Mathematics High School

Answers................

Answers

Answer 1

Answer:

x=1

Step-by-step explanation:

log2( x^2 -x+2) = 1+2log2(x)

Rewriting 1 as log2(2)

log2( x^2 -x+2) = log2(2)+2log2(x)

We know that a log b = log a^b

log2( x^2 -x+2) = log2(2)+log2(x^2)

we know log a + log b = log (ab)

log2( x^2 -x+2) = log2(2*x^2)

Since the bases are the same the terms inside must be equal

x^2 -x+2 = 2x^2

Subtract 2x^2 from each side

-x^2 -x+2 = 0

Multiply by -1

x^2 +x-2 = 0

Factor

(x+2)(x-1)=0

Using the zero product property

x+2 = 0 x-1=0

x=-2 x=1

Checking the solutions

log2( x^2 -x+2) = 1+2log2(x)

X cannot be negative because 2 log2(x) cannot be negative

log2( 1^2 -1+2) = 1+2log2(1)

x=1

Answer 2

[tex]\\ \rm\Rrightarrow log_2(x^2-x+2)=1+2log_2x[/tex]

[tex]\\ \rm\Rrightarrow log_2(x^2-x+2)=log_22+2log_2x[/tex]

[tex]\\ \rm\Rrightarrow log_2(x^2-x+2)=2log_2(2x)[/tex]

[tex]\\ \rm\Rrightarrow log_2(x^2-x+2)=log_2(2x^2)[/tex]

[tex]\\ \rm\Rrightarrow x^2-x+2=2x^2[/tex]

[tex]\\ \rm\Rrightarrow x^2+x-2=0[/tex]

[tex]\\ \rm\Rrightarrow (x+2)(x-1)=0[/tex]

x=-2,1

log is always positive so x=1

Laws used

log_a(a)=1loga^m=mlogalog(ab)=loga+logb

Related Questions

The midpoint of line segment AB is (1,2). if the coordinates of A are (1,0) what are the coordinates of B

Answers

The required coordinate of B will be at (1, 4)

When a point bisects a line, it cuts the line into two equal parts and the point on that line is known as its midpoint. The expression for calculating the midpoint of a line is expressed as;

[tex]M(X, Y)= [{ \frac{x_2+x_1}{2} , \frac{y_2+y_1}{2} ][/tex] where:

[tex]X =\frac{x_2+x_1}{2} \\Y=\frac{y_2+y_1}{2}[/tex]

From the question, we are given the following coordinate points

[tex]X=1\\x_1=1\\[/tex]

Get x₂;

[tex]X =\frac{x_2+x_1}{2}\\1 =\frac{x_2+1}{2}\\2=x_2+1\\x_2=2-1\\x_2=1\\[/tex]

Get y₂;

[tex]Y =\frac{y_2+y_1}{2}\\2 =\frac{y_2+0}{2}\\2 \times 2=y_2+0\\4=y_2+0\\y_2=4\\[/tex]

Hence the coordinate of B will be (1, 4)

Learn more about the midpoint here: https://brainly.com/question/18315903

PLEASE ANSWER ASAP

Select the correct answer.
Solve the rational equation.

A.
x = 15
B.
x = 10
C.
x = 3
D.
x = -18

Answers

Answer:

D: x = -18

Step-by-step explanation:

A good way to solve this it to input all options until you find the one that fits for both options.

Option A :

15 + 6 / 15 - 3 = 21 / 12 or 7/4

So this one doesn't work.

Option B :

10 + 6 / 10 - 3 = 16 / 7

So this one also doesn't work.

Option C:

3 + 6 / 3 - 3 = 9 / 0 which is 0 by the laws of dividing by zero.

This one also doesn't work leaving only one option.

Option D:

-18 + 6 / -18 - 3 = -12 / -21 or 4 / 7

And by solving we can find out we did our work correctly and get our answer.

A car of 1000 kg starts to move from rest and travels a distance of 150 m in 10 second. How much force is needed?

Answers

Initial velocity=u=0m/sDistance=s=150mTime=t=10sAcceleration=a

Using second equation of kinematics

[tex]\\ \sf\longmapsto s=ut+\dfrac{1}{2}at^2[/tex]

[tex]\\ \sf\longmapsto 150=0(10)+\dfrac{1}{2}a(10)^2[/tex]

[tex]\\ \sf\longmapsto 150=\dfrac{1}{2}\times 100a[/tex]

[tex]\\ \sf\longmapsto 50a=150[/tex]

[tex]\\ \sf\longmapsto a=\dfrac{150}{50}[/tex]

[tex]\\ \sf\longmapsto a=3m/s^2[/tex]

Mass=m=1000kgForce=F

Using newtons second law

[tex]\\ \sf\longmapsto F=ma[/tex]

[tex]\\ \sf\longmapsto F=1000(3)[/tex]

[tex]\\ \sf\longmapsto F=3000N[/tex]

Suppose Cab Company A charges a flat fee of $4.50 plus an additional $0.25/mile. Cab Company B charges a flat fee of $1 plus an additional $0.75/mile.

First, define variables. Then write two equations: one equation will represent the cost of choosing Cab Company A, and the other equation will represent the cost of choosing Cab Company B.

Answers

Hope this helps!

Could you go to my profile and go to the social studies questions, should be for 7 points, please help with all questions! Giving brainliest!

What is the result of rounding 8,888,888 to the nearest ten?

Answers

Answer:

8,888,890

Step-by-step explanation:

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The midpoint of a sègment is (6,-4) and one endpoint is (13,-2). Find the coordinates of the other endpoint.

Answers

let other one be (x,y)

We know midpoint formula

[tex]\boxed{\sf (x,y)=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)}[/tex]

[tex]\\ \sf\longmapsto (6,-4)=\left(\dfrac{13+x}{2},\dfrac{-2+y}{2}\right)[/tex]

[tex]\\ \sf\longmapsto \dfrac{13+x}{2}=6[/tex]

[tex]\\ \sf\longmapsto 13+x=12[/tex]

[tex]\\ \sf\longmapsto x=12-13[/tex]

[tex]\\ \sf\longmapsto x=-1[/tex]

And

[tex]\\ \sf\longmapsto \dfrac{-2+y}{2}=-4[/tex]

[tex]\\ \sf\longmapsto -2+y=-8[/tex]

[tex]\\ \sf\longmapsto y=-8+2[/tex]

[tex]\\ \sf\longmapsto y=-6[/tex]

Answer:

(- 1, - 6 )

Step-by-step explanation:

Given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is

( [tex]\frac{x_{1}+x_{2} }{2}[/tex] , [tex]\frac{y_{1}+y_{2} }{2}[/tex] ) ← midpoint formula

Use this formula on the endpoints and equate to the coordinates of the midpoint.

let the other endpoint = (x, y) , then

[tex]\frac{13+x}{2}[/tex] = 6 ( multiply both sides by 2 )

13 + x = 12 ( subtract 13 from both sides )

x = - 1

[tex]\frac{-2+y}{2}[/tex] = - 4 ( multiply both sides by 2 )

- 2 + y = - 8 ( add 2 to both sides )

y = - 6

The coordinates of the other endpoint are (- 1, - 6 )

100 POINTS!!!
Fill in the missing work and justification for step 3 when solving 2(x + 1) = 10.

Step Work Justification
1 2(x + 1) = 10 Given
2 2x + 2 = 10 Distributive Property
3
4 2x = 8 Simplify
5 two times x over two equals eight over two Division Property of Equality
6 x = 4 Simplify

a. 2x + 2 + 2 = 10 + 2; Addition Property of Equality
b. 2x + 2 − 2 = 10 − 2; Subtraction Property of Equality
c. (2x + 2)(2) = 10(2); Multiplication Property of Equality
d. the quantity two times x plus two all over two equals ten over two; Division Property of Equality

Answers

Answer: x = 4

Step-by-step explanation:

2(x+1)=10

Distributive properties

a*(b+c)=(a*b)+(a*c)

Using distributive properties

Then

2*(x+1)=(2*x)+(2*1)

2*(x+1)=2x+2

Now, commutative properties

a*b=b*a

Addition is cumulative

a+(-b)=(-b)+a

Therefore applying to 2x+2

2x+2+(-2)=2x+(-2)+2

Then, applying to the equation

2x+2+(-2)=10+(-2), +×-=-

2x+2 -2=10-2

2x=8

Using division properties

ax=b

If a is none zero

Then ax/a=b/a

Therefore x=b/a

Applying that to 2x=8

2x=8. Divide both side by 2 which is none zero

2x/2= 8/2

x=4

Option B

Subtraction Property of equality

please click thanks and mark brainliest if you like :)

Answer:

2x + 2 − 2 = 10 − 2; Subtraction Property of Equality

Mark me, It would be my very first!!

Help with number 11 anyone?

Answers

Answer:

y = 3/5×x + 1

Step-by-step explanation:

Slope intercept form y= mx + b

since slope = 3/5 => y= [tex]\frac{3}{5}[/tex]x + b

Plug point (-5,-2) to the equation -2 = [tex]\frac{3}{5}[/tex] x (-5) + b

=> b=1

Can anyone describe the errors with the problems? For example the first answer is they did not distribute the negative

Answers

Yes they put that over they’re

Answer:

see image

Step-by-step explanation:

A parabola has x-intercepts at x=-3 and x=4. What the equation of the parabola?

Answers

Answer:

x² - x - 12 = 0

Step-by-step explanation:

Given the x- intercepts are x = - 3 and x = 4 , then the factors are

(x + 3) and (x - 4)

Expressing as a zero product

(x + 3)(x - 4) = 0 ← expand using FOIL

x² - x - 12 = 0

Two truck leave a factory at a sametime.one travel east at 60 miles per hour and other went 30 miles per hour. In how many hour will they be 150 miles apart ?

Answers

Answer:

2.5hrs apart.

Step-by-step explanation:

150÷60= 2.5

150÷60=5

therefore 5-2.5 =2.5

128 is the product of hectors score and 8

Fastest answer will be the brainliest

Answers

Answer:

The equation would be 8h= 128

Step-by-step explanation:

Answer:

Step-by-step explanation:

128=8h

When you divide both sides by 8, you end up with:

Given that E=MC find E when M=20 and C =2.5

Answers

Answer:

50 or 125

Step-by-step explanation:

if u want E=MC then it would be 20 ×2.5=50

if u what to find E=MC² then it would be 20×2.5×2.5 =125

ACCORDING TO ME THIS SHOULD BE THE ANSWER, BUT NOT QUITE SURE ABOUT THIS.

Answer:

E = 50

Step-by-step explanation:

If M=20 and C=2.5, replace the letters in the equation with their numerical values so E=20*2.5

20*2.5 = 50

thus E=50

What is the height of an iscocles trapizoid, if the lengths of its bases are 5m and 11m and the length of a leg is 4m?

Answers

Answer:

x=√5

Step-by-step explanation:

Use the pythagorean theorem

Find the value of x for which l||m

Answers

Answer:

30 =x

Step-by-step explanation:

The angles are correcting angle and corresponding angles are equal when the lines are parallel

55 = x+25

Subtract 25 from each side

55-25 = x+25

30 =x

Answer:

x = 30

Step-by-step explanation:

The 55 degree angle is congruent with the angle of x

55* = m∠x

Step 1. Take the equation of x (x + 25*) and line it up with 55

(x + 25) = 55

Step 2. Solve by subtracting both sides by 25

x = 30

the average temperature for the week of January 7-14 was -16degrees Celsius. the average temperature for the week of January 15-22 was 3 degrees celcies. what is the absolute value of the difference between these two temperatures?

Answers

Answer:

Step-by-step explanation:

The difference between the two numbers is 3-(-16), or 19. |19| is 19.

what is the gcf of 36, 126, and 210?

Answers

Answer:

Greatest common factor (GCF) of 36 and 210 is 6.

Step-by-step explanation:

Answer:

Brainliest, please! (Almost an Ace!)

Step-by-step explanation:

Look at the smallest factor, 36. Find its factors.

36: 1, 2, 3, 6, 12, 18, 36

Out of all of them, which is the biggest one that 126 and 210 are also divisible by?

We see that they're divisible by 1, 2, 3, and 6.

Our answer is 6.

2.
Determine whether the matrices are inverses.

Answers

Answer:

Yes these are....

Note: all you have to do for these problems is to multiply the two matrices, and see if the answer is 1,0

0,1

you can multiply them by hand or use an online tool...

see the image supplied... it is a free site, and even shows the steps

Step-by-step explanation:

-5 1 0.5 -0.5

-7 1 3.5 -2.5

1 0

0 1

Use the parabola tool to graph the quadratic function
f(x)= -1/2x^2 + 7
Graph the parabola by first plotting its vertex and then plotting a second point on the parabola.

Answers

Answer:

That's the graph for the function f(x)= -1/2 x^2 + 7

The vertex is f(0) = 7

Select All the correct answers

Select all the statements that are true for the following systems of equations.

System A
2x-3y=4
4x.y = 18

System B
3x - 4y 5
y = 5x + 3

System C
2x-3y - 4
12x-3y 54

1. All three systems have different solutions.

2. Systems A and B have different solutions

3. Systems A and C have the same solution

4. Systems B and C have the same solution

5. System C simplifies to
2x - 3y = 4 and 4x - y = 18 by dividing the second equation by three

Answers

Answer:

Step-by-step explanation:

kjddhllkfewtuikkbccjg

Is -626 an integer ? If yes, why.

Answers

Answer:

Step-by-step explanation:

Because intergerss are there positive opposite and its negative

Answer and Step-by-step explanation:

-626 is an integer because it is a whole number, not a fraction.

Integers can be both positive and negative numbers. What can't be an integer are fractions and decimals.

#teamtrees #PAW (Plant And Water)

I hope this helps!

Can someone help me with 1-5 and create problems for 6-10

Answers

The problem is that you need to subtract 15÷42 would get you 74 cherry pie will be a cantaloupe into a torch a computer is a wiring device that could help you in life the answer is 82

The mean (average) weight of three boys is 40 pounds. One of the boys weighs 50 pounds. The other two boys have the same weight. Find weight of each of the boys?

Answers

Answer:

The weights are 50 lb, 35 lb, and 35 lb.

Step-by-step explanation:

The three boys weight x, y, and z pounds.

One boy weighs 50 lb, so x = 50. The other 2 boys have the same weight, so y = z.

The average weight is the sum of the three weights divided by 3.

(x + y + z)/3 = 40

(50 + y + y)/3 = 40

2y + 50 = 120

2y = 70

y = 35

z = y = 35

Answer: The weights are 50 lb, 35 lb, and 35 lb.

Answer: 35 lb, 35 lb, and 40 lb

Step-by-step explanation:

(50+X+X)/3 = 40

50 + 2X = (40)(3)

2X = 120 - 50

X = 70/2

X = 35

2x2
The value of the expression + x(100 - 15x) when x = 5 is
X

Answers

Answer:

129

Step-by-step explanation:

2*2+x(100-15x)

2*2+5(100-15*5)

2*2+5(100-75)

2*2+5*25

4+125

129ans

Divide 11 in two parts so that theis product is 24.

Answers

Answer:

8 and 3

Step-by-step explanation:

8+3=11

8×3=24

this is the answer

3.What mathematical property is used to get the resulting
expression for each line? Complete the table below.
Line 1: (7 + 10x) + 3
Line 2:
(10x + 7) + 3
Line 3:
10x + (7 + 3)
Line 4:
10x + 10

Answers

Answer:

what is the condition of loss ?1)sp>mp 2)CP>sp 3) sp>CP 4)mp>spThe UN has 4 main purposesTo keep peace throughout the world;To develop friendly relations among nations;To help nations work together to improve the lives of poor people, to conquer hunger, disease and illiteracy, and to encourage respect for each other’s rights and freedoms;To be a centre for harmonizing the actions of nations to achieve these goals

Principles of United Nations

View all

These principles include the equality and self-determination of nations, respect of human rights and fundamental freedoms and the obligation of member countries to obey the Charter, to cooperate with the UN Security Council and to use peaceful means to resolve conflicts.

https://en.m.wikipedia.org › wiki

Chapter I of the United Nations Charter - Wikipedia

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About featured snippets

Answers

Answer:

[tex]\frac{-27b^{6}}{c^{18}}[/tex]

Step-by-step explanation:

first distribute the ^3, -3^3=-27, for the variables, (x^y)^3=x^(3y) so (b^2)^3=b^6 and (c^-6)^3=c^-18. now we have [tex]-27b^{6}c^{-18}[/tex]. Next we have to get rid of the negative in c^-18. x^-y=1/x^y so c^-18=[tex]\frac{1}{c^{18}}[/tex], plug it in and you get [tex]\frac{-27b^{6}}{c^{18}}[/tex]

Need help with this pls help

Answers

Answer:

Step-by-step explanation:

find the value of x from the value of 13,x,6,8,if the mean (x) is 10

Answers

Answer:

Step-by-step explanation:

4 numbers

average is 10

10 * 4 = 40

13 + 6 + 8 = 27

40 - 27 = 13

The graph of a linear relation passes through the point (-2,7) and has a slope of 1/6.
Determine an equation for this linear relation in slope intercept form.

Answers

Answer:

Step-by-step explanation:

eq. of any line withslope 1/6 is

y=1/6x+c

∵ it passes through (-2,7)

so 7=1/6(-2)+c

c=7+1/3=22/3

eq. of line is

y=1/6x+22/3

Answer:

y = 1/6x + 7 1/3

Step-by-step explanation:

Slope intercept form is y=mx+b where m is the slope and b is the y intercept

y = 1/6x+b

Substitute the point into the equation

7 = 1/6(-2)+b

7 = -1/3+b

Add 1/3 to each side

7 1/3 = b

y = 1/6x + 7 1/3

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