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
iragen [17]
2 years ago
15

The height of a triangle is 5 less than its base. The area of the triangle is 42 square inches. Find the height and base

Mathematics
1 answer:
Bond [772]2 years ago
6 0

This can be solved using simple algebra.

Let's take the base as x

It's give that the height is the base - 5.

So, the height is (x - 5)

Now plug those in the formula for finding the area of the triangle and you get:

(x^2 - 5x)/2 = 42

x^2 - 5x = 84

x (x - 5) = 84

After solving the equation, you get x = 12 and x = -7. Since lengths can't be negative, we ignore the one with the negative value.

Since x was the base, the base = 12 and the height was x - 5 so 12 - 5 = 7

:D

You might be interested in
38/58 in it's simplest form
Ainat [17]
19/29

Find the common factor which in this case is 2. Divide numerator and denominator by common factor. You’re left with 19/29. Since 19 and 29 don’t have any common factors it is in its simplest form.
6 0
3 years ago
From a standard deck of cards, a 5-card hand is dealt. Calculate the number of hands that contain 4 diamonds and 1 black king
rjkz [21]

Answer:

1430

Step-by-step explanation:

Given that a standard deck of cards is 52 cards, we have 13 Diamonds and we need 4 diamonds.

Hence, we have 13C4.

Also, we have 4 kings in a standard deck of cards, and in which we have 2 black kings but we need 1 king.

Hence we have a 2C1

Therefore:

13C4 * 2C1

=> 13! ÷ [4! (13 - 4)!] * 2! ÷ [1! (2-1)!]

=> 13! ÷ [4! (9)!]

=> (1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10 x 11 x 12 x 13) ÷ [(1 x 2 x 3 x 4) (1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9)]

=> (10 x 11 x 12 x 13) ÷ 24

=> (17160 ÷ 24) * (24 ÷ 6)

=> 715

2! ÷ [1! (2-1)!]

=> 2

Hence, we have 715 * 2

=> 1430

Hence, in this case, the correct answer to the question is 1430

7 0
3 years ago
(HELP!!!) Please Factor Completely: <br> 9x^2y^2-27x^2y-72y^2+216y
Olegator [25]

Answer:

Can u space them out so i know which ones are exponents

Step-by-step explanation:

4 0
2 years ago
20 + (-3.05) + (-9.8)
3241004551 [841]
20+(-3.05)+(-9.8)=20-3.05-9.8=7.15
7 0
3 years ago
Read 2 more answers
A helicopter is flying above a town. the local high school is directly to the east of the helicopter at a 20° angle of depressio
guapka [62]
Answer: 4.5 miles

Explanation:

When you draw the situation you find two triangles.

1) Triangle to the east of the helicopter

a) elevation angle from the high school to the helicopter = depression angle from the helicopter to the high school = 20°

b) hypotensue = distance between the high school and the helicopter

c) opposite-leg to angle 20° = heigth of the helicopter

d) adyacent leg to the angle 20° = horizontal distance between the high school and the helicopter = x

2) triangle to the west of the helicopter

a) elevation angle from elementary school to the helicopter = depression angle from helicopter to the elementary school = 62°

b)  distance between the helicopter and the elementary school = hypotenuse

c) opposite-leg to angle 62° = height of the helicopter

d) adyacent-leg to angle 62° = horizontal distance between the elementary school and the helicopter = 5 - x

3) tangent ratios

a) triangle with the helicpoter and the high school

tan 20° = Height / x ⇒ height = x tan 20°

b) triangle with the helicopter and the elementary school

tan 62° = Height / (5 - x) ⇒ height = (5 - x) tan 62°

c) equal the height from both triangles:

x tan 20° = (5 - x) tan 62°

x tan 20° = 5 tan 62° - x tan 62°

x tan 20° + x tan 62° = 5 tan 62°

x  (tan 20° + tan 62°) = 5 tan 62°

⇒ x = 5 tant 62° / ( tan 20° + tan 62°)

⇒ x = 4,19 miles

=> height = x tan 20° = 4,19 tan 20° = 1,525 miles

4) Calculate the hypotenuse of this triangle:

hipotenuese ² = x² + height ² = (4.19)² + (1.525)² = 19.88 miles²

hipotenuse = 4.46 miles

Rounded to the nearest tenth = 4.5 miles

That is the distance between the helicopter and the high school.
5 0
3 years ago
Read 2 more answers
Other questions:
  • Use completing the square to solve (x-12)(x+4)=9 for x
    14·2 answers
  • the figure is made of up of a cone and a cylinder, to the nearest whole number what is the approximate volume of this figure. PL
    14·1 answer
  • Given triangle ABC with coordinates A(−5, 4), B(−5, 1), and C(−7, 0), and its image A′B′C′ with A′(−1, 0), B′(−4, 0), and C′(−5,
    6·2 answers
  • What is the geometric mean of 5 and 18?
    11·2 answers
  • The Unique Glass Company reported sales of $24 million in 1995, and sales increased by 15% each year for the next 10 years.
    15·1 answer
  • Find the measure of angle b 32<br><br> please help:)?
    12·1 answer
  • A sweater which originally cost $ 38.40 is on sale 25% off. Carmen has gift card worth $15 off, but the gift card can only be us
    14·1 answer
  • To divide 572/4 Stanley estimated to place the first digit of the quotient. In which place is the first digit of the quotient?
    5·1 answer
  • The area of a rectangle is 72 sq. ft. If the length is twice the width, what is the measure of the length of the rectangle?
    8·2 answers
  • What is the factored form of 35y + 21?
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!