4x³ - 4x + 3 is divided by (2x-1)
Complete question:
4x³ - 4x + 3 is divided by (2x - 1). Find the quotient and the remainder
Answer:
The quotient = 2x² + x - ³/₂ and the remainder = ³/₂
Step-by-step explanation:
Given function;
4x³ - 4x + 3 divided by (2x-1)
Use long division method to obtain the remainder and the quotient.
2x² + x - ³/₂
-----------------------
2x - 1 √4x³ - 4x + 3
- (4x³ - 2x²)
----------------------------
2x² - 4x + 3
- ( 2x² - x)
-----------------------------
-3x + 3
-(-3x + ³/₂)
----------------------------
³/₂
Therefore, the quotient = 2x² + x - ³/₂ and the remainder = ³/₂
Plzz I beg someone to finish ALL of this :(. I’ve stayed up all night to do this but I couldn’t figure all of them out. Pls pls pls!!! ill mark you brainliest n I can give you a thank you such as 5 Stars in return. Please take your time and I hope you all have a amazing day!
(Spam/same words/diff pics/)
Answer:
Step-by-step explanation:
1)
9:10
+ 0:45
9:55
so at 9:55 she finished her eating.
2)
10:25
- 2:15
8:10
so test started at 8:10
3)
9:15
-7:30
2:15
si games duration was 2;15
4)
2:40
+25
3:05
se reached home at 3:05
The graphs of g(x) = x³- ax² + 6 and h(x) = 2x² + bx + 3 touch when x = 1. Therefore, the tangent to
the curve of g at x = 1 is also the tangent to the curve of h at x = 1.
Determine the coordinates of this point of contact of the two graphs.
Answer:
[tex](1,\, 10)[/tex].
Step-by-step explanation:
Differentiate each function to find an expression for its gradient (slope of the tangent line) with respect to [tex]x[/tex]. Make use of the power rule to find the following:
[tex]g^\prime(x) = 3\, x^2 - 2\, a\, x[/tex].
[tex]h^\prime(x) = 2\, (2\, x) + b = 4\, x + b[/tex].
The question states that the graphs of [tex]g(x)[/tex] and [tex]h(x)[/tex] touch at [tex]x = 1[/tex], such that [tex]g^\prime(1) = h^\prime(1)[/tex]. Therefore:
[tex]3 - 2\, a = 4 + b[/tex].
On the other hand, since the graph of [tex]g(x)[/tex] and [tex]h(x)[/tex] coincide at [tex]x = 1[/tex], [tex]g(1) = h(1)[/tex] (otherwise, the two graphs would not even touch at that point.) Therefore:
[tex]1 - a + 6 = 2 + b + 3[/tex].
Solve this system of two equations for [tex]a[/tex] and [tex]b[/tex]:
[tex]\begin{aligned}& a + b = 2 \\ & 2\, a + b = -1\end{aligned}[/tex].
Therefore, [tex]a = -3[/tex] whereas [tex]b = 5[/tex].
Substitute these two values back into the expression for [tex]g(x)[/tex] and [tex]h(x)[/tex]:
[tex]g(x) = x^3 + 3\, x^2 + 6[/tex].
[tex]h(x) = 2\, x^2 + 5\, x + 3[/tex].
Evaluate either expression at [tex]x = 1[/tex] to find the [tex]y[/tex]-coordinate of the intersection. For example, [tex]g(1) = 1 + 3 + 6 = 10[/tex]. Similarly, [tex]h(1) = 2 + 5 + 3 = 10[/tex].
Therefore, the intersection of these two graphs would be at [tex](1,\, 10)[/tex].
Which is the graph of f(x) = (2) -x
Answer:
In other words y = 2-x
Put in some values of x and see which graph matches the given ys.
The last graph
Answer:
b
Step-by-step explanation:
Question 1 of 10
Which of the following is equal to the rational expression when x#5?
x² - 25
X-5
A. x + 5
B. X-5
1
C
x+5
O D. X+5
X-5
SUBMIT
Answer:
A. x + 5
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to RightAlgebra I
Terms/CoefficientsFactoringStep-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle \frac{x^2 - 25}{x - 5}[/tex]
Step 2: Simplify
Factor: [tex]\displaystyle \frac{(x - 5)(x + 5)}{x - 5}[/tex]Divide: [tex]\displaystyle x + 5[/tex]The world population in 2000 was approximately 6.08 billion. The annual rate of increase
was about 1.26%
which year will it be when the population reaches 7.5 billion?
Answer:
6
Step-by-step explanation:
21. Glass Vase You are taking a glass-blowing class and have created a vase in the
shape of a sphere. The vase will have a hole in the top so you can put flowers in it
and it will sit on a stand. The radius of your vase is 21 inches. Use the formula
= ar to write an expression for the volume of your vase.
V
Answer:
V = 12,348·π
Step-by-step explanation:
The given parameters of the glass Vase are;
The shape of the glass vase = A sphere
The radius of the vase, r = 21 inches
The given formula for finding the volume of a sphere is [tex]V = \dfrac{4}{3} \cdot \pi \cdot r^3[/tex]
Therefore, when r = 21 inches, we get;
[tex]V = \dfrac{4}{3} \cdot \pi \cdot 21^3 = {12,348 \cdot \pi}[/tex]
Therefore, the expression for finding the equation of the spherical glass vase, V = 12,348·π
Please help if can and show work
Answer:
Step-by-step explanation:
What is the value of the expression below?
(+8) +3.545
0 17.
17
7
10
니
18
10
○ 212
0 24를
please type it correctly and i can help Step-by-step explanation:
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used. Match the questions with their solutions. 5 80 6 200 8 150 Joshua has 11 baskets of apples. In total, he has 88 apples. How many apples are there in 1 basket? arrowRight Mindy can type 40 words per minute. How many words can she type in 5 minutes? arrowRight Jessica had 20 balloons, which she distributed among 4 of her friends. How many balloons did each friend get? arrowRight Max can make 1 greeting card in 5 minutes. How many greeting cards can he make in 30 minutes? arrowRight
Answer:
1.) 8 ; (2.) 200 ; (3.) 5 ; (4.) 6
Step-by-step explanation:
1.)
Number of apple baskets = 11
Total number of apples = 88
Number of apples per basket = 88 / 11 = 8
2).
Number of words per minute = 40
Number of words that can be typed in 5 minutes :
40 * 5 = 200 words
3.)
Number of balloons = 20
Number of friends = 4
Number of balloons per friend = 20/4 = 5
4.)
Time required to make 1 greeting card = 5 minutes
Number of greeting cards that can be made in 30 minutes :
30 minutes / 5 minutes = 6 greeting cards
Please help I’ll give brainliest
Answer:
add
Step-by-step explanation:
The exponent "product rule" tells us that, when multiplying two powers that have the same base, you can add the exponents. In this example, you can see how it works. Adding the exponents is just a short cut! The "power rule" tells us that to raise a power to a power, just multiply the exponents.
Hope this is helpful
Answer:
Add
Step-by-step explanation:
Hope it helps you
Please mark as brainliest
Thank You
Người ta nuôi cá trong một bể xây mặt bể là hình chữ nhật có chiều dài là 80m chiều rộng 60m. Trên mỗi mét vuông mặt bể người ta thả 12 con cá giống đến mỗi kỳ thu hoạch trung bình mỗi con cân nặng 240g giá bán 32000 đồng/kg và thấy lãi khi qua kỳ thu hoạch này là 200 triệu. Hỏi vốn mua cá giống và chi phí trong đợt này là bao nhiêu?
I will give branliest if it let's me! Please help! I'll give 5 star rating, thanks and 40+ points!
Answer:
B
Step-by-step explanation:
These are corresponding angles if i remember correctly.
Answer:
Supplementary
Step-by-step explanation:
The angles add up to 180 degrees
Parallel to y = 3x − 2 and passes through (1, 4)
Answer:
y=3x + 1
Step-by-step explanation:
slope is same
insert coordinates into x and y values
determine y-intercept
Which could be the missing data item for the given set of data if the median of the complete data set is 65?
66, 43, 35, 78, 74, 37, 65, 66, 76, 78, 80, 43, 56, 60
A. 71
B. 75
C. 69
D. 50
Answer:
B.) 75
Step-by-step explanation:
Answer: B 75
Step-by-step explanation:
the coordinates of three vertices of a rectangle are -2, 3, -2, -1, and 3, -1. what are the coordinates of the fourth vertex
Answer:
(3,-5)
Step-by-step explanation:
We first cal ulate the distance
According to the histogram, which interval of time do most students spend on the Internet?
0 - 30 minutes
31 - 60 minutes
61 - 90 minutes
91 - 120 minutes
Answer:
91 - 120 minutes
Step-by-step explanation:
In a histogram, the bar highest suggests the most common, so most students spend 91 - 120 minutes in this histogram.
Sara can weed a garden in 30 minutes. When her brother Hamdan helps her, they can weed the same garden in 20 minutes. How long would it take Hamdan to weed the garden if he
worked by himself?
a. Write an expression for Hamdan's rate, using n for the number of hours he would take to
weed the garden by himself.
b. Write an equation to show the amount of work completed when they work together.
c. How long would it take Hamdan to weed the garden by himself?
Answer:
Let's define:
S as the rate at which Sara can weed a garden.
We know that:
S*30min = 1 garden
And let's define H as the rate at which Hamdan can weed a garden, we know that when they work together, they can complete the job in 20 minutes, then
(S + H)*20min = 1 garden
a) Here we get:
H*n = 1 garden
where n is the number of hours that he would take (note that in two previous equations we have minutes, so we need to use a change of units)
b) The equation is
(S + H)*20min = 1 garden
c) ok, we know two things:
(S + H)*20min = 1 garden
S*30min = 1 garden
first, let's convert both times to hours:
60 min = 1 hour
then:
30 min = (30/60) hours = 0.5 hours
20 min = (20/60) hours = 0.33 hours
Then the equations become:
(S + H)*0.33 hours = 1 garden
S*0.5 hours = 1 garden
Le's solve the second equation for S:
S = (1 garden /0,5 hours) = 2 gardens/hour.
Now we can replace this in the other equation to get:
(2 garden/hour + H)*0.33 hours = 1 garden
2 garden/hour + H = (1 garden)/(0.33 hours) = 3 gardens/ hour
H = 3 gardens/hour - 2 gardens/hour = 1 gardens/hour
This means that the rate of Hamdan is 1 gardens/hour, so he can weed a garden in one hour.
Then:
(1 garden/hour)*n = 1 garden
n = ( 1 garden)/((1 garden/hour)) = 1 hour
Find the area of this circle in square centimeters. Use 3.14 for π . Round to 2 decimal places if necessary. Enter only the number π
Answer:
113.04 is the answer
Step-by-step explanation:
Use the formula for finding the area of a circle.
Area= pi times radius to the second power.
First you had to divide your diameter by 2 to get 6. Then 6 squared, to get 36. Then finally 36x3.14.
If this trapezoid is moved through the
translation (x+3, y-2), what will the
coordinates of C'be?
5
00
NO
A
D
1
-7 -6 -5
4
-3
1
2
3
4
-2 -1 0
-1
C' = (1, [?])
-2
Given:
The rule of translation is:
[tex](x+3,y-2)[/tex]
The trapezoid ABCD on the graph.
To find:
The coordinates of the point C'.
Solution:
From the given graph, it is clear that the coordinates of point C are (-2,4).
The rule of translation is:
[tex](x,y)\to (x+3,y-2)[/tex]
Using this rule of translation, we get
[tex]C(-2,4)\to C'(-2+3,4-2)[/tex]
[tex]C(-2,4)\to C'(1,2)[/tex]
Therefore, the coordinates of the point C' are (1,2).
Which expression is equivalent to 10^-4
Answer:
[tex] \frac{1}{10000} [/tex]Step-by-step explanation:
[tex] {10}^{ - 4} [/tex]
[tex] \frac{1}{ {10}^{4} } [/tex][tex] \frac{1}{10000} [/tex]Hope it is helpful...Find how many kilometers they traveled by
bike.
Enter the correct answer.
George and Carmen went on a bicycle
trip. They took a bus to their starting
point, and then biked the rest. They
traveled 325 kilometers in total, and
they biked 75 kilometers more than they
were bussed.
000
DONE
Clear all
2
Let x = kilometers traveled by bike and
y = kilometers traveled by bus. Find how many kilometers they traveled by bike
Answer:
Step-by-step explanation:
Biking is x and bussing is y. We know that the total distance is 325. Thus, the first equation in this system is
x + y = 325 (which says that the km traveled by bike plus the km traveled by bus totaled 325 km).
We also know that the pair biked 75 km more than they rode, giving us the second equation in our system:
x = y + 75. Now we use simple substitution and plug y + 75 in for x in the first equation:
(y + 75) + y = 325 and
2y + 75 = 325 and
2y = 250 so
y = 125 km. They rode the bus for 125 km and biked for 325 - 125 which is 200. And the difference is 75 km, as it should be!
please please!! help!!
9514 1404 393
Answer:
2
Step-by-step explanation:
Each orange vertex is twice as far from the origin as the corresponding black vertex. Each orange line segment is twice as long as the corresponding black line segment. The scale factor is 2.
Find the distance between the points (1,5) and (3,0). Round your answer to the nearest tenth.
Answer:
5.4 units
Step-by-step explanation:
Hi there!
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex] where two given points are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]
Plug in the given points (1,5) and (3,0)
[tex]d=\sqrt{(3-1)^2+(0-5)^2}\\d=\sqrt{(2)^2+(-5)^2}\\d=\sqrt{4+25}\\d=\sqrt{29}\\d=5.4[/tex]
Therefore, the distance between the two points when rounded to the nearest tenth is 5.4 units.
I hope this helps!
Give reasons.
a.
Mass is a physical quantity.
The diameter of a circle is 9 m. Find the circumference \textit{to the nearest tenth}to the nearest tenth.
Answer:
[tex]C=28.3m[/tex]
Step-by-step explanation:
From the question we are told that:
Diameter [tex]d=9m[/tex]
Radius[tex]r=4.5m[/tex]
Generally the equation for Circumference of a circle is mathematically given by
[tex]C=2\pi r\\\\\C=2*\pi*4.5m[/tex]
[tex]C=28.3m[/tex]
Answer:
Step-by-step explanation:
From the question we are told that:
Diameter
Radius
Generally the equation for Circumference of a circle is mathematically given by
Have a good day
Step-by-step explanation:
i WILL mark brainliest !!!!
John had a total of $150. He purchased a DVD box set which costs $50 as well as a single DVD. He is left with $75. Which equation could be used to find the cost p of the DVD?
a. 150 + 50 + p = 75
b. 150 + 50 + 75 = p
c. 150 − 50 + 75 = p
d. 50 + p + 75 = 150
ps: absurd answers will be reported !!
Answer:
please mark as brilliant
What is the domain of y= log 5x
Answer:
all positive real numbers, (0, ∞)
Step-by-step explanation:
The log function is not defined for 0 or for negative numbers.
The domain of the log function is all positive real numbers.
Answer: all positive real numbers
Sum of two digit number is9.When we interchange the digits it is found that the resulting new number becomes twice the other number. What are the numbers
Answer:
4 and 5
Step-by-step explanation:
Let the numbers be x and y
If their sum is 9, hence;
x + y = 9 ....1
When reversed
10y+x = 2(10x+y)
10y+x = 20x + 2y
10y - 2y = 20x - x
8y = 19x
y = 10x/8 ...2
Substitute equation 2 into 1;
From 1;
x+y = 9
x +(10x/8) = 9
18x/8 = 9
18x = 72
x = 72/18
x = 4
Since x+y =9
y = 9-x
y =9-4
y = 5
Hence the numbers are 4 and 5
If a is a non-zero constant, determine the vertex of y = -3(x + a)^2 - 6
Answer:
Vertex is (-a, -6), where a ≠ 0.
General Formulas and Concepts:
Algebra I
Coordinates (x, y)QuadraticsAlgebra II
Vertex Form: y = a(bx - h)² + k
a is the vertical scale factorb is the horizontal scale factor(h, k) is the vertexStep-by-step explanation:
Step 1: Define
y = -3(x + a)² - 6
↓ Identify variables
a = -3
b = 1
(h, k) = (-a, -6)