MATHEMATICS HIGH SCHOOL

What value of k satifies the equation 7(7 - k) +3k = -2(9k + 4) + 15

Answers

Answer 1

Answer:

To find the value of k that satisfies the equation 7(7 - k) + 3k = -2(9k + 4) + 15, you can follow these steps:

1. Distribute the constants and variables on both sides of the equation:

7 * 7 - 7 * k + 3k = -2 * 9k - 2 * 4 + 15

2. Simplify both sides:

49 - 7k + 3k = -18k - 8 + 15

3. Combine like terms on each side:

(49 - 8) - 4k = -18k + 15

41 - 4k = -18k + 15

4. Move the variable terms to one side and the constant terms to the other side by adding 18k and subtracting 41 from both sides:

41 - 4k + 18k = 15

14k - 41 = 15

5. Add 41 to both sides to isolate the variable term:

14k = 15 + 41

14k = 56

6. Finally, divide by 14 to solve for k:

k = 56 / 14

k = 4

So, the value of k that satisfies the equation is k = 4.

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What is the approximate volume of the cone with a height of 9 cm and a radius of 15 cm.

Answers

V = (1/3) pi r^2 h where r is the radius of the circular base and h is the height of the cone.

V = (1/3) pi (15)^2 * 9

V = 675 pi
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The number 24 has eight factors.

True
False

Answers

The factors for 24 are 1,2,3,4,6,8,12,24 so true

the factors are 1 and 24, 2 and 12, 3 and 8, 4 and 6 therefore it is true

Name the Property of Equality that justifies the statement: If m<A + M<B = M<C. Then, M<A = M<C - M<BTransitive Property
Symmetric Property
Reflexive Property
Subtraction Property

Answers

The subtracton property of equality allows you to subtract the same amount from both sides of an equation without changing the truth of the equation.

Answer:

subtraction property

Step-by-step explanation:

Two angles in a triangle add up to 108 degrees what is the size of the third angle

Answers

72 degrees
Because a triangle is 180 degrees and 180-108 is 72.

David's car could cover one lap of the Indy 500 in about 90 seconds. Chris' car could cover one lap in about 54 seconds. If both cars left the same starting point at the same time, after how many seconds would they meet again at the starting point?

Answers

After 270 seconds, both cars will meet again at the startingpoint.

To find the time at which both cars meet again at the starting point, we need to find the least common multiple (LCM) of their lap times. The LCM is the smallest positive integer that is divisible by both lap times.

David's car lap time = 90 seconds

Chris' car lap time = 54 seconds

Now, let's calculate the LCM:

Find the prime factors of each lap time:

90 = 2 × 3² × 5

54 = 2 × 3³

Take the highest power of each prime factor:

LCM = 2 × 3³ × 5

= 2 × 27 × 5

= 270 seconds

So, after 270 seconds, both cars will meet again at the startingpoint.

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