If x = -4 is a root of f(x), then dividing f(x) by x + 4 leaves a remainder of 0.
Compute the quotient,
(x³ - kx + 12) / (x + 4)
x³ = x² • x, and
x² (x + 4) = x³ + 4x²
Subtract this from the dividend (f(x)) to get an initial remainder of
(x³ - kx + 12) - (x³ + 4x²) = -4x² - kx + 12
-4x² = -4x • x, and
-4x (x + 4) = -4x² - 16x
Subtract this from the previous remainder to get a new one of
(-4x² - kx + 12) - (-4x² - 16x) = (16 - k) x + 12
(16 - k) x = (16 - k) • x, and
(16 - k) (x + 4) = (16 - k) x + 64 - 4k
which gives the next remainder,
((16 - k) x + 12) - ((16 - k) x + 64 - 4k) = 4k - 52
4k - 52 does not divide x, so we're done and what we've shown is
f(x) / (x + 4) = x² - 4x + 16 - k + (4k - 52)/(x + 4)
(just gathering the bold terms above and the last remainder)
The remainder should be 0, so that
4k - 52 = 0
4k = 52
k = 13
ples halp ples tysm....
-3(2+4k)+7(2k-1)
A. 2k-13
b. 8k-13
c. 2k+13
d. 2k-7
9514 1404 393
Answer:
A. 2k -13
Step-by-step explanation:
-3(2 +4k) +7(2k -1)
= -6 -12k +14k -7 . . . . . . eliminate parentheses
= (-12 +14)k -6 -7 . . . . . . group like terms
= 2k -13 . . . . matches choice A
PLEASE HELP NOBODY EVER ANSWERS MY QUESTIONS Rip van Winkle has fallen asleep for a very long time.
The length of his beard (in millimeters) as a function of time (in weeks) is graphed.
How long was Rip van Winkle's beard when he fell asleep?
Answer:
10 millimeters
Step-by-step explanation:
Don't listen to the other answerer who was trolling, I will actually help you. To find how long his beard was when he fell asleep, we need to find the y-intercept. The y-intercept marks how long his beard was right when he fell asleep. From looking at the graph, we can see that the y-intercept is 10. This means his beard was 10 millimeters long when he fell asleep. I hope this helps!
Answer:
10 meters
Step-by-step explanation:
if you look at the start os the graph, I shows that the Y intercept is 10, therefore, the answer is 10 meters.
- a friendly 8th grader :)
please help!! it’s due soon:(
Answer:
Step-by-step explanation:
AC ≅ AD ; BC≅ BD Given
AB ≅ AB Reflexive property of congruence
ΔACB ≅ ΔADB Side Side Side Postulate
Find the 70th term of the following arithmetic sequence 4,12,20,28
Answer:
556
Step-by-step explanation:
formula
L = a + (n - 1)*d
Givens
n = 70
a = 4
d = 8
Solution
t = 4 + (70 - 1)*8
t = 4 + 69*8
t = 4 + 552
t = 556
Help please! I’ll give brainliest too!
Answer:
y-intercept: -5
Slope: 4
Equation: y = 4x - 5
Step-by-step explanation:
✔️The y-intercept is the value of y when x = 0. From the table of values, it shows that when x = 0, y = -5. Therefore:
y-intercept (b) = -5
✔️using two pairs from the table, (1, -1) and (2, 3):
[tex] Slope (m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{3 -(-1)}{2 - 1} = \frac{4}{1} = 4 [/tex]
Slope = 4
✔️To write an equation for the function, substitute m = 4, and b = -5 into y = mx + b.
Thus:
y = 4x +(-5)
y = 4x - 5
which graph represents the solution to this inequality
Answer:
C
Step-by-step explanation:
Answer
it is: C
Step-by-step explanation:
1) Given: H is the midpoint of EG
mZE = mZG
G
D
Prove: ADEH - AFGH
H.
E
F
It is E
Duhhhhhhhhhhhhh
What subfield of mathematics requires the most spatial reasoning?
No answer needed, just need to get rid of all my points.
Answer:
brainlest?
Step-by-step explanation:
......
Answer: I looked it up and got a couple of answers of spatial reasoning. Don’t know if that helps but yeah thats what I got lol
Step-by-step explanation:
Help me please solve this
9514 1404 393
Answer:
a) no
b) yes
Step-by-step explanation:
a) You cannot draw the graph around x=0 without lifting your pencil. The function is not continuous at x=0.
__
b) You can draw the graph around x=1 without lifting your pencil. The function is continuous at x=1.
_____
Additional comment
In technical terms, the limit from the left at x=0 is 2; the limit from the right is 3. These are different, so the function is not continuous there.
On the other hand, the left and right limits at x=1 are the same (both 2), and are equal to the value of the function at that point (f(1)=2). Hence, the function is continuous at x=1.
A carnival sold 450 tickets on Saturday. The ticket sales showed that 126 of the ticket sales were adult tickets. What percent of the tickets sold on Saturday were adult tickets?!PLEASE ANSWER!!!
Answer:
28%
Step-by-step explanation:
hope this helps, have a good day
Simplifying radicals! Please help me & Show WORK
Answer:
Solving the radical [tex]4\sqrt{2}(-4\sqrt{15}+3\sqrt{18})[/tex] we get [tex]\mathbf{-16\sqrt{30}+72}[/tex]
Step-by-step explanation:
We need to simplify the radical: [tex]4\sqrt{2}(-4\sqrt{15}+3\sqrt{18})[/tex]
Prime factors of 18 are: 2x3x3
Replacing [tex]\sqrt{18}[/tex] with its factors
[tex]4\sqrt{2}(-4\sqrt{15}+3\sqrt{18})\\=4\sqrt{2}(-4\sqrt{15}+3\sqrt{2\times3\times3})\\=4\sqrt{2}(-4\sqrt{15}+3\sqrt{2\times3^2})[/tex]
We know that [tex]\sqrt{3^2}=3[/tex]
[tex]=4\sqrt{2}(-4\sqrt{15}+3\times3\sqrt{2})\\=4\sqrt{2}(-4\sqrt{15}+9\sqrt{2})[/tex]
Multiplying [tex]4\sqrt{2}[/tex] with terms inside the bracket
[tex]=4\sqrt{2}(-4\sqrt{15})+4\sqrt{2}( 9\sqrt{2}))\\=-16\sqrt{2}\sqrt{15}+36\sqrt{2} \sqrt{2}[/tex]
We know that [tex]\sqrt{2} \sqrt{2}=2[/tex]
[tex]=-16\sqrt{2*15}+36(2)\\=-16\sqrt{30}+72[/tex]
So, solving the radical [tex]4\sqrt{2}(-4\sqrt{15}+3\sqrt{18})[/tex] we get [tex]\mathbf{-16\sqrt{30}+72}[/tex]
C(x) = 5x^2 + x + 7 and
d(x) = x^2 – 10
d(c(3))
Answer:
d(c(3))=30I5
Step-by-step explanation:
C(3)=5×9+3 +7=55
d(c(3))= ( 55)^2-10= 3O 15
The length of a picture frame is 1cm less than twice the width(frame is NOT a square). The area is 28cm^2. Find the length and width of the picture frame.
Answer:
length is 7cm, and the width is 4cm
Step-by-step explanation:
The length of a picture frame is 1cm less than twice the width(frame is NOT a square). The area is 28cm^2. Find the length and width of the picture frame.
The area of the frame = Length * Width
A = LW
If the length of a picture frame is 1cm less than twice the width, then;
L = 2W - 1
Substitute into the formula;
A = (2W-1)W
A = 2W^2 - W
28 = 2W^2 - W
2W^2 - W - 28 = 0
2W^2 - 8W +7W- 28 = 0
2W(W-4)+7(W-4) = 0
2W+7 = 0 and W - 4 = 0
W =- -7/2 and W = 4
Width cannot be negative
W = 4cm
Since A = LW
L = A/W
L = 28/4
L = 7cm
Hence the length is 7cm, and the width is 4cm
Bargains warehouse has 3 shirt special. Christina bought 3 shirts on sales for $35.97 if she would have only bought one shirt, she would have paid $16.24. How much money is Christina saving on each shirt by buying 3 shirts on a special?
Answer:
12.75 Its correct
Step-by-step explanation:
Answer:
12.75
Step-by-step explanation:
1) A person can pay $16 for a membership to the science museum and then go to the
museum for just $3 per visit. What is the maximum number of visits a member of the
science museum can make for a total cost of $37?
visits
Please hurry
7 visits
Step-by-step explanation:
All I did was minus 16 from 37 to get 21, then divided that by 3.
Need help on this one.
I JUST DONT WHAT TO DO IT
Answer: Bottom Left
Step-by-step explanation:
Answer:
bottom left
Step-by-step explanation:
cuz it makes sense
two equations in standard for equivalent to x+y=-10
Help people help!!!!
Answer:
I think that it is
C
Please let me know if it is not correct!!!!
Answer:
A would most likly be the answer
Step-by-step explanation:
because in the equation sinse A = -5 1/4 which is whe he was at the end hopefully you understand
HELP ASAP PLZ NEED IR SNDWWRED AS PAST AS POSSIBLE
Answer:
I would say, 2.5
Step-by-step explanation:
Because the calculator said 2.67
Don’t worry about the one at the bottom BUT HELP MEEEEE
Answer:
e. 79/30 f. 18.2
Step-by-step explanation:
Find f(−5) if f(x)=|x+1|. Type a numerical answer in the space provided. Do not type spaces in your answer.
===============================================
Work Shown:
f(x) = |x+1|
f(-5) = |-5+1| .... x is replaced with -5
f(-5) = |-4|
f(-5) = 4
which equation shows that the pythagorean identity is true for Ø=pi? select the equation that is the form sin^2(pi)+cos^2(pi)=1
a.0^2 +1^2=1
b.0^2 +(-1)^2=1
c. 1^2+0^2=1
d.(-1)^2+0^2=1
Answer: For This Specific Question it is B, But there is a question very similar that doesn't have the pi's in the equation and the answer to that one is A.
Step-by-step explanation: Very sorry if this is confusing :)
Pythagorean identities are three basic identities for trigonometric ratios. The equation that is of the form [tex]\sin^2(\pi) + \cos^2(\pi) =1[/tex] is given by: Option B: [tex]0^2 + (-1)^2 = 1[/tex]
Equations which shows that the Pythagorean identities are true will be verifying them for some specific angles. For that we need to know about Pythagorean identities.
What are Pythagorean identities?[tex]sin^2(\theta) + cos^2(\theta) = 1\\\\1 + tan^2(\theta) = sec^2(\theta)\\\\1 + cot^2(\theta) = csc^2(\theta)[/tex]
Using the first Pythagorean Identity to get one of its special case
For angle being [tex]\pi[/tex] radians(or equal to 180 degrees), we have:
[tex]sin(\pi) = 0\\cos(\pi) = -1[/tex]
Thus, for the first Pythagorean identity at angle [tex]\pi[/tex] radians, we get:
[tex]sin^2(\pi) + cos^2(\pi) = 1\\\\0^2 + (-1)^2 = 1[/tex]
Thus, the equation that is of the form [tex]\sin^2(\pi) + \cos^2(\pi) =1[/tex] is given by: Option B: [tex]0^2 + (-1)^2 = 1[/tex]
Learn more about Pythagorean identities here:
https://brainly.com/question/24287773
Jada sells ground paprika.
Her weekly profit (in dollars) as a function of the amount of paprika she sold that week (in kilograms) is graphed.
What is Jada's profit if she sells 60 kilograms of paprika?
Answer:
200
Step-by-step explanation:
Find 60 kilos then just follow the line up till you reach the blue line
4a.
An iron bar is heated. Its length, L, in millimetres can be modelled by a linear function, L=mT+c, where T is the temperature measured in degrees Celsius (°C).
At 150°C the length of the iron bar is 180 mm.
Write down an equation that shows this information.
4b.
At 210°C the length of the iron bar is 181.5 mm.
Write down an equation that shows this second piece of information.
4c.
At 210°C the length of the iron bar is 181.5 mm.
Hence, find the length of the iron bar at 40°C.
(really need most help on last one)
Answer and Step-by-step explanation:
Please help me:):):)
Answer:
c - 8 ≥ 25
Step-by-step explanation:
Reduce the ratio to the lowest term: 60 : 75
Answer:
4 : 15 is the answer for 60 : 75 to the lowest term
help asap Its distributive property so 6x55 i need the second part how to write it out like
(and then) a number + some other number and then what it equals 5th grade math
Answer:
I don't know exactly what you need but I have two ways.
Step-by-step explanation:
if you need to make an example: 6x55+ 6(3f-12)= or something along those lines.
or if you just need that answer then 330
I'm sorry if that's not what you were wondering
There are 4 sharks and 5 dolphins. Write the ratio of sharks to dolphins. Then find and interpret the value of the ratio.
Answer:
here is the ratio 1 : 1.25 (sharks: dolphins)
Step-by-step explanation:
The ratio of sharks to dolphins is 4 : 5
How to obtain real measurements from the ratio of two measurements?Suppose the real measurements were "a" and "b"
This shows that to get the real measurements from the given ratio, we need to assume to have some factor possibly cancelled from both the numerator and the denominator.
Thus, a = px, b = qx
Given Number of sharks = 4
Number of dolphins = 5
Therefore, the ratio of sharks to dolphins
= 4 : 5
Or 1 : 1.25
Number of animals = number of sharks + number of dolphins
Number of animals = 4 + 5 = 9
Learn more about ratio here:
brainly.com/question/186659
#SPJ2
A waiter earned a 7% tip. What decimal is equivalent to 7%?
Record your answer and fill in the bubbles on your answer document. Be sure to use the
correct place value.