Answer:
1. Option B is the correct answer.
2. The point (1,0) lies on the graph of p(x)=x⁴-2x³-x+2.
Step-by-step explanation:
1. Dividing x³-7x²+15x-9 with (x-1).
[tex]\frac{x^3-7x^2+15x-9}{x-1}=x^2-6x+9[/tex]
Factorizing x²-6x+9 we will get
x²-6x+9 = (x - 3)(x-3)
x³-7x²+15x-9 = (x-1)(x - 3)(x-3)
Option B is the correct answer.
2. We have p(x)=x⁴-2x³-x+2
That is y = x⁴-2x³-x+2
We have coordinates (1,0), substituting
y = 1⁴-2 x 1³-1+2 = 0
So when we are substituting x value as 1 we are getting y as zero, so the point lies in curve.
A carpenter is building a rectangular bookcase with diagonal braces across the back, as shown. The carpenter knows that ∠ADC is a right angle and that m∠BDC is 32° greater than m∠ADB. Write and solve an equation to find m∠BDC and m∠ADB
What is the solution set for [-x]=10
3x+1/5y=7 solve for y.
12 25 10 38 12 19 8 12 17 41 7 22 10 19 12 16 5 14 find the mean, median, and mode of these weights
In quadrilateral ABDC, AB ∥ CD. Which additional piece of information is needed to determine that ABDC is a parallelogram?
A) AB ≅ CD
B) AC ≅ BD
C) AB ⊥ BD
D) CD ⊥ BD
The additional piece of information is needed to determine that ABDC is a parallelogram is,
⇒ AB ≅ CD
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
In quadrilateral ABDC,
⇒ AB ∥ CD.
Now,
We know that;
When opposite side of a quadrilateral are parallel and equal to each other, then the quadrilateral are called a parallelogram.
Here, In quadrilateral ABDC,
⇒ AB ∥ CD.
Hence, The additional piece of information is needed to determine that ABDC is a parallelogram is,
⇒ AB ≅ CD
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What is the remainder when 14,952 is divided by 41
Answer:
the answer is 28 A
Step-by-step explanation:
What common angle do CDG AND FCE share?
FBG is congruent to DBE
CEF is congruent to CGD
CDG is congruent to CFE
GCE is congruent to ECG
Answer:
The correct option is 4.
Step-by-step explanation:
From the given figure it is noticed that the triangle CDG and triangle FCE have a common vertex C. So both triangle are sharing same angle at vertex C.
In triangle CDG and triangle FCE
[tex]\angle GCD\cong \angle FCE[/tex]
If the length of two adjacent sides increases, then the inclined angle remains the same.
If the side CD increased to E and side CF increased to G, then
[tex]\angle GCE\cong \angle ECG[/tex]
Therefore option 4 is correct.
Change 56/7 to a whole or mixed number
Which graph represents the solution to the inequality?
What is the length of TW
Answer:
32 units.
Step-by-step explanation:
We have been given a graph of a line segment and we are asked to find the length of line segment TW.
Upon looking at our graph we can see that point U divides segment TW in two equal parts (TU and UW), which means that length of TW will be two times the length of TU or UW.
We have been given the length of TU is 16 units. To find the length of segment TW we will multiply 16 by 2.
[tex]\text{Length of TW}=2\times 16=32[/tex]
Therefore, the length of line segment TW will be 32 units.
In a simple regression model y = ß0 + ß1x + ε, ß1 represents the ________.
In the regression model, y = β₀ + β₁ x + ε, β₁ represents the slope of the regression line.
What is a regression model?A regression model offers a function that explains the association between one or more independent variables and a response, dependent, or target variable. A linear regression model, for instance, may be used to explain the link between height and weight.
The standard equation of regression model is y = a + bx
The given regression model,
y = β₀ + β₁ x + ε
The coefficient of the x in the regression model shows the slope of the regression line.
Hence, β₁ represents the slope of the regression line.
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Find the value of x for which p is parallel to q, if m∠1 = (4x) and m∠3 = 100. The diagram is not to scale.
a. 96
b. 25
c. 104
d. 100
The are of a rectangle is 117 square centimeters. The width of the rectangle is 9 centimeters. What is the length of the rectangle?
2x + 5 = 10
What is the first operation used in solving this equation?
A) addition
B) division
C) multiplication
D) subtraction
In 2010, Washington Township created recreational soccer programs for the spring and fall seasons. The table shows the number of participants who registered for each season during the first four years,
Participation in Town Soccer Programs
Year
Spring league
Fall league
year;2010
spring league;68
fall league;145
year;2011
spring league;79
fall league;148
year;2012
spring league;90
fall league;151
year; 2013
spring league; 101
fall league; 154
Which statement best describes the programs?
A) Participation in the spring league is increasing more than twice as fast as participation in the fall league.
b)Participation in the spring league is increasing at a slightly faster rate than participation in the fall league.
C) Participation in the fall league is increasing more than twice as fast as participation in the spring league.
D) Participation in the fall league is increasing at a slightly faster rate than participation in the spring league.
Answer:
Option A is the answer.
Step-by-step explanation:
Table is given as
Year 2010 2011 2012 2013
Spring league 68 79 90 101
Fall league 145 148 151 154
Now as per given table we will analyze each option given
A). Difference in spring league participation increasing every year = 79-68 = 11
Difference in Fall league increasing every year = 148-145 = 3
Therefore option A is true because [tex]\frac{11}{3}>3[/tex] Spring league is increasing more than twice as fast as fall league.
B). This option is not true because participation in the spring league is increasing nearly 4 times of Fall league.
C) False. Spring league participation is more than fall league.
D) False. Same as option C because spring league participation is more than fall league.
I skip counted starting at 70. I never said the number 82 even though I counted beyond it. Which of these numbers could I have been counting by? 2, 5, or 10
Answer:
5 or 10
Step-by-step explanation:
counting by 2's - 70, 72, 74, 76, 78, 80, 82 82 is here, Incorrect
counting by 5's -70, 75, 80, 85, 90 Never said 82, Correct
counting by 10's - 70, 80, 90- Never said 82, Correct
Eliana's calculator displays a number as 5.378 E9.
What is this number in standard form?
Enter your answer in the box.
Answer:
5,378,000,000
Step-by-step explanation:
5.378E9
5.378 x 10^(9)
5,378,000,000
what is the simplified form of 3abc/abc, when abc does not equal 0? explain using the properties of real numbers
Find the value of k so that the equation has the solution set {-3}
3(2x-1) = x(2-k)
Can anyone solve this problem???
One person can complete a typing project in 6 hours, and another can complete the same project in 8 hours. How long will it take the two people working together to complete the project???
Time taken to complete the project if two people worked together is required.
It would taken around 3.4 hours to complete the project if both the people worked together
Time taken to complete the work by first person is 6 hours
Time taken to complete the work by second person is 8 hours
The work equation will be be
[tex]\dfrac{1}{6}+\dfrac{1}{8}=\dfrac{1}{x}\\\Rightarrow \dfrac{4+3}{24}=\dfrac{1}{x}\\\Rightarrow x=\dfrac{24}{7}\approx 3.4\ \text{hours}[/tex]
So, it would taken around 3.4 hours to complete the project if both the people worked together.
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how to describe and compare a box plot.
7 1/8 - 3 1/2 =? Please help me
Round .895 to the nearest hundredths
Write an equation of the line that has a slope of 6 and contains (1,1) in point-slope form.
The tubs of yogurt are sold for 75¢ each. Twenty percent of this is profit for the food company. How much profit does the company make on each tub? Show your work
Solve for p: 3p-2(p-4) =7p+6
Plz help asap
Thanks
Analyze the statements below and complete the instructions that follow. p: A point has a y-coordinate of zero. q: A point lies on the x-axis. Determine the truth values of the statements
If it is Christmas, then it is the 25th of December. Identify the hypothesis and the conclusion of the conditional statement. hypothesis: it is the 25th of December; conclusion: it is Christmas hypothesis: it is Christmas; conclusion: it is the 25th of December hypothesis: it is not the 25th of December; conclusion: it is not Christmas hypothesis: it is not Christmas; conclusion: it is not the 25th of December
Answer:
c
Step-by-step explanation:
How to find components of a vector given magnitude and angle?
The components of the vector in rectangular form given magnitude and angle can be found by using the following formulas: [tex]x = \|\vec r\|\cdot \cos \theta[/tex], [tex]y = \|\vec r\| \cdot \sin \theta[/tex].
How to determine the magnitude and angle of a vector
Let be a vector in rectangular form, that is, a vector of the form (x, y). The magnitude can be found by applying the square root of the dot product of the vector or the Pythagorean theorem and the direction is determined by applying inverse trigonometric functions:
Magnitude (linear algebra approach)[tex]\|\vec r\| = \sqrt{(x,y)\,\bullet\,(x,y)}[/tex] (1)
Magnitude (algebra approach)[tex]\|\vec r \| = \sqrt{x^{2}+y^{2}}[/tex] (2)
Directionθ = tan⁻¹ (y/x) (3)
And the components of the vector can be found by applying the following formulas:
[tex]x = \|\vec r\|\cdot \cos \theta[/tex] (4)
[tex]y = \|\vec r\| \cdot \sin \theta[/tex] (5)
The components of the vector in rectangular form given magnitude and angle can be found by using the following formulas: [tex]x = \|\vec r\|\cdot \cos \theta[/tex], [tex]y = \|\vec r\| \cdot \sin \theta[/tex].
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You can find the components of a vector given its magnitude and angle by using the cosine function to find the horizontal component, and the sine function to find the vertical component.
Explanation:To find the components of a vector given its magnitude and angle, you will use basic trigonometric ratio principles. These principles typically involve the use of sine (sin) and cosine (cos) functions.
First, consider a vector V with magnitude (or length) denoted by |V| and an angle θ from the positive x-axis. The components of the vector can be resolved into horizontal (x-direction) and vertical (y-direction) components.
The x-component (Vx) of the vector can be found using the equation:
Vx = |V| cos(θ).
Similarly, the y-component (Vy) of the vector can be found using the equation:
Vy = |V| sin(θ).
These equations are derived from the definitions of the sine and cosine functions in a right triangle, which is formed by the vector V and its components.
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Number 8. Solve the equation for variable d. Correct answer will get brainliest.