Solve for x in the equation below(all in picture).

Solve For X In The Equation Below(all In Picture).

Answers

Answer 1

Answer:

x = - 5, x = 2

Step-by-step explanation:

Using the rules of logarithms

log x - log y = log ([tex]\frac{x}{y}[/tex] )

[tex]log_{b}[/tex] x = n ⇔ x = [tex]b^{n}[/tex]

note that log x = [tex]log_{10}[/tex] x

Given

log (x² + 3x) - log10 = 0, then

log([tex]\frac{x^2+3x}{10}[/tex] ) = 0, thus

[tex]\frac{x^2+3x}{10}[/tex] = [tex]10^{0}[/tex] = 1 ( multiply both sides by 10 )

x² + 3x = 10 ( subtract 10 from both sides )

x² + 3x - 10 = 0 ← in standard form

(x + 5)(x - 2) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 5 = 0 ⇒ x = - 5

x - 2 = 0 ⇒ x = 2

Solution is x = - 5, x = 2

Answer 2

Answer:

The equation has the solution(s) x = - 5, and x = 2

Step-by-step explanation:

Let's start by adding log(10) to either side of the equation --- (1)

[tex]\log _{10}\left(x^2+3x\right)-\log _{10}\left(10\right)+\log _{10}\left(10\right)=0+\log _{10}\left(10\right)[/tex]

= [tex]\log _{10}\left(x^2+3x\right)=\log _{10}\left(10\right)[/tex]

If you recall, one property proves that [tex]\log _{10}\left(10\right):\qu 1[/tex]. We can substitute this value back into the simplified equation --- (2)

[tex]\log _{10}\left(x^2+3x\right)=1[/tex]

We can also apply the logarithmic definition, If logₐ(b) = c then b = aᶜ. Using this definition we receive a further simplified equation --- (3)

[tex]x^2+3x=10^1[/tex]

[tex]x^2+3x=10[/tex]

Solving for the expression we receive the solution(s) x = 2, and x = - 5, our first option.

Note : The first solution is correct, but I wanted to take a slightly different approach


Related Questions

solve 5(2+n)=3(n+6)
it’s for my AQR class

Answers

Answer:

n = 4

Step-by-step explanation:

We can expand, getting 10 + 5n = 3n + 18.

Then, combine all like terms, getting 5n - 3n = 18 - 10, which can be rewritten as 2n = 8.

Solve this by dividing both sides by 2, and get n = 4.

Answer: so its n=4

Step-by-step explanation:   This problem will require distribution

5(2+n) = 3(n+6)

10+5n=3n+18

Move all the variables on one side

5n-3n=18-10

2n=8

Divide by 2

n=4

5 ( 2 + n ) = 3 ( n + 6 )

First distribute the 5 and the 3. By doing that, your equation should look like

10 + 5n = 3n + 18 Now, subtract 3n from both sides, this way all the " n " would be on the same side making it easier to solve

By subtracting 3n from both sides the equation would be

10 + 2n = 18 Now subtract 10 from both sides

By subtracting 10 from both sides your equation should be

2n = 8 Divide 2 from both sides

By dividing your equation should look like

n = 4 which is your answer

Help me plz I’ve never been good with math

Answers

Its 16.

So you have 12 miles on that trail, and markers every 2/3 of the way there. If you were to divide 2 with 3 then you can get the decimal of the fraction. Which in this case it’s 0.75. So every single 0.75 of the mile there is a marker. Divide 12 with 0.75 and you get 16 markers.


Hoped this helped in some way.

Convert 15.8 square meters (m^2 ) into square feet ( ft^2).​

Answers

Answer:

Step-by-step explanation:

1 sq. meter = 10.7639 sq.feet

15.8 sq. m = 15.8 * 10.7639

                 = 170.06962 sq. feet

What is the difference between 4.5 and - 3.75

Answers

Answer:

.75

Step-by-step explanation:

Solve it: x + 9 - 7 = 15

Answers

Answer:

x = 13

Step-by-step explanation:

Rearrange: x = 15 + 7 - 9, x = 13

Answer:

X=2

Step-by-step explanation: First 9-7=2 then subtract 2 from both sides and you should be left with X=13

Every morning, siblings Jack and Jill roll a regular six-sided die to determine who will get to ride in the front seat on the way to school. If the number is even, Jack gets to ride in the front. If the number is odd, Jill gets to ride in the front.

Answers

Answer:

3/6

LCM of 6 and 20= 60

3/6=1/2=10/20=10days

so estimated 10 days

❤️ PLEASE HELP QUICK!! ILL GIVE BRAINLIST ANSWER!! ❤️

Answers

Answer:

3x² + 10x + 5

Step-by-step explanation:

Sum the sides together for perimeter (P)

Starting with the base and going clockwise

P = x² + 5x - 2 + x² + 5 + x² + 1 + 4 + 3x - 3 + 2x ← collect like terms

  = 3x² + 10x + 5

Molly earns a rebate each month on her movie tickets and books. She earns $0.25 for each movie ticket and $2 for each book. Last month molly purchased 4 movie tickets and earned $17. How many books did molly purchase last month?

Answers

Answer:

8 books

Step-by-step explanation:

Earning for each ticket is $0.25 and for each book is $2

If total earning for 4 tickets and x books is $17, then the equation is:

0.25*4 + 2x = 171 + 2x = 172x = 16x = 16/2x = 8

So Molly purchased 8 books

In a small town, 68% of the people I need television, 72% owned radio, 12% owned neither television nor radio
Represent the information on a Venn diagram
What percentage of the population owned television only?

Answers

Answer:

The total of people is the 100%.

68% owns a tv.

72% owns radios.

12% does not own anything.

Now, if we add those, we have:

12% + 68% + 72% = 152%.

This is larger than the 100%, then this means that there is a percentage of people that have both Tv and Radio, this percentage is:

152% - 100% = 52%

We have a surpass because we are adding those 52% two times (because they belong in two different groups)

So, the table is:

68% owns a tv.

72% owns a radio.

12% does not own anything.

52% owns both, radio and tv.

68% - 52% = 16% owns only tv.

72% - 52% = 20% owns only radio.

Then the Venn diagram consist in two circles, one with the 72%, other with the 68%, in such way that the circles have an intersection of the 52%.

9.48 as a mixed number in simplist form

Answers

Answer:

9 12/25.

Step-by-step explanation:

9.48 as a mixed number in simplest form:

948/100

948/100= 948 ÷ 4/100 ÷ 4

948/100= 948 ÷ 4/100 ÷ 4= 237/25

948/100= 948 ÷ 4/100 ÷ 4= 237/25= 9 12/25

9 12/25 is the mixed number.

A fair die is thrown once.find the probability that an odd number appears?

Answers

Hi

on a regular dice you have  3 even number  :  2 ;4;6

                                                3  odd number : 1;3;5

so probability to have an odd number is : 3/6 = 1/2

Answer:

1/2

Step-by-step explanation:

On normal six-sided die, there are the numbers: 1, 2, 3, 4, 5, and 6.

The odd numbers are 1, 3, and 5.

There is a [tex]\frac{1}{6}[/tex] chance that you will roll any number specifically. Since you stated 3 numbers, the probability that you will roll any of those three numbers is [tex]\frac{3}{6}[/tex], which is equivalent to [tex]\frac{1}{2}[/tex].

Which table shows the reflection of f(x) across the x-axis?
The first picture is the given table and the other three are the possible answers.

Answers

Answer:

The correct option is;

x,                f(x)

-5,               3

-1,               -2

2,               -4

6,                 1

Step-by-step explanation:

The reflection of a point (x, y) across the x-axis is given by the relation;

Coordinate of the pre-image (x, y) [tex]\overset{Reflection \ across \ the \ x-axis}{\rightarrow}[/tex] Coordinate of image (x, -y)

Therefore, we have for the points as follows;

(-5, -3)  [tex]\overset{Reflection \ across \ the \ x-axis}{\rightarrow}[/tex] (-5, 3)

[tex](-5, -3) \mapsto (-5, 3)[/tex]

(-1, 2)  [tex]\overset{Reflection \ across \ the \ x-axis}{\rightarrow}[/tex] (-1, -2)

[tex](-1, 2) \mapsto (-1, -2)[/tex]

(2, 4)  [tex]\overset{Reflection \ across \ the \ x-axis}{\rightarrow}[/tex] (2, -4)

[tex](2, 4) \mapsto (2, -4)[/tex]

(6, -1)  [tex]\overset{Reflection \ across \ the \ x-axis}{\rightarrow}[/tex] (6, 1)

[tex](6, -1) \mapsto (6, 1)[/tex]

evaluate ∛27 and explain your answer. Please do not answer just for points

Answers

Answer:

3

Step-by-step explanation:

(27) ^1/3

We want to know what number times itself 3 times is equal to 27

3*3*3 = 27

(3^3)^1/3

3

Answer:

[tex]\Huge \boxed{3}[/tex]

Step-by-step explanation:

[tex]\sqrt[3]{27}[/tex]

27 is a perfect cube.

A number when multiplied by itself 3 times gives 27.

[tex]\sqrt[3]{3 \times 3 \times 3}[/tex]

[tex]\sqrt[3]{3^3 }=3[/tex]

The cube root of 27 is 3.

Solve 27 and 29, will give BRAINLIST!!

Answers

Answer:

see below

Step-by-step explanation:

27.

We can use ratios to solve

152 dollars     532 dollars

---------------- = ----------------

4 days              x days

Using cross products

152x = 4*532

152x =2128

Divide each side by 152

152x/152 = 2128/152

x =14

14 days

29.

1 inch        2/3 inches

------------ = ----------------

6.5 ft          x ft

Using cross products

1x = 2/3 * 6.5

x = 4.333333

c = 4 1/3 ft

Answer:

[tex]\Large \boxed{\mathrm{27. \ 14 \ days}} \\ \\ \Large \boxed{\mathrm{29. \ 4 \frac{1}{6} \ feet}}[/tex]

Step-by-step explanation:

(27)

We can apply ratios to solve for the problem.

Let x be the missing value.

[tex]\displaystyle \frac{152}{4} =\frac{532}{x}[/tex]

Cross multiply.

152 × x = 532 × 4

152x = 2128

Divide both sides by 152.

x = 14

(29)

We can apply ratios to solve for the problem.

Let x be the missing value.

[tex]\displaystyle \frac{1}{6\frac{1}{4} } =\frac{\frac{2}{3} }{x}[/tex]

Cross multiply.

1 × x = 6 1/4 × 2/3

x = 6 1/4 × 2/3

Convert mixed fraction to improper fraction.

x = 25/4 × 2/3

x = 50/12

Simplify.

x = 25/6 or 4 1/6

What is the total number of common tangents that can be drawn to the circles

Answers

Answer:

A. 0

Step-by-step explanation:

The circles are concentric. I.e there is no point where the circumferences of both circles ever touch each other. Hence there can be no tangent line possible that can be common to both circles at the same time.


HELP can someone know this. It’s just about integers

Answers

I'll do the first two to get you started.

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

Problem 1

Answer:  0-7+11 = 4

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

Explanation:

The bottom arrow is where we start. Specifically at 0 on the number line.

Then we move 7 units to the left. This is represented by -7 on the number line. So -7 is part of the addition equation.

Then we move 11 units to the right to arrive at 4 on the number line. This is the same as adding 11 to -7 to get -7+11 = 4 and that is the same as 0-7+11 = 4

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

Problem 2

Answer:  1 + (-5) + 9 = 5

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

Explanation:

We now start at 1 on the number line. Move 5 units to the left to get to -4

Moving 5 units to the left is the same as subtracting 5, or adding on -5

So far we have 1 + (-5) which simplifies to -4

The last thing we do is add on 9 to go from -4 to 5. In other words, we move 9 units to the right when we go from -4 to 5

In terms of an equation,  -4 + 9 = 5

So overall, that's how I got 1 + (-5) + 9 = 5

Change this radical to an algebraic expression with fractional exponents

Answers

Answer:

X^(3÷5)

Step-by-step explanation:

radical basicly works as ÷ in the power.

Rewrite 2(x + 3y - 2z) using the Destributive Property

Answers

Answer:

2x+6y-4z

Step-by-step explanation:

multiply the two by each term and coefficient inside of the parentheses

Someone help asap! pls

Answers

answer: -5p^2 - m^2 +29m - 23
^= square
Pls ask if needed step by step explanation

In a survey, 200 people were asked if they smoke and whether or not they exercise regularly (more than twice a week). The results are summarized in the table
below

Answers

Answer/Step-by-step explanation:

a. % of people who smoke = no. of people who smoke ÷ total no. of people surveyed × 100

Total no. of people who smoke is given = 4 + 36 = 40

Total people surveyed = 200

% of people who smoke = [tex] \frac{40}{200}*100 = \frac{40}{2}*1 = 20 percent [/tex]

a. % of people who do not exercise regularly = no. of people who do not exercise regularly ÷ total no. of people surveyed × 100

Total no. of people who do not exercise regularly = 36 + 134 = 170

Total people surveyed = 200

% of people who smoke = [tex] \frac{170}{200}*100 = \frac{170}{2}*1 = 85percent [/tex]

when you form General ideas the rules based on your experiences and hit up vacations you call that form of reasoning ___.​

Answers

The answer would be induction

Whhen you form General ideas the rules based on your experiences and hit up vacations you call that form of reasoning what?

[tex]\huge\tt\red{AnswEr}[/tex]

[tex]\huge\implies\tt\underline{Induction}[/tex]

Which property of equality was used to solve this equation?
-5x=4
-5x/-5=4/-5
X=-4/5
A.addition property of equality
B.
subtraction property of equality
C. multiplication property of equality
D.
division property of equality

Answers

Answer:

D. Division property of equality.

Step-by-step explanation:

[tex] - 5x = 4 \: \: \: \frac{ - 5x}{ - 5} = \frac{4}{ - 5} \: \: \: \: x = \frac{ - 4}{5} [/tex]

We divided the terms on both sides by -5.

Hope this helps ;)❤❤❤

Please help! offering 15 points and a thanks with brainiest

Answers

Answer:

[tex]\huge\boxed{ 12\ people}[/tex]

Step-by-step explanation:

At least 6 hours means that the people took at least 6 hours and at most any number that is greater than 6. Here the greatest no. is 10.

So, the range for this will be 6-10

No. of People who sleep for 6-8 hours = 9

No. of People who sleep for 8-10 hours = 3

No. of People who sleep for 6-10 hours = 9+3

=> 12 people

What is (are) the solution(s) to the equation
2
(x−4)
2
=50

Answers

Answer:

x = 9 and x = -1

Step-by-step explanation:

This equation should be written all on one line:

2(x - 4)^2 = 50

using " ^ " to denote exponentiation.

Dividing both sides by 2 yields

(x - 4)^2 = 25

We must solve for x - 4, and then for x alone:

Taking the square root of both sides, we get:

x - 4 = ±5

which yields two separate solutions:  x = 9 and x = -1

Determine the standard form of the equation of the line that passes through (-7, 8) and (0, 2)

Answers

Answer:

The answer is

[tex]y = - \frac{6}{7} x + 2[/tex]

Step-by-step explanation:

Equation of a line is y = mx + c

where

m is the slope

c is the y intercept

To find the equation we must first find the slope

Slope of the points (-7, 8) and (0, 2) is

[tex]m = \frac{2 - 8}{0 + 7} = - \frac{6}{7} [/tex]

After that use the formula

y - y1 = m(x - x1)

To find the equation of the line

Equation of the line using point (0,2) and slope - 6/7 is

[tex]y - 2 = - \frac{6 }{7} (x - 0)[/tex][tex]y - 2 = - \frac{6}{7} x[/tex]

We have the final answer as

[tex]y = - \frac{ 6}{7} x + 2[/tex]

Hope this helps you

Simplify.
Rewrite the expression in the form 4^n

Answers

Answer:

4^(-2)

Step-by-step explanation:

4^6 * 4^-8

Since the bases are the same, and we are multiplying, we can add the exponents

4^(6-8)

4^(-2)

4^(-2) would be your answer

You buy 3 bags of Hot Cheetos
for $2.00 and a coke for $1.50. What is
change if you pay with $10?

Answers

Answer:

2.50

Step-by-step explanation:

Each bag of cheetos are 2 dollars. So 6 dollars for all of them. Add that by 1.50 and get 7.50 total. subtract that from ten and you get 2.50

Drag equations to each row to show why the equation of a straight line is y = 3x, where 3 is the slope. Math item stem image

Answers

Answer:

Step-by-step explanation:

The question lacks appropriate diagram. Find the diagram attached.

Slope is the change in coordinate of the y coordinate to the x coordinate.

Mathematically, slope m = ∆y/∆x

From the diagram ∆y is the same as 3 (along the vertical) while ∆x is the same as 1 (along the horizontal)

m = ∆y/∆x = 3/1

∆y/∆x = 3/1

y/x = 3/1

Cross multiply

y × 1 = 3 × x

y = 3x

Hence the slope of the line is y = 3x

Answer:

you need to add the picture next time :)

Step-by-step explanation:

y/x=3/1 is the first blank

y=3x is the last one

hope that helps:)

Dwayne is walking on a straight sidewalk. He spots
a vertical flagpole 10 feet to his right. His friend
Ursula says that the flagpole and sidewalk can be
used to model two lines. Which term best describes
the sidewalk and the flagpole?

Answers

Answer:

Skew lines

Step-by-step explanation:

Skew lines are two straight lines in three dimensional space that are neither parallel nor do they intersect Examples of skew lines are the front sidewalk and a line that goes along one of the top edges of the house, or lines that connecting opposite edges of a regular tetrahedron

Other examples of skew lines can be found in non co-planar non parallel, parts of a bridge.

Mind helping me out with these? Find the mean and range of the following data. 50, 60, 48, 72, 23, 98, 100 . The marks in a subject for 12 students are as follows: 31, 37, 35, 38, 42, 23, 17, 18, 35, 25, 35, 29. For the given data, find the (a) Mean (b) Mode (c) Median. If the mean of 26, 28, 25, x, 24 is 27, find the value of x.

Answers

Answer:

1. Mean- 64.43

  Range- 77

2. Mean- 30.42

   Mode- 35

   Median- 20

Step-by-step explanation:

1. Mean- 50+60+48+72+23+98+100= 451

              451 divide by 7= 64.43

   Range- biggest no. - smallest no.     100-23=77

2. Mean- 31+37+35+38+42+23+17+18+35+25+35+29= 365 -->

               365 divide by 12= 30.42

   Mode- most repeated no= 35

   Median- 2 middles-- 23+17=40 then divide by 2= 20.

Answer:

first:

mean=64.43

range=77

second:

mean =30.42

mode=35

median=33

x=-76

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