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2 years ago

2^m ÷ 2^ -4 = 4^5 pls help

Mathematics

1 answer:

kvv77 [185]2 years ago

4 0

Answer:

m = 6

Step-by-step explanation:

$\frac{a^{m}}{a^{-n}}=a^{m+n}\\\\$

2^m ÷ 2^ -4 = 4^5

$\frac{2^{m}}{2^{-4}}=(2^{2})^{5}\\\\\\2^{m+4} = 2^{2*5}\\\\2^{m+4} = 2^{10}$

Compare the powers,

m + 4 = 10

m = 10 - 4

m = 6

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In a child's bank are 11 coins that have a value of S1.85. The coins are either

Karo-lina-s [1.5K]

Answer:

The child has 6 dimes and 5 quarters.

Step-by-step explanation:

Let q and d represent the number of quarters and of dimes respectively.

Then q + d = 11 (Equation A), and ($0.25/quarter)q + ($0.10/dime)d = $1.85 (Equation B).

Multiply the 2nd equation by 100 to remove the decimal fractions:

25q + 10d = 185 (Equation C)

Now multiply the 1st equation by -10 to obtain -10q - 10d = -110 (Equation D), and combine this result with Equation C:

-10q - 10d = -110

25q + 10d = 185

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15q = 75, and so q = 75/15 = 5.

According to Equation A, q + d = 11. Replacing q with 5, we get:

5 + d = 11, and so d = 6.

The child has 6 dimes and 5 quarters.

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3 years ago

the number of Roberto's baseball cards is 3/4 the number of David's cards. If Roberto gives 1/2 of his cards to David, what will

Nataliya [291]

Answer:

The ratio between Roberto and David is 3:11

Step-by-step explanation:

If Roberto were to have 18 cards when we start, then David would have 24. Roberto has 3/4 the amount that David has. Then Roberto gives half of his cards (9) to David. Roberto now has 9 cards and David has 33.

3 0

2 years ago

Find an equation of the circle that has center (1, -1) and passes through (5, -6).

Sloan [31]

Answer:

Step-by-step explanation:

(x-1)²+(y+1)²=41

6 0

3 years ago

What is the value of x 3x 2x 55

Juli2301 [7.4K]

Answer:

Step-by-step explanation:

3x+2x+55=180

5x+55=180

5x=180-55

5x=125

X=125/5

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So the value of X is 25

8 0

2 years ago

Draw an angle in standard position whose terminal side contains the point

kvasek [131]

Answer:

The distance of the point from the origin = 9.29 units.

Step-by-step explanation:

Given point:

(7,-6)

The angle lies such that the terminal side of the angle contains the given point.

To draw the angle and find the distance from the origin to the given point.

Solution:

The terminal side of the angle is where the angle ends with the initial side being the positive side of the x-axis.

So, we can plot the point (7,-6) by moving 7 units on the x-axis horizontally and -6 units on the y-axis vertically.

We can find the distance of the point from the origin by find the hypotenuse of the triangle formed.

Applying Pythagorean theorem.

$Hypotenuse^2=Shorter\ Leg^2+Shortest\ Leg^2$

$Hypotenuse^2 = (7)^2+(-6)^2$

$Hypotenuse^2=49+36\\Hypotenuse^2=85$

Taking square root both sides :

$\sqrt{Hypotenuse^2}=\sqrt{85}$

$Hypotenuse = 9.29\ units$

Thus, the distance of the point from the origin = 9.29 units.

The figure is shown below.

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3 years ago