The polynomial equation x³ + 2x² + 4x+8 can be expressed as the method of factor polynomial exists (x² + 4)(x + 2).
What is a factoring method?The factoring process concerns removing factors from an experiment and then using them in the analytical method of factor analysis.
Polynomials exist as expressions with one or more terms with a non-zero coefficient. A polynomial can contain more than one term.
A mathematical expression of one or more additional algebraic terms each of which consists of a constant multiplied by one or more variables presented to a nonnegative integral power.
Given: x³ + 2x² + 4x+8
x³ + 2x² + 4x+8 = 0
simplifying the equation, we get
(x³+2x²)+(4x+8 )= 0
x²(x+2)+4(x+2)= 0
factorizing the above equation, we get
(x+2)(x²+4) = 0
Therefore, the polynomial equation x³ + 2x² + 4x+8 can be expressed as the method of factor polynomial exists (x² + 4)(x + 2).
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Evaluate the function f(x) = –2x2 – 3x + 5 for the input value –3.
−22
–4
2
32
Hi there,
please see below for solution steps :
‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
Evaluate by substituting :
[tex]\begin{gathered} \boldsymbol{f(x)=-2x^2-3x+5; \ evaluate \ when \ x=-3} \\\boldsymbol{Write \ -3 \ everywhere \ you \ see \ and \ x :}\\\boldsymbol{f(-3)=-2(-3)^2-3(-3)+5}\\\boldsymbol{Evaluate \ using \ Order \ of \ Operations :}\\\boldsymbol{f(-3)=-2(9)+9+5= > -18+9+5= > -18+14= > -4}\end{gathered}[/tex]
Therefore, the answer is [tex]\LARGE\textbf{-4}[/tex].
I hope the answer - and steps - made sense to you !!
Happy Learning !!
‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
Please help 3.7Q3. Please type the answer in order.
Step-by-step explanation:
since the y- axis stands for velocity (and the x-axus for time), speeding up means when the curve goes up (increasing velocity), and slowing down means when the curve goes down (decreasing velocity), all when reading the graph from left to right (small time values to larger time values).
(a)
speeding up
t in [0, 1)
or
0 <= t < 1
I would exclude t = 1, because at that point the slope is 0, there is no speeding up there.
slowing down
t in (1, 3)
or
1 < t < 3
the same argumentation for excluding 1 and 3, because there the slope of the curve turns 0 (just the turning point from one tendency to the other), and there is no speeding up or slowing down at these points.
(b)
speeding up
t in (1. 2)
or
1 < t < 2
slowing down
t in [0, 1) or in (2, infinity)
or
0 <= t < 1 || 2< t < infinity
we could use 3 instead of infinity, as this seems to be the last point of the drawn curve, but normally this kind of drawing tells me "infinity".
The Red Label Scotch Company is planning to produce 600 litres of Scotch Whisky. Three components A, B & C are mixed to form the final product. Component A, B and C cost Rs.10, Rs.15 and Rs.20 per litre respectively. In the final product, the amount of A component to be 2½ times the amount of component C. The total cost of the components should be Rs.8250. Determine the quantity of each components which should be included in the final product. (Use inverse of matrix Method).
Answer:
c
Step-by-step explanation:
What is the slope of the graph shown below?
Answer:
Option 3: -2
Step-by-step explanation:
The slope of the graph is negative, and the only option with a negative term for the slope is -2.
So the slope of the graph is -2.
Name a pair of opposite rays on plane L.
Answer:
GC and GD
Step-by-step explanation:
The only points on plane L are: J, C, G, D
GC and GD
Checking account A charges a monthly service fee of $12 and a wire transfer
fee of $10.50, while checking account B charges a monthly service fee of $21
and a wire transfer fee of $8.50. Which checking account is the better deal if
4 wire transfers are made per month?
A. Checking account B IS the better deal, because its total monthly
fees amount to $55, while those for checking account A amount to
$54.
B. Checking account B is the better deal, because its total monthly
fees amount to $54, while those for checking account A amount to
$55.
C. Checking account A is the better deal, because its total monthly
fees amount to $55, while those for checking account B amount to
$54.
c
D. Checking account A is the better deal, because its total monthly
fees amount to $54, while those for checking account B amount to
$55.
For only 4 wire transfers, Checking account A has a monthly fee of $54, while checking account B has a monthly fee of $55, so the correct option is D.
Which checking account is better?Checking account A charges a monthly fee of $12, plus $10.50 for each wire transfer, then the total cost if you make 4 wire transfers is:
C = $12 + $10.50*4 = $54
For checking account B, we have a fixed cost of $21, plus $8.50 per each wire transfer, then the total cost for 4 wire transfers is:
C' = $21 + 4*$8.50 = $55
So, if you make only 4 wire transfers per month, checking account A is a better option.
Then we can see that the correct option is D.
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need heeeelp please
Answer:
376.99112cm²
Step-by-step explanation:
A=2 pi rh + 2 pi r²
A=(2 x pi x 5 x 7) + (2 x pi 5²)
pi 22/7
The state lottery board is examining the machine that randomly picks the lottery numbers. On each trial, the machine outputs a ball with one of the digits 0 through 9 on it. (The ball is then replaced in the machine.) The lottery board tested the machine for 20 trials and got the following results.
Using the probability concept, we have that:
a) The experimental probability is of 0.75 = 75%.
b) The theoretical probability is of 0.5 = 50%.
c) As the number of trials increases, the probabilities are expected to get closer, though they might not be equal.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes. For an experimental probability, these number of outcomes are taken from previous trials. A theoretical probability is calculated before any trial, and as the number of trials increase, the experimental and theoretical probabilities get closer.
From the table, there were 20 trials, and 2 + 3 + 4 + 4 + 2 = 15 resulted in even numbers, hence the experimental probability is:
p = 15/20 = 0.75 = 75%.
For a fair machine, even and odd numbers should be equally as likely, hence the theoretical probability is of 0.5 = 50%.
For item c, we have that as the number of trials increases, the probabilities are expected to get closer, though they might not be equal.
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AN aquariums dimension are 3 1/4 x 2ft x 1 3/4. what is the volume of the aquarium
The volume of the rectangular prism aquarium = 17 1/16 ft.
What is the Volume of a Rectangular Prism?Volume of a rectangular prism = (l)(w)(h), where:
Length of the prism = lWidth of the prism = wHeight of the prism = hThe aquarium is a rectangular prism. Its dimensions are given as:
Length (l) = 3 1/4 ft
Width (w) = 3 ft
Height (h) = 1 3/4 ft
Substitute
Volume of the rectangular prism aquarium = (3 1/4)(3)(1 3/4)
Volume of the rectangular prism aquarium = (13/4)(3)(7/4)
Volume of the rectangular prism aquarium = (13 × 3 × 7)/(4 × 4)
Volume of the rectangular prism aquarium = (273)/(16)
Volume of the rectangular prism aquarium = 17 1/16 ft.
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Graph the function y=√x+1-4. Which point lies on the graph?
a.) (-2,3)
b.) (1,4)
c.) (-1,-4)
d.) (0,4)
The probability that Greg is on time for a given class is 14% . If there are 30 classes during the semester, what is the best estimate of the number of times out of 30 that Greg is on time to class? Round your answer to the nearest integer.
The number of times that Greg is on time to class is 4
How to estimate the number of times that Greg is on time to class?The given parameters are:
Probability that Greg is on time, p = 14%
The sample size, n = 30
The estimate of the number of times that Greg is on time to class is
E(x) = np
Substitute the known values in the above equation
E(x) = 30 * 13%
Evaluate the product
E(x) = 3.9
Approximate
E(x) = 4
Hence, the number of times that Greg is on time to class is 4
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En la siguiente sucesión numérica 8,7,11,10,14 los dos números siguientes son
To find the missing numbers in the sequence, we must identify the rule by which they change.
The sequence starts at 8 and then decreases by 1, therefore, the second term is 7. The third term increases by 4 units with respect to the second, going from 7 to 11, and the fourth decreases again by 1, now remaining at 10.
The fifth term increases again by 4 units, from 10 to 14. This already gives us a clear idea of the rule that the sequence follows.
Decrease 1, increase 4, decrease 1, increase 4,…₊₄ ₊₄
8 , 7, 11, 10, 14,...,⁻¹ ⁻¹ ⁻¹
In this way, the sixth element must decrease by 1, that is 13 and the seventh must increase by 4, that is 17.
8, 7, 11, 10, 14, 13, 17,…
The next numbers that the numerical sequence are 13 and 17, to complete. ✅
What is the perimeter of angle DEF to the nearest tenth of a unit?
helppppp
tysm
===========================================================
Explanation:
Let's use the distance formula to find the distance from D to E
[tex]D = (x_1,y_1) = (-7,2) \text{ and } E = (x_2, y_2) = (3,4)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(-7-3)^2 + (2-4)^2}\\\\d = \sqrt{(-10)^2 + (-2)^2}\\\\d = \sqrt{100 + 4}\\\\d = \sqrt{104}\\\\d = \sqrt{4*26}\\\\d = \sqrt{4}*\sqrt{26}\\\\d = 2\sqrt{26}\\\\d \approx 10.198\\\\[/tex]
Note: uppercase D refers to the point, while lowercase d is the distance from D to E.
The length of segment DE is roughly 10.198 units long.
----------------
Repeat for the distance from E to F.
[tex]E = (x_1,y_1) = (3,4) \text{ and } F = (x_2, y_2) = (5,-7)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(3-5)^2 + (4-(-7))^2}\\\\d = \sqrt{(3-5)^2 + (4+7)^2}\\\\d = \sqrt{(-2)^2 + (11)^2}\\\\d = \sqrt{4 + 121}\\\\d = \sqrt{125}\\\\d = \sqrt{25*5}\\\\d = \sqrt{25}*\sqrt{5}\\\\d = 5\sqrt{5}\\\\d \approx 11.1803\\\\[/tex]
Segment EF is roughly 11.1803 units long.
----------------
Repeat for the distance from F to D.
[tex]F = (x_1,y_1) = (5,-7) \text{ and } D = (x_2, y_2) = (-7,2)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(5-(-7))^2 + (-7-2)^2}\\\\d = \sqrt{(5+7)^2 + (-7-2)^2}\\\\d = \sqrt{(12)^2 + (-9)^2}\\\\d = \sqrt{144 + 81}\\\\d = \sqrt{225}\\\\d = 15\\\\[/tex]
Unlike the others, this result is exact.
----------------
Add up the three segment lengths to get the perimeter
DE + EF + FD
10.198 + 11.1803 + 15
36.3783
The perimeter is approximately 36.3783 units which rounds to 36.4
The answer has been confirmed with GeoGebra.
We want to obtain a sample to estimate a population mean. Based on previous evidence, researchers believe the population standard deviation is approximately
σ
=
24.4
. We would like to be 99.5% confident that the estimate is within 0.5 of the true population mean. How large of a sample size is required?
n
=
Using the z-distribution, it is found that a sample size of n = 18,805 is required.
What is a z-distribution confidence interval?The confidence interval is:
[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]
The margin of error is:
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.z is the critical value.n is the sample size.[tex]\sigma[/tex] is the standard deviation for the population.For this problem, the parameters are:
[tex]z = 2.81, \sigma = 24.4, M = 0.5[/tex].
Hence we solve for n to find the needed sample size.
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]0.5 = 2.81\frac{24.4}{\sqrt{n}}[/tex]
[tex]0.5\sqrt{n} = 24.4 \times 2.81[/tex]
[tex]\sqrt{n} = 48.8 \times 2.81[/tex]
[tex](\sqrt{n})^2 = (48.8 \times 2.81)^2[/tex]
n = 18,805.
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Answer:
Step-by-step explanation:
What if the estimate is within 1 of the population mean?
A 13km stretch of road needs repairs. Workers can repair 3 1/2 km of road per week.
How many weeks will it take to repair this stretch of road?
The computation shows that the number of weeks that it take to repair this stretch of road will be 4 weeks.
How to compute the number of weeks?From the information given, we are told that a thirteen kilometers stretch of road needs repairs and that the workers can repair three and half kilometers of road per week.
The question is simply for us to calculate the number or weeks that it will take to be able to repair the stretch of road.
Therefore, based on the information given, it should be noted that to get the number of weeks that will be used to repair the road, we simply have to divide the total distance or the road by the distance that is repaired every week.
Therefore, the number of weeks that it will take to be able to repair this stretch of road will be:
= 13/3.5
= 3.7
= 4 weeks approximately
Therefore, based on the information given, the number of weeks that's required is 4 weeks.
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Can someone please help me with this ty
Answer:
92 degrees
Step-by-step explanation:
The sum of the exterior angles will be 360.
67 x 4 = 268. That means that the last angles must be 92 (360 - 268)
Ali’s ate 1/3 of a pizza for lunch. Later, she ate 2/5 of the remaining pizza as a snack. How much of the pizza did she eat altogether?
Although all of the following systems can be solved via the substitution method, substitution would be the best method for solving which system.
Group of answer choices
Using the substitution method, the system of equation that is easily solved is:
c. y = 2x + 3
2x + y = 5
How to Solve A System of Equations Using the Substitution Method?Using the substitution method to solve a system of equations is best when one of the equations have one isolated variable that we can simply plug its value into the second equation.
For example, given the system of equations:
y = 2x + 3 --> eqn. 1
2x + y = 5 --> eqn. 2
Substitute y = (2x + 3) into eqn. 2 and find x:
2x + y = 5 --> eqn. 2
2x + 2x + 3 = 5
4x + 3 = 5
4x = 5 - 3
4x = 2
x = 2/4
x = 1/2
Substitute x = 1/2 into eqn. 1 to find y
y = 2x + 3 --> eqn. 1
y = 2(1/2) + 3
y = 1 + 3
y = 4
From the above, we can see that the system of equations that is quite easy to solve using the substitution method is:
c. y = 2x + 3
2x + y = 5
The rest of the equations are quite different and not as straightforward as solving as this using the substitution method.
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Find the mode for the scores 3,760, 5,200, 8,750, 4,400, 5,250
Answer:
no mode
Step-by-step explanation:
no number appears more than once
therefore there is no mode
Please help thank you asap
Answer:
[tex]y=-2x+1[/tex]
Step-by-step explanation:
Looking at the line can ensure that the slope is negative
The rise/run is 4/-2, ten the slope is:
[tex]s=\frac{-4}{2} =-2[/tex]
b intercept is 1
The equation:
[tex]y=-2x+1[/tex]
Hope this helps
Which set of ordered pairs represents a function?
{(-6,-4), (1, -7), (-4, 3), (-4, 8)}
{(-8, -3), (-8, 9), (9, 6), (1, -4)}
{(4,1), (-6, 6), (5,-2), (-4,1)}
{(-3, 6), (-1,0), (-8, 1), (-8, -3)}
Answer:
{(4,1), (-6, 6), (5,-2), (-4,1)} set of ordered pairs represents a function.
Step-by-step explanation:
Because every element or component of domain has unique image in co-domain.
Hope its helpful :-)
If so, please mark me as brainlist :-)
If there are 12 donuts per box, which of the following equations will give you the number of boxes, x, that Joe needs to buy?
The equation that would give the number of boxes, x, that Joe needs to buy is 12x = 60. The correct option is c.) 12x = 60
Writing an equationFrom the question, we are to determine the equation that will give the number of boxes, x, that Joe needs to buy
From the given information,
Joe needs 60 donuts to feed his construction crew
Also,
There are 12 donuts per box
This means he needs to buy 60/12 boxes of donut
Since the number of boxes Joe needs to buy is x
∴ 60/12 = x
60 = 12x
12x = 60
Hence, the equation that would give the number of boxes, x, that Joe needs to buy is 12x = 60. The correct option is c.) 12x = 60
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IF A BASEBALL TEAM CONSISTS OF 18 PLAYERS, HOW MANY POSSIBLE GROUPS
OF 9 MAN TEAMS ARE POSSIBLE?
The number of ways men can be selected from the team of 18 is 48,620ways
Combination and PermutationPermutation has to do with arrangement while combination has to do with selection.
If a baseball team consists of 18 players and 9 man are possible in the team, the number of ways the men can be chosen is calculated using the combination formula below;
nCr = n!/(n-r)!r!
Given the following
n =18
r = 9
Substitute
18C9 = 18!/(18-9)!9!
18C9 = 18!/9!9!
18C9 = 48,620
Hence the number of ways men can be selected from the team of 18 is 48,620ways
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find the value of x,y in the given figure with reasons.
Answer:
answer
x= 40°
Step-by-step explanation:
x= 40° [ base angle of isocles triangle]
The graph shows the side view of a water slide
Step-by-step explanation: Given that the graph shows the side view of a water slide with dimensions in feet.
We are to find the rate of change between the points (0, ?) and (?, 40).
From the graph, we note that
the y co-ordinate for the x co-ordinate 0 is 80 and the x co-ordinate for the y co-ordinate 40 is 5.
So, the given two points are (0, 80) and (5, 40).
The rate of change for a function f(x) between the points (a, b) and (c, d) is given by
Therefore, the rate of change for the given function between the points (0, 80) and (5, 40) is
Thus, the required rate of change is -8.
Show Work Please Thank You
Answer:
[tex] \frac{\pi}{4} [/tex]
Step-by-step explanation:
[tex] \sf let \: y = { \tan }^{ - 1} ( \tan \frac{3\pi}{4} ) \\ \\ \sf \hookrightarrow \tan y = \tan \frac{3\pi}{4} \\ \\ \sf \hookrightarrow \tan y = \tan(\pi - \frac{\pi}{4} ) \\ \\ \sf \hookrightarrow \tan y = \tan( - \frac{\pi}{4} ) \\ \\ \sf \hookrightarrow \tan y = - \tan \frac{\pi}{4} \\ \\ \boxed {\hookrightarrow{ \bold{y = - \frac{\pi}{4} } } }[/tex]
WILL GIVE BRAINLIEST
(04.01, 04.02 HC)
Jackie runs and dances for a total of 55 minutes every day. She dances for 25 minutes longer than she runs.
Part A: Write a pair of linear equations to show the relationship between the number of minutes Jackie runs (x) and the number of minutes she dances (y) every day. (5 points)
Part B: How much time does Jackie spend running every day? Show your work. (3 points)
Part C: Is it possible for Jackie to have spent 45 minutes dancing if she runs and dances for a total of exactly 55 minutes and dances for 25 minutes longer than she runs? Explain your reasoning. (2 points)
A. The pair of linear equations are: x + y = 55 and y = x + 25
B. Number of time she spend running everyday is: 15 minutes.
C. It is not possible.
How to Write a System of Linear Equations?A system of equations consist of linear equations that have unknown variables whose values make the linear equations in the system true.
Part A: To write a pair of linear equations, do the following,
Let x represent the time Jackie runs
Let y represent the time Jackie dances
We are given that, Jackie runs and dances for a total of 55 minutes every day, therefore, the first linear equation would be:
x + y = 55 --> equation 1
We are also given that Jackie dances for 25 minutes longer than she runs, therefore, the second linear equation would be:
y = x + 25 --> equation 2
Therefore, the two pair of linear equations that shows the relationship between the number of minutes Jackie runs and dances everyday are:
x + y = 55
y = x + 25
Part B: Substitute y = (x + 25) into equation 1
x + y = 55 --> equation 1
x + x + 25 = 55
2x + 25 = 55
2x = 55 - 25
2x = 30
x = 15
Therefore, the number of time she spend running everyday is: 15 minutes.
Part C:
If she spent 45 minutes dancing (y = 45), and x = 15, substitute the values into x + y = 55 to find out if it is possible.
15 + 45 = 55
60 = 55 (not true)
Therefore, it is not possible.
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how many cubic meters in 179.66 cubic centimeters
Answer:
0.00018
Step-by-step explanation:
formula:Divide the volume by 1e+6
e) 1 cubic centimetres = 1÷1000000 cubic meter. Rewrite in scientific notation
[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Here we go ~
[tex]\qquad \sf \dashrightarrow \: 1 \: \: cm {}^{3} = \cfrac{1}{1000000} \: \: m {}^{3} [/tex]
[tex]\qquad \sf \dashrightarrow \: 1 \: \: cm {}^{3} = \cfrac{1}{10 {}^{6} } \: \: m {}^{3} [/tex]
[tex]\qquad \sf \dashrightarrow \: 1 \: \: cm {}^{3} = {}{10 {}^{ - 6} } \: \: m {}^{3} [/tex]
HELP ASAP WILL GIVE BRAINLIEDT IF CORRECT!!!!!!!
Find the equation to the line below
Answer:
y = 3/2x + 2
Step-by-step explanation:
y = mx + c
y = gradient(x intercept) + y intercept
y = 3/2x + 2
Answer:
[tex]\sf y =\dfrac{3}{2}x+2[/tex]
Step-by-step explanation:
Equation of line:Pick any two points on the line.
(0,2) and (2 , 5)
(0,2) ⇒ x₁ = 0 & y₁ = 2
(2,5) ; x₂ = 5 & y₂ = 5
[tex]\sf \boxed{\bf Slope =\dfrac{y_2-y_1}{x_2-x_1}}[/tex]
[tex]\sf =\dfrac{5-2}{2-0}\\\\=\dfrac{3}{2}[/tex]
Equation of line in point slope form:
[tex]\sf y - y_1 =m(x -x_1)[/tex]
Point(0 ,2) and m = 3/2
[tex]\sf y - 2 = \dfrac{3}{2}(x -0)\\\\ y - 2 = \dfrac{3}{2}x\\\\[/tex]
Equation of line in slope y-intercept form:
[tex]\sf y =\dfrac{3}{2}x+2[/tex]
