Answer:
he additive inverse of:
a) [tex]-6x^2-x-2[/tex] is : [tex]6x^2+x+2[/tex]
b) [tex]6x^2-x+2[/tex] is : [tex]-6x^2+x-2[/tex]
c) [tex]6x^2+x-2[/tex] is : [tex]-6x^2-x+2[/tex]
d) [tex]6x^2+x+2[/tex] is : [tex]-6x^2-x-2[/tex]
Step-by-step explanation:
You need to consider that the additive inverse of a polynomial is that polynomial that consists of the opposite of each term of the polynomial given.
Then, the additive inverse of:
a) [tex]-6x^2-x-2[/tex] is : [tex]6x^2+x+2[/tex]
b) [tex]6x^2-x+2[/tex] is : [tex]-6x^2+x-2[/tex]
c) [tex]6x^2+x-2[/tex] is : [tex]-6x^2-x+2[/tex]
d) [tex]6x^2+x+2[/tex] is : [tex]-6x^2-x-2[/tex]
I NEED HELP PLEASE, THANKS! Use Cramer's Rule to find the solution of the system of linear equations, if a unique solution exists. –5x + 2y – 2z = 26 3x + 5y + z = –22 –3x – 5y – 2z = 21 A. (–1, –7, 2) B. (–6, –1, 1) C. (–1, 3, 1) D. no unique solution
Answer:
Option B
Step-by-step explanation:
We are given the following system of equations -
[tex]\begin{bmatrix}-5x+2y-2z=26\\ 3x+5y+z=-22\\ -3x-5y-2z=21\end{bmatrix}[/tex]
Now by Cramer's Rule, we would first write down the matrix of the coefficients , replacing each column with the answer column -
[tex]\begin{bmatrix}-5&2&-2\\ 3&5&1\\ -3&-5&-2\end{bmatrix}[/tex] ,
[tex]\begin{bmatrix}26\\ -22\\ 21\end{bmatrix}[/tex]
Replace each column of the coefficients shown at the top, with the answer column at the bottom respectively -
[tex]\begin{bmatrix}-5&2&26\\ 3&5&-22\\ -3&-5&21\end{bmatrix}[/tex]
Now solve through Cramer's Rule -
x = Dx / D = - 6,
y = Dy / D = - 1,
z = Dz / D = 1
Solution = ( - 6, - 1, 1 ) = Option B
-5 x + 2 y - 2 z = 263 x + 5 y + z = -22 - 3 x - 5 y - 2 z = 21
Answer is x=-6,\:z=1,\:y=-1
I paid twice as much by not waiting for a sale and not ordering on line. Which ofthe following statements is also true?
(a) I paid 200% more than I could have online and on sale.
(b) I paid 100% of what I could have online and on sale.
(c) I paid 200% of what I could have online and on sale.
(d) I paid 3 times what I could have online and on sale.
Answer:
Option (c).
Step-by-step explanation:
It is given that, I paid twice as much by not waiting for a sale and not ordering online.
Let the cost of items ordering online be x.
So, now i am paying twice of x = 2x
Now, we have find 2x is what percent of x.
[tex]Percent =\dfrac{2x}{x}\times 100=200\%[/tex]
It means, I paid 200% of what I could have online and on sale.
Therefore, the correct option is (c).
According to the New York Stock Exchange, the mean portfolio value for U.S. senior citizens who are shareholders is $183,000. Assume portfolio values are normally distributed. Suppose a simple random sample of 51 senior citizen shareholders in a certain region of the United States is found to have a mean portfolio value of $198,000, with a standard deviation of $65,000.
a. From these sample results, and using the 0.05 level of significance comment on whether the mean portfolio value for all senior citizen shareholders in this region might not be the same as the mean value reported for their counterparts across the nation, by using the critical value method. Establish the null and alternative hypotheses.
b. What is your conclusion about the null hypothesis?
Answer:
The test statistic value t = 1.64 < 2.0086 at 0.05 level of significance
Null hypothesis is accepted
The mean portfolio value for all senior citizen shareholders in this region might not be the same as the mean value reported for their counterparts across the nation
Step-by-step explanation:
Step(i):-
Given mean of the population (μ) = $183,000
Given mean of the sample (x⁻) = $198,000
Given standard deviation of the sample (S) = $65,000.
Mean of the sample size 'n' = 51
level of significance α = 0.05
Step(ii):-
Null hypothesis : H₀ : There is no significance difference between the means
Alternative Hypothesis :H₁: There is significance difference between the means
Test statistic
[tex]t = \frac{x^{-}-mean }{\frac{S.D}{\sqrt{n} } }[/tex]
[tex]t = \frac{198,000- 183,000 }{\frac{ 65,000}{\sqrt{51} } }[/tex]
t = 1.64
Step(iii)
Degrees of freedom ν = n-1 = 51-1 =50
t₀.₀₅ = 2.0086
The calculated value t = 1.64 < 2.0086 at 0.05 level of significance
Null hypothesis is accepted
Final answer:-
There is no significance difference between the means
The mean portfolio value for all senior citizen shareholders in this region might not be the same as the mean value reported for their counterparts across the nation
suppose your given the formula n=3m-2l if you know that l= m+2 how could you rewrite that formula
n=m+4
step-by-step explanation:given formula,
n=3m-2l
and,
l=m+2
here in this question We have to substitute the values of "l" in the formulae
we get,
n=3m-2(m+2)
n=3m-2m+4
n=m+4
so if we complete the process correctly we get n=m+4
Find the Prime factors of 1729. Arrange the factors in ascending order. Find a relation between
consecutive prime factors
Answer:
prime factors in ascending order of 1729 is 7 , 13 , 19
relation between consecutive prime factors is 6
Step-by-step explanation:
given data
number = 1729
solution
we get here factors of 1729
1729 = 7 × 13 × 19
so that required prime factors in ascending order of 1729 is 7 , 13 , 19
and
now we get relation between these prime factors is the difference between consecutive prime factors is
13 - 7 = 6
19 - 13 = 6
so relation between consecutive prime factors is 6
Step-by-step explanation:
Prime factors of the number 1729 are 7,13,19
i.e. 1729 =7×13×19
The factors in ascending order are 7,13,19.
Clearly we can see that each consecutive prime factors have difference of 6.
13-7=6
19-13=6
The length of a rectangle is 3 yd longer than its width. If the perimeter of the rectangle is 62 yd, find its width and length
Answer:
Length=17 yds, Width=14 yds
Step-by-step explanation:
62=x+x+(x+3)+(x+3)
4x+6=62
4x=56
x=14
x+3=17
Line segment ON is perpendicular to line segment ML. What is the length of segment NP?
Answer:
2 units.
Step-by-step explanation:
In this question we use the Pythagorean theorem which is shown below:
Given that
The right triangle OMP
The hypotenuse i.e OM is the circle radius =5 units.
The segment MP = 4 units length
Therefore
[tex]OP^2 + MP^2 = OM^2[/tex]
[tex]OP^2 + 4^2 = 5^2[/tex]
[tex]OP^2 + 16 = 25[/tex]
So OP is 3
Now as we can see that ON is also circle radius so it would be 5 units
And,
ON = OP + PN
So,
PN is
= ON - OP
= 5 units - 3 units
= 2 units
Answer:
2
Step-by-step explanation:
You are reading the draft of a scientific paper that your co-worker has written. In the paper, he draws a sample from a population and computes the following two confidence intervals for : A 95% confidence interval of (90.21,100.37) A 99% confidence interval of (93.61.98.53) How do you know your co-worker made a mistake? He computed more than one confidence interval using the same sample data. Your co-worker did not round to 3 decimal places in his confidence interval upper and lower bounds The 99% confidence interval should be wider than the 95% confidence interval He is not a statistic, so it doesn't make any sense to compute confidence intervals for it. There is nothing wrong with his statements.
Answer:
The correct option is (C).
Step-by-step explanation:
The general form of a confidence interval is:
[tex]CI=SS\pm CV\cdot SE[/tex]
Here,
SS = Sample statistic
CV = critical value
SE = standard error
The width of the confidence interval is:
[tex]\text{Width}=2\cdot CV\cdot SE[/tex]
The width of the confidence interval is dependent upon the critical value and hence dependent upon the confidence level.
As the confidence level increases the critical value increases hence in turn increasing the width of the interval.
And as the confidence level decreases the critical value decreases hence in turn decreasing the width of the interval.
In this case the 95% confidence interval is, (90.21,100.37).
And the 99% confidence interval is, (93.61.98.53).
It is clear by looking at the two intervals that the 95% confidence interval is wider than the 99%. Thus, this clearly indicates that the co-worker made a mistake.
The correct option is (C).
Identify whether each phrase is an expression, equation, or inequality.
Answer:
Step-by-step explanation:
a+b-c+d is expression
1/3<r/9 is inequality
and the last one is an equation
an inequality contains one of the 4 symbols
in an expression there is no equal sign
Please answer question now in two minutes
Answer:
V lies in the exterior of <STU.
Step-by-step explanation:
V lies in the exterior of <STU.
Solve 3v2 – 84 = 0, where v is a real number.
Round your answer to the nearest hundredth.
If there is more than one solution, separate them with commas.
If there is no solution, click on "No solution".
Answer:
The given equation has two solutions
[tex]v = (-5.29, \: 5.29)[/tex]
Step-by-step explanation:
The given equation is
[tex]3v^2 - 84 = 0[/tex]
Let’s solve the equation
[tex]3v^2 - 84 = 0 \\\\3v^2 = 84 \\\\v^2 = \frac{84}{3} \\\\v^2 = 28 \\\\[/tex]
Take the square root on both sides
[tex]\sqrt{v^2} = \sqrt{28} \\\\v = \sqrt{28} \\\\v = \pm 5.29 \\\\[/tex]
So the equation has two solutions
[tex]v = (-5.29, \: 5.29)[/tex]
Also refer to the attached graph of the equation where you can verify that the equation has two solutions.
Note:
It is a very common mistake to consider only the positive value and not the negative value.
Consider the square root of 25
[tex]\sqrt{25} = \pm 5 \\\\Since \\\\5 \times 5 = 25 \\\\-5 \times -5 = 25 \\\\[/tex]
That is why we have two solutions for the given equation.
Three girls of a group of eight are to be chosen. In how many ways can this be done?
Answer:
Step-by-step explanation:
8P3=8*7*6=336
Ujalakhan01! Please help me! ASAP ONLY UJALAKHAN01. What's (x-1)(x-1)?
Answer:
x^2-2x+1
Step-by-step explanation:
We can solve this by using FOIL
First, Outside, Inside, Last
Multiply the x with the x to get x^2
Then x times -1 for the outside numbers to get -x
Then -1 times x for the inside numbers to get -x
And finally -1 and -1 for the last numbers to get 1
Add the two -x to get -2x.
Put it all together
x^2-2x+1
Answer:
[tex]x^2-2x+1[/tex]
Step-by-step explanation:
=> (x-1)(x-1)
USING FOIL
=> [tex]x^2-x-x+1[/tex]
=> [tex]x^2-2x+1[/tex]
A farmer is building a fence to enclose a rectangular area consisting of two separate regions. The four walls and one additional vertical segment (to separate the regions) are made up of fencing, as shown below. A rectangular area consisting of two separated regions. If the farmer has 162 feet of fencing, what are the dimensions of the region which enclose the maximal areas?
Answer:
The maximal area will be "1093.5 square feet".
Step-by-step explanation:
Let,
Length = L feet
Breadth = b feet
Given Total fencing = 162 feet
According to the question,
[tex](2\times L)+(3\times b)=162[/tex]
[tex]2L+3B=162[/tex]
[tex]L=\frac{162-3b}{2}[/tex]
[tex]L=81-\frac{3}{2}b[/tex]
As we know,
[tex]Area=Length\times breadth[/tex]
[tex]=(81-\frac{3}{2}b)\times b[/tex]
[tex]=81b-\frac{3}{2}b^2[/tex]
Now, we required to decrease or minimize the are. So for extreme points:
[tex]\frac{dA}{db}=0[/tex]
or,
[tex]\frac{dA}{dB}=\frac{d}{db}(81-\frac{3}{2}b^2 )=0[/tex]
[tex]81-\frac{3}{2}\times 2\times b=0[/tex]
[tex]b=\frac{81}{3}[/tex]
[tex]b=27 \ feet[/tex]
Now on putting the value of b, we get
[tex]l=81-\frac{3}{2}\times 27[/tex]
[tex]=81-40.5[/tex]
[tex]=40.5 \ feet\\[/tex]
So that the dimensions will be:
⇒ 40.5 feet by 27 feet
Therefore when the dimension are above then the area will be:
= [tex]81\times 27-\frac{3}{2}\times 27\times 27[/tex]
= [tex]2187-\frac{3}{2}\times 729[/tex]
= [tex]2187-1093.5[/tex]
= [tex]1093.5 \ square \ feet[/tex]
A glass vase has a circular rim with a diameter of 5in. How many inches of ribbon are needed to go once around the rim? Use 3.14
Answer:
31.4 inches
Step-by-step explanation:
The circumference of a circle has the formula 2πr.
2 × π × 5
= 10 × 3.14
= 31.4
31.4 inches of ribbon is needed to go once around the rim.
Answer:
15.7 inches of ribbon.
Step-by-step explanation:
This question is basically asking for the circumference of the glass vase's rim. We can calculate that by multiplying the diameter by π, which in this case, is 3.14.
The diameter is 5 inches, so all you need to do is 5 * 3.14 = 15.7 inches of ribbon.
Hope this helps!
Help me with this problem, thank you<3
Answer:
1,050 workers
Step-by-step explanation:
25% = 0.25
0.25 × 1400 = 350
1400 - 350 = 1050
Hope this helps.
The population of the city of Peachwood is currently 12,000 and increases every year at a rate of 5%. The function that describes the model is ƒ(x) = 12000 • 1.05x. Which of the following choices would be the number of people in the city after one year?
Answer: 12600
Step-by-step explanation:
We are given the function that f(x) = 12000 * 1.05x
the x in f(x) is the amount of years that passed in the city of Peachwood, and the f(x) is the total population of Peachwood
These are two key elements in this function,
Therefore after 1 year the equation would be f(1) = 12000*1.05(1)
or f(1) = 12600
Please answer this correctly
Answer:
1/5
Step-by-step explanation:
The number 5 or greater than 4 is 5.
1 number out of 5 total parts.
= 1/5
P(5 or greater than 4) = 1/5
GO DEEPER
In the last six months, Sonia's family used 456, 398,655, 508,
1,186, and 625 minutes on their cell phone plan. In an effort to spend less
time on the phone each month, Sonia's family wants to try and keep the
mean cell phone usage at 600 minutes or less. Over the last 6 months,
by how many minutes did the mean number of minutes exceed their goal?
Answer:
46
Step-by-step explanation:
Please only answer if you are 100% sure about the answer.
Answer:
Choice C.
Step-by-step explanation:
Your choice is correct
2 stands for a starting point which is 2 feet from the home
As the ant moves, over time, the distance increases according to the function
piece-wise functions
Answer:
see the attachment for a graphdomain: all real numbersrange: -6 and y>-5Step-by-step explanation:
The graph below was created by a graphing utility.
It shows no horizontal gaps: f(x) is defined for all values of x, so the domain is all real numbers.
It shows a vertical gap between y=-6 and y>-5. So, the range is in two parts:
{-6} ∪ {y > -5}
What is 6 1/2 subtracted by 2 2/3
Answer:
The answer to this equation is 3 5/6
Step-by-step explanation:
in order to solve this problem, we must first turn these fractions into improper fractions. We can do this by multiplying the base number with the denominator and adding the numerator to that number.
6 1/2 = 13/2
2 2/3 = 8/3
Now, set up your equation.
13/2 - 8/3
Change the denominators to the same number so it will be easier to subtract.
39/6 - 16/6
Now subtract.
23/6 = 3 5/6
Answer:
3 5/6
Step-by-step explanation:
6 1/2 - 2 2/3 = 13/2 - 8/3
(39 - 16)/6 = 23/6 = 3 5/6
Let mZA = 40°. If zB is a complement of ZA, and ZC is a supplement of ZB, find these measures.
mZB =
mZC =
Angle b= 50
Angle c= 130
Complementary angles are two angles that add to equal 90
Supplementary angles are two angles that add to equal 180
To find the measurement of angle b, subtract 40 from 90 (50)
To find the measurement of angle c, subtract 50 from 180 (130)
The measures of complementary and supplementary angles are given by m∠B = 50° and m∠C = 130°
What are Supplementary and Complementary Angles?Supplementary angles are two angles that add up to 180 degrees. In other words, if angle A and angle B are supplementary, then:
A + B = 180°
Complementary angles are two angles that add up to 90 degrees. In other words, if angle A and angle B are complementary, then:
A + B = 90°
Given data ,
If m∠A = 40°, then its complement ∠B = 90° - m∠A = 90° - 40° = 50°.
Since ∠C is a supplement of ∠B, we know that m∠C + m∠B = 180°.
Therefore, we can solve for m∠C by rearranging this equation to get:
m∠C = 180° - m∠B
Substituting the value we found for m∠B, we get:
m∠C = 180° - 50° = 130°
Hence , the angles are mZB = 50° and mZC = 130°.
To learn more about complementary and supplementary angles click :
https://brainly.com/question/14690981
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A hiker starting at point P on a straight road wants to reach a forest cabin that is 2 km from a point Q, 3 km down the road from P . She can walk 8 km/hr along the road but only 3 km/hr through the forest. She wants to minimize the time required to reach the cabin. How far down the road should she walk before setting off through the forest straight for the cabin?
Answer:
2.19 km
Step-by-step explanation:
If x is the distance she walks down the road before turning, then the total time is:
t = x/8 + √((3 − x)² + 2²) / 3
t = x/8 + √(9 − 6x + x² + 4) / 3
24t = 3x + 8√(13 − 6x + x²)
24t = 3x + 8(13 − 6x + x²)^½
Take derivative of both sides with respect to x.
24 dt/dx = 3 + 4(13 − 6x + x²)^-½ (-6 + 2x)
When t is a minimum, dt/dx = 0.
0 = 3 + 4(13 − 6x + x²)^-½ (-6 + 2x)
-3 = 4(13 − 6x + x²)^-½ (-6 + 2x)
3 / (6 − 2x) = 4(13 − 6x + x²)^-½
3 / (24 − 8x) = (13 − 6x + x²)^-½
(24 − 8x) / 3 = (13 − 6x + x²)^½
(24 − 8x)² / 9 = 13 − 6x + x²
576 − 384x + 64x² = 117 − 54x + 9x²
459 − 330x + 55x² = 0
Solve with quadratic formula.
x = [ 330 ± √((-330)² − 4(55)(459)) ] / 2(55)
x = (330 ± √7920) / 110
x = 2.19 or 3.81
Since 0 < x < 3, x = 2.19.
Select the correct answer. Vector u has its initial point at (-7, 2) and its terminal point at (11, -5). Vector v has a direction opposite that of vector u, and its magnitude is three times the magnitude of u. What is the component form of vector v? A. v = B. v = C. v = D. v =
Answer:
Step-by-step explanation:
vector u=<(11-(-7),(-5-2)>=<18,-7>
as direction is opposite to u
so vector v=-3(18,-7)=(-54,21)
Suppose you toss a coin 100 times and get 65 heads and 35 tails. Based on these results, what is the probability that the next flip results in a tail?
Answer:
[tex] P(Head) = \frac{65}{100}=0.65[/tex]
[tex] P(Tail) = \frac{35}{100}=0.35[/tex]
And for this case the probability that in the next flip we will get a tail would be:
[tex] P(Tail) = \frac{35}{100}=0.35[/tex]
Step-by-step explanation:
For this case we know that a coin is toss 100 times and we got 65 heads and 35 tails.
We can calculate the empirical probabilities for each outcome and we got:
[tex] P(Head) = \frac{65}{100}=0.65[/tex]
[tex] P(Tail) = \frac{35}{100}=0.35[/tex]
And for this case the probability that in the next flip we will get a tail would be:
[tex] P(Tail) = \frac{35}{100}=0.35[/tex]
S=4LW+2WH;S+=136,L6,W=4 WHAT IS H
Answer:
H=5
Step-by-step explanation:
Answer:
5
Step-by-step explanation:
S=4lw+2wh
Put S as 136, l as 6, w as 4, and solve for h.
136 = 4(6)(4)+2(4)H
136 = 8h + 96
-8h = 96 - 136
-8h = -40
h = -40/-8
h = 5
A bowl has 85 pieces of candy. Nineteen children empty the bowl of candy. Some children take 3 pieces, some children take 5 pieces, and 1 child takes 7 pieces of candy. How many children take 3 pieces of candy?
Answer:
6
Step-by-step explanation:
12*5=60
6*3=18
1*7=7
hope this help
Suggest changing to “On the graph of an exponential function representing growth, what happens to the slope of the graph as x increases?”
Answer:
If we have a growing exponential relation, we can write it as:
f(x) = A*r^x
Where A is the initial amount, r is the rate of growth, in this case, r > 1 (because is a growing exponential relation)
Now, the "slope" of the graph in x, is equal to the derivate of f(x) in that point, and we have:
f'(x) = A*(r^x)*ln(r)
Now, remember that r > 1, then ln(r) > 0.
then, f'(x) is a growing function as x grows, and f'(x) grows exponentially, this means that the slope of the graph also grows exponentially as x grows.
Consider the function g(x) = x^12. Describe the range of the function.
Answer:
0 ≤ g(x) < ∞
Step-by-step explanation:
The range is all non-negative numbers.
___
g(x) is an even-degree polynomial with a positive leading coefficient, so it opens upward. There is no added constant, so its minimum value is zero. The function can take on all values zero or greater.
range: [0, ∞)