Answer:
[tex](x^{3} + 9\, x^{2} + 14\, x - 12)[/tex].
Step-by-step explanation:
Let [tex]p(x)[/tex] denote the polynomial in question.
The question states that dividing [tex]p(x)[/tex] by [tex](x + 3)[/tex] gives the quotient [tex](x^{2} + 6\, x - 4)[/tex] (with no remainder.) In other words:
[tex]\displaystyle \frac{p(x)}{x + 3} = x^{2} + 6\, x - 4[/tex].
Multiply both sides by [tex](x + 3)[/tex] to find an expression for the polynomial in question, [tex]p(x)[/tex]:
[tex]p(x) = (x^{2} + 6\, x - 4)\, (x + 3)[/tex].
Expand this expression to obtain:
[tex]\begin{aligned}p(x) &= (x^{2} + 6\, x - 4) \, (x + 3) \\ &= x\, (x^{2} + 6\, x - 4) \\ & \quad + 3\, (x^{2} + 6\, x - 4) \\ &= x^{3} + 6\, x^{2} - 4\, x \\ &\quad + 3\, x^{2} + 18\, x - 12 \\ &= x^{3} + 9\, x^{2} + 14\, x - 12\end{aligned}[/tex].
If the value of a is 8 in f(x)=ax^2 what does the graph look like?
A) a parabola that opens down
B) a parabola that opens up
C) a parabola that opens left
D) a parabola that opens right
Answer:
B
Step-by-step explanation:
Graphs with x^2 look like a U shape as the negative x values will still result in a positive y value since a negative squared is a positive.
Serenity needed to get her computer fixed. She took it to the repair store. The technician at the store worked on the computer for 4.5 hours and charged her $62 for parts. The total was $309.50. What was the cost of labor, per hour?
Answer:
the cost of labor per hour is $55
Step-by-step explanation:
Let C = cost of labor per hour
Let h = hours worked
Let p = cost of parts
Let t = total price
[tex]c = \frac{t - p }{h} \\\\c = \frac{309.50 - 62}{4.5} \\\\c = \frac{247.50}{4.5} \\\\c = 55[/tex]
You roll a number cube once. What is the theoretical probability that you roll a 3 or 1? Enter your answer as a simplified fraction.
Answer:
2/6 or 1/3
Step-by-step explanation:
If it was a average 6 sided cube then 1/3 of the numbers are 3 and one.
the tree diagram represents an experiment consisting two trials
Answer:
0.35
Explanation:
P ( B and D )0.5 * 0.70.35Follow the branch B and then branch D
multiply both the selected probabilities to calculate total probability.Answer:
0.35
Step-by-step explanation:
To find the probability of a sequence of events, multiply along the branches representing those events.
Therefore, P(B and D) = 0.5 x 0.7 = 0.35
** refer to the attached diagram **
PLEASE HELP TAKING TEST RN what are the midline, amplitude, period of this function?
Answer:
midine y=2
amplitude -3
period 5pie
Find the area of each circle with the given radius or diameter. Use 3.14 for pi.
Answer: (Note*: Radius is half of the diameter, so the d = 2 and d = 12 have been converted into radius's instead to solve the problem).
r^2 = 4 in: 50.24 in^2.
r^2 = 2 in: 12.56 in^2.
d = 2 or r^2 = 1 in: 3.14 in^2.
r^2 = 8 in: 200.96 in^2.
d = 12 or r^2 = 6 in: 113.04 in^2.
Step-by-step explanation: To find the area of a circle, you need the radius squared times pi, which is 3.14. The following is solved below:
4^2 x 3.14 = 50.24 in^2.
2^2 x 3.14 = 12.56 in^2.
1^2 x 3.14 = 3.14 in^2.
8^2 x 3.14 = 200.96 in^2.
6^2 x 3.14 = 113.04 in^2.
Therefore, the following above are the answers you need.
Let me know if this is right! :)
Answer:
r = 4.) 50.24
r = 2.) 12.56
d = 2.) 3.14
r = 8.) 200.96
d = 12.) 113.04
Step-by-step explanation:
The formula for finding the area of a circle would be π(pi) x r (radius)²
1.) r = 4
4 x 4 = 16
16 x 3.14 = 50.24
2.) r = 2
2 x 2 = 4
4 x 3.14 = 12.56
3.) d = 2
2 ÷ 2 = 1
1 x 1 = 1
1 x 3.14 = 3.14
4.) r = 8
8 x 8 = 64
64 x 3.14 = 200.96
5.) d = 12
12 ÷ 2 = 6
6 x 6 = 36
36 x 3.14 = 113.04
-kiniwih426
Can someone help me?
Answer:
What are you trying to do you have not Explained to us
Step-by-step explanation:
What is the median of the data represented by the box plot?
A number line ranging from 0 to 143.75 with a box encompassing the numbers 12.5, 20, and 65.
Enter your answer in the box.
Can someone help me with B and D, i’ll give branliest! :)
1 . Maisa is 1.5 m tall and Arman is 175 cm tall . What is the ratio of their heights ?
Please add solution
Thank you so much
Answer:
6:7
Step-by-step explanation:
1.5 m=150 cm
ratio of their hight is 150/175=30/35=6/7
=6:7
The proportion equation is A = 6 : 7
What is Proportion?The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.
The proportional equation is given as y ∝ x
And , y = kx where k is the proportionality constant
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Given data ,
Let the proportion equation be represented as A
Now , the value of A is
The height of Maisa is P = 1.5 m
The value of 1.5 m = 150 cm
And , the height of Arman = 175 cm
So , the proportion is
A = height of Maisa / height of Arman
Substituting the values in the equation , we get
A = 150 / 175
A = 6/7
Therefore , the value of A is 6 : 7
Hence , the proportion is 6 : 7
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#SPJ2
Simplify the radical expression-
I’ll give Brainliest to the first person
Answer:
2ײY²¹ is the Answer
Thank you:)
The perimeter of a rectangle is 52 inches. The rectangle is 15 inches long. How wide
is the rectangle?
22 inches
37 inches
18.5 inches
11 inches
Answer:
11 inches
Step-by-step explanation:
The perimeter of a rectangle is 2*(base) + 2*(height), or P = 2B + 2H
P = 2B + 2H
P = 2B + 2H
52 inches = 2(15 in) + 2H
2H = 22 inches
B = 11 inches
in a sale, the price of a computer is reduced by 20%. At this reduced price the shopkeeper still makes a profit of 20%. What would have been his percentage profit if the computer had been sold at full price?
Based on the price the computer was reduced by and the profit the shopkeeper still made, if the computer was sold at full price, the profit percentage would have been 50%.
What would the profit have been at full price?First assume a price the computer was sold at. We'll go with $100.
At this price, the shopkeeper still made a profit of 20% which means that the cost price was;
= 100 / (1 + 20%)
= $83.33
Based on the discounted price of $100, the full price was:
= 100 / (1 - 20%)
= $125
The profit the shopkeeper would have made is:
= (Full price - Cost price) / Cost price x 100%
= (125 - 83.33) / 83.33 x 100%
= 50%
#SPJ1
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PART A
Mrs. Jackson is planning an outdoor barbeque. She will cook 2 ears of corn per person plus two extra. If 16 people plan to come, how many ears of corn will Mrs. Jackson cook?
Answer:
34
Step-by-step explanation:
2 x 16 + 2
_________
2 x 16 = 32
_________
32 + 2 = 34
Answer:
30 or 64
Step-by-step explanation:
30 Because... 2 corns for every one till they rech 15..
that's mean (2 x 15)
64 Because... 2 corns plus 2 extra if they rech 16....
that's mean (4x16)
a dartboard has a diameter of 16 inches. What are its radius and circumstance? Round to the nearest hundredth. Use 3.14 for pi
The bakers at healthy bakery can make 320 bagels in 10 hours. How many bagels can they make in 15 hours? What was the rate per hour?
[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]
Let's use Unitary method ~
[tex]\qquad \sf \dashrightarrow \:10 \:hr = 320 \: bagels[/tex]
[tex]\qquad \sf \dashrightarrow \: 1\: hr = (320 \div 10) \: bagels[/tex]
[tex]\qquad \sf \dashrightarrow \:1 \: hr = 32 \: bagels[/tex]
So, the rate per hour is 32 bagels ~
[tex]\qquad \sf \dashrightarrow \:15 \: hr = (15 \times 32) \: bagels[/tex]
[tex]\qquad \sf \dashrightarrow \:15 \: hr = 480\: bagels[/tex]
So, they can prepare 480 bagels in 15 hours
Answer:
480 bagels
Step-by-step explanation:
320 bagels in 10 hours.
⇒ 320 bagels = 10 hours
Divide 10 both sides to find the rate per hour:
⇒ 320/10 bagels = 10/10 hours
⇒ 32 bagels = 1 hours
Multiply 15 both sides to find the number of bagels in 15 hours
⇒ 32 bagels = 1 hours
⇒ 32 x 15 bagels = 1 x 15 hours
⇒ 480 bagels = 15 hours
your older sister tells you that you seem to be short for your age. in school, your teacher measured your height and that of your classmates to compute for your BMI. you teacher tells you that your height belongs to the 9th decile in the class. assuming you and your classmates have similar ages, would you agree with what your sister says? why?
Answer:
No.
Step-by-step explanation:
No, because the 9th decitile is equal to the 90th decitile, and so that means that you're tall.
In a times table test, Mr. Dolan's students score 21, 25, 17, 23, 25, 21, 27, 21, and 18 out of a total of 35. Find the measures of center and then type a numerical answer only in spaces below. mean = median = mode =
The measures of center of the students score are:
Mean = 22
Median = 21
Mode = 21
What are Measures of Center?Measures of center of a data distribution are the mean, median, and mode.
Given the data, 21, 25, 17, 23, 25, 21, 27, 21, 18:
Mean = sum of all data values / number of data values = 198/9 = 22
Median = the middle value in the ordered data set = 21
Mode = the most appeared data value = 21 (appeared 3 times)
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A gold bar is similar in shape to a rectangular prism. A gold bar is approximately in. In. In. If the value of gold is per ounce, about how much is one gold bar worth? Use the formula w11. 15n, where w is the weight in ounces and nvolume in cubic inches, to find the weight in ounces. Explain how you found your answer
Answer:
I thnk the answer is in the next question go do that then
Step-by-step explanation:
then come back and figure it out
What is the volume, in cubic in, of a cylinder with a height of 8 in and a base radius of
2 in, to the nearest tenths place?
Answer:
V=100.5
Step-by-step explanation:
hopes this helps
Akeelah makes lanyards for her friends. She uses 12 feet of cord to make a
total of 6 lanyards. Which expresses the unit rate for the length of cord
needed to make one lanyard?
Answer:
2 feet of cord
Step-by-step explanation:
Hey there!
In order to find out what the length of cord needed to make one lanyard, we need to take into consideration how much cord she needed to make for 6 lanyards
It says that she used 12 feet of cord to make 6 lanyards meaning that for one lanyard, she used 2 feet feet of cord to make one lanyard
To find that out, all you need to do is divide the two numbers together to find out how much cord was needed to make one lanyard
So Akeelah needs 2 feet of cord to make one lanyard
GRADE 9 maths! due tonight please help!!
Answer:
Step-by-step explanation:
Which expression is equivalent
Answer:
it should be A i think
Step-by-step explanation:
i used a calculator
-5x-15+25x-30
Help me please
Answer:
[tex]\boxed{\sf{20x-45}}[/tex]
Step-by-step explanation:
To solve this problem, all you have to do is isolate the x from one side of the equation.
-5x-15+25x-30First, you have to combine like terms.
→ -5x+25x-15-30
Then, you subtract the numbers from left to right.
→ -15-30=-45
Rewrite the problem down.
→ -5x+25x-45
By similar, add to elements.
→ -5x+25x=20x
Rewrite the problem down.
⇒ 20x-45
Therefore, the correct answer is 20x-45.I hope this helps you! Let me know if my answer is wrong or not.
Answer:
20x - 45
Step-by-step explanation:
Start by grouping like terms ( -5x and 25x) , ( -15 and -30):
= -5x + 25x - 15 - 30
Subtract the numbers: -15 -30 = -45
= -5x + 25x - 45
Combine like terms ( 5x and 25x):
= 20x - 45
Choose the polynomial written in standard form. x2 4x4 10x6 x4 4x3 10x x7 4x3 10x4 x6 4x3 10x7
The polynomial that is written in standard form out of the given options is given by: Option 2: x^4 + 4x^3 + 10x
What is standard form of a polynomial?Suppose the considered polynomial is of only one variable.
Then, the standard form of that polynomial is the one in which the terms with higher exponents are written on left side to those which have lower exponents.
What are terms in polynomials?Terms are added or subtracted to make a polynomial. They're composed of variables and constants all in multiplication.
Example:
[tex]x^3 + 3x +5[/tex]
is a polynomial consisting 3 terms as [tex]x^3, 3x \: \rm and \: 5[/tex]
Cheking all the options for them being in standard form or not:
Option 1: [tex]x^2 + 4x^4 + 10x^6[/tex]Second term has 4 as exponent, but on its left, the first term has 2 as exponent. So higher expoent holding term is not on left. Thus, this polynomial is not in standard form.
Option 2: [tex]x^4 + 4x^3 + 10x[/tex]4 > 3 > 1 (comparing the exponents), and the terms holding them are also in this order (left to right).
Thus, this polynomial is in standard form.
Option 3: [tex]x^7 + 4x^3 + 10x^4[/tex]Not in standard form because the last term has bigger power then the term on its left.
Option 4: [tex]x^6 + 4x^3 + 10x^7[/tex]Not in standard form because the last term has bigger power then the term on its left.
Thus, the polynomial that is written in standard form out of the given options is given by: Option 2: x^4 + 4x^3 + 10x
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11) Ryan and three friends went to Fridays the bill was $123,42 If they gave an 18 percent tip, how much did they have to pay if they divided the total bill equally?
A linear model is used to determine the amount owed on a loan of $5,000 with simple interest of 4.25%. The model is A = 5000 + 5000(0.0425t), where A is the Amount (total principal plus interest) required to
Use the model to determine how long it would take for the loan amount to reach $7,000. Round to the nearest tenth
Answer:
9.4
Step-by-step explanation:
Hey there!
The question is asking us to use the model to find how long it would take for the loan amount to reach 7,000
In order to answer this, we need to make 7,000 equal to the equation:
7000=5000+5000(0.0425t)
Subtract 5000 from both sides
2000=5000(0.0425t)
Now we simplify the RHS
2000 = 212.5t
Now you divide both sides by 212.5 to get t by itself
t=9.41
So it would take 9.4 months for the loan amount to reach 7000
Which of these pairs are like terms?
20 x, 0.8 x
17, 3 x
14 x, 14 x2
0.5 x, 0.5 y
The pair of algebraic expressions which are like terms is; 20x and 0.8x.
What are like terms?Algebraic expressions are pronounced as like terms if the terms contain the same variable raised to the same exponent.
check all options:
20x, 0.8x
same variable and exponent
17, 3x
Not same variable
14x, 14x²
Same variable, not same exponent
0.5x, 0.5y
Not same variable
On this note, it follows that the terms 20x and 0.8x are like terms.
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Mrs. smith has $1500 in a retirement account earning 5% interest. each year she makes an additional deposit of $500 to her account. after 3 years, what would her account balance be?
Answer:
$3,312.69
Step-by-step explanation:
What she started with: $1500
Year 1: 1500 + 1500(.05) + 500 = $2,075
Year 2: (2.075)1.05 + 500 = $2,678.75
Year 3: (2678.75)1.05 + 500 = $3,312.69
How many groups of tens would represent the value of the digit 4 in the number 14752?
A. 4
B. 40
C. 400
D. 4000
show me why
Answer:
C. 400
Step-by-step explanation:
The number 14752 is "Fourteen thousand, seven hundred and fifty two"
The 1 is the place of ten thousands ⇒ 10,000
The 4 is the place of thousands ⇒ 4,000
The 7 is the place of hundreds ⇒ 700
The 5 is the place of tens ⇒ 50
The 2 is the place of units ⇒ 2
So we need to find how many groups of tens are in 4000.
To do this, divide 4000 by 10.
To divide anything by 10, simply move the decimal point one place to the left.
Therefore, there are 400 groups of ten in 4000
as 400 × 10 = 4000
