Answer:
f(x) = x^3 - x^2 -2x
Step-by-step explanation:
If x = a is a zero of a polynomial, then x-a is a factor of the polynomial. Given the factors of a polynomial, the polynomial can be obtained by multiplying the factors.
The factors of the given polynomial are;
x - 2
x + 1
x
Multiplying the first two factors;
(x-2)(x+1) = x^2 + x -2x -2
= x^2 -x -2
We finally multiply this result by x to obtain our polynomial;
f(x) = x ( x^2 -x -2)
= x^3 - x^2 -2x
which is a cubic polynomial since it has 3 roots.
Answer:
f(x) = x³ - x² - 2x
Step-by-step explanation:
given a polynomial with zeros x = a, x = b, x = c
Then the factors are (x - a), (x - b) and (x - c)
and the polynomial is the product of the factors, that is
f(x) = k(x - a)(x - b)(x - c) ← where k is a multiplier
--------------------------------------------------------------------
Here the zeros are x = 2, x = - 1 and x = 0, thus the factors are
(x - 2), (x + 1) and (x - 0) , thus
y = kx(x - 2)(x + 1) ← let k = 1 and expand factors
= x(x² - x - 2) = x³ - x² - 2x
Hence a possible polynomial is
f(x) = x³ - x² - 2x
a bag of cement mix has a mass of 15.6 kilograms which number sentence will tell how many grams of mass the bag of cement mix has
A 15.6 x 1,000
B15.6 ÷ 100
C15.6 ÷1,000
D15.6 x 100
Answer:
Option A. 15.6 x 1,000
Step-by-step explanation:
we have that
A bag of cement mix has a mass of 15.6 kilograms
Remember that
1 kg=1,000 g
Convert Kg to g
15.6 kg=15.6*1,000=15,600 g
Anissa is considering buying her first home. The house she is interested in buying is priced at $139,000. Anissa qualifies for a 30-year mortgage at 6.45%. What will be her monthly mortgage payment?
Answer:
A
Step-by-step explanation:
Answer:
The correct answer is option A.
Step-by-step explanation:
The EMI formula is ::
[tex]\frac{p*r*(1+r)^{n} }{(1+r)^{n}-1 }[/tex]
Here,
p = 139000
r = [tex]6.45/12/100=0.005375[/tex]
n = [tex]30*12=360[/tex]
Now, putting these values in formula we get,
[tex]\frac{139000*0.005375*(1+0.005375)^{360} }{(1+0.005375)^{360}-1 }[/tex]
[tex]\frac{139000*0.005375*(1.005375)^{360} }{(1.005375)^{360}-1 }[/tex]
= $874.01
Therefore, option A is the answer.
Match the measureable quantity giving by its formula with the appropriate unit(s)
volume =(length)(width)(height)
area = (length)(width)
speed= distance/time
perimeter=2 (length)+2 (width)
cubic centimeters
square meter
meter per second
meter
Answer:
See explanation
Step-by-step explanation:
Volume is three dimensional so it is measured in cubic units
Volume =(length)(width)(height) [tex]\to[/tex] cubic centimeters
Area is two dimensional, it is measured in square units.
Area = (length)(width) [tex]\to[/tex] square meter
Speed is derived from two basic quantities (length and time). It is measured is meters per seconds.
Speed= distance/time [tex]\to[/tex] meter per second
Perimeter is distance around an object. It is measured in meters
Perimeter=2 (length)+2 (width) [tex]\to[/tex] meter
Matching Quantities with Units
How much more would $5,656.30 earn in 5 years, compounded monthly at 4.1%, when compared to the interest on $5,656.30 over 5 years, at 4.1% compounded quarterly?
Answer:
[tex]\$4.81[/tex]
Step-by-step explanation:
we know that
The compound interest formula is equal to
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
step 1
in this problem we have
[tex]t=5\ years\\ P=\$5,656.30\\ r=0.041\\n=12[/tex]
substitute in the formula above
[tex]A=\$5,656.30(1+\frac{0.041}{12})^{12*5}=\$6,940.82[/tex]
step 2
in this problem we have
[tex]t=5\ years\\ P=\$5,656.30\\ r=0.041\\n=4[/tex]
substitute in the formula above
[tex]A=\$5,656.30(1+\frac{0.041}{4})^{4*5}=\$6,936.01[/tex]
step 3
Find the difference
[tex]\$6,940.82-\$6,936.01=\$4.81[/tex]
What is the area of the trapezoid below? 30 POINTS!!!
Answer:
180 units²
Step-by-step explanation:
Let's find the length of the dashed line (which is the length of the trapezoid). Use the Pythagorean Theorem:
7² + h² = 25², or h² = 625 - 49 = 576. Thus, h = √576 = 24.
The average width of the trapezoid is:
(7+4) + 4
w = ---------------- = 15/2
2
The area of a trapezoid is (average width of trapezoid)(length of trapezoid), and here that comes to:
15
A = -------- * 24 = 180 units²
2
Hope this help!!!
Have a nice day!!!
Sorry for all the late night / early morning questions running on three days with little sleep trying to graduate
Answer:
measure of angle R is 75.897° or 75.90°.
Step-by-step explanation:
To solve use the formula Sin A/ a= Sin B/ b. our angle A is 52°, opposite it is side a so 26. Let angle R be our B so opposite it is b which measure 32.
sin 52°/26 = Sin B/32, cross multiply
32 (sin 52°) = 26 Sin B, multiply both side by 1/26
32 (sin 52°)/26 = Sin B
32 (0.78880107536...)/26 = Sin B
0.969593891... = Sin B
Sin^-1 (0.969593891..) = B
B = 75.89703075 or Angle R is 75.90°
What is the difference between a sequence and a series? What is the difference between a geometric and an arithmetic sequence?
Answer:
Sequence: ordered list of numbers
Series: sum of the terms of a sequence
Arithmetic sequence: the difference between the terms is constant
Geometric Sequence: the ratio between the terms is constant
Step-by-step explanation:
The difference between a series and a sequence is that a sequence is a list of numbers that follow a pattern or rule.
For example
1, 3, 5, 7, 9...
[tex]a_n = 1 +2(n-1)[/tex]
On the other hand, a series is the sum of the terms of a sequence.
1 + 3 + 5 + 7 + 9 + ...+ n
[tex]\sum_{n=1}1 +2 (n-1)[/tex]
----------------------------------------------------------------------------------
The difference between an arithmetic sequence and a geometric sequence is that:
for the arithmetic sequences the subtraction of:
[tex]a_n - a_{n-1} = d[/tex]
Where d is a constant called difference..
In the Arithmetic sequence the difference between the terms is constant
For the geometric sequences, it is satisfied that the quotient between two consecutive terms is:
[tex]\frac{a_{n-1}}{a_n} = r[/tex]
Where r is a constant value called common ratio
In geometric Sequence the ratio between the terms is constant
Final answer:
A sequence is an ordered list of numbers, while a series is the sum of the terms of a sequence. An arithmetic sequence has a constant difference between terms, while a geometric sequence has a constant ratio.
Explanation:
Difference Between Sequence and Series
A sequence is an ordered list of numbers following a specific pattern, while a series is the sum of the terms of a sequence. For example, in the sequence 2, 4, 6, 8, ..., each term is 2 more than the previous term. However, when these terms are added together, for instance, 2 + 4 + 6 + 8, we get a series.
Difference Between Geometric and Arithmetic Sequences
An arithmetic sequence is characterized by a constant difference between consecutive terms. For example, the sequence 3, 7, 11, 15, ... has a common difference of 4. On the other hand, a geometric sequence has a common ratio between consecutive terms, such as the sequence 2, 6, 18, 54, ... where each term is 3 times the previous term.
Don’t understand this question pllsss helppp
Answer:
A. -50
Step-by-step explanation:
The question is asking you to find the Y point as they gave you the X.
(0,-50). -50 on the y-axis explains the x of 0. If you though it was 14 or -6, it is not because they have the x of -6 and the y of 0.
Answer:
C. 14
Step-by-step explanation:
The given graph represents a polynomial function r(x).
We want to find an x-value that satisfies
r(x)=0.
The solution to the function whose graph is shown are the x-intercepts of the graph.
We can read from the graph that, the x-intercepts are;
[tex]-6[/tex] and [tex]14[/tex].
Hence the solutions are x=-6 and x=14.
From the given options a solution to r(x) is 14.
The correct choice is C
give me a list of factors for 50?
Answer:
1, 2, 5, 10, 25, 50
Step-by-step explanation:
Janie has 12 pieces of 8 pieces of fruit are bananas
Answer:
2/3 of the fruits are bananas. :)
Step-by-step explanation:
What is the sign of the third term of the expansion of (x - y)n for n = 3, 4, and 5?
a.
positive
b.
negative
ANSWER
a.
positive
EXPLANATION
The given binomial expansion is:
[tex] {(x - y)}^{n} [/tex]
We can see that the second term is negative (-y).
When we expand this binomial for n=3,4, and 5, the sign is got to alternate.
The first term is positive
The second term negative
The third term is positive
The first choice is correct.
Answer:
A;)
Step-by-step explanation:i dont have negative sign
The line plot shows the weights of packages of meat available at a grocery store. The 3 lightest packages cost $4.40 per pound. The remaining packages cost $4.80 per pound. If a customer buys all available packages, how much does she spend? Choose the numbers to complete the statements.
Answer:
$42.40
Step-by-step explanation:
The horizontal axis is in fractions.
The three lightest are two [tex]\frac{5}{8}[/tex] pounds & one [tex]\frac{6}{8}[/tex] pounds. Each cost $4.40 per pound.
So cost = 4.40(5/8+5/8+6/8) = $8.8
Remaining costs 4.80 per pound. We add up the remaining and multiply by 4.80 to get their cost.
cost = [tex]4.80(1+1\frac{1}{8}+1\frac{1}{8}+1\frac{1}{8}+1\frac{2}{8}+1\frac{3}{8})=33.6[/tex]
Hence, total cost = 8.8 + 33.6 = $42.40
Answer:
40.40 is actually the answer for the last one and the first one is 8.80
then the second one is 33.60 so yw
Step-by-step explanation:
Which expression can be used to determine the reference angle for an angle, x, measuring 150°?
Answer:
To find the reference angle measuring x for angle in Quadrant II the formula is:
180° - x = 180° - 150° = 30°
Answer: the reference angle is 30°
The expression we can use to determine the reference angle for an angle, x, measuring 150° is 180°-X=150°
⇒ X=180°-150°
What is the angle? In geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle. angles mean “corner”. The two rays are called the sides of an angle, and the common endpoint is called the vertex.An angle is formed when two straight lines or rays meet at a common endpoint.Learn more about angle here:-https://brainly.com/question/25716982
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Need help please brainliest and 50 points
The slope is 2/-2, so -1. The y-intercept is 2. So, y=-x+2
what is the solution to the system graphed below? (1,1) (1,-1) (-1,1) (-1,-1)
Answer:
(-1, -1)
Step-by-step explanation:
The two lines intersect in the third quadrant, at (-1, -1), so that is the solution.
The solution to the system graphed below is (-1,-1) which is option D.
What is a graph?It is a collection of various points and it is used to draw lines of different functions or equations by finding out two points and by joining them.
How to identify points on the graph?We have to check solution of the system graphed in the question. There are two lines graphed. Both are intersecting each other at one point. A solution of a line exists at a point where they are intersecting. If we try to find the point then we need to identify origin first and then according to x and y axis points will be found. The required points will be (-1,-1).
Hence the solution of graphed system is (-1,-1).
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Help i'm not good at finding other measurements!!
A triangle has an area of 221.16 square inches. The height of the triangle is 29.1 inches. What is the length of the triangle?
Answer:
15.2
Step-by-step explanation:
A spherical boulder is 14 ft in diameter and weighs almost 6 tons. Find the volume. Use 3.14 for pi.
To find volume, we will use the following equation: V=4/3piR^3
The correct answer should be 1436.76
The volume of the spherical boulder will be 1,436.027 cubic feet.
What is the volume of the sphere?Let r be the radius of the sphere. Then the volume of the sphere will be given as,
V = 4/3 πr³ cubic units
A spherical boulder is 14 ft in diameter. Then the radius is calculated as,
r = d / 2
r = 14 / 2
r = 7 feet
Then the volume of the spherical boulder is calculated as,
V = 4/3 πr³
V = 4/3 x 3.14 x 7³
V = 1,436.027 cubic feet
The volume of the spherical boulder will be 1,436.027 cubic feet.
More about the volume of the sphere link is given below.
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Which equation is NOT a linear? function
Answer:
Step-by-step explanation:
A linear function involves two variables which are in their first power form, such as x and y.
A nonlinear function may include two variables, one or more of which are of the 2nd or higher power.
Unfortunately, you did not share the possible answer choices, so I cannot be more specific. I'd suggest you repost this question, with answer choices, if you still want guidance here.
y = x^2 - 2 is NOT a linear function, because of that power (2). Note how all the other choices show x to the 1st power.
A linear function is represented by an equation in the form y = a + bx and generates a straight line when plotted on a graph. Any equation that does not fit this form, such as quadratic, exponential, trigonometric, or inverse functions, which generate curves when plotted, are not linear functions.
Explanation:The question asks which equation is not a linear function. A linear function is one that can be represented by an equation in the form y = a + bx, where 'a' and 'b' are constants and 'x' is the independent variable. This form of function generates a straight line when plotted on a graph, with 'b' representing the slope of the line and 'a' representing the y-intercept, where the line crosses the y-axis.
An equation that does not fit this form is not a linear function. For instance, a quadratic function, represented by a second-order polynomial equation such as y = ax^2 + bx + c, is not linear. These types of equations generate curves when plotted on a graph, not straight lines.
Futhermore, any other function types such as exponential, trigonometric, or inverse, which generate curves that are not straight lines when plotted, are also not linear functions.
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What information does the mode of a data set provide?
Answer:
The frequency of a number
Step-by-step explanation:
The mode in a data set provides how frequent a number in a data set appears.
For example, take the following data set:
1, 2, 2, 3, 3, 3, 3, 4, 5, 6, 7, 7, 8, 8, 8, 9, 10
The mode of this data set would be 3.
This is because 3 is repeated more frequently in the data set than any other number.
1, 2, 2, 3, 3, 3, 3, 4, 5, 6, 7, 7, 8, 8, 8, 9, 10
I hope this helps!
Which triangle has a bigger area:
1. A triangle with sides measuring 300, 400, and 500.
2. A triangle with sides measuring 300, 400, and 700.
The 2nd triangle has a bigger area, because since it has 2 sides that are equal to the first and its 3rd side is larger than the 1st triangle, it would have larger area, because it would have to have a larger area to have a larger side.
Answer:
Which triangle has a bigger area:
1. A triangle with sides measuring 300, 400, and 500.
2. A triangle with sides measuring 300, 400, and 700.
Step-by-step explanation:
The second triangle has the largest area, because although the two triangles have two sides with the same size, the third is larger in the second triangle, 700 of the second, versus 500 of the first, and hence the area is also greater than in the first.
If someone could help me with this it would be much appreciated as it is gcse practise and I don’t get it
Answer:
Bryan's answer is wrong because when we calculate the equation, the product will not be 36, since 2³ will be equal to 8, and 3² will be equal to 9, the product of 8 and 9 is 72, twice as much as the result we needed.
The correct equation here should be: 2² × 3² = 36
2² × 3² = 4 × 9 = 36
SHORT ANSWER: 36
HOPE IT HELPS LOVE.
Solve for y
220-y = 29
Answer:
y = 191
Have a great day :)
Hope this helps !
5INGH
Step-by-step explanation:
220 - y = 29
( - 220 from both sides )
- y = - 191
( × -1 on both sides )
y = 191
Answer:
y= 191
Step-by-step explanation:
This is a one step process:
Subtract 220 from both sides to get y by itself, and you have your answer! (since both sides are negative mulltipy both, to get a positive solution)
Find the volume of a rectangular prism that is 8 inches high, 12 inches long, and 5 inches wide.
A
360 in.³
B
480 in.³
C
420 in.³
D
240 in.³
Answer:
B 480 in.³
Step-by-step explanation:
Volume of a rectangular prism is given by
V = l*w*h
V = 8*12*5
V =480 in ^3
Lance's shoe collection is made up of Nike's and Adidas. Altogether , he has 17 pairs of shoes, but he has 3 more Nikes than he has Adidas. How many does he have of each pair?
Write two equations
state your solution
Answer:
Adidas pairs are 7, nikes are 10
Step-by-step explanation:
10n+7a=shoes total
7x+3=Nikes x=7
Carl bought 19 apples or 2 different varieties to make pies. The total cost of apples was $51.00. Granny Smith apples cost $3.00 per pound and Gala apples cost $2.50 per pound. How man pounds of Granny apples did Carl buy?
Answer:
12 Granny Smith and 7 Gala apples (total 19 apples)
Explanation:
Let me put this equation first:
X: number of Granny Smith apples
(19-X): number of Gala apples
cos
t
=
X
⋅
0.25
+
(
19
−
X
)
⋅
0.30
5.10
=
0.25
X
+
5.70
−
0.30
X
5.10
−
5.70
=
−
0.05
X
−
0.60
=
−
0.05
X
and
X
=
12
Number of Granny Smith apples is 12.
The rest (19-12) is number of Gala apples. Number of Gala apples is 7.
This satisfies your equation.
Number of Granny Smith apples 12 and number of Gala apples is 7.
What’s the answer!!! Please help ASAP
Answer: It equals y to the twentieth power.
Step-by-step explanation: when you have a power to a power, like this example, it's essentially saying, y to the power of 4 times y to the power of four times times y to the power of 4 times y to the power of 4 times y to the power of 4, so y to the fourth is being repeated 5 times, so just multiply 5*4 to get 20.
Answer:
y²⁰
Step-by-step explanation:
(y⁵)⁴ is the same as writing y⁵×y⁵×y⁵×y⁵ 4 times. For the exponent, all you have to do is add all the 5's and you'll get y²⁰. I hope this helps:)
a number cube is rolled and a coin is tossed what is the probability that a number greater than four is rolled and the coin comes up heads
Answer:
[tex]\frac{1}{6}[/tex]
Step-by-step explanation:
In probability, "AND" means "multiplication" and "OR" means "addition".
Here, we are looking for probability of number greater than 4 "AND" probability of heads
so we find the individual probabilities and "multiply".
There are 6 numbers in a cube and number greater than four are 5 & 6, so 2 numbers. Hence
Probability of number greater than 4 is 2/6 = 1/3
Now,
In coin there is only head and tail, so probability of coming up heads is 1/2
Now we multiply both:
1/3 * 1/2 = 1/6
Hence
probability that a number greater than four is rolled and the coin comes up heads is 1/6
Which form of payment can you lose and NOT get your money back?
Debit Card
Credit Card
Check
Cash
Answer:
cash
Step-by-step explanation:
You cannot get your money back once you lose cash since it's not connected to any bank or financial institution, unlike debit cards, credit cards, or checks.
Explanation:The form of payment that you can lose and not get your money back is cash. When you lose cash, there is no way to trace it or stop it like you can with a check, debit, or credit card. This is because cash is not linked to any banking or financial institution, so no protections are in place to recover lost or stolen cash. On the other hand, if you lose a debit card, credit card, or check, you can immediately inform your bank or card issuer to freeze your account or cancel the check, thereby protecting your money.
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A sample of a population of 100 students is collected. Five students playing dodge ball at recess are asked if they prefer playing outdoors or indoors. Which of the following is not true of the sample?
The sample is not large enough.
The question is biased.
The sample is not random.
The students are not part of the population.
Answer:
D. The students are not part of the population
Step-by-step explanation:
The first three options are true of this sample. D is the only option that is not true.
Answer:
The students are not part of the population.
Step-by-step explanation:
lena made $90 for 5hours of work at the rate how many hours would she have to work to make 324$
hiii
here is the solution
hope it helps