Answer:
61780
Step-by-step explanation:
Given that x² -x -2 is a factor of x³ +3 x² +ax +b, calculate the values of a and b and hence find the remaining factor.
Answer:
[tex]a = -6, b = - 8[/tex]
Remaining factor = [tex]x+4[/tex]
Step-by-step explanation:
Given that:
Two polynomials:
[tex]x^{2} -x-2[/tex] and [tex]x^3 +3 x^2 +ax +b[/tex]
[tex]x^{2} -x-2[/tex] is a factor of [tex]x^3 +3 x^2 +ax +b[/tex].
To find:
The values of [tex]a[/tex] and [tex]b[/tex] from the cubic equation and the remaining factor.
Solution:
Let us first of all, factorize [tex]x^{2} -x-2[/tex].
[tex]x^{2} -2x+x-2=0\\\Rightarrow x(x-2)+1(x-2)=0\\\Rightarrow (x+1)(x-2)=0\\\Rightarrow x = -1, 2[/tex]
There are two factors of the given quadratic equation.
These two factors must also be factors of the cubic equation as well.
Putting [tex]x = 2[/tex]:
[tex]2^3 +3 \times 2^2 +a\times 2 +b =0\\\Rightarrow 2a+b=-20 ..... (1)[/tex]
Putting [tex]x = -1[/tex]:
[tex](-1)^3 +3 \times (-1)^2 +a\times (-1) +b =0\\\Rightarrow -a+b=-2 ..... (2)[/tex]
Subtracting (2) from (1):
[tex]3a = -18\\\Rightarrow a = -6[/tex]
From equation (1):
[tex]2\times (-6) + b=-20\\\Rightarrow b = -8[/tex]
Putting the values of [tex]a[/tex] and [tex]b[/tex] in the cubic equation, we get:
[tex]x^3 +3 x^2 -6x -8[/tex]
Dividing the cubic equation with quadratic, we get:
[tex]\dfrac{x^3 +3 x^2 -6x -8}{x^{2} -x-2} = x+4[/tex]
13. Puan Zakiah bought a house at price RM380 000 by cash. After 5 years, she sold the house at price RM620 000. The total charges involved in sales and purchase agreement
was RM42 000. Calculate the return on investment of Puan Zakiah.
A 49.5%
C 56.9%
B 52.1%
D 74.2%
logan enjoys taking his dog to the park. he walks doen hickory st. turns into maple ave. to meet his friend, brett, and then continues on maple ave. to the park. what is the approximate distance from bretts house to the park
Answer:
ummm there is no chart or multiple choice so imma go off a limb here and say 1/2 mile
hope this helps
sorry if its wrong i had no chart
Step-by-step explanation:
Answer:
2 miles
Step-by-step explanation:
he walks to to maple avenue to meet his friend is a mile,so to continue his walk on maple avenue to the park is another mile.
What is the value of x?
(57-5)
Your answer:
x = 15
x = 13
x = 60
ox=37
pls helpppppo
Answer:
x = 13
Step-by-step explanation:
All triangles equal 180 degrees
Since this is an equilateral triangle, all angles have the same measurement
180 degrees divided by 3 angles = 60 degrees per angle
Make an equation based on the info given:
60 = 5x - 5
Solve:
*add 5 to both sides*
65 = 5x
*divide both sides by 5*
13 = x
Which unit is bigger?
millimeter
centimeter
meter
kilometer
Answer:
The answer is kilogram
Step-by-step explanation:
The answer is a kilogram because a kilogram is 1,000 times larger than one gram (so 1 kilogram = 1,000 grams). A centimeter is 100 times smaller than one meter (so 1 meter = 100 centimeters). A dekaliter is 10 times larger than one liter (so 1 dekaliter = 10 liters).
Hope this helps!!
Help me pleaseee on this plss
Answer:
a(n)= -4n-6
Step-by-step explanation:
If you plug the number of the sequence in as n in the equation (1=-10, 2=-14, etc.) and then plug the actual number (-10, -14, etc.) in as the a(n), for each of the equations, the only one that works with all four is the first one.
12. Write an equation in slope-intercept form that passes through (5,-2) and (-16,4).
Answer:
Slope: (y2-y1)/(x2-x1)
(4+2)/(-16-5) = 6/-21 = -2/7
Y = -2/7x + b
5 = -2/7(-2) + b, b = 31/7
Equation: y = -2/7x + 31/7
Step-by-step explanation:
What is the measure of AC?
Answer:
A or B
Step-by-step explanation:
Find the decimal that is equivalent to:
7/12
OA) 1.714
OB) 0.583
C) 0.0583
OD) 0.583
Answer:
B
Step-by-step explanation:
It ain't no step to dat
Situation #3: Jamie can type 243 words in 3 minutes. How many words can
she type in 10 minutes?
Answer:
810 words
Step-by-step explanation:
243 words per 3 minutes
243/3 to get 81 words per minute
81 times 10 = 810
What is the inverse of the function f(x) = one-quarterx – 12? h(x) = 48x – 4 h(x) = 48x + 4 h(x) = 4x – 48 h(x) = 4x + 48
Answer:
The inverse of the function f(x) is h(x) = 4x + 48 ⇒ (D)
Step-by-step explanation:
To find the inverse of a function do these steps
Replace f(x) by ySwitch x and ySolve to find the new yReplace y by [tex]f^{-1}[/tex](x)Let us do these steps to solve the equation
∵ f(x) = [tex]\frac{1}{4}[/tex]x - 12
→ Replace f(x) by y
∴ y = [tex]\frac{1}{4}[/tex]x - 12
→ Switch x and y
∴ x = [tex]\frac{1}{4}[/tex]y - 12
→ Add 12 to both sides
∵ x + 12 = [tex]\frac{1}{4}[/tex]y - 12 + 12
∴ x + 12 = [tex]\frac{1}{4}[/tex]y
→ Multiply each term by 4
∵ 4(x) + 4(12) = 4([tex]\frac{1}{4}[/tex]y)
∴ 4x + 48 = y
→ Switch the two sides
∴ y = 4x + 48
→ Replace y by h(x)
∴ h(x) = 4x + 48
∴ The inverse of the function f(x) is h(x) = 4x + 48
Answer:
h(x) = 4x + 48 ⇒ (D)
Step-by-step explanation:
i just did it
simplify
3x+6y+5y-2y
please explain i need help :(
30 points help!!!!!!!!!!!
The following function represents the production cost f(x), in dollars, for x number of units produced by company 1:
f(x) = 0.25x2 − 8x + 600
The following table represents the production cost g(x), in dollars, for x number of units produced by company 2:
x g(x)
6 862.2
8 856.8
10 855
12 856.8
14 862.2
Based on the given information, determine which company has a lower minimum and find the minimum value.
g(x) at (10, 855)
f(x) at (16, 536)
g(x) at (16, 536)
f(x) at (10, 855)
Answer:
the answer is f(x) at (16, 536)
The chart shows how many people have signed up to go on a field trip each day. 62 students are allowed to go on the field trip. On
which day would you expect that number to be reached?
A)
8
B)
9
o
10
D
11
Answer:
c 10
Step-by-step explanation:
the number is increasing by 4. keep adding 4 until you reach 62, day 10
What is the slope of the line that passes through the points (-2,3) and (-14, -5)?
Write your answer in simplest form
A restaurant charges a $100 setup fee, plus $15 per guest, to host a private party.
The table below shows the cost of hosting a private party for a certain number of
guests.
Answer: 775
Step-by-step explanation: $15 for each guest (so you need to multiply 15 by 45) then add the $100 setup fee!
Ellen needs to make b batches of blueberry scones this weekend for her family's brunch party. She needs 2 cartons of blueberries for each batch, and each carton costs $4. Pick all the expressions that represent how much Ellen will spend on blueberries.
Answer:
Ellen will spend
$4(2b) on blueberries
Where b = number of batches of Blueberry scones she wants to make
Step-by-step explanation:
From the above question:.
Ellen needs to make b batches of blueberry scones this weekend for her family's brunch party.
Since she needs 2 cartons of blueberries for each batch, and each carton costs $4
1 batch = 2 cartons of blueberries
b batches =
Cross Multiply
b × 2 cartons
= 2b cartons of blueberries.
We also know that:
1 carton blueberries = $4
2b cartons of blueberries = x
Cross Multiply
x = 2b × $4
Therefore, Ellen will spend :
$4(2b) on blueberries
Please help brainiest will give you!
Find the slope of it!
A. -3
B. -1/3
C. 1/3
D. 3
Pls help, my moms gonna tell if i fail
Answer:
0 and 3, I think those are the answers cause they make the most sense
Step-by-step explanation:
Simplify the expression below using laws of exponents.
Answer: 36/[tex]K^{2}[/tex]
Step-by-step explanation:
The k on top will cancel the k to the second power.
So the only number in the numerator is 1.
Then the 1 qill go away because you cant divide anything by 1.
The expoenet -2 that was at the top near K will become positive.
Then distribute
What is 11% of 600?
80
45
60
66
Answer:
66 is the answer to your question
Answer:
66
Step-by-step explanation:
11 % = 0.11
600 × 0.11 = 66
there are between 25 and 43 students in a class
the ratio of boys to girls is 5 : 7
how many students are in the class?
Answer:
36
Step-by-step explanation:
Since the sum of the ratios is 5+7=12 the total number of students must be divisible by 12
The only number within the given range is 36
The number of students should be in the class should be considered as the 36.
Calculation of the number of students:Since
there are between 25 and 43 students in a class
the ratio of boys to girls is 5 : 7
So here the total ratio should be like
= 5 + 7
= 12
So here the number of students should be divisible by 12
So, it should be 36
Learn more about ratio here: https://brainly.com/question/13111469
The two pentagons shown are similar.
8 cm
879
879
9 cm
8 cm
16 cm
3 cm
6 cm
not drawn to scale
What is the value of x?
O A. 6 cm
B. 9 cm
ОО
C. 12 cm
D. 14 cm
Explain when it is appropriate to use a benchmark percent in solving a problem.
Answer:
The most common benchmark percents are 0%, 10%, 25%, 50%, 75% and 100%.
These benchmark values are sometimes used when estimating a solution involving percentages.
Real-World Example
If an item costs $36.00 and there is a 7% sales tax, the benchmark of 10% can be used to mentally estimate the sales tax of the item.
10% of 36, done mentally, is 3.6.
Since 7% is a bit less than 10%, the sales tax will be a bit less than $3.60.Step-by-step explanation:
A container has 12 1/2 cups of pancake mix. A serving uses exactly 1 1/2
cups
• How many full servings are in the container?
• How many cups of pancake mix are left over?
Enter each answer on a separate line.
Answer:
8 full servings
Step-by-step explanation:
1/2 cup of mix left
Which mixture would taste different? Mixture 1: 1 cup water, 1.5 teaspoons drink mix Mixture 2: 2 cups water, 1/2 teaspoon drink mix Mixture 3: 1 cups water, 1/4 teaspoon drink mix Mixture 1 Mixture 2 Mixture 3
Answer:
Drink 1 will taste different.
Step-by-step explanation:
Given the mixtures:
Mixture 1: 1 cup water and 1.5 teaspoons drink mix
Mixture 2: 2 cups water and [tex]\frac{1}{2}[/tex] teaspoons drink mix
Mixture 3: 1 cup water and [tex]\frac{1}{4}[/tex] teaspoons drink mix
To find:
Which of the mixtures will taste different?
Solution:
To answer this, we need to find the ratio of all the mixtures.
First of all, Let us make ratio of water as 1 quantity.
Ratio of 1st mixture = 1 : [tex]\frac{3}{2}[/tex]
Ratio of Mixture 2 contains 2 cups of water.
Let us divide the ratio of mixture 2 with 2, we get:
[tex]\frac{2}{2}:\dfrac{\frac{1}{2}}{2}\\\Rightarrow 1:\dfrac{1}{4}[/tex]
Ratio of 3rd mixture = [tex]1:\frac{1}{4}[/tex]
Ratio of drink mix of 1st mixture with 1 cup water is different.
So, drink 1 will taste different.
Which of the scatterplots have no correlation? Check all that apply.
On a graph, points curve up and down.
On a graph, points are grouped together to form a horizontal cluster.
On a graph, points are grouped together to form a vertical cluster.
On a graph, points are grouped together and decrease.
On a graph, points are scattered over the graph.
Answer:
2, 3, and 5
Step-by-step explanation:
got it right on test.
The scatterplots (B), (C), and (E) have no correlation. which is the correct answer would be options (B), (C), and (E)
What is the Scatter plot?The variables in the scatter plot made from the data are described by the independent variable, time, which is graphed along the horizontal axis.
When analyzing data with more than two variables, a scatter plot is used, which has a separate vertical axis for each variable.
According to the given option,
The second has no slope, therefore there is no correlation.
The third has a zero average slope with no upward or descending trend; no correlation.
The fifth has a general increasing tendency and will have a non-zero correlation.
Thus, the scatterplots (B), (C), and (E) have no correlation.
Hence, the correct answer would be options (B), (C), and (E),
Learn more about the Scatter plot here:
brainly.com/question/1386565
#SPJ6
look at the picture that's the problem I need help with
Answer:
I think its A
Step-by-step explanation:
The number of DVDs sold at a store in a month was 925 and the number of DVDs sold decreased by 12 per month. The number of Blu-ray discs sold in the same store in the same month was 507 and the number of Blu-ray discs sold increased by 26 per month. Let d represent the number of discs sold and t represent the time in months. Write a system of equations by filling in the blanks:
Answer:
See below
Step-by-step explanation:
DVD's sold:
d = 925 - 12tBlu-rays sold:
d = 507 + 26tSolving the system we get the number of month t when the disks sold are equal:
925 - 12t = 507 + 26t26t + 12t = 925 - 50736t = 418t = 418/36t = 11.6 monthsan angle is equal to five times of its complement then what is its measures
Answer:
Then the complement of it = 90-x. Given that An angle is equal to 5 times its complement. x = 75. Hence the measure of an angle = 75.
Step-by-step explanation: