Solution :
Given :
[tex]$f(x)=x^3-x^2-18x+19$[/tex]
By using the remainder theorem, if f(x) is divided by (x-k) and the remainder is 'r', then
[tex]$f(x)=(x-k)q(x)+r$[/tex]
Here, k = 4
Therefore, divide the f(x) with (x - 4) to find the q(x) and r.
__________________
[tex]$x-4$[/tex] | [tex]$x^3-x^2-18x+19$[/tex] | [tex]$x^2+3x-6$[/tex]
[tex]$x^3-4x^2$[/tex]
------------------------------------
[tex]$3x^2-18x$[/tex]
[tex]$3x^2-12x$[/tex]
-------------------------------------
[tex]$-6x+19$[/tex]
[tex]$-6x+24$[/tex]
-------------------------------------
[tex]$-5$[/tex]
Therefore,
q(x) = [tex]$x^2+3x-6$[/tex]
r = -5
[tex]$f(x)=(x-4)(x^2+3x-6)-5$[/tex]
[tex]$f(4)=(4-4)(4^2+3 \times 4-6)-5$[/tex]
[tex]$=-5$[/tex]
Rebecca wants to prove that if the diagonals in parallelogram are perpendicular, then it is a rhombus. Select the appropriate rephrased statement for Rebecca's proof
Answer:
The answer is C
Step-by-step explanation:
Khan Academy
Answer:
C
Step-by-step explanation:
Mhanifa Plz help me with this thank you!
Answer:
D
Step-by-step explanation:
This is an example of the Pythagorean theorem.
In triangle BEH, the sum of the squares of the sides of the two smaller sides, BE and BH is equal to the longest side squared, EH.
At an auto repair shop. 3.5 hours of labour costs $311.50. What is the labour
charge for a 5 hour job?
445 . Answer:
Step-by-step explanation:
How many minutes are there in 12.5 hours?
Answer:
750 minutes
Step-by-step explanation:
Answer:
750 minutes would be your answer
Step-by-step explanation:
Last week at a gym, 120 people participated in a biking class. The number of people who ran on a treadmill
was 150% of the number of people who participated in a biking class. How many people ran
a treadmill at
the gym last week?
people ran on a treadmill at the gym last week.
Show work ~ Aniya v
Answer:
180
Step-by-step explanation:
This basically means that one and a half of the amount of people that took a biking class ran on the treadmill.
There are two ways to solve
1. [tex]\frac{150*120}{100}[/tex]
2. [tex]120+\frac{120\\}{2}[/tex]
To do the first one:
1. Multiply the values in the numerator
18000/100
2. Divide
180
To do the second one:
1. Divide the fraction
120 + 60
2. Add
180
solve the system by substitution 3x-y=10 2x=y
Answer
X=10 and y=20
Step-by-step explanation:
since y=2x, you need to substitute that into the equation to get:
3x-(2x)=10
And evaluate:
x=10
Then substitute 10 into the equation: 2x=y:
2(10)=y
evaluate:
20=y
Now go back to the original equation to check your answer and substitute the values in:
3(10)-(20)=10
30-20=10
10=10
Help!!! I do not seem to understand this problem well.
Step-by-step explanation:
weeks. days. (wk,d)
2. 14. (2,14)
4. 28. (4,28)
6. 42. (6,42)
8. 56. (8,56)
8. A truck is carrying peach juice, pear juice,
and grape juice bottles in a ratio of 4:3:5. If
there are 76 peach juice bottles, then how many
pear juice bottles are there?
Answer:
57 pear juices
Step-by-step explanation:
because we know we have 76 peach juices and the ratio is 4, so we get 19. This means that 19=x. And then we multiply 19 by 3 and we get 57.
Cups by the water cooler are in the shape of a cone. The height is 15 cm and the diameter is 7.6 cm.
What is the volume of one water cooler cup, in cubic centimeters? (Use 3.14 for
π.)
Answer:
226.7 cm³
Step-by-step explanation:
The cone volume formula is V = (1/3)(base area)(height).
Here that comes out to V = (1/3)(pi)(3.8 cm)^2·15 cm, or 226.7 cm³
Can someone please help me answer this question asap thank you . No links please and thank you .
What is the probability that someone in your class wants the New England Patriots to win
Answer:
Step-by-step explanation:
It all depends on how many people are in your class.
To calculate probability
Determine a single event with a single outcome.
Identify the total number of outcomes that can occur.
Divide the number of events by the number of possible outcomes.
To determine the probability, Use the formula
What is the formula of probability?
P(A) is the probability of an event “A” n(A) is the number of favourable outcomes. n(S) is the total number of events in the sample space.
P(A | B) = P(A∩B) / P(B)
Layla is going to invest $5,200 and leave it in an account for 15 years. Assuming the interest is compounded monthly, what interest rate, to the nearest tenth of a percent, would be required in order for Layla to end up with $13,800?
Answer:
6.5%
Step-by-step explanation:
I just know
how do this math problem?
of shaded region shapes
question 2)
find the area of each shape.
All measurements are in centimetres.
and please explain me to how to do this cuz I don't understand my teacher in maths
Answer:
photo isn't clear, first of all u have to click clear picture
find the arc length of the bolder arc
A) 283.5 mi
C) 733.0 mi
B) 10.2 mi
D) 73.3 mi
Answer:
d its d :)
Step-by-step explanation:
i already did that
Please help! Thank you!
Answer:
X=sigma xi/no of observation
5= (?) /4
5*4=sum of all numbers
20=sum of all the observation
If you are helped by this answer pls tag me brianliest I really want it
THANK YOU.......
Suppose three moons A, B, and C orbit 100,000 kilometers above the surface of a planet. Suppose m ZABC = 90°, and the planet is 20,000 kilometers in diameter. Draw a diagram of the situation. How far is moon A from moon C?
Answer:
Step-by-step explanation:
Please see diagram attached.
Moon A and C are 100,000km + 10,000 = 110,000km from center of planet.
So they are 110,000 + 110,000 = 220,000km apart.
Answer:
Step-by-step explanation:
AC is 220000km according to the drawing:
Some parents will drive 17 children to summer camp. Each parent can fit 4 children in a car.
What is the fewest number of parents needed to drive all the children?
Answer:
5
Step-by-step explanation:
This Question: 1 pt
20 of 20
This Qu
th
The pH of a fruit juice is 2.9. Find the hydronium ion concentration, [H30 * ), of the juice. Use the formula pH = -log[H30*]
The hydronium ion concentration [H30 + ] is approximately moles per liter.
(Use scientific notation. Use the multiplication symbol in the math palette as needed. Round to the nearest tenth as needed.)
Answer:
scientific" (and any subsequent words) was ignored because we limit queries to 32 words.
Your search - This Question: 1 pt 20 of 20 This Qu th The pH of a fruit juice is 2.9. Find the hydronium ion ... - did not match any documents.
Suggestions:
Make sure that all words are spelled correctly.
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Suppose that the path of a newly discovered comet could be modeled by using one branch of the equation x2/4 - y2/9=1, where distances are measured in astronomical units. Name the vertices of the hyperbola and then graph the hyperbola.
Answer:
the answer is A just tool the quiz lesson 5 hyperbolas Algebra 2B unit 5 these are the correct answers
1.A
2.B
3.D
4.A
5.B
6.D
7.A
hopes this helps everyone
The hyperbola has two vertices at (-2,0) and (2,0)
We have given that the equation
[tex]\frac{x^2}{4}-\frac{y^2}{9}=1[/tex]
What is the equation of the hyperbola?[tex]\frac{x^{2} }{a^2}+\frac{y^2}{b^2} =1[/tex]
Compare the above equation of the hyperbola with given equation
therefore a=2
vertices are (-a,0) and (a,0)
Therefore the vertices are (-2,0) and (2,0)
See the graph of the hyperbola in link given below.
The hyperbola has two vertices at (-2,0) and (2,0)
To learn more about hyperbola visit:
https://brainly.com/question/2351925
Find the distance between the pair of points (6. - 22) and (1. - 23) The distance is
I need help with this question
Answer:
2n=12
Step-by-step explanation:
The next step would be to subtract four from each side getting 2n=12 or B
Which of the following is a proportion?
Answer:
the second one
Step-by-step explanation:
HELP I MARK BRAIN thing
Answer:
It would be A. x < 6
Step-by-step explanation:
The number line shows it is less than six with a closed circle and the arrow pointing towards the left of it
What is the value of 4^3
Answer:
the answer is 64
Step-by-step explanation:
becasue 4 time 4 is 16 and 16 times 4 is 64. You have to multiply 4 against itself 3 times.
Answer:
64
Step-by-step explanation:
4³ = 4 · 4 · 4 = 64
John saved up enough money to buy a $20 can of shoe shine after paying for the $150 pair of Nikes. How much money did he save in all?
Answer:
170$
Step-by-step explanation:
150+20=170
Answer:
Step-by-step explanation:
170
32 is 4 more than twice a
number. What is the number?
Answer:
The number you are looking for is 14.
Figure A to figure B?
Is that right?
Answer:
d
Step-by-step explanation: cause thats the only answer that will maked sense
a baker made 192 trays of muffins. they were 14 muffins in each tray. how many muffins were there in all?
Helpppp I need this for rn thank youuuuu❤️
Answer:
-1,7
0,-3
1,-7
5,47
Step-by-step explanation:
-x-=+
which graph represents a function
Answer:
a
Step-by-step explanation:
Answer:
dfvgbhnm,kmjnhbgvx
Step-by-step explanation:
c vgbhjnmk,jnhbgvfc
