Answers
Answer:
Question 4
Simplifying the expression [tex]\frac{x^2-10x-24}{x^2-3x-108}[/tex] we get [tex]\frac{x-2}{x-9}[/tex] and x≠9 or x≠2
Option D is correct option.
Question 5
Simplifying the expression: [tex]\frac{8x-16}{x^2-13x+22}[/tex] we get [tex]\frac{8}{x-11}, x\neq 11[/tex]
Option C is correct.
Step-by-step explanation:
Question 4
Simplify completely [tex]\frac{x^2-10x-24}{x^2-3x-108}[/tex]
For simplifying the above expression we have to find find factors of numerators and denominators
First finding factors of numerator [tex]x^2-10x-24[/tex]
[tex]x^2-10x-24\\ = x^2-12x+2x-24 \\= x(x-12)+2(x-12) \\=(x-12)(x-2)[/tex]
So, the factors of [tex]x^2-10x-24[/tex] are [tex](x-12)(x-2)[/tex]
Now finding factors of denominator [tex]x^2-3x-108[/tex]
[tex]x^2-3x-108\\=x^2-12x+9x-108\\=x(x-12)+9(x-12)\\=(x+9)(x-12)[/tex]
So, factors of [tex]x^2-3x-108 are (x-12)(x+9)[/tex]
Now, replacing numerators and denominators with their factors
[tex]\frac{x^2-10x-24}{x^2-3x-108}\\=\frac{(x-12)(x-2)}{(x+9)(x-12)}\\Cancelling\:(x-12) \: from\:numerator\:and\:denominator\\=\frac{x-2}{x-9}[/tex]
so, simplifying the expression [tex]\frac{x^2-10x-24}{x^2-3x-108}[/tex] we get [tex]\frac{x-2}{x-9}[/tex] and x≠9 or x≠2
Option D is correct option.
Question No 5
Simplify the expression: [tex]\frac{8x-16}{x^2-13x+22}[/tex]
For simplifying the above expression we have to find find factors of numerators and denominators
First finding factors of numerator [tex]8x-16[/tex]
Taking 8 common:
[tex]8x-16\\=8(x-2)[/tex]
So, factors of [tex]8x-16[/tex] are [tex]8(x-2)[/tex]
Now finding factors of denominator : [tex]x^2-13x+22[/tex]
[tex]x^2-13x+22\\=x^2-11x-2x+22\\=x(x-11)-2(x-11)\\=(x-2)(x-11)[/tex]
Now, replacing numerators and denominators with their factors
[tex]\frac{8x-16}{x^2-13x+22}\\=\frac{8(x-2)}{(x-11)(x-2)}\\Cancelling\:(x-2)\\=\frac{8}{x-11}, x\neq 11[/tex]
So, simplifying the expression: [tex]\frac{8x-16}{x^2-13x+22}[/tex] we get [tex]\frac{8}{x-11}, x\neq 11[/tex]
Option C is correct.
Related Questions
Laurissa rolls two number cubes each with the numbers 1 through 6. Laurissa adds the numbers that appear on the roll. Which two sums have an equal chance of occuring?
Answers
Answer:
5 and 11
Step-by-step explanation:
find the slope of the line passing through the given points
Answers
Answer:
-5/6
Step-by-step explanation:
Slope= y2-y1/x2-x1
Answer:
The slope is -5/6
Step-by-step explanation:
You can use the method rise over run and count how many squares it takes to go from the y coordinate 4 to the y coordinate -1, which is -5. You can then count how many squares you need to get from the point -3 to 3 which is 6. Or you can use the formula to find slope, (y2-y1)/(x2-x1) and plug in you numbers.
there are two food trucks for sale that would be perfect for your business. the blue food truck is in perfect condition, but 8,000 more than the green food truck. The green food truck is in need of repairs to make it fully functional. The two trucks together cost 172,000. How much does each food truck cost
Answers
Answer:
blue truck-$82000 green truck-$90000
Step-by-step explanation:
x+8000=y
x+y=172000
I need help with geometry
Answers
Answer:
Segment QR is the shortest
Answer:
qr
Step-by-step explanation:
is a stockbroker. Earns % commission each week. Last week, sold $ worth of stocks. How much did make last week in commission? If averages that same amount each week, how much did make in commission in 2011?
Answers
Answer:
a. $583
b. $30,316
Step-by-step explanation:
a. Commission last week;
= 5,300 * 11%
= $583
b. Commission in 2011 assuming weekly earnings of $583.
= 583 * 52 weeks
= $30,316
Which mixed number is equivalent to the improper fraction?
23/8
A. 2 1/8
B. 2 7/8
C. 3 1/8
D. 3 7/8
Answers
Answer:
B: 2 7/8
Step-by-step explanation:
Explanation: In my opinion I’m guessing B is the answer bc that’s will be the only mixed number equivalent too the improper fraction.
SOMEONE HELPPPPPP Meeee pleaseeeee
Answers
Answer:
yes they are.
Step-by-step explanation:
if you were to divide the numbers in the first triangle by 2.5 you would get the numbers of the other triangles and vice versa for the other triangle
Meghan ran 9/12 of a mile and skipped 8/12 of a mile how far around the track did meghan go in total. Use the benchmark fraction 1/2, 1, and 0 to help you estimate each answer before you solve
Answers
Answer:
Megan went a total distance of 1 5/12 miles
Step-by-step explanation:
Here, we want to calculate the total distance worked around the track
We are told that she ran 9/12 and skipped 8/12
The total distance around the track will be the sum of these two
Mathematically, that will be;
9/12 + 8/12
= 17/12 = 1 5/12
1. In 24. 68, the digit
is in the hundredths place.
2. In 2.942, the digit is in the thousandths place.
3. In 45.3165, the digit 1 is in the
place
4. In 22.5608, the digit 8 is in the
place.
5. In 821.9034, the digit 3 is in the
place.
Exercise 3: Write the place value and value of number 8. Fi
Place Value
Example:
99.3428
Ten Thousandths
0
1) 12.5928
2.) 43.7891
3.) 15.8931
4.) 23.9684
Answers
Answer:
wha gh filled out of my friends house to myself I don't want you so very true but I'm going back and
The probability of rolling a 6 on a number cube is 1/6. What is the complement of rolling a 6
Answers
Answer:
5/6
Step-by-step explanation:
The complement of rolling 6 will be all the possible outcomes except rolling 6 which is 5/6
I need help with this, I CANNOT get this wrong.
Answers
Answer:
Transitive
Step-by-step explanation:
If A = B and B = C then A = C
Transitive
Solve for y
8y - 8 = 4x
Answers
Answer:y= 1/2x +1
Step-by-step explanation: This is your answer
Answer:
Step-by-step explanation:
8y - 8 = 4x
Add 8 to both sides
8y = 4x + 8
Divide both sides by 8
y = [tex]\frac{4x + 8}{8}[/tex]
(16x^2 + 27x)/ 6x
Is this in the simplest form?
Answers
[tex] \frac{16 {x}^{2} + 27x}{6x} [/tex]
[tex] \frac{ {16x}^{2} }{6x} + \frac{27x}{6x} [/tex]
[tex] \frac{16x}{6} + \frac{27}{6} [/tex]
[tex] \frac{16x + 27}{6} [/tex]
find the third proportion to 8 and 12
Answers
Answer:
let the third proportion be x.
then 8,12 and x are in proportion
then 8:12=12:x
8x=12×12
x=144/8=18
Step-by-step explanation:
i need severe help Plz
Answers
Answer:
-12
Step-by-step explanation:
Mark as Brainliest.
Because I am Indian and solving your question from India.
Solve the following equation for y
24x - 8y = 72
I need help right now as fast as u can
Answers
Answer:
Step-by-step explanation:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
24*x-8*y-(72)=0
STEP
1
:
Pulling out like terms
1.1 Pull out like factors :
24x - 8y - 72 = 8 • (3x - y - 9)
Equation at the end of step
1
:
STEP
2
:
Equations which are never true:
2.1 Solve : 8 = 0
This equation has no solution.
A a non-zero constant never equals zero.
Equation of a Straight Line
2.2 Solve 3x-y-9 = 0
Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).
"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.
In this formula :
y tells us how far up the line goes
x tells us how far along
m is the Slope or Gradient i.e. how steep the line is
b is the Y-intercept i.e. where the line crosses the Y axis
The X and Y intercepts and the Slope are called the line properties. We shall now graph the line 3x-y-9 = 0 and calculate its properties
Graph of a Straight Line :
Calculate the Y-Intercept :
Notice that when x = 0 the value of y is 9/-1 so this line "cuts" the y axis at y=-9.00000
y-intercept = 9/-1 = -9.00000
Calculate the X-Intercept :
When y = 0 the value of x is 3/1 Our line therefore "cuts" the x axis at x= 3.00000
x-intercept = 9/3 = 3
Calculate the Slope :
Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is -9.000 and for x=2.000, the value of y is -3.000. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of -3.000 - (-9.000) = 6.000 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)
Slope = 3
Geometric figure: Straight Line
Slope = 3
x-intercept = 9/3 = 3
y-intercept = 9/-1 = -9.00000
What value of a is a solution to this equation?
1=3+a
4
Answers
Answer:
1=a4+3
Step 1: Subtract a^4+3 from both sides.
1−(a4+3)=a4+3−(a4+3)
−a4−2=0
Step 2: Add 2 to both sides.
−a4−2+2=0+2
−a4=2
Step 3: Divide both sides by -1.
−a4
−1
=
2
−1
a4=−2
Step 4: Take root.
a=±(−2)(
1
4
)
Answer:
No real solutions.
The graphs below have the same shape. What is the equation of the blue
graph?
A. g(x) = (x+4)^2
b. g(x) = x^2-4
c. g(x) = x^2+4
d. g(x) = (x-4)^2
Answers
It has a horizontal shift of 4 to the right
(D) [tex]g(x)=(x-4)^{2}[/tex]
Graphs:The set of ordered pairings (display style [tex](x,y)[/tex]) of a function (display style [tex]f(x)=y[/tex]) in mathematics is known as the graph of that function. These pairs are Cartesian coordinates of points in two-dimensional space and so constitute a subset of this plane in the typical case where "display style [tex]x[/tex]" and "display style [tex]f(x)[/tex]" are real values.Graph equations:Equations with graphs as the unknowns are known as graph equations in graph theory. The concept of isomorphism is one of the key issues in graph theory. Different graph equations may be used to express the aforementioned graphs.Therefore, the correct equation for the blue graph is [tex]g(x)=(x-4)^{2}[/tex].
Know more about the Graphs here:
https://brainly.com/question/4025726
#SPJ2
The following equation has two different solutions. Solve the equation and place one solution in each answer box. The LARGER answer goes in Box1. The SMALLER solution should go in Box2. Solve for x : x 2 + 11 x + 18 = 0
Answers
Answer:
would that be 31 if if im wrong im just nine Step-by-step explanation:
Alex stayed up 20 a week How many hours did Alex stay up in 12 weeks?
Answers
Answer:
240 hours
Step-by-step explanation:
1 week = 20 hours
12 weeks = 20 × 12
= 240 hours
I mark brainliest! please help!
which graph shows all the values that satisfy 2/9x+ 3> 4 5/9
Answers
Answer:
The first option
Step-by-step explanation:
2/9 x + 3 > 4 5/9
2/9x > 4 5/9 - 3
2/9x > 14/9
x > 14/9 ÷ 2/9
x > 7
If you had a choice between investing $1,000 in a mutual fund that are 7.5% compound interest or a bond that earns simple interest at 7.5% which would you prefer and why
Answers
Answer:
mutual fund
Step-by-step explanation:
Step one:
given data
let say the investment plan will span for 5 years
so for mutual fund
P= $1000
r= 7.5%= 0.075
t= 5
compound interest
A= P(1+r)^t
substituting
[tex]A= 1000(1+0.075)^5\\\\A=1000(1.075)^5\\\\A=1000*1.436\\\\A=$1436\\\\[/tex]
$1436
so for bond
P= $1000
r= 7.5%= 0.075
t= 5
simple interest
A= P(1+rt)
substituting
[tex]A= 1000(1+0.075*5)\\\\A=1000(1+0.375)\\\\A=1000(1.375)\\\\A=1375\\\\[/tex]
A=$1375
$1375
I would go for mutual fund compounded interest because it offers extra
$61 (1436-1375) for the same investment capital
Mr.Chang has a class of 18 students. He can spend $21 on each student to buy math supplies for the year. He first buys all of his students calculators, which cost a total of 170.64. After buying the calculators, how much does he have left to spend on each student
Answers
Answer:
572557486637778886367828766664728274747447378328288273
Answer: $11.52 left for each student
Step-by-step explanation:
First, divide the total amount of money spent by the total amount of students. 170.64/18. You will get $9.48. So, that means that so far Mr. Chang has spent $9.48 on each student. Then, just subtract $9.48 from $21 (which is the total amount he is willing to spend on each student. You should get $11.52. So, Mr. Chang has $11.52 left to spend on each student. Hope this helps!
A cell phone plan charges $39.95 a month plus 15 cents per text message sent and 15 cents per text message received. Using s to represent the number of text messages sent in one month and r to represent the number of text messages received in one month, the following equation can be used to calculate the total monthly cost, c:
c = 39.95 + 0.15(s + r)
If it is known that the total monthly cost is $53.45 and 63 text messages were received, solve for s, the total number of text messages sent.
Answers
Answer:
c= 39.95 +0.15 (s + r) (take the 63 received and plug it in for r and 53.45 in for c then solve)
53.45= 39.95 +0.15 (s +63) (use the distributive property)
53.45 = 39.95 + 0.15s + 9.45 (combine like terms on the right side)
53.45 = 49.40 +0.15s (subtract 49.40 from both sides)
4.05 = 0.15s (divide both sides by 0.15 so isolate s)
s= 27 (how many text messages were sent)
Step-by-step explanation:
I hope this helps :)
Answer:
s=27
Step-by-step explanation:
Leslie used 25% of a half-gallon of milk for a recipe. How many ounces of milk were left?
Answers
Answer:
One moment...I'm figuring it out...the answer is 48 ounces.
Step-by-step explanation:
How is the number in the square root called (number 4) how can I place that in a calculator
Answers
The 4 in the symbol is the index of the radical sign √.
Whether you can write this expression on a calculator depends on the calculator... If you have one with a CAS (that is, a "computer algebraic system"), chances are there is a built-in button for things like square roots and cube roots, and possibly roots of higher indices. If not, you can always express a radical expression using a fractional exponent, such as
[tex]\sqrt x\iff x^{\frac12}[/tex]
or
[tex]\sqrt[3]{x}\iff x^{\frac13}[/tex]
or
[tex]\sqrt[4]{x}\iff x^{\frac14}[/tex]
and so on. So the given expression could be typed in as (16*x^6*y^7)^(1/4), for instance.
I'm guessing you have to simplify the given expression. You could end up with
∜(16x ⁶y ⁷) = ∜(2⁴ x ⁴ x ² y ⁴ y ³)
… = 2xy ∜(x ² y ³)
(assuming x and y are positive)
height up to 46 decimeter convert it's height in meters
Answers
Answer:
6.5m
Step-by-step explanation:
65/10 = 6.5m
hope u can understand...
Answer:
4.6 meter
Step-by-step explanation:
you can convert decimeter to meter by dividing 10
Look at the photo
Show your work
FIRST TO ANSWER CORRECTLY GETS 22 POINTS AND BRAINIEST
Answers
Answer:
We can't even see the whole questions so how do you expect us to awnser it when we can't even see the full questions
be the first to answer and u will get a brainlliest
Answers
Answer:
Step-by-step explanation:
go on mathify and ask
hurrryyyyy please :))
Answers
Answer:32
Step-by-step explanation:
Answer:
32, Trust me mate, Its 32