The simplest way to factor polynomials is to use the greatest common factor.
How to illustrate the polynomial?It should be noted that the polynomial simply means the expression of more than two algebraic terms.
In this case, the simplest way to factor polynomials is to use the greatest common factor. This simply had to do with the largest factor that the numbers share.
Other methods that can be utilized include the grouping method, the sum of the difference in cubes and in two squares.
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Which of the following options is a polynomial with a root 2i and exactly 2
real roots?
A. F(x)=x²-x²³ +2x² - 4x-8
B. F(x)=x²-x² + 4x-4
C. F(x)=x²-x³-6x² +4x+8
OD. F(x)= x³ + x² + 4x+8
The polynomial with a root 2i and exactly 2 real roots is F(x)=x³-x² + 4x-4
Factorizing polynomial functionsGiven the polynomial function below
F(x)=x³-x² + 4x-4
Group
F(x)=(x³-x²) + (4x-4)
f(x) = x²(x-1)+4(x-1)
f(x) = (x²+4)(x-1)
If f(x) = 0
x²+4 = 0 and x -1. = 0
x² = -4 and x = 1
x = ±2i and -1
Hence polynomial with a root 2i and exactly 2 real roots is F(x)=x³-x² + 4x-4
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Explain in your own words why you think a tangent of a circle is always perpendicular to the radius at the point of tangency
Explain in your own words why you think angles formed by drawing lines from the ends of the diameter of a circle to its circumference form a right angle
A radius and diameter are parts of a circle. Thus the reasons required in the question are given as;
i. A tangent is always perpendicular to the radius of a circle because they are always at a right angle.
ii. A line that is drawn from the end of a diameter of a circle to its circumference form a right angle because they are always perpendicular.
A circle is a figure that is bounded by a curved line which is called its circumference. Some of its parts are radius, diameter, chord, sector, etc.
A diameter is a line from one point on the circumference of a circle to another through its center.A radius is a line drawn from the center of a circle to its circumference. Thus a radius is half of the diameter.A tangent is an external line drawn to meet the circumference of a circle at a point,Thus the reasons required in the question are given as;
i. A tangent is always perpendicular to the radius of a circle because they are always at a right angle.
ii. A line that is drawn from the end of a diameter of a circle to its circumference form a right angle because they are always perpendicular.
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3,
Which expression is equivalent to
56x7y5, if x #0 and y# 0?
Answer:
1960
Step-by-step explanation:
1960
times 56 times 7 time 5 = 1960
a man is walking a 300 foot long field at the same time his daughter is walking towards him from the opposite end . The man is walking 9 feet per second and the daughter is moving 6 feet per second . How many seconds will it take them to meet somewhere in the middle?
Answer:20ft
Step-by-step explanation:Because you add the numbers up 9 and 6 you get 15 so 300/15=20
20x15 equals 300 so it goes both ways
1) The rational function shown could be used to the number of arrests, f(x), per 100,000 drivers, for driving under the influence of alcohol, as a function of a driver’s age, x.
[tex]f(x)=\frac{27725(x-14)}{x^2+9} -5x[/tex]
a) Describe the trend you see in the graph, in context.
b)Use a graphing utility to determine the age that corresponds to the greatest number of arrests.
The age that has the maximum number of arrest is 25 years
The trend on the graphThe equation of the function is given as:
[tex]f\left(x\right)\ =\ \frac{27725\left(x\ -\ 14\right)}{x^{2\ }+\ 9}-5x[/tex]
See attachment for the graph of the function.
The end behavior of the graph is
[tex]\mathrm{as}\:x\to \:+\infty \:,\:f\left(x\right)\to \:-\infty \:,\:\:\mathrm{and\:as}\:x\to \:-\infty \:,\:f\left(x\right)\to \:+\infty \:[/tex]
This means that:
As the age of the driver increases, arrested drivers decreases and as the age of the driver decreases, arrested drivers increases
The age that has the maximum arrest
From the graph, the maximum is:
Maximum = (25.388, 356.166)
Remove the y values
Maximum = 25.388
Approximate
Maximum = 25
Hence, the age that has the maximum arrest is 25
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An acute triangle has two sides measuring 8 cm and 10 cm. What is the best representation of the possible range of values for the third side, s?
2 < s < 18
6 < s < 12.8
s < 2 or s > 18
s < 6 or s > 12.8
Applying the triangle inequality theorem, the best representation for the third side is: A. 2 < s < 18.
What is the Triangle Inequality Theorem?According to the triangle inequality theorem, the sum of any two sides of a given triangle must be greater than the length of the measure of the third side of the triangle.
Thus, given an acute triangle has sides, 8 cm and 10 cm, applying the triangle inequality theorem, the range of sides would be calculated as shown below:
10 - 8 < s > 8 + 10
2 < s > 18
The range of values for the third side is: A. 2 < s < 18.
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Answer: A. 2 < s < 18.
Step-by-step explanation:
Applying the triangle inequality theorem, the best representation for the third side is: A. 2 < s < 18.
Hello, I know it is kinda late but here's a question.
9 = 4a - 2
What is a?
Worth 15 points!
The solution of the linear equation is a = 11/4.
How to solve the linear equation?Here we have the linear equation:
9 = 4a - 2
We want to solve this for a, so we need to isolate a on one side of the equation.
First, we can add 2 on both sides to get:
9 + 2 = 4a
11 = 4a
Now we can divide both sides by 4 to get:
11/4 = a
The solution of the linear equation is a = 11/4.
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Solve for x. NEED HELP
Answer:
22.470
Step-by-step explanation:
In this example you have to use the trigonometric function sine which is defined as [tex]sin(\theta) = \frac{opposite}{hypotenuse}[/tex]
Plug in known values:
[tex]sin(64) = \frac{x}{25}[/tex]
Multiply both sides by 25
[tex]sin(64) * 25 = x[/tex]
Approximate sin(64) using a calculator:
[tex]0.89879 * 25 = x[/tex]
Simplify
[tex]22.470 \approx x[/tex]
Made Eyewear wants to conduct a survey on consumers who wear glasses. It wants to give every person who wears glasses in the United States an equal chance of being chosen for the survey. First, though, it needs to separate those who wear glasses from those who do not. What type of sampling should Made Eyewear use
Stratified sampling is used by Made Eyewear
Stratified sampling is is where we divide the population into groups by some characteristic such as age or occupation or gender. Then make sure our survey includes people from each group in proportion to how many there are in the whole population.
Example of this sampling is A stratified sample is one that ensures that subgroups (strata) of a given population are each adequately represented within the whole sample population of a research study. For example, one might divide a sample of adults into subgroups by age and use of eyeglasses, like 18–29, 30–39, 40–49, 50–59, and 60 and above
So, Stratified sampling is used by Made Eyewear
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Find the measure of angleq, the smallest angle in a triangle whose sides have lengths 4, 5, and 6. round the measure to the nearest whole degree. 34° 41° 51° 56°
The measure of the ∠Q = 41°
By law of cosines:
a law in trigonometry: the square of a side of a plane triangle equals the sum of the squares of the remaining sides minus twice the product of those sides and the cosine of the angle between them.
Which can we stated as:
[tex]{q}^2 = {p}^2 + {r}^2 - 2prcos(Q)\\{4}^2 = {6}^2 + {5}^2 - 2*6*5*cos(Q)\\\\[/tex]
solving equation using normal algebra:
60cos(Q) = 36 + 25 - 16
60 cos(Q) = 45
cos(Q) = 45/60
cos(Q) = 3/4
[tex]Q = {cos}^{-1} (\frac{3}{4})\\[/tex]
Thus, Q = 41°
Hence, the measure of the smallest angle in a triangle whose sides have lengths 4, 5, and 6. ∠Q is 41°.
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Assume that two marbles are drawn without replacement from a box with 1 blue, 3 white, 2 green, and 2 red marbles. Find the probability that both marbles are red.
[tex]|\Omega|=8\cdot7=56\\|A|=2\cdot1=2\\\\P(A)=\dfrac{2}{56}=\dfrac{1}{28}[/tex]
I need help with the question in the image, thank you.
Step-by-step explanation:
First, there is a vertical stretch by a factor of 3,
Next, there is a horizontal compression by a factor of 2.
Reflect about the y axis.
After, shift to the right 3 units horizontally,
Finally , shift upwards 7 units
Two chains of clothing stores, Impulse Clothing and Opal Essence, were founded in the same year, although some outlets of Opal Essence were operating under a different name before Opal Essence was founded. The owner of Impulse Clothing uses the equation below to represent the number of clothing stores, C, he owns x years after the brand's founding. C = 2x The owner of Opal Essence uses the equation below to represent the number of clothing stores, C, she owns x years after the original brand's founding. C = x + 5 Using graphing technology, complete the statements.
By combining the equations we can found that the number of impulse clothing and Opal essence stores by equations be C (3x+5)/2 where x is the number of years after the brand's founding.
Given The equation showing number of impulse clothing stores is C=2x. The equation showing number of clothing stores be C=x+5.
We have to first plot both the equations on the graph.
For plotting we need points which can be calculated as
C=2x
when x=1 ,C or y=2
when x=3 , C or y=6
C=x+5
when x=0 ,C or y=5
when x=1 ,C or y=6
By combining both equations we get
C=(3x+5)/2
Plot this also and finding points
when x=0 , C=5/2
when x=1 , C=4
Hence the combination of both statements which shows the total stores owned is C=(3x+5)/2
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Answer:
So, after
3
years, Impulse Clothing and Opal Essence will own the same number of clothing stores.
The total number of stores during that year will be 8.
Madison and Aiden share a reward of $36 in a ratio of 1:5. What fraction of the total reward does Madison get?
Answer:
1/6
Explanation:
$36 in 1:5
so, the total amount of shares is 6 (1+5)
36 / 6 = 6
$6 per share
shared in the ratio of 1:5
5 x 6 = 30
1:5
M:A
$6:$30
Madison gets $6. Or, 6/36 of the total (which, simplified, is 1/6)
Hope this makes sense!
If (x – 3)(x + 5) = 49, then what is the value of the expression (x – 4)(x + 6)?
In a group of 26 students, 4 study both art and biology. 5 study biology but not art. 5 study neither subject. given that a randomly selected student studies art, what is the probability the student studies art and biology?
[tex]\huge\boxed{25\%}[/tex]
We need to find the number of students that study art first. This includes the students who study both art and biology (4) and the students who study art but not biology.
We know the counts for every category except for "art but not biology", so we can use subtraction.
[tex]26-4-5-5=12[/tex]
This means that 12 students study art but not biology, which combines with the 4 who study both subjects to give us 16 art-studying students.
Now, we just need to find the probability that a student studies both subjects (4 students) given that they study art (16 students).
This is simple division.
[tex]4/16=0.25=25\%[/tex]
A coordinate plane with a vertical line passing through (negative 3, negative 3), (negative 3, 0) and (negative 3, 3). What is the equation of the graphed line written in standard form? x = –3 y = –3 x + y = –3 x – y = –3
Answer:
x = - 3
Step-by-step explanation:
A vertical line parallel to the y- axis has equation
x = c
where c is the value of the x- coordinates the line passes through
the line passes through (- 3, 0 ) and (- 3, 3 ) with x- coordinates - 3 , then
x = - 3 ← equation of vertical line
Find the surface area. Round to the nearest tenth.
Answer:
66.4 in^2
Step-by-step explanation:
Surface area is defined as the area around the surface of a 3-dimensional solid. The shape we are given here is a triangular prism with a square base. This means it contains one square and 4 triangles on the surface. To find the surface area, we just need to find the areas of all 5 surface shapes and add them up. We have been given that the square has a side length of 4 inches, meaning the area is 4^2 or 16. The area of a triangle is (1/2)base*height. The base length is 4 inches and the height is 6.3, and (1/2)*4*6.3 is 12.6. Note that, since there are four triangles, we have to multiply this value by 4 (12.6*4 = 50.4). Now we have the area of the square and the area of all the triangles put together, so we can just add them up:
16 + 50.4 = 66.4
No Solutions
5x - 2x + 7 - x = _x + _
Answer:
2x+7
Step-by-step explanation:
To Simplify an Expression , we combine Like-Terms
So for our Question , we have Terms with x and Constant Term
Combine Terms with x : 5x-2x-x=2x
Constant Term : 7
Then 5x-2x+7-x = 2x+7
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Equation: }[/tex]
[tex]\mathbf{5x - 2x + 7 - x = }[/tex] ________[tex]\mathbf{\ x \ + }[/tex]________
[tex]\huge\textbf{Simplify the left side of the equation, to}\\\huge\textbf{get the result of the right side of the}\\\huge\textbf{equation.}[/tex]
[tex]\huge\textbf{Simplifying the LEFT side:}[/tex]
[tex]\mathbf{5x - 2x + 7 - x}[/tex]
[tex]\mathbf{= 5x - 2x + 7 - 1x}[/tex]
[tex]\huge\textbf{Combine the like terms:}[/tex]
[tex]\mathbf{= (5x - 2x - 1x) + (7)}[/tex]
[tex]\mathbf{= 5x - 2x - 1x + 7}[/tex]
[tex]\mathbf{= 3x - 1x + 7}[/tex]
[tex]\mathbf{= 2x + 7}[/tex]
[tex]\huge\textbf{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\frak{2\mathsf{x} + 7}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]The __________ is a measure of dispersion that is used in constructing confidence intervals for the mean and in evaluating research hypotheses.
The standard deviation is a measure of dispersion that is used in constructing confidence intervals for the mean and in evaluating research hypotheses.
In statistics, the same old deviation is a degree of the amount of variation or dispersion of a hard and fast of values. A low well-known deviation suggests that the values tend to be close to the suggested of the set, while an excessive widespread deviation shows that the values are spread out over a much broader range.
It tells you, in common, how some distance every rating lies from the suggestion. In everyday distributions, a high well-known deviation approach that values are typically far from the implied, while a low popular deviation suggests that values are clustered close to the mean.
Fashionable deviation tells you ways to unfold out the statistics is. It is a degree of the way some distance each location cost is from the suggest. In any distribution, about ninety-five% of values may be inside 2 preferred deviations of the suggested.
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Steve can complete 100m dash in 10 seconds paul can run it in 12 seconds how does their times compare?
Steve is 1.2 times faster than Paul.
What is a ratio?The quantitative relationship between two values indicating how frequently one value is contained within the other.
For example: Speed = Distance / Time
Total distance covered by both Steve and Paul = 100m
Total time taken by Steve = 10s
Steve's speed = 100 / 10 = 10m/s
Total time taken by Paul = 12s
Paul's speed = 100 / 12 = 8.33m/s
Ratio of Steve's speed to Paul's speed = 10 / 8.33 = 1.2
Hence we can say that Steve is 1.2 times faster than Paul.
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Eli claims that the product of 6 superscript 5 and 5 superscript negative 3 is 6 squared. which explains whether eli is correct?
Answer:
Eli is incorrect. He added the exponents even though the bases are not the same.
Step-by-step explanation:
6^5 * 5^-3 = 6^2
5^-3 = 1/5^3 = 1/125
6^5 = 7776
7776*1/125 = 7776/125 = 62.2 approximately
Answer:
Eli is incorrect. He added the exponents even though the bases are not the same.
Step-by-step explanation:
Edge
James bought a cake that weighs 3 and 1 over 4 pounds. How many ounces does the cake weigh? Show your work. (5 points)
[16 ounces = 1 pound]
Part B: A running tap dispenses 0.15 gallons of water every second. How many pints of water is dispensed after 20 seconds? Show your work. (5 points)
[1 gallon = 4 quarts, 1 quart = 2 pints]
The weight of James cake in ounces is 52 ounces and the Pint of water dispensed in 20 seconds is 24 pints
WeightWeight of cake = 3 1/4 pounds1 pound = 16 ounces
Number of ounces the cake weigh = 3 1/4 pounds × 16 ounces
= 13/4 × 16
= (208) / 4
= 52 ounces
Water dispensed per second = 0.15 gallonsNumber of seconds = 20 seconds1 gallon = 4 quarts
0.15 gallon = 0.6 quarts
1 quart = 2 pints
0.6 quart = 1.2 pints
Pint of water dispensed in 20 seconds = 1.2 × 20
= 24 pints of water
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CAN ANYONE HELP PLEASE
Answer:
x = 8
Step-by-step explanation:
Every angle in an EQUILATERAL triangle = 60°
so 9x -12 = 60
9x = 72
x = 8
Step-by-step explanation:
[tex]9x - 12 = \frac{180}{3} = 60 \\ [/tex]
[tex]9x = 60 + 12[/tex]
[tex]9x = 72[/tex]
[tex]x = \frac{72}{9} \\ [/tex]
[tex]x = 8[/tex]
hence the value of x is 8...
9. The length of a rectangle is 2p cm and its breadth is p cm. When the length of the rectangle is increased by 25% and the breadth is decreased by 25%, determine the percentage change in (i) its perimeter, (ii) its area.
Answer:
The answers are:
(i) 108.33%
(ii) 93.75%
Step-by-step explanation:
The original area and perimeter are as follow:
Perimeter = 2l + 2w
= 2(2p) + 2(p)
= 4p + 2p
= 6p cm
Area = l * w
= 2p * p
= 2p^2 cm^2
A 25% increase of the length is = 2p * (1 + 25%) = 2p * 1.25 = 2.5p cm
A 25% decrease of the breadth is = p * (1 - 25%) = p * 0.75 = 0.75p cm
Perimeter = 2l + 2w
= 2(2.5p) + 2(0.75p)
= 5p + 1.5p
= 6.5p cm
Area = l * w
= 2.5p * 0.75p
= 1.875p^2 cm^2
Now that we have found the changes, let's calculate the percentage changes
Percentage change of perimeter:
x% * 6p = 6.5p
x/100 * 6p = 6.5p
x * 6p = 6.5p * 100
x = 650p/6p
x = 108.33
Percentage change of area:
x% * 2p^2 cm^2 = 1.875p^2 cm^2
x/100 * 2p^2 cm^2 = 1.875p^2 cm^2
x * 2p^2 cm^2 = 1.875p^2 cm^2 * 100
x = 187.5p^2 cm^2 / 2p^2 cm^2
x = 93.75
Answer:
i = 8 1/3%
ii = -6 1/4%
Step-by-step explanation:
The previous answer is wrong this is the correct one:
Because they are using the same variable P let's assume P = 10
Length increase 25% = 10 + (10 x 25%) = 10 + 2,5 = 12,5 cm
Breath decreased 25% = 10 - (10 x 25%) = 10 - 2,5 = 7,5 cm
i. Original Perimeter : 2(L) + 2(B) = 2(2p) + 2(p) = 2(2x10) + 2(10) = 2(20) + 2(10) = 60cm
Modified Perimeter : 2(L) + 2(B) = 2(2p) + 2(p) = 2(2x12,5) + 2(7,5) = 2(25) + 2(7,5) = 65cm
The percentage change is
65-60/60 x 100
= 5/60 x 100
= 500/60
= 8 2/6% simplified 8 1/3%
ii. Original Area: L x B = 2p x p = 2(10) x 10 = 20 x 10 = 200 cm^2
Modified Area: L x B = 2p x p = 2(12,5) x 7,5 = 25 x 7,5 = 187,5 cm^2
The percentage change is
187,5-200/200x 100
= - 12,5/200 x 100
= - 1250/200 = - 6 1/4 %
That is the Correct answer. Hope that help
What is the root of the polynomial equation x (x minus 2) (x 3) = 18? use a graphing calculator and a system of equations.
The root of the polynomial equation x (x-2) (x + 3) = 18 is x = 3.
Concept: An expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable(s).
Given:
x (x-2) (x + 3) = 18
Divide both sides of the equation by x:
x (x-2) (x + 3) / x = 18 / x
(x-2) (x) + 3) = 18 / x
You can use the following simultaneous equations.
(1) y = (x-2) (x + 3)
(2) y = 18 / x
Using a graphing calculator, we get:
x = 3, y = 6 → point = (x, y) = (3,6)
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please assist me wit this question
Answer: 65
Step-by-step explanation:
By the geometric mean theorem, the length of the altitude to the hypotenuse has length [tex]\sqrt{25 \cdot 144}=60[/tex]
So, by the Pythagorean theorem,
[tex]x=\sqrt{60^2 + 25^2}=65[/tex]
PLEASE HELP
The graph of g(x) is shown.
The graph has...
#1.
a. the same horizontal asymptote as function g
b. a horizontal asymptote at y = 5
c. a horizontal asymptote at y = 8
#2. The graph has...
a. the same vertical asymptote as function g
b. a vertical asymptote at x = -7
c. a vertical asymptote at x = -5
d. a vertical asymptote at x = 3
On the given graph, we can see that we have:
Horizontal asymptote at y = 3Vertical asymptote at x = -2The correct option would be a in both cases.
What can we conclude about the graph of g(x)?We want to study the asymptotes of the graph
If we look at the graph, we can see that the horizontal asymptote (denoted by the horizontal dashed line) is at y = 3.
the graph has a horizontal asymptote (or two actually) at y = 3.
For the vertical asymptote we just look at the vertical dashed line, it is at x = -2
Notice that none of these coincides with the options, so the only options that can be correct (depending on the graph of g(x), which is not shown) are option "a" in both cases.
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Drag the tiles to the correct boxes to complete the pairs
68% of the data lies within one standard deviation from the mean
95% of the data lies within two standard deviation from the mean
99.7% of the data lies within three standard deviation from the mean
What is empirical rule?The empirical rule states that for a normal distribution, 68% of the data lies within one standard deviation from the mean, 95% of the data lies within two standard deviation from the mean and 99.7% of the data lies within three standard deviation from the mean
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Six more than a number
cubed.
n^3 + 6
I'll make n stand for the number
Six more means adding extra 6 onto our number cubed.
So, n x n x n = n^3
(n^3 means n cubed)
Thus, answer is n^3 + 6
Hope this helps!