if you're good at logarithms please help me with question h and show full working out ty ;)

If You're Good At Logarithms Please Help Me With Question H And Show Full Working Out Ty ;)

Answers

Answer 1

Answer: [tex]x=\frac{31}{2}[/tex]

Step-by-step explanation:

[tex]2log_a(x+2)=log_a(x+9)+log_a(x-3)[/tex]

The first thing we are going to do is to get rid of the 2 in front of the first logarithm. To do this, we have the power property that says:

[tex]log_aX^n=nlog_aX[/tex]

Basically, the number in front, is the power of the number in the middle.

Let's rewrite this.

[tex]log_a(x+2)^2=log_a(x+9)+log_a(x-3)[/tex]

Now, in order to add logarithms with the same base (in this case "a"), we write the same base of the logarithm, and multiply their values.

[tex]log_a(x+2)^2=log_a(x+9)(x-3)[/tex]

Multiply the parentheses.

[tex]log_a(x+2)^2=log_a(x^2-3x+9x-27)[/tex]

Combine like terms;

[tex]log_a(x+2)^2=log_a(x^2+6x-27)[/tex]

Solve the binomial on the left side.

[tex]log_a(x^2+4x+4)=log_a(x^2+6x-27)[/tex]

When we have logarithms with same base, we equal their values.

[tex]x^2+4x+4=x^2+6x-27[/tex]

Subtract [tex]x^2[/tex]

[tex]x^2-x^2+4x+4=x^2-x^2+6x-27\\4x+4=6x-27[/tex]

Subtract 6x

[tex]4x-6x+4=6x-6x-27\\-2x+4=-27[/tex]

Subtract 4

[tex]-2x+4-4=-27-4\\-2x=-31[/tex]

Divide by -2.

[tex]x=\frac{-31}{-2}\\ x=\frac{31}{2}[/tex]


Related Questions

20. (x, y) → (x + 3. y - 6)

Answers

Answer:

Step-by-step explanation:

The indicated operation will do two things:  1) translate the relevant graph 3 units to the left and 2) translate it 6 units down.

Complete 4 A,B 9 for points.

Answers

Answer:

R = (1/t) (A/P - 1)

T = (1/r) (A/P - 1)

The lower the average monthly temperature, the higher the monthly heating bill.


There is a low correlation between the average monthly temperature and the monthly heating bill.


There is no correlation between the average monthly temperature and the heating bill.


The lower the average monthly temperature, the lower the monthly heating bill.

Answers

The first option is correct

pls helppp
The slope of the line segment joining the points (2, 3) and (2, -6) is undefined.


a)True b) False

Answers

Answer:

True

Step-by-step explanation:

The points (2,3) and (2,-6) are undefinable because it makes a vertical line. The slope cannot be defined.

If a cross section was cut that was parallel to the base of a triangular prism below a shape with that cross section be ?
A. Square
B. Triangle
C. Parallelogram
D. Rectangle

Answers

The answer is A) square
The answer would be A


Help plz!!!!!!!!
In the diagram, Cand D are located such that AB is divided into three equal parts. What are the coordinates of Cand D?
A.(1.3). D(3,1)
B.(-3,0). D(3-6)
C.(20.3). D(3, 0)
D. (-1.5, 3), 011.5, 0)​

Answers

Answer:

itsc c (0,3) ,d(3,0)

Step-by-step explanation:

If AB is divided into three equal parts then coordinates of C is  (0, 3) and D coordinates are (3, 0)

What is Coordinate Geometry?

A system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space.

Divide AB into three equal parts

[tex]X_{c}-X_{a}=\frac{1}{3} (X_{B}-X_{D})[/tex]

=3

[tex]Y_{a}-Y_{c}=\frac{1}{3} (Y_{A}-Y_{B})[/tex]

=3

So C is (0, 3)

[tex]X_{B} -X_{D} =\frac{1}{3} \times 9[/tex]

=3

[tex]Y_{D} -Y_{B} =\frac{1}{3} \times 9[/tex]

=3

So D coordinates are (3, 0)

Hence, if AB is divided into three equal parts then coordinates of C is  (0, 3) and D coordinates are (3, 0)

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49 increased by twice a number m

Answers

Answer:

The third one I think

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

First -> twice m is -> 2m

Then

49 increased so -> 49+2m

Find the volume of the following cone. Use 3.14 for π.

Question 2 options:



9847.04 cubic meters


39388.16 cubic meters


10257.33 cubic meters


41029.33 cubic meters

Answers

Answer:

A. 9847.04 cubic meters

Step-by-step explanation:

Answer:

B; 39388.16 cubic meters

Step-by-step explanation:

I think the following information will make things clearer:

The formula for finding the volume of a cone is V = πr²h/3:

We can substitute our lengths to find out the volume.

[tex]28^{2} = 784\\48 \: \div \: 3 = 16\\16\: \cdot \: 784 \: \cdot \: 3.14\\= 39,388.16[/tex]

Thusly, the volume of the cone is [tex]\boxed{39,388.16}[/tex].

Hope this helps!! ((:

Write an equation of the line that passes through (-4,3) and (0,6).
An equation is y =

Answers

Answer:

y= ¾x +6

Step-by-step explanation:

The equation of a line is usually written in the form of y=mx+c, where m is the gradient and c is the y-intercept.

Let's find the gradient first.

[tex]gradient = \frac{y1 - y2}{x1 - x2} [/tex]

Using the formula above,

[tex]m = \frac{6 - 3}{0 - ( - 4)} \\ m = \frac{3}{4} [/tex]

subst. the value of m into the equation.

[tex]y = \frac{3}{4} x + c[/tex]

To find c, substitute a coordinate.

When x=0, y=6,

[tex]6 = \frac{3}{4} (0) + c \\ 6 = 0 + c \\ c = 6[/tex]

Thus, the equation of the line is [tex]y = \frac{3}{4} x + 6[/tex].

When 40% of a number is added to twice the number, the result is 88. What is the number?

Answers

17.6 because you do the working out backwards :)

Answer:

36.67 or 36 and 2/3

Step-by-step explanation:

.4x + 2x = 88 divide by .4

x + 5x = 220 add like terms

6x = 220 divide by 6

x = 36.67 or 36 and 2/3

Simplify (2a – 5)2 using the square of a binomial formula.
Question 20 options:

A)

4a2 – 20a + 25

B)

4a2 – 25

C)

4a2 – 10a + 25

D)

4a2 + 25

Answers

I’m not sure about the answer but I know it wouldn’t be D because it’s positive. I think it maybe B though. Hope this helps!

Answer:

B

Step-by-step explanation:

0-o

what is 1000 + 903 efwkfhawrjkarlvkjvheargjdvbejeqbgjvkdsfbwrilcjeabjesbwelvkjabvwelrgkjahfhfwahfsaldkjfasdjfhsakdflsadjfshadjkfsahsaduhfaewsfhiaowsadlkffhsdflksfahflksadfsalslkfdlahsfaweiofwahfesdfdsakfsak;falskhfdsadfojanefwuhrohafdhsd,fesuighfdsdhasfl;sfkdsdguegreffjsafakslfdsdfhfdsaklfawfieow

Answers

Answer:

1903

Step-by-step explanation:

Answer:

the answer is 1903

Step-by-step explanation:

What is the value of x ?

Answers

Answer:

720

Step-by-step explanation:

you just need to multiply

i think it’s 720 i’m pretty sure

100 POINTS NEEDED RIGHT NOW! On a graph plot the points where the following function crosses the x-axis and y-axis g(x) = -5^x+5

Answers

Answer:

see below

Step-by-step explanation:

X-AXIS

when a graph intersects the x-axis, the y value is always 0.  

Ex.  Points (1,0), (-5,0), (-3,0), (6,0), etc. are all on the x-axis because y = 0.  

to find where the graph crosses the x-axis, let y or g(x) = 0

0 = -5^x + 5  subtract 5 from both sides

-5 = -5^x       if x is 1, that would produce -5 = -5

(1,0) x axis

Y-AXIS

when a graph intersects the y-axis, the x value is always 0.

Ex.  Points (0, 1), (0, -2), (0, 3), etc. all lie on the y-axis because x = 0.

to find where teh graph crosses the y-axis, let x = 0

does the exponent "x" apply to (-5) or just 5?  

[tex]-5^{x} or (-5)^{x}[/tex]

(-5)^0 + 5    any number with a 0 power is 1

1 + 5 = 6

(0, 6)

or -5^0 + 5

       -1  +  5 = 4

(0, 4)

Answer:

The person above is correct. this is just confirmation

Step-by-step explanation:

True or false.
If the dilated image is larger than the pre-image, then the scale factor of the dilation is less than 1.

Answers

Answer:

False

Step-by-step explanation:

In order for the dilated image to become larger, it has to have a scale factor that is more than one not less than one.

False, Because If the scale factor is greater than 1, the image is larger than the preimage.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We know that;

If the scale factor is between 0 and 1, the image is smaller than the preimage. Dilations with a scale factor between 0 and 1 are called reductions.

And, If the scale factor is greater than 1, the image is larger than the preimage. Dilations with a scale factor greater than 1 are called enlargements.

Thus, The given statement is false.

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Provide the reflected ordered pair for each of the given ordered pairs. Reflect the ordered pair ( − 4 , 5 ) across the y-axis Reflect the ordered pair ( 0 , 3 ) across the x-axis

Answers

(-4, 5) changed to (4, 5)
(0, 3) changed to (0, -3)

Examine these points on line u and line v.
Line u: (9,-8), (5,4)
Line v: (4,2), (7.-7)
How many points of intersection are there between line
u and line v?
zero
one
two
infinitely many

Answers

Answer:There are zero interception.

Step-by-step explanation:

The equation to Line U: is  y=-3x +19  and the equation to line V  is  y=-3x +14

So as you can see ,the lines have the same slopes but different y-intercepts.This means the lines are going to be parallel when being graph.Parallel lines never cross or intersect so there  is no points of intersection.

Answer:

A. zero.

Step-by-step explanation:

i took the assignment.

What is the equation of the graphed line written in standard
form?
X-4y=4
X+4y=4
Y=1/4x-1
Y=-1/4x-1

Answers

Answer: Choice A)  x-4y = 4

Explanation:

Choices C and D are in slope intercept form, and not standard form, so we can rule them out. It's been choice A and choice B.

Solve for y in choice A, and you should get y = (1/4)x-1. The slope is 1/4. The positive slope tells us the line moves uphill as you move from left to right. In contrast, x+4y = 4 has a negative slope because it solves to y = (-1/4)x+1. Therefore, choice B can be eliminated.

To confirm that choice A is the correct answer, plug in each point and see if we get a true equation. Let's start with (0,-1)

Plug in (x,y) = (0,-1)

x-4y = 4

0-4(-1) = 4 ...  replace x with 0, replace y with -1

0+4 = 4

4 = 4 ... true equation, so the point (0,-1) works

Now try the other point

x-4y = 4

4-4(0) = 4 .... plug in (x,y) = (4,0)

4-0 = 4

4 = 4 ... works as well

Both points make the equation true, so they are both on the same line.

If function g(x) = x2 + 2 is a transformation of the quadratic parent function, f(x) = x2, where is the y-intercept of function g located?

A.
(0,-2)
B.
(2,0)
C.
(0,2)
D.
(-2,0)

Answers

Answer:

The y-intercept of function g located at (0,2)

Step-by-step explanation:

Function :[tex]g(x)=x^2+2[/tex]

g(x) is a transformation of the quadratic parent function

We are supposed to find the where is the y-intercept of function g located

y intercept = the y-coordinate of a point where a line, curve, or surface intersects the y-axis i.e. x =0

So, substitute x = 0 in function

g(x)=x^2+2

g(0)=0^2+2

g(0)=2

So,(x,y)=(0,2)

So, The y-intercept of function g located at (0,2)

Answer:

c

Step-by-step explanation:

What’s the answer
m 1 = 3x, m 2 = 4xº, m 3 = 2x, find x.

10
20
30
40

Answers

Answer:

x = 20

Step-by-step explanation:

assuming if this was a triangle

3x + 4x +2x = 180

9x = 180

180/9 = 20

Answer:

20

Step-by-step explanation:

You know that the angle measurements in a triangle add up to 180 degrees.

using the equation 3x+4x+2x= 180, you can find x

Simplify:

9x=180

x=20

Your answer is B) x = 20

Hope this helps!

How are the solution sets to s<3 and |s|<3 different ?

Answers

Answer:

The solution set for [tex]s<3[/tex] would be (-∞,3)

The solution set for [tex]|s|<3[/tex] would be (-3,3)

Step-by-step explanation:

The solution set for [tex]s<3[/tex] can be any number that is lower than 3.

When we have the inequality  [tex]|s|<3[/tex], we need to rewrite this without the absolute values to find our answer

[tex]|s|<3[/tex]

[tex]s<[/tex] ± [tex]3[/tex]

This can be be split into [tex]s<3, s<-3[/tex]

But, there one thing that needs to be done to the inequality with the-3. As we multiplied it by a -1 to make it negative, we must reverse the sign of the inequality. This leaves us with [tex]s<3, s>-3[/tex]

Now, we can combine these to get one inequality

[tex]-3<s<3[/tex]

Name three exponent rules

Answers

Three examples of exponent rules are;

Product of Powers Rule
Quotient of Powers Rule
Power of a Power Rule

Hope this helps!

Answer:

Quotient rules

Derivative rule

Negative exponents

hope this helps

Mr. Franco's records show that 44% of his students bring their own lunches to school. What is the percent and decimal of the students who DO NOT bring their own lunches.

Answers

Answer:

Percentage 56%

Decimal 0.56

Step-by-step explanation:

As percentages are out of 100, to work out the people who did not bring their own lunches you would simply minus the percentage of people that do which is 44 by 100, this gives you 56. this is because subtracting it from 100 we are removing the people that did from the total and so will leave us with the percentage of people that did not.

To work out the percentage who did not bring in their own lunches as a decimal you would divide the percentage of 56 by 100, this gives you 0.56. This is because percentages are out of 100%.

1) Minus 44 from 100.

[tex]100-44=56%[/tex]

2) Divide 56 by 100.

[tex]56/100=0.56[/tex]

The average age of people attending a concert was 23 years old, with a standard deviation of 7. What percentage of people at the concert were older than 37 years old?

Answers

Answer:

2.28%

Step-by-step explanation:

We have that the mean (m) equals 23 and that the standard deviation (sd) is 7.

We can calculate the value z and in this way we can calculate the probability in this case with the calculation of the normal distribution table:

z = m - x / sd

we know that x is 37, replacing:

z = (23 - 37) / 7

z = -2

according to the normal distribution table the value of z = -2, is equivalent to 0.0228

So the probability is 2.28%

HELP ME ASAP!!

Which of the following tables represents a function?


x 1 −1 4 −4
y 8 8 10 10

x 2 2 3 3
y 6 −6 7 7

x 5 −5 5 −5
y 10 11 12 13

x 2 2 7 7
y 2 3 4 5

Answers

Answer:

1)  x 1 −1 4 −4

   y 8 8 10 10

Step-by-step explanation:

x 1 −1 4 −4

y 8 8 10 10

When each input in set x has exactly one output in set y, the relation is a function.

ALL OF THESE ARE NOT FUNCTIONS !!!!!!!!!!

x 2 2 3 3         number 2 has 2 different outputs → not a function

y 6 −6 7 7

x 5 −5 5 −5     number 5 and -5 have 2 different outputs → not a function

y 10 11 12 13

x 2 2 7 7      2 and 7 have 2 different outputs → not a function

y 2 3 4 5

Answer:

A.   x 1 −1 4 −4

  y 8 8 10 10

Step-by-step explanation:

Choose the function to match the graph.

f(x) = log x + 2
f(x) = log x - 2
f(x) = log (x + 2)
f(x) = log (x - 2)

Answers

Answer:

C; f(x)=log(x+2)

Step-by-step explanation:

During the 1920's there was an overproduction of consumer goods. What happened to the price of goods when demand did not increase?

Prices Increased
Prices decreased
Prices Skyrocketed
Prices stayed the same

Answers

Answer:

Prices decreased

Step-by-step explanation:

What happened to the price of goods when demand did not increase is prices decreased.

For the given equation, find the values of a, b, and c, determine the direction in which the parabola opens, and determine the y-intercept. Decide which table best illustrates these values for the equation:
y = x squared + 7 x

Answers

Answer:

a=1, b= 7, c=0

Opens upward since a is positive(meaning it has a minimum vertex)

Y-int: (0,0)

Step-by-step explanation:

y=[tex]x^{2}[/tex]+7x

In order to find, the y-intercept, x has to be 0, so plug in 0 for x

y=[tex]0^{2}[/tex]+7(0)

y=0

So the y intercept: (0,0)

The equation form a parabola that opens up and the y intercept is at y = 0. a = 1, b = 7 and c = 0

What is a quadratic function?

A quadratic function is in the form:

y = ax² + bx + c

Given that:

y = x² + 7x, hence:

a = 1, b = 7 and c = 0

The equation form a parabola that opens up and the y intercept is at y = 0.

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14
Select the decimal that is equivalent to
40

Answers

Answer

40% = 0,4

Explantion

Divide 40 by 100

remove the 0s from both side

it will be

4 ÷ 10=

you go one step to the right and add a zero before the dot

which equal to

0.4

How many 1/4 pound
hamburgers can be made
from 2 1/2 pounds of ground
beef?

Answers

Answer:

9 hamburgers

Step-by-step explanation:

[tex]\frac{1}{4}[/tex] × 2 = [tex]\frac{1}{2}[/tex]

[tex]\frac{1}{2}[/tex] × 5 =[tex]2\frac{1}{2}[/tex]

[tex]\frac{1}{4}[/tex] × 9 =2 [tex]\frac{2}{4}[/tex]     2

,so 9 hamburgers can be made

We need to find the number of quarter pound hamburgers that can be made from given the amount of ground beef.

10 quarter pound hamburgers can be made.

The amount of ground beef available is [tex]2\dfrac{1}{2}[/tex] pounds.

One hamburger has a mass of [tex]\dfrac{1}{4}[/tex] pound.

[tex]1\ \text{hamburger}=\dfrac{1}{4}\ \text{pound of beef}[/tex]

[tex]\\\Rightarrow 1\ \text{pound of beef}=4\ \text{hamburgers}[/tex]

[tex]2\dfrac{1}{2}\ \text{pound of beef}=(2+\dfrac{1}{2})\times4=10\ \text{hamburgers}[/tex]

So, a total of 10 quarter pound hamburgers can be made.

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