Answers
Answer:
p(x) = x⁴ -7x³ +59x² -343x +490
Step-by-step explanation:
Each root is the zero of a binomial factor. That is, for root x = a, the polynomial has a factor (x -a). Complex roots come in conjugate pairs, so if there is a root 7i, there is also a root -7i.
__
The given roots mean the polynomial can be written in factored form as ...
p(x) = (x -2)(x -5)(x -7i)(x -(-7i))
We can combine multiply these factors together to simplify the polynomial.
p(x) = (x² -7x +10)(x² +49)
p(x) = x⁴ -7x³ +59x² -343x +490
_____
Additional comment
Combining the conjugate complex roots uses the special form for the factoring of the difference of squares.
a² -b² = (a -b)(a +b)
(x -7i)(x +7i) = x² -(7i)² = x² -49i² = x² +49 . . . . . where i = √(-1)
Related Questions
Winston is making steaks for his 7 friends. If each steak is 7.2 oz, how much steak is Winston making?
Answers
Answer:
3.15 lbs or 50.4 oz
Step-by-step explanation:
multiply steak oz by the number of steaks
7.2 * 7 = 50.4
to convert oz to lbs divide by 16
50.4/16 = 3.15
your answer is 50.4 oz or 3.15 lbs
hope this helps:)
simplify 8w+12/4 and make it correct
Answers
Answer:
[tex]8w+\frac{12}{4}[/tex] = 8w+3
[tex]\frac{8w+12}{4}[/tex] = 2w+3
Step-by-step explanation:
For [tex]8w+\frac{12}{4}[/tex], you can divide 12 by 4 which is three.
For [tex]\frac{8w+12}{4}[/tex], you have to divide each term. 8w is the same as 8·w. 8·w/4 is 2·w. 12/4 is 3.
The correct value of this simplified expression is 8w + 3
This question is related to algebraic expression and simplification.- Algebraic expression is a mathematical sentence that involves letters accompanied by real numbers, where it can be a variable or unknown.
- Simplification of a number is just the division of the same divisor by the numerator and denominator.
Given the expression: 8w+12/4, the only term in this expression that can be simplified is the fraction. So let's divide these two numbers by the number 2:
8w + 12 / 4
8w + 12 ÷ 2 / 4 ÷ 2
8w + 6 /2
It is still possible to simplify this expression - dividing the numerator by the denominator, so:
8w + 6 /2
8w + 6 ÷ 2
8w + 3
Therefore, the correct answer of this expression will be 8w + 3
could someone PLEASE help me with this slope activity? any help would be appreciated, ive been stuck on it for days. this is 10th grade geometry, whoever helps i will gladly give you 5 stars, im just rlly stuck on this
Answers
Answer:
Slope = (y₁-y₂) / (x₁- x₂)JMy₁ = 1
y₂ = -3
x₁ = 2
x₂ = 2
Slope = ( 1 + 3) / 0 = undefined
JK
y₁ = 1
y₂ = 4
x₁ = 2
x₂ = 5
Slope = ( 1-4) / (2-5) = 1
KL
y₁ = 4
y₂ = 1
x₁ = 5
x₂ = 7
Slope = (4-1) / ( 5-7 ) = -1.5
MLy₁ = -3
y₂ = 1
x₁ = 2
x₂ = 7
slope = (-3-1) / ( 2-7) = 4/5
(Express the answer as dollar.cents)
Answers
Answer:
$46.20
Step-by-step explanation:
Do 8.80 times 7 to get 61.6 then divide by four to get 15.40 then subtract it by 61.6 to get 46.20
How many degress will the hour hand of a well clock move from 1:00am to 4:00am
Answers
Answer:
90
Step-by-step explanation:
each minute on the clock is 6 degrees so 6*5=30= 1 hour
30*3=90 because 3 hours
Which expression calculates the time in hours and object takes to travel 38 miles at the speed of 2 m/h?
38/2
38—2
38+2
38 • 2
Answers
Reason:
Distance = rate*time
time = distance/rate
time = (38 miles)/(2 mph)
time = 38/2 hours
time = 19 hours
( 8 + 92 ) - 4 x 10 what is it
Answers
Answer: 60
8 + 92 = 100
4 × 10 = 40
100 + 40 = 60
Answer:
[tex]60[/tex]
Step-by-step explanation:
[tex](8 + 92) - 4 \times 10[/tex]
[tex]100 - 4 \times 10[/tex]
[tex]100 - 40[/tex]
[tex]60[/tex]
Hope this helps!
PPPPPPPPPPPPPPPPLLLLLLLLLLLLLLLLEASE Help
Answers
Answer:
4cm
Step-by-step explanation:
sin(30) = 2/x (using trigonometry)
rearrange for x to give x = 2/sin(30)
then x = 4cm (using calculator)
SIMILARLY:
You can use 2/cos(60) to also give 4cm
Jamal is looking for a summer job. One job pays $10 per hour. Another pays $15 per hour but requires a uniform that costs $50. What are the two quantities that vary in relation to each other in this situation?
Answers
Answer:
Jamel work one job per hour pays =$10
Jamel work Another pays=$15
Jamel Uniform costs=$50
Total situation=$7,500
A class contains 5 girls and 5 boys. Two are selected for a class committee. What is the probability that a girl and boy are selected?
Answers
Answer:
20/39.
Step-by-step explanation:
There are a total of 13 students.
Prob(Boy is selected) = 8/13
Prob(Girl is then selected) = 5/12
So probability ( Boy selected then a girl) = 8/13 * 5/12 = 10/39
- and the probability of Girl then a boy selected is also 10/39
So the required probability = 2 * 10/39
= 20/39.
A number cube has edges of 8 centimeters. What is the surface area of the number cube?
-64 square centimeters
-192 square centimeters
-384 square centimeters
-512 square centimeters
Answers
Answer:
384 square centimeters
Step-by-step explanation:
The surface area formula for a cube is 6L^2
(L=length or in this case edge)
Plug in values and solve the formula.
SA=6L^2
SA=6(8^2)
SA=6(64)
SA=384 square centimeters
Does anybody know this?The two pentagons shown are similar if the area of the smaller pentagon is 232m^3 find the area of the larger pentagon
Answers
Answer:
(a) 362.5 m²
Step-by-step explanation:
The ratio of areas is proportional to the square of the ratio of side lengths.
__
scale factorlarger/smaller = (35 cm)/(28 cm) = 5/4
areaThe larger area is the square of this scale factor times the smaller area.
(5/4)²(232 m²) = 362.5 m²
_____
Additional comment
We assume the units are intended to match. It is impossible for a pentagon with a side length of 28 cm to have an area of 232 m². A regular pentagon with a side length of 28 cm will have an area of about 0.1349 m².
A window is shaped like a parallelogram
The base of the window is 14.25 inches.
The area is 356.25 square inches. What
is the height of the window?
Answers
Answer:
Do the area divided by the base on a calculator for the answer
Answer:
Height of the window= 25 inches
Step-by-step explanation:
Area of a parallelogram : base * height (of the side taken as base)
so height = area/base = 356.25/14.25 = 25 inches
I need help with my math!! help me pleaasee.
Answers
Answer:
60 degrees
Step-by-step explanation:
Angles in a triangle add up to 180
79 add 41 is 120
180 minus 120 is 60
79+41= 120
180-120=60
X=60
whats the median number mode and mean for 95, 97, 100, 86, 78, 96
Answers
Answer:
Mean = 92
Median = 95.5
There is no mode.
What is mean, median, and mode?
Mean, median, and mode are terms in math when it comes to looking at charts and sets/groups of numbers.
1. The mean is the average of a data set.
2. The median is the middle of a data set.
3. The mode is the most common number in a data set.
Mean is found by adding the numbers and dividing the sum by the number of numbers in the list. This is what is most often meant by an average. The median is the middle value in a list ordered from smallest to largest. The mode is the most frequently occurring value on the list.
Before we start, let's put the set of numbers in order from least to greatest,
95, 97, 100, 86, 78, 96
78, 86, 95, 96, 97, 100
Now that we have done that let's find the mean,
78 + 86 + 95 + 96 + 97 + 100 = 552
There are 6 numbers in this set so we need to divide 552 by 6,
552 ÷ 6 = 92
92 is the mean/average of this data set,
Now let's find the median,
If we take a look at the data set we can see that there are two numbers in the middle because there are 6 in total,
78, 86, 95, 96, 97, 100
Because there are two values that are in the middle we need to add them up and divide the sum of them by 2,
95 + 96 = 191
191 ÷ 2 = 95.5
95.5 is the median of this data set,
Now let's find the mode,
If we take a look at the date set we can see that none of the numbers are repeated,
So this means there is no mode to this data set,
Therefore the mean is 92, the median is 95.5, and there is no mode.
Julia earned $2,000 during the month of September. Use the paycheck statement to find the missing amounts and percent rates of the taxes Julia paid. I WILL MARK BRAINLIEST. only want answers
Answers
Julia paid $124 to social security as a payroll tax, $29 in Medicare as a payroll tax, 13% of her income to the federal government as an income tax, and 6% of her income to state government as an income tax.
What is the income tax rate?It is defined as the tax rate applied on the solely earned money by a single entity.
Julia paid to social security as a payroll tax = 6.2% of 2000
= (6.2×2000)/100
= $124
Julia paid to Medicare as a payroll tax = 1.45% of 2000
= (1.45×2000)/100
= $29
Julia paid a percent of her income to the federal government as an income tax:
= (260/2000)×100
= 13%
Julia paid a percent of her income to state government as an income tax:
= (120/2000)×100
= 6%
Thus, Julia paid $124 to social security as a payroll tax, $29 in Medicare as a payroll tax, 13% of her income to the federal government as an income tax, and 6% of her income to state government as an income tax.
Learn more about the income tax here:
brainly.com/question/17075354
#SPJ1
Statistical uncertainty in estimates associated with the fact that surveys do not interview every individual in the population of interest is called __________. Group of answer choices measurement error sample bias probability sampling sampling error
Answers
Statistical uncertainty in estimates associated with the fact that surveys do not interview every individual in the population of interest is called Sampling Error , Option D is the correct answer.
What is Sampling Error ?Sampling error is the difference between the estimated value and the true value if the whole population was enumerated while doing the sampling.
By following the sampling principles one can keep the sampling error to the minimum.
The knowledge of the sampling error will help in evaluating the sampling process and defining gits efficiency.
The factors that affect Sampling Error are
Sample Size: When the sample size is large , the Sampling error decreases , They do not have a direct proportion.Sample Design : These define how the sample will be taken , cluster , random , stratified , Different methods have different extent of sampling error , The design should be selected according to the population and resources constraints.Population Variability : The variability in the population increases the sampling error as the sampling is then cannot be uniform and cannot represent the entire population , By increasing sample size , the population variability can be minimized and so the sampling error.Statistical uncertainty in estimates associated with the fact that surveys do not interview every individual in the population of interest is called sampling Error.
Therefore , Option D is the correct answer.
To know more about Sampling Error
https://brainly.com/question/15375591
#SPJ1
Felipe bought 32 ounces of nuts at the store. How much is this in pounds?
Answers
Answer:
2 pounds (lbs)
Step-by-step explanation:
Give an example of a strong, negative correlation
coefficient.
Answers
Answer:An example of a strong negative correlation would be -0.97 whereby the variables would move in opposite directions in a nearly identical move.
Step-by-step explanation:An example of a strong negative correlation would be -0.97 whereby the variables would move in opposite directions in a nearly identical move.
Here's the question, please help!
Answers
#1
x²/2+y²/3(2sint)²/2+(3sint)²/34sin²t/2+9sim²t/32sin²t+3sim²t5sin²tFalse
#2
x²+y²4sin²t+9sin²t13sin²tFalse
#3
3x²+2y²3(4sin²t)+2(9sin²t)12sin²+18sin²t30sin²tFalse
None of the above
Answer:
None of these
Step-by-step explanation:
To convert the parametric curve into Cartesian form,
rewrite the equation for [tex]x[/tex] to make [tex]\sin t[/tex] the subject:
[tex]x=2\sin t[/tex]
[tex]\implies \sin t=\dfrac{x}{2}[/tex]
Substitute this into the given equation for [tex]y[/tex]:
[tex]\begin{aligned}y & =3 \sin t\\\implies y & = 3 \left(\dfrac{x}{2}\right)\\y& = \dfrac{3}{2}x\end{aligned}[/tex]
Therefore, the Cartesian form of the parametric curve is:
[tex]y=\dfrac{3}{2}x[/tex]
Further Information
[tex]\dfrac{x^2}{2}+\dfrac{y^2}{3}=1 \quad \textsf{is the equation of a vertical ellipse}[/tex]
[tex]\textsf{with center (0, 0), co-vertex }\sf \sqrt{2}, \textsf{ and vertex }\sqrt{3}[/tex]
[tex]x^2+y^2=6 \quad \textsf{is the equation of a circle}[/tex]
[tex]\textsf{with center (0, 0) and radius }\sf \sqrt{6}[/tex]
[tex]3x^2+2y^2=1 \quad \textsf{is the equation of a vertical ellipse}[/tex]
[tex]\textsf{with center (0, 0), co-vertex }\sf \dfrac{\sqrt{3}}{3}, \textsf{ and vertex }\dfrac{\sqrt{2}}{2}[/tex]
Express 2x² - 12x + 7 in the form a (x + b)² + c, where a, b and c are constants.
Answers
Answer:
2(x-3)² - 11 where a = 2, b = -3, c = -11
Step-by-step explanation:
Taking the first 2 terms,
2x² - 12x ==> 2(x² -6x) [1]
x² -6x can be rewritten as (x -3)² - 9 [2]
since (x-3)² = x² -6x + 9
Substituting for x² -6x in [1] we get
2(x² -6x) = 2((x -3)² - 9 ) = 2(x-3)² -18
Therefore substituting for 2x² - 12x in the original equation we get
2x² - 12x + 7 = 2(x-3)² -18 + 7 ==> 2(x-3)² -11
this is in the form (a(x+b) + c where a = 2, b = -3 and c= -11
Cross-check
2(x-3)² - 11 ==> 2 (x² -6x +9) -11 ==> 2x² -12x +18 - 11 ==> 2x² -12x + 7
Donald bought a box of golf balls for $9.26. There were 18 golf balls in the box. About how much did each golf ball cost?
Answers
Answer:
$0.51 per golf ball.
Step-by-step explanation:
9.26 divided by 18 is 0.51.
Answer:
$1.94 dollars
Step-by-step explanation:
hehe
8 ft
6 ft
Find the area of this figure. Round your
answer to the nearest hundredth. Use
3.14 to approximate i.
A = [? ] ft2
Answers
Answer:
49.12 ft squared
Step-by-step explanation:
1/2(6*8) = 24
1/2(16)pi = 8pi = 25.12
total: 49.12
Simplify 12.4 and 12.39
Answers
Answer:
12.4 and 12.39 = 4.836x12
Step-by-step explanation:
You just really like math to answer this one ngl
Answers
Answer:
p(a tail on the second toss) = 4/8
p(exactly one head) = 3/8
p(a head on each of the last two tosses) = 2/8
Step-by-step explanation:
HELP I WILL MARK BRAINIEST IF YOU HELP
Answers
Answer:
3.5 Is the answer, this is dialation
Answer:
x = 28
Step-by-step explanation:
Since none of the current side values of Triangle 1 can be increased by the same values to represent Triangle 2, we have to divide the values of Triangle 1 by half.
T1 S1: 10 / 2 = 5
T1 S2: 8 / 2 = 4
T1 S3: 12 / 2 = 6
Now in order to find out the value that you need to multiply these sides by, you need to divide Triangle 2's values by Triangle 1's simplified side values.
T2 S1: 35 / 5 = 7
T2 S2: x / 4 = ?
T2 S3: 42 / 6 = 7
Triangle 2's Side 1 becomes 7 and Triangle 2's Side 2 becomes 7 as well. Because the value of x is unknown and both Triangle's sides seem to be the same value of 7, you can safely assume that Triangle 2's Side 2 will also have a value of 7.
x / 4 = 7
x = 7(4)
x = 28
somebody please help me
Answers
Answer:
1/18
Step-by-step explanation:
I have provided a tree diagram showing all the possibilities
Answer:
[tex]P=\frac{2}{9}=0.222\\[/tex] for green ball
[tex]P=\frac{2}{8} =0.25[/tex] for red ball
Step-by-step explanation:
For green ball probability will be,
[tex]P=\frac{2}{9}=0.222\\[/tex]
while for the red ball, it will be,
[tex]P=\frac{2}{8} =0.25[/tex]
What is the answer to the problem 20.754 - 14.526
Answers
Answer:
6.228
Step-by-step explanation:
PLEASE EASY 20 POINTS A new park in the shape of a hexagon will have 6 sides of equal length.
On a scale drawing, the coordinates of the vertices of the park are (26.5, 12), (38.5, 7), (26.5, 2), (13.5, 2), (1.5, 7), and (13.5, 12).
How long is each side of the park?
Answers
Answer:
13
Step-by-step explanation:
26.5 - 13.5 = 13
please answer 60 points
Answers
Answer:
c. 90 cm³
Step-by-step explanation:
Formula applied :
Volume (triangular prism) = Base × Height
Solving :
⇒ Volume = 9 cm² x 10 cm
⇒ Volume = 90 cm³
The answer option is c
Answer:
c. 90 cm³
Step-by-step explanation:
Formula
Volume of a right prism = area of base × height
Given:
area of base = 9 cm²height = 10 cmSubstitute the given values into the formula:
⇒ Volume = 9 cm² × 10 cm
= 90 cm³