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Find (4.54×10^8)-(3.98×10^8)

horrorfan [7]

Answer:

$5.6 *10^7$

Step-by-step explanation:

Given

$(4.54*10^8)-(3.98*10^8)$

Required

Solve

$(4.54*10^8)-(3.98*10^8)$

Apply distributive law of algebra

$(4.54 - 3.98) *10^8$

Evaluate the expression in bracket

$(0.56) *10^8$

Remove bracket

$0.56 *10^8$

When a number is in standard form: $a * 10^n$

The value of a must be: $1 \le a \le 10$

So, the expression becomes:

$5.6 *10^{-1}*10^8$

Apply law of indices

$5.6 *10^{-1+8}$

$5.6 *10^7$

5 0

3 years ago

PLEASE HELP ASAP

leva [86]

Answer:

1. 68/89

2. 46/267

Step-by-step explanation:

1. The total number of people in drama or athletics can be found by adding up all categories where a person fits at least one of the criteria:

51+11+12+15+108+7=204

Now we need to add up the total number of people in all categories:

51+11+12+15+108+7+63=267

Finally, we divide the total number of people in either drama or athletics by the total number of people in all categories:

204/267 = 68/89

2. The total number of people in athletics and drama can be found by adding up all categories where a person fits both criteria:

15+12=27

The total number of people in music and athletics can be found by adding up all categories where a person fits both criteria:

7+12=19

Now, we add both of these numbers together and put it all over the total number of people:

27+19=46

46/267

7 0

3 years ago

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

$t = -1$

Hence, the values of t are: -3, -1

7 0

3 years ago

Read 2 more answers

Find the translation that moves the figure 2 to figure 3 on the coordinate plane.

laila [671]

………………………………………………….

5 0

3 years ago

Perform the following division 3 3/4÷2/8

tamaranim1 [39]

3 3/4 ÷ 2/8
=15/4 ÷ 2/8
=15/4 × 8/2
=120/8
=15

8 0

4 years ago

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