Fully factor the numerator and denominator of each rational expression. Write as one fraction by multiplying the numerators together and multiplying the denominators together.
Multiplication:
Step 1: Factor both the numerator and the denominator.
Step 2: Write as one fraction. Write it as a product of the factors of the numerators over the product of the factors of the denominators. DO NOT multiply anything out at this point.
Step 3: Simplify the rational expression.
Step 4: Multiply any remaining factors in the numerator and/or denominator.
Multiplying Rational Expressions Involving Quadratics with Leading Coefficients of 1
Step 1: Fully factor the numerator and denominator of each rational expression.
Step 2: Write as one fraction by multiplying the numerators together and multiplying the denominators together.
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Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options. The radius of the circle is 3 units. The center of the circle lies on the x-axis. The center of the circle lies on the y-axis. The standard form of the equation is (x – 1)² + y² = 3. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
The three true statements are:
The standard form of the equation is (x – 1)² + y² = 3.
The center of the circle lies on the x-axis.
The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
What is the center of the circle?
A circle is named by the point in the center. A radius is a line segment from the center of the circle to the edge. A diameter is a line segment that passes through the center of a circle.
The true statements are:
The standard form of the equation is (x – 1)² + y² = 3.
The center of the circle lies on the x-axis.
The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
Given an equation of x2 + y2 – 2x – 8 = 0, we can make the following observations:
We can complete the square to get the equation in standard form. (x – 1)² + y² = 3². This is true statement.
The center of the circle is (1,0) which is on the x-axis, this statement is true.
The radius is 3 units, which is the same as the radius of the circle x² + y² = 9 (3²). This statement is true.
The center of the circle does not lie on the y-axis as its x-coordinate is not 0.
Hence, The three true statements are:
The standard form of the equation is (x – 1)² + y² = 3.
The center of the circle lies on the x-axis.
The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
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A company sells two different safes. The safes have different dimensions, but the same volume. What is the height of Safe B?
Answer:
h = 18 in.
Step-by-step explanation:
Both safes are in the shape of a rectangular prism
The volume of a rectangular prism = L X w X H
where L = length, W = width and H = height
Safe A has volume 18 x 15 x 24
Safe B has volume 20 x 18 x h
Both volumes are equal and we have to find h
Equating both expressions
20 x 18 x h = 18 x 15 x 24
Dividing by 18 on both sides will get rid of the 18 in the product
(20 x 18 x h)/18 = (18 x 15 x 24)/18
20h = 15 x 24
20h = 360
h = 360/20
h = 18 in.
Express the area of the shaded region in the room shown algebraically
Let f and g be the functions given by f (x) = e^x and g (x) = x^4. On what intervals is the rate of change of f (x) greater than the rate of change of g (x)? (A) (0.831, 7.384) only(B) (0.831) and (&.384)(C) (0.816) and (1.430, 8.613)(D) (0.816, 1.430) and (8.613)
The rate of change of a function at a point is given by its derivative. To compare the rate of change of f(x) and g(x) at different points, we need to find the derivative of both functions and compare them.as explained below :
The derivative of f(x) = e^x is f'(x) = e^x
The derivative of g(x) = x^4 is g'(x) = 4x^3
Now we need to compare the two derivatives to find on which intervals the rate of change of f(x) is greater than the rate of change of g(x). To do this, we will find the point of intersection between the two functions and compare them.
e^x = 4x^3
Taking the natural logarithm of both sides we get:
x = ln(4x^3) / ln(e)
Approximating we get x ≈ 0.816 and x ≈ 1.430 and x ≈ 8.613
For x < 0.816, e^x < 4x^3, so the rate of change of f(x) is smaller than the rate of change of g(x)
For x > 8.613, e^x > 4x^3, so the rate of change of f(x) is greater than the rate of change of g(x)
Between 0.816 < x < 1.430 and 1.430 < x < 8.613, e^x = 4x^3, so the rate of change of f(x) is equal to the rate of change of g(x).
So the answer is (D) (0.816, 1.430) and (8.613)
Note that the answer (B) (0.831) and (&.384) is not possible as the point of intersection is a number and not an interval and the answer (A) (0.831, 7.384) is not correct as the point of intersection is 1.430 and 8.613 not 0.831 and 7.384
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Michelle made a bead necklace that was 13 inches long. The length of the necklace, in inches, is equal to 3 added to one-seventh the number of beads, b. How many beads did Michelle use for her necklace?
The number of beads used for Michelle necklace is 70.
How to find the number of necklace Michelle used for the necklace?Michelle made a bead necklace that was 13 inches long. The length of the necklace, in inches, is equal to 3 added to one-seventh the number of beads, b.
The number of beads Michelle used for her necklace can be calculated as follows:
number of beads she used for her necklace = b
Therefore,
13 = 3 + 1 / 7 b
13 - 3 = 1 / 7 b
10 = 1 / 7 b
cross multiply
b = 10 × 7
b = 70
Therefore,
number of beads she used for her necklace = 70
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what is the slope through the line of (-6, -3) and (-2, -8)
Answer:m=-5/4
Step-by-step explanation: The formula for finding slope is y1-y2 / x1-x2 so when plugging in these coordinates, you get -3-(-8)/-6-(-2). When simplified -3-(-8) is 5 and -6-(-2) is -4, so the answer is -5/4. You can also switch the numbers so its -8-(-3) / -2-(-6) and still get the same answer.
for all graphs, be sure to correctly and completely label all axes and curves and use arrows to indicate the direction of any shifts. (10 points)
Due to weaker aggregate demand, the negative demand shock will cause the aggregate demand curve to move to the left.
Result: A lower output and price level.
Part B:
Explanation of part B
Result of negative supply shock , aggregate demand falls cause the lower demand for the money . This will lead towards the left shift in money demand.(MD 1 TO MD 2(R1 TO R2)
Part c:
Interest rate and bond price are related inversely . Due to negative demand shock the interest rate falls down. vice-versa bond price will rise.
Part D:
Due to fall in the interest rate central banks will follow contractionary fiscal policy which will increase interest rate and reduce the money supply.
Part E :
If the central banks need to increase the money supply by $80 billion. Central banks need to buy securities in exchange of cash .This will Raise the money supply.
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find the missing term in the series given below 3,12,25,42?88
Answer:
63
Step-by-step explanation:
the value of the difference between the terms increases by 4 as the series continues.
basically, this shows that the difference between 3 and 12 is 9, the difference between 12 and 25 is 13 (which is 4 more than 9), the difference between 25 and 42 is 17 (which is 4 more than 12), and so on.
using this pattern, all we have to do is find the next difference- the one between 42 and the missing term.
to do this, we take the previous difference, 17, and add 4. this gives us 21.
we then add 21 to 42 to get the next term: 63.
hope this helped, good luck!
Please help (Geometry)
PICTURE INCLUDED
Answer: [tex]\triangle TUS \cong \triangle QRP[/tex]
Step-by-step explanation:
When naming congruent triangles, corresponding vertices must have the same positions in the names of the triangles.
The Institute of Medicine compared the United States to comparable high-income countries. Which of the following is accurate?
O The United States had lower rates of birth outcomes than other countries (including infant and maternal mortality),
O The United States had more years lost to alcohol and drug use than most other countries.
O The United States had longer life expectancy than most other countries.
O The United States had lower rates of adolescent pregnancy than most other countries.
The Institute of Medicine compared the United States to comparable high-income countries in terms of various health outcomes.
The findings revealed that the United States had lower rates of birth outcomes than other countries (including infant and maternal mortality). The US also life expectancy than most other countries, as well as more years lost to alcohol and drug use. Lastly, the US had lower rates of adolescent pregnancy than most other countries.
The Institute of Medicine also calculated the health gap between the US and other countries, which was defined as the difference between the health outcomes of the US and the health outcomes of the other countries. This gap was calculated by subtracting the US health outcome rate from the average of the other countries' health outcome rates. For example, to calculate the infant mortality gap, the infant mortality rate in the US (5.8 deaths per 1,000 live births in 2018) was subtracted from the average infant mortality rate of the other countries (3.5 deaths per 1,000 live births). This resulted in a health gap of 2.3 deaths per 1,000 live births.
Overall, the Institute of Medicine's comparison revealed that the US was lagging behind other countries in terms of various health outcomes.
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Another way to express cis 75∘+cis 83∘+cis 91∘+⋯+cis 147∘
the value of theta in the given complex expression is equal to 16°.
Given, a number. [tex]rcis\theta, is[/tex] expressed by.
cis75° + cis83° + cis91°+.... + cis147°.
we have to find the value of angle in degrees.
The function cisA is a shorthand way of writing the equivalent expression cisA=cosA+i sinA
By definition: CisA=CosA+iSinA
This form simplifies complex arithmetic and allows for the study of complex analysis, as well as reduces the workload in writing the expressions.
now, we have to find the sum of the given expressions.
[tex]cis75+cis83+cis91+...+cis147 as, cis\theta=e^{i\theta}[/tex]
[tex]e^{75i}+e^{83i}+e^{91}+....+e^{147i}\\\\e^{\frac{75\pi}{180} }+e^{\frac{83\pi}{180} }+.....+e^{\frac{147\pi}{180} }[/tex]
on using geometric sum of the series we get,
[tex]Sum=\frac{e^{\frac{75i\pi}{180}}(1-e^{\frac{72i\pi}{180} ) }}{(1-e^{\frac{8i\pi}{180} })}\\ \\\theta=16[/tex]
the value of theta of the angle be 16 degree.
the complete question is.
The number cis 75 + cis 83 + cis91 +...+ cis 147 is expressed in the form r cis(theta), where 0 <= theta < 360.
Find theta in degrees.
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For the following exercises, find the level curves of each function at the indicated value of c to visualize the given function. h(x,y) = 2x-y, c=0, -2,2
The level curves of the function h(x,y) = 2x-y at c = 0, -2, 2 are y = 2x, y = 2x + 2, y = 2x - 2 respectively.
A level curve (also called a contour line or an isocline) of a function is a curve that represents all the points where the function has a constant value. To find the level curve of a function at a given value of c, we need to set the function equal to c and solve for the variables.
For h(x,y) = 2x-y, we can find the level curves at c = 0, -2, 2 by setting the function equal to c and solving for x and y:
c = 0: 2x - y = 0y = 2xc = -2: 2x - y = -2y = 2x + 2c = 2: 2x - y = 2y = 2x - 2The level curves of h(x,y) = 2x-y at c = 0, -2, 2 are the lines y = 2x, y = 2x + 2, y = 2x - 2 respectively. Each line represents a different value of c and separates the domain of x and y into different regions where the function takes on that constant value.
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Let X be a number between 0 and 1 produced by a random number generator. Assuming that the random variable X has a uniform distribution, find the following probability: P(X > 0.49)
The probability of a random variable X with a uniform distribution being greater than 0.49 can be calculated using the formula P(X > 0.49) = 1 - P(X ≤ 0.49).
Since X has a uniform distribution, it means that the probability of any number between 0 and 1 occurring is the same. Therefore, P(X ≤ 0.49) = 0.49.
The probability of X being greater than 0.49 can be calculated using the formula for uniform distributions, which is P(X>a) = 1 - P(X≤a). In this case, P(X>0.49) = 1 - P(X≤0.49). The probability of X being less than or equal to 0.49 can be calculated by multiplying the probability of each individual outcome (since they are all equally likely) by the number of outcomes that satisfy the condition .Substituting this into the formula to calculate P(X > 0.49), we get P(X > 0.49) = 1 - 0.49 = 0.51. Therefore, the probability of a random number generated being greater than 0.49 is 0.51.
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Which of the following statements correctly reflect the rule governing rounding in a calculation? Select all that apply. Check all that apply. O The number of significant figures in the answer are determined by an average of the number of significant figures in all the quantities involved. O The least certain measurement determines the certainty of the answer. O Rounding is necessary when there are too many digits after a calculation. O All answers are rounded to two decimal places after a calculation. Read about this Do you know the answer?
The least certain measurement determines the certainty of the answer.
What guidelines apply when rounding sig figs?
(1) The final digit that is preserved is raised by one if the digit to be eliminated is greater than 5. As an illustration, 12.6 is rounded to 13.
(2) The last digit that remains is left alone if the digit to be dropped is less than 5. As an illustration, 12.4 is rounded to 12.
Which of the following statements best describes the significant figures rule?
Use the following 3 principles to calculate how many significant figures are present in a number: The significance of non-zero digits is constant.
A significant zero is one that comes in between two significant digits. ONLY the decimal part has any significance when there is a final zero or trailing zeros.
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Find the measure of each angle that adds up to 180
Answer:
? = 50°
Step-by-step explanation:
we have a right triangle, therefore with an angle of 90° (red sign) and an angle of 40°, knowing that the sum of the interior angles of all triangles is 180° we remove the known angles from 180° and find the value of angle "?"
180 - 90 - 40 =
50°
During the week Jimmy spent $45 eating out, gained $55 mowing lawns and spent $15on gas. What was Jimmy's change in dollars at the end of the week?
The change in dollars at the end of the week is - $5
How to determine the amount received as changeFrom the question, we have the following parameters that can be used in our computation:
Amount spent = $45
Amount gained = $55
Amount spent on gas = $15
The change is then calculated as
Change = Amount gained - Amount spent - Amount spent on gas
Substitute the known values in the above equation, so, we have the following representation
Change = 55 - 45 - 15
Evaluate
Change = -5
Hence, the change is a deficit of $5
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5 1/8 equals 4 + 1 + 1/8 = 4 + blank 8 + 1/8 =
The blanks in the equation are filled as below
5 1/8 = 4 + 1 + 1/8 = 4 + 1/8 8 + 1/8 = 5 1/8
How to fill the blanks in the equationTo fill the blanks the equation is written completely in figures
5 1/8 = 4 + 1 + 1/8 = 4 + 8 + 1/8 =
From the knowledge of equality to maintains a true equation the last blank should be equal to 5 1/8.
With this information, we use addition operation to solve for the first blank as follows.
let the first blank be x
4 + 8 + 1/8 = 5 1/8
4 + x * 8 + 1/8 = 5 1/8
4 + 8x + 1/8 = 5 1/8
collection like terms
8x = 5 1/8 - 4 - 1/8
8x = 1
divide both sides by 8
x = 1/8
the blanks are 1/8 and 5 1/8
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A dinner was held to raise money for a children's museum. A ticket for one person cost $200 and a ticket for a couple (two people) cost $350. A total of 130 people attended the dinner, and the ticket sales total was $24,000. What is the total number of tickets that were sold?
There were 50 single tickets sold and 40 couples tickets were sold.
What is the equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that is equal.
Let's call the number of single tickets sold "x". Then the number of couple tickets sold would be "y".
We know the total number of attendees is 130, so we can write the equation:
x + 2y = 130
We also know that the total revenue from the ticket sales is $24,000, so we can write another equation using the cost of the tickets:
200x + 350y = 24,000
We now have a system of two equations that we can solve for x and y then we get the values are:
x = 50 and y = 40
So, 50 single tickets were sold and 40 couples tickets were sold.
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The solution of a system of equations is (3,2). One of the solutions in the system is 2x + 3y = 12. Write an equation in slope-intercept form that could be the second equation in the system.
y = -2/3x + 4 is an equation in slope-intercept form that could be the second equation in the system.
What are Systems of equations?simultaneous equations, a system of equations Two or more equations in algebra must be solved jointly (i.e., the solution must satisfy all the equations in the system). The number of equations must match the number of unknowns for a system to have a singular solution.
There are four methods for solving systems of equations: graphing, substitution, elimination, and matrices.
Given, The solution of a system of equations is (3,2). One of the solutions in the system is 2x + 3y = 12.
From the general formula of Slope intercept form:
y = mx + c
where,
m = slope
c = y-intercept of the equation
Thus in our case,
2x + 3y = 12
=> 3y = -2x + 12
=> y = -2/3x + 4
thus, the Slope of the line = -2/3
and another coordinate (0, 4)
Therefore, an equation in slope-intercept form that could be the second equation in the system is y = -2/3x + 4.
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Karin wants to use the distributive property to mentally find the value of
19⋅42+19⋅58
.
Which expression can she use?
Answer:
19(42 + 58)
Step-by-step explanation:
19(100)
1900
cab fare in new york city is $7.50 for for the first mile, +$3 for each additional mile. what is the longest distance you can travel for $30
Answer:7
Step-by-step explanation:
BA
6. Kathleen spent $231 on concert tickets
for herself and 11 friends. Each ticket
cost the same.
Part A
Estimate the cost of each ticket. Write an
equation to show your work.
Part B
Find the exact cost of each ticket.
Compare your answer to your estimate
to check for reasonableness.
The equation of cost of each ticket is 11k = 231 and the exact cost of each ticket is $21.
What is algebraic expression ?
Algebraic expression can be defined as the combination of variables and constants .
Given,
Kathleen spent $231 on concert tickets for herself and 11 friends. Each ticket cost the same.
So we have to find the cost of each ticket. Write an equation to show your work and the exact cost of each ticket. Compare your answer to your estimate to check for reasonableness.
From the given information ,
The equation to show the work could be ,
231 = k * 11
SO, this is the equation 11k = 231 .
we can say that,
= $231 / 11
= $21
Hence, the equation of cost of each ticket is 11k = 231 and the exact cost of each ticket is $21
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Match the statistical measure to its notation or name. population mean [Choose ] sample mean [Choose) population variance [Choose] sample variance [Choose ]population standard deviation [Choose] sample standard deviation [Choose ] number of population data values [ Choose] number of sample data values [Choose]
Population Mean is the statistical indicator to its designation or nomenclature.
What is meant by Population Mean?A population is a distinct group of individuals that can be distinguished for the purposes of data collection and analysis by at least one feature. Populations are used in statistics and other branches of mathematics. The population mean can be computed by dividing the sum of all values in the given data/population by the total number of values in the given data/population. We can refer to the total of a set of numbers as a sum. An entire set of people is referred to as a population, regardless of whether that set includes an entire country or just a number of people who share a certain trait. In statistics, the group of people from which a statistical sample is taken for a research is referred to as a population.Therefore,
The formula for the population mean, which is the population's average score on a certain variable, is: μ = ( Σ Xi ) / N. The population mean is represented by the symbol "."
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If the angle of elevation of P from Q is 38, then the angle of depression of Q from P is:
Answer:
52°
Step-by-step explanation:
The angle of depression is 90 - angle of elevation
So angle of depression = 90 - 38 = 52°
Question 2 (1 point) The results of a survey of 70 Programming students on learning preferences were as follows: 50 liked to learn visually, 45 liked learning through listening and 35 liked learning through videos. 5 liked using all three channels, 32 liked to learn visually and through listening, 22 liked to learn both visually and videos, 14 liked to learn through listening and videos. How many preferred learning only through videos? options-(9, 17 ,13, 4)
9 students preferred learning only through videos.
What is inclusion-exclusion from the data provided?Inclusion-exclusion is a principle used in counting to find the total number of elements in a union of sets by subtracting the elements that are counted multiple times and adding back in the elements that are not counted at all.
The number of students who preferred learning only through videos is 17.
This can be found by using the principle of inclusion-exclusion:
35 students liked to learn through videos
14 students liked to learn through listening and videos
5 students liked all three channels
So, 35 - 14 + 5 = 26 students liked to learn through videos and listening
Therefore, 35 - 26 = 9 students preferred learning only through videos.
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Polynomial 1: 4x2
+ 5x − 4
Polynomial 2: 4x2
+ 4x − 2
Question 1
What is the difference when polynomial 2 is subtracted from polynomial 1?
Responses
A x − 2x − 2
B x − 6x − 6
C x + 6x + 6
D x + 2
Answer:
x + 2 (Choice D)
Step-by-step explanation:
The two polynomials are
P1 = 4x² + 5x - 4
and
P2 = 4x² + 4x - 2
P1 - P2
==> (4x² + 5x - 4 ) - (4x² + 4x - 2)
Expanding brackets we get
==> 4x² + 5x - 4 - 4x² - 4x + 2 (signs inside the second parentheses are
reversed because of the - sign preceding it)
Group similar terms and add the coefficients
==> (4x² - 4x²) +(5x - 4x) +(-4 + 2)
==> 0 + x + 2
==> x + 2 (Choice D)
Jada measured the height of a plant in a science experiment and finds that, to the nearest 1/4 of an inch, it is 4.75 inches.
The actual length of the tree based on the information is 19 inches.
How to calculate the word problem?A word problem in mathematics simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge to solve the real life scenario given.
Since Jada measured the height of a plant in a science experiment and finds that, to the nearest 1/4 of an inch, it is 4.75 inches.
The actual length will be:
= 4.75 × 4
= 19 inches
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Complete question
Jada measured the height of a plant in a science experiment and finds that, to the nearest 1/4 of an inch, it is 4.75 inches. What is the actual length of the tree?
pls help me
Josh is the owner of CranBog, a Cranberry Bog in Massachusetts. Cranberry production at CranBod can be represented by the inequality y ≤ 150x - 3100
under normal climate conditions, where y
is the annual production of cranberries at CranBog, in thousands of pounds, and x
is the number of acres of land that produce cranberries.
The TRUE statements about the inequality y ≤ 150x - 3100 are:
A) For a solution to be viable, both x and y must be integers.E) The ordered pair (40, 2900) is a solution to the inequality and means that with 40 acres of land, CranBog can produce 2,900 (in thousands of) pounds of cranberries.What is inequality?Inequality refers to a mathematical statement claiming the inequality of two or more mathematical expressions.
The following types and inequality symbols represent inequalities:
Less than (<)Greater than (>)Not equal to (≠)Less than or equal to (≤)Greater than or equal to (≥).Check:
Ordered pairs (40, 2900)
y ≤ 150x - 3100
y ≤ 150(40) - 3100
y ≤ 6,000 - 3100
y ≤ 2900
Thus, the true statements about this inequality are Options A and E.
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ABC is straight angle.BD is drawn so that two adjacent angles are created. m ABC = 22x - 9 and m CBD = 4x + 7. does BD bisector ABC?show your work.
Yes, BD is the bisector of ∠ABC.
What is geometry?Geometry is a branch of mathematics that deals with shapes, sizes, angles, and dimensions of objects.
Given is that ABC is straight angle. BD is drawn so that two adjacent angles are created. It is given that m ∠ABD = 22x - 9 and m∠ CBD = 4x + 7.
For BD to be the bisector of ∠ABC, ∠ABD and m∠ CBD should be equal. So we can write -
22x - 9 = 4x + 7
22x - 4x = 16
18x = 16
x = 8/9
Now, we can write -
m ∠ABD = 22x - 9 = 22 x 8/9 - 9 = 10.55°
m ∠ABD = 10.55° ...... (1)
m ∠CBD = 4x + 7 = 4 x 8/9 + 7 = 10.55°
m ∠CBD = 10.55° ...... (2)
m ∠ABD = m ∠CBD
Yes, BD is the bisector of ∠ABC.
Therefore, yes, BD is the bisector of ∠ABC.
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in an equilateral triangle the altitude is sqrt7 find the length of the sides
Answer:
Length of each side = 3.055
Step-by-step explanation:
The relationship between altitude h and side a of an equilateral triangle is
[tex]h = \dfrac{\sqrt{3} }{2} a\\\\\\\rightarrow a = \dfrac{ 2h}{{\sqrt{3} }}\\\\[/tex]
Given h = √7.
we get
[tex]a = \dfrac{2\sqrt{7} }{\sqrt{3} }\\\\a = 2 \sqrt{\dfrac{7}{3}}\\\\a = 2\times 1.5275\\\\a = 3.055\\\\[/tex]
