What is the result of adding -3x²-5x +1 and 8x²-2x-9?
Answers
Hi!
Your answer is \(5x^2-7x-8\).
We are asked:
\((-3x^2-5x+1)+(8x^2-2x-9)\)
As we are adding them, we can remove the parenthesis.
\(-3x^2-5x+1+8x^2-2x-9\)
Now, we can switch the order of the terms around to cause like terms to be by each other:
\(-3x^2+8x^2-5x-2x+1-9\)
Finally, add like terms:
\(5x^2-7x-8\)
5x² -7x -8 is the result of adding the polynomials -3x²-5x +1 and 8x²-2x-9. The result obtained by combining the like terms.
The two polynomials are -3x²-5x +1 and 8x²-2x-9.
To add the two polynomials, you simply combine like terms.
Like terms are terms that have the same variable raised to the same power.
In this case, the variables are x² and x.
Let's add the given polynomials:
= -3x²-5x +1 + 8x²-2x-9
Group the like terms:
= -3x²+ 8x²-5x-2x+1-9
Combine like terms:
= 5x² -7x -8
Hence, 5x² -7x -8 is the result of adding -3x²-5x +1 and 8x²-2x-9.
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Related Questions
4. Amy, Betty and Carol have 96 books altogether. Betty has 6 books less than Amy and Carol has half as many as Betty. How many books does each girl have?
Answers
The Amy has 42 books, Betty has 36 books, and Carol has 18 books.
Let's set up equations to represent the given information:
Let A represent the number of books Amy has.
Let B represent the number of books Betty has.
Let C represent the number of books Carol has.
Let's say Amy has x books.
Betty has 6 books less than Amy, so Betty has (x - 6) books.
Carol has half as many books as Betty, so Carol has (x - 6)/2 books.
According to the problem, the total number of books they have is 96.
So, we can write the equation:
x + (x - 6) + (x - 6)/2 = 96
To solve the equation, we can simplify it by multiplying through by 2 to remove the fraction:
2x + 2(x - 6) + (x - 6) = 192
2x + 2x - 12 + x - 6 = 192
5x - 18 = 192
5x = 210
x = 42
Amy has 42 books.
Betty has (42 - 6) = 36 books.
Carol has (36)/2 = 18 books.
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The following are the annual incomes (in thousands of dollars) for 8 randomly chosen, U.S. adults employed full-time.
44, 44, 54, 54, 65, 39, 54, 44
Send data to calculator
(a) What is the mean of this data set? If your answer is not an
integer, round your answer to one decimal place.
(b) What is the median of this data set? If your answer is not
an integer, round your answer to one decimal place.
(c) How many modes does the data set have, and what are
their values? Indicate the number of modes by clicking in the
appropriate dircle, and then indicate the value(s) of the
mode(s), if applicable.
0
Zero modes
one mode:
Two modes:
Answers
Answer:
(a) To find the mean of the data set, sum up all the values and divide by the total number of values.
44 + 44 + 54 + 54 + 65 + 39 + 54 + 44 = 398
Mean = 398 / 8 = 49.75
Rounded to one decimal place, the mean of this data set is 49.8.
(b) To find the median of the data set, i need to arrange the values in ascending order first:
39, 44, 44, 44, 54, 54, 54, 65
The median is the middle value in the sorted data set. In this case, we have 8 values, so the median is the average of the two middle values:
(44 + 54) / 2 = 98 / 2 = 49
Rounded to one decimal place, the median of this data set is 49.0.
(c) To determine the modes of the data set, identify the values that appear most frequently.
In this case, the mode refers to the value(s) that occur(s) with the highest frequency.
From the data set, i see that the value 44 appears three times, while the value 54 also appears three times. Therefore, there are two modes: 44 and 54.
When ordering the Kids' Lunch at Burger Universe, the customer must choose a size, a type of bun, a side order, and a type of fruit drink. Here are the possibilities for each choice. Choice Possibilities Size: junior, Small, Medium, Large Type of bun Plain bun, Sesame seed bun Side order Fries, Onion rings Fruit drink Orange, Grape, Cherry, Lemonade How many Kids' Lunches are possible?
Answers
The number of Kid's Launches that are possible is 128. This is solved using Combination Principle.
What is combination in Math?A combination in mathematics is a selection of elements from a set with distinct members, where the order of selection is irrelevant.
Hence,
The number of possible "Sizes" from the specified 4 sizes are ⁴C₁
The number of sorts of bun that is possible from the specified two bun types is: ²C₁
From the four sides, the number of possible side purchases is: ⁴C₁
Of the available four drinks, the number of the possible drinks is: ⁴C₁
Now the possible number of all lunches are:
⁴C₁ x ²C₁ x ⁴C₁ x ⁴C₁
= 4 x 2 x 4 x 4
= 128
Hence the number of Kid's Lunches that are possible are 128.
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The houses on a city block were thought to be valued at $175,000, $163,000,
$142,000, $135,000, $191,000, $122,000, and $147,000, respectively. But a
public assessor has determined that the value of each house is actually
$20,000 higher than previously thought. According to the public assessor,
what is the median value of the houses?
O A. $162,000
O B. $167,000
O c. $155,000
O D. $147,000
SUBMIT
Answers
Answer:
$167,000
Step-by-step explanation:
THAT'S THE ANSWER.COM
The median value of the houses is $167,000.
MedianWhat is median value?The middle number in a collection of numbers is known as the median.
How median is calculated?Check to see if 'n' is an even number of values.Find the two numbers that are in the centre of the table of data. Adding the two middle numbers together and dividing the result by two will yield the average of the two numbers.The median is the outcome of this average.Calculation for the median of the houses:The initial value of the 7 houses were,
$175,000, $163,000, $142,000, $135,000, $191,000, $122,000, and $147,000.
As, the value of each house were increased by $20,000.
The value of houses after increment,
$195,000, $183,000, $162,000, $155,000, $211,000, $142,000, and $167,000.
Arrange the values in the increasing order.
$142,000, $155,000, $162,000$, 167,000, $183,000, $195,000, $211,000.
Since, the given data has 7 values which is a odd number. So, values come in the middle is $167,000.
Therefore, the median value of the houses is $167,000.
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Help on this question pls .... (the question is at the top) I will cashapp you I have been waiting for this answer for the longest
Answers
Answer:
$59.94
Step-by-step explanation:
So for this question, you need to find 8% of 748.
You can do this by multiplying .08 by 748:
.08(748) = 59.94
Answer:
149.6
Step-by-step explanation:
A circle has a radius of 10.4 cm the angle at the centre of the sector is 120 calculate the area of the sector
Answers
Answer:
sector area: 113.3
Step-by-step explanation:
PLEASE HELP 100 points to who ever gives me the answer Compare the numbers using >, <, or =.
a) -2 3
b) |-12| |15|
c) 3 -4
d) |15| |-12|
e) 7 -11
Answers
Answer:
a) -2 < 3
b) |-12| < |15| (the absolute value of -12 is 12 so that's comparing 12 to 15)
c) 3 > -4
d) |15| > |-12|
e) 7 > -11
If these cylinders and prisms were broken into two separate groups, what would be an equivalent ratio to 8/2? i dont have much longer and btw it doesn't have a picture.
100 points?
Answers
The Equivalent ratio to 8/2 is 4/1, 24/6, 32/8 and 48/12.
We have,
Cylinder and prism.
Here we have to find the equivalent ratio to 8/2.
First simplifying the given ratio as
8/2
= (4 x 2)/2
= 4 /1
Now, some more ratios equivalent to 8/2.
1. 8/2 x 3/3 = 24/ 6
2. 8/2 x 4/4 = 32/8
3. 8/2 x 6/6= 48/12
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QUESTION in the diagram below the following are rectangles. ACEG ;BCDJ ; JDEF and HJFG is a square AB =AH = x ;BC=5 ; HG=3 Area of a square= s×s= s² Area of a rectangle= l×b Determine the area of ine following, some cases love answer terms of . DO NOT MEASURE THE DIAGRAM) 2.1.1 ABJHUnit 2.1.2 BCDJ: Units Units 2.1.3 DEFJ 2 2.1.4 HJFG Units 22 write in terms of the length of 2.2.1 AC 2.22 AC Units
Answers
The area of the rectangle ACEG is the amount of space on it, and the area of square HJFG is 9 square units
How to determine the area of the figures?The area of a rectangle is:
Area = Length * Width
The area of a square is:
Area = Length * Length
From the question, the given parameters are:
AB =AH = x ;
BC=5;
HG=3
This means that the area of square HJFG is:
Area = HG * HG
Area = 3 * 3
Area = 9
Note that the other areas cannot be calculated because the question is incomplete
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There are 2 white chocolates for every plain chocolate in a box of chocolates.
There are no chocolates of any other colour in the box.
There are 10 plain chocolates in the box.
How many chocolates are there in the box altogether?
Answers
Answer:
Step-by-step explanation:
10 x 2=20 white chocolate
10+20=30 chocolates altogether
The HCF of three numbers is 8 and the sum of these numbers is 80. List the possible set of such three numbers.
Answers
Let's denote the three numbers A, B, and C.
Given that the highest common factor (HCF) of these three numbers is 8 and their sum is 80, we can consider possible combinations of numbers that satisfy these conditions.
Since the HCF is 8, all three numbers must be divisible by 8. Additionally, the sum of the numbers is 80, so we need to find combinations of three numbers that satisfy both conditions.
Let's list the possible combinations:
(8, 16, 56): In this case, A = 8, B = 16, and C = 56. All three numbers are divisible by 8, and their sum is 8 + 16 + 56 = 80.(16, 8, 56): Here, A = 16, B = 8, and C = 56. Again, all three numbers are divisible by 8, and their sum is 16 + 8 + 56 = 80.(24, 8, 48): In this combination, A = 24, B = 8, and C = 48. All three numbers are divisible by 8, and their sum is 24 + 8 + 48 = 80.(8, 24, 48): Similarly, A = 8, B = 24, and C = 48. All three numbers are divisible by 8, and their sum is 8 + 24 + 48 = 80.These are the four possible sets of three numbers that satisfy the given conditions: (8, 16, 56), (16, 8, 56), (24, 8, 48), and (8, 24, 48).
a student spends 18 out of 35 of his pocket money on transport and fruit what is the fraction left?
Answers
To find the fraction of pocket money left after spending on transport and fruit, we need to subtract the amount spent from the total pocket money and express it as a fraction.
The student spends 18 out of 35 of his pocket money, which means he has (35 - 18) = 17 units of his pocket money left.
Therefore, the fraction of pocket money left can be written as 17/35.
which point is the incenter of the triangle?
Answers
A simple random sample of size has mean and standard deviation.Construct a confidence interval for the population mean.The parameter is the population The correct method to find the confidence interval is the method.
Answers
ANSWER:
EXPLANATION:
A simple random sample of size has mean and standard deviation. Construct a confidence interval for the population mean. The parameter is the population The correct method to find the confidence interval is the method.
The sample size is not given. Mean and Standard Deviation are not given.
To construct a confidence interval for the population mean, first find out the margin of error of the sample mean. This is why you need a confidence interval. If you are 90% confident that the population mean lies somewhere around the sample mean then you construct a 90% confidence interval.
This is equivalent to an alpha level of 0.10
If you are 95% sure that the population mean lies somewhere around the sample mean, your alpha level will be 0.05
In summary, get the values for sample size (n), sample mean, and sample standard deviation.
Make use of a degrees of freedom of (n-1).
On any given day, the number of users, u, that access a certain website can be represented by the inequality | 125-u | -<30. Which of the following represents the range of users that access the website each day?
Answers
Answer: D
Step-by-step explanation:
Answer:
D. 95 ≤ u ≤ 155
Step-by-step explanation:
A vehicle's distance d in miles is given by the function d(r,t)=r⋅t, in which r is the rate in miles per hour and t is the time in hours. What happens to the value of d if the rate is tripled and the time increases by 3 hours?
Answers
If the rate is tripled and the time increases by 3 hours, the value of d will increase by a factor of 12.
What is Distance?The length along a line or line segment between two points on the line or line segment.
Distance=√(x₂-x₁)²+(y₂-y₁)²
The original distance, d(r,t), can be expressed as d(r,t) = rt.
Value of d if the rate is tripled and the time increases by 3 hours
The new distance, d(3r,t + 3), can be expressed as d(3r,t + 3) = 3r(t + 3).
The new distance d(3r,t + 3) = 3r(t + 3)
= 3rt + 3(3r)
= 3rt +9r
= 3d(r,t) + 9r
Therefore, if the rate is tripled and the time increases by 3 hours, the value of d will increase by a factor of 3 + 9 = 12.
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y=x+2
y+1= – 4x
Is this ordered pair a solution of the system of equations? Help:(
Answers
Put value of y in Equation 1 in Equation 2.
\( \looparrowright \sf y + 1 = - 4x\)
\( \\ \\ \)
\( \looparrowright \sf (x + 2) + 1 = - 4x\)
\( \\ \\ \)
\( \looparrowright \sf x + 2 + 1 = - 4x\)
\( \\ \\ \)
\( \looparrowright \sf x +3= - 4x\)
\( \\ \\ \)
\( \looparrowright \sf x + 4x= - 3\)
\( \\ \\ \)
\(\looparrowright \sf 5x= - 3\)
\( \\ \\ \)
\(\looparrowright \sf x= \dfrac{ - 3}{5} \)
\( \\ \\ \)
Let's find value of y :
\( \\ \\ \)
\(\looparrowright \sf y=x+2\)
\( \\ \\ \)
\(\looparrowright \sf y= \dfrac{ - 3}{5} +2\)
\( \\ \\ \)
\(\looparrowright \sf y= \dfrac{ - 3 + 10}{5} \)
\( \\ \\ \)
\(\looparrowright \sf y= \dfrac{7}{5} \)
Solution:
\(\looparrowright \sf \bigg( \dfrac{ - 3}{5} , \dfrac{7}{5} \bigg)\)
Segment AB has endpoints at A(-14, 12) and B(10, – 4). Point C lies on AB at C(-5,6). Which of the following
represents the ratio of AC to BC?
Answers
The ratio of the length AC to BC is 11:18
Distance between two pointsThe formula for calculating the distance between two points is expressed as:
\(D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)
For the length AC
\(AC = \sqrt{(-9)^2+(6)^2} \\AC = \sqrt{(-14+5)^2+(12-6)^2} \\AC = \sqrt{81+36} \\AC\approx 11\)
For the length of BC
\(BC = \sqrt{(15)^2+(10)^2} \\BC = \sqrt{225+100} \\BC\approx 18\)
Hence the ratio of the length AC to BC is 11:18
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Help please! I’ll give brainliest!
Answers
Answer:
i think the answer is B
i am sorry if this is wrong
Step-by-step explanation:
The national mean annual salary for a school administrator is $90,000 a year (The Cincinnati Enquirer, April 7, 2012). A school official took a sample of 25 school administrators in the state of Ohio to learn about salaries in that state and to see if they differed from the national average. Click on the datafile logo to reference the data.
A. Formulate hypotheses that can be used to determine whether the population mean annual administrator salaries in Ohio differ from the national mean of $90,000.
B. The sample data for 25 Ohio administrators is contained below. What is the p-value for your hypothesis test in part A?
C. At alpha = 0.05, can your null hypothesis be rejected? What is your conclusion?
D. Repeat the preceding hypothesis test using the critical value approach?
Salary Data
77600
76000
90700
97200
90700
101800
78700
81300
84200
97600
77500
75700
89400
84300
78700
84600
87700
103400
83800
101300
94700
69200
95400
61500
68800
Answers
A student is graduating from college in 18 months but will need a loan in the amount of $6,720 for the last three semesters. The student may receive either an unsubsidized Stafford Loan or
a PLUS Loan. The terms of each loan are:
Unsubsidized Stafford Loan: annual interest rate of 3.99%, compounded monthly, and a grace period of six months from time of graduation.
PLUS loan: annual interest rate of 4.99%, compounded monthly, with a balance of $7,241.17 at graduation
Which loan will have a higher balance and by how much at the time of repayment?
O The Stafford loan will have a higher balance by $107.41 at the time of repayment.
O The PLUS loan will have a higher balance by $107.41 at the time of repayment.
O The Stafford loan will have a higher balance by $36.53 at the time of repayment.
O The PLUS loan will have a higher balance by $36.53 at the time of repayment.
Answers
The Stafford loan will have a higher balance of $36.53 at the time of repayment.
The correct option is C.
What is a loan calculation formula?The formula:
PV = PMT/i[1 - {1/(1+i)ⁿ]
PV denotes the loan sum.
PMT stands for "monthly payment," I for "interest rate" (interest rate % divided by 12), and "n" for the number of months (term of the loan in months)
To compare the balances of the two loans at the time of repayment, we need to calculate the total amount owed for each loan.
For the Unsubsidized Stafford Loan:
The total loan amount is $6,720, and the annual interest rate is 3.99%, compounded monthly.
Therefore, the monthly interest rate is 3.99% / 12 = 0.3325%. The loan has a grace period of 6 months, so interest will not start accruing until 6 months after graduation.
The loan will be repaid over a period of 10 years, or 120 months.
Using the formula for the future value of an annuity, the total amount owed for the Unsubsidized Stafford Loan is:
FV = PMT x [(1 + r)ⁿ - 1] / r
where PMT is the monthly payment, r is the monthly interest rate, and n is the number of months.
We can solve PMT using a loan repayment calculator, such as the one found on bankrate.com, and we get a monthly payment of $73.80. Plugging this into the formula, we get:
FV = $73.80 x [(1 + 0.003325)¹¹⁴ - 1] / 0.003325
FV = $9,222.41
Therefore, the total amount owed for the Unsubsidized Stafford Loan at the time of repayment is $9,222.41.
For the PLUS Loan:
The loan amount is $7,241.17, and the annual interest rate is 4.99%, compounded monthly. Therefore, the monthly interest rate is 4.99% / 12 = 0.4158%. Interest starts accruing immediately, and the loan will be repaid over a period of 10 years, or 120 months.
Using the same formula, the total amount owed for the PLUS Loan is:
FV = PMT x [(1 + r)ⁿ- 1] / r
Again, using a loan repayment calculator, we get a monthly payment of $78.93. Plugging this into the formula, we get:
FV = $78.93 x [(1 + 0.004158)^120 - 1] / 0.004158
FV = $9,258.94
Therefore, the total amount owed for the PLUS Loan at the time of repayment is $9,258.94.
Comparing the two loan amounts, we see that the Unsubsidized Stafford Loan will have a higher balance of $36.53 ($9,222.41 - $9,258.94) at the time of repayment.
Therefore, the answer is:
The Stafford loan will have a higher balance of $36.53 at the time of repayment.
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consider the following probability distribution: 1 2 3 4 5 0.1 0.15 0.40 0.25 0.10 find (write it up to second decimal place).
Answers
The mean value is 1.19
x p(x) x*p(x) X^2p(x)
1 0.1 0.1 0.1
2 0.15 0.3 0.6
3 0.4 1.2 3.6
4 0.25 1 4
5 0.1 0.5 2.5
Sum 1 3.1 10.8
Mean =Σx * p(x)
u=3.1
Variance=σ^2
=Σx*p(x)-u^2
=10.8-(3.1)^2 =1 .19
A probability distribution is a frequency distribution that has been idealised. A frequency distribution is a description of a particular sample or dataset. It is the number of times each possible variable value appears in the dataset.
The probability of occurrence determines how many times a value appears in a sample. Probability is a number between 0 and 1 that indicates the likelihood of an event occurring:
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the product of two numbers is 1575. if one is 63,what will the other number be?
Answers
Answer:
25
Step-by-step explanation:
1575/63=25
Answer:
25Step-by-step explanation:
1575/63 = 25
63 x 25 = 1575
Please explain your answer. Will mark Brainliest (question 9)
Answers
The initial investment of the function is 20 dollars.
The rate growth in percentage is 4%.
The investment after 10 years is 29.6 dollars.
How to solve function?The function \(y=20(1.04)^{t}\) represents the value y of a saving account after t years.
Therefore, the initial investment of the function is 20 dollars.
The rate growth in percentage can be calculated as follows;
rate growth in percent = 0.04 × 100
rate growth in percent = 4 %
Let's find the value of the investment after 10 years.
Therefore,
\(y=20(1.04)^{t}\)
t = 10
\(y=20(1.04)^{10}\)
\(y=20(1.48024428492)\)
y = 29.6048856984
Therefore, the investment after 10 years is as follows:
y = 29.6 dollars
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6(3 + 2) + (8 – 2 x 4) =
Answers
Answer:
30
Step-by-step explanation:
6(3 + 2) + (8 - 2 × 4)
Always apply the law of BIDMAS when solving an expression
6(3 + 2)
18 + 12
30
(8 - 2 × 4)
= 8
8 - 8 = 0
30 + 0 = 30
PLEASE I NEED HELP !!!!!!!!!!!!!
Answers
Please Help if you can!! I also have more questions in my profile!
Answers
Answer:
none
Step-by-step explanation:
because the zeros usually intercept with the x-axis and the parabola is nowhere near that! hope it helps!
Suppose that a sequence is defined as follows.a₁ = -4, an=3an-1+7 for n>2List the first four terms of the sequence.
Answers
The sequence is defined as
an = 3an - 1 + 7
This means that
a2 = 3(a(2 - 1) + 7
a2 = 3a1 + 7
From the information given ,
a1 = - 4
Thus,
a2 = 3 * - 4 + 7 = - 12 + 7
a2 = - 5
a3 = 3(a(3 - 1) + 7
a3 = 3a2 + 7
a3 = 3 * - 5 + 7 = - 15 + 7
a3 = - 8
a4 = 3(a(4 - 1) + 7
a4 = 3a3 + 7
a4 = 3 * - 8 + 7 = - 24 + 7
a4 = - 17
Thus, the first four terms of the sequence are
- 4, - 5, -
A cake has CIRCUMFERENCE of 20.41 inches. What is the AREA of the cake? Use 3.14 to approximate n. Round to the nearest tenth, but enter it without a label. Enter your answer in the box.
Answers
Circumference of a circle is
\(P=2\times\pi\times r\)where r is the radius, and P the value of circunference or perimeter, then replace P and pi to solve r
\(\begin{gathered} 20.41=2\times3.14\times r \\ 20.41=6.28r \\ \frac{20.41}{6.28}=\frac{6.28}{6.28}r \\ \\ 3.25=r \end{gathered}\)radius is 3.25 inches
Area
Apply formula of the area of a circle
\(A=\pi\times r^2\)repalce pi and r to find the area
\(\begin{gathered} A=3.14\times(3.25)^2 \\ A=3.14\times10.5625 \\ A=33.16625 \end{gathered}\)The rounded value of the area is 33.2 square inches
Calculate the height (in m) of a cliff if it takes 2.41 s for a rock to hit the ground when it is thrown straight up from the cliff with an initial velocity of 8.14 m/s. (Enter a number.)
How long (in s) would it take to reach the ground if it is thrown straight down with the same speed? (Enter a number.)
Answers
The height of the cliff is 7.57m and the time to reach the ground when thrown straight down is 0.814s
What is motion under gravity?Motion under gravity refers to the movement of an object whose vertical motion is affected by the presence of gravity. The force that attracts objects downwards is GRAVITY. In fact, gravity works towards the centre of the Earth.
When an object is moving upward,it is moving against gravity and when it is moving down it is moving with gravity.
from equation of motion
H= ut-1/2gt^2( the object is moving upward)
where h is the height of the cliff and u is the initial velocity and g is acceleration due to gravity
(g=10ms^-2).
therefore h= 8.14×2.41-(1/2×10×2.41)
= 19.62-12.05
h= 7.57m
when the object is thrown Down,
V = u + gt
u will be 0 at top before coming down
V = gt
t= 8.14/10
= 0.814s
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