Answer:
f(x) = x³ – 3x² – 10x + 24 = (x + 3)(x – 2)(x – 4)Step-by-step explanation:
I would use the Horner method.
f(x) = x³ – 3x² – 10x + 24
f(2) = 2³ - 3·2² - 10·2 +24 = 0 ⇒ x=2 is the root of function
So:
| 1 | -3 | -10 | 24 |
2 | 1 | -1 | -12 | 0 |
therefore:
f(x) = x³ – 3x² – 10x + 24 = (x – 2)(x² – x – 12)
For x² – x – 12:
[tex]x=\dfrac{1\pm\sqrt{(-1)^2-4\cdot1\cdot(-12)}}{2\cdot1}=\dfrac{1\pm\sqrt{1+48}}{2}=\dfrac{1\pm7}{2}\\\\x_1=\dfrac{1+7}{2}=4\ ,\qquad x_2=\dfrac{1-7}{2}=-3[/tex]
It means:
f(x) = x³ – 3x² – 10x + 24 = (x – 2)(x – 4)(x + 3)
Preston bought 16 donuts. There were d donuts in each box. Choose the expression that shows how many boxes of donuts Preston bought
Answer:
What are the option?
Step-by-step explanation:
A recipe says to use 3 cups of flour to make 48 cookies. How many cups of
flour are needed for 80 cookies?
Choose the correct answer below for the following problem:
(‒489) + (‒764) =
A.
‒1,253
B.
275
C.
1,253
D.
‒275
Step-by-step explanation Answer:
A -1253
-489-764 = -1253
Mrs. Johnson earned $31,500.00 in salary this year. Her salary will increase by 10% next year. Mrs. Johnson is paid on a monthly basis. By how much will her monthly salary increase when she receives her raise?
Answer:
34650 dollars by next year
Step-by-step explanation:
Answer:
Step-by-step explanation31500x.10. 3150. 31500+3150. 34650. 34650/12 2887.50. 31500/12. : 2625. Difference per month 262.50
In a final year examination, 33 students pass in Chinese, 29 students pass in English, 20 students pass in both subjects and 8 students fail in both subjects. How many students are in the class?
Answer:
50
Step-by-step explanation:
33+29= 62
62-20= 42
42+8= 50 students
What is the end behavior of the function f(x)=2e^x? Select the two correct answers.
As x approaches infinity, f(x) approaches infinity.
As x approaches negative infinity, f(x) approaches infinity.
As x approaches infinity, f(x) approaches 0.
As x approaches infinity, f(x) approaches negative infinity.
As x approaches negative infinity, f(x) approaches 0.
Answer:
As x approaches infinity, f(x) approaches infinity. As x approaches negative infinity, f(x) approaches 0.Step-by-step explanation:
F (x) = x^2 + 4x; Find f (−7)
Answer:
f(-7) = 21
General Formulas and Concepts:
Pre-Alg
Order of Operations: BPEMDASStep-by-step explanation:
Step 1: Define
f(x) = x² + 4x
f(-7) is x = -7
Step 2: Solve
Substitute: f(-7) = (-7)² + 4(-7)Evaluate: f(-7) = 49 + 4(-7)Multiply: f(-7) = 49 - 28Subtract: f(-7) = 21Which choice shows the correct solution to 2528 ÷ 8?
Answer:
B.
Step-by-step explanation:
Hope it helps!
What is 6000 times 8000 plus 3000-20
Answer:
48,002,980
Step-by-step explanation:
Have a good day
20% of a is 11. what is a
Answer:
2.2
Step-by-step explanation:
11*.20 = 2.2
So that is 20% on 11.
Hope this helps!
PLEASE HELP WITH GEOMETRY
Answer:
acute triangle
Step-by-step explanation:If the square of the length of the longest side of a triangle is less than the sum of the squares of the lengths of the other two sides, then the triangle is an acute triangle.
For which equation is a = 4 not the solution?
9 a = 36
5 a = 54
8 a = 32
6 a = 24
9x4=36 X
8x4=32 X
6x4=24 X
5x4=20, not 54.
So 5xA=54 is the correct answer
hope it helps!
The rectangle below has an area of 12y^2+21y^512y 2 +21y 5 12, y, squared, plus, 21, y, start superscript, 5, end superscript. The width of the rectangle is equal to the greatest common monomial factor of 12y^212y 2 12, y, squared and 21y^521y 5 21, y, start superscript, 5, end superscript. What is the length and width of the rectangle? \text{Width} =Width=start text, W, i, d, t, h, end text, equals
Answer:
This means that the width = 3y²
The length = 4y+7y³
Step-by-step explanation:
Given
Area of the rectangle = 12y^2+21y^5
Width of the rectangle is the greatest common monomial of 12y^2 and 21y^5
First let us get the greatest common monomial of 12y^2 and 1^5
12y^2 = (3 * y * y) * 4
21y^5 = (3 * y*y)*y*y*y* 7
Hence the greatest common monomial is 3 * y * y = 3y²
Factor out 3y² from the area function;
12y^2+21y^5
3y² (4y+7y³) = Area of the rectangle
Length * Width = 3y² (4y+7y³)
On comparing both sides of the equation
This means that the width = 3y²
The length = 4y+7y³
Answer:
4y^2
Step-by-step explanation:
what number do these base ten blocks show
Susan makes a purchase of $175 and is charged 7.75% for sales tax. What is the total cost of the purchase if Susan charges it on a credit card with a daily interest rate of 0.039% and pays the balance off at the end of 30 days? a. $176.17 b. $186.70 c. $190.77 d. $200.26
Answer:
C. 190.77
Step-by-step explanation: edge 2022
The required, total cost of the purchase is $190.77. Option C is correct.
What is the percentage?The percentage is the ratio of the composition of value to the overall composition of value multiplied by 100.
Here,
To calculate the total cost of the purchase, we first need to calculate the amount of sales tax and add it to the original price.
Sales tax = 7.75% of $175 = 0.0775 x $175 = $13.56
Total cost of purchase = $175 + $13.56 = $188.56
If Susan charges the purchase to her credit card and pays it off after 30 days, she will be charged interest on the outstanding balance for those 30 days. The interest rate is 0.039% per day, which is equivalent to 1.17% per month (0.039% x 30).
The interest charged on the outstanding balance after 30 days will be:
Interest = $188.56 x 1.17% = $2.20
Therefore, the total cost of the purchase, including sales tax and credit card interest, will be,
Total cost = $188.56 + $2.20 = $190.76
Therefore, the total cost of the purchase is $190.77.
Learn more about percentages here:
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Find the GCF of the following set of numbers
260, 80, 50
Answer:
10
Step-by-step explanation:
The factors of 50 are: 1, 2, 5, 10, 25, 50
The factors of 80 are: 1, 2, 4, 5, 8, 10, 16, 20, 40, 80
The factors of 260 are: 1, 2, 4, 5, 10, 13, 20, 26, 52, 65, 130, 260
In all of these numbers, we can see that 10 is common throughout and 10 is also the greatest factor all these numbers share.
Hope this helps you :)
Can somebody please help me out
Answer:
Right so, you would first graph your center point. Then, based on the radius, you would make four points. Let's say your center point is (0,0) and your radius is 2. You would make a point at (-2,0), (2,0), (0,-2), and (0,2). You would then draw a circle through those points. Let me know if you need any further clarification!
2(5x + 3) - 2(2x - 3)
Factor: 6(x + 2)
Simplify: 6x + 12
Answer:
[tex]\boxed {6x + 12}[/tex]
Step-by-step explanation:
Solve the following expression:
[tex]2(5x + 3) - 2(2x - 3)[/tex]
-Use Distributive Property:
[tex]2(5x + 3) - 2(2x - 3)[/tex]
[tex]10x + 6 - 4x + 6[/tex]
-Combine like terms:
[tex]10x + 6 - 4x + 6[/tex]
[tex]\boxed {6x + 12}[/tex] (final answer)
select the group of numbers that are ordered least to greatest.
Answer: I think it’s the 2nd, 3rd and 4th
Step-by-step explanation:
Help me solve this problem please
Answer: A
Step-by-step explanation: If you fill in the x-intercept and the y-intercept and solve -4(2) + 20 = 12 And -4(3) + 20 = 8
if you solve for those you would get your y-intercept
Jack has $65 to spend on art supplies. He needs to buy an easel that costs $18. He also wants to buy some canvases that cost $11 each
Which of the following inequalities represents the amount of money Jack can spend if he buys n canvases?
A:65 >(line underneath sign)18 + 11n
B:65 > 18 + 11n
С:65 < (line underneath sign) 18 + 11n
D:65 < 18 + 11n
Answer:
C
Step-by-step explanation:
Jack can spend less than or equal to. So C is correct.
The inequality represents the given situation is 65 ≥ 18 + 11n will be correct thus, option (A) is correct.
What is inequality?A difference between two values indicates whether one is smaller, larger, or basically not similar to the other.
In essence, a comparison of any two values reveals whether one is less than, larger than, or equal to the value on the opposite side of the equation.
As per the given,
Total budget = 65
Total spent = 18 + 11n where n is the number of canvases.
Total spent ≤ total budget
18 + 11n ≤ 65
Hence "The inequality represents the given situation is 65 ≥ 18 + 11n will be correct".
For more about inequality,
brainly.com/question/20383699
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An earthworm times 2 cm into the ground each day the earth worm tunnels at about the same place every day how many days will it take the earthworm to tunnel 14 cm
Answer:
7 days
Step-by-step explanation:
Given that:
Distance tunneled into the ground each day = 2cm
The rate is the same everyday ;
Hence, to. Tunnel 14cm into the ground , it will take the earthworm;
1 day = 2cm
x days = 14cm
Cross multiply :
2x = 14
x = 14 /2
x = 7
Hence, it will take 7 days for the earthworm to tunnel 14cm
Which set of line segments could create a right triangle?
24, 30, 35
12, 18, 30
18, 24, 30
18, 24, 35
thirdStep-by-step explanation:
To solve the following system by elimination of the x terms, if the first equation were multiplied by -4, by what number would you multiply the second equation?
Answer:
6
Step-by-step explanation:
Multiply by 6 and you can eliminate x or y.
Given the angle measures of a triangle are 3x + 6 degrees, 4x + 2 degrees and 10x + 2 degrees, determine the 3 angles in this triangle?
Answer:
36,42,102
Step-by-step explanation:
A triangle is 180° total so your equation to find x is:
3x+6+4x+2+10x+2=180°
17x+10=180
17x=170
x=10
to find the individual sides:
3(10)+6=36
4(10)+2=42
10(10)+2=102
to make sure this is right, add 36+42+102. It should equal 180 and it does
HELP MEE Simplify the expression : (5x + 3y) + (2x + 12y)
Answer:
7x+15y
Step-by-step explanation:
Answer:
15y+7x
Step-by-step explanation:
Simply the equation by combining like terms
3. What is the slope and the y-intercept of
the line represented by equation:
2x + y = 1?
Explanation:
Answer:
The slope is -2/1 or simplified -2 and the y-intercept is 1
Step-by-step explanation:
Answer: Slope:-2 and y-intercept:1
Step-by-step explanation:
y=1 because the y by itself means 1.
The slope is a -2 because you have to do the opposite.
I used a calculator for math for the answer
Someone please help me!
Two planes travel at a constant speed which plane a travels 2000 and 800 miles in five hours Plan B travels 3885 miles in seven hours which plane is faster
Answer:
Since its speed is higher, plane 1 is faster than plane 2.
Step-by-step explanation:
Comparing Speeds
The formula for the speed of an object who travels a distance d in a time t is:
[tex]\displaystyle v=\frac{d}{t}[/tex]
We have to compare the speeds of the two planes:
The first plane travels d1=2800 miles in t1=5 hours
The second plane travels d2=3885 miles in t2= 7 hours
Calculate both speeds as follows:
[tex]\displaystyle v_1=\frac{d_1}{t_1}[/tex]
[tex]\displaystyle v_1=\frac{2800}{5}[/tex]
[tex]v_1=560\ mi/h[/tex]
[tex]\displaystyle v_2=\frac{d_2}{t_2}[/tex]
[tex]\displaystyle v_2=\frac{3885}{7}[/tex]
[tex]v_2=555\ mi/h[/tex]
Since its speed is higher, plane 1 is faster than plane 2.
Plz help I’ll mark brainliest
Answer:
J
Step-by-step explanation:
I did it in my head so?? ya
gl