(x - 3) is a factor of the polynomial f(x) = x³ - 3x² + 4x - 12 since f(3) = 0.
To solve the problem, recall the factor theorem.
Factor Theorem states that if we have a polynomial f(x) and if (x - a) is a factor of f(x), then f(a) = 0
The given function is:
f(x) = x³ - 3x² + 4x - 12
To see whether x - 3 is a factor of f(x) = x³ - 3x² + 4x - 12, we need to find f(3).
Substitute x = 3 into f(x):
f(3) =3³ - 3(3)² + 4(3) - 12
f(3) = 27 - 27 + 12 - 12
f(3) = 0
Since f(3) = 0, then x -3 is a factor of x³ - 3x² + 4x - 12
Your question is incomplete, but most probably your question was:
Is x - 3 a factor of the polynomial x³ - 3x² + 4x - 12?
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What is ideal or real solution?
Answer:
An Ideal solution follows the Raoult's law strictly
A Real solution shows deviation from the Raoult's law.
Step-by-step explanation:
5. The base of a rectangular prism has
an area of 23 square cm. The height of
the rectangular prism is 3 cm. What is
the volume of this rectangular prism?
Answer:
1. length×width × height
4×9×10
=360cm
2.base×height
36×65
=2340 inches
The circumference is 79.5
Need help with finding the diameter and radius
Answer:
Step-by-step explanation:
[tex]C=\pi D[/tex]
[tex]79.5=\pi D\\[/tex]
divide by [tex]\pi[/tex]
D = 25.30
radius = [tex]\frac{d}{2}[/tex]
[tex]\frac{25.30}{2} =12.65[/tex]
Answer:
r approx 12.7
d approx 25
Step-by-step explanation:
Find the volume and round to the nearest hundredths place when necessary.
Answer:
This is a prism since both sides are the same triangle,
Lets find the area of the triangle first then multiply it by the width which is 16.
20.5(base or height) x 13.3(height or base) = 272.65
272.65 divided by 2 ( x 1/2) = 136.325 is your area, now we multiply by the width.
136.325 x 16 = 2,181.2 mm3 is your volume.
Whenever coming across these types of volumes we must first find a shape and find its area then multiply it by the figure's height.
Formula area of a triangle:
B(base) x H(height) x 1/2(basically just dividing by 2)
5
Isabella wants to create 23 ounces of new hand lotion, with a minimum 15% concentration of beeswax, from a mixture of two lotions.
One lotion has a 21% concentration of beeswax, and the second lotion has a concentration of 5% beeswax. Based on the inequality
below, how much of the 21% lotion, x, will she need?
O A. x≥ 14.375
O B.
x2 15.33
OC.
x2 20.125
O D. x2 11.5
0.21x+0.05(23-x) ≥ 3.45
Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values.
What are Inequalities?The term "inequality" refers to a relationship between two expressions or values that is not equal to one another. Inequality originates from an imbalance, thus.
In order to get the variable on its own, you can solve a lot of straightforward inequalities by adding, removing, multiplying, or dividing the two sides. But as a result of them, the direction of the inequality will change: Using a negative number to divide or multiply both sides. right and left sides are switched.
An inequality results from the comparison of two or more algebraic expressions using the symbols, >, or. They are the mathematical expressions with unequal sides.
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The cost of Katie’s meal at a restaurant is $15.00. She is charged 7.0% tax and leaves a tip of x dollars. Katie spent a total of $20.05 on the meal, tax, and tip.
Answer:
$5.05
Step-by-step explanation:
Which of the following points is a solution to the system of equations shown?
y - x = -1
x + y = -5
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[tex]\quad \qquad \huge \bf \dag \: Answer \: \dag[/tex]
`●.`●.`●.`●.`●.`●.`●.`●.`●.`●.`●.`●.`●.`●.`●.`●.`●.`●.
[tex] \underline{ \large \rm Solution} : [/tex]
[tex]\rm Given : [/tex]
Two equations are -
y - x = -1 (i)x + y = -5 (ii)[tex] \rm Procedure : [/tex]
Considering the equations as (i) and (ii) respectively
From equation (i) -
y = x - 1put this value of y in equation (ii) -
x + y = -5x + x - 1 = -52x = -5 + 12x = -4 x = -2Next thing to do would be to put value of x we got in equation (i) to get y
y - x = -1y - (-2) = -1 y + 3 = -1 y = -1 - 3 y = -4Values asked are :
[tex] \rightarrow \rm y = - 4[/tex]
[tex] \rightarrow \rm x= - 2[/tex]
`●.`●.`●.`●.`●.`●.`●.`●.`●.`●.`●.`●.`●.`●.`●.`●.`●.`●.
[tex] \large \bf hope \: \: it \: \: helps \: - dabI [/tex]
`●.`●.`●.`●.`●.`●.`●.`●.`●.`●.`●.`●.`●.`●.`●.`●.`●.`●.
How do you graph 3 4 on a number line?
By drawing a number line and then marking it as 0 and 1, and by dividing the distance in 8 equal parts we can graph 3/4 on the number line, where 3/4 = 6/8, which will be equal to the sixth part from the left end.
A number line is a diagram of a graded straight line used to represent real numbers in introductory mathematics. It is assumed that every point on a number line corresponds to a real number, and that every real number corresponds to a point.
A horizontal line with evenly spaced numerical increments is referred to as a number line. How the number on the line can be answered depends on the numbers present.
For drawing 3/4 on a number line, we will follow the following steps:
We will first draw a line and mark 0 and 1 on it.
In between 0 and 1, we will divide the total distance into 8 equal parts, where one part will represent (1/8)th portion.
As 3/4 can be written as 6/8 which will be equal to 6 parts out of those 8 parts.
Hence. by marking there we can locate 3/4 on the number line.
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The correct question should be like:
How do you plot 3/4 on number line
How do you convert log to the base e to log to the base 10?
To convert the log base 2 to log base 10, we can use the change of base formula for logarithms. The change of base formula for logarithms is as written:
log b(x)=logc(x) logc(b)
By Using this formula, we can convert or find log base 2 to log base 10, where log base 10 is called the common logarithm, and we denote log10 (x) as log(x). The change of base formula gives the following:
log2(x)=log10(x)log10(2)=log(x)log(2)
This gives us the formula we can use to convert a logarithm with base 2 to a common logarithm with base 10.
The log function of e to the base 10 is denoted as “log 10 e”. Where the value of e is 2.7182818. The natural log function of e is denoted as “log e e”.
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Please answer all with explanation
Answer:
1:Exponents are not involved..try this 34% 1/2 + ==% 98) ::*37 21 /) ( ^ 11 56/77
2:make a little close parenthesis and make a little = and % x2 RX then multiply it 9 by 9
3:477/^54*(7632)**% 87÷32×(76*09×23) 2/8=97
4:9a/(92 28 ^^_× (32
Step-by-step explanation:
HOPE IT HELPS!!
Find the Highest Common Factor (HCF) of 36 and 48
Answer: 12
Step-by-step explanation:
-16x-32y=52 solve for y
Answer: I think 7/2?
Step-by-step explanation:
Cual es mayor 0.08 o 0.2
Answer:
0.2
Step-by-step explanation:
Answer:
0.2 es mayor.
Step-by-step explanation:
0.2>0.08
8/9 to what power equals 64/81
2nd
Step-by-step explanation:
8/9 to the second power equals to 64/81. Hope this helps!
Answer:
Hi
x = exponent
64 = 8·8 = 8^2
81 = 9·9 = 9^2
64/81 = 8^2/9^2 = (8/9)^2
(8/9)^2 = (8/9)^x
x = 2
Step-by-step explanation:
Please consider giving me brainliest.
The sum of two consecutive even numbers is 34. What numbers is it
Answer:
16 and 18
16 + 18 = 34 .......... .....
Mav is making pizzas for a pizza party. Each pizza requires 4/5 pound of cheese. How many pounds of cheese does she need to make 5 pizzas? Express your answer in simplest form.
Answer:
4 pounds of cheese
Step-by-step explanation:
4/5*5=4
What are 3 examples of perfect squares?
Three examples of perfect squares is 1) 9, as it is equal to 3 x 3.2) 16, as it is equal to 4 x 4.3) 25, as it is equal to 5 x 5.
What is perfect squares?Perfect squares are numbers that can be expressed as the product of two equal integers, such as 4, 9, and 16. These numbers can be written as the square of a single number, such as 2² = 4, 3² = 9, and 4² = 16. Perfect squares are also known as whole squares, and they provide an easy way to find the square root of a number.
Perfect squares are numbers that are the result of multiplying a number by itself. For instance, 4 is a perfect square because it is equal to 2 x 2.
Similarly, 9 is a perfect square because it is equal to 3 x 3. Perfect squares can be easily identified by their square root, which is the number that can be multiplied by itself to produce the perfect square.
For example, the square root of 16 is 4, since 4 x 4 = 16.
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Ron killed 8 times as many spiders as Harry,H (Write an expression to represent the following situations)
Answer:
Ron killed 8 times as many spiders as Harry: R = 8 * H
Step-by-step explanation:
This expression represents the situation in which Ron killed 8 times as many spiders as Harry.
210 students were asked whether they want to go to a water park or a roller skating rink for a class party.
I
• 50 students are girls who want to go to the water park.
• 45 students are girls who want to go skating.
60 students are boys who want to go to the water park.
Water park Skating Total
Boys
60
55
115
Girls
50
45
95
Total
110
100
210
Answer:
60.3
Step-by-step explanation:
hope this helps
Find and state the inverse of the function, and also state whether the inverse is a function.
((3,5), (2,8), (1.5), (0.3))
The inverse of the function is {(5, 3), (8, 2), (5, 1), (3, 0)} and it is not a function
How to determine the inverse of the functionFrom the question, we have the following parameters that can be used in our computation:
((3,5), (2,8), (1.5), (0.3))
The above ordered pairs can be represented a
(x, y)
This means that the inverse function is
(y, x)
So, we have the following expression
(y, x) = {(5, 3), (8, 2), (5, 1), (3, 0)}
Also, the inverse is not a function
This is so because the x value 5 has different y values 3 and 1
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Need help ASAP! Due very soon please help
Answer:
Lemme get you numba first
Answer:
y = -3/4x + 36
Step-by-step explanation:
You move down three spaces and over 4 spaces on the graph
36 is the y intercept of the line
What is the Average Rate of Change of the graph below from -5 < t < 8
Answer:47
Step-by-step explanation
solve (x-3)^2=49. select the values of x
Answer:
x1=-4 x2=10
Step-by-step explanation:
step 1: x-3 = +/- 7 <--- take the square roots of both sides of the equation and use both positive and negative roots
step 2: x-3 = -7
x-3=7
step 3: x-3=-7--> x=-4
x-3=7--> x=10
step 4:x1=-4, x2=10 is the answer
Find value of y
[tex] {y}^{2} - 58 = 25 \times 4 + 11[/tex]
Hello there!
Answer:
y = ± 13
Step-by-step explanation:
[tex]y {}^{2} - 58 = 25 \times 4 + 11 \\ y {}^{2} - 58 = 100 + 11 \\ y {}^{2} - 58 = 111 \\ y {}^{2} - 58 - 111 = 111 - 111 \\ y {}^{2} - 169 = 0 \\ (y + 13)(y - 13) = 0 \\ y = - 13 \: \: \: and \: \: \: y = 13[/tex]
What is the revolution of the Earth and Moon?
The revolution of the Earth and Moon refers to their orbits around the Sun. The Earth's revolution takes time of 365.24 days, and the Moon's revolution takes 27.32 days.
The revolution of the Earth and Moon is the path of the two celestial bodies around the Sun. The Earth takes 365.24 days to complete one revolution, which is also known as one year. The Moon, on the other hand, takes 27.32 days to complete one revolution, which is also known as one lunar month.
The revolution of the Earth and Moon refers to their orbits around the Sun, with the Earth taking 365.24 days and the Moon taking 27.32 days to complete one revolution.The revolution of the Earth and Moon refers to their orbits around the Sun. The Earth's revolution takes 365.24 days, and the Moon's revolution takes time of 27.32 days.
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what is the estimate value of
Answer:
1.99
Step-by-step explanation:
Pi is 3.14
So result is 1.99
hello i need urgent help with this assignment.
Answer:
AD = 1 3/4y + 5/8x - 3
Step-by-step explanation:
AD = 1/4x + 2y + 3 - 1/4y + 3/8x - 6
combine like terms:
AD = 1 3/4y + 5/8x - 3
The mode of the raw data given as: 4, 7, 4, 3, 2, 7, 7, 6, 4, 7, 8
Answer:
7, since it is the number that pops up the most in the set of data given here
Hope that helps! :)
-Aphrodite
Step-by-step explanation:
Find the midpoint between these points.
(1,3) (5.1)
someone please help asap !!!
Answer:SOLUTION
The midpoint for two points P=(px,py) and Q=(qx,qy) is M=(px+qx2,py+qy2).
We have that px=1, py=3, qx=5, qy=1.
Thus, M=(1+52,3+12)=(3,2).
ANSWER
M=(3,2)A
Step-by-step explanation:
Answer:
The midpoint is (3, 2)
Step-by-step explanation:
To find the x-coordinate of the midpoint, average the x-coordinates 1 and 5:
1 + 5
xm = ----------- = 3
2
y-coordinate:
1 + 3
ym = ----------- = 2
2
The midpoint is (3, 2)
If you buy 3 CD’s at the original cost of 9.99 but you have a 10% off coupon and the sales tax is 6% what is your total