Answer:
a = 4 and b = - 30
Step-by-step explanation:
Expand the left side and compare like terms on both sides, that is
(x + 2)(x - 3)(x + 5) ← expand the first pair of factors using FOIL
= (x² - x - 6)(x + 5) ← distribute
= x³ + 5x² - x² - 5x - 6x - 30 ← collect like terms
= x³ + 4x² - 11x - 30
Compare like terms with x³ +ax² - 11x + b
4x² and ax² ⇒ a = 4
+ b and - 30 ⇒ b = - 30
The requried simplified values of a and b are given as 4 and -30 respectively.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
here,
Given expression,
(x+2)(x-3)(x+5) = x³+ax²-11x+b
(x + 2)[x² +2x -15 ] = x³+ax²-11x+b
x³ +4x² -11x - 30 = x³+ax²-11x+b
Comparing both sides,
a = 4 and b = -30
Thus, the requried simplified value of a and b are given as 4 and -30 respectively.
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How many extraneous solutions does the equation below have? StartFraction 9 Over n squared + 1 EndFraction = StartFraction n + 3 Over 4 EndFraction 0 1 2 3
Answer:
a. 0
Step-by-step explanation:
hope this helps!
The solutions to the equation n³+3n²+n-33=0 are n=-11, n=-3, and n=1.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.
Given that, 9/(n²+1) = (n+3)/4.
Here, 9×4=(n²+1)×(n+3)
36=n²(n+3)+1(n+3)
36=n³+3n²+n+3
n³+3n²+n+3-36=0
n³+3n²+n-33=0
The equation n³+3n²+n-33=0 can be solved by factoring. The factors of -33 are -1 and 33. Since the coefficient of the n³ term is 1, this means that n-1 and n+33 are factors of the equation.
Dividing both sides of the equation by n-1, we get:
n²+3n+33/(n-1)=0
Factorizing the numerator, we get:
(n+11)(n+3)=0
Solving this equation, we get n=-11 and n=-3.
Therefore, the solutions to the equation n³+3n²+n-33=0 are n=-11, n=-3, and n=1.
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Solve for Q. Reduce any fractions to lowest terms. Don’t round your answer, I don’t use mixed fractions.
50q + 43 > -11q +70
Answer:
q > 27/61
Step-by-step explanation:
50q + 43 > -11q +70
Add 11 q to each side
50q+11q + 43 > -11q+11q +70
61q +43 > 70
Subtract 43 from each side
61q+43-43 > 70-43
61q > 27
Divide each side by 61
61q/61 >27/61
q > 27/61
Answer:
q > 27/61
Step-by-step explanation:
hope this helps!!
SOMEONE HELP PLSSS
suppose your friends parents invest $10,000 in an account paying 5% compounded annually. what will the balance be after 5 years?
Answer:
12,762.82$
Step-by-step explanation:
10,000(1+0.05)^5
2. Use the image below to answer the question.
D
E
F
Using the segment addition postulate, find the length of segment EF.
Answer:
26
Step-by-step explanation:
I subtracted DF and DE to find the missing difference for the segment EF. I'm not sure if this is correct though. I hope it helps.
The length of line segment EF is 26.
What is a line segment ?A line segment is a subset of a line which has two endpoints.
A ray has one end point and extends indefinitely on the other direction.
A line extends indefinitely on both of it's directions.
From the given data
Line segment DF has a length 38 and line segment DE has a length 12.
To find the length of line segment EF we have to subtract the length of line segment DE from length segment DF.
∴ EF = DF - DE
EF = 38 - 12'
EF = 26.
So, the line segment EF has a length of 26.
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If g(x) = x^2, find g (3)
Answer:
g(3)=9
Step-by-step explanation:
We want to find what g(x), or y is, when x is equal to 3.
Therefore, we can substitute 3 in for x in the equation
g(x)=x^2
g(3)=3^2
Evaluate the exponent
g(3)=3*3
g(3)=9
PLEASE HELP!!
The figure is made up of a rectangle and 2 right triangles.
What is the area of the figure?
O 1259 units2
O 1292 units2
O 1413 units2
O 1566 units2
The rectangle is 28×34 and the two triangles are (1/2) 11 (28) and (1/2) (9)(34)
A = 28(34) + (1/2) 11 (28) + (1/2) (9)(34)
A = 1259
Answer: 1259 sq units
helpppppppppppppp meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee plzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz ASAP
Answer:
7x=42
Solve:
7x=42
7x=42/7
/7
x = 6
6 is the maximum cost lisa can spend for each party favor bag.
How to do the problem and what the answer is this thing is due today(30 points!)
Answer:
40°
Step-by-step explanation:
complementary angels makes the sum of two angles = 90°
so
<ABC + < CBD = 90°
if <ABC = 50°
then 90° - 50° = 40°
6 Trendy T-Shirts has decided to manufacture a new design. It will
cost $400 plus $3 per shirt to produce them, and Trendy plans to
spend $5000 on advertising. The shirts will sell for $12 each.
A. How many shirts must be sold to break even (total cost equals
income from sales)?
B. What is Trendy's income (or total cost) for that many shirts?
Answer:
A)
400+3x+5000=12x
5400 = 9x
x =600
B)
Profit: zero (break even)
Total cost or Income from 600 Sales: $7200
The dimensions of a figure are doubled, how many times larger will the volume be? Only enter numerical answers
Answer:if you double all of the dimensions of a rectangular prism, you create a similar prism with a scale factor of 2. The surface area of the similar prism will increase as the square of the scale factor (22 = 4) and the volume will increase as the cube of the scale factor (23 = 8).
Step-by-step explanation:
Scale factor are used to increase or diminish the original figrure. The new volume will be 8times larger than the initial volum
Scale factorsScale factor are used to increase or diminish the original figrure.
Assume the original dimension of the figure is a, b and c, the volume of te figure will be expresed as:
A = length * width * heiht
A = abc
If the measure of the sides are doubled, hence;
New volume = 2a * 2b * 2c
New volume = 8abc
Ratio = 8abc/abc
Ratio = 8
Hence the new volume will be 8times larger than the initial volume
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Marcus realized that he misplaced his credit card and that it may have been stolen. He was worried that it could be misused. He called the credit
card company and notified them that the card had been misplaced. A few hours later, he got a text message stating that a purchase of $1,650
had been made using his card. He called the credit card company again and reported this fraudulent transaction. He also informed them that he
had notified them the card was missing before the fraudulent transaction was made. The credit card company official reassured Marcus that he would not have to pay this amount. Which law protects Marcus in this scenario?
A. Federal Trade Commission Act
B. Fair Debt Collection Practices Act
C. Fair Credit Billing Act
D. Dodd-Frank Wall Street Reform and Consumer Protection Act
Answer:
C. Fair Credit Billing Act
Step-by-step explanation:PLATO
Which expression is equivalent to ? Assume that the denominator does not equal zero.
Answer:
A) 4ab^2
Step-by-step explanation:
19*4 = 76
(a^2*b^3)/(a*b) = a*b^2
Implies, option A.
What is the volume of a cylinder, in cubic inches, with a height of 2 inches and a base diameter of 4 inches? Round to the nearest tenths place
Answer:
the answer for the volume of the cylinder is V≈25.13in³
Answer:
h=2 d=4
r=4/2 , radius is half of the diameter
r=2
V=π r^2h
V= π x (2)²×2
substitute variables into formula V=25.132741228718
the nearest tenths place V=25.1 inches
Jay borrows $8,000 at a rate of 1.9% interest per year. What is the amount due at the end of 6 years if the interest is compounded continuously?
$8,965.21
$10,027.21
$8,966.02
$25,014.15
Pleeeease show your work on how you solved it because I keep getting 8,962.90 which isn't an option and last time I asked this question, no one explained how to solve it
Interest formula: A = Pe^rt
A = amount
P = principal amount
r = interest rate
t = time
We know that in the question we have:
P = 8,000
r = 0.019
t = 6
Now, solve with the given values:
A = 8000e^(0.019*6)
A = 8000e^(0.114)
A = 8966.016...
Round to the nearest hundredth:
8966.016... → 8,966.02
Therefore, the answer is [ $8,966.02 ]
Best of Luck!
Answer:
$8,966.02
Step-by-step explanation:
Amount = 8000 × e^(6 × 1.9/100)
Amount = 8000 × e^0.114
Amount = 8966.016999
Joseph's company offers a reimbursement package of $0.45 per mile plus
$175 a year for maintenance. If x represents the number of miles, which
equation below models C the total amount of reimbursement the company
offers?
•A. C = 0.45 + 175x
•B. C = 0.45x + 175
•C. C = 45 + 175x
•D. C = 45x + 175
Answer:
B
Step-by-step explanation:
175 is the yearly cost which is the constant
The cost is related to the miles so that’s why they’re multiplied together
The total amount of reimbursement the company offers will be C = 0.45x + 175. Then the correct option is B.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
Joseph's company offers a reimbursement package of $0.45 per mile plus $175 a year for maintenance.
Let 'x' be the number of miles and 'C' be the number total amount. Then the equation of the line is given as,
C = 0.45x + 175
The total amount of reimbursement the company offers will be C = 0.45x + 175. Then the correct option is B.
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−2y<8
y<−8
y<−4
y>−8
y>−4
Answer:
y > -4
Step-by-step explanation:
−2y<8
Divide each side by -2, remembering to flip the inequality since we are dividing by a negative
-2y/-2 > 8/-2
y > -4
Answer:
Last option
y > -4
Step-by-step explanation:
-2y < 8
Switch sides
-8 < 2y
-4 < y
Or
y > -4
Find def, help geometry
Answer:
d
Step-by-step explanation:
1/2 +2/6
A)
1
_
6
B)
3
_
8
C)
5
_
6
D)
5
_
5
So the right answer is 5/6.
Look at the attached picture
Hope it will help you
Good luck on your assignment
Answer:
[tex] \frac{5}{6} [/tex]
Answer C is correct.Step-by-step explanation:
[tex] \frac{1}{2} + \frac{2}{6} \\ \frac{6 + 4}{6 \times 2} \\ \frac{10}{12} \frac{ \div 2}{ \div 2} \\ = \frac{5}{6} [/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
Please do this for points and brainleyst awnser
Write the expression: 3 divided by the sum of x and 9. A) 3 + 9 x B) x 3 + 9 C) x + 9 3 D) 3 x + 9
What is the product of 2x + y and 5x – y + 3?
Answer:10x^2+11xy-6y^2
Step-by-step explanation:
( 2 x + 3 y ) ( 5 x − 2 y ) = 2 x ( 5 x − 2 y ) + 3 y ( 5 x − 2 y )
= 10 x 2 − 4 x y + 15 x y − 6y 2
= 10 x 2 + 11 x y -6 y 2 .
Question 1 of 10
2 Points
Harry took out an 80/20 mortgage to buy a house costing $175,000. The first
(80%) mortgage has an interest rate of 4.75%, and the second (20%)
mortgage has an interest rate of 7.525%. Both the first mortgage and the
second mortgage are 30-year fixed-rate mortgages. What is his total
mortgage payment for this house?
A. $730.31
B. $975.63
C. $245.32
D. $805.87
Answer:
Its b got it correct
The total monthly mortgage payment for the house is $975.63
What is percentage?A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.
here, we have,
The principle amount is $175000
80% of 175000 is = = $140000
20% of 175000 is = = $35000
Emi formula is :
p*r*(1-r)^n/(1-r)^n-1
For 1st part:
p = 140000
r = 4.75/12/100=0.00395
n = 360
Putting values in formula we get
= $729.508
For 2nd part:
p = 35000
r = 7.525/12/100=0.00627
n = 360
Putting values in formula we get
= $245.301
Adding both the monthly payments:
974.809 dollars
This is closest to option A.
So, option A is the answer.
And for 30 years the mortgage payment will be = 351226.80 dollars
Hence, The total monthly mortgage payment for the house is $975.63.
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Which of the following properly describe “slope”?
Answer:
#3 1/2
Step-by-step explanation:
if you start where the line and the boxes in the graph line up like at (0,-2) and then you go up 1 and right 2 the line will be there again line up with the boxes and since slope is rise/run it is 1/2
Which number is divisible by 5
A 44
B 125
C 116
D 114
Answer:
B
Step-by-step explanation:
A group of friends went to play minigolf at Adventureland. Anna's score was 26 putts, Daniela's score was 313131 putts, Luiza's score was 39 putts, and Vera's score was 32 putts.
Find the mean absolute deviation (MAD) of the data set.
Answer:
3.5
Step-by-step explanation:
1 / 3
First, let's find the mean.
\dfrac{26+31+39+32}{4} = \dfrac{128}{4}= \blueD{32} \text{ putts}
4
26+31+39+32
=
4
128
=32 puttsstart fraction, 26, plus, 31, plus, 39, plus, 32, divided by, 4, end fraction, equals, start fraction, 128, divided by, 4, end fraction, equals, start color #11accd, 32, end color #11accd, start text, space, p, u, t, t, s, end text
Hint #22 / 3
Next, let's find the distance each data point is from the mean.
Data point Distance from the mean
262626 \blueD{32}-26 = 632−26=6start color #11accd, 32, end color #11accd, minus, 26, equals, 6
313131 \blueD{32}-31 = 132−31=1start color #11accd, 32, end color #11accd, minus, 31, equals, 1
393939 39-\blueD{32} = 739−32=739, minus, start color #11accd, 32, end color #11accd, equals, 7
323232 32-\blueD{32} = 032−32=032, minus, start color #11accd, 32, end color #11accd, equals, 0
Hint #33 / 3
The mean absolute deviation (MAD) is the mean of the distances from the mean.
\dfrac{6+1+7+0}{4} = \dfrac{14}{4}= 3.5\text{ putts}
4
6+1+7+0
=
4
14
=3.5 putts I hope it helps.
Find the mean,median and range of the following list of values and choose the correct result.
8, 9, 10, 10, 10, 11, 11, 11, 12, 13
Mean: 10.5
Median: 10.5
Range: 5
--------------------------------------------
To find the mean you order the numbers then add then divide.
Add
8+9+10+10+10+11+11+11+12+13=105
Divide
105÷10=10.5
Mean = 10.5
--------------------------------------------
Finding the median essentially involves finding the value in a data sample that has a physical location between the rest of the numbers.
Find the middle number. Put your left finger on 8 and your right finger on 13. Move your left finger to the right to 10 and move your right finger to 11.
the middle number is 10.5 so therefore it is the median.
--------------------------------------------
To find the range you subtract the biggest number to the smallest number.
Subtract
13-8=5
Therefore 5 is the range
Answer:
The median is 10.5 the range is 5 and the mean is 10.5
Step-by-step explanation:
To find the median you have to cross out each number till you get 2 since there are 10 numbers together then add 10 and 11 and get 21 divide by 2 which gives you 10.5 to find the mean add all the numbers then divide 105 by 10 and get 10.5 to find the range take 13-8 and get 5
the inverse of this equation
Answer:
[tex]{f}^{ - 1}(x) = \frac{x + 11}{ - 5} [/tex]
Step-by-step explanation:
[tex]f(x) = - 5x - 11 \\ - 5x - 11 =x \\ - 5x = x + 11 \\ {f}^{ - 1}(x) = \frac{x + 11}{ - 5} [/tex]
Olivia flips a two-sided counter and then spins a spinner with six equal-size sections labeled 1 through 6. One side of the counter is red. The other side is yellow. She performs this experiment 80 times. The relative frequency of tossing red and spinning a number greater than three was 25 . What is the difference between the number of expected outcomes and the number of actual outcomes?
Answer:
The difference between the number of expected outcomes and the number of actual outcomes = 5
Step-by-step explanation:
She tosses a two sided counter and spins a spinner with six equal sized sections numbered 1 to 6.
Probability of the counter landing on either of the two sides is exactly = (1/2)
Probability of the counter landing on the red side = (1/2)
Probability of the spinner landing in a region greater than 3 = Probability of the spinner landing in a region of 4, 5 or 6. = (3/6) = (1/2)
In one toss and spin, the probability of a toss landing on red and the spinner landing on a number greater than 3 = p = (1/2)×(1/2)
p = (1/4)
Expected number of times that a toss will land on a red and a spinner will land on a number greater than 3 in 80 trials
= np = 80 × (1/4) = 20
Number of actual times that the toss lands on a red and a spinner lands on a number greater than 3 in 80 trials = 25
The difference between the number of expected outcomes and the number of actual outcomes = 25 - 20 = 5
Hope this Helps!!!
Please help with this
Answer:
C. [tex]c = \frac{-7+-\sqrt{129} }{8}[/tex]
Step-by-step explanation:
Before we start, you can think of the variable "c," as x.
The quadratic formula/equation is:
[tex]x = \frac{-b+-\sqrt{b^2-4ac} }{2a}[/tex]
The setup is:
[tex]ax^2+bx+c=0[/tex]
[tex]4c^2+7c-5=0[/tex]
Plug in the numbers accordingly to the letter associated, like so:
[tex]x = \frac{-7+-\sqrt{7^2-4(4)(-5)} }{2(4)}[/tex]
[tex]x = \frac{-7+-\sqrt{49+80} }{8}[/tex]
[tex]x = \frac{-7+-\sqrt{129} }{8}[/tex]
What is the solution to the equation = 3?
x = 1
x = 3
x = 9
x = 27
Multiply both sides by 9.
x/9 = 3
(x/9) * (9) = (3) * (9)
x=27
The solution of the expression x/9 = 3 is,
⇒ x = 27
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
We have to given that;
The expression is,
⇒ x/9 = 3
Now, Simplify the expression as;
⇒ x/9 = 3
Multiply by 9, we get;
⇒ 9 × x/9 = 9 × 3
⇒ x = 27
Thus, The solution is,
⇒ x = 27
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