Order the steps to solve the equation
log(x^2-15)= log(2x) form 1 to 5

x^2-2x-15=0
Potential solutions are -3 and 5
x^2-15=2x
x-5=0 or x+3=0
(x-5)(x+3)=0

Answers

Answer 1

Answer:

Step-by-step explanation:

When the base of a logarithm is not specified, it is assumed that the base is 10. Therefore we have:

[tex]log_1_0(x^2-15)=log_1_0(2x)[/tex]

Intuitively you can see that if the two arguments inside of the logarithm equal each other, then both sides will be equal to each other. Therefore, you can say the following requirement:

[tex]x^2-15=2x[/tex]

Subtract 2x on both sides to get:

[tex]x^2-2x-15=0[/tex]

Use the quadratic formula to solve for 'x' to get:

[tex]x=(-b+\sqrt{b^2-4ac} )/2a[/tex]

[tex]x=(-b-\sqrt{b^2-4ac} )/2a[/tex]

Beginning with the first solution:

[tex]x=(-(-2)+\sqrt{(-2)^2-4(1)(-15)} )/2(1)[/tex]

[tex]x=2+\sqrt{4+60} )/2[/tex]

[tex]x=(2+\sqrt{64}) /2[/tex]

[tex]x=(2+8)/2[/tex]

[tex]x=5[/tex]

Second solution:

[tex]x=(-(-2)-\sqrt{(-2)^2-4(1)(-15)} )/2(1)[/tex]

[tex]x=(2-\sqrt{4+60} )/2[/tex]

[tex]x=(2-8)/2[/tex]

[tex]x=-6/2[/tex]

[tex]x=-3[/tex]

Since the 'x' value inside of the logarith is squared, the -3 is a valid solution. Ordinarily, the log function cannot take on negative values.


Related Questions

Complete the calculations so that each shows the correct sum of difference (GIVING 30 POINTS)

Answers

Answer:

See below ↓↓↓

Step-by-step explanation:

a) 2 . 1 4 0             b) 2 9 . 9 9          c) 6 . 1 5 7

+ 1 . 7 2 5              +    1 . 4 2             - 1 . 0 0 9

   3 . 8 6 5                 3 1 . 4 1               5 . 1 4 8

Tyrell and Marianne start at the same point. Tyrell walks 2.5 miles north in a straight path. Marianne walks 6.0 miles east in a straight path. How many miles apart are they at the end of their walks rounded to the nearest hundredth mile?

Answers

Answer: 6.5 is the answer.

Step-by-step explanation:

Point x (-6,3) is translated 2 units left and 5 units down. Write the coordinates of X'

Answers

Answer:

X' (-8,-2)

Step-by-step explanation:

You move -6 two spaces to the left making -8 and 3-5 = -2

If you help I’ll give brainlist thing pleaseeee

Answers

Answer:

a. y = 10

b. x = 5 - (5y/2)

c. y = 6x - 11

Step-by-step explanation:

a.

2(y - 3) = 4

2y - 6 = 4

2y = 10

y = 5

b.

2x + 5y = 10

2x = 10 - 5y

x = 5 - (5y/2)

c.

6x + 3y = 4y + 11

6x = y + 11

y = 6x - 11

d.

I don't know this one, sorry.

Is this just a fancy way of saying to graph the point (2,-6) or am I supposed to graph a line?​

Answers

Answer:

I do know what that is saying it's saying the rise of the line is going to be -6 and the run is going to be 2.

Step-by-step explanation:

Your supposed to graph a line I don't exactly remember how to do it but yeah you're supposed to graph the line.

choose the imensions that represen this rectlangl



answer

length:2/5
width: 3/6

length:2/4
width:3/4

length:2/3
width:3/5

length:2/3
width:3/4

Answers

Answer:B

Step-by-step explanation:I hope it help

Find the missing
information.
Arc length-1.5 ft
Radius-?
Central angle-pie/4 rad
Round to the nearest thousandth.

Answers

Answer:

1.91 ft

Step-by-step explanation:

Formula

l = rα

where :

l = arc lengthr = radiusα = central angle

Solving for r

l = rαr = l/αr = 1.5/(π/4)r = 6/πr = 1.90985932 ftr = 1.91 ft (nearest thousandth)

Graph the system.
y=x2+4x+1
y−x=1
As you graph your parabola, plot the vertex as your first point, followed by a point on the parabola.

Answers

Answer:

y = 6 x + 1

y = 1 x + 1

'^' :)))))

Solve for x and round to nearest tenth <3

Answers

it might be 45! best of luck:)

What is the scale factor???

Answers

Answer:

I believe your answer is 2 because that is the difference in the width of the cars.

FREE BRAINLIEST Write the equation for the parabola that has x− intercepts (−3,0) and (4,0) and y− intercept (0,12).

Answers

Answer:

f(x) = -x^2 + x + 12.

Step-by-step explanation:

f(x) = a(x - 4)(x + 3)    as the x-intercepts are  -3 and 4.

a is some costant.

At the y intercept x = 0 so we have:

y = 12 = a(0-4)(0+3)

12 = -12a

a = -1

So our eaution is f(x) = -(x - 4)(x + 3)

= -(X^2 - x - 12)

=  -x^2 + x + 12

show that the relation R in R define as R = {(a, b): a<_ b}, is reflexi when transistor but not symmetry​

Answers

Answer:

R is reflexive and transitive but not symmetric.

Step-by-step explanation:

R = {(a, b); a ≤ b}

Clearly (a, a) ∈ R as a = a.

R is reflexive.

Now,

(2, 4) ∈ R (as 2 < 4)

But, (4, 2) ∉ R as 4 is greater than 2.

R is not symmetric.

Now, let (a, b), (b, c) ∈ R.

Then,

a ≤ b and b ≤ c

→ a ≤ c

→ (a, c) ∈ R

R is transitive.

Thus, R is reflexive and transitive but not symmetric.

The mathematic department of a college has 14 male professors, 12 female professors , 14 male teaching assistants , and 11 female teaching assistants. If a person is selected at random from the group, find the probability that the selected person is a
Professor or a male
The probably be an integer or a traction Simptly you answer)

Answers

Answer:

Male

Step-by-step explanation:

There are 28 males and 26 professors so you are more likely to choose a male rather than professor of any other gender!

Which ones are correct?

Answers

Answer:

2 only

Step-by-step explanation:

This answer assumes that we can assume that lines which look straight are straight.
Straight angles are also known as 180 degree angles, and if a straight angle is cut in half, then the two parts must add up to 180 degrees. In the first picture, we see that 90-x and 90+x are the angle measurements.
(90-x)+(90+x)=90+90+x-x=180 degrees
the second one has angles 97 and 83, which add up to 180 degrees
the third one has angles which add up to more than 180 degrees, so any answer containing the third one as being correct is wrong.
The answer should be 1 and 2, but, that isn't an answer. Looking back at 1, it can be seen that if x is a negative number, or if x was a number greater than 180 degrees, then the picture would not work, so 1 is invalid. this leaves only 2, so 2 only.

Solve the following linear inequalities given in the first column and choose the appropriate results

Answers

Solution 1

7(g - 19) ≥ -14

7g - 133 ≥ -14

7g  ≥ -14 + 133

7g ≥ 119

g ≥ 17

Solution 2

3(7g+17) > -19 + 14g

21g + 51 > -19 + 14g

21g - 14g > -19 -51

7g > -70

g > -10

Solution 3

6(-6g + 6) > -2(19g - 17)

-36g  +36 > -38g + 34

-36g + 38g > 34 - 36

2g > -2

g > -1

Using the Rule of 72, how long would it take for Anthony to double his investment of $5,000 in a
money market account that earns 7% per year?

Answers

Answer: About 10.2857 years

=============================================================

Explanation:

For the rule of 72, we divide the number 72 over the interest rate without the percent sign. We do not convert to decimal form. Simply erase the percent sign.

For example, if the interest rate was 6%, then we estimate it would take 72/6 = 12 years for the amount to double.

In this case of a 7% interest rate, the doubling time is roughly 72/7 = 10.2857 years.

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

Extra Notes:

The starting deposit doesn't matter, so we can ignore the "5000". The interest rate must stay the same the entire time.

PLEASE HELP I AM CHOOSING BRAINLIEST

Answers

Answer:

0

Step-by-step explanation:

since (x + 7) is a factor (aka. a multiple of) (x + 7) that means there cannot be a remainder. h(x) = n(x+7) , n being any whole number

for example

2(x+7) would be a factor of (x+7) and 2(x+7)/(x+7) = 2 will not leave a remainder

The circumference of a circle is 44π cm. find the diameter, the radius, and the length of an arc of 110.

Answers

Answer:

Step-by-step explanation:

Can someone solve this for me please.

Answers

Answer:

y= .5x+2

Step-by-step explanation:

Slope= 2/4 (rise over run) = .5

B/ y intercept = 2

y=.5x+2

An equilateral triangle with side length 19 cm is shown in the diagram, work out the height of the triangle. Give your answer rounded to 1 DP. The diagram is not drawn accurately.

Answers

Answer:

h = 16.5

Step-by-step explanation:

Remark

The formula below really is the Pytharagan formula disguised.

h^2 = hypotenuse (side)^2 - (1/2 side)^2

Givens

side = 19 cm

Solution

h^2 = 19^2 - (1/2*19)^2      Substitute given into formula

h^2 = 361 - (9.5)^2            square 9.5

h^2 = 361 - 90.25             Subtract

h^2 = 270.75                    Take the square root of both sides

√h^2 = √270.75

Answer: h = 16.5

Find the area of a circle with a radius of 21 inches. Use 22/7 for pi .

Answers

Answer:

okay so the area is 1386inches2

Step-by-step explanation:

[tex]area \: of \: a \: circle = \pi {r}^{2} \\ = \frac{22}{7} \times {21}^{2} \\ = \frac{22}{7} \times 441 \\ = 1386 {inches}^{2} [/tex]

What is the surface area of the cylinder with height 4 in and radius 5 in? Round your answer to the nearest thousandth.

Answers

Answer:

282.74

Step-by-step explanation:

Answer:

[tex]\fbox{Surface area of cylinder = 282.6 sq. in.}[/tex]

Step-by-step explanation:

Given:

Shape of object = cylinder

height of cylinder= 4 inches

radius of cylinder= 5 inches

To find:

surface area of cylinder = ?

Solution:

we know that,

[tex]surface \: area \: of \: cylinder =2\pi{rh} + 2\pi {r}^{2}\\Substituting \:the \:constant\: (π =3.14)\\and \:given\: data,\\2\pi{rh} + 2\pi {r}^{2} \: =\\ 2×3.14×5×4+2×3.14× {5}^{2} \\2\pi{rh} + 2\pi {r}^{2} = 125.6 + 157 \\ 2\pi{rh} + 2\pi {r}^{2} = 282.6\\ \fbox{Surface area of cylinder = 282.6 sq. in.}[/tex][/tex]

THANKS FOR JOINING BRAINLY COMMUNITY!

PLSSS help if you TURLY know THISS

Answers

Answer:

that would be C.) 1 and 1/8

Step-by-step explanation:

becuase the denominator never changes and you would make it a mixed number versus leaving it as 9/8

Answer: c

Step-by-step explanation:

Add the numerators

7+2=9

8 out of the 9 will make a whole number

9-8=1

The last 1 in the numerators will make 1/8

1 and 1/8

Write an expression that is equivalent to 1.5a +4.7+0.25a-0.3-0.5a

Answers

Answer:

1.25a-4.4

Step-by-step explanation:

you take :1.5a+0.25a-0.5a=1.25

then:4.7+0.3=4.4

1.25a-4.4

but am not sure sorry

Answer:

1.25a + 4.4

Step-by-step explanation:

Collect like terms and simplify

1.5a +4.7 + 0.25a - 0.3 - 0.5a = a(1.5 + 0.25 - 0.5) + (4.7 - 0.3) = 1.25a + 4.4

Please help me con la resolución porfa

Answers

Answer:

2,591 esta bien la respuesta

35. Eastview Junior High students order sweatshirts and T-shirts in either purple or gold. Of the
students who ordered a sweatshirt, the relative frequency of ordering a gold one is half of the
relative frequency of ordering a purple one. Which two-way table could show the data from the
orders?

Answers

but if two equals three then give me a two because i’m not a three!!!!!

Can y’all help me on this graph work asap pls

Answers

Just divide one of number of tickets by which ever of the ticket prices that goes on a line, like for example $24 divided by 3 equals $8 a ticket

A giant tortoise can walk about
1/10 meter per second on land. A cooter turtle can walk about
1/2 meter per second on land.
How long would it take a giant tortoise to travel 2 meters?
2 ÷ 1/10 = 2 ? 10 =

Answers

Answer:

its already on brainy hope this helps

Step-by-step explanation:

The rate of giant tortoise is 1/10 meters per each second.

The rate of cooter turtle is 1/2 meters per each second.

How long would it take a giant tortoise to travel 5 meters?

1 second : 1/10 m = X : 5 m

1/10x = 5

x = 50 seconds

How much longer would it take a giant tortoise than a cooter turtle to travel 10 meters on land?

1 second : 1/2 m = X : 10 m

1/2x = 10

x = 20 seconds

So the giant turtle can travel 5 meters in 50 seconds.

So the cooter turtle can travel 10 meters in 20 seconds.

PLS HELP!!!!For each sequence determine whether appears to be a ARITHMETIC or GEOMATRIC or neither ( pictures attached)

Answers

Answer:

The first one is geometric. The second one is gemetric. The last one is arithmetic.

Step-by-step explanation:

Sasha is mailing a photo box that has the dimensions shown in a rectangular box that is 12.5 inches long, 4.2 inches wide, and 12.5 inches tall. If one bag of packing material holds 75 cubic inches of material, how many bags does Sasha need to buy to fill the space around the photo box?

Answers

The number of bags that Sasha would need to fill the space around the photo box is 9 bags.

How many bags would be needed?

The first step is to determine the volume of the photo box. The photo box has the shape of a cuboid. A cuboid is a three-dimensional object. It has six sides and six vertices.

Volume = length x width x height

12.5 x 4.2 x 12.5 = 656.25

Bags needed - 656.25 / 75 = 9

To learn more about how to determine the volume of a cuboid, please check: https://brainly.com/question/8890358

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