed.

  • WITH REPLACEMENT: Find the probability of drawing three queens in a row, with replacement. We pick  a card, write down what it is, then put it back in the deck and draw again. To find the P(QQQ), we find the

probability of drawing the first queen which is 4/52.

  • The probability of drawing the second queen is also  4/52 and the third is 4/52.
  • We multiply these three individual probabilities together to get P(QQQ) =
  • P(Q)P(Q)P(Q) = (4/52)(4/52)(4/52) = .00004 which is very small but not impossible.
  • Probability of getting a royal flush = P(10 and Jack and Queen and King and Ace of the same suit)
5 0
2 years ago
What is the absolute value of -135​
sammy [17]

135

with math any absolute number cant be negative so you just make it positive

7 0
2 years ago
Read 2 more answers
Expression for all solutions to the equation cos(theta) = 1 + 3cos(theta)
OleMash [197]
\cos\theta=1+3\cos\theta\implies 0=1+2\cos\theta\implies \cos\theta=-\dfrac12

On the unit cirlce, the cosine of an angle is negative whenever the angle falls in the interval \dfrac\pi2.

If you recall your special triangles, this cosine occurs for angles of x=\dfrac{2\pi}3 and x=\dfrac{4\pi}3.

More generally, this occurs for x=\dfrac{2\pi}3+2n\pi and x=\dfrac{4\pi}3+2n\pi, where n is an integer.
7 0
3 years ago
Hii please answer, thank you :)
Kipish [7]

Answer:

Eddie used the incorrect ratio for sin

Step-by-step explanation:

sinT = \frac{opposite}{hypotenuse} = \frac{UV}{UT} = \frac{8}{17} , then

∠ T = sin^{-1} (\frac{8}{17} )

7 0
2 years ago
What are the solutions of the system of equations y = –(x + 2)2 + 1 and y = 2x + 5?
Scilla [17]

Answer:

(–4, 5) and (–2, 1)

Step-by-step explanation:

8 0
1 year ago
Other questions:
  • The area of a triangle is represented by the expression (x2+92x+2) square units. If the length of the base is represented by the
    9·1 answer
  • How do you turn 0.875 into a fraction
    5·1 answer
  • 1. A point at (3, 2) is rotated 180° clockwise about the origin.
    12·1 answer
  • Shirts are on sale for 25% of the original price of $45 what is the sale price
    10·1 answer
  • Solve the system by substitution.<br> y = -7x + 6<br> 5x + y = 2
    5·1 answer
  • For all values of x,<br> f(x) = 2x - 6<br> and<br> g(x) = x2 + 2<br> a) Find g(3)<br> b) Find fg(3)
    7·1 answer
  • Kayla runs 3/4 mile in 1/10 hour assuming she runs at a constant rate what is her speed in miles per hour
    8·1 answer
  • Packages of ramen noodles are on sale at the grocery store for $.20 each. Lucy decides to stock up since she had a $3 off coupon
    7·1 answer
  • Help please quick! show work please.<br> Use the area to find the value of x:
    10·2 answers
  • Use the diagram to the right to name the following.
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!