Answer:
(x-1) ( x -i) (x+i)
Step-by-step explanation:
x^3 -2x^2 +x-2
Factor by grouping
x^3 -2x^2 +x-2
x^2(x-2) +1(x-2)
Factor out (x-2)
(x-2) (x^2+1)
Rewriting
(x-1) ( x^2 - (-1)^2)
(x-1) ( x -i) (x+i)
Answer:
Should be b
Step-by-step explanation:
Since it's a multiple choice question you know that -2 or 2 has to be a root for the cubic.
You can test both -2 and 2 and see that replacing x for 2 has the expression evaluate to 0.
Then, since you know the imaginary roots have to be conjugates, you get B.
Isaac is working two summer jobs, making $8 per hour walking dogs and making $16
per hour tutoring. In a given week, he can work a maximum of 8 total hours and must
earn no less than $80. If x represents the number of hours walking dogs and y
represents the number of hours tutoring, write and solve a system of inequalities
graphically and determine one possible solution.
Answer:
8 x 8 =64 + 16 x 8 = 128 =$192
Step-by-step explanation:
Can I please get help with B
Answer:
sure just bring the question and it will be answered
A digital clock shows hours and minutes. How many times between one minute after midnight and one minute before midnight does the clock show the same when it is read forwards or backwards (for example : 15:51)
Answer:
60 seconds make 1 minute,60 minute make 1 hours.
What fraction equals 4
Here are a few 4/1 , 8/2 , 12/3
4, 8/2, 12/3 are equal to 4, when simplified, which means they are equivalent in nature.
What is fraction?A fraction is defined as numerical representation for part of a whole which represents a rational number.
If the denominator is 1, the numerator can be taken as 4, so the fraction would become \(\frac{4}{1}\) = 4
If the denominator is 2, the numerator can be taken as 8, so the fraction would become \(\frac{8}{2}\) = 4
If the denominator is 3, the numerator can be taken as 12, so the fraction would become \(\frac{12}{3}\) = 4
Thus, 4, 8/2, 12/3 are equal to 4, when simplified, which means they are equivalent in nature.
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Find the equation of the line that passes through (2,-1) and is parallel to y = 4 − 2 x . Leave your answer in the form y = m x + c
Answer:
y = -2x + 3
Step-by-step explanation:
The slope intercept equation of a straight line is \(y=mx+b\),
where m is the slope and b is the y-intercept.
Therefore, the slope of \(y=4-2x\) is -2.
If a line is parallel to another line, they have the same slope.
Therefore, the slope (m) of the new line is also -2.
Using the point-slope form of a linear equation, where m = -2 and
\((x_1,y_1)\) is a point on the line (2, -1):
\(\implies y-y_1=m(x-x_1)\)
\(\implies y+1=-2(x-2)\)
\(\implies y=-2x+3\)
pls can u gus tell me the ans and explanation
Answer:
2325 mL
Step-by-step explanation:
Let x = total volume of the tank. When we fill 4/5 of water into the tank, the amount of water we have can be expressed by 4x/5. Then we only keep 1/3 of that amount (poured away 2/3 of the water), so the amount of water is 4x/15. Thus we set up the equation like this:
4x/15 = 620
4x = 9300
x = 2325
Thus the tank can contain a maximum of 2325 mL.
Round 4.57438 to the nearest tenths place
4.57438 to the nearest tenths place is 5.
Find the area of the region bounded by
• y = √x,
• y = 2-x², and
y = -√2x.
The area of the Region bounded by y = √x, y = 2-x², and y = -√2x is $\frac{32}{15}$.
To find the area of the region bounded by y = √x, y = 2-x², and y = -√2x, we need to graph the equations and determine the points of intersection. Then we can integrate to find the area.
Firstly, we'll graph the equations and find the points of intersection:
y = √xy = 2-x²y = -√2xGraph of y = √x, y = 2-x², and y = -√2xWe need to solve for the points of intersection, so we'll set the equations equal to each other and solve for x:√x = 2-x²√x + x² - 2 = 0Let's substitute u = x² + 1:√x + u - 3 = 0√x = 3 - u
(Note: Since we squared both sides, we have to check if the solution is valid.)u = -2x²u + x² + 1 = 0 (substituting back in for u
)Factoring gives us:u = (1, -2)We can then solve for x and y:x = ±1, y = 1y = 2 - 1 = 1, x = 0y = -√2x = -√2, x = 2y = 0, x = 0Graph of y = √x, y = 2-x², and y = -√2x with points of intersection to find the area, we need to integrate.
The area is bounded by the x-values -1 to 2, so we'll integrate with respect to x:$$\int_{-1}^0 (2 - x^2) - \sqrt{x} \ dx + \int_0^1 \sqrt{x} - \sqrt{2x} \ dx$$
We can then simplify and integrate:$$\left[\frac{2x^3}{3} - \frac{2x^{5/2}}{5/2} + \frac{4}{3}x^{3/2}\right]_{-1}^0 + \left[\frac{2x^{3/2}}{3} - \frac{4x^{3/2}}{3}\right]_0^1$$$$= \frac{4}{3} + \frac{4}{3} - \frac{4}{15} + \frac{4}{3} - \frac{4}{3}$$$$= \frac{32}{15}$$
Therefore, the area of the region bounded by y = √x, y = 2-x², and y = -√2x is $\frac{32}{15}$.
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There are 14 girls and 15 boys in a sixth grade math class. What is the ratio of girls to total students?
Credit card A has an APR of 20.8% and an annual fee of $60, while credit card
B has an APR of 24.6% and no annual fee. All else being equal, which of these
equations can be used to solve for the principal, P, the amount at which the
cards offer the same deal over the course of a year? (Assume all interest is
compounded monthly.)
The amount at which the cards offer the same deal over the course of a year is a $2,333.33
Since credit card finance charge is the fee associated with using credit.
Credit card issuers use the finance charges to minimize non-payment risks and earn some profits for extending credit to cardholders.
Data and Calculations:
Card A Credit B
APR 20.8% 24.6%
Annual fee $60 $0
To calculate the balance required, the required equation is
= 22%x + $40 = 24.6%x
Where x = required balance
Thus,
= 0.208x + $60 = 0.246x
= $60 = 0.03x (0.246x- 0.208x )
= 0.03x = $60
x = $60 /0.03
x = $2,333.33
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M = I1+I₂ 31 +32 2 Now let's substitute in our given values. (-2 , 2) = ((-5 Find 2 and y2 We will now set up two equations to solve for our two unknowns of x2 and y₂. (-5 X2 (-5+₂) -5+22), (7+)) 2 - +₂)/2 = We will first want to multiply by 2 on both sides and will get −5+₂= -4 Adding 5 to both sides we get = 7 This is the coordinate of point B. Now we will set up the equation to solve for y2 +y2)/2 =
The coordinates of point B are (-3, 17).
The given equation is M = I₁ + I₂ = 31 + 32.
Now let's substitute in our given values:
(-2, 2) = ((-5 + x₂) / 2, (-5 + 2 + y₂) / 2)
We will now set up two equations to solve for our two unknowns, x₂ and y₂:
Equation 1: (-5 + x₂) / 2 = -4
Multiply both sides by 2:
-5 + x₂ = -8
Add 5 to both sides:
x₂ = -3
This gives us the x-coordinate of point B.
Equation 2: (-5 + 2 + y₂) / 2 = 7
Simplify:
(-3 + y₂) / 2 = 7
Multiply both sides by 2:
-3 + y₂ = 14
Add 3 to both sides:
y₂ = 17
This gives us the y-coordinate of point B.
Therefore, the coordinates of point B are (-3, 17).
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8.
How is the graph of y=2(3)^x+1 -4 translated from the graph of y=2(3)^x?
A. 4 units left and 1 unit down
B. 4 units right and 1 unit up
C. 1 unit left and 4 units down
D. 1 unit right and 4 units up
Answer:câu B
Step-by-step explanat
v iorìtoọnggfbgbhbfhgbgfbngfyturtgrvbgntrhfhrefngvfdhrrfvbnfgthgm :
Express this number in scientific notation.
3.868.000.000
Answer:
3.868.000.000
=3 868.000.000
=3, 868.000.000
=3, 868 × 10⁹
Brainiest Question + 30 points
What is 63(4)+89-45(58+256²)
Answer:
-2,951,389
Step-By-Step Explanation:
63(4)+89-45(58+256²)
63(4)+89-45(58+65536)
63(4)+89-45(58+65536)
63(4)+89-45(65,594)
252+89-45(65,594)
252+89-2,951,730
-2,951,389
Susan has 4 cup of raisins and she is dividing them into 3/8 cup
servings. How many servings will she have?
Answer:
32/3 servings
Step-by-step explanation:
4 / (3/8) =
(4/1) x (8/3) =
32/3
-6(2x+2)+3(y-8)
plz answer me fast plzz
Answer:
-12x+3y-36
Step-by-step explanation:
-6(2x+2)+3(y-8)
-12x-12+3y-24
-12x+3y-36
Answer:
-12x+(-12)+(3y-24)
-12x-12+3y-24
-12x+3y-36
Raul has $460 in his checking account. Each month, $45 is automatically deducted from his account to pay for his cell phone plan. He makes no other deposits or withdrawals. He wants to always have more than $100 in his account. What is the greatest number of months he can pay for his cell phone and still have more than $100 in his account?
7 months
8 months
9 months
10 month
Answer:
8 months
Step-by-step explanation:
because it's right just trust me
Answer:
8 months
Step-by-step explanation:
right on edge nuity <3
Solve for the missing side length. Round to the nearest tenth.
5.8
5.2
5.4
5.6
Answer:
C) 5.4-------------------------
Given two legs of a right triangle and we need to find the hypotenuse.
Use Pythagorean theorem:
\(PQ = \sqrt{QR^2+PR^2}\)\(PQ = \sqrt{2^2+5^2} =\sqrt{29} =5.385 = 5.4\ (rounded)\)The matching choice is C.
HELPPPPP
Lisa is framing a rectangular painting length more than twice the widthShe uses 30 inches of framing material. What the length of the paintingWrite equation and solve.
A.3w+3=30;21
b.3w+3=30;9
C.6w+6=30;11
D.6w + 6 = 30 = 4
Answer:
6w = 30
Step-by-step explanation:
We should know that the 30 inches of framing material were used to frame the four sides of the rectangle.
The perimeter of the rectangle is what we should be considering, whenever we are dealing with frames.
This is 2 X (length + width)
From the questions, we can get the dimensions of the rectangle using clues from the various statements made.
From the statement"a rectangular painting length more than twice the width" we can see that the
L = 2w ------------------------- equation 1
substituting this value into the formula for the perimeter of the rectangle we have
30 = 2(2w + w)
30 = 6w
w= 5
from equation 1
L =2 X (5) = 10
Hence, we can set up the equation
6w = 30
However, the closest option to what we have is option D
6w + 6 = 30 - 4
complete question:
Lisa is framing a rectangular painting. The length is three more than twice the width. She uses 30 inches of framing material. What is the length of the printing? Write an equation and solve
Answer:
D.6w + 6 = 30 = 4
Step-by-step explanation:
perimeter = 30 inches
width = w
length = 2w + 3
perimeter of a rectangle = 2l + 2w
where
w = width
l = length
Therefore,
perimeter of a rectangle = 2(2w + 3) + 2w
perimeter of the rectangle = 4w + 6 + 2w
perimeter = 6w + 6
recall
perimeter = 30 inches
6w + 6 = 30
6w = 24
divide both sides by 6
w = 24/6
w = 4
The following data values represent a population. What is the variance of the
values?
8, 10, 14,4
A. 14
B. 10
C. 9
D. 13
Answer:
D: 13
So first you write down your equation ( its on the picture I posted) Then you need to find the mean which is the sum of all the values over the number of values you have (n) After finding your mean, you subtract it from every value you have. To check if what you have done is correct you add all the values you got after subtracting, if you get 0 your answer is correct. Then you square each of those answers you get after you subtract. You get the total which you then divide by the number of values you have (n)
I hope you understand, I am not that good at explaining. And I am not completely sure with my answer, but I think it's correct.
if f(x)=4/3x-9 what is f^-1(-3)
9514 1404 393
Answer:
4.5
Step-by-step explanation:
The value of x that makes f(x) = -3 is ...
4/3x -9 = -3
4/3x = 6 . . . . . . add 9
x = 6(3/4) = 18/4 = 9/2 = 4.5 . . . . multiply by 3/4
f^-1(-3) = 4.5
In an activity, students are pulling marbles from a large jar containing blue and red marbles. In their sample,
students will calculate the proportion of red marbles. Which of the following is a correct statement about sampling
variability?
A- The larger the sample size of marbles, the larger the sampling variability
B- The smaller the sample size of marbles, the smaller the sampling variability
C- The larger the sample size of marbles, the closet the sample proportion of red marbles will be the true proportion of red marbles in the jar
D- The smaller the sample size of marbles, the closet the sample proportion or red marbles will be to the true proportion of red marbles in the jar
Answer:
Step-by-step explanation:
C
The statement about sampling variability is "the larger the sample size of marbles, the closer the sample proportion of red marbles will be to the true proportion of red marbles in the jar".
What is the proportion?A mathematical assessment of two numbers is called a proportion. If two sets of provided numbers rise or fall in the same relation, then the ratios are said to be directly proportional to each other.
Students are selecting marbles from a large jar of blue and red marbles in an exercise.
Students will compute the proportion of red marbles in their sample. The closer the sample percentage of red marbles is to the genuine proportion of red marbles in the jar, the greater the sample size of the marble's sampling variability.
Thus, the larger the sample size of marbles, the closer the sample proportion of red marbles will be to the true proportion of red marbles in the jar.
Hence, the correct answer would be an option (C).
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A tree casts a shadow 35m long. At the same time, a sign post casts ashadow 7m long. The sign post is 4.5 m tall. How tall is the tree?
It is given that a tree casts 35m long shadow and at the same time a pole casts a shadow 7m tall.The pole is 4.5m tall.
So make 2 similar triangles as follows:
As both shadows are cast at the same time, the angle is essentially the same.
\(\begin{gathered} \tan \theta=\frac{4.5}{7}\ldots(i) \\ \tan \theta=\frac{AB}{35}=\frac{4.5}{7} \\ AB=\frac{4.5\times35}{7}=22.5m \end{gathered}\)Hence the height of tree is 22.5m.
let d be diagonal, with repeated diagonal entries grouped contiguously. show that if a commutes with d, then it must be block diagonal.
As, a is block diagonal, with diagonal blocks of size \(m_1 \times m_1\), \(m_2 \times m_2\), \(\dots\), \(m_k \times m_k\), respectively. So, if a commutes with d, then it must be block diagonal.
Let's suppose that d is a diagonal matrix with repeated diagonal entries grouped contiguously, i.e.,
d = \(\begin{pmatrix} D_1 & 0 & 0 & \cdots & 0 \ 0 & D_1 & 0 & \cdots & 0 \ 0 & 0 & D_2 & \cdots & 0 \ \vdots & \vdots & \vdots & \ddots & \vdots \ 0 & 0 & 0 & \cdots & D_k \end{pmatrix}\),
where \(D_1, D_2, \dots, D_k\) are scalars and appear with frequencies \(m_1, m_2, \dots, m_k\), respectively, so that \(m_1 + m_2 + \dots + m_k = n\), the size of the matrix.
Suppose that \(a\) is a matrix that commutes with d, i.e., ad = da.
Then, for any \(i \in {1, 2, \dots, k}\), we have
\(ad_{ii} = da_{ii}\)
Here, \(d_{ii}\) denotes the \(i$th\) diagonal entry of d, i.e., \(d_{ii} = D_i\) for \(i = 1, 2, \dots, k\). Since d is diagonal, \(d_{ij} = 0\) for \(i \neq j\), and
hence
\(ad_{ij} = da_{ij} = 0\)
for all \(i \neq j\).
Therefore, a is also diagonal, with diagonal entries \(a_{ii}\), and we have
\(a = \begin{pmatrix} a_{11} & 0 & 0 & \cdots & 0 \ 0 & a_{11} & 0 & \cdots & 0 \ 0 & 0 & a_{22} & \cdots & 0 \ \vdots & \vdots & \vdots & \ddots & \vdots \ 0 & 0 & 0 & \cdots & a_{kk} \end{pmatrix}\)
Thus, a is block diagonal, with diagonal blocks of size \(m_1 \times m_1\), \(m_2 \times m_2\), \(\dots\), \(m_k \times m_k\), respectively.
Therefore, if a commutes with d, then it must be block diagonal.
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Please help i’m not smart
Answer the questions about the following function.
x + 6
f(x) =
x-12
(a) Is the point (5,-2) on the graph of f?
(b) If x= 3, what is f(x)? What point is on the graph of f?
(c) If f(x) = 2, what is x? What point(s) is (are) on the graph of f?
(d) What is the domain of f?
(e) List the x-intercepts, if any, of the graph of f.
(f) List the y-intercept, if there is one, of the graph of f.
(g) What are the zeros of f?
The given rational function has a vertical asymptote at x = 12, and the
graph has x and y-intercept at the negative x and y-axis.
Response:
(a) The point (5, -2) is not on the graph
(b) f(x) = -1
The point on the graph of f is (-1, 3)(c) If f(x) = 2, x = 30
The point on the graph of f is (30, 2)(d) Domain = (-∞, 12) ∪ (12, ∞)
(e) x-intercept is at x = -6, which is the point (-6, 0)
(f) The y-intercept is at y = -0.5, which is the point (0, -0.5)
(g) A zeros of f, is x = -6
Which method is used to evaluate the rational function?The possible given function is presented as follows;
\(f(x) =\mathbf{\dfrac{x + 6}{x - 12}}\)
(a) When x = -2, we have;
\(f(-2) = \dfrac{(-2) + 6}{(-2) - 12} = \dfrac{4}{-14} = \mathbf{-\dfrac{2}{7}}\)
Therefore;
The point (\(-\frac{2}{7}\), -2) is on the graph, which gives;
The point (5, -2) is not on the graph(b) If x = 3, we have;
\(f(3) =\mathbf{ \dfrac{3 + 6}{3 - 12}} = \dfrac{9}{-9} =-1\)
f(3) = -1The point on the graph of f is (-1, 3)(c) If f(x) = 2, we have;
\(f(x) =2 = \mathbf{ \dfrac{x + 6}{x - 12}}\)
2·(x - 12) = x + 6
2·x - x = 6 + 2 × 12 = 30
x = 30
If f(x) = 2, x = 30The point on the graph of f is (30, 2)(d) The domain which is the list of possible x-values, which is expressed as follows;
Domain; -∞ < x < 12, and 12 < x < ∞
Which gives;
Domain = (-∞, 12) ∪ (12, ∞)(e) The x-intercepts are;
\(0 = \mathbf{ \dfrac{x + 6}{x - 12}}\)
x-intercept is at x = -6, which is (-6, 0)(f) The y-intercept
\(At \ the \ y-intercept, \ f(x) = \dfrac{0 + 6}{0 - 12} = -\dfrac{1}{2} = \mathbf{ -0.5}\)
The y-intercept is at y = -0.5, which is (0, -0.5)(g) The zeros of the graph, f, are the points at which the graph crosses the x-axis which at the point x = -6
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Determine if the system has a solution. If it does, how many? {4y-x=12 and 3y+3=-3
Answer:
The system has a solution at (-20,-2).
Step-by-step explanation:
To find the solution of the system, you need to find where the two equations intersect, or are equal to each other. You may do this with a calculator, but I find it much easier using a graphing software online, like Desmos.
Once I graphed these two equations, I found that they intersected each other at the point (-20,-2), so the system has ONE solution.
At x=-20, both equations have y=-2.
**I would also like to note that the second equation, y will ALWAYS equal -2, so you're really just finding where the first equation equals that as well.**
Ghana van company invested P45 700 for two years at a rate of 12%per annum compounded for quarter year. Work out the compound interest over the two years
\(~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$45700\\ r=rate\to 12\%\to \frac{12}{100}\dotfill &0.12\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &2 \end{cases}\)
\(A = 45700\left(1+\frac{0.12}{4}\right)^{4\cdot 2}\implies A=45700(1.03)^8 \implies A \approx 57891.39 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{earned interest}}{57891.39~~ - ~~45700} ~~ \approx ~~ \text{\LARGE 12191.39}\)
This diagram shows a pre-image △ABC and its image, △A′′B′′C′′ , after a series of transformations.
Select from the drop-down menus to correctly complete the statements.
△ABC is
1. reflected across the y-axis.
2. rotated 90 degrees counterclockwise about the origin.
3. translated 4 units right
to become △A′B′C′. Then △A′B′C′ is
1. reflected across the x-axis.
2. reflected across the line y = x
3. rotated 90 degrees counterclockwise about the origin
to become △A′′B′′C′′ . Because the transformations are
1. both rigid
2.not both rigid,
The pre-image and image are
1. congruent
2. not congruent
Using translation concepts, we have that:
△ABC is 3. translated 4 units right to become △A′B′C′. Then, △A′B′C′ is 3. rotated 90 degrees counterclockwise about the origin to become △A′′B′′C′′ .Because the transformations are both rigid, the pre-image and the image are congruent.What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.
On the translation of △ABC to △A′B′C′, the rule applied to the vertices is:
(x,y) -> (x + 4, y).
Hence it was translated 4 units right.
On the translation of △A′B′C′ to △A′′B′′C′', the rule is given by:
(x,y) -> (-y,x).
Hence it was rotated 90 degrees counterclockwise about the origin.
The triangle keeps the same size after the translations, hence:
Because the transformations are both rigid, the pre-image and the image are congruent.
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Help 20 points (show your work)
The measure of angle ADC in the geometric system is equal to 55°.
How to determine the value of an angle related to a geometric system
In this question we find a geometric system formed by a quadrilateral and an angle vertical to a vertex of the quadrilateral. Angle CDE is supplementary to angles EDF and ADC. Two angles are supplementary whose sum of measures equals 180°. Therefore:
m ∠ CDE + m ∠ EDF = 180°
(2 · x + 1) + (x - 7) = 180°
3 · x - 6 = 180°
3 · x = 186°
x = 62
m ∠ CDE = 2 · x + 1
m ∠ CDE = 2 · 62 + 1
m ∠ CDE = 125°
m ∠ ADC = 180° - 125°
m ∠ ADC = 55°
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