Simplify the rational expression(picture and choices attached)! 15 points and will give Brainliest. Due soon.
Answers
Answer:
The answer should be:
[tex]=\frac{8x^3-18x}{3x+2}[/tex]
The closest answer is A, so I'll go with that.
Step-by-step explanation:
So we have the rational expression:
[tex]\frac{4x^3-9x}{2x-7}\div\frac{3x^2+2x^2}{4x^2-14x}[/tex]
First, remove the division sign. To do so, turn the division into multiplication and flip the second term:
[tex]\frac{4x^3-9x}{2x-7}\cdot \frac{4x^2-14x}{3x^2+2x}[/tex]
Now, simplify. From the first term, in the numerator, factor out a x. On the second term, factor out a 2x in the numerator and a x in the denominator:
[tex]\frac{x(4x^2-9)}{2x-7}\cdot\frac{2x(2x-7)}{x(3x+2)}[/tex]
Multiply straight across:
[tex]\frac{x(4x^2-9)(2x)(2x-7)}{(2x-7)(x)(3x+2)}[/tex]
Cancel out the (2x-7):
[tex]\frac{x(4x^2-9)(2x)}{x(3x+2)}[/tex]
Cancel out the x:
[tex]\frac{(2x)(4x^2-9)}{(3x+2)}[/tex]
At this point, we can factor the (4x^2-9) term, but we won't be able to cancel it out. Thus, this is the simplest it can get.
To get the answer, expand the numerator:
[tex]=\frac{8x^3-18x}{3x+2}[/tex]
Thus, the answer is...
A?
Answer:
The right solution is option a : [tex]\frac{8x^2 - 18}{3x+2}[/tex]
Step-by-step explanation:
We have to simplify the following rational expression,
[tex]\frac{4x^3-9x}{2x-7}[/tex] ÷ [tex]\frac{3x^3+2x^2}{4x^2-14x}[/tex]
Take into account the rule (a / b) / (c / d) = ad / bc. This simplifies the expression a bit further --- (1)
[tex]\left(4x^3-9x\right)\left(4x^2-14x\right)[/tex] ÷ [tex]\left(2x-7\right)\left(3x^3+2x^2\right)[/tex]
Let's now factor each individual expression as demonstrated below. Afterwards we can substitute back into the expression above --- (2)
Goal - Factor : (4x³ - 9x)(4x² - 14x),
4x³ - 9x ⇒ x(4x² - 9)
4x² - 14x ⇒ 2x(2x - 7)
[tex]x\left(4x^2-9\right)\cdot \:2x\left(2x-7\right) = 2x^2\left(4x^2-9\right)\left(2x-7\right)[/tex]
That leaves us with the following expression,
[tex]2x^2\left(4x^2-9\right)\left(2x-7\right)[/tex] ÷ [tex]\left(2x-7\right)\left(3x^3+2x^2\right)[/tex]
As you can see the " 2x - 7 " cancel out, and the " x² " cancel as well, leaving us with a further simplified expression,
[tex]2\left(4x^2-9\right)[/tex] ÷ [tex]3x+2[/tex]
Which can also be rewritten as [tex]8x^2 - 18[/tex] ÷ [tex]3x + 2[/tex] = [tex]\frac{8x^2 - 18}{3x+2}[/tex], in other words the first option.
Related Questions
in the adjoining figure, ABC is a right-angled triangle, where
B = 90°, AB = 3 cm and AC
3V2 cm, find the size of ®.
Answers
Answer:
the value of theta i 45°
For what value of a is a(2x+3)=9x+15+x an identity?
Answers
Answer:
Expand the left side, group like terms on both sides, and get
(2a)x + 3a = 10x + 15
To be true for all x, equate like terms from both sides and get
2a = 10
3a = 15
Solution: a = 5
You can test the answer.
Step-by-step explanation:
Expand the left side, group like terms on both sides, and get
(2a)x + 3a = 10x + 15
To be true for all x, equate like terms from both sides and get
2a = 10
3a = 15
Solution: a = 5
You can test the answer.
Find the coordinates of point A, if point M(-1, 2) is the midpoint of segment AB and B has coordinates of (3, -5) A. ( -5, 9) B. ( 1, -1 ) C. ( 4, 3) D. ( -2 , 4)
Answers
Answer:
A. (-5,9)
Step-by-step explanation:
hard to explain but i found the distance of M and B which is (4,7). using this i added that with M which equals (-5,9)
(sorry for bad explanation)
Which expression represents the measure of segment RS? A.7x – 3 B.7x + 5 C.x + 5 D.x – 3
Answers
Answer:
D) x-3
Step-by-step explanation:
(4x+1)-(3x-4)=
4x-3x+1-4=
x-3
what is 5/13 rounded to the nearest tenth
Answers
Answer:
5 thirteenth ti the nearest tenth Is .6
Answer:
0.4
Step-by-step explanation:
First make it a decimal:
5/13 (divide)
0.38 (round)
So you get 0.4
help me pls brainliest+10pts
Answers
Answer:
It is A
Step-by-step explanation:
It is A: it shows the total change in Akash's account because he paid the bill
In a bank statement the amount that you pay always shows negative it means the money withdraw from the account
solve the given equation: 2 x ( x + 3 ) − 6 ( x + 3 ) = 0 2 x ( x + 3 ) - 6 ( x + 3 ) = 0
Answers
Answer:
x = 3 or x = -3
Step-by-step explanation:
Solve for x over the real numbers:
2 x (x + 3) - 6 (x + 3) = 0
Expand out terms of the left hand side:
2 x^2 - 18 = 0
2 x^2 - 18 = 2 (x^2 - 9):
2 (x^2 - 9) = 0
Divide both sides by 2:
x^2 - 9 = 0
x = (0 ± sqrt(0^2 - 4 (-9)))/2 = ( ± sqrt(36))/2:
x = sqrt(36)/2 or x = (-sqrt(36))/2
sqrt(36) = sqrt(4×9) = sqrt(2^2×3^2) = 2×3 = 6:
x = 6/2 or x = (-6)/2
6/2 = 3:
x = 3 or x = (-6)/2
(-6)/2 = -3:
Answer: x = 3 or x = -3
Korey completely covered a square counter top using 103.5 ft² of tile without any overlap. Which measurement is closest to the side length of this counter top in feet? A. 10 ft B. 11 ft C. 27 ft D.55 ft
Answers
The measurement is closest to the side length of this counter top in feet is 10.17ft
Area of a squareThe formula for calculating the area of a square is expressed as:
area of a square = L^2
where
L is the length of a square
Given the following parameter
A = 103.5ft^2
Substitute
103.5ft^2 = L²
L = √103.5
L = 10.17ft
Hence the measurement is closest to the side length of this counter top in feet is 10.17ft
he measurement is closest to the side length of this counter top in feet is 10.17ft
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Christopher has breakfast at a cafe and the cost of his meal is $36.00dollar sign, 36, point, 00. Because of the service, he wants to leave a 10%, percent tip.
Answers
Answer: $39.60
Step-by-step explanation:
Here is the correct question:
Christopher has breakfast at a cafe and the cost of his meal is $36.00 . because of the service he wants to leave a 10% tip.What is his total bill including tip?
His total bill will be the addition of the cost of his meal and the tip. This will be:
= $36.00 + (10% × $36.00)
= $36.00 + $3.6
= $39.60
His total bill including tip is $39.60
Need to find x please.
Answers
Answer:
4 MIUSE 90 PLUSE 22
Step-by-step explanation:
Mia is making fruit punch for her birthday party. She puts 120 milliliters of cherry juice into a pitcher. Then she adds 250 milliliters of raspberry juice. She tops it off with sparkling water. How many milliliters of juice does she use?
Answers
Answer: She used 370 milliliters of juice
Step-by-step explanation:
Answer the two please 1. A monopoly playing board is in the shape of a square.The sides measure 19 inches. What is the area of the monopoly board? Use the golf scores below to answer quest 2 72,75,82 75,72,74 2. What is the median golf score? A.74.5 B.74 C.75.5 D.75
Answers
Use calculator to decide whether each statement is true or false. It may be that a true statement will lead to results that differ in the last decimal place due to rounding error.
tan² 72° 25' + 1 = sec² 72° 25'
Answers
Answer: 72.416
Step-by-step explanation:
help me with this please! I haven’t found the solution since 11:30 am
Answers
Answer:
PT = 22
Step-by-step explanation:
Given that T is the midpoint of PQ, then
PT = TQ , substitute values
5x + 2 = 7x - 6 ( subtract 5x from both sides )
2 = 2x - 6 ( add 6 to both sides )
8 = 2x ( divide both sides by 2 )
4 = x
Thus
PT = 5x + 2 = 5(4) + 2 = 20 + 2 = 22
Evaluate the expression for the given value of x.
−7x + 6 for x = −7
Answers
Answer:
[tex]\Huge \boxed{\mathrm{55}}[/tex]
Step-by-step explanation:
[tex]-7x + 6[/tex]
Put x as -7 and evaluate the expression.
[tex]-7(-7)+6 \\\\\\ 49+6 \\\\\\ 55[/tex]
Michael solved this inequality as shown: Step 1: -6(x + 3) + 10 < -2 Step 2: -6x − 18 + 10 < -2 Step 3: -6x − 8 < -2 Step 4: -6x < 6 Step 5: x > -1 What property justifies the work shown between step 3 and step 4? A. transitive property B. division property of inequality C. distribution property D. addition property of inequality
Answers
Answer:
D. addition property of inequalityStep-by-step explanation:
Given the step 3 and 4 of the solution Step 3: -6x − 8 < -2 Step 4: -6x < 6
From step 3;
-6x − 8 < -2
Michael got the step 4 by adding 8 to both sides of the inequality as shown;
-6x − 8 + 8 < -2 + 8
-6x < 6 (Step 4)
Since Michael added 8 to both sides of the inequality, the property that justifies the transition from step 3 to step 4 is the addition property of inequality. Addition property is the property that adds an integer to both sides of an inequality without altering the inequality sign and also retaining the inequality equation.
Express the formula d=rt in teens of the time, t use your formula to find the time the distance is 49 and the rate is 8.
Answers
Answer:
d=rt
rt=d
t= d/r
t= 40/8
t= 5
Please help, find what X is. 42 - X = 29
Answers
Answer:
X = 13
Step-by-step explanation:
42 - X = 29
Subtract 42 from each side
42-42 - X = 29-42
-X = -13
Multiply each side by -1
X = 13
Employees in 2012 paid 4.2% of their gross wages towards social security (FICA tax). How much will someone earning $43,047 a year pay towards social security?
Answers
Answer:
$1807.94
Step-by-step explanation:
Given that:
Annual income = $43047
Social security (FICA tax) = 4.2% of the gross wages
To find:
Social security paid = ?
Solution:
Social security (FICA tax) is calculated by finding the 4.2% of the Total Gross Annual income.
i.e. for the given value, the social security paid can be calculated as:
4.2% of $43047
[tex]\Rightarrow \dfrac{4.2}{100}\ of \ \$43047\\\Rightarrow \dfrac{42}{1000}\times 43047\\\Rightarrow 0.042\times 43047\\\Rightarrow \bold{\$1807.97}[/tex]
Therefore, the Social Security paid is $1807.94.
Answer those please
Answers
11.) 0.5.
12.) 0.25.
13.)1/2,0.49,55%.
14.)2/5,0.6,35%.
15.) To get a whole number from a fraction you have to multiply the fraction by the denominator of the fraction=5/9×9=5.
or you can say that can add 4/9 to 5/9=9/9=1 a whole number also
12. 0.25
that’s all i know
A map has a scale of 6 in. = 8 mi. If you measured the distance between two cities to be 25 in. On the map, how many miles would it actually be?
Answers
Answer:
33 2/6 miles
Step-by-step explanation:
So we know that every 6 inches equals 8 miles. To find one mile, we would divide both sides by 8, so every 6/8 of an inch is 1 mile. if the two cities are 25 in apart on a map, that means that we can first do 6*4:8*4 for the ease of it to get 24 inches and 32 miles. So so far it's already 32 miles. Then we have to calculate the leftover one inch. To find out how many miles one inch is, we can divide both sides by 6, so one inch=8/6 of a mile.
So then we add 32+8/6=33 2/6
Tell me if that works for you
which expression is equivalent to (-4^-5)^0
Answers
Answer:
can't see the options.
Step-by-step explanation:
Given directed line segment PR below, find the coordinates of Q on PR
such that the ratio of PQ to QR is 2:1.
Answers
Answer:
[tex](\frac{4}{3},-3)[/tex]
Step-by-step explanation:
The location of a point O(x, y) which divides line segment AB in the ratio a:b with point A at ([tex]x_1,y_1[/tex]) and B([tex]x_2,y_2[/tex]) is given by the formula:
[tex]x=\frac{a}{a+b}(x_2-x_1)+x_1\\ \\y=\frac{a}{a+b}(y_2-y_1)+y_1[/tex]
From the graph, the location of the point is P(2, 5), R(1, -7). Let point Q be (x, y) which divides PR in ratio 2:1. Coordinates of point Q is at:
[tex]x=\frac{a}{a+b}(x_2-x_1)+x_1=\frac{2}{2+1}(1-2)+2=\frac{2}{3}(-1)+2=\frac{4}{3} \\ \\y=\frac{a}{a+b}(y_2-y_1)+y_1=\frac{2}{2+1}(-7-5)+5= \frac{2}{3}(-12)+5=-3[/tex]
Point Q is at [tex](\frac{4}{3},-3)[/tex]
How many solutions does the equation −4a + 4a + 3 = 8 have?
Answers
Answer:
none
Step-by-step explanation:
Answer:
It does not have any solution because 3 is not equal to 8
A new top-selling DVD is marked 20% off at Discount DVD, where it normally sells for $29.90. The same disc sells for $28.60 at Value Video, where you have a coupon for 15% off anything in the store. Where would you buy the DVD? Explain how you decided and be sure to include work to support your answer.
Answers
Answer:
You would buy the DVD at Discount DVD.
Step-by-step explanation:
To decide where to buy the DVD, you have to determine the price at each store after the discount is applied.
-Discount DVD: $29.90*0.2=$5.98
$29.90-$5.98=$23.92
-Value Video: $28.60*0.15=$4.29
$28.60-$4.29=$24.31
According to this, you would buy the DVD at Discount DVD because it is where you will get the lower price.
Can a translation, a reflection, or a rotation of a figure ever result in an image with
a different size or shape? Explain.
Answers
Answer:
no, it will always be the same size and image just in a different placement.
Step-by-step explanation:
No, a translation, a reflection, or a rotation of a figure never results in an image with a different size or shape.
What is a translation?Each point in a figure is moved the same distance in the same direction using a type of transformation known as translation.
Each point in a figure is transformed into a rotation by rotating it a specific amount of degrees around another point.
Reflection is a type of transformation that flips a shape along a line of reflection, also known as a mirror line, such that each point is at the same distance from the mirror line as its mirrored point.
Hence, a translation, a reflection, or a rotation of a figure never results in an image with a different size or shape.
To know more about translation follow
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When I take half of my number and add two, I get twenty-four. What is my number?
Answers
Every natural number is an integer. True or false?
Answers
Answer:
yes every natural number is integer
because intezer is collection of positive and negative numbers....
Answer:
Step-by-step explanation:
Hello friend!!!
It's TRUE
Natural numbers are the range of numbers from 1 to infinite.
Integers are made up of positive as well as negative numbers.
Since natural numbers are positive numbers, they are also integers.
Hope this helps
plz mark as brainliest!!!!!
What's the only place in this world who's Fahrenheit and Celsius degrees can be equal?
Answers
Antarctica , I think
Step-by-step explanation:
perform the indicated operation. 2i(3-4i)+8(4-5i)(4+5i)
Answers
Answer: 336+6i
The key to solving this problem is to choose which parts you should solve first.
2i(3-4i)+8(4-5i)(4+5i)
let's divide this expression to three parts:
2i(3-4i), 8 and (4-5i)(4+5i)
first let's solve 2i(3-4i):
2i(3-4i) =
2i × 3 + 2i × -4i =
6i - 8i² =
6i + 8
(4-5i)(4+5i):
(4-5i)(4+5i) =
16 + 20i - 20i -25² =
16 + 25 =
41
8(4-5i)(4+5i):
8(4-5i)(4+5i) = 8 × 41 = 328
Now let's put back these parts:
2i(3-4i)+8(4-5i)(4+5i) =
6i + 8 + 328 =
6i +336 OR 336 +6i