Answer:
x=3
Step-by-step explanation:
log (x^2 - 1) - log (2x + 2) = 0
Add log (2x + 2) to each side
log (x^2 - 1) = log (2x + 2)
Since the logs with the same base are equal the x^2 -1 must equal 2x+2
x^2 -1 = 2x+2
Subtract 2x+2 from each side
x^2 -1 -2x-2 = 2x+2 -2x-2
x^2 -2x-3 = 0
Factor
What number multiplies to -3 and adds to -2
-3 *1 =-3
-3+1 =-2
(x-3) (x+1) =0
Using the zero product property
x-3 =0 x+1 =0
x=3 x=-1
Check to see if solutions are valid
x = -1
log ((-1)^2 - 1) - log (2*-1 + 2) = 0
log(0) - log 0 = 0
Log 0 is undefined x =-1 not a valid solution
x = 3
log ((3)^2 - 1) - log (2*3 + 2) = 0
log(8) - log 8 = 0
valid
What is the value of the expression 2 x 7 + 9 − 3 ÷ 3?
a 24
b 22
c 32
d 36
Answer:
22?
Step-by-step explanation:
just follow PEMDAS. first multiply then divide then add then subtract
The line passing through which two points is parallel to the line x - 2y = 16?
A) -6,-1 and 2,-5
B) -4,-6 and 2,-9
C) -5,7 and 0,-3
D) -1, 5 and 3,13
E) -4,7 and -2,8
Answer:
E) -4,7 and -2,8
Step-by-step explanation:
parallel lines have same slope
x - 2y = 16
y = 1/2 x -8 slope: 1/2
E. slope = Δy / Δx = (8-7) / (-2 - -4) = 1/2
Using the slope, it is found that the line passing through points (-4,7) and (-2,8), option E, is parallel to the given line.
----------------------
The equation of a line, in slope-intercept formula, is given by:
[tex]y = mx + b[/tex]
In which m is the slope.If two lines are parallel, they have the same slope.Given two points, the slope is given by change in y divided by change in x.----------------------
The line given is:
[tex]x - 2y = 16[/tex]
In slope-intercept formula:
[tex]2y = x - 16[/tex]
[tex]y = \frac{x}{2} - 8[/tex]
----------------------
In this question, we want a line with an slope of 1/2.
At option E, the points are (-4,7) and (-2,8), thus, the slope is:
[tex]m = \frac{8 - 7}{-2 - (-4)} = \frac{1}{-2 + 4} = \frac{1}{2}[/tex]
Thus, the line passing through points (-4,7) and (-2,8), option E, is parallel to the given line.
A similar problem is given at https://brainly.com/question/22532445
4) Which pair of triangles is congruent by Angle - Angle- Side
Answer:
2
Step-by-step explanation:
Two angles are congruent, and one side is congruent in the pair of triangles, option 2.
Answer:
2 should be the answer
Step-by-step explanation:
since two angles are equal and one side in equal you can write triangle ABC=TAY by angle angle side axiom
Which of these does NOT represent the number of minutes in a hour?
Answer:
the question is cut in half
Marshall Middle School is planning a field trip to see Romeo and Juliet at the local theater. The cost of a teacher ticket is $25 and the cost of a student ticket is $13. Write an expression to show the cost of t teacher tickets and s student tickets.
Answer:
25t + 13sStep-by-step explanation:
Teacher ticket = $25Student ticket = $13Expression to show the cost of t teacher tickets and s student tickets:
25t + 13sHarry catches the train from Belfast to Dublin at 4pm. The average speed of the train is 70 mph and the distance between Belfast and Dublin is 105 miles. What time does Harry arrive in Dublin?
Answer:
[tex]Arrival\ Time = 5:30\ pm[/tex]
Step-by-step explanation:
Given
[tex]Current\ Time = 4pm[/tex]
[tex]Speed = 70mph[/tex]
[tex]Distance = 105miles[/tex]
Required
Determine the arrival time
First, we calculate the time taken from Belfast to Dublin using:
[tex]Speed = \frac{Distance}{Time}[/tex]
Substitute values to the expression.
[tex]70 = \frac{105}{Time}[/tex]
Cross Multiply
[tex]70 * Time = 105[/tex]
[tex]Time = \frac{105}{70}[/tex]
[tex]Time = 1.5\ hour[/tex]
Arrival time is then calculated as:
[tex]Arrival\ Time = Current\ Time + Time\ Taken[/tex]
[tex]Arrival\ Time = 4pm + 1.5\ hour[/tex]
[tex]Arrival\ Time = 5:30\ pm[/tex]
Simplify
7⁸×7³×7⁴÷7⁹×7⁵
Answer:
7^53
Step-by-step explanation:
8x3=24
24x4=96
96/9=10.6
10.6x5=53
Answer:
7^11
Step-by-step explanation:
There is a rule for simplifying exponents: n^a + n^b = n^a+b.
The rule applies here too. 7 is the n and the exponents on top are a and b. Following the rule:
[tex] {7}^{8} \times {7}^{3} = {7}^{8 + 3} = {7}^{11} [/tex]
Then you continue this formula:
11+4-9+5 = 11
Since the end result is 11 the answer is
[tex] {7}^{11} [/tex]
The triangles below are congruent and their corresponding parts are marked.
Answer:
I think it's a but I'm not 100 percent sure but I'd say a
A man has a garden measuring 40m by 24m. He wants to divide it equally into the minimum number of square plots
Complete question :
A man has a garden measuring 40m by 24m. He wants to divide it equally into the minimum number of square plots. what is the length of each square plot?
Answer:
8 m
Step-by-step explanation:
Given that :
Dimension of garden = 40m by 24m
Length of garden = 40m
Width of garden = 24m
To Obtain the length of each square plot if the garden is divided into minimum number of square plots ; we take the highest common factor of the dimension:
Length (40) = 1, 2, 4, 5, 8, 10, 20, 40
Width (24) = 1, 2, 3, 4, 6, 8, 12, 24
The highest common factor here is 8 ;
Thus, the length of each square plot is 8m
Find the value of x in a triangle 68 27
What is the inverse of the function f(x) = one-ninth * x + 2?
Answer:
Please mark as brainliest!!!!
Step-by-step explanation:
https://brainly.com/question/1144043
Answer:
f⁻¹(x) = 9x - 18Step-by-step explanation:
Given
f(x) = 1/9x + 2Let the inverse be y= f⁻¹(x)
To find inverse change x ⇒ y and solve for y:
x = 1/9y + 29x = y + 18y = 9x - 18So the inverse is:
f⁻¹(x) = 9x - 18I need help thank you
Answer:
16n + 41
Step-by-step explanation:
2(-n - 3) - 7(5 + 2n) (Given)
-2n - 6 - 35 - 14n (Distribute)
-16n - 41 (Add like terms)
16n + 41 (Divide by a factor of -1)
Answer:
B. -16n - 41
Step-by-step explanation:
Use the distributive property:
2(-n - 3) - 7(5 + 2n)
-2n - 6 - 35 - 14n
Combine like terms:
(-2n - 14n) + (-6 - 35)
-16n - 41
1+y=-4/5x-2
Solve for Y
Step-by-step explanation:
y=-4/5x-2-1
y=-4/5x-3
y/4=5x-3
(y/4)-3 =5x
(y-12)/4=5x
The solution for y will be y = -4/5x-3
What is expression?Numbers, symbols and operators grouped together that show the value of something.
Given an expression, 1+y=-4/5x-2
Solving for y, we get
1+y=-4/5x-2
y = -4/5x-2-1
y = -4/5x-3
Hence, The solution for y will be y = -4/5x-3
For more references on expression, click;
https://brainly.com/question/14083225
#SPJ2
A student says that the sum difference, product and quotient of two
are always integers. Do you agree? Explain
Answer:
The quotient of two integers may not always be an integer.
Therefore, I do not agree when a student says that the sum difference, product, and quotient of two are always integers.
Step-by-step explanation:
The student is not largely correct!
The sum, difference, and product of two integers is indeed always an integer.
But, the quotient of two integers may not always be an integer.
For example, the quotient of integers 4 and 2 will be an integer.i.e.
4/2 = 2
But, if we take the quotient of 2 and 3, the result will not be an integer.i.e.
2/3 = 0.67
Therefore, I do not agree when a student says that the sum difference, product, and quotient of two are always integers.
find cos b in the triangle
A 5/12
b 12/13
c12/5
d 5/13
Answer:
D
Step-by-step explanation:
cos β
= Adjacent / Hypotenuse
= 5/ 13
Answer:
5/13
Step-by-step explanation:
Halle has $48 saved for a new computer. Then she receives birthday money giving her a total of $290 saved. How much birthday money did she receive?
3. As a fundraiser the school has a pie eating contest. Matt eats 2.75 pies in 300 seconds. b. Use place value, multiplication with powers of 10, or equivalent fractions to explain what is happening mathematically to the decimal points in the divisor and dividend before dividing.
Answer:
Using equivalent fractions, the time Matt takes to eat 1 pie is 1200/11 which is the same as [tex]109\frac{1}{11}[/tex] seconds
Step-by-step explanation:
The number of pies Matt eats = 2.75 pies
The time duration Matt eats 2.75 pies = 300 seconds
Mathematically, the time duration for Matt to eat one pie is given as follows;
The time to eat 2.75 pies = 300 seconds
Dividing both sides of the equation by 2.75 gives;
The time to eat 2.75/2.75 pie = 300/2.75 seconds
2.75/2.75 = 1, therefore, we have;
The time to eat 1 pie = 300/2.75 seconds
The equivalent fraction of 3000/2.75 = 1200/11
Therefore;
The time Matt takes to eat 1 pie = 1200/11 seconds
Find the measure of angle x. _
[tex]x + 120 = 180[/tex]
(linear pair of angles)
[tex]x = 180 - 120[/tex]
[tex]x = 60[/tex]
The mk family ochard has 120 apple trees and 90 pear trees.if each fruit tree produces an average of 590 pounds of fruit per year, about how many pounds of fruit can the ochard produce in one year
If the gas station is selling 5 bottles of water for $10, what is the unit price of each bottle of water?
Answer:
2
Step-by-step explanation:
5 bottles = 10 dollars
divide by 5 to get 1 bottle
now divide 10 by 5 that will be 2
2$ for 1 bottle
Ted weighs twice as much as Julie Mike was three times as much as Julie together Ted Mike and Julie weigh 210 lb what is the weight of each person
Answer: Ted weighs 70 Julie weighs 35 mike weighs 105
Step-by-step explanation:
I looked it up ;-)
6. How many sides has a regular poly- gon when each interior angle is 108°? 144°? 120°? 150°? 140°? 90°? 12870?
Answer:
there are 'n' sides of the regular polygon. Thus, the measure of the angle of the quad, are 36°, 12°, 108° and 144°. Thus, the required number of sides of the regular polygon is 5.
Step-by-step explanation:
This graph shows the amount of charge left on my
computer, c, after I have been awake for h hours.
Enter an equation that
describes the relationship
between c and h.
Submit
Answer:
c= -20h + 90
Step-by-step explanation:
The equation that describes the relationship between c and h is:
[tex]c= -20h + 90[/tex]
We have the graph that shows the amount of charge left on computer, c, after h hours.
Let us consider two points (h, c) on the graph
(0,90) and (4.5, 0)
Now the equation of the line passing through two points
[tex]\frac{c-90}{h-0} =\frac{0-90}{4.5-0} \\c-90=-20h\\c=-20h+90[/tex]
So, the equation that describes the relationship between c and h is:
[tex]c= -20h + 90[/tex]
Learn more:https://brainly.com/question/16934180
which one is it???? .
Answer:
option A, I guess .....
.
There are 42 boys in the sixth grade. The number of girls in the sixth grade is 35. Lonnie says that
means the ratio of the number of boys in the sixth grade to the number of girls in the sixth grade is
16:5.
Is Lonnie correct? Show why or why not.
Answer:
Lonnie is incorrect because the ratio is 6:5 and not 16:5.
Step-by-step explanation:
First, create a ratio comparing the number of boys to girls:
42:35
This can be simplified since both numbers are divisible by 7:
42:35
Divide each number by 7:
6:5
So, Lonnie is incorrect because the ratio is 6:5 and not 16:5.
Answer:
incorrect i think
Step-by-step explanation:
the ration would be 6:5
What is the average rate of change of f over the interval -1
on a separate sheet of paper and upload the work as a photo. Show all
appropriate work necessary for full credit.
f(x)=
x² - x - 1
Answer:
Average rate of change for the function [tex]f(x)= x^2-x-1[/tex] over the interval -1<x<1 is -1
Step-by-step explanation:
We need to find average rate of change of f over the interval -1 < x < 1
The function given is: [tex]f(x)= x^2-x-1[/tex]
The formula used to find average rate of change is:
[tex]Average\:rate\:of\:change=\frac{f(b)-f(a)}{b-a}[/tex]
We have, a = -1 and b = 1
Finding f(b) when b=1
[tex]f(x)=x^2-x-1\\f(1)=(1)^2-(1)-1\\f(1)=1-1-1\\f(1)=-1[/tex]
Now, finding f(a), when a= -1
[tex]f(x)=x^2-x-1\\f(-1)=(-1)^2-(-1)-1\\f(1)=1+1-1\\f(-1)=2-1\\f(-1)=1[/tex]
Now, putting values and finding average rate of change
[tex]Average\:rate\:of\:change=\frac{f(b)-f(a)}{b-a}\\Average\:rate\:of\:change=\frac{f(1)-f(-1)}{1-(-1)}\\Average\:rate\:of\:change=\frac{-1-(1)}{1-(-1)}\\Average\:rate\:of\:change=\frac{-1-1}{1+1}\\Average\:rate\:of\:change=\frac{-2}{2}\\Average\:rate\:of\:change=-1[/tex]
So, average rate of change for the function [tex]f(x)= x^2-x-1[/tex] over the interval -1<x<1 is -1
Approximately 10% of the population is left-
handed. If a school had a student population
of 1200 students, how many of them could
you expect to be right-handed?
Answer:
1080
Step-by-step explanation:
if 10 percent are left handed that means that 90 percent are right handed
number of people that are right handed = 0.9 × 1200number of people that are right handed = 1080Answer:
120
Step-by-step explanation:
10%=0.1
1200*0.1=120
18% is what number of 63?
Answer:
[tex] 18 \%\: of \: x = 63 \\ \frac{18}{100} x = 63 \\ x = \frac{63 \times 100}{18} \\ x = 350[/tex]
350 is the right answer.Answer:
350
Step-by-step explanation:
To figure out the number, divide 63 by 18%
63/0.18 = 350
You can check by doing the opposite operation with your answer:
350 · 0.18 = 63
55.57
What is the equation of the line that is parallel to the
given line and passes through the point (12, -2)?
Oy=-x +10
Oy=-x + 12
Oy=-x- 10
Oy=x - 12
Answer:10
Step-by-step explanation:and a slope 2/12 roof slope means your roof has 2 inches of vertical drop for every 12 inches of horizontal distance.Aug
The equation of the line that is parallel to the given line and passes through the point (12, -2) is y = 5/6(x)-12
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
The slope of line passing through the points (12, 6) and (0, -4)
Slope = -4-6/0-12
=-10/-12
=5/6
Now let us find y intercept passing through (12, -2)
-2=5/6(12)+b
-2=10+b
-12=b
Hence, the equation of the line that is parallel to the given line and passes through the point (12, -2) is y = 5/6(x)-12
To learn more on slope of line click:
https://brainly.com/question/16180119
#SPJ7
Natalie went skydiving. She jumped out of the plane at 3,080 feet above the ground. At 1,710 feet above the ground her parachute deployed, and instead of continuing to fall, she rose 35 feet. At this point, how far is she from the plane? Explain how you found your answer. PLEASEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE HELP