A number is multiplied by 8 , and that product is added to 2 . the sum is equal to the product of 2 and 21 . find the number.
Answers
8x+2=2*21
8x=40
x=5
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Factor completely: a2 - a - 20
Answers
Answer:
b² + 12b + 32 = (b + 8)(b + 4)
a² - a - 20 = (a - 5)(a + 4)
Step-by-step explanation:
b² + 12b + 32
To factor, let's find two numbers that multiply to 32, and add to 12.
I find the two numbers as 4 and 8.
We can expand 12b as 4b + 8b, and factor the pairs.
Factor:
- b² + 12b + 32
- b² + 4b + 8b + 32
- (b² + 4b) + (8b + 32)
- b(b + 4) + 8(b + 4)
- (b + 8)(b + 4)
The factored form is (b + 8)(b + 4)
a² - a - 20
Using the same process, find two numbers that multiply to -20 and add to -1
The numbers are 4 and -5
Factor:
- a² - a - 20
- a² + 4a - 5a - 20
- (a² + 4a) + (-5a - 20)
- a(a + 4) -5(a + 4)
- (a - 5)(a + 4)
The factored form is (a - 5)(a + 4)
Answers
Answer: x = - 10
Step-by-step explanation:
a) Linear Pair: 138 + ∠a = 180° --> ∠a = 42°
b) Triangle Sum Theorem: ∠a + 2∠b = 180° --> ∠b = 69°
c) Vertical Angles Theorem: ∠b = ∠c --> ∠c = 69°
d) Congruent sides implies congruent angles: ∠c = ∠d --> ∠d = 69°
∠2) Triangle Sum Theorem: ∠c + ∠d + ∠2 = 180°
69° + 69° + ∠2 = 180°
∠2 = 42
x) m∠2 = 42
x + 52 = 42
x = -10
Answers
The sum of all the positive integers from square root 14 to squareroot 80 is 30.
What is a perfect square?
A perfect square is a number system that can be expressed as the
square of a given number from the same system.
We need to find the sum of all the positive integers from square root 14 to squareroot 80.
√14 = 3.74
√80 = 8.94
Thus, √14 +√80
4 + 5+ 6 + 7 + 8
= 30
Therefore, the sum of all the positive integers from square root 14 to squareroot 80 is 30.
Learn more about perfect square;
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Answer:
The sum is 30.
Step-by-step explanation:
Don’s wires measure 3 inches, 5 inches, and 12 inches.
Margo’s wires measure 6 inches, 8 inches, and 14 inches.
Sonji’s wires measure 12 inches, 8 inches, and 17 inches.
Liam’s wires measure 16 inches, 8 inches, and 27 inches.
Which student chose pieces that can be used to construct a triangle?
a. Don
b. Margo
c. Sonji
d. Liam
Answers
Answer:
C. Sonji
Step-by-step explanation:
Since, a triangle is possible if the sum of any two sides is greater than third side,
The measure of Don’s wires,
3 inches, 5 inches and 12 inches
Since, 3 + 5 < 12
Thus, by the above statement we can not make a triangle with The measure of Don’s wires.
The measures of Margo's wires,
6 inches, 8 inches and 14 inches,
Since, 6 + 8 = 14,
⇒ we can not make a triangle with The measure of Margo's wires.
The measures of Sonji's wires,
12 inches, 8 inches, and 17 inches,
12 + 8 > 17,
8 + 17 > 12
12 + 17 > 8
⇒ we can make a triangle with the measure of Sonji's wires.
The measures of Liam’s wires,
16 inches, 8 inches, and 27 inches
16 + 8 < 27
⇒ we can not make a triangle with The measure of Liam’s wires.
Hence, option 'C' is correct.
Answers
The 4th root of 1 is 1 (because 1x1x1x1x1=1).
The 4th root of 81 is 3 (because 3x3x3x3=81).
So 81^(-1/4) = 1/3
Answers
Answer:
Idk
Step-by-step explanation:
Answer:7200 gallons
Step-by-step explanation: