Answers
Related Questions
Explain how to easily decide whether x - 6 is a factor of the polynomial P(x) = x ^ 7 - 5x ^ 5 + 2x ^ 4 - x ^ 2 + 9 without performing long division .
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[tex]\text{According to the factor theorem,}\\\\x-a~ \text{is a factor of}~ f(x)~ \text{if}~ f(a) = 0, ~ \text{where}~ a \in\mathbb{R}\\\\\text{Given that,}\\ \\P(x) = x^7 -5x^5 +2x^4 -x^2 +9\\\\P(6) = 6^7 -5\cdot 6^7 +2 \cdot 6^4 -6^2 +9 = 243621 \neq 0\\\\\text{Since} ~ P(6)\neq 0~, ~ x -6 ~ \text{is not a factor of P(x).}[/tex]
If a polynomial has two local maxima and two local minima, can it be of odd degree?
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Answer:
yes, it can be of odd degree
Step-by-step explanation:
The local maxima and minima correspond to zeros in the derivative of the function. The degree of the polynomial will be 1 more than some multiple of 2 greater than the number of zeros in the derivative.
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based on derivativeFor 2 each of local maxima and minima, the derivative will have 2+2 = 4 real zeros. The degree of the polynomial will be 1 greater, hence of degree 5 (or more). The polynomial must be of odd degree.
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based on behavior away from extremaThe local extrema must alternate: a maximum must be followed by a minimum, or vice versa. When there are an even number of each kind, the end extrema will be of opposite kinds. The end behavior of the function will be upward from a minimum and downward from a maximum. Hence the end behaviors must be in opposite directions--characteristic of an odd-degree polynomial.
The polynomial must be of odd degree.
_____
Additional comment
A polynomial with real coefficients will have an even number of complex roots. The complex roots of the derivative of a polynomial have no effect on the number or kind of extrema.
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Attached is an example of a polynomial with 2 maxima and 2 minima. It is of 5th degree.
Use properties of operations to write two expressions that are equivalent
to 2n + (8 + 32).
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The equivalent expressions of 2n + (8 + 32)are 2n + 40 and 2(n + 20)
How to determine the equivalent expressions?The expression is given as:
2n + (8 + 32)
The first equivalent expression
Evaluate the sum of the numbers in the bracket
2n + (8 + 32) = 2n + 40
This means that 2n + 40 and 2n + (8 + 32) are equivalent.
The second equivalent expression
In (a), we have:
2n + (8 + 32) = 2n + 40
Factor out 2 from the expression
2n + (8 + 32) = 2(n + 20)
This means that 2(n + 20) and 2n + (8 + 32) are equivalent.
Hence, the equivalent expressions are 2n + 40 and 2(n + 20)
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write square root of 5 x square root 10 in the form of b square root of 2 where b is an integer
simplify fully square root of 27 x square root of 75
Answers
Answer:
a)b= 5
b)45
Step-by-step explanation:
a) 5 times ten is 50 . the two factors of 50 are 25 and 2. The square root of 25 is 5, so that's the answer.
b) 27 × 75 is 2025 and the base root is 45², then with the radical and exponent we reduce the index by 2 to get 45.
[tex]\textbf{a)}\\\\~~~\sqrt 5 \times \sqrt{10}\\\\=\sqrt{5} \times \sqrt{5 \times 2}\\\\=\sqrt{5} \times \sqrt 5 \times \sqrt 2\\\\=\left(\sqrt 5 \right)^2 \times \sqrt 2\\\\=5\sqrt 2\\\\\text{It is now in a form of} ~ b\sqrt2 ~ \text{where} ~b = 5.\\\\\\[/tex]
[tex]\textbf{b)}\\\\~~~\sqrt{27} \times \sqrt{75}\\\\=\sqrt{9 \times 3} \times \sqrt{25 \times 3}\\\\=\sqrt 9 \times \sqrt 3 \times \sqrt{25} \times \sqrt 3\\\\=3\times 5 \times \left(\sqrt 3 \right)^2\\\\=15 \times 3\\\\=45[/tex]
(x+y)2-2(x+y)(a+x)+(a+x)2
Answers
Answer:
2ax−2ay−2x2−2xy+2a+4x+2y
Step-by-step explanation:
Let's simplify step-by-step.
(x+y)(2)−2(x+y)(a+x)+(a+x)(2)
Distribute:
=(x)(2)+(y)(2)+−2ax+−2ay+−2x2+−2xy+(a)(2)+(x)(2)
=2x+2y+−2ax+−2ay+−2x2+−2xy+2a+2x
Combine Like Terms:
=2x+2y+−2ax+−2ay+−2x2+−2xy+2a+2x
=(−2ax)+(−2ay)+(−2x2)+(−2xy)+(2a)+(2x+2x)+(2y)
=−2ax+−2ay+−2x2+−2xy+2a+4x+2y
Answer:
=−2ax−2ay−2x2−2xy+2a+4x+2y
Tera buys 10 pencils for $1.99.
About how much $ does each pencil
cost?
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Answer:
19 cents or 0.199
Step-by-step explanation:
Hope it helped!
Answer:
19 cents
Step-by-step explanation:
divide total cost by amount of items
Select the graph of y=cot x.
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Because of the vertical asymptote and the change in concavity, we conclude that the correct option is B.
Which is the graph of cotangent of x?Remember that cot(x) = 1/tan(x).
Then we can rewrite:
cot(x) = cos(x)/sin(x).
We know that for x = 0, we have:
cot(0) = cos(0)/sin(0) = 1/0
Then we have a vertical asymptote that tends to ± infinity.
The only graph that meets this condition is the second and the third one, and by the curvature (we need to have a change of concavity/convexity) in the tangent function.
From that, we conclude that the correct option is B.
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How many ways are there to choose a soccer team consisting of 3 forwards, 4 midfield players, and 3 defensive players, if the players are chosen from 8 forwards, 6 midfield players and 8 defensive players?
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Using the combination formula, it is found that there are 47,040 ways to form a soccer team.
What is the combination formula?Each of the different groups or selections can be formed by taking some or all of a number of objects, irrespective of their arrangments is called a combination.
[tex]^mC_k = \dfrac{m!}{k! \times (m-k)!}[/tex]
A soccer team consisting of 3 forwards, 4 midfield players, and 3 defensive players, if the players are chosen from 8 forwards, 6 midfield players and 8 defensive players
Since they are independent of each other, the total number of combinations will be;
[tex]^mC_k = \dfrac{8!}{3! \times (5)!} \times \dfrac{6!}{4! \times (2)!} \times \dfrac{8!}{3! \times (5)!} \\\\^mC_k =47,040[/tex]
Hence, There are 47,040 ways to form a soccer team.
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The length of a rectangle is 3 inches more than the width. The area is 10 square inches. Find the dimensions
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Answer:
Width = 2
Length = 5
Step-by-step explanation:
let A be the area of the rectangle
L be the length of the rectangle
w be the width of the rectangle
Formula: ‘area of a rectangle’
A = L × w
…………………………………………………
A = L × w
⇔ 10 = (w + 3) × w
⇔ 10 = w² + 3w
⇔ w² + 3w - 10 = 0
Solving the quadratic equation w² + 3w - 10 = 0 :
Δ = 3² - 4(1)(-10) = 9 - (-40) = 9 + 40 = 49
then √Δ = 7
[tex]\Longrightarrow w=\frac{-b+\sqrt{\Delta } }{2a} =\frac{-3+7}{2} =2[/tex]
[tex]or\ w=\frac{-b-\sqrt{\Delta } }{2a} =\frac{-3-7}{2} =-5[/tex]
-5 is not valid ,because w represents the width
which must be a positive number
Then w = 2
Conclusion:
Width = 2
Length = 2 + 3 = 5
There are 10 pink marbles and 10 black marbles. Find the probability?
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Answer:
50% to pull either a black or pink marble.
Step-by-step explanation:
The reason for this is due to the fact you have an equal amount of marbles of 2 different colors, so the chance of pulling one marble is not over another unless you remove say 1 pink marble, therefore the black marbles would have a higher percentage of being pulled instead of pink.
The average Wealth of a person in Richville is $150,000 and the average wealth of a
person in Poorville 15 $20,000. Suppose Richville and Poorville combine to form Mediumville.
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Triangle DEF is a right triangle with point F at the origin. Segment DE has endpoints located at D(8, 0) and E(0, −2). What is the area of triangle DEF?
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Answer: 8
Step-by-step explanation:
Using the formula [tex]A=\frac{1}{2}bh[/tex],
[tex]A=\frac{1}{2}(8)(2)=\boxed{8}[/tex]
Suppose that y varies inversely with the square of x and y = 50 when x = 4. Find y when x = 5
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Answer:
y = 32.
Step-by-step explanation:
y = k/x^2 where k is the constant of variation
When y = 50 x = 4, so
50 = k / (4)^2
f = 50 * 4^2 = 800.
So the relation is
y = 800/x^2
When x = 5
y = 800/5^2
= 32.
Question 2
Which sign makes the following statement true? 2/5 ___ 6/15
1. =
2. >
3.
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Answer:
1 is answer
Step-by-step explanation:
2*3/5*3___6/5
You attend a baseball game with friends and visit the snack stand between innings. Soda costs $2 a can, and a box of popcorn costs $1.50. You have $15 with you, and you wish to buy more cans of soda than boxes of popcorn. If x represents the number of cans of soda and y the number of boxes of popcorn, which graph represents the inequalities in this scenario? A. graph A B. graph B C. You attend a baseball game with friends and visit the snack stand between innings. Soda costs $2 a can, and a box of popcorn costs $1.50. You have $15 with you, and you wish to buy more cans of soda than boxes of popcorn. If x represents the number of cans of soda and y the number of boxes of popcorn, which graph represents the inequalities in this scenario? A. graph A B. graph B C. graph C D. graph D C D. graph D
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Answer:
I feel that is would be D
Step-by-step explanation:
This is the most reasonable awnser.
Which
Which of the following are characteristics of the graph of the linear parent
function?
Check all that apply
A. It is a parabola.
B. It has a slope of 2.
C. It goes through the origin.
O
D. It is a straight line.
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Answer:
All of the following are answers:
B) It has a slope of 2
C) It goes through the origin
D) It is a straight line
Step-by-step explanation:
trust me
What are all of the prime numbers between 30 and 40?
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Answer:
the prime numbers between 30 and 40 are 31 and 37 come on its so easy
Find the area of this irregular figure. Please explain in steps how you did it so I know how to do it for the next question please its not needed but would be appreciated
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Work Shown:
A = area of the rectangle
A = length*width
A = 26*15
A = 390 square feet
B = area of the triangle
B = base*height/2
B = 8*9/2
B = 72/2
B = 36 square feet
C = total area
C = A+B
C = 390+36
C = 426 square feet
Which graph represents f of x equals square root of the quantity x plus 3 end quantity minus 2?
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This function shows a horizontal translation of the parent function to the left and 2 units up.
Square root functionThe parent function of a square root function is expressed as:
f(x) = √x
According to the question, we are to plot the expression f(x) = √x+ 3 - 2
This function shows a horizontal translation of the parent function to the left and 2 units up. The required graph will be in the 2nd quadrant of the graph as shown;
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Answer:
It should be the first one.
help please!!! i need to turn this in tomorrow
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Answer:
$10955.6157151671
Step-by-step explanation:
Amount [A] = [tex]P(1+r)^{t}[/tex]
Here, P = principal (which is $5000)
r = rate of interest in decimal form(which is 0.04)
t = time in years (which is 20)
Substituting,
[tex]$5000(1+0.04)^{20}[/tex] = $10955.6157151671
can anyone help me with this with easy tricks
We also have to find volume
I have exams tommorow
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Answer:
1,120 cm³
Step-by-step explanation:
Hello!
Think about it this way: There is a rectangular prism, with lengths of 20cm, 12cm, and 10cm, and another rectangular prism cut out of it with lengths, of 8cm, 8cm, and 20cm.
Larger rectangular prismVolume = L * W * H
V = 20cm * 12cm * 10cmV = 2,400cm³Cut-Out Rectangular PrismV = L * W * H
V = 8cm * 8cm * 20cmV = 1,280cm³Subtract:
2,400cm³ - 1,280cm³1,120cm³The total volume is 1,120cm³
Select the correct answer. Given the following formula, solve for y. w=x-y/2 -z
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Given the following formula, w=x-y/2 -z. The value of y is y = x - 2w + wz .
What is a simplification of an expression?Usually, simplification involves proceeding with the pending operations in the expression.
Like, 5 + 2 is an expression whose simplified form can be obtained by doing the pending addition, which results in 7 as its simplified form.
Simplification usually involves making the expression simple and easy to use later.
Given the following formula,
w=x-y/2 -z
We need to solve for y.
[tex]w = \dfrac{x-y}{2 -z}[/tex]
By cross multiplication
[tex]w\times (2 -z)= {x-y}\\\\2w - wz = x - y[/tex]
subtract x both side
2w - wz -x = x - y -x
y = x - 2w + wz
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3p + 4 ≥ −14 and 1 – 5p ≥ 39
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Answer:
1) p ≥ -6
2) p ≤ -38/5
Step-by-step explanation:
3p + 4 ≥ -14
Subtract 4 to both sides
3p ≥ -14 - 4
3p ≥ -18
Divide 3 to both sides
p ≥ -18/3
p ≥ -6
[tex]\rule[225]{225}{2}[/tex]
1 - 5p ≥ 39
Subtract 1 to both sides
-5p ≥ 39 - 1
-5p ≥ 38
Divide -5 to both sides
p ≤ -38/5
[tex]\rule[225]{225}{2}[/tex]
Calculate the area of the bowl
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Im going to assume that you want the area of a circle.
We already have radius, which is the only variable that we need, now we just have to plug it into the area for the circle:
π(28²)
Multiplying this, you get 2461.76 cm³
evaluate 10 + 8÷4 - 12
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Answer:
zero
Step-by-step explanation:
pemdas
1. 5 M 20 CM of cloth is needed to stitch a shirt how much clothes will be needed to stitch 449 shirts
2. I have a pack of 100 rupees notes in series which start from number code 412 to 425 how much money do I possess
3. a tailor stitches 120 suits in one month. find out how many suits he stitches in an year
4. Radha can swim 348 m in 5 minutes what distance can she in 50 minutes
full explanation pls
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#1
Length in cm
500+20=520cmShirts=449Total length
449(520)233480cm2334m 80cm#2
Total notes
425-412+1=14Total money
100(14)1400|
Total suits per month=120
per year
120(12)1440suits#4
Total 5mins
50/5=10total distance
348(103480mSolve the following factorize and the en- equation of quadrate equation X² + 5x + 7 x = 0
Answers
Answer:
{-12,0}
Step-by-step explanation:
first to solve this can collect like terms and add
X² +12x=0
and solve it by factorization method
X² +12x=0
x(x+12)=0
it means x multiplied by x = X² then x multiplied by 12 = 12x
so this means x or (x+12) equals to zero
x=0 and (x+12)=0
x+12=0
x=-12
so the solution set is {-12,0}
but can also be done by formula method
Use SOHCAHTOA to find the side measure. Show work. Round to one decimal place.
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Using trigonometric ratios, the measure of side n to one decimal is 6.6 units.
How to solve for a side using trigonometric ratios?Using the trigonometric principle
SOHCAHTOA,
cos 20 = adjacent / hypotenuse
adjacent side = n
hypotenuse side = 7
Therefore,
cos 20° = n / 7
cross multiply
n = 7 cos 20°
n = 7 × 0.93969262078
n = 6.5778483455
n = 6.6 units
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14/2+5x4?? can anyone help me??
Answers
Answer: 27
Step-by-step explanation:
Use PEMDAS (Parenthesis,Exponents,Multiplication,Division,Addition,Subtraction)
to solve this problem. First multiply 5 times 4 to get 20. Then divide 14 by 2 to get 7. Lastly, add those two answers to get 27 as the final answer.
Circle D is inscribed with triangle A B C. The measure of arc A B is 76 degrees. Point E is on the circle between points B and C.
What is the measure of arc BEC in circle D?
134°
150°
209°
210°
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Answer: 134°
Step-by-step explanation:
Since angle ABC is equal to 75, we know that the arc in front of it (arc AC) is 150. We then start to add all the know arc angle measures together. So, our equation to finding arc BEC 360-150+76= BEC arc.
Answer:
134
Step-by-step explanation:
cause yeah