Answers
================================================
Explanation:
Let's focus on the root x = 2i. Square both sides to get rid of the imaginary component and then get everything to one side.
x = 2i
x^2 = (2i)^2
x^2 = 4i^2
x^2 = -4
x^2+4 = 0
You should find that the root x = -2i leads to x^2+4 = 0 as well.
So the equation x^2+4 = 0 produces the complex roots x = 2i and x = -2i. This tells us that x^2+4 is a factor of the answer. The other factor is x-5 due to the real number root x = 5.
We'll multiply those two factors mentioned:
(x-5)(x^2+4)
w(x^2+4) ..... let w = x-5
wx^2 + 4w
x^2(w) + 4(w)
x^2(x-5) + 4(x-5) .... plug in w = x-5
x^3 - 5x^2 + 4x - 20
----------
The last step is to triple each term so that we go from the leading term of x^3 to 3x^3. This will give us a lead coefficient of 3.
So we go from this
x^3 - 5x^2 + 4x - 20
to this
3x^3 - 15x^2 + 12x - 60
after tripling everything. This expression has the same roots as the previous one. Scaling the function only stretches it vertically, but the roots aren't changed.
Related Questions
Jake drew a scale drawing of a house. He used the scale 10 inches = 6 feet. What is the scale factor of the drawing?
Simplify your answer and write it as a fraction.
Answers
Answer:
5:36
Step-by-step explanation:
12 inches = 1 foot, so 6 feet = 72 inches
10:72, reduces to 5:36
write an equation in slope intercept form of the line that passes through the points (-3,6) and (0,0)
Answers
Answer:
y=-2x
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(0-6)/(0-(-3))
m=-6/(0+3)
m=-6/3
m=-2
y-y1=m(x-x1)
y-6=-2(x-(-3))
y-6=-2(x+3)
y=-2x-6+6
y=-2x
Note that the slope-intercept form is y=mx+b where m=slope and b=y-intercept.
Hi can someone pls help me with this!!!
Answers
the domain is the x value (first number) and the range is the y value (second number)
(if a number appears more than once in the domain or range, like in number 1 you don't have to write it again.)
to graph the domain and range you just plot the points,
and to map them you have to put the x values in the first oval and the y values in the second, usually in order from smallest to largest.
then you have to draw arrows connecting each x value to the y value that was in the same pair. just like when writing down the domain/range, if a number comes up again you don't have to write it down again. instead, you might have two or more arrows connecting to the same number.
how do you compute the area of the triangle
Answers
1/2 *b*h
or
bh/2
(b is base;H is height)
URGENT!!!!!!!!!!!!!!! :
m(x) = -1/2f(x - 3) - 1
Answers
Answer:
-1/2f I think
Step-by-step explanation:
distribute the -1/2
use differentiation rules
calculate all together
then simplify
Hope this helps
Find the slope-intercept equation of the line
that passes through (5, -3) and has a
slope of -1/2
Answers
Answer:
y = -1/2x - 1/2
Step-by-step explanation:
lmk if you want an explanation
A flying disc has a 7 3/4 inch radius. What is its approximate circumference,
rounded to the nearest inch?
Answers
Answer:
49 in
Step-by-step explanation:
The circumference of a circle with radius r is ...
C = 2πr
The disc with the given radius has a circumference of ...
C = 2π(7.75 in) ≈ 49 in
solve 5/4 × (− 9/2 )
Answers
Answer:
-40/8= -5
Step-by-step explanation:
Multiply the top to get -40 then the bottom to get 8. When you simplify, you get -5.
Answer:
-5.625
Step-by-step explanation:
5/4 × (-9/2)
=5×(-9)/4×2
=-45/8
=-5.625
(-a + (-b)) + (-c) = -(a + b) + (-c)
A:associative
B:commutative
C:distributive
D:opposite of a sum
Answers
Answer: c
Step-by-step explanation:
Find the equation that has a slope of -2 and passes through the point (0,4)
pleaseeeee
Answers
Answer:
y=-2x+4
Step-by-step explanation:
y=mx+b
y=-2x+b
4=-2(0)+b
4=0+b
4=b
y=-2x+4
A student wants to check six websites. Four of the websites are social and two are school-related. After checking just two sites, she has to leave for school. What is the approximate probability that she checked a social website first, then a school-related website? 0. 042 0. 267 0. 533 0. 667.
Answers
The approximate probability that she checked a social website first, then a school-related website is 0.267.
First step is to calculate the Total number of websites
Total number of websites=Number of school websites+Number of social websites
Total number of websites=2+4
Total number of websites=6
Second step
Probability of checking the social website first
Probability of checking social website=Number of social websites/Total number of websites
Probability of checking social website= 4/6
Third step
Since one social website is checked which means that she is left with 3 social website and 2 school websites
Total number websites=2+3
Total number websites=5
Forth step
Probability of checking social website=Number of school websites/Total number websites
Probability of checking social website=2/5
Fifth step
Probability= 4/6 x 2/5 = 0.2666
Probability=0.267(Approximately)
Inconclusion the approximate probability that she checked a social website first, then a school-related website is 0.267.
Learn more about probability here:https://brainly.com/question/25688842
Answer:
0.267
Step-by-step explanation:
Total websites = school websites (2) + social websites (4) = 6
Checking social website = social websites (4) /Total websites (6) = 2/3
Total websites is 5
Checking social website = school websites (2) /Total websites (5)
4/6 x 2/5 = 0.2666
Answer: 0.267
Hope this helps :)
I NEED HELP I NEED HELP I NEED HELP I NEED HELP I NEED HELP
Answers
What do you mean? What’s the question?
Answer:
Unknown
Step-by-step explanation:
Question, not provided.
Consider the graph.
Which function best represents the distance remaining, in miles, after
x
minutes?
f
(
x
)
=
10
7
x
+
35
f ( x ) = 10 7 x + 35
f
(
x
)
=
7
10
x
+
35
f ( x ) = 7 10 x + 35
f
(
x
)
=
−
7
10
x
+
35
f ( x ) = − − 7 10 x + 35
f
(
x
)
=
−
10
7
x
+
35
f ( x ) = − − 10 7 x + 35
Answers
Answer:
X=5
The factors of x^2 + 2x - 35 are
(X-5) (x+7)
Set x equal to zero & solve
X-5=0
X=5
Step-by-step explanation:
2. A small university is trying to monitor its electricity usage. For a random sample of
30 weekend days (Saturdays and Sundays), the student center used an average of 94.26 kilowatt hours (kWh) with standard deviation 43.29. For a random sample of 60 weekdays, (Monday - Friday), the student center used an average of 112.63 kWh with standard deviation 32.07.(Please show work)
a) Test, at the 5% level, if significantly more electricity is used at the student center, on average, on weekdays than weekend days. Remember to check the conditions, identify the hypotheses, define your parameter, find the test statistic, find the p-value, and give a conclusion in context.
b) Construct a 95% confidence interval for the difference in mean electricity use at the student center between weekdays and weekend days. Use two decimal places in your margin of error.
Answers
Using the t-distribution, it is found that:
a) Since the test statistic is greater than the critical value for the right-tailed test, it is found that there is enough evidence to conclude that significantly more electricity is used at the student center, on average, on weekdays than weekend days.
b) The 95% confidence interval for the difference in mean electricity use at the student center between weekdays and weekend days is (3.56, 33.18).
Item a:
At the null hypothesis, it is tested if there is no difference, that is, the subtraction is at most 0, hence:
[tex]H_0: \mu_1 - \mu_2 \leq 0[/tex]
At the alternative hypothesis, it is tested if there is difference, that is, the subtraction is positive, hence:
[tex]H_1: \mu_1 - \mu_2 > 0[/tex]
The standard errors are given by:
[tex]s_1 = \frac{32.07}{\sqrt{60}} = 4.14[/tex]
[tex]s_2 = \frac{43.29}{\sqrt{30}} = 7.9[/tex]
The distribution of the difference has mean and standard deviation given by:
[tex]\overline{x} = \mu_1 - \mu_2 = 112.63 - 94.26 = 18.37[/tex]
[tex]s = \sqrt{s_1^2 + s_2^2} = \sqrt{4.14^2 + 7.9^2} = 8.92[/tex]
The standard deviation are given for the samples, hence, the t-distribution is used.
The test statistic is given by:
[tex]t = \frac{\overline{x} - \mu}{s}[/tex]
In which [tex]\mu = 0[/tex] is the value tested at the hypothesis.
Hence:
[tex]t = \frac{\overline{x} - \mu}{s}[/tex]
[tex]t = \frac{18.37 - 0}{8.92}[/tex]
[tex]t = 2.06[/tex]
The critical value for a right-tailed test, as we are testing if the mean is greater than a value, with a significance level of 0.05 and 30 + 60 - 2 = 88 df is [tex]t^{\ast} = 1.66[/tex]
Since the test statistic is greater than the critical value for the right-tailed test, it is found that there is enough evidence to conclude that significantly more electricity is used at the student center, on average, on weekdays than weekend days.
Item b:
The interval is:
[tex]\overline{x} \pm t^{\ast}s[/tex]
Hence:
[tex]\overline{x} - t^{\ast}s = 18.37 - 1.66(8.92) = 3.56[/tex]
[tex]\overline{x} + t^{\ast}s = 18.37 + 1.66(8.92) = 33.18[/tex]
The 95% confidence interval for the difference in mean electricity use at the student center between weekdays and weekend days is (3.56, 33.18).
A similar problem is given at https://brainly.com/question/25812826
WHAT IS 62729287937927497393884x0
I NEED HELP!!!!!!!!!
PLEASEEEEEE
Answers
Answer:your mom
Step-by-step explanation:
[tex]\huge \bf༆ Answer ༄[/tex]
Any value multiplied by Zero gives Zero, therefore ~
[tex] \sf62729287937927497393884 \times 0 = 0[/tex]Find the equation of line through (-15,9) with slope 4/5 in slope-intercept form.
Answers
Answer:
well, we know it is
y = -4 x + b
so all we need is b
5 = -4(9) + b
5 = -36 + b
b = 41
so
y = -4 x + 41
Help pls + brainliest
Answers
Answer:
Letter C.
Step-by-step explanation:
Lap 1 be x
Lap 2 be y
Line graph: plot the values, and will get C.
help plz
help
help
help
help
help
help
Answers
Answer:
A
Step-by-step explanation:
-|x+3| has a x-intercept of -3. A is the only option with -3 as an x-intercept.
-hope it helps
Answer:
answer be A
Step-by-step explanation:
The following diagram shows the side view of a roof and attic space of a newly constructed
home. Find m
A. 20°
B. 40°
C. 60°
D. 25°
Answers
Answer:
A 20
Step-by-step explanation:
yeah-ya....... right?
Find the sum in SIMPLEST form:
3/10+1/10=
A 4/20
B 2/5
C 4/10
D 1/5
Answers
Answer:
B. 2/5
Step-by-step explanation:
I hope this helps!
Answer:
B 2/5
Step-by-step explanation:
i need the answr for 3+x=10 please explain as well
Answers
Answer:
7
Step-by-step explanation:
basically just subtract 10-3=7 then to check 3+7=10
Answer:
x = 7
Step-by-step explanation:
3 + x = 10
-3 -3
x = 7
you subtract by 3 on both sides (because the opposite property of addition is subtraction) to cancel it out and isolate the x.
which mapping diagram does NOT represent a function from x > y ?
Answers
Answer:
A
Step-by-step explanation:
In a function, each x value must have a singular y value. This means that one x-value (the values on the left) may not have a line pointing to 2 different y-values (the values on the right). In the first relation, the x-value of 6 points to both 4 and 6. This means that the value repeats, and in a function x-values cannot repeat.
However, y-values can repeat. So, situations like that seen in D, where both the x-values of 2 and 4 equal the y-value of 6 are fine.
Answer:
It's A
Step-by-step explanation:
Find the value of x.
Answers
Answer:
X=24
Step-by-step explanation:
(X+16)°+6x=180°(being co-interior angle)
7x=180-16
X=164÷7
X=23.428
X=23
or,
(3x-1)+5x=180(being co-interior angle)
8x=181
X=181÷8
X=22.625=23
-2/9 (-5/3) I Ready Multiply and Divide Rationals.
Answers
Help help hep math math
Answers
Answer:
96
Step-by-step explanation:
C=πd
C=?
π=3
d=32
C=3×32
Therefore C=96
13^5/13^x=13^4
Does anyone know how to solve this?
Answers
[tex]\frac{13^5}{13^x} =13^4 =>13^{5-x} =13^4\\ =>5-x=4=> x=5-4=1[/tex]
ANSWER: x = 1
ok done. Thank to me :>
Maya has $15 to spend. She spent $5.50, including tax, to buy a notebook. She needs to save $7.75, but she wants to buy a snack. If cookies cost $0.25 per package including tax, what inequality would show the maximum number of packages that Maya can buy? Solve your inequality by showing your work and steps. (10 points)
(no links and I will give brainliest)
Answers
Answer: 7 packages.
Step-by-step explanation:
Let x represent number of cookie packages.
We have been given that Maya has $15 to spend. She spent $5.50, including tax, to buy a notebook.
Amount left after buying notebook would be .
As Maya needs to save $7.75, so money left to buy cookies would be .
We are also told that cost of each cookie package is $0.25. The cost of x packages would be .
The cost of x packages should be less than or equal to 7.75.
Therefore, Maya can buy at-most 7 packages.
Have a great Day/Night
Answer:
7 packages
Step-by-step explanation:
Let x represent number of cookie packages.
We have been given that Maya has $15 to spend. She spent $5.50, including tax, to buy a notebook.
Amount left after buying notebook would be .
As Maya needs to save $7.75, so money left to buy cookies would be .
We are also told that cost of each cookie package is $0.25. The cost of x packages would be .
The cost of x packages should be less than or equal to 7.75.
Therefore, Maya can buy at-most 7 packages.
The value of a small airplane depreciates exponentially every year after it is
purchased. The value, in thousands of dollars, alt), of Plane X, t years after purchase
can be approximated by this function.
Answers
Answer: the operation can be said as x( 576-68)t-5= x
Step-by-step explanation:
You can see this because I am smart and just am
What is the equation of the line that passes through the point (-8,3) and has a slope of -1/4
Answers
y=-1/4x+1 is the equation of the line that passes through the point (-8,3) and has a slope of -1/4
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
We have to find equation of the line that passes through the point (-8,3) and has a slope of -1/4
m=-1/4
Let us find y intercept
3=-1/4(-8)+b
3=2+b
b=1
Hence, y=-1/4x+1 is the equation of the line that passes through the point (-8,3) and has a slope of -1/4
To learn more on slope of line click:
https://brainly.com/question/16180119
#SPJ2
Questions 1 3 5 7 range and graph not needed
Answers
Answer:
thx for the 25 points, I know you meant to give it to me(≧▽≦)