Determine the value of x for which a || b if m∠1 = 60 - 2x and m∠5 = 70 - 4x.50
5
4
10

Answer:

to find the right answer multiple by 2

Step-by-step explanation:

and you get 14/16

The area of Mr. Cole’s bedroom is82 square feet. Therefore, the correct answer is option B.

Area is the amount of space occupied by a two-dimensional figure. In other words, it is the quantity that measures the number of unit squares that cover the surface of a closed figure. The standard unit of area is square units which is generally represented as square inches, square feet, etc.

The given figure can be divided into two rectangles.

One with the dimensions 10 ft by 5 ft.

Other with the dimensions 8 ft by 4t.

We know that, the area of a rectangle is Length×Width.

Here, area of a rectangle with the dimensions 10 ft by 5 ft is

square feet

Area of a rectangle with the dimensions 8 ft by 4 ft is

square feet

Now, area = 50+32

= 82 square feet

Therefore, the correct answer is option B.

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Answer:

The answer is 82 square feet

Step-by-step explanation:

An easy way to do this is to split it into two rectanlges. You can do 10*5 and 8*4 as the dimensions to the two rectangles or you can do 2*4 and 9*8.

I am going to do the first option.

The area of a rectangle is length times width.

Rectangle one can be the one with the dimensions 10 and 5 and the length and width.

Rectangle two can be the one with the dimensions 8 and 4 and the length and width.

Area of rectangle one = 50 feet^2

Area of rectangle two = 32 feet^2

Since we split a large irregular shape into two bits, we must add them together, which results in 82 feet^2.  

Final answer:

To reach a savings goal of $300,000 at the end of 25 years, you need to invest approximately $4,206.42 semiannually with a 5% interest rate compounded semiannually.

Explanation:

To calculate the amount of money you need to invest semiannually to reach a savings goal of $300,000 at the end of 25 years, you can use the formula for the future value of an annuity:

FV = P * ((1 + r/n)^(n*t) - 1) / (r/n)

Where FV is the future value, P is the amount you need to invest each period, r is the interest rate per period (5% in this case), n is the number of compounding periods per year (2 for semiannual compounding), and t is the number of years.

Inserting the given values into the formula:

FV = P * ((1 + 0.05/2)^(2*25) - 1) / (0.05/2)

Solving for P:

P = FV * (r/n) / ((1 + r/n)^(n*t) - 1)

Substituting the values:

P = 300,000 * (0.05/2) / ((1 + 0.05/2)^(2*25) - 1)

Calculating the value of P, we find:

P ≈ 4206.42

Therefore, you need to invest approximately $4,206.42 semiannually to reach your savings goal of $300,000 in 25 years.

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Answer:

Step-by-step explanation:

The given quadratic equation is expressed as

x^2 + 17x − 12 = −84

Adding -84 to the left hand side and the right hand side of the equation, it becomes

x^2 + 17x − 12 + 84 = −84 + 84.

x^2 + 17x + 72 = 0

We would find two numbers such that their sum or difference is 17x and their product is 72x^2. The two numbers are 8x and 9x. Therefore

x^2 + 8x + 9x + 72 = 0

x( x + 8) + 9(x + 8) = 0

x + 9 = 0 or x + 8 = 0

x - 9 or x = 8