Multiply the rational expressions and express the product in simplest form. When typing your answer for the numerator and denominator be sure to type the term with the variable first.\frac{\left(2x^2+9x-35\right)}{\left(x^2+10x+21\right)}\cdot \frac{\left(3x^2+2x-21\right)}{\left(3x^2+14x-49\right)}The numerator is AnswerThe denominator is Answer
Answers
Given:
The expression is,
[tex]\frac{(2x^2+9x-35)}{(x^2+10x+21)}\times\frac{(3x^2+2x-21)}{(3x^2+14x-49)}[/tex]Simplify the expression,
[tex]\begin{gathered} \frac{(2x^2+9x-35)}{(x^2+10x+21)}\times\frac{(3x^2+2x-21)}{(3x^2+14x-49)} \\ =\frac{2x^2-5x+14x-35}{x^2+3x+7x+21}\times\frac{3x^2-7x+9x-21}{3x^2-7x+21x-49} \\ =\frac{x(2x^{}-5)+7(2x-5)}{x(x^{}+3)+7(x+3)}\times\frac{x(3x^{}-7)+3(3x-7)}{x(3x^{}-7)+7(3x-7)} \\ =\frac{(2x-5)(x+7)}{(x+3)(x+7)}\times\frac{(3x-7)(x+3)}{(3x-7)(x+7)} \\ \text{Cancel the common factor } \\ =\frac{2x-5}{x+3}\times\frac{x+3}{x+7} \\ =\frac{2x-5}{x+7} \end{gathered}[/tex]Answer:
Numerator is 2x - 5.
Denominator is x + 7.
Related Questions
Could please get help with this math. I need help weather each of the triangles can be the HL congruence property?
Answers
In order to use the HL congruence property, the triangles must have the hypotenuses and one pair of corresponding legs with the same length.
(a)
These are right triangles and have only one pair of legs with the same length, therefore the answer is NO.
(b)
These right triangles have one pair of legs with the same length and a common hypotenuse, therefore the answer is YES.
(c)
These triangles are not right triangles, therefore the answer is NO.
(d)
These right triangles have one pair of legs with the same length and the hypotenuses also have the same length, therefore the answer is YES.
If the population of Alaska in 2000 was
622,000 and 733,000 in 2020, assuming
exponential growth, what would the
population be in 2050?
[?] people
Answers
Using mathematical operations, the population of Alaska in 2050 will be 8,99,500.
What are mathematical operations?An operation is a function in mathematics that transforms zero or more input values into a clearly defined output value. The operation's arity is determined by the number of operands.A mathematical action is called an operation. Mathematical operations include addition, subtraction, multiplication, division, and finding the root.So, the population in 2050:
Population increases from 2000 to 2020:733,000 - 622,000 = 1,11,000Population change in 20 years = 1,11,000In 10 years = 1,11,000/2 = 55,500So, poulation in 5050:
2020 (20 years) ⇒ 2040 (00 years) ⇒2050= 733,000 + 1,11,000 + 55,500= 8,99,500Therefore, using mathematical operations, the population of Alaska in 2050 will be 8,99,500.
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Answer: 937,723
Step-by-step explanation:
F(x) = x^2 -4x + 6
Find the value of f( - 4)
Write the answer as an integer or a decimal number.
Answers
Answer:
38
Step-by-step explanation:
[tex]f(-4)=(-4)^2-4(-4)+6 \\ \\ =16+16+6 \\ \\ =38[/tex]
f(-4) = (-4)^2 -4(-4) +6
f(-4 = 16+16+6
f(-4) = 38)
An ion has a charge of +7. How far is it from being neutral? a. -0.07b. -7c. 7d. 70e. 0.7
Answers
If the ion has a charge of +7, in irder to get to neutral (charge zero), one needs to subtract 7 charges from it. Therefore it is -7 far from being neutral.
Then the correct answer is option "b" in the list.
Question 36 of 50
Which of the following choices is the correct range for the function h(x) = -3x2 if the domain is (0, -2, 1)?
(0, -6, -3)
(0, -12, 3)
None of these choices are correct.
(0, 6, -3)
(0, 12, 3)
Answers
The range of the function, h(x) = - 3x² with domain of (0, -2, 1) are (0, -12, -3). Therefore, non of the options is correct.
How to find range of a function?The domain of a function is the set of all possible inputs for the function.
In other words, the domain of a function are the independent values of the function.
Domain are usually represented by the x value.
The range of a function refers to all the possible values y could be.
Therefore, the function is as follows:
h(x) = - 3x²
Therefore, the domain are (0, -2, 1).
The range that represents the domain can be computed as follows:
h(0) = - 3(0)² = 0
h(-2) = - 3(-2)² = -12
h(1) = - 3(1)² = -3
Therefore, non of the choices are correct. The range of those domain are (0, -12, -3)
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Solve for x 5(x - 3) = -11
Answers
In order to solve this equation for x, the first step is using the distributive property of multiplication:
[tex]a(b+c)=a\cdot b+a\cdot c[/tex]So, solving the equation for x, we have:
[tex]\begin{gathered} 1.\text{ Distributive property on the left side:}\\ \\ 5x-5\cdot3=-11\\ \\ 5x-15=-11\\ \\ 2.\text{ Add 15 to both sides:}\\ \\ 5x-15+15=-11+15\\ \\ 5x=4\\ \\ 3.\text{ Divide both sides by 5:}\\ \\ \frac{5x}{5}=\frac{4}{5}\\ \\ x=\frac{4}{5} \end{gathered}[/tex]Therefore the solution is x = 4/5 or x = 0.8.
Check whether the sequence is arithmetic. If so, find the common difference d.
1, 10, 19, 28,37
Answers
Answer: 9
Step-by-step explanation: 1+9 =10
10+9=19
19+9=28
28+9=37
What should the side length be, to the nearest hundredth, for each petit four?
Answers
Cube is a 3D closed structure in which each adjacent side is perpendicular to each other and every side is equal to each other. Let the side of cube be 's'cm.
The formula for the Volume(V) of a cube is,
[tex]V=s^3[/tex]Given
[tex]V=67cm^3[/tex]Therefore,
[tex]67=s^3[/tex]Evaluate for s
[tex]\therefore s=\sqrt[3]{67}=4.06154\approx4.06cm[/tex]Hence, the value for the side length of each petit four is 4.06cm.
Answer:
4.06 cm
Step-by-step explanation:
since it is a cube it is the cube root of 67 and I popped it in the calculator and got 4.06 of the answer rounded from the 100th place
OGRAPHS AND FUNCTIONSFinding slopes of lines parallel and perpendicular to a line given.
Answers
We have the next line:
[tex]-5x\text{ - 7y = -8}[/tex]Solve the equation using the slope-intercept form:
[tex]y\text{ = mx + b}[/tex]Where m is the slope and b is the y-intercept:
Solving the equation:
-5x - y7 = -8
Add 5x on both sides
-5x + 5x - y7 = -8 + 5x
-7y = -8 +5x
Divide by 7 into both sides:
-7y/7 = (-8 +5x)/7
-y = (-8 +5x)/7
Multiply by -1 to calcel the negative sign:
(-1)(-y) =(-1)* (-8 +5x)/7
y = (8 -5x)/7
y = -5x/7 + 8/7
Now, we need to find the slope of a line perendicular to this line.
"Two lines are perpendicular if and only if their slopes are negative" reciprocals"
So the slope, in this case, is -5x/7
To find the perpendicular line use:
-5x/7 * m = -1
Solve the equation m:
m = (-1)/(-5x/7)
m = 7/5x
So m = 7/5x is the slope of the perpendicular line.
To find the parallel line use:
"Two lines are parallel lines if they do not intersect. The slopes of the"
lines are the same."
So m = -5x/7
Suppose 2x + 6y= 12. Find y if:x = −4y = ?
Answers
Given the equation:
[tex]2x+6y=12[/tex]If we know that x = -4, then:
[tex]2\cdot(-4)+6y=12[/tex]Solving for y:
[tex]\begin{gathered} -8+6y=12 \\ 6y=12+8 \\ 6y=20 \\ y=\frac{20}{6} \\ \therefore y=\frac{10}{3} \end{gathered}[/tex]Help please show your work please
Answers
Therefore Bill will be able to stay 8 days in his vacation.
Given:
Money Bill saved = $3500
Expenditure for plane tickets = $816
Expenditure per day for hotel = $125
Expenditure per day for food = $100
Expenditure per day for sightseeing = $95
Let the no of days Bill can stay be x.
Therefore,
Expenditure for x days for hotel = $125x
Expenditure for x days for food = $100x
Expenditure for x days for sightseeing = $95x
Therefore according to the question:
125x + 100x + 95x + 816 = 3500
=> 320x = 3500 - 816
=>x =8.3
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What is 3804 divided by 7?
Answers
Answer: 3
Step-by-step explanation:
i am working on an assignment and it just says canceling fractions like 1. 14 over 28 = not sure what to do here?
Answers
SOLUTION
This is
[tex]\frac{14}{28}[/tex]Now, both 14 and 28 are divisible by 2. So, 2 will cut 14 to give 7, and 2 will cut 28 to give 14 so you have
[tex]\begin{gathered} \frac{14}{28} \\ \text{cutting each by 2 you have } \\ \frac{7}{14} \end{gathered}[/tex]Now, only 7 can cut 7 and 14. 7 will cut 7 to get 1 and, 7 will cut 14 to get 2. So we have
[tex]\begin{gathered} \frac{7}{14} \\ \text{cutting each by 2 we have } \\ \frac{1}{2} \end{gathered}[/tex]Hence the answer is
[tex]\frac{1}{2}[/tex]integrate 1∫^-1 (2-x/3) dx
Answers
Answer:
Step-by-step explanation:
[tex]\int~x^{-1}(2-x/3) dx \\\int\frac{2-x/3}{x} dx\\=\int\frac{2}{x} dx-\int~x^{-2/3}~dx\\=2 ln ~x-\frac{x^(-2/3+1)}{-2/3+1} +c\\=lnx^2-3x^{1/3}+c[/tex]
George drives a delivery route thatcovers 320 miles each day. He works8 hours each day. How many miles doesGeorge drive each hour?
Answers
Gorge drives 40 miles each hour
Explanation:Distance covered per day = 320 miles
Number of hours George works per day = 8 hours
Distance covered by George per hour = 320/8
Distance covered by George per hour = 40 miles
Gorge drives 40 miles each hour
I need help with "E" and "F" :)
Answers
Derivative of the given function
E. f(x) = [1 + sin ³(x^5)]² = sin ⁶(x⁵) +2 sin ³(x^5) + 1
F. f(x) = arcsin√sinx = cos x / 2sinx^1/2√ 1- sinx .
According to the chain rule, the derivative of a composite function is equal to the inner function derivative with respect to x times the inner function derivative with respect to each individual composite function.
E) f(x) = [1 + sin ³(x^5)]²
Rearrange terms
[sin ³(x^5) + 1]²
Expand the square
[sin ³(x⁵) + 1]²
[sin ³(x^5) + 1] [sin ³(x^5) + 1]
Distribute
(sin ³(x⁵) + 1) sin ³(x^5) + 1 (sin ³(x^5) + 1)
(sin ⁶(x⁵) + 1) (sin ³(x^5) + 1) (sin ³(x^5) + 1)
Multiply by 1
sin ⁶(x⁵) + 1 sin ³(x^5) + 1 sin ³(x^5) + 1
Combine the terms
sin ⁶(x⁵) + sin ³(x^5) + sin ³(x^5) + 1
sin ⁶(x⁵) +2 sin ³(x^5) + 1
Hence, the solution of the derivative
f(x) = [1 + sin ³(x^5)]² = sin ⁶(x⁵) +2 sin ³(x^5) + 1
Hence, E. f(x) = [1 + sin ³(x^5)]² = sin ⁶(x⁵) +2 sin ³(x^5) + 1
F. f(x) = arcsin√sinx = cos x / 2sinx^1/2√ 1- sinx . is the derivative of the functions .
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Find the equation of the linear function represented by the table below in slope-intercept form. XY-153-117-2711-43
Answers
First, we have to find the slope, using the following formula.
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Let's use the points (-1,5) and (7, -27). Where,
[tex]\begin{gathered} x_1=-1 \\ x_2=7 \\ y_1=5 \\ y_2=-27 \end{gathered}[/tex]Then, we use these values to find the slope.
[tex]m=\frac{-27-5}{7-(-1)}=\frac{-32}{8}=-4[/tex]Now we use the point-slope formula.
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-5=-4(x-(-1)) \\ y-5=-4(x+1) \\ y-5=-4x-4 \\ y=-4x-4+5_{} \\ y=-4x+1 \end{gathered}[/tex]Therefore, the slope-intercept form is y = -4x+1.HELP ASAP!!!!!
Point P is shown on the number line below. The distance between point Q and point P is 6 ½ units.
P
-12-10-8-6-4-2 0 2 4 6 8 10 12
a. Which number could represent point Q?
b. Explain how you determined your answer.
Answers
a: The number which could represent point Q are +2.5 or -10.5.
b. For determining the point Q add and subtract 6.5 units from point P.
What is meant by the term number line?A number line is a graphical portrayal of numbers on such a straight line in mathematics. A number line has numbers that are sequentially placed at equal distances across its length. It can be extended in any direction indefinitely and is generally denoted horizontally.A number line's numbers increase when moving from left to right as well as decrease when moving from right to left.A number line can represent any type of number, including fractions, decimals, integers, and so on.For the given question;
The distance between point Q and point P is 6 ½ units.
The location of point P is (-4) (seen from the number line).
a. The number could represent point Q are either +2.5 or -10.5.
b. Determine the number;
Add 6 ½ units = 6.5 units to (-4)
= -4 + 6.5
= + 2.5
Thus, point Q = + 2.5
Now, subtract 6 ½ units = 6.5 units to (-4).
= -4 - 6.5
= -10.5
Thus, point Q = + 2.5.-10.5.
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i have to use trig ratios to find the unknown angle measurement or side length.
Answers
In order to find x, we apply the trigonometric ratio
Given:
[tex]\begin{gathered} \text{angle, }\theta=57^0 \\ \text{adjacent = x} \\ \text{hypotenuse}=10 \end{gathered}[/tex]Hence,
[tex]\begin{gathered} \cos 57^0=\frac{\text{ adjacent}}{\text{ hypotenuse}}=\frac{x}{10} \\ \cos 57^0=\frac{x}{10} \\ x=10\times\cos 57^0 \\ x=10\times0.5446 \\ x=5.446 \end{gathered}[/tex]Therefore, the value of x, the adjacent side is 5.45 units to the nearest hundredth
Select all the correct answers.
A triangular frame has two side lengths measuring 18 inches and 12 inches. Which values are possible lengths for the third side?
20 in
32 in
28 in
6 in
24 in
30 in
Answers
As per the Pythagoras theorem, the possible length of the third side are 30 or 32.
Pythagoras theorem:
Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“.
Given,
A triangular frame has two side lengths measuring 18 inches and 12 inches.
Here we need to find the possible length of the third sides.
WE know that, the third side of a must be greater than the sum of the other two sides.
So, we have to add the given sides then w get get the value,
=> 18 + 12
=> 30.
So, therefore, the third side must be greater than 30.
From the given options the possible values of the third side are 30 and 32.
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Answer:24 in. 28in. 20in.
Step-by-step explanation:
Solve (t+2)3/4 =2 where t is a real number.t=
Answers
Solution:
Given the equation:
[tex]\begin{gathered} (t+2)^{\frac{3}{4}}=2 \\ \text{where t is a real number} \end{gathered}[/tex]step 1: Take both sides of the equation to the power of 4.
Thus,
[tex]\begin{gathered} ((t+2)^{\frac{3}{4}})^4=(2)^4 \\ \Rightarrow(t+2)^3=16 \end{gathered}[/tex]step 2: Take the cube root of both sides of the equation.
Thus,
[tex]\begin{gathered} \sqrt[3]{(t+2)^3}=\sqrt[3]{16} \\ \Rightarrow(t+2)=16^{\frac{1}{3}} \\ \end{gathered}[/tex]step 3: Solve for t.
[tex]\begin{gathered} 16^{\frac{1}{3}}^{} \\ \text{can be rewritten as} \\ (2^4)^{\frac{1}{3}}=2^{\frac{4}{3}} \\ \text{thus, we have} \\ t+2=2^{\frac{4}{3}} \\ \text{subtract 2 from both sides of the equation} \\ t+2-2=2^{\frac{4}{3}}-2 \\ \Rightarrow t=2(2^{\frac{1}{3}}-1) \\ =2(1.25992-1) \\ \Rightarrow t=2(0.25992) \\ \therefore t=0.51984 \end{gathered}[/tex]Hence, the value of t in the equation is evaluated to be 0.51984.
A population of values has a normal distribution with μ=126.7 and σ=78.3. You intend to draw a random sample of size n=242.
Answers
In a population of values having a normal distribution with (μ = 126.7) and (σ = 78.3), and we intend to draw a random sample of size (n = 242),
(i) The probability that a single randomly selected value is greater is than 119.2 is 0.54
(ii) The probability that a sample of size (n = 242) is randomly selected with a mean greater than 119.2 is 0.932
As per the question statement, a population of values has a normal distribution with (μ = 126.7) and (σ = 78.3) and we intend to draw a random sample of size (n = 242).
We are required to calculate:
(i) The probability that a single randomly selected value is greater is than 119.2
(ii) The probability that a sample of size (n = 242) is randomly selected with a mean greater than 119.2
Let us assume that, a random variable "X" follows normal distribution with mean (μ = 126.7), standard deviation (σ = 78.3) and a sample size of (n = 242).
(i) The probability that a single randomly selected value is greater is than 119.2 is,
P (X > 119.2) = [1 - P(X < 119.2)]
= [1 - P{(X - μ)/σ < (119.2 - 126.7)/78.3}]
= [1 - P{Z < (-0.096)}]
= (1 - 0.462)...[Using Excel Function "NORMSDIST (-0.096)]
= 0.538
≈ 0.54
(ii) The probability that a sample of size (n = 242) is randomly selected with a mean greater than 119.2 is.
P(X bar > 119.2) = [1 - P( < 119.2)]
= [1 - P{(X bar - μ)/(σ/√n) < (119.2 - 126.7)/(78.3/√242)}]
= [1 - P{(X bar - μ)/(σ/√n) < (119.2 - 126.7)/5.033}]
= [1 - P{Z < (-1.49)}]
= (1 - 0.068)...[Using Excel Function "NORMSDIST (-1.49)]
= 0.932
Probability: Probability is the branch of mathematics concerning numerical descriptions about the extent to which an event is likely to occur, or how likely it is that, a proposition is true, and is measured by the ratio of the favorable cases to the whole number of cases possible.Sample: In statistics, quality assurance, and survey methodology, sampling is a logical selection of a subset (a statistical sample) of individuals from within a larger statistical population to estimate characteristics of the whole population.To learn more about Samples and Probability, click on the link below.
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18-?=32
Find the ?
Thank you so much for the help
Answers
Answer:
-14
Step-by-step explanation:
[tex]18-?=32 \\ \\ -?=14 \\ \\ ?=-14[/tex]
18-50=32
3x+2y=10 and 2x+3y=-4parallel perpendicular or neither
Answers
also...could i pls have brainliest?
Please help. Albert invested money into the stock market, and the table represents his earnings. What type of function could be used to model his bank account as a function of time? Justify your answer.
Answers
Answer:
You have the right answer
Step-by-step explanation:
In September, there were 16 members in the music club. In October, the number of members was 24. What was the percent increase from September to October?20 out of 22 students passed the quiz. What percentage of students passed the quiz?A real estate agent sold a house for $178,000. He makes 5.5% commission. How much did he make?The original price of a shirt is $23. It is 20% off. What is the sale price?
Answers
Percentage increase from September to October = 50%
Explanations:Number of members in the music club in September = 16
Number of members in the music club in October = 24
Increase in members from September to October = 24 - 16
Increase in members from September to October = 8
Percent increase from September to October = (8/16) x 100
Percentage increase from September to October = 100/2
Percentage increase from September to October = 50%
PLEASE HELP IM SICK AND I DONT UNDERSTAND.DO IN 30 MINS!!!!!!
Answers
Answer:
x = 7Step-by-step explanation:
The given angles are corresponding angles and as such have same measure.
Set equation and solve for x:
14x + 12 = 16x - 216x - 14x = 12 + 22x = 14x = 7Events in a sample space that are equally likely to occur. what is the method called??
Answers
These events are called "Equally likely Events" and it useful to use when the outcomes of an experiment are equally likely to happen.
what is the answer to -4=r-6solve for r
Answers
-4 = r-6
Add 6 to both sides of the equation:
-4+6 = r-6+6
2 = r
r=2
Calculate the length of the bolded arc. Round your answer to the nearest hundredth (two decimal places). No units are needed.
Answers
The length of arc is given as:
[tex]\begin{gathered} \text{length of arc = }\frac{\theta}{360}_{}\times2\times\pi\times r \\ r\text{ is the radius of the circle} \\ \\ \theta=165^0 \\ r=11ft \end{gathered}[/tex]Therefore, we can solve for the length of the arc:
[tex]\begin{gathered} \text{length of arc =}\frac{165}{360}\times2\times\pi\times11=10.0833\pi \\ \text{length of arc=31.6777ft}^2 \\ \\ To\text{ the nearest hundredth:} \\ \text{length of arc = 31.68ft}^2 \end{gathered}[/tex]