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2 years ago

Which logarithmic equation is equivalent to the exponential equation below e^2x=7

1 answer:

4 0

$\bf log_{{ a}}{{ b}}=y \iff {{ a}}^y={{ b}}\qquad\qquad 
% exponential notation 2nd form
{{ a}}^y={{ b}}\iff log_{{ a}}{{ b}}=y \\\\
-----------------------------\\\\
e^{2x}=7\iff log_e(7)=2x\iff ln(7)=2x$

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The area of the square adjacent to two sides of a right triangle are 29.25 square units and 13 units 30 POINTS

Otrada [13]

Answer:

$x=6.5\ units$

Step-by-step explanation:

step 1

Find the length side of the smaller square

The area of the square is equal to

$A=a^{2}$

$a^{2}=13$

$a=\sqrt{13}\ units$

step 2

Find the length side of the larger square

The area of the square is equal to

$A=b^{2}$

$b^{2}=29.25$

$b=\sqrt{29.25}\ units$

step 3

Find the value of x

Applying the Pythagoras Theorem

$x^{2} =a^{2}+b^{2}$

substitute the values

$x^{2} =13+29.25$

$x^{2} =42.25$

$x=6.5\ units$

6 0

2 years ago

You deposit $10,000 in a money-market account that pays an annual interest rate of 4.4%. The interest is compounded quarterly. H

sergiy2304 [10]

Total = principal * (1 + rate/n)^n*years
where "n" is the number of compounding periods per year
Total = 10,000 * (1 + .044/4)^4*2
Total = 10,000 * (1.011)^8
Total = 10,000 * 1.0914635699 
Total = 10,914.64

3 0

3 years ago

What is the equation of the line that passes through the point -3/5 and has a slope of -2

Gemiola [76]

Answer:

y = -2x - 1

Step-by-step explanation:

y = mx + b

slope = m

y = -2x + b

5 = -2x * -3 + b

5 = 6 + b

-1 = b

y = -2x - 1

Let me know if I'm wrong :)

8 0

2 years ago

What is 2+8-y equal to

Alecsey [184]

Answer:

0.25

Step-by-step explanation:

8 0

2 years ago

A researcher is interested in estimating the average salary of police officers in a large city. She wants to be 95% sure that he

inn [45]

Answer:

The sample size is 183.

Step-by-step explanation:

Given:

σ = $1050, ppulatin standard deviation

99% confidence interval

Accuracy = +/- $200

The accuracy is given by

z*(σ/√n)

where

z* = 2.576 for 99% confidence level (from tables)

n = sample size

Therefore

2.576(1050/√n) = 200

√n = (2.576*1050)/200 = 13.524

n = 182.9

The sample size is 183

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6 0

2 years ago