Ask question

Ask question

All categories

2 years ago

6

Solve the quadratic equation by square roots: 1. 4x²= 81 2. (4x-3)²+7=39

1 answer:

Nataly [62]2 years ago

7 0

Answer:

see explanation

Step-by-step explanation:

(1)

given

4x² = 81 ( divide both sides by 4 )

x² = $\frac{81}{4}$ ( take the square root of both sides )

x = ± $\sqrt{\frac{81}{4} }$ = ± $\frac{9}{2}$

---------------------------------------------------------------------

(2)

subtract 7 from both sides

(4x - 3)² = 32 ( take the square root of both sides )

4x - 3 = ± $\sqrt{32}$ = ± 4 $\sqrt{2}$

Add 3 to both sides

4x = 3 ± 4 $\sqrt{2}$ ( divide both sides by 4 )

x = $\frac{3}{4}$ ± $\sqrt{2}$

You might be interested in

In 2013, the moose population in a park was measured to be 5,100. By 2018, the population was measured again to be 5,200. If the

natka813 [3]

Answer:

$P(t) = 5100e^{0.0039t}$

Step-by-step explanation:

The exponential model for the population in t years after 2013 is given by:

$P(t) = P(0)e^{rt}$

In which P(0) is the population in 2013 and r is the growth rate.

In 2013, the moose population in a park was measured to be 5,100

This means that $P(0) = 5100$

So

$P(t) = 5100e^{rt}$

By 2018, the population was measured again to be 5,200.

2018 is 2018-2013 = 5 years after 2013.

So this means that $P(5) = 5200$ .

We use this to find r.

$P(t) = 5100e^{rt}$

$5200 = 5100e^{5r}$

$e^{5r} = \frac{52}{51}$

$\ln{e^{5r}} = \ln{\frac{52}{51}}$

$5r = \ln{\frac{52}{51}}$

$r = \frac{\ln{\frac{52}{51}}}{5}$

$r = 0.0039$

So the equation for the moose population is:

$P(t) = 5100e^{0.0039t}$

5 0

2 years ago

relationship between two quantities in which the ratio of one quantity to the other quantity quantity is constant

Anastaziya [24]

<span>Proportional Relationship should be the correct answer.</span>

8 0

2 years ago

Is y=x a proportional linear equation

Dmitry [639]

Answer: yes.

Step-by-step explanation:

7 0

3 years ago

If you are on a ship at sea navigating to a point that is 300 miles north and 400 miles west, find the distance from tour ship t

s344n2d4d5 [400]

Answer:

$\huge \boxed{\mathrm{500 \ miles}}$

Step-by-step explanation:

A right triangle is formed.

300 miles and 400 miles are the legs of the triangle.

We can apply Pythagorean theorem.

$c=\sqrt{300^2 +400^2 }$

$c=\sqrt{90000 +160000}$

$c=\sqrt{250000}$

$c=500$

8 0

2 years ago

Is 6^-2 positive or negative? Explain.

Gnoma [55]

Answer:

It's positive when you have 6^-2 it's the same as having $(\frac{1}{6})^{2} \\$ . So 6^-2 it's 1/36.

Step-by-step explanation:

7 0

3 years ago