MATHEMATICS HIGH SCHOOL

Arielle is building the wooden framework for the roof of a house. She needs the angle created by the vertical and horizontal boards of the frame to be a right angle. The height of the vertical board is 12 feet. The length of the horizontal board is 15 feet. The support beam that will connect the ends of the two boards measures 20 feet.

Answers

Answer 1
Answer: a² + b² = c²  ⇒ right triangle
a² + b² < c² ⇒ obtuse triangle
a² + b² > c² ⇒ acute triangle

a = 12 ft ; b = 15 ft ; c = 20 ft

12² + 15² = < > 20²
144 + 225 = < > 400
369 < 400 OBTUSE TRIANGLE

√369 = 19.21

20 - 19.21 = 0.79 

It is an obtuse triangle. About 0.8 foot needs to be removed from the 20-foot board to create a right triangle.
Answer 2
Answer:

Answer:

It is b

Step-by-step explanation:

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Josh was asked to solve the equation 15x-19=4x+11 His first step resulted in the equation 15x=4x=30 Describe what Josh did in his first step.

Answers

Answer:

Added 19 to each side

Step-by-step explanation:

15x-19=4x+11

Add 19 to each side

5x-19+19=4x+11+19

5x = 4x+30

Answer:

added 19 and 11

4x - 7 < 5 which is not a solution to the inequality

Answers

First, you want to subtract 7 from both sides. On the left, it cancels out, so you're just left with 4x. On the right, your left with -2. Then, you divide 4 on both sides. On the left, it cancels out, and on the right it leaves you with 0.5. Anything below 0.5 (for ex 0, 0.25) would be correct. Anything above will be incorrect. Hope this helped!
First you want to subtract 7 from both sides. On the left, it cancels out, so you're just left with 4x. On the right, your left with -2. Then, you divide 4 on both sides. On the left, it cancels out, and on the right it leaves you with 0.5. Anything below 0.5 (for ex 0, 0.25) would be correct. Anything above will be incorrect. Hope this helped!!

The larger leg of a right triangle is 3cm longer than its smaller leg. The hypotenuse is 6cm longer than the smaller leg. how many centimeters long is the smaller leg  please explain how you got it 

Answers

b=a+3\n c=a+6\n a^2+b^2=c^2\n\n a^2+(a+3)^2=(a+6)^2\n a^2+a^2+6a+9=a^2+12a+36\n a^2-6a-27=0\n a^2-9a+3a-27=0\n a(a-9)+3(a-9)=0\n (a+3)(a-9)=0\n a=-3 \vee a=9\n

The length can't be negative, so the answer is 9 cm.
Let the smaller leg be x.

Thus, larger leg = 3 +x
Thus, hypotenuse = 6 + x

Applying pythagoras theorum ;

(6+x)^2 = x^2 + (3+x)^2 \n \n or, 6^2 + 12x + x^2 = 3^2 + 6x + x^2 \n \n i.e., 36 + 12x = 9 + 6x \n \n =>6x = 45 \n \n => x = 9

Thus, the length of smaller peg is 9 cm.

What is the answer to 3(2M-6)

Answers

Hey there!

\bold{3(2m-6)}\n \bold{Distribute\downarrow}\n\bold{3(2m) + 3(-6)}\n\bold{3(2m)=6m}\n \bold{3(-6) =18}\n \n \n \n \boxed{\boxed{\bold{Answer: 6m-18}}}\huge\checkmark

Good luck on your assignment and enjoy your day!

~\frak{LoveYourselfFirst:)}

-36-(-40)
Please I need this ASAP

Answers

Answer:

4

Step-by-step explanation:

  1. -36 - (-40) = -36 + 40
  2. -36 + 40 = 4

I hope this helps!

Answer:

4

Step-by-step explanation:

because -36+ 40 =4 you take the subtraction and give it to the 40

What is the factored form of 6n4 – 24n3 + 18n? 6 n (n Superscript 4 Baseline + 4 n cubed + 3n) 6 n (n Superscript 4 Baseline minus 4 n cubed + 3 n) 6 n (n cubed minus 4 n squared + 3) 6 n (n cubed + 4 n squared + 3)

Answers

6n(n³ - 4n² + 3)  is the factored form.

What is expression?

Expressions is the defined as mathematical statements that have a minimum of two terms containing variables or numbers.

Given that,

⇒6n⁴ - 24n³ + 18n

factor out 6n from each term

⇒6n(n³ - 4n² + 3)

There are two factors 6n and (n³ - 4n² + 3) of given expression.

Learn more about expression here:

brainly.com/question/13947055

#SPJ5

Answer:

6n(n³ - 4n² + 3)

Step-by-step explanation:

Given

6n^(4) - 24n³ + 18n ← factor out 6n from each term

= 6n(n³ - 4n² + 3) ← which may be factored further if required
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