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densk [106]
3 years ago
7

You exercised 24 hours each month for a year. How many hours did you exercise by the end of the year? You may be able to do the

math mentally thanks to expanded notation and the Distributive Property.
Mathematics
2 answers:
dedylja [7]3 years ago
7 0

Answer:

288 hours.

Step-by-step explanation:

You exercise 24 hours in 1 month.

There are 12 months in one year.

24 * 12 = 288

Therefore, you exercised 288 hours in one year.

alexgriva [62]3 years ago
4 0

Answer:

Calculation with Distribution

24 (1+1+1+1+1+1+1+1+1+1+1+1)

24*1+24*1+24*1+24*1+24*1+24*1+24*1+24*1+24*1+24*1+24*1+24*1

24+24+24+24+24+24+24+24+24+24+24+24

288 hours

You did 288 hours of exercise.

Calculation without Distribution

24(1+1+1+1+1+1+1+1+1+1+1+1)

24(12)

288 hours

You did 288 hours of exercise.

Step-by-step explanation:

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Answer:

X=11 Y=9

Step-by-step explanation:

6 0
3 years ago
Last year at this time we had 250 employees. Due to attrition , we lost 12% of our workforce. How many employees are working now
Brums [2.3K]
You have 220 workers now
3 0
3 years ago
Read 2 more answers
PLease answer !!! Find constants $A$ and $B$ such that \[\frac{x + 7}{x^2 - x - 2} = \frac{A}{x - 2} + \frac{B}{x + 1}\] for all
Xelga [282]

Answer:

1. (A,B) = (3,-2)

2. The values of t are: -3, -1

Step-by-step explanation:

Given

\frac{x + 7}{x^2 - x - 2} = \frac{A}{x - 2} + \frac{B}{x + 1}

|t| = 2t + 3

Required

Solve for the unknown

Solving \frac{x + 7}{x^2 - x - 2} = \frac{A}{x - 2} + \frac{B}{x + 1}

Take LCM

\frac{x + 7}{x^2 - x - 2} = \frac{A(x+1) + B(x-2)}{(x - 2)(x-1)}

Expand the denominator

\frac{x + 7}{x^2 - x - 2} = \frac{A(x+1) + B(x-2)}{x^2 - 2x + x -2}

\frac{x + 7}{x^2 - x - 2} = \frac{A(x+1) + B(x-2)}{x^2 - x -2}

Both denominators are equal; So, they can cancel out

x + 7 = A(x+1) + B(x-2)

Expand the expression on the right hand side

x + 7 = Ax + A + Bx - 2B

Collect and Group Like Terms

x + 7 = (Ax + Bx)  + (A - 2B)

x + 7 = (A + B)x + (A - 2B)

By Direct comparison of the left hand side with the right hand side

(A + B)x = x

A - 2B = 7

Divide both sides by x in (A + B)x = x

A + B = 1

Make A the subject of formula

A = 1 - B

Substitute 1 - B for A in A - 2B = 7

1 - B - 2B = 7

1 - 3B = 7

Subtract 1 from both sides

1 - 1 - 3B = 7 - 1

-3B = 6

Divide both sides by -3

B = -2

Substitute -2 for B in A = 1 - B

A = 1 - (-2)

A = 1 + 2

A = 3

Hence;

(A,B) = (3,-2)

Solving |t| = 2t + 3

Because we're dealing with an absolute function; the possible expressions that can be derived from the above expression are;

t = 2t + 3    and   -t = 2t + 3

Solving t = 2t + 3

Make t the subject of formula

t - 2t = 3

-t = 3

Multiply both sides by -1

t = -3

Solving -t = 2t + 3

Make t the subject of formula

-t - 2t = 3

-3t = 3

Divide both sides by -3

t = -1

<em>Hence, the values of t are: -3, -1</em>

7 0
2 years ago
Read 2 more answers
A. P(5 &lt; X &lt; 9)<br>B. P(X &gt;7)<br>​
enot [183]

i think it is A. P(5<X<9)

8 0
3 years ago
please help i rly need it my math teacher gave me over 30 assignments and a project that are all due tomorrow today and i want t
Sedaia [141]

Answer:

x= -14

Step-by-step explanation:

-14 subtracted by 2 is -16, since its absolute it means its positive, meaning its 16 greater than 14, I may be wrong so just to let you know. Depends on how the teacher wants it to be.

8 0
3 years ago
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