Priya wants to sketch a graph of the polynomial f defined by f(x)=x^3+5x^2+2x-8. She knows f(1)=0, so she suspects that (x-1) could be a factor of x^3+5x^2+2x-8 and writes (x^3+5x^2+2x-8) = (x-1) (?x^2+?x+?) and draws a diagram.
1. Finish Priya's diagram
2. Write f(x) as the product of (x-1) and another factor.
3. Write f(x) as the product of three linear factors.
4. Make a sketch of y=f(x).
Answers
Given the polynomial f(x)=x³+5x²+2x-8 and f(1)=0.
Factorization is the process of determining the components of a given value or mathematical statement. The integers that are multiplied to create the original number are known as factors. The components of 18 include, for instance, 2, 3, 6, 9, and 18, as well as;
18 = 2 x 9
18 = 2 x 3 x 3
18 = 3 x 6
In a similar way, the factors in the case of polynomials are the polynomials that are multiplied to create the original polynomial. For instance, (x + 2) (x + 3) are the elements of x2 + 5x + 6. The original polynomial is produced when we multiply both x +2 and x +3. We can also locate the polynomials' zeros after factorization. Zeroes in this situation are x = -2 and x = -3.
2. Now, to write f(x) as the product of (x-1) and another factor.
x³+5x²+2x-8 = (x-1)(x²-6x+8).
3. Now, to write f(x) as the product of three linear factors.
x³+5x²+2x-8 = (x-1)(x²-6x+8)= (x-1)(x-4)(x-2)
4. Look at the sketch below.
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Related Questions
The area of a rectangular piece of land is 2/3 square mile.
One dimension is 1 1⁄2 miles.
Answers
Answer:
4/9 miles
Step-by-step explanation:
[tex]\sf Area = \dfrac{2}{3} \ square \ miles\\[/tex]
[tex]\sf length = 1\dfrac{1}{2}=\dfrac{3}{2} \ miles[/tex]
[tex]\sf Width \ of \ rectangle = \dfrac{Area}{length}[/tex]
[tex]\sf = \dfrac{2}{3} \div \ \dfrac{3}{2}\\\\ =\dfrac{2}{3}*\dfrac{2}{3}\\\\ =\dfrac{4}{9} \ miles\\[/tex]
Use KCF method for faction division.
K- Keep the first fraction.
C - Change the division to multiplication.
F - Flip the second fraction.
On a coordinate plane, a circle has a center at (0, 0). Point (3, 0) lies on the circle.
Distance formula: StartRoot (x 2 minus x 1) squared + (y 2 minus y 1) squared EndRoot
Does the point (2, StartRoot 6 EndRoot) lie on the circle shown? Explain.
Yes, the distance from (3, 0) to (0, 0) is 3 units.
Yes, the distance from (0, 0) to (2, StartRoot 6 EndRoot) is 3 units.
No, the distance from (3, 0) to (2, StartRoot 6 EndRoot) is not 3 units.
No, the distance from (0, 0) to (2, StartRoot 6 EndRoot) is not 3 units.
Answers
Answer: Option (4)
Step-by-step explanation:
We know that the radius of the circle is 3.
Using the distance formula, the distance from the given point to the center is
[tex]\sqrt{(\sqrt{6}-0)^{2}+(2-0)^{2}} = \sqrt{10} \neq 3[/tex]
Answer:d
Step-by-step explanation:
P(x) Q(x) = R(x); if P(x)
72 Am
R(x); if P(x)=x+2 and R(x) = x³ - 3x² - 6x-2, what is Q(x)?
Answers
Answer:
Q(x) is = to 11x² that's my answer
True or false? Any fraction made up of two natural numbers is a rational number. Explain your answer.
Answers
Rational numbers are numbers that can be written in the form of a/b where a and b are integers.
What are Rational and Irrational numbers?Rational numbers are numbers that can be written in the form of a/b where a and b are integers.
Example: 1/2, 3.5 (which is writable as 7/5), 2(which is writable as 4/2), etc.
Irrational numbers are those real numbers that are not rational numbers.
For example √2, π, √13, etc.
It is an important thing to Know that all natural numbers are integers, and all integers are rational numbers. That means natural numbers are not irrational.
The given statement that any fraction is made up of two natural numbers is a rational number is true.
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Which exponential equation is equivalent to this logarithmic equation? (2)
Answers
Answer:
A. e⁴=xStep-by-step explanation:
Log x=4 ➡️ e⁴=x or x= e⁴
Hope it helps
Please help!!!!!!!
picture below
Answers
If the function is vertically stretched by a factor of 3, the resulting function will be g(x) = [tex]3(5^{x-2})[/tex]
Vertical stretch of a functionGiven the parent function f(x) = x, if the function is vertically stretched by k units, the resulting function will be g(x) = kx
Given the parent function
f(x) = [tex]5^{x-2}[/tex]
If the function is vertically stretched by a factor of 3, the resulting function will be g(x) = [tex]3(5^{x-2})[/tex]
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I WILL GIVE BRAINIEST
The measure of angle N is (3x + 18) degrees . The measure of angle B is (2x + 142) degrees. If angle N is the supplement of angle B, what is the measure of the two angles?
Answers
Answer:
N: 30 B:150
Step-by-step explanation:
Supplementary angles add up to 180 meaning their equations must also add up to 180:
(3x + 18) + (2x + 142) = 180
Solve for x:
5x + 160 = 180
5x = 20
x = 4
Substitute 4 in all values of x to obtain the measure of the two angles:
N: 3(4) + 18 = 30
B: 2(4) + 142 = 150
Rewrite the rational exponent as a radical exponent ^{^3\sqrt{2^7}}
Answers
Answer:
4 ^3sqrt(2)
Step-by-step explanation:
two 2's can come out of the square root and it leaves one left in it and 2x2 is 4 which is on the outside.
Explanation: have to do step by step
PLEASE HELP ASAP!!!!
What is the rectangular equivalence to the parametric equations?
x(θ)=3cosθ+2,y(θ)=2sinθ−1 , where 0≤θ<2π .
Drag a term into each box to correctly complete the rectangular equation.
____ + ________ = 1, where the x is on the interval _______
options:
(x-2)^2/9
(x+2)^2/9
(x-1)^2/4
(x+1)^2/4
(y-2)^2/9
(y+2)^2/9
(y-1)^2/4
(y+1)^2/4
[-3,3]
[-3,1]
[-2,2]
[-1,5]
Answers
The correct answer is option A [tex](\dfrac{x-2}{3})^2+(\dfrac{y+1}{2})^2=1[/tex] it will be an ellipse.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Let's consider the following trigonometric identity:
Sin²[tex]\theta[/tex] + Cos²[tex]\theta[/tex] = 1
Each trigonometric function is cleared respectively in given parametric equations:
[tex]Cos \theta = \dfrac{x-2}{3}[/tex] and [tex]Sin\theta =\dfrac{y+1}{2}[/tex]
The equivalent expression in rectangular form is:
[tex](\dfrac{x-2}{3})^2+(\dfrac{y+1}{2}^)^2 = 1[/tex]
Therefore the correct answer is option A [tex](\dfrac{x-2}{3})^2+(\dfrac{y+1}{2})^2=1[/tex] it will be an ellipse.
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If a data set has many extremely small data values, than the median will be
Answers
Answer:
If a data set has many extremely small data values, than the median will be the same.
What is the median?The middle number in a given sequence of number, taken as the average of the two middle numbers when the sequence has an even number of numbers.
The median is resistant to change no matter extremely small or large values.
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8. What least number must be subtracted from 13601 to get a number exactly divisible by 87?
Answers
Answer:
29
Step-by-step explanation:
87×156+29=13601
First do 13601/87=156.3333...
156 × 87 = 13572
13601-13572=29
so, 87×156+29=13601
Answer:
29Step-by-step explanation:
What least number must be subtracted from 13601 to get a number exactly divisible by 87?
13601 : 87 = 156 and remainder 29
so your answer is 29
---------------
check
(13601 - 29) : 87 =
13572 : 87 = 156
Find the value of x.
A. 6.6
B. 5.5
C. 8.8
D. 1.1
Answers
Answer:
the answer is D
Step-by-step explanation:
the answer is D because the
Answer: d
Step-by-step explanation:
Point-Slope Form
*See photo*
Answers
Answer:
y = 3x - 5
Step-by-step explanation:
We know that the equation 'y = 3x + ?' intersects the point (1, -2). This means that when x = 1, y = -2 in out equation above. To solve this just plug in the x and y values to get '?'.
[tex]y = 3x + ?\\-2 = 3(1) + ?\\-5 = ?[/tex]
Now that we know '?' is -5, we write it back into slope intercept form, so our final answer is y = 3x - 5
Sparky bought a rare Mickey Mantle baseball card for $16,500 that is increasing 8% in value every year. How much will the card be worth in 7 years?
Answers
Answer: 28,278.10
Step-by-step explanation:
[tex]a_{7} =16500(1.08)^7[/tex]
[tex]a_{7} =28278.1[/tex]
Question 20 The sports budget for cricket, football, and netball was divided in the ratio 5: 3:2, respectively. The total sports budget is $1.200,000. How much money will netball receive? A. B. C. D. + O A OB O C O D $120,000 $240,000 $360,000 $600,000 Question 20 The sports budget for cricket , football , and netball was divided in the ratio 5 : 3 : 2 , respectively . The total sports budget is $ 1.200,000 . How much money will netball receive ? A. B. C. D. + O A OB O C O D $ 120,000 $ 240,000 $ 360,000 $ 600,000
Answers
Using proportions, it is found that the amount that netball will receive is of:
B. $240,000
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
Due to the ratios, the proportion of funding that is destined to netball is given by:
[tex]p = \frac{2}{5 + 3 + 2} = \frac{2}{10} = 0.2[/tex]
Hence, out of $1.200,000, the amount destined to netball is:
A = 0.2 x $1.200,000 = $240,000.
Which means that option B is correct.
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9.
Let f(x) = 2x + 2. Solve f−1(x) when x = 4. (1 point)
Answers
Answer:
1
Step-by-step explanation:
The value of the output given by the inverse for a given input is the same as the input of the original function that results in the output equal to the given input.
So, 2x + 2 = 4, meaning the answer is 1
In which part of the graph is the distance from home decreasing?
Answers
Answer:
A) 2
Step-by-step explanation:
Because the slope is negative of line 2 the distance is getting smaller
mZACB = (6y-7)° and mZDCA = (8y - 1)°.
B
A
D
|
C
What is mZACB?
Answers
Answer: [tex]35^{\circ}[/tex]
Step-by-step explanation:
Angles ACB and DCA add to form angle ACB, which is a right angle, so:
6y - 7 + 8y - 1 = 90 [angles that add to form a right angle add to 90 degrees]14y - 8 = 90 [combine like terms]14y = 98 [add 8 to both sides]y = 7 [divide both sides by 14]So, [tex]m\angle ACB=6(7)-7=\boxed{35^{\circ}}[/tex]
Under her cell phone plan, Sarah pays a flat cost of $69 per month and $4 per gigabyte. She wants to keep her bill at $83.80 per month. Write and solve an equation that can be used to determine g, the number of gigabytes of data Sarah can use while staying within her budget.
Answers
Answer:
83.80 = 69 + 4x
x = 3.7
Sarah can use up to 3.7 gigabytes per month to stay within her budget
Step-by-step explanation:
83.80 = 69 + 4x
14.8 = 4x
x = 3.7
The number of gigabytes of data Sarah can use while staying within her budget is 3.7 gigabyte.
Given that, Sarah pays a flat cost of $69 per month and $4 per gigabyte.
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 =.
Let the number of gigabyte be g.
69+4g=83.80
The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.
Now, 4g=83.80-69
⇒ 4g=14.8
⇒ g=14.8/4
⇒ g=3.7 gigabyte
Therefore, the number of gigabytes of data Sarah can use while staying within her budget is 3.7 gigabyte.
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I want to know the answer quick
Answers
Answer:
[tex]\fbox {B. Exponential Decay}[/tex]
Step-by-step explanation:
As the exponent is applied to a number less than 1, the future values of the function f(x) will become smaller and smaller. Hence, it represents exponential decay.
What is the answer for 4x+1/3=20?
Answers
Answer:
x = 59/12
Step-by-step explanation:
4x + 1/3 = 20
4x = 20 - 1/3
12x/3 = 60/3 - 1/3
12x = 60 - 1
12x = 59
x = 59/12
Check:
4*59/12 + 1/3 = 20
236/12 + 4/12 = 20
240/12 = 20
Step-by-Step Solution:
4x + 1/3 = 20
(4 * 3)x/3 + 1/3 = 20
12x/3 + 1/3 = 20
12x + 1 = 20 * 3
12x + 1 = 60
12x = 60 - 1
12x = 59
=> x = 59/12
Therefore, x = 59/12
Solve for x. The triangles are similar.
Answers
Answer:
[tex]\fbox {D. 10}[/tex]
Step-by-step explanation:
As the triangles are similar :
45/55 = (12x - 3)/143
9/11 = (12x - 3)/143
9 x 13 = 12x - 3
12x = 117 + 3
12x = 120
x = 10
Answer:
D. 10
Step-by-step explanation:
We can use similar triangles to solve this question. ΔRSE ≅ ΔFGE by SAS. We can set up this similarity equations: [tex]\frac{SE}{GE} = \frac{RE}{FE}[/tex] . Plugging in the numbers from the diagram, we get [tex]\frac{45}{12x-3} = \frac{55}{143}[/tex] . Using cross multiplication, we get the following equation:
[tex]45 * 143 = 55 *(12x-3)\\ 6435 = 660x - 165\\6600 = 660x\\x = 10[/tex]
Our final answer is D. 10
factoris fully 2ab² + 8a²b
Answers
Answer:
2ab(b + 4a)
Step-by-step explanation:
2ab² + 8a²b
Factor Out the 2:
2(ab² + 4a²b)
Factor Out the a:
2a(b² + 4ab)
Factor Out the b:
2ab(b + 4a)
Help me please I need this for tomorrow please please
Answers
Please Help!
The manager of a home electronics store is considering re-pricing a new model of digital camera. At the current price of $680, the store sells about 70 cameras each month. Sales data from other stores indicate that for each $20 decrease in price, about 5 more cameras would be sold. The table shows some x and y values; where x is the number of price decreases and y is the revenue.
a) How many price decreases should the manager apply?
b) What price produces the maximum revenue?
c) What is the maximum revenue?
Answers
The reduction in price that will be applied is $200.
How to calculate price?From the given information, the price function will be:
P - 680/(680 - 660) = (Q - 70)/(70 - 75)
P = -4Q + 960
Revenue will be:
= Price × Quantity
= (-4Q + 960)Q
= 4Q² + 960Q
Differentiating this will be Q = 120
Price will be:
= (-4 × 120) + 960
= 480
The reduced price will be:
= 680 - 480
= 200
The maximum revenue will be:
= 480 × 120
= 57600
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Select the correct answer from each drop-down menu.
Determine the best measure of center and the skew of the data distribution.
(23, 29, 12, 14, 27, 23, 23, 18, 23, 1, 7, 18, 43, 24, 28, 17, 32, 33, 38)
Answers
The central tendency of the given data will be 22.79.
What is mean?Mean is defined as the ratio of the sum of the number of the data sets to the total number of the data.
There are 3 ways in which we can express the centre of the data given: (1) mean or average, (2) mode, (3) median
For the mean, we sum up all the given and divide them by the number of data
mean = 433 / 19 = 22.79
For the mode, we just determine which among the given data appears more frequently and in this given that is 23.
For the median, we arrange the numbers from highest to lowest and determine which number will appear in the centre. Since there are 19 data, we need to find which among them will appear to be the 10th. That is also 23.
So, the value that would best describe the central tendency is 23. Since the values to the left of 23 are more scattered than those to its right, the distribution exhibits negative.
Therefore central tendency of the given data will be 22.79.
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need help asap!!! ill give brainliest for right answer!
A rectangular pyramid has a height of 6 units and a volume of 40 units3. Shannon states that a rectangular prism with the same base area and height has a volume that is three times the size of the given rectangular pyramid. Which statement explains whether Shannon is correct?
A rectangular prism in which BA = 20 and h = 6 has a volume of 40 units3; therefore, Shannon is incorrect.
A rectangular prism in which BA = 6.67 and h = 6 has a volume of 40 units3; therefore, Shannon is incorrect.
A rectangular prism in which BA = 20 and h = 6 has a volume of 120 units3; therefore, Shannon is correct.
A rectangular prism in which BA = 6.67 and h = 6 has a volume of 120 units3; therefore, Shannon is correct.
Answers
Answer:
A rectangular prism in which BA = 20 and h = 6 has a volume of 120 units3; therefore, Shannon is correct
Got it right one the test! <3
What is the measure of the apothem, rounded to the nearest hundredth of a centimeter?
Answers
The measure of apothem is 1.75 cm.
The complete question is
The area of the regular octagon is 10.15 cm2.
What is the measure of the apothem, rounded to the nearest hundredth of a centimeter?
What is an Octagon ?A polygon with eight sides , eight angles and eight vertices is called an octagon.
If a is the Side of the octagon.
10.15 = 2(1+√2) a²
a² = 10.15 / [2×(1+1.414)]
a² = 2.10
a = 1.45 cm
Therefore the side = 1.45 cm
A = 8 × (a × h)/2
If we consider 8 equilateral triangles with
a = face of octagon
h = Apothem of octagon
10.15 = 8 × (1.45 × h)/2
h = 10.15 /4/ 1.45
h = 1.75 cm
Therefore the measure of apothem is 1.75 cm.
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Solve the equation 7(w +13) = 35.
) What is the value of w?
Answers
Answer: -8
Step-by-step explanation:
7(w+13)=35 [given]w+13=5 [divide both sides by 7]w = -8 [subtract 13 from both sides]Answer:
7(w+13)=35
7w + 91 =35
7w=35-91
7w= -56
7w/7 = -56/7
w=-8
Find the probability of drawing a heart from the standard deck of cards and then drawing a 5 from any suit after the first card is replaced in the deck. Write as a fraction in simplest form.
Answers
The probability of drawing a heart from the standard deck of cards and then drawing a 5 is 1/52
How to determine the probability?In a standard deck of cards, we have:
Total = 52
Heart = 13
5's = 4
Since the cards are replaced, the probability is calculated as:
P(Heart and 5) = Heart/Total * 5s/Total
This gives
P(Heart and 5) = 13/52* 4/52
Evaluate
P(Heart and 5) = 1/52
Hence, the probability of drawing a heart from the standard deck of cards and then drawing a 5 is 1/52
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