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]
What is the value of x in the equation below?
One-third (12 x minus 24) = 16
2
6
8
10
Answer:
X=2
Step-by-step explanation:
Using distributive property: 1/3(12x-24)=16
4x- 8=16
Using oposite oporations on both sides:
4x-8=16
4x+8=16-8
4x=8
8/4=2
x=2
can I have brainliest please
Answer:
a
Step-by-step explanation:
PLEASE HELP ME NOW ASAP I HAVE A MIN LEFT
Answer: B
Step-by-step explanation:
6m+5=m+20 pls help now
Answer:
m = 3
Step-by-step explanation:
Answer:
m = 3
Step-by-step explanation:
6m + 5 = m + 20
6m + 5 - 5 = m + 20 - 5
6m = m + 15
6m - m = m - m + 15
5m = 15
5m ÷ 5 = 15 ÷ 5
m = 3
i need help to pass math
Answer:
40.82
Step-by-step explanation:
Answer:
13
Step-by-step explanation:
C = 2πr
81.64 = 2(3.14)r - divide both sides by 2
40.82 = 3.14r - divide both side by 3.14
13 = r
elationship between Two Vallables Use the graph to find the relationship between the two variables. Select all that apply. O The two variables are books and months. O The two variables are 4 and 8. O Books is the independent variable, and months is the dependent variable. O Months is the independent variable, and books is the dependent variable. The relationship is y = 4x. The relationship is x = 4y. 8
Answer:
A D E <3 your welcome!
Answer:
b c and f :)
Step-by-step explanation:
hope this helps :)
Measures of center and variation can be used to describe data sets. Choose ALL statements about these measures that are true.
The mean, or average is a measure of center
The range of data set is a measure of center
The median of a data set is a measure of variability.
Measures of variability describe how the values in a data set vary.
Measures of Center describe all values in a data set with a single number
Answer:
These are the answers:
A) The mean, or average, is a measure of center.
D) Measures of variability describe how the values in a data set vary.
E) Measures of center describe all values in a data set with a single number.
The mean, or average is a measure of center
Measures of variability describe how the values in a data set vary.
Measures of Center describe all values in a data set with a single number
What is Median?The median is the value that's exactly in the middle of a data set when it is ordered. It's a measure of central tendency that separates the lowest 50% from the highest 50% of values. The steps for finding the median differ depending on whether you have an odd or an even number of data points
Arrange the data points from smallest to largest.
If the number of data points is odd, the median is the middle data point in the list.
If the number of data points is even, the median is the average of the two middle data points in the list.
Given data ,
The following statements about measures of center and variation are true:
The mean, or average, is a measure of center.
Measures of variability describe how the values in a data set vary.
Measures of center describe all values in a data set with a single number.
The statement "The range of data set is a measure of center" is false. The range is a measure of variability, not center.
The statement "The median of a data set is a measure of variability" is also false. The median is a measure of center, not variability
To learn more about median click :
https://brainly.com/question/28687994
#SPJ2
PLEASEEEEEEEEEEEEEEEEEEEEEEEEEEEEE HELPPPPPPPPPPPP
Answer:
L=74
W=77
Step-by-step explanation:
Answer:
L=74 and W=77
Step-by-step explanation:
first the area of a rectangle is length of breath
A=L X W
4514= L X 61
61L=4514
L=4514/61
L=74m
b. perimeter =2(L + W)
338=2*92+ 2W
338=184+2W
2W=338-184
2W=154
W=154/2
W=74
Mrs. James has $40.50 to spend at the store. She wants to buy a dress that costs thirty dollars and necklaces that cost $3.50. How many necklaces can she buy?
Answer:
3 necklaces
Step-by-step explanation:
$40.50-$30.00=$10.50 Subtract her total money and cost of dress
$10.50-$3.50=$6.00 subtract each necklace price from remaining money
$6.00-$3.50=$3.50 keep subtracting price of necklace
$3.50-$3.50=$0 that was 3 necklaces
Help please...NO LINKS
Un grupo de 4 amigos va al cine y las entradas les han costado 24$.¿cuanto pagaria en total un grupo de 7 amigos por sus entradas?
hi
4 entries are 24 so one entry is 24/4 = 6
so 7 friends pay 6*7 = 42
pls help 1755.97809915 round to the nearest cent
Answer:
1755.98
Step-by-step explanation:
1755.97809915
1 cent is 1 hundredth of a dollar, so to round to the nearest cent means to round to the nearest hundredth.
The 7 in boldface is the hundredths place.
Drop all digits to the right of the 7.
1755.97
dropped digits: 809915
Look at the leftmost digit that was dropped (in boldface). If it is from 0 to 4, you are done, and the answer is 1755.97. If the leftmost digit that was dropped is from 5 to 9, the hundredths digit goes up by 1. Here, the first digit that was dropped is an 8, so the 7 in the hundredth place goes up 1 to 8.
Answer: 1755.98
What is the best estimate for 42% of 68?
Answer:
29 when rounded up 27 when rounded down and 28.56 in genral
Step-by-step explanation:
Answer:
28 or 30
Step-by-step explanation:
42 to 40 and 68 to 70 then
hope this helps :b
PLEASE HELP !
Determine whether each equation represents a linear or a nonlinear function
Select Linear or Nonlinear for each equation
Step-by-step explanation:
Note:
Linear equations will never exponents in its equation such as
[tex] {x}^{2} \\ y = {x}^{3} [/tex]
as those equations will produce curly graphs.
Nonlinear equations will either contain exponents or logarithms (eg. ln2)
need help fast with math problem!!!!
plz help i will give brainliest
Answer:
[tex] m\angle XYZ = 70\degree [/tex]
Step-by-step explanation:
By exterior angle theorem:
4x° = 2x° + 70°
4x° - 2x° = 70°
2 x° = 70°
2x = 70
x = 70/2
x = 35
[tex] m\angle XYZ = 2x\degree [/tex]
[tex] m\angle XYZ = 2\times 35\degree [/tex]
[tex] m\angle XYZ = 70\degree [/tex]
The area of the rectangle shown below is 36 square units. Set up and solve an equation to find the value of x
Answer:
x = 3 is the answer :)
hope this helps
i really need help please
Answer:
a = 4, x = 1
Step-by-step explanation:
The opposite sides of a parallelogram are congruent , then
WX = YZ , that is
a² + 5a = 5a + 16 ( subtract 5a from both sides )
a² = 16 ( take the square root of both sides )
a = ± [tex]\sqrt{16}[/tex] = ± 4
Since a > 0 , then a = 4
Also
XY = WZ , that is
x² + 6x = 4x + 3 ( subtract 4x + 3 from both sides )
x² + 2x - 3 = 0 ← in standard form
(x + 3)(x - 1) = 0 ← in factored form
Equate each factor to zero and solve for x
x + 3 = 0 ⇒ x = - 3
x - 1 = 0 ⇒ x = 1
Since x > 0 , then x = 1
A cone has a volume of 200.96 cubic centimeters and a height of 12 centimeters. What is its radius? Use ≈ 3.14 and round your answer to the nearest hundredth. r ≈ centimeters
Answer:
Radius = 4 cmStep-by-step explanation:
Formula:
r = √[ (3 * v) / (π * h) ]
x + 2x +17=25 I need the answer and need do you know how to check if it's right
Answer:
x=8/3
Step-by-step explanation:
x+2x+17=25
3x+17=25
3x=8
x=8/3
Answer:
X = [tex]\frac{8}{3\\}[/tex]
Step-by-step explanation:
Omar divided a circular pizza into 8 equal sections. He gave his friend
3 sections. Explain why the amount he gave to his friend can be represented
by a point plotted to the right of 0 on a number line. Then write the
amount he gave to his friend as a decimal.
Answer:
the amount he gave his friend is a positive fraction, therefore to the right of 0 on the number line. the decimal is 3/8 which = 0.375
7b^2-63b+140 Factor the polynomial (show your work)
Answer:
7 (b - 5) (b- 4)
6x – 9 = 33 Check
please and thank you
Answer:
x = 7
Step-by-step explanation:
6x - 9 = 33
6x = 33 + 9
6x = 42
x = 42 / 6
x = 7
6x - 9 = 33
6 x 7 - 9 = 33
42 - 9 = 33
33 = 33
Hope that helps!
Answer: x=7
Step-by-step explanation:
6x-9=33
for x
6x=33+9
6x=42
x=42/6
x=7
for checking put value of x
6*7-9=33
42-9=33
33=33
16 years 6 months =
months?
Answer:
198 months
Step-by-step explanation:
12 months in a year times 16 years plus 6 months is 198
Determine the length of the hypotenuse. Round your answer to the nearest tenth, if necessary.
Answer:
12.7
Step-by-step explanation:
[tex]9^{2}+9^{2}= 162\\\\\sqrt{162}= 12.7[/tex]
Can u please help me??
It would be very helpful if u could write down the answer on a piece of paper(50pts)
Answer:
Given GP:
tₙ = (1/3)ⁿ⁻¹We see that:
t₁ = 1, r = 1/3Sum of n terms:
Sₙ = t₁(1 - rⁿ)/(1 - r)Sₙ = [1 - (1/3)ⁿ] / (1 - 1/3) = [1 - (1/3)ⁿ] / (2/3) = 3/2 [1 - (1/3)ⁿ] Sₙ = 3/2 [1 - (1/3)ⁿ]Vince and 11 of his friends went out for pizza on Saturday night to celebrate Vince’s birthday. The cost of the pizza and soft drinks before sales tax and tip was $47.96. What is the amount of sales tax for the bill if the rate is 7%?
Answer:
$3.36
Step-by-step explanation:
47.96×7%=$3.357
Answer:
About $3.36
47.96 x 0.07 = 3.3572 rounded up is 3.36
PLEASE HELP I GIVE BRAINLIEST
29 thanks and no links or you get reported
Answer:
$480.11 (C)
Step-by-step explanation:
$575.26 - $95.15 = $480.11
Reduce your fraction into lowest terms.
Translate the following words into an ALGEBRAIC EXPRESSION:
The difference of three and twice a number plus one
Answer:
3-2x+1
Step-by-step explanation:
If we indicate x the generic number we can write this expression
3-2x+1
when a sign of an operation is not expressed it means that the operation is multiplication
2x means 2*x
