Given the equation log2x + log2(x – 7) = 3, solve for x.

Answers

Answer 1

Answer:

         x∈{-1, 8}

Step-by-step explanation:

[tex]\log_2x +\log_2(x-7) = 3\\\\\log_2[x\cdot(x-7)]= 3\log_22\\\\\log_2(x^2-7x)= \log_22^3\\\\x^2-7x=2^3\\\\x^2-7x-8=0\quad\implies \quad a=1\,,\ \ b=-7\,,\ \ c=-8 \\\\x=\dfrac{-(-7)\pm\sqrt{(-7)^2-4\cdot1\cdot(-8)}}{2\cdot1}= \dfrac{7\pm\sqrt{49+32}}{2} =\dfrac{7\pm\sqrt{81}}{2}\\\\x=\dfrac{7+9}2=8\qquad\vee\qquad x=\dfrac{7-9}2=-1[/tex]


Related Questions

n/-5 = 7
What is n

Please answer with an explanation of how you completed the equation

Answers

Answer: n= -35

Step-by-step explanation: N= 7(-5) =-35

What is the factored form of n2 - 25?
?
(n-25)(n-1)
(n - 5)(n + 5)
(n + 5)(n + 5)
LO (n - 25)n + 1)

Answers

Answer:

(n-5)(n+5)

Step-by-step explanation:

n^2-25

(n-5)(n+5)

CAN SOMEONE PLEASE HELP ME I WLL MARK BRAINLIEST!!!

Answers

Answer:

1/2 inch: 3 feet

Step-by-step explanation:

It says in the bottom right corner.

Answer:2tt

Step-by-step explanation:

huh

PLZ I NEED HELP!!A tree is 12 feet tall and casts a shadow 9 feet long. A building nearby casts a shadow that measures 24 feet. How tall is the building?
A. 24
B. 21
C. 27
D. 32

Answers

Answer:

D. 32 feet

Step-by-step explanation:

A tree is 12 feet tall and casts a 9-foot shadow.

The shadow is 3/4 the length of the tree (9/12 = 3/4).

We know the shadow of a nearby building is 24 feet long.

That would be 3/4 of the height of the building.

So, fidn the reciprocal of 3/4 (4/3) and multiply by 24.

24/1 * 4/3

Cross-cancellation

8/1 * 4/1

8 * 4

The building is 32 feet tall, which is D.

a company sets up a food booth at the county fair. the fee for the food booth is 100$ plus 5$ per day. which expression can be used to determine how much money it would cost after x days?

Answers

Answer:

Total cost after x days = 100 + 5(x)

Step-by-step explanation:

Given:

Fixed cost = $100

Per day charges = $5

Find:

Total cost after x days

Computation:

Assume;

Number of days = x

Total cost after x days = $100 + $5(x)

Total cost after x days = 100 + 5(x)

You want to limit the amount of television you watch to an average of at most 2 hours a week during and eight week period. How many hours x can you watch in the eight weeks to meet your goal.

Answers

Answer:

x = 16hours

Step-by-step explanation:

Given

Total number of hours to watch the television a week is 2 hours, that is;

2hours =1 week

We are to find the number of hours to watch in eight weeks to meet the goal

x hours = 8 weeks

Divide both expressions;

2/x = 1/8

Cross multiply

1 * x = 2*8

x = 16

Hence he will use 16hours to watch the television in 8 weeks

list the integers within the interval
[tex] 8 \leqslant x < 16[/tex]


Answers

8,9,10,11,12,13,14,15

do not include 16 as it is not equal to (the line underneath the ‘crocodile’ whereas the ‘crocodile’ next to 8 has a line therefore it is equal to and so you include it.

Which is a graph of the solution of the inequality -5m+10>70

Answers

Answer:

solving form; m< -12  

Step-by-step explanation:

On a linear graph there would be an open circle on the number -12 and the line would be pointing left

click to see the problem

Answers

Answer:

C is your correct answer i think

Step-by-step explanation:

I think the answer would be C

help plz plz plz plz will mark brainliest

Answers

Answer:

x = 68°

Step-by-step explanation:

Let us solve the question

In the given figure

∵ The ray WD bisects ∠ZWN

→ That means it divides the angle into two equal angles, ∠ZWD and ∠DWN

m∠ZWD = m∠DWN

∵ m∠ZWD = 5v - 7

∵ m∠DWN = 4v + 8

→ Equate the measures of the two angles

5v - 7 = 4v + 8

→ Add 7 to both sides

∵ 5v - 7 + 7 = 4v + 8 + 7

5v = 4v + 15

→ Subtract 4v from both sides

∵ 5v - 4v = 4v - 4v + 15

v = 15

∵ x = m∠ZWD

x = 5v - 7

→ Substitute v by 15

∵ x = 5(15) - 7

∴ x = 75 - 7

x = 68°

are you a robot cause i think you are

Answers

No I am not a robot what u mean
i am not. I’m actually an alien i come from planet Kepler-452b. Don’t know if the world knows my planet yet. They were supposed to find out in 2020 when i arrived

Given the two angles:

1) two angles are:
Congruent
Supplementary
Complementary

2) because they are...
Corresponding
Consecutive interior
Alternate exterior
Alternate interior

Answers

Answer:

congruent, alternate exterior

Step-by-step explanation:

For the first question, the angles are congruent (they are not complementary because they dont add p to 90 degrees, and they are not supplementary because they dont add up to 180 degrees so they must be congrunet)

For the second- they are alternate exterior (i know that they are on the outisde so they are exterior)

Solve the following multi-step equation: 4(2 - 4x) - 3x = 65

Answers

Answer:

x = -3

Step-by-step explanation:

4(2 - 4x) - 3x = 65

Distribute the 4.

8 - 16x - 3x = 65

Combine like terms.

8 - 19x = 65

-19x = 57

Divide by -19 to isolate x.

x = 57/-19

x = -3

Check.

4(2 - 4(-3)) - 3(-3) = 65

4(2 - (-12) + 9 = 65

4(14) + 9 = 65

56 + 9 = 65

65 = 65

The solution of the given linear equation 4(2 - 4x) - 3x = 65 is  -3.

Two algebraic expressions separated by an equal symbol in between them and with the same value of the expression are called equations.

Example = 2x +4 = 12

here, 4 and 12 are constants and x is variable.

The solution of the equation 4(2 - 4x) - 3x = 65 is calculated as:

4(2 - 4x) - 3x = 65

Multiply the expressions inside the brackets,

8 - 16x -3x = 65

8 - 19x = 65

Subtract 8 from both the sides,

-19x = 65- 8

-19x = 53

Divide both side by -19

[tex]x = \dfrac{-53}{19}[/tex]

Thus, the value of x is -3.

Learn more about equations here:

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which value of x is the solution set of 2(3x-1)≥4x-6

Answers

Answer:

-1

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Equality Properties

Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtract Property of Equality

Step-by-step explanation:

Step 1: Define

2(3x - 1) ≥ 4x - 6

Step 2: Solve for x

Distribute 2:                                 6x - 2 ≥ 4x - 6Subtract 4x on both sides:          2x - 2 ≥ -6Add 2 on both sides:                   2x ≥ -4Divide 2 on both sides:               x ≥ -2

Here we see that any value x greater than or equal to -2 would work as a solution.

help plz plz plz plz

Answers

Step-by-step explanation:

2(4y-44)°+2(3y+35)°=360°

(8y-88)°+(6y+70)°=360°

(8y+6y+70-88)°=360°

(14y-12)°=360°

14y=360°+12°

14y=372°

y=372°/14

y=27°

acute angle

(4y-44)° =4(27)°-44°

=108°-44°=64°

...............°__________°.................​

Answers

Answer:

35

Step-by-step explanation:

i pretty sure

Hey again!

The answer to your question is 122.5 feet²

We can find the dimensions of the new figure:

2 x 3.5 = 7

5 x 3.5 = 17.5

Area = length x width, so 7 x 17.5 = 122.5

Hope it helps!

Omgggg please please please help me I really really really need help on this. Please can you guys help me solve this problem?

Answers

Answer:

The volume of the figure is: 60840[tex]\pi ^3[/tex], or approximately about 191037.6 ft^3.

Step-by-step explanation:

This 3D figure can be split into two separate figures, a half-sphere, and a cone.

Let's first try to find the volume of the half-sphere.

The formula for the volume of the half-sphere is [tex]\frac{2}{3}\pi r^3[/tex], so substituting 39 for r gives us a volume of 39546[tex]\pi \\\\[/tex]ft^3, or about 124174.44 ft^3.

Next, let's find the volume of the cone. We see that the radius of the cone is once again 39 ft, and the height of the cone i s just 81-39, or 42 ft.

The volume of a cone is [tex](\pi r^2h)/3[/tex], and substituting 39 for r and 42 for h, we obtain a result of 21294[tex]\pi^3[/tex], or about 66863.16

Thus, the final volume of the figure is: 60840[tex]\pi ^3[/tex], or approximately about 191037.6 ft^3

WILL MARK BRAINLIEST!! This goes to a part 2 of my last post. Sketch a new graph of this relationship.​

Answers

What can I find the part 2

help please!!!!!!!!!!!!!!!!!!!!!!!

Answers

9514 1404 393

Answer:

  a) $336

  b) $1036

Step-by-step explanation:

a) The interest is computed using the formula ...

  I = Prt

where P is the amount invested at rate r for t years.

  I = $700·0.08·6 = $336

The interest earned is $336.

__

b) The balance of the account is the sum of the original amount and the interest earned:

  balance = $700 +336 = $1036

The balance of the account is $1036.

In his last basketball game, Chris attempted a total of 25 shots and made 18 of them.What is the ratio of how many shots missed and how many shots made?

Answers

Answer:

7:18

Step-by-step explanation:

Chris attempted a total of 25 shots

He made 18 shots

Number of shots missed= 25-18

= 7

Therefore the ratio of shots missed and shots made can be calculated as follows

7:18

Hence the ratio is 7:18

Which property is demonstrated by the equation (5 + a) + 3 = (a + 5) + 3?

Answers

Answer:

Communitive Property

Step-by-step explanation:

Commutative property = 2 + 3 = 3 + 2 or 2(3) = 3(2)

Associative Property = (2 x 3) 5 = 2 (3 x 5) or (2 + 3) + 5 = 2 + (3 + 5)

Inverse Property = 2 + (-2) = 0 or (2/1)(½) = 1

Basic Definitions:

Commutative Property - Gives you the ability to switch the order of the numbers in an expression.

Associative Property - Let's you move the parenthesis in an expression but not the numbers.

Inverse - Uses numbers like 0 and 1.

Using these basic definitions and examples, we can summarize that the best answer would be Communitive Property

Which method will NOT get you to the point (4,3.5)?
A. Starting at the origin, go 3.5 spaces to the right and then 4 spaces up.
B. Starting at the origin, go 3.5 spaces up and then 4 spaces to the right.
C. Starting at the origin, go 4 spaces to the right and then 3.5 spaces up.
D. Put one finger on 4 on the x-axis, and put another finger halfway between 3 and 4 on the y-axis. Move the first finger up and the second finger to the right until they meet.

Answers

Answer:

A. Starting at the origin, go 3.5 spaces to the right and then 4 spaces up.

Step-by-step explanation:

if you were to plot this then the point would be (3.5,4) instead of (4,3.5)

Starting at the origin, go 3.5 spaces to the right and then 4 spaces up will not get you to the point (4,3.5) but will get you (3.5, 4). The correct option is A.

What are coordinates?

Coordinates are a pair of integers (Cartesian coordinates), or occasionally a letter and a number, that identify a certain place on a grid, often referred to as a coordinate plane.

We have the point (4, 3.5).

And let the point (x, y).

By comparing,

we get,

x = 4 and y = 3.5

That means, the value in the x coordinate is 4 and y coordinate is 3.5.

As the signed distance from the origin in the direction along the x-axis, the first value x is known as the x-coordinate (or x-component). The x-coordinate indicates the distance from the y-axis to the right (if x is positive) or left (if x is negative).

Additionally, the y-coordinate indicates how many steps are needed to up either positively or negatively on the y-axis.

So, the point is 4 point right from the origin and 3.5 point up from the origin.

Therefore, starting at the origin, go 3.5 spaces to the right and then 4 spaces up will not get you to the point (4,3.5)

To learn more about the coordinates;

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Lin is reading a 47-page book. She read the first 20 pages in 35 minutes. Rounding to the nearest minute, how long will it take Lin to finish the entire book?

Answers

Answer: 82.25 minutes

Step-by-step explanation:

First convert the minutes she took to hours. This would be:

= 35/60

She is reading at a speed of 20 pages per 35/60 hours.

To finish 47 pages therefore, she will take:

= (47 * 35/60) / 20

= 1.37083 hours

Converted to minutes that would be:

= 1.37083 * 60 mins

= 82.25 minutes

Are x+x^2 and u+u^2 the same function? If x and u are for all real numbers? A- these are the same function B- If x and u are two different numbers, the functions are different C- there is not enough information to answer this question.

Answers

Answer:

(a) These are the same function

Step-by-step explanation:

Given

[tex]x + x^2[/tex] and [tex]u + u^2[/tex]

Required

Are they the same?

Yes, they are the same function and this is proved below.

[tex]x + x^2[/tex]

Represent as a function:

[tex]f(x) = x + x^2[/tex]

[tex]u + u^2[/tex]

Represent as a function

[tex]f(u) = u + u^2[/tex]

Let x = u

Substitute u for x in [tex]f(x) = x + x^2[/tex]

[tex]f(u) = u + u^2[/tex]

This implies that:

[tex]f(x) = f(u)[/tex]

[tex]x + x^2 =u + u^2[/tex]

PS: The information that x and u are real numbers are for all real numbers; So, we can not assume that x and u are different numbers

Hence:

(b) and (c) are wrong

Select "equivalent" or "not equivalent" for each pair of expressions.
Expressions
equivalent or not equivalent?
5x - 7+ 3x and 3x – 7+ 5x equivalent not equivalent
4y + 9 + 3y and 3y+9+ 4y equivalent not equivalent
62 - 2x + 4 and 4 + 2z. - 62 equivalent not equivalent

Answers

Answer:

Step-by-step explanation:

1. Not

2. Yes

3. not

What is the answer of this q ❓​

Answers

Answer:

68

Step-by-step explanation:

lets mijdkdefbdhnrr

what is the measure of the central angle that represents blue backpacks?

Answers

Answer:

Yes it is 10

Step-by-step explanation:

4+8 890-5+764+88=765678987654

Answers

Answer:

no its 1749

Step-by-step explanation:

Find the equation of the line through the points (-2,-9) and (5,12)
y =

Answers

Answer:

y - 12 = 3(x - 5)

Step-by-step explanation:

Going from (-2, -9) to (5, 12), x (the run) increases by 7 and y (the rise) increases by 21.  Thus, the slope of this line is m = rise / run = 21/7 = 3.

Using the point-slope formula y - k = m(x - h), we get:

y - 12 = 3(x - 5)

How many should I have?

Answers

Answer:

You should have 95 bananas.

Step-by-step explanation:

multiply 19 by 5.

Answer:

95 bananas ..I'm here for the points

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