Answer:
8.49 inches
Step-by-step explanation:
x^2 + 7^2 = 11^2
x^2 + 49 = 121
X^2 = 121 - 49
x^2 = 72 (then take square root on both sides)
x = 8.49 inches
Answer: C
Hello,
Step-by-step explanation:
WZ=7-3=4
YW²=XW*WZ=3*4=12 ==> WY=2√3
In the right triangle YWZ, using the Pythagorean's theorem:
YZ²=WY²+WZ²=12+4²=28
YZ=2√7≅5.29150....
Answer C
Answer:
see explanation
Step-by-step explanation:
x² + 3x + 7 = 5 ( subtract 5 from both sides )
x² + 3x + 2 = 0 ← in standard form
(x + 2)(x + 1) = 0 ← in factored form
Equate each factor to zero and solve for x ( zero product rule )
x + 2 = 0 → x = - 2
x + 1 = 0 ⇒ x = - 1
--------------------------------------------------------------
x² - 2 = - 2x² + 5x ( subtract - 2x² + 5x from both sides )
3x² - 5x - 2 = 0 ← in standard form
(3x + 1)(x - 2) = 0 ← in factored form
Equate each factor to zero and solve for x
3x + 1 = 0 ⇒ 3x = - 1 ⇒ x = - 
x - 2 = 0 ⇒ x = 2
------------------------------------------------------------
(x + 3)² + 4x = 0 ← expand left side using FOIL and simplify
x² + 6x + 9 + 4x = 0
x² + 10x + 9 = 0 ← in standard form
(x + 9)(x + 1) = 0 ← in factored form
Equate each factor to zero and solve for x
x + 9 = 0 ⇒ x = - 9
x + 1 = 0 ⇒ x = - 1
Answer:
3. r = -8
4. x = -5
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
Step-by-step explanation:
<u>Step 1: Define equation</u>
2(-5r + 2) = 84
<u>Step 2: Solve for </u><em><u>r</u></em>
- Divide 2 on both sides: -5r + 2 = 42
- Subtract 2 on both sides: -5r = 40
- Divide -5 on both sides: r = -8
<u>Step 3: Check</u>
<em>Plug in r into the original equation to verify it's a solution.</em>
- Substitute in <em>r</em>: 2(-5(-8) + 2) = 84
- Multiply: 2(40 + 2) = 84
- Add: 2(42) = 84
- Multiply: 84 = 84
Here we see that 84 does indeed equal 84.
∴ r = -8 is a solution of the equation.
<u>Step 4: Define equation</u>
264 = -8(-8 + 5x)
<u>Step 5: Solve for </u><em><u>x</u></em>
- Divide both sides by -8: -33 = -8 + 5x
- Add 8 to both sides: -25 = 5x
- Divide 5 on both sides: -5 = x
- Rewrite: x = -5
<u>Step 6: Check</u>
<em>Plug in x into the original equation to verify it's a solution.</em>
- Substitute in<em> x</em>: 264 = -8(-8 + 5(-5))
- Multiply: 264 = -8(-8 - 25)
- Subtract: 264 = -8(-33)
- Multiply: 264 = 264
Here we see that 264 does indeed equal 264.
∴ x = -5 is a solution of the equation.
He used 53 pounds. I got this by using two equations.
a+b=117
and
5.8a+4.1b= 569.8
I took the first equation and subtracted 'b' so the equation looked like a=117-b.
I then plugged in 117-b into the second equation, so it ended up looking like this:
5.8 (117-b)=569.8
5.8 times 117 is 678.6. And 5.8 times negative b is negative 5.8b.
The equation now looks like this:
678.6-5.8b+4.1b=569.8
Add like terms
678.6-1.7b=569.8
Then subtract 678.6 from both sides
-1.7b= -108.8
divide each side by -1.7
you get b= 64.
But because you are looking for how many pounds for a, subtract 64 from 117. You get 53. 53 is the answer.
