Answer:
-4, -2, 4
Step-by-step explanation:
You want the roots of the polynomial x³ +2x² -16x -32.
FactorsThe polynomial can be factored by grouping:
x³ +2x² -16x -32
= (x³ +2x²) -(16x +32) . . . . . . group pairs of terms
= x²(x +2) -16(x +2) . . . . . . . . factor each group
= (x² -16)(x +2) . . . . . . . . . . . . factor out the common factor
Now, the difference of squares can be factored:
= (x -4)(x +4)(x +2)
RootsThe zero product rule tells us the roots are the values of x that make the factors zero:
x -4 = 0 ⇒ x = 4
x +4 = 0 ⇒ x = -4
x +2 = 0 ⇒ x = -2
The roots of the polynomial are {-4, -2, 4}.
__
Additional comment
The factorization of the difference of squares is a special form:
a² -b² = (a +b)(a -b)
Answer:
-2, -4, and 4 are the correct answers on edge
Step-by-step explanation:
Evaluate the expression if a = −2, b = −3, c = 2, x = 2.1, y = 3, and z = −4.2.
4a−|3b+2c|
The value of the expression when evaluated is: -18.
How to Evaluate an Expression?Evaluation of an expression involves plugging in the values of the given variables and then solving to determine the value of the expression in it's simplest form.
Given the expression, 4a - |3b + 2c|, to evaluate, substitute a = -2, b = -3, c = 2 into the expression and solve:
4(-3) - |3(-3) + 2(2)|
-13 - |-9 + 4|
-13 - |-5|
-13 - 5
= -18
The value of the expression is: -18.
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suppose that pulse rates among healthy adults are normally distributed with a mean of 80 beats/minute and a standard deviation of 10 beats/minute. what proportion of healthy adults have pulse rates that are more than 86 beats/minute? round your answer to at least four decimal places.
The Proportion of healthy adults have pulse rates that are more than 86 beats/minute is 27.42%
Z- Score gives an idea how far a data point is from mean .
z = x- μ / σ where numerator is difference between the random variable and the actual mean dividing by the standard deviation .
Given , mean = 80beats/minute
standard deviation = 10 beats/minute
x = 86 beats/minute
Applying z score formula :
z-score = (x-mean)/standard deviation
P(x>86) = P(z > 86-80/10)
=P(z>6/10)
=P(z>0.6) = 1 - P(z<0.6)
= 1 -0.7257
= 0.2742
Hence, the proportion of healthy adults have pulse rates that are more than 86 beats/minute is 0.2742
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Write the correct function in the table below
HELP ASAP
The function that represent the given table is f(x) = 2n+1.
In the given question we have to write the correct function for the table given below.
The given table is
x y
0 3
1 5
2 7
3 9
We can write it as
x y
0 3=1+2
1 5=3+2
2 7=5+2
3 9=7+2
So we can see that in each odd number we are adding 2.
So the function should be
f(x) = (2n−1)+2
f(x) = 2n−1+2
f(x) = 2n+1
Hence, the function that represent the given table is f(x) = 2n+1.
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Jim ate 3/4 of his lunch. What fraction of it was left?
Jim ate 3/4 part of his lunch is in fraction form then the left part of his lunch is a fraction equal to 1/4 .
Fraction : A fraction represents a part of whole . It is a numerical value. It is evaluated by dividing a whole into number of parts . It has two parts one is called numinator (dividend) and other one is denominator ( divisor) . Denominator tells you how many part of lunch is divided into.
Types : Three types are
proper fractionimproper fraction mixed fractionWe have given in question that,
Jim ate 3/4 of his lunch .
let his lunch be x as a whole number .
Now , 3/4 part of x is ate by Jim i.e 3x/4
left part of x = x - 3x/4 = x/4
so, 1/4 part of x i.e lunch is left .
Hence, after eating the 3/4 of lunch by Jim the left part of lunch is 1/4 .
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what is the answer to 5=6h+5(h-5)
Answer: the answer is 30/11
Step-by-step explanation:
hope it helps:)
Tiffany’s allowance is reduced $1. 25 every time she forgets to clean her room. If she forgets to clean her room 7 times this month, by how much money is tiffany’s allowance reduced?.
The amount of money that is reduced from Tiffany's allowance is $8.75
The amount of allowance reduced every time she forget to clean her room = $1.25
Number of times that she forgets to clean her room = 7 times this month
The amount of money is reduced from Tiffany's allowance = Number of times that she forgets to clean her room × The amount of allowance reduced every time she forget to clean her room
Here we have to use the multiplication to find the amount
Substitute the values in the equation
The amount of money is reduced from Tiffany's allowance = 7 × 1.25
Multiply the terms
= $8.75
Hence, the amount of money that is reduced from Tiffany's allowance is $8.75
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8. Emily predicted her car
payment to be
$250 each month. Her actual car
$275 each month.
payment is
Enrique predicted his car
payment to be $200 each month. His actual
car payment is $225 each month.
a. By what percent was Emily's prediction off?
b. By what percent was Enrique's prediction off?
Emily's prediction was off by 9.09%
Enrique's prediction was off by 11.11%
What is a percentage?The percentage is calculated by dividing the required value with the total value and multiplying it by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
We have,
Emily:
Each month payment = $250
Each month actual payment = $275
The percentage prediction is off by.
= (275 - 250) / 275 x 100
= 25/275 x 100
= 9.09%
Enrique:
Each month payment = $200
Each month actual payment = $225
The percentage prediction is off by.
= (225 - 200)/225 x 100
= 25/225 x 100
= 11.11%
Thus,
Emily's prediction was off by 9.09%
Enrique's prediction was off by 11.11%
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Do the following three lengths form a right triangle? 10, 10, 20
Answer:
No, these three sides can't form a triangle====================
Triangle inequality theorem states that the sum of any two sides must be greater than the remaining side.
We see 10 + 10 = 20, so this is contradicting the mentioned theorem, therefore these lengths are not good to form a triangle.
We see 10 + 10 = 20, so this is contradicting the mentioned theorem, therefore these lengths are not good to form a triangle.
Given,
The lengths of triangle is given as:
10 , 10 and 20
To check the following three lengths form a right triangle.
Now, According to the question:
What is triangle inequality theorem ?
The triangle inequality theorem describes the relationship between the three sides of a triangle. According to this theorem, for any triangle, the sum of lengths of two sides is always greater than the third side.
So, The length of triangle are 10, 10, 20
10 + 10 = 20
We see 10 + 10 = 20, so this is contradicting the mentioned theorem, therefore these lengths are not good to form a triangle.
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6. Fill in the missing numbers so that the scaling is consistent. For part (a) what number is represented
for each letter?
12
SHOW YOUR WORK!
a.
Point A: Point B: 52 Point C:
The number represented on number line by (A) -13 (B) 26 (C) 65
According to the number line given in part a
there are for parts in between 0 to 52
To find the numbers in one part = 52/4
= 13
Therefore,
For (A)
0 - 13 = -13
For (B)
0 + 2*13 = 26
For (C)
52 + 13 = 65
Hence, A is -13, B is 26 and C is 65.
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One Step Trinomial, Two Step Factoring
Factor:
x^2 - 12x + 35
Answer:
You can FACTOR x^2-12x+35 by using the AC method
This means the answer will be:
(x-7)(x-5)
I hope this helps!
(Brainliest is optional)
6. Your parent promises to make you a smoothie using
the blender while you're mowing the lawn. The blender
makes a sound that is 88 decibels. What is the intensity
of the sound of the blender?
The intensity of the sound that is 88 decibels of the blender is 6.3×10⁻⁴ W/m².
Decibels:
Decibel is unit used to measure the intensity of a sound or the power level of an electrical signal by comparing it with a given level on a logarithmic scale.
Given,
Your parent promises to make you a smoothie using the blender while you're mowing the lawn. The blender makes a sound that is 88 decibels
Here we need to find the intensity of the sound of the blender
In order to find the intensity, we have to do the following steps,
First, we have to divide the decibel level by 10.
=> 88/10 = 10/10 log (x / 1 x 10⁻¹²)
Now, we have to use that value as the exponent of the ratio.
=> 8.8 = log (x / 1 x 10⁻¹²)
Finally, we have to use that power of ten to find the intensity in Watts per square meter.
=> 6.3×10⁻⁴ .
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if you place a 38- foot ladder against the top of a 32-foot building, how many feet will the bottom of the ladder be from the bottom of the building? round to the nearest tenth of a foot.
Answer:
6 feet
Step-by-step explanation:
38-32=6
Deon is going to rent a truck for one day. There are two companies he can choose from, and they have the following
prices.
Company A charges an initial fee of $41.50 and additional 70 cents for every mile driven.
Company B charges an initial fee of $35 and an additional 80 cents for every mile driven.
For what mileages will Company A charge less than Company B?
Write your answer as an inequality, using m for the number of miles driven.
Answer:
Step-by-step explanation:
answer = company b
20 units rotated to 90 cc reflected over the x axis and translated 6 units down is ?
Answer:
.
Step-by-step explanation:
find measure of each missing angle PLSSSS HELP
The interior angles of the triangle are 43°, 43° and 94°. The exterior angle of the triangle is 86°.
How to find interior and exterior angles of a triangle?A triangle is polygon with three sides. The sum of angles in a triangle is 180 degrees.
The triangle above is an isosceles triangle. The base angles of a triangle is congruent.
Therefore, the base angles are 5x - 12 and 5x -12.
The sum of the remote interior angles is equal to the opposite exterior angles.
5x - 12 + 5x - 12 = 8x - 2
10x - 24 = 8x - 2
10x - 8x = -2 + 24
2x = 22
x = 22 / 2
x = 11
Therefore,
5x - 12 = 5(11) - 12 = 43°
Third angle = 180 - 43 - 43 = 94°
Exterior angle = 8x - 2 = 8(11) - 2 = 86°
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12.) Find m22 if m2XVW = 64°.
V
2
W
P
X
The value of the angle ∠2 = 32° using angle bisector.
What is angle bisector?
In geometry, the ray, line, or segment that divides a given angle into two equal pieces is known as the angle bisector. For instance, a 60-degree angle will be split into two angles of 30 degrees each by an angle bisector. It splits one angle into two smaller congruent angles, to put it another way.
An angle in a triangle is divided into two equal or congruent angles by a straight line known as the angle bisector. Each triangle can have one angle bisector for each of its three vertices. The intersection of these three angle bisectors in a triangle is referred to as the triangle's incenter.
The given angle ∠XVW = 64°
VP is a bisector,
So the angle ∠XVW will be divided equally.
So ∠2 = 32°
Hence the angle of the bisector ∠2 = 32°.
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factorise x squared +3x - 40
Answer:
(x-5)(x+8)
Step-by-step explanation:
Factors of -40:
-1, 40
-2, 20
-4, 10
-5, 8
-5 + 8 =3
x^2+3x-40
x^2 -5x +8x -40
=(x-5)(x+8)
Leroux health insurance is considering changing the options in one of their health care plans (plan a) based on customer feedback that prescriptions and regular visits to the doctor are too expensive for the insured individual. How can leroux reduce the costs of regular health care without driving up the price of their health care plan? leroux health insurance plan a cost: monthly premium: $248. 00 annual deductible: $5,500. 00 co-pays: brand-name prescriptions $35. 00 generic prescriptions $15. 00 visits: primary care physician: $40. 00 specialist: $60. 00 urgent care: $125. 00 emergency room: $325. 00 a. Reduce the monthly premium but increase the co-pay amounts to compensate for the lower premium. B. Reduce the annual deductible, but increase the co-pay amounts so that the monthly premium can stay the same. C. Reduce the co-pay amounts but increase the annual deductible so that the monthly premium can stay the same. D. Reduce the co-pay amounts but increase the monthly premium to compensate for the lower deductible.
Leroux can reduce the costs of regular health care without driving up the price of their health acre plan by : (c) Reducing the co-pay amounts but increase the annual deductible so that the monthly premium can stay the same.
Since the customers are complaining that the cost of regular visits and prescriptions ($15) are too expensive for them based on the plan they choose, this means that the purpose of the health insurance plan which is to reduce the overwhelming cost burden on individuals when trying to access proper healthcare is not be implemented successfully.
The co-pay amount which is usually known as the out-of-pocket amount that insurers pay whenever they go for regular doctor visits ( covered service in the insurance package ) and reducing this amount will reduce the immediate cost which makes the customers to complain about how expensive assessing a doctor on regular visits are.
The effect of the increased annual deductible is one way to push the immediate burden of paying a higher co-pay amount by the customer.
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Which value of x solves the equation cos x° = sin (20° + x°), where 0 < x < 90?
sin x = cos (90 - x) or cos x = sin (90 - x)
This identity holds when the two angles are complementary
i.e. they sum up to 90 degrees.
The value of x is 35°
What are trigonometric identities?There are three commonly used trigonometric identities.
Sin x = 1/ cosec x
Cos x = 1/ sec x
Tan x = 1/ cot x or sin x / cos x
Cot x = cos x / sin x
We have,
cos x° = sin (20° + x°), where 0 < x < 90
We know that,
sin x = cos (90 - x) or cos x = sin (90 - x)
This identity holds when the two angles are complementary
i.e. they sum up to 90 degrees.
x + 90 - x = 90
Now,
cos x = sin (20 + x)
x + 20 + x = 90
2x + 20 = 90
2x = 70
x = 35
Thus,
The value of x is 35°
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What’s the answer to this ?? Does anyone know it ??
Please explain the steps and how you got the answer ): i have a ton more of these to answer and i need to know how to do it.
ONLY ANSWER IF YOU KNOW IT ! WILL REPORT UR ANSWER IF U PUT ANYTHING ELSE.
The equilibrium quantity is 97 items and equilibrium price is $582
The equation of the price when quantity demanded
p = 873 - 3q
The equation of the price when quantity supplied
p = 6q
At equilibrium price and quantity
873 - 3q = 6q
Move the like terms to one side
6q + 3q = 873
Add the like terms
9q = 873
q = 873 / 9
Divide the terms
q = 97 items
Substitute the value of q in the equation 2
p = 6q
p = 6 × 97
Multiply the terms
p = $582
Hence, the equilibrium quantity is 97 items and equilibrium price is $582
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Find the value of 49^-1/2
Find the value of (27/125)^2/3
The value of [tex]49^{-1/2}[/tex] is 1/7 and the value of [tex](\frac{27}{125}) ^{2/3}[/tex] is 9/25.
According to the question,
We have the following expressions:
[tex]49^{-1/2}[/tex]
Now, we will convert the base of these expressions in exponential form in such a way the denominator of powers will get divided:
[tex]7^{2*(-1/2)}[/tex]
[tex]7^{-1}[/tex]
Or it can be 1/7 because we have positive exponents.
Now, we have another expression:
[tex](\frac{27}{125}) ^{2/3}[/tex]
We will follow the same steps to solve this expression:
[tex](\frac{3}{5}) ^{3*2/3}[/tex]
[tex]\frac{3}{5} ^{2}[/tex]
Now, expanding the numerator and denominator of the fraction by multiplying them two times, we have the following fraction:
9/25
Hence, the value of [tex]49^{-1/2}[/tex] is 1/7 and the value of [tex](\frac{27}{125}) ^{2/3}[/tex] is 9/25.
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Erica worked 14 hour lat week and 20 hour thi week. If he earn $9 per hour how much did he earn during thee two week?
Answer:
$306
Step-by-step explanation:
we know that
Erika earns 9$ per hour
so
By proportion
Find how much she earn during the total hours of two weeks
The total hours of two weeks is equal to
[tex]14+20=34 hours[/tex]
[tex]\frac{9}{1} \frac{money}{hour} = \frac{x}{34} \frac{money}{hours}[/tex]
[tex]x =34[/tex]×[tex]9[/tex]
x = 306$
therefore
the answer is
$306
For which value of does the matrix have one real eigenvalue of algebraic multiplicity ?.
the matrix has one real eigenvalue of algebraic multiplicity.
[1-λ k
1 -7-λ] =(1-λ)(-7-λ)-(1)(k) = λ² +6λ -(k+7)
Mathematics has several different subfields, including algebra. Algebra is the study of mathematical symbols and the rules for using them in formulas; it is a common thread that runs through practically all of mathematics.
Since many applications of mathematics include the manipulation of variables, which are frequently represented by Roman letters, elementary algebra is a prerequisite. For the most part in education, the study of algebraic structures like groups, rings, and fields is referred to as abstract algebra (the term is no more in common use outside the educational context). In contemporary presentations of geometry, linear algebra—which deals with linear equations and linear mappings—is used.
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5 km to m convert the following
Answer:
5 km = 5000 m
Hope this helps : )
Need help on algebra
The required value of the given equation when x = 5 is y = 585.5
What is an algebra ?The area of mathematics known as algebra is used to help express issues or circumstances into mathematical expressions. We employ integers with definite or fixed values in algebra, such as 2, 7, 0.068, etc. In addition to integers, algebra uses variables like x, y, and z.
Given : y = 114.50x + 13
To find ; The value of this equation when x = 5
Thus to find this value we have to simply substitute the value of x in the given equation
Hence, we will get ,
y = 114.50 × 5 + 13
this implies y = 572.5 + 13
which is equal to y = 585.5
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The perimeter of a garden is 40 feet. The length is two more than four times the width. Write a system of equations where x represents the width and y represents the length.
Answer:
2(x+y) = 40y = 2 +4xStep-by-step explanation:
You want a system of equations for the width (x) and length (y) of a rectangle with a perimeter of 40 feet and length 2 more than 4 times the width.
EquationsOne equation can give the relation for the perimeter:
2(x +y) = 40
The other can express the relation between width and length:
y = 2 +4x
Your system of equations is 2(x+y) = 40, and y = 2+4x.
__
Additional comment
The solution is (x, y) = (3.6, 16.4) feet.
Malik's budget for chocolate chips for the week is $25. How many whole pounds of chocolate chips can he order
Given a budget of $25, the whole pounds of chocolate chips that Malik can order is 11 pounds of chocolate.
How to find the chocolate chips ordered?For up to 3 pounds, the supplier will charge Malik $4 per pound. This means that after buying 3 pounds of chocolate chips, the amount Malik would be left with it:
= Malik budget - (Price of 4 pounds x 4 pounds)
= 25 - (4 x 3)
= $13
The number of pounds of chips that Malik an buy at $1.50 per pound is:
= 13 / 1 .50
= 8 whole pounds
The total number of whole pounds that Malik can order is:
= 3 + 8
= 11 pounds
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If robert reads 2pages per minute, how many pages could she read in 1 1/2 hours?
Robert can read 180 pages in [tex]1\frac 12[/tex] hours
How to determine the number of pages?The given parameters in the question are:
Speed = 2 pages per minute
Number of hours = [tex]1\frac 12[/tex] hours
The number of pages to read in this time can be calculated using the following equation
Number of pages = Speed * Number of hours
Substitute the known values in the above equation So, we have the following equation
Number of pages = 2 * [tex]1\frac 12[/tex]
Convert the units
Number of pages = 2 * [tex]1\frac 12[/tex] * 60
Evaluate
Number of pages = 180
Hence, the number of pages is 180 pages
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Dimples is a dominant trait (D). The Punnett square shows a cross for this trait between two parents.
What is the probability that the offspring will have dimples?
25%
50%
75%
100%
Answer: 50%
Hope this helps!
Evaluate-2(^-6)(2^3)
Answer:
-1/8
Step-by-step explanation:
-2³/2⁶ negative exponents go in the denonimator
-1/2³ subtract exponents since the denonimator is larger
-1/8 simplify