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
Which peicewise function is shown in the graph?
Answer:
Option (1)
Step-by-step explanation:
From the graph of the piecewise function,
There are two pieces of the function,
1). Segment (1) having x < 0
2). Segment (2) having x ≥ 0
Segment (1),
Segment starts with a hollow circle at x = 0 and passes through two points (0, 1) and (-2, 2)
Slope of the segment = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
= [tex]\frac{2-1}{-2-0}[/tex]
= [tex]-\frac{1}{2}[/tex]
Equation of the segment passing through (-2, 2) with slope = [tex]-\frac{1}{2}[/tex],
[tex]y-y'=m(x-x')[/tex]
[tex]y-2=-\frac{1}{2}(x+2)[/tex]
[tex]y=-\frac{1}{2}x-1+2[/tex]
[tex]y=-\frac{1}{2}x+1[/tex]
[tex]y=-0.5x+1[/tex] For x < 0
Segment (2),
Segment starts with a solid circle at x = 0 and passes through (0, -2) and (2,2)
Slope of the segment = [tex]\frac{2+2}{2-0}[/tex]
= 2
Equation of the segment passing through (0, -2) and slope = 2,
y - y' = m(x - x')
y + 2 = 2(x - 0)
y = 2x - 2 For x ≥ 0
Therefore, Option (1) will be the correct option.
Tasha is planning an expansion of a square flower garden in a city park. If both the length and the width of the original garden are each increased by *3m*, the new total area of the garden will be *49* squared meters. Find the length of each side of the original garden.
Answer:
4 m
Step-by-step explanation:
Since the flower garden is square :
Both length and width are equal :
Let :
Original side length = x
Increased length = x + 3
Area of square = s² (s = side length)
New area = 49 m²
That is ;
(x + 3)² = 49
Original length, x can be calculated thus ;
Take square root of both sides
x + 3 = √49
x + 3 = 7
x = 7 - 3
x = 4
Hence, original length of each side = 4 m
The sum of Aini’s age and Wani’s age is 62 years old. Three years later, Aini’s age is three times Wani’s age. How old is Aini now?
Answer:
48 years old
Step-by-step explanation:
a + w = 62
a+3 = 3(w+3) =>a+3=3w+9
=> a-3w = 6
a+ w = 62
a- 3w= 6
________-
4w = 56
w = 14
so, the Aini's age now is 62-14 = 48 years old
semoga membantu
Question 5 of 10
In the diagram below, 30 is parallel to XY. What is the value of x?
769
Answer:
D
Step-by-step explanation:
a and 76° are corresponding angles and are congruent , then
x = 76° → D
simplify
[tex] \frac{2e + f}{8e - 2e {}^{2} } \times \frac{4e - e {}^{2} }{2ef + f {}^{2} } [/tex]
The answer is 1/2f
my answer is in the image above
Set up an equation and solve for x
Answer:
x = -10
Step-by-step explanation:
verticle angles are congruent
80 + x = 70
Subtract 80 from both sides
x = -10
Figure PQRS is a parallelogram. The expressions represent the measures of the angles in degrees.
Parallelogram P Q R S is shown. Angle Q is (20 + 2 x) degrees and angle R is (6x) degrees.
What is the value of x?
5
10
20
25
Given:
In parallelogram PQRS, [tex]m\angle Q=(20+2x)^\circ,\ m\angle R=6x^\circ[/tex].
To find:
The value of x.
Solution:
In a parallelogram, the consecutive interior angles are supplementary angles.
In parallelogram PQRS,
[tex]m\angle Q+m\angle R=180^\circ[/tex] (Supplementary angles)
[tex](20+2x)^\circ+(6x)^\circ=180^\circ[/tex]
[tex](20+8x)^\circ=180^\circ[/tex]
[tex]20+8x=180[/tex]
Subtracting 20 from both sides, we get
[tex]8x=180-20[/tex]
[tex]8x=160[/tex]
Divide both sides by 8.
[tex]\dfrac{8x}{8}=\dfrac{160}{8}[/tex]
[tex]x=20[/tex]
Therefore, the correct option is C.
Answer:
c
Step-by-step explanation:
I need help with my math! Can you please help me!!
Answer:
[tex]y=-|x-1|+3[/tex]
Step-by-step explanation:
The graph of the function ([tex]y=|x|[/tex]) can be described as a perfect (v) shape composed of two lines with the equation ([tex]y=x[/tex]) and ([tex]y=-x[/tex]) with a range of ([tex]y\geq 0[/tex]). In the depicted graph, this function has undergone some transfomrations. The general format for a transformation of an absolute value function is the following;
[tex]y=(+-)n|x-k|+h[/tex]
The function can be inverted if the sign of (n) is (-). As per the given graph, the function is inverted, thus the answer will have a (-) sign in front of it. One can see that the (n) value has to be (1) or rather not present since the function has no scaling factor.
[tex]y=-|x|[/tex]
The function has been shifted (k) units to the right, one can see that the given function's vertex is (1) unit to the right, thus the equation of the function has a (1) in the position of (k).
[tex]y=-|x-1|[/tex]
The function is shifted (3) units up, thus the position of (h) is occupied by a (3).
[tex]y=-|x-1|+3[/tex]
Therefore the following answer choice is correct, as it fits all of the requirements;
[tex]y=-|x-1|+3[/tex]
jose bought "n" packs of pencils. Each pack has 12 pencils. Write an equation to represent the total number of pencils "p" that josé bought.
Answer:
nx12=p
Step-by-step explanation:
So every pack has 12 pencils. You multiply the packs of pencils that José bought with how much pencils per pack. Since José bought "n" packs of pencils, the equation is nx12. But the answer is also unknown since we don't know how much packs José bought, so the answer is "p", or the total number of pencils José bought.
During a sale, a store offered a 20% discount on a stereo system that originally sold for $320. After the sale, the discounted price of the stereo system was marked up by 20%.
Answer:
354 $ is correct
Step-by-step explanation:
your v id dead
A typical serving of fish is 4 ounces. What is this serving size in grams?
Answer:
the answer is 113.398 grams
Can someone help me please really need help? I’ll help you back please & thanks
Find the reciprocal of 9.
the reciprocal of 9 is 1 divided by 9, i.e. 1/9
In the ordered pair below, which value represents the input to a function?
(2, 3)
Answer:
2
Step-by-step explanation:
In an order pair
(x,y)
The first number is the input and the second number is the output
(2,3) 2 is the input and 3 is the output
Which fraction equals the ratio of rise to run between the points (0, 0) and (6, 7)? A. B. C. D.
Answer:
7 / 6
Step-by-step explanation:
Given the points:
points (0, 0) and (6, 7)
Point 1 : x1 = 0 ; y1 = 0
Point 2 : x2 = 6 ; y2 = 7
The rise = y2 - y1 = 7 - 0 = 7
The run = x2 - x1 = 6 - 0 = 6
Ratio of Rise to Run = Rise / Run = 7 / 6
Over a 24-hour period, the tide in a harbor can be modeled by one period of a sinusoidal function. The tide measures 5.15 ft at midnight, rises to a
high of 10.2 ft falls to a low of 0.1 ft, and then rises to 5.15 ft by the next midnight
What is the equation for the sine function f(x), where x represents time in hours since the beginning of the 24-hour period, that models the
situation?
Enter your answer in the box
Answer:
f(x)=5.05 sin((pi/12)x) + 5.15
Step-by-step explanation:
pls help due in 1 hr
Answer:
x = 10.6
Step-by-step explanation:
Soh...
Sine = Opposite / Hypotenuse
...cah...
Cosine = Adjacent / Hypotenuse
...toa
Tangent = Opposite / Adjacent
sin(49) = 8/x
x = 8/sin(49)
x = 10.6
AB and CF are parallel find x
Show CLEARLY how you got your answers with reasons
Answer:
x = 152°
Step-by-step explanation:
∠ BDE = ∠ ABD = 76° ( alternate angles )
Since DE = BE then Δ BDE is isosceles with base angles congruent
∠ DBE = ∠ BDE = 76°
The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.
x is an exterior angle of the triangle, then
x = 76° + 76° = 152°
PLEASE HELP! Code/answer
Answer:
29
7 : 27
Step-by-step explanation:
Ratio expresses the relationship between two or more numbers. It shows the frequency of the number of times that one value is contained within other value(s).
The ratio of students to teachers is 2:29
this means that for every 2 teachers, there are 29 students
There are 7 doctors and 27 nurses. this means that the ratio of doctors to nurses is 7 : 27
find the vaule of a in ax+by=c
Answer:
a=[tex]\frac{c-by}{x}[/tex]
Step-by-step explanation:
To find a, we need to change the equation so a is the variable that is left by itself. So...
ax+by=c Get rid of anything else besides the x and its coefficient.
-by -by
ax=c-by Because a has to be completely isolated, get rid of its coefficient.
/x /x
a=[tex]\frac{c-by}{x}[/tex]
Hope this helps and have a great day :D
Answer:
[tex]a x + by = c \\ ax = c - by \\ \frac{ax}{x} = \frac{c - by}{x} \\ a = \frac{c - by}{x}[/tex]
Which of the following uses set builder notation to denote the set of all (real) multiplicative inverses?
Answer Choices In Picture
Answer:
First Option
Step-by-step explanation:
If q||r, solve for x
Answer:
12
Step-by-step explanation:
Since they are parallel then
(7x - 8) + (11x - 28) = 180
18x - 36 = 180
18x = 216
x = 12
________ collect money from investors, create capital, and offer various investment options.
Fill in the blank
its 2 words
[tex]\sf\purple{Mutual \:funds}[/tex] collect money from investors, create capital, and offer various investment options.
[tex]\circ \: \: { \underline{ \boxed{ \sf{ \color{green}{Happy\:learning.}}}}}∘[/tex]
A survey was done to determine the relationship between gender and subject preference. A total of
56 students were surveyed to determine if they liked math, English, social studies, or science as their
favorite subject. The results were then broken down based on whether the respondent was male or
female.
The question is incomplete. The complete question is :
A survey was done to determine the relationship between gender and subject preference. A total of 56 students were surveyed to determine if they liked math, English, social studies, or science as their favorite subject. The results were then broken down based on whether the respondent was male or female.
Which of the following is the closest to the joint relative frequency of being a male who likes social studies ?
Solution :
A two way table used in statistics and mathematics is used to show the frequencies or the relative frequencies for any two categorical variables. One of the category is represented by the rows while the other categories by a column.
Here, in this table it is given that the total surveyed = 56 students
From the table, we know that number of males who likes social studies = 8
Therefore, the closest to the joint relative frequency for being a male who likes the subject social studies is given by :
[tex]$=\frac{8}{56}$[/tex]
[tex]$=\frac{1}{7}$[/tex]
=0.14
In ΔOPQ, PQ = 14, QO = 13, and OP = 20. Which list has the angles of ΔOPQ in order from smallest to largest?
Answer:
The answer is A, that's the correct one
Identify the type of function represented by
f(x) = 4.2%
O A. Exponential growth
O B. Exponential decay
O C. Decreasing linear
O D. Increasing linear
A turkey has a mass of 6 kilograms. A bag of sweet potatoes has a mass of 2 kilograms. How many more grams does the turkey weigh than the sweet potatoes?
Answer:
the correct answer is 4,000 grams
In the cafeteria tables are arranged in groups of 4, with each table seating 8 students. How many students can sit at 10 groups of tables?
how do i solve for x with an equation that says 19 = x - 3
Answer: x = 22
Step-by-step explanation: Since x is unknown, we want to isolate it and determine what it equals. We know that x - 3 gives us 19, but we don't want to know what x - 3 is, just x. So we can add three to both sides of the equation, to get our answer and keep it balanced. As a result, we get x = 22
Answer:
x = 22
Step-by-step explanation:
19 = x - 3
Add 3 to each side
19 + 3 = x - 3 + 3
Simplify
22 = x
Solve the following inequality for qq. Write your answer in simplest form. -6q+7≤8q-3
Answer:
q ≥ 5/7
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityAlgebra I
Terms/CoefficientsStep-by-step explanation:
Step 1: Define
Identify
-6q + 7 ≤ 8q - 3
Step 2: Solve for q
[Subtraction Property of Equality] Subtract 8q on both sides: -14q + 7 ≤ -3[Subtraction Property of Equality] Subtract 7 on both sides: -14q ≤ -10[Division Property of Equality] Divide -14 on both sides: q ≥ 5/7Here we see that any number q greater than or equal to 5/7 would work as a solution to the inequality.
Answer:
q ≥ [tex]\frac{5}{7}[/tex]
Step-by-step explanation:
Given
- 6q + 7 ≤ 8q - 3 ( add 6q to both sides )
7 ≤ 14q - 3 ( add 3 to both sides )
10 ≤ 14q ( divide both sides by 2 )
5 ≤ 7q ( divide both sides by 7 )
[tex]\frac{5}{7}[/tex] ≤ q , then
q ≥ [tex]\frac{5}{7}[/tex]
