The expressions are factors of the polynomial 3x4 - 14x³ 3x²+54x -40 are
(x + 4)(x + 2)(x + 1)(x - 1)What are polynomials?Generally, To factor a polynomial using synthetic division, we need to find a factor of the polynomial that can be divided into the leading coefficient and the constant term of the polynomial.
In this case, the leading coefficient is 3 and the constant term is -40. One factor of 3 and -40 is (-4)(10).
The complete factorization of the polynomial is 3x⁴ - 14x³ + 3x² + 54x - 40 gives The remainder is 0, so the other factor is (x - 4)(x + 2)(x - 1)(x + 1).
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which of the following statements regarding the expansion of xyn are correct? A. The coefficients of xn and y^n both equal 1.
B. For any term x^ay^b in the expansion, a + b = n.
C. For any term x^ay^b in the expansion, a - b = n.
D. The coefficients of x^ay^b and x^by^a are equal.
Although part of your question is missing, you might be referring to this full question: Which of the following statements regarding the expansion of (x + y)^n are correct?
By expanding the exponential expressions, the answers are option A, B, and D.
The exponential expressions: (x + y)^n
Which means that we multiply the polynomial (x + y) by itself n times.
How do we analyze each statement?Option A.
This statement is true, because there is only one x in the original polynomial, and we multiply it by itself n times, then we can have only one term equal to x^n (or y^n).
Option B.
This statement is true, because if we multiplicate the variables by themselves n times, then the degree of the term also has to be n. Since for a term: (x^a)*(y^b) the degree is a + b; then it always be a + b = n.
Option C.
This statement is false, because of the same reasons in Option B.
Option D.
This statement is true, because in the original polynomial the coefficients of y and x are the same, then in the expansion the coefficients of the reflected terms like (x^a)*(y^b) and (x^b)*(y^a) are equal.
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The amount of goods and services that costs $200 on January 1, 1997 costs $230.16 on January 1, 2006. Estimate the cost of the same goods and services on January 1, 2013. Assume the cost is growing exponentially. Round your answer to the nearest cent. Table
As per the exponential growth function, the cost of the same goods and services in January 1, 2013 is $291.54
Exponential growth function:
In statistics, exponential growth function mean a pattern of data that shows greater increases with passing time, creating the curve of an exponential function.
Given,
The amount of goods and services that costs $200 on January 1, 1997 costs $230.16 on January 1, 2006.
Here we need to estimate the cost of the same goods and services on January 1, 2013 and also assume the cost is growing exponentially. Round your answer to the nearest cent.
Here we know that the value of
Cost on 1997 = $200
Cost on 2006 = $230.16
So, the time difference is
=> 2006 - 1997 = 6
And the amount difference is
=> $30.16
So, based on the exponential growth function, the cost of goods and services at the time of 2013 is
=> 200 + ( 1 + 30.16)⁶
=> 200 + 91.54
=> 291.54
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4 is multiplied by the difference of 5 and a number.
Answer:
The difference is multiplied by 4 can be represented as 4 (x - 1/2) According to the question, 4 (x - 1/2) = 5 x - 1/2 = 5/4 x = 5/4 + 1/2 x = (5 + 2)/4 x = 7/4 Therefore, the number is 7/4.
Step-by-step explanation:
Answer:
Step-by-step explanation:
Im assuming the question is to write this into actual numbers,
answer: 4(5-x)
Suppose the life time (in hours) of a battery brand is normally distributed. A random sample of 16 batteries results in a sample variance of
3.25
hours
2
. We want to test if there is significant/sufficient evidence in the sample data to claim that the variance of the battery life population is different than 4 hours
2
at significance level of
0.05
. Which of the following is INCORRECT? A.
H 0
:σ 2
=4 vs H 1
:σ 2
=4
B. The test statistic is found to be
12.1875
C. We should reject the null hypothesis and there is sufficient evidence to claim that the variance of battery life is different than 4 hours
2
at significance level of
0.05
. D. None of the above.
there is not sufficient evidence to claim that the variance of the battery life population is different than 4 hours2 at a significance level of 0.05.
answer is D. None of the above.
To test if there is significant evidence to claim that the variance of the battery life population is different than 4 hours2, we can use a chi-square test.This is how the test statistic is computed:
X2 = (n-1)*(s2/σ2)
where n is the sample size, s2 is the sample variance and σ2 is the population variance.
In this case, n = 16, s2 = 3.25 and σ2 = 4
X2 = (16-1)*(3.25/4) = 12.1875
The critical value of X2 with 15 degrees of freedom and α = 0.05 is 24.996. Therefore, since 12.1875 < 24.996, we fail to reject the null hypothesis, and there is not sufficient evidence to claim that the variance of the battery life population is different than 4 hours2 at a significance level of 0.05.
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I need this please help me
Answer:
isnt it 72
Step-by-step explanation:
since it is that kind of triangle
jennie charges $200 per passenger for a sunset sailing tour on her catamaran, while paul charges $250 per passenger. we can define the amount of money each person earns per cruise as a random variable. let a
According to the given charges, the mean of the sum would be as follows $1,692.5 and the difference of the amount of money earned by Jennie and Paul would be $-232.5
Mean:
In statistics, mean refers the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers
Given,
As Jennie charges $200 per passenger for a sunset sailing tour on her catamaran, while Paul charges $250 per passenger. we can define the amount of money each person earns per cruise as a random variable.
Here we need to find the mean and the difference of the amount of money earned by Jennie and Paul.
Let us consider x be the amount earned by Jennie and y be the amount earned by Paul.
While we looking into the given question , we have identified the value of the following,
=> Money earned by Jennie(A) = 200x
=> Money earned by Paul(B) = 250 X
Here the value of μ = $730 and σ = $ 192.62 for Jennie
And the value of Paul is μ = $962.5 and σ = $253.425
Then the mean of the sum is calculated as,
=> 730 + 962.5 = 1292.5
Similarly, the difference of the amount of money is calculated as,
=> -232.5
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Answer:
D) On average, Jennie makes $232.50 less than Paul in a typical cruise.
Step-by-step explantion
Find the measure of all three angles of the triangle with vertices at the pointsP(1,2,3); Q(3,4,2); and R(4,0,2).
The inverse cosine function to find the measures of the = arccos(-sqrt)
What is measure of angles?
Angle measure can be defined as the measure of the angle formed by the two rays or arms at a common vertex.
To find the measures of the angles of a triangle, you can use the Law of Cosines, which states that the square of the length of a side of a triangle is equal to the sum of the squares of the lengths of the other two sides minus twice the product of the lengths of the other two sides and the cosine of the angle opposite the side in question.
In this case, we are given the coordinates of the vertices of the triangle and we want to find the measures of the angles. To do this, we can use the distance formula to find the lengths of the sides of the triangle and then use the Law of Cosines to find the cosines of the angles.
The distance formula is:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2 + (z2 - z1)^2)
where d is the distance between the two points with coordinates (x1, y1, z1) and (x2, y2, z2).
Using this formula, we can find the lengths of the sides of the triangle as follows:
PR = sqrt((4 - 1)^2 + (0 - 2)^2 + (2 - 3)^2) = sqrt(9 + 4 + 1) = sqrt(14)
PQ = sqrt((3 - 1)^2 + (4 - 2)^2 + (2 - 3)^2) = sqrt(4 + 4 + 1) = sqrt(9)
QR = sqrt((4 - 3)^2 + (0 - 4)^2 + (2 - 2)^2) = sqrt(1 + 16 + 0) = sqrt(17)
Now we can use the Law of Cosines to find the cosines of the angles:
cos A = (PR^2 + PQ^2 - QR^2) / (2 * PR * PQ)
= (14 + 9 - 17) / (2 * sqrt(14) * sqrt(9))
= (-4) / (2 * sqrt(14) * sqrt(9))
= -2 / (sqrt(14) * sqrt(9))
cos B = (QR^2 + PQ^2 - PR^2) / (2 * QR * PQ)
= (17 + 9 - 14) / (2 * sqrt(17) * sqrt(9))
= (2) / (2 * sqrt(17) * sqrt(9))
= 1 / (sqrt(17) * sqrt(9))
cos C = (QR^2 + PR^2 - PQ^2) / (2 * QR * PR)
= (17 + 14 - 9) / (2 * sqrt(17) * sqrt(14))
= (12) / (2 * sqrt(17) * sqrt(14))
= 6 / (sqrt(17) * sqrt(14))
Finally, we can use the inverse cosine function to find the measures of the angles:
A = arccos(-2 / (sqrt(14) * sqrt(9)))
= arccos(-2 / (2 * sqrt(7) * sqrt(3)))
= arccos(-1 / sqrt(7) * sqrt(3))
= arccos(-sqrt)
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Which equation represents a line that passes through two negative 1/2 and has a slope of 3?; Which equation represents a line that has a slope of 1/3 and passes through point 2 1?; Which equation represents a line that passes through (- 9 3 and has a slope of?; Which equation represents a line that passes through 5 1 and has a slope of StartFraction one half EndFraction?
The equation of the line is y+1/2=3(x-2) when a line with a slope of 3 and passes through the points (2, -1/2).
Given that,
We have to find what is the equation describes a line with a slope of 3 and passes through the points (2, -1/2).
We know that,
The equation of the line is represented by (y-y₁)=m(x-x₁)
Here,
Point (2,-1/2)
Slope is 3.
Substitute in the equation,
(y-(-1/2)=3(x-2)
(y+1/2)=3(x-2)
Therefore, The equation of the line is y+1/2=3(x-2) when a line with a slope of 3 and passes through the points (2, -1/2).
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a 60-hz induction motor is needed to drive a load at approximately 895rpm. part a determine the maximum number of poles required to drive the load at 895 rpm . express your answer as an integer. p
The maximum number of poles required to drive the load is 8.
full load speed = 120*f/p
850 = 120*60/p
p = 120*60/850
p = 8.47
since no. of poles are even so
p = 8
if number pole p = 8
synchronous speed Ns = 120*f/p = 120*60/8 = 900RPM
SLIP = (Ns - N)/Ns
s = (900-850)/900
s = 0.056
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which of the following numbers does not have 8 as a factor? A. 25424, B. 15000, C. 36502, D. 10008
By dividing, we find The number that does not have 8 as a factor is C. 36502.
what is factor?A factor of a number is a positive integer that divides evenly into the number. For example, the factors of 6 are 1, 2, 3, and 6.
what is division?Division is a mathematical operation that involves dividing one number (the dividend) by another number (the divisor) to determine the quotient, which is the result of the division.
to check whether 8 is a factor of 25424, you can divide 25424 by 8:
25424 / 8 = 3178
Since the result is an integer, 8 is a factor of 25424.
To check whether 8 is a factor of 15000, you can divide 15000 by 8:
15000 / 8 = 1875
Since the result is an integer, 8 is a factor of 15000.
To check whether 8 is a factor of 36502, you can divide 36502 by 8:
36502 / 8 = 4562.75
Since the result is not an integer, 8 is not a factor of 36502.
To check whether 8 is a factor of 10008, you can divide 10008 by 8:
10008 / 8 = 1251
Since the result is an integer, 8 is a factor of 10008.
Therefore, the number that does not have 8 as a factor is C. 36502.
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A restaurant offers delivery for their pizzas the total cost is a delivery fee added to the price of the pizzas one costumer pays 25 to have 2 pizzas delivered another customer pays 58 to 5 pizzas how many pizzas are delivered to a customer who pays 80 explain or show your reasoning
The number of pizzas delivered to a customer who pays $ 80 is 7 pizzas
What is an Equation of a line?
The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the number of pizzas be x₁ = 2
Let the cost of 2 pizzas be y₁ = $ 25
So , the first point A ( x₁ , y₁ ) = A ( 2 , 25 )
Now ,
Let the number of pizzas be x₂ = 5
Let the cost of 5 pizzas be y₂ = $ 58
So , the second point B ( x₂ , y₂ ) = B ( 5 , 58 )
Therefore , the slope of the 2 points is given by
Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope m = ( 58 - 25 ) / ( 5 - 2 )
Slope m = 33 / 3
Slope m = 11
Therefore , the equation of the line is given by
y - y₁ = m ( x - x₁ )
Substitute the value of m in the equation , we get
y - 25 = 11 ( x - 2 )
y - 25 = 11x - 22
Adding 25 on both sides of the equation , we get
y = 11x + 3
So , the equation of line is y = 11x + 3
Now , the customer pays $ 80 , so to find the number of pizzas the customer gets can be calculated by substituting the value of y = 80
And ,
y = 11x + 3
80 = 11x + 3
Subtracting 3 on both sides of the equation , we get
11x = 77
Divide by 11 on both sides of the equation , we get
x = 7 pizzas
Therefore , the number of pizzas is 7 pizzas
Hence ,
The number of pizzas delivered to a customer who pays $ 80 is 7 pizzas
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Which of these quantities is a vector?
A. Time
B. Momentum
C. Distance
D. Speed
On solving the provided question, by the given information we can say that Momentum is a vector quantity.
What is vector quantity?A physical quantity that only has magnitude is known as a scalar quantity. such as distance, speed, mass, density, etc. However, vector quantities—which include displacement, velocity, acceleration, force, and mass—are physical quantities that have both magnitude and direction.
Momentum is a vector quantity.
It is directed and has a magnitude. According to Isaac Newton's second law of motion, the force pushing a particle has an equal and opposite effect on the time rate at which its momentum changes. Consider Newton's laws of motion.
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Show the solution and answer
(3x + 5)(x - 9)
A rectangular package to be sent by a postal service can have a maximum combined length and girth (perimeter of a cross section) of 114 inches (see figure). Find the dimensions of the package of maximum volume that can be sent. (Assume the cross section is square.)
X= ??????
Y= ???????
The dimensions of the rectangular package with the condition of maximum volume is equal to x = 19inches and y = 38inches.
As given in the question,
Let us consider length of the cross section which is square be x
Perimeter of the cross section is 4x
And y be the length of the rectangular package
Maximum combined ( length + perimeter of the cross section ) = 114
y + 4x = 114
⇒ y = 114 -4x
Volume of the package 'V' = x²y
⇒V = x²(114 -4x)
⇒V = 114x² -4x³
Differentiate both the side of the equation with respect to x,
dV/dx = 228x - 12x²
For maximum Volume
dV/dx =0
228x -12x² = 0
⇒12x( 19 -x ) =0
⇒12x = 0 or 19 - x =0
⇒x =0 or x =19
x =0 is not possible
⇒x =19inches
y = 114 - 4(19)
= 38inches
Therefore, the dimensions of the rectangular package with the given condition of volume is equal to x = 19inches and y = 38inches.
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Roberta took two tests. She scored 10 points more on the second test. Her average score for the two tests was 75 points. If x= her score on the first test, and y= her score on the second test, then the average is given by the formula x+y2. What did she score on the second test? She scored points on the second test. The solution is
If Roberta took two tests. She scored 10 points more on the second test. she score 70 on the second test.
How to find the number of score?Average score = (x+y)/2
he scored 10 points less on the second test than he did on the first.
y = x - 10
Replace y with x-10
(x + x - 10) / 2
(2x-10)/2
Average score on both tests is 75
(2x-10)/2 = 75
Multiply both sides of this equation by 2
2x-10 = 150
Add 10 to both sides
2x = 160
Divide both sides by 2x
x = 160/2
x = 80 (She got 80 on the first test)
He got 80 - 10 = 70 (She got 70 on the second test)
(80+ 70) / 2 = 150/2 = 75 (She got average of 75 on both tests)
Therefore she scored 70 on the second test is your solution.
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Put the following equation of a line into slope-intercept form, simplifying all fractions. 3x+6y= -18
Answer: [tex]y=-\frac{1}{2} x-3[/tex]
Step-by-step explanation:
[tex]3x+6y=-18[/tex]
[tex]-3x[/tex] [tex]-3x[/tex]
[tex]6y=-3x-18[/tex]
[tex]\frac{6y}{6} =\frac{-3x}{6} -\frac{18}{6}[/tex]
[tex]y=-\frac{1}{2 } x-3[/tex]
1. At a clothing store, a pair of jeans costs $75. Using a coupon, Terese buys the jeans for $18.75 less than the original price. Complete the table.
Dollar Amount
Percentage
% off the original amount.
3.
The coupon gives Terese
How much did Terese pay for the jeans (before tax)?
it is:
4. In a bag of candy, 25% are yellow. There are 60 candies in the bag. How man' yellow candies are there?
5. For one math test, Blair had to answer 35 questions. Of those 35 questions, h answered 27 correctly. What percent did Blair get on his math test? Round to nearest percent.
6. Jeffrey has 60% as much money as Louis. Louis has $110. Select all true
statements.
• Jeffrey has $66.
• Jeffrey has $44.
• Jeffrey has - as much as Louis.
• Jeffrey has as much as Louis.
• Jeffrey has $48.
• Louis has as much as Jeffrey
• Louis has
as much as Jeffrey
1. Completing the percentage table about the payment for a pair of jeans bought by Terese at a clothing store is as follows:
Dollar Amount Percentage
% off the
original amount
$75 25%
2. The coupon gives Terese 25% off the original amount.
3. The amount Terese paid for the jeans (before tax) was $56.25.
4. The number of yellow candies in the bag is 15.
5. In the Math test, Blair, who answered 27 questions correctly out of 35, scored 77 percent.
6. The true statement about the amount of money Jeffrey has concerning Louis is A. Jeffry has $66.
a) Clothing Store:Cost of a pair of jeans = $75
Coupon value = $18.75
Amount paid = $56.25
The coupon percentage = 25% ($18.75/$75 x 100)
b) Bag of Candy:Yellow candy = 25%
The total number of candies in the bag = 60
The number of yellow candy = 15 (60 x 25%)
c) Math Test:The total number of questions = 35
The number of questions answered correctly = 27
Percent scored by Blair = 77% (27/35 x 100)
d) Jeffrey and Louis:The amount of money Louis has = $110
The percentage of Louis' money that Jeffry has = 60%
The amount Jeffry has = $66 ($110 x 60%)
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Please help!!
What is 9 x (46+70) 5 - 32 (40 - 219) =
9 x (46+70) 5 - 32 (40 - 219) = 11428
Using the BODMAS rule, we solve the brackets first,
9 x (46+70) 5 - 32 (40 - 219)
= 9 x 116 x 5 - 32 x -179
Next, we solve the multiplication signs
9 x 116 x 5 - 32 x -179
= 5520 - ( -5728)
Solving the subtraction sign, we get
5520 - ( -5728)
= 11428
Hence, the answer is 11428
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Which ordered pair is a solution to the system of linear equations 2x 3y equals 6?; What does 0 0 indicate about the solutions of the system Brainly?; What does 0 0 mean regarding the solution to the system?
The ordered pair which is a solution to the system of linear equations (0,2).
In mathematics, a system of linear equations refers to a collection of one or more linear equations which involve the same variables. In order to solve the system of linear equations, multiply each equation by a constant such as the coefficient of one variable becomes the same.
Hence, multiply 2x + 3y= 6 by 3 and –3x + 5y = 10 by 2.
3 (2x + 3y= 6)
6x + 9y = 18
2(–3x + 5y = 10)
-6x + 10 y = 20
Adding the two equations
6x + 9y = 18
-6x + 10 y = 20
19y = 38
y = 2
Substitute y in either of the equations:
2x + 3(2)= 6
2x = 6 – 6 = 0
x = 0
Hence, the solution is (0, 2)
The ordered pair (0,0) is not a solution as it will invalid the given linear equation.
Note: The question is incomplete. The complete question probably is Which ordered pair is a solution to the system of linear equations? 2x + 3y= 6 and –3x + 5y = 10. (0,2) (2,0) (3,2) (2,3)
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A scatter plot containing the point (4,9) has the regression equation y=5x+2 what is the residual e when x=4?
Answer:
the observed value of 9 is 13 units lower than the predicted value of 22.
Step-by-step explanation:
A residual is the difference between the observed value of a data point and the predicted value of that data point based on a given model. In a regression analysis, the residual is calculated using the formula e = y - y', where y is the observed value, y' is the predicted value, and e is the residual.
In this case, we are given the point (4,9) and the regression equation y = 5x + 2. Plugging in the value x = 4 into the regression equation, we get:
y' = 5(4) + 2 = 22
Since we are also given that the observed value of the point (4,9) is 9, we can plug these values into the formula for the residual to calculate the residual:
e = 9 - 22 = -13
Therefore, the residual e when x = 4 is -13. This means that the observed value of 9 is 13 units lower than the predicted value of 22.
given the plot of normal distributions a and b below, which of the following statements is true? select all correct answers.Select all correct answers Select all that apply: A has the larger mean. B has the larger mean The means of A and B are equal A has the larger standard deviation. B has the larger standard deviation. The standard deviations of A and B are equal.
Correct option is C
The plot of normal distributions A and B
A has the larger standard deviation
Standard Deviation
A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.
In statistics, the standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean of the set, while a high standard deviation indicates that the values are spread out over a wider range.
The name standard deviation for SD came from Karl Pearson. I would guess no more than that he wanted to recommend it as a standard measure. If anything, I guess that references to standardization either are independent or themselves allude to SD.
Mean
In statistics, the mean is one of the measures of central tendency, apart from the mode and median. Mean is nothing but the average of the given set of values. It denotes the equal distribution of values for a given data set. The mean, median and mode are the three commonly used measures of central tendency.
Normal Distribution
Normal distribution, also known as the Gaussian distribution, is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean. In graphical form, the normal distribution appears as a bell curve.
The plot of normal distributions A and B
A has the larger standard deviation
Correct option is C
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Writing equations of lines
Write the equation of each line with the given information
through: (-5, -3), perp. to y = -5/7x -5
Answer:
y = [tex]\frac{7}{5}[/tex] x + 4
Step-by-step explanation:
Perpendicular slopes are opposite reciprocals.
So the slope is 7/5
Us the slope and the point to find the y intercept
m = 7/5
x = -5
y = -3
y= mx + b
-3 = (7/5)(-5) + b
-3 = -7 + b Add 7 to both sides
4 = b
y = mx + b
y = 7/5 x + 4
If other factors are held constant, which of the following sets of data would produce the largest value for an independent-measures t statistic? The two samples both have n 15, with sample variances of 20 and 25. The two samples both have n 15, with variances of 120 and 125. The two samples both have n 30, with sample variances of 20 and 25. The two samples both have n 30. with variances of 120 and 125 Save Question 15 (1 point) For the repeated measures t statistic. df n1 + n2 2 n1 -1)+ (n2 1) Save Question 16 (1 point
If other factors are held constant, sets of data that would produce the largest value for an independent-measures t statistic is the two samples both have n =30, with sample variances of 20 and 25
In a T test, the T statistic is used to help you decide whether to accept or reject the null hypothesis.
You utilize it in a manner that is quite similar to using a Z-score. When you don't know the population standard deviation or have a limited sample size, you use the t statistic.
You employ the T statistic with a p value while performing a hypothesis test. Your results' likelihood of being the result of chance is indicated by the p-value. Typically, in statistics, you use a T Test with a T Statistic rather than a Z score because you don't know much about the population.
To have larger t value , Combined standard deviation should be less
Therefore, n should be large and standard deviation should be less
Hence , The two samples both have n=30, with sample variances of 20 and 25 will provide us larger t-statistics
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Use the number line to plot –3, 1, and 3. Which statements are true? Select all that apply. –3 > 1 –3 = 3 1 < 3 –3 < 1
Both the inequalities (- 3 > 1 - 3 = 3) and (1 < 3 - 3 < 1) are false.
What is a expression? What is a mathematical equation? What do you mean by domain and range of a function?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.For any function y = f(x), Domain is the set of all possible values of [y] that exists for different values of [x]. Range is the set of all values of [x] for which [y] exists.We have the following integers -
- 3, 1 and 3.
The given inequality are -
- 3 > 1 - 3 = 3
1 < 3 - 3 < 1
- 3 > 1 - 3 = 3
- 3 > - 2 = 3
Which is false.
1 < 3 - 3 < 1
1 < 0 < 1
Which is false.
Therefore, both the inequalities (- 3 > 1 - 3 = 3) and (1 < 3 - 3 < 1) are false.
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>) Solve:
1) 7 millions
thousands
hundred
Answer:
70
Step-by-step explanation:
1 million = 10 hundred thousands because 100,000 x 10 = 1,000,000
multiply the polynomial (x 2y)(x2 - 2xy 4y2). write your answer in descending order. please use the palette below to enter your answer.
The descending order of the polynomial is (x³ + 8y³)
The term polynomial in algebra is defined as an expression which is composed of variables, constants and exponents, that are combined using mathematical operations such as addition, subtraction, multiplication and division
Here we have given that (x+2y)(x²−2xy+4y²)
And we have to multiply the polynomial and write your answer in descending order.
Here we have the polynomial (x+2y)(x²−2xy+4y²).
Now, we have to use the identity
=> a³ + b³ = ( a² − ab + b² ) ( a + b ) ,
Now, we have to apply these identity one the given polynomial, then we get,
=> ( x + 2y ) ( x² − 2xy + 4y² )
=> (x³ + ( 2 y )³) = (x³ + 8 y³) .
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which expotential function has a y-intercept of (0, -4)?
HELP WILL MARK BRAINLIEST
Answer:
[tex]y=2^x-5[/tex]
Step-by-step explanation:
The y-intercept occurs when x = 0.
Therefore, substitute x = 0 into each equation to find its y-intercept.
[tex]\begin{aligned}\implies y&=(-4)^0\\&=1\end{aligned}[/tex]
[tex]\begin{aligned}\implies y&=2^0-5\\&=1-5\\&=-4\end{aligned}[/tex]
[tex]\begin{aligned}\implies y&=3^0+4\\&=1+4\\&=5\end{aligned}[/tex]
[tex]\begin{aligned}\implies y&=(0)^{-4}\\&=0\end{aligned}[/tex]
Therefore, the exponential function that has a y-intercept of (0, -4) is:
[tex]\large\boxed{y=2^x-5}[/tex]
what is 7.04 as a mixed number
Answer:
you answer is 7 1/25
Step-by-step explanation:
0.04 ---> 1/25
7 ---> 7
7 + 1/25 = 7 1/25
A 32-foot ladder leans against the building. Find the ground distance from the foot of the ladder to the building, if the angle of elevation is 45 °.
Answer:
Below
Step-by-step explanation:
This is a right triangle
the two legs are equal and the hypotenuse is 32 ft
Here is a way to calculate the answer with Pythagorean theorem
32 ^2 = L^2 + L^2
512 = L^2
L = sqrt (512) = 22.6 ft
The graph of the function f(x) = (x + 2)(x + 6) is shown below.
On a coordinate plane, a parabola opens up. It goes through (negative 6, 0), has a vertex at (negative 4, negative 4), and goes through (negative 2, 0).
Which statement about the function is true?
The function is positive for all real values of x where
x > –4.
The function is negative for all real values of x where
–6 < x < –2.
The function is positive for all real values of x where
x < –6 or x > –3.
The function is negative for all real values of x where
x < –2.
the interval, the function returns zero (-6,-2) –6 < x < –2
What is a function?
A unique kind of relation called a function is one in which each input has precisely one output. In other words, the function produces exactly one value for each input value. The graphic above shows a relation rather than a function because one is mapped to two different values. The relation above would turn into a function, though, if one were instead mapped to a single value. Additionally, output values can be equal to input values.
The x-values are input into the function machine. The function machine then performs its operations and outputs the y-values. The function within can be any function.
The given f(x) = (x + 2)(x + 6)
In this function, a quadratic equation is represented (vertical parabola open upward)
The vertex stands for a minimum.
the use of a graphing tool
view the attached image
x=-6 and x=-2 are the x-intercepts.
Point: the y-intercept
The point is called the vertex.
The range ——-> is the domain. (-∞,∞) (All real numbers) (All real numbers)
The range is in the range [-4,].
x -6 or x > -2 make the function positive.
For the interval, the function returns zero (-6,-2) –6 < x < –2
Hence, the interval, the function returns zero (-6,-2) –6 < x < –2
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