Answer:
[tex](x-(3+\sqrt5))[/tex] or [tex](x-3-\sqrt5)[/tex] is a factor of the given polynomial.
Step-by-step explanation:
Let us learn the concept with an example first.
Let the polynomial be a quadratic function [tex]g(x)[/tex].
[tex]g(x) = x^{2} -5x+6[/tex]
The roots of [tex]g(x)[/tex] are 2 and 3.
Putting [tex]x= 2\ in \ g(x)[/tex]
[tex]2^2-5\times 2+6 = 4-10+6 =0[/tex]
Putting [tex]x= 3\ in \ g(x)[/tex]
[tex]3^2-5\times 3+6 = 9-15+6 =0[/tex]
Putting x = 2 or x = 3, g(x) = 0 [tex]\therefore[/tex] The roots of equation g(x) are 2 and 3.
Now, let us try to factorize g(x):
[tex]x^{2} -2x-3x+6\\\Rightarrow x(x -2)-3(x-2)\\\Rightarrow (x-3)(x-2)[/tex]
so, the equation can be written as:
[tex]g(x) = x^{2} -5x+6=(x-3)(x-2)[/tex] where 3 and 2 are the roots of equation.
The factors are (x-3) and (x-2).
[tex]\therefore[/tex] for the polynomial f(x) which has roots [tex]3+\sqrt5\ and\ -6[/tex] will have a factor:
[tex](x-(3+\sqrt5))[/tex] or [tex](x-3-\sqrt5)[/tex]
Which is greater 36÷(4×3) or 54-48-(16÷4
Step-by-step explanation:
36 ÷ (4 x 3)
36 ÷ 12
= 3
54 - 48 - (16 ÷ 4)
54 - 48 - 4
= 2
So first one is greater
A is any nonnegative real number and b is a square root of that number. Is a a function of b, b a function of a, both, or neither?
Answer:
B is a function of A
Step-by-step explanation:
If you do something to another thing, it is a function of that.
Below you are given a partial computer output from a multiple regression analysis based on a sample of 16 observations.
Coefficients Standard Error
Constant 12.924 4.425
x1 -3.682 2.630
x2 45.216 12.560
Analysis of Variance
Source of Degrees of Sum of Mean
Variation Freedom Squares Square F
Regression 4853 2426.5
Error 485.3
We want to test whether the variable x1 is significant. The critical value obtained from ttable at the 1% level is:_______.
1. ±2.650.
2. ±2.921.
3. ± 2.977.
4. ± 3.012.
Answer:
4. ± 3.012
Step-by-step explanation:
Hello!
Assuming that for both variables X₁ and X₂ n₁= n₂ = 16
You need to test at 1% if the variable is significant, this means, if the slope for X₁ is different from zero (β₁≠0) using the t-statistic and the critical value approach.
The hypotheses are:
H₀: β₁= 0
H₁: β₁≠ 0
α: 0.01
[tex]t= \frac{b_1-\beta_1}{Sb_1} ~t_{n_1-3}[/tex]
The degrees of freedom "n₁-3" are determined by the number of parameters that you estimate for the multiple regression, in this case there are three "β₁" "β₂" and "δ²e"
The rejection region for this test is two-tailed, the critical values are:
±[tex]t_{n-3;1-\alpha /2}= t_{13;0.995}= 3.012[/tex]
I hope this helps!
BÉ is an angle bisector of ZABC.
If mŁABE = 2x + 20 and mZEBC = 4x - 6,
determine the value of x.
B.
x = [? ]
what is 3 + 3 × 3 + 3 =
Answer:
15
Step-by-step explanation:
PEMDAS
3x3 = 9
3+3 = 6
9+6 = 15
By the BODMAS rule we get, 3 + 3 × 3 + 3 = 15
The acronym BODMAS rule is used to keep track of the right sequence of operations to do when solving mathematical issues. Brackets (B), order of powers or roots (O), division (D), multiplication (M), addition (A), and subtraction (S) are all represented by this acronym (S).
3 + 3 × 3 + 3 =
3 × 3 = 9
3 + 9 + 3 = 15.
Therefore, the correct answer is 15.
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Determine f(-1) (3). Use the following table of values
Answer:
-5
Step-by-step explanation:
The value of x that gives f(x) = 3 is -5.
[tex]f^{-1}(3)=-5[/tex]
how many are 4 x 4 ?
There is a bag filled with 4 blue and 5 red marbles. A marble is taken at random from the bag, the colour is noted and then it is replaced. Another marble is taken at random. What is the probability of getting at least 1 red?
Answer:
[tex]\dfrac{65}{81}[/tex] or 80.25%
Step-by-step explanation:
Number of blue Marbles = 4
Number of Red Marbles = 5
Total Number of marbles =4+5=9
[tex]P(B)=\dfrac49\\\\P(R)=\dfrac59[/tex]
In the experiment, two marbles are chosen one after the other with replacement.
The possible outcomes are: BB, BR, RB and RR
The probability of getting at least 1 red
=P(BR or RB or RR)
=P(BR)+P(RB)+P(RR)
[tex]=\left(\dfrac49\times\dfrac59\right) + \left(\dfrac59\times\dfrac49\right)+\left(\dfrac59\times\dfrac59\right)\\\\=\dfrac{20}{81}+\dfrac{20}{81}+\dfrac{25}{81}\\\\=\dfrac{65}{81}[/tex]
Expressed as a percentage, we have:
[tex]\dfrac{65}{81}\times100=80.25\%[/tex]
The probability of getting at least 1 red is 80.25%.
20 pts! If Quadrilateral J K L M is congruent to quadrilateral C B D A, which pair of sides must be congruent? Segment J K and Segment A B Segment J K and Segment C B Segment J M and Segment A D Segment J M and Segment B C
Answer:
segment I'm and segment ad
Answer:
The answer is B
Step-by-step explanation:
The radius of a sphere is 3 inches. Which represents the volume of the sphere? 12π cubic inches 36π cubic inches 64π cubic inches 81π cubic inches
Answer:
36pi
Step-by-step explanation:
Answer:
36pi
Step-by-step explanation:
i got it right on my test
4) A large number of people were polled and asked which of four different animals were their
favorite. 13% said Penguin, 21% said Iguana, 22% said Parrot, and 44% said Turtle. Suppose you
decide to carry out a simulation given these percentages. You decide to select two digits at a
time. Which would be a proper assignment of digits for these teams?
a) 01-13 = Penguin, 01-21 = Iguana, 01-22 = Parrot, 01-44 = Turtle
b) 00-13 = Penguin, 14-34 = Iguana, 35-56 = Parrot, 57-99 = Turtle
c) 01-13 = Penguin, 14-35 = Iguana, 36-58 = Parrot, 59-99 & 00 = Turtle
d) 01-13 = Penguin, 14-34 = Iguana, 35-56 = Parrot, 57-99 & 00 = Turtle
e) None of these
Answer:
d) 01-13 = Penguin, 14-34 = Iguana, 35-56 = Parrot, 57-99 & 00 = Turtle
Step-by-step explanation:
13 − 01 + 1 = 13
34 − 14 + 1 = 21
56 − 35 + 1 = 22
99 − 57 + 1 + 1 = 44
Please help ASAP thanks in advance
Answer:
P(0,4)
Q(2,0)
Step-by-step explanation:
We khow that both P and Q are lying in the line : 4x+2y=8
4x+2y=82y = -4x+8y= -2x+4 P(0,y) ⇒y= -2*0+4=4 ⇒ P(0,4) Q(x,0)⇒ 0=-2*x+4 ⇒ x= 2⇒ Q(2,0)Solve this correctly for brainliest !!!!!! 3(7) + 2 • |7 - 8| - 12
Answer:
3(7) + 2* |7 - 8| - 12 = 11
Step-by-step explanation:
3(7) + 2* |7 - 8| - 12
21 + 2* |-1| - 12
21 + 2* 1 - 12
21 + 2 - 12
23 - 12 = 11
Hope this helps! :)
find the gradient of the line segment between the points N(-1,2) and M(-6,3)
Answer:
1/5
Step-by-step explanation:
Gradient is another word for slope. To find the gradient, we have to use a formula.
A client would like a logo printed onto a canvas that is at least 70 inches tall. The original logo is 4.5 inches wide by 3.6 inches tall. Which dimensions will keep the logo in proportion and large enough to meet the client's requirements?
Answer:
to find the dimension I would get 3.6/4.5=x/70 amd u get 3.6*70=4.5x and u get 252=4.5x and x=56
Step-by-step explanation:
Answer:
Step-by-step explanation:
Let the width of logo printed on canvas = x inches
Dimensions are in proportion
[tex]\frac{70}{x}=\frac{3.6}{4.5}\\[/tex]
Cross multiply
70 * 4.5 = x * 3.6
x * 3.6 = 315
[tex]x=\frac{315}{3.6}\\\\=\frac{3150}{36}\\\\x=87.5inches[/tex]
Find the distance from R to S on the graph. Round to the nearest tenth.
Answer:
7.2
Step-by-step explanation
plug the values in in the distance formula
the points are -3,3 and 1, -3
sqrt((-3-1)^2+(3-(-3))^2)
sqrt(16)+(36)
sqrt(52)
approximately 7.2
WILL GIVE BRAINLIEST TO ANSWER:)) <33
Q: A committee of six people is to be formed from a pool of six grade 11 students and seven grade 12 students. Determine the probability that the committee will have two grade 11 students.
Answer: 5/26
Step-by-step explanation: 6/13 x 5/12
What is if we divide 8 by 4 multiply by 6 and add 2 then subtract 2 what is the result?
Answer:
its its 12.
Step-by-step explanation:
=8÷4×6+2-2
=2×6+2-2
=12+2-2
=14-2
=12 is answer..
Answer:
12
Step-by-step explanation:
8÷4×6+2-2
=2×6+2-2
=12+2-2
14-2
=12
If two chords in a circle are congruent, then they are
_____
Answer:
A
Step-by-step explanation:
Two congruent chords in a circle have the same distance from the center.
If two chords in a circle are congruent, then they are the same distance from the center of the circle .
What are the properties of equal chords of a circle?The properties of Equal Chords of a Circle are:
In a circle equal-chords are equidistant from the center.Equal-chords of congruent circles are equidistant from the corresponding centers.In a circle equal chords subtend equal angles at the center.According to the question
If two chords in a circle are congruent, then they are
Now,
By properties of Equal Chords of a Circle
The equal chords will be equal distance from the center of the circle .
Hence, If two chords in a circle are congruent, then they are the same distance from the center of the circle .
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Sean has some candy bars that he wants to give away. He is going to give each person 1/18 of a bar, and he has 2 3/4 to give away How many people will get candy? PLS HELP MEEE
Answer:
49 people
Step-by-step explanation:
Take the amount of candy and divide by the amount in a serving
2 3/4 ÷ 1/18
Change to an improper fraction
(4*2+3)/4 ÷ 1 /18
11/4 ÷ 1/18
Copy dot flip
11/4 * 18/1
198/4
49.5
Round down since people do not want half a serving
49 people
Answer: 2 29/36
Step-by-step explanation:
The number of chocolate chips in a bag of chocolate chip cookies is approximately normally distributed with mean 1261 and a standard deviation of 118. (a) Determine the 30th percentile for the number of chocolate chips in a bag. (b) Determine the number of chocolate chips in a bag that make up the middle 98% of bags. (c) What is the interquartile range of the number of chocolate chips in a bag of chocolate chip cookies?
Answer:
(A) 1199.168
(B) 1503.372
(C) 159.17728
Step-by-step explanation:
(A) To determine the 30th percentile for the number of chocolate chips in the bag, we find the z-score for the 30th percentile.
Found using a z-table or z-calculator, the z-score for the 30th percentile is -0.524
The formula for finding X (the number of items in a given percentile) is:
X = M + Z(S.D.)
Where M is the mean, Z is the specific z-score of the sought percentile and S.D. is the standard deviation.
So for the 30th percentile,
X = 1261 + (-0.524)(118)
X = 1261 - 61.832 = 1199.168
(B) The number of chocolate chips that make up the middle 98% of chips in the bag is
X = 1261 + (2.054)(118)
X = 1261 + 242.372 = 1503.372
(C) For normal distributions, Interquartile range is Q3 - Q1, that is; 3rd quartile minus 1st quartile.
This is within 1.34896 standard deviations of the mean.
IQR = (1.34896)(118)
IQR = 159.17728
ASAP will give brainliest Which of the following formulas would find the surface area of a right cylinder where h is the height, r is the radius, LA is the lateral area, and BA is the base area?
Answer:
A. BA + 2πrh
C. 2πr² + 2πrh
Step-by-step explanation:
height of cylinder = h
Radius of cylinder = r
=>Lateral area of cylinder = LA (THis is the area of the cylinder excluding the area of its circular bases)
L.A of a cylinder = 2πrh
=>Base area = BA (this is the area of both circular bases of the cylinder)
Area of circle = πr²
Area of the 2 circular bases of the cylinder (BA) = 2(πr²) = 2πr²
=>Surface area of a right cylinder = B.A + L.A
= 2πr² + 2πrh
The formulas that can be used to find surface area of a right cylinder from the given options are:
A. BA + 2πrh (note: BA = 2πr², LA = 2πrh)
C. 2πr² + 2πrh
1/9 − y2 when factored is:
Answer:
Step-by-step explanation:
hello
[tex]\dfrac{1}{9}-y^2=(\dfrac{1}{3})^2-y^2=(\dfrac{1}{3}-y)(\dfrac{1}{3}+y)=\dfrac{(1-3y)(1+3y)}{9}[/tex]
hope this helps
If y = x2 + 2x , find the value of y when x = 3
and
If y = x3 - 3 , find the value of y when x = 2 plsss help me
Answer:
y=15; y=5
Step-by-step explanation:
y=x2+2x
plug in x as 3:
y=3 2+ 2*3
y=9+6
y=15
Next problem:
y=x3-3
plug in x as 2:
y=2 3-3
y=8-3
y=5
y = 0.8x+ 7.2
20x + 32y = 48
Step-by-step explanation:
y = 0.8x+ 7.2 ..........(1)
20x + 32y = 48 .........(2)
Substitute (1) in (2)
20x +32*(0.8x+7.2) = 48 expand
20x + 25.6x+230.4 = 48 add
45.6x+230.4 = 48 transpose and simplify
45.6x = 48-230.4 = -182.4
x = -182.4 / 45.6
x = -4
Answer:
x=-4, Y=4
Step-by-step explanation:
20x+32(0.8x+7.2)=48
45.6x =48-230.4
x=-4
substitute x=-4 in y eqn
y=-3.2+7.2
y=4
0.3y+ z y 0, point, 3, y, plus, start fraction, y, divided by, z, end fraction when y=10y=10y, equals, 10 and z=5z=5z, equals, 5.
Answer:
5
Step-by-step explanation:
Substitute the given values and do the arithmetic.
[tex]0.3y+\dfrac{y}{z}=0.3\cdot 10+\dfrac{10}{5}=3+2=\boxed{5}[/tex]
Jane is collecting data for a ball rolling down a hill. She measures out a set of different distances and then proceeds to use a stop watch to find the time it takes the ball to roll. What are the independent, dependent, and control variables in this experiment?
Answer:
Step-by-step explanation:
The independent variables are the input values which are not dependent on the other value.
The dependent variables are the output values whose values depends on the value of some other number.
The independent variable in this case is the data on the set of distances she measured out.
The dependent variable in this case is the the time (measured by the stopwatch) it takes for the ball to roll.
The control variable in this case study is the size of ball, slope of hill, weight of ball etc.
Suppose that 3 is a factor of a, a is a divisor of 12, and a is positive. What is the number of possible values of a?
Answer:
3
Step-by-step explanation:
12 is divisible by: 1, 2, 3, 4, 6, 12
Because 3 is a factor of a, that means 3 multiplied by another number equals a. Additionally, a is a divisor of 12, meaning a multiplied by another number equals 12.
Out of the numbers, 12 is divisible by, only 3 are also divisible by 3: 3, 6, 12 This gives three possible values of a.
The regular price of a baseball cleats is $80. If the cleats are on sale for 45% off. then: (how to solve this two questions?) a) What is the value of the discount, in dollars? b) What is the final selling price of the cleats, before tax?
Answer:
The discount is 36 dollars
The sale price is 44 dollars
Step-by-step explanation:
First find the discount by multiplying the original price by the discount rate
80*45%
Change to decimal form
80*.45
36
The discount is 36 dollars
The sale price is the original price minus the discount
80-36
44
The sale price is 44 dollars
Factor completely 2x⁴y³-12x³y²-8x²y