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2 years ago

Which of the following equations is equivalent to b^y=x

Mathematics

1 answer:

zalisa [80]2 years ago

8 0

Step-by-step explanation:

$\text{De}\text{finition of logarithm}:\\\\\log_ab=c\iff a^c=b,\ \text{where}\ a>0\ \wedge\ a\neq1\ \wedge\ b>0\\\\\text{Therefore your answer is}\\\\\large\huge{\boxed{B.\ y=\log_bx}}\\\\\log_bx=y\iff b^y=x$

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Write the slope-intercept form of the equation that passes through the point (-1, 2) and is parallel to the line y = 3/2x + 6

horsena [70]

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Answer: $\textsf{y = 3/2x + 7/2}$

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Given: $\textsf{Passes through (-1, 2) and parallel to y = 3/2x + 6}$

Find: $\textsf{The equation in slope-intercept form}$

Solution: In order to determine the equation we know that our line is going to be parallel which means that the slope is the same and we need to use the point-slope form to help us. After plugging in the values we just simplify and solve for y to convert to slope-intercept form.

Plug in the values

$\textsf{y - y}_1\textsf{ = m(x - x}_1\textsf{)}$

$\textsf{y - 2 = 3/2(x - (-1))}$

Simplify and distribute

$\textsf{y - 2 = 3/2(x + 1)}$

$\textsf{y - 2 = (3/2 * x) + (3/2 * 1)}$

$\textsf{y - 2 = 3/2x + 3/2}$

Add 2 to both sides

$\textsf{y - 2 + 2 = 3/2x + 3/2 + 2}$

$\textsf{y = 3/2x + 3/2 + 2}$

$\textsf{y = 3/2x + 7/2}$

Therefore, after completing the steps we were able to determine that the equation that fits the description is y = 3/2x + 7/2.

4 0

1 year ago

The price of a pair of shoes is $45.90. The sales-tax rate is 5 percent. How much sales tax do you need to pay?

Airida [17]

45.90*0.05=2.295. The answer is $2.30 when you round it off.

5 0

2 years ago

What is the number of possible outcomes if three quarters are tossed and the total numbers of heads and tails are counted? A) 2

Gre4nikov [31]

Answer:

D). 8.

Step-by-step explanation:

Each quarter will come up heads or tails - that is 2 possibilities.

So for 3 tosses the number of outcomes is 2*2*2 = 8.

3 0

2 years ago

Read 2 more answers

4000-1375 and I need work

zheka24 [161]

4000
-1375
———

Take 1 from the number 4 and have it go down the line of zeros.

39910
-1375
———-

Subtract

39910
-1375
———-
2,625

I hope this helped!

8 0

2 years ago

Amuseumcharges forgeneraladmission and exhibitions. Admission and 3 exhibitionscosts $45. Admission and 5 exhibitionscosts $65.

leonid [27]

Answer:

The price of the admission is 15.

Step-by-step explanation:

From the information given, you can write the following equations:

a+3e=45 (1)

a+5e=65 (2), where:

a is the admission cost

e is the exhibition cost

First, you can solve for a in (1):

a=45-3e (3)

Second, you can replace (3) in (2):

45-3e+5e=65

45+2e=65

2e=65-45

2e=20

e=20/2

e=10

Finally, you can replace the value of e in (3):

a=45-3e

a=45-3(10)

a=45-30

a=15

According to this, the price of the admission is 15.

3 0

2 years ago