Answers
The solution is shown below:
[tex] x^{2} +16 \\ \\ = x^{2} +(4)^{2} \\ \\ = x^{2} -(-1)(4)^{2} \\ \\ = x^{2} -i^{2} (4)^{2} \\ \\ = x^{2} -(4i)^{2} \\ \\ =(x+4i)(x-4i) [/tex]
Related Questions
hey can you please help me posted picture of question
Answers
x² - 4x - 12 = 0
x² - 6x + 2x - 12 = 0
x(x-6) +2(x-6) = 0
(x+2)(x-6) = 0
This means the roots of the function are x=-2, and x=6 and the graph will cross x axis at these two points. From the given graphs, the graph B seems to cross these points.
So the answer to this question is option B
Suppose you are the treasurer of the drama club.The cost of scripts for the spring musical is $254. The cost of props and costumes is $400. You must also pay $1.20 per ticket to the play's director. You charge $4.00 per ticket and you also expect to make $150 on refreshments. How many tickets will the drama club need to sell to break even?
Answers
$254 +400 -150 = $504
Expected income per ticket is
$4.00 -1.20 = $2.80
To break even, the number of tickets that must be sold is
$504/$2.80 = 180
The drama club needs to sell 180 tickets to break even.
find the least common multiple LCM of 10 and 5
Answers
The least common multiple is 2
Answer: I hope this is helpful
Step-by-step explanation:
10LCM of 5 and 10 is 10. LCM, also known as Least Common multiple or Lowest common multiple, is the smallest or the least positive integer that is divisible by the given set of numbers. In the given set of numbers 5 and 10, 10 is the least number that is divisible by both 5 and 10.
***HELP***
Given that ABC ~ DEC, find the value of x. If necessary, round your answer to two decimal places.
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AB / CB = DE / CE
x / 5 = (18 - x) / 25
5x = 18 - x
6x = 18
x = 3
What is the factorization of the polynomial below x^2-3x-40
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________
What are the next three terms in the sequence? -6,5,16,27, ...
A.38, 49, 60
B.37, 47, 57
C.36, 45, 54
D.36, 46, 56
Answers
The next three terms of the given sequence are 38, 49, and 60. The correct option is A.38, 49, 60
Linear sequenceFrom the question, we are to determine the next three terms in the given sequence
The given sequence is
-6,5,16,27, ...
From the given sequence, we can observe that the common difference of the sequence is 11
That is,
5 - -6 = 5 + 6 = 11
16 - 5 = 11
27 - 16 = 11
Thus, the next term after 27 will be
27 + 11 = 38
The next one will be
38 + 11 = 49
The next one will be
49 + 11 = 60
Hence, the next three terms of the given sequence are 38, 49, and 60. The correct option is A.38, 49, 60
Learn more on Linear sequence here: https://brainly.com/question/24608344
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Simplify 1 · 0 - 0/y
Answers
There are 10 people on a team. 5 are chosen. which expression gives number of ways
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Number of ways to select 5 = Total number C Number to be chosen. Where "C" stands for combination
Substituting;
Number of ways to select 5 from 10 people = 10C5 = 10!/{5!*(10-5)!} = 10!/(5!*5!) = 252 ways
Heather and Joel bought a house for $157,200 and know that the house appreciates every year. They keep track of their house value for 5 years and model their data with the exponential equation
Answers
FV=P(1+r)^n
where:
n=time
p=principle
r=rate
First we need to estimate the rate. The value of the house after 5 years is $ 190,000
thus plugging the values in the equation and solving for r we get:
190000=157200(1+r)^5
1.20865=(1+r)^5
getting the fifth root of both sides we obtain:
1.0386=1+r
thus
r=0.0386~3.86%
thus the value of the house after 8 years will be:
FV=157200(1.0386)^8
FV=$212,879.6936
The question relates to house appreciation and quality in mathematics. The house's value appreciates each year, an occurrence that Heather and Joel could monitor. House appreciation allows them to determine the annual interest rate and the value of their house after a particular period, and Ben and Freda's specifics help illustrate this situation.
Explanation:The question pertains to the concept of housing appreciation and equity in Mathematics. In this situation, Heather and Joel will observe that the value of their home increases annually due to appreciation. The value of their home after a certain period can be modeled using an exponential equation, taking the initial amount as the purchasing price, and the rate as the annual appreciation percentage.
For example, looking at Freda's situation, she bought a house for $150,000. Now, if she were to sell it, she would get $250,000. This increase in price from $150,000 to $250,000 would demonstrate the appreciation of her house over time. Similarly, Ben bought a house for $100,000 and borrowed the rest after a 20% down payment. As he pays the loan, his equity in the house increases and the house's increase in value also appreciates his equity.
Learn more about House Appreciation and Equity here:https://brainly.com/question/15073504
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what is the answer for this math question
Answers
1/10×3/2=3/20 cups
0.15=15%=3/20 as decimal*percent
Please help me with this.
Answers
We are given the first term and the common difference.
So,
[tex]a_{1}=-10 \\ \\ d=5[/tex]
Using these values in the given equation, we get:
[tex] a_{n} =-10+(n-1)*5 \\ \\ a_{n} = -10 + 5n - 5 \\ \\ a_{n} = 5n -15[/tex]
So, option C gives the correct answer.
solve the system using the substituion method
-4x+y=8
x-3y=9
Answers
x - 3y = 9
x = 9 + 3y
-4x + y = 8
-4(9+3y) + y = 8
-36 - 12y + y = 8
-36 - 11y = 8
-11y = 44
-y = 4
y = -4
x - 3y = 9
x - 3(-4) = 9
x + 12 = 9
x = 21
So, your answers are y = -4 and x = 21.
Hope this helps!
what is the value of the expression 8.5 - 10.2 + -7.4
Answers
8.5 - 10.2 = -1.7
Next, add -7.4 to -1.7
-7.4 (+) - 1.7 = -9.1
Your final answer is -9.1
Answer: −9.1
Step-by-step explanation:
8.5−10.2−7.4
=−1.7−7.4
=−9.1
PLEASE MARK BRAINLIEST
hello can you please help me posted picture of question
Answers
The probability of choosing one of them is 2 out of 75 while the probability of choosing the other one is 1 out of 74. 74 band members, not counting the other person (you or your bother).
Computation:
P = 2 / 75 * 1 / 74
= 0.0266... * 0.01351...
= 1 / 2,775
You can also multiply 75 with 74 to get a total of 5,550 then divide it by 2 students to be selected to get 2,775. Meaning one out of 2,775 possibilities.
The figure is made up of a cylinder and a half sphere. What is the volume of the composite figure? Round to the nearest hundredth.
radius: 4mm
cylinder length: 7mm
Answers
[volume of the composite figure]=volume of cylinder + volume hemisphere
volume cylinder=pi*r²*h
r=4 mm
h=7 mm
volume cylinder=pi*4²*7----> 351.68 mm³
volume of hemisphere=(4/6)*pi*r³
r=4 mm
volume of hemisphere=(4/6)*pi*4³----> 133.97 mm³
[volume of the composite figure]=351.68+133.97----> 485.65 mm³
Alice makes 8 bracelets. there are 4 red beads on each bracelets. witch number sentence shows the total number of beads used?
Answers
But 8 bracelets times 4 red beads equals 32 beads in total
8 * 4 = 32
5 ln ( x + 8 ) solve the equation for x
Answers
If we make it an equation, then we can solve for x.
a = 5*ln(x +8)
a/5 = ln(x +8) . . . . . . . divide by 5
e^(a/5) = x +8 . . . . . . take the antilog
e^(a/5) -8 = x . . . . . . . subtract 8
If your expression is equal to "a", then x is ...
x = e^(a/5) -8
The ratio of a model car to the size of an actual car is 1:40. If the model is 4.5 inches long, what is the length of the full size car in inches and in feet?
Answers
4x40=180
.5x40=20
180+20=200
Determine whether the series is convergent or divergent by expressing sn as a telescoping sum. ∞ 4 n(n + 2) n = 1
Answers
∞ 4n(n +2)n = 1
a cone with radius 2 feet and height 8 feet is shown.
Answers
The volume of the cone is approximately 33.51 cubic feet when rounded to the nearest hundredth
Use the formula for the volume of a cone, which is:
[tex]V = \frac{1}{3} \pi r^2 h[/tex]
Where:
[tex]V[/tex] is the volume of the cone,[tex]r[/tex] is the radius of the base of the cone,[tex]h[/tex] is the height of the cone.Given:
Radius [tex]r = 2\;\text{ft}[/tex]Height [tex]h = 8\;\text{ft}[/tex]Substitute the given values into the volume formula:
[tex]V = \frac{1}{3} \pi (2)^2 (8)[/tex]
Calculate the radius squared:
[tex]2^2 = 4[/tex]
Multiply the squared radius by the height and [tex]\pi[/tex]:
[tex]4 \times 8 \times \pi = 32\pi[/tex]
Divide by 3 to get the volume:
[tex]V = \frac{32\pi}{3} \approx \frac{32 \times 3.14159}{3} \approx 33.51\;\text{cubic feet}[/tex]
Complete question
A cone with a radius of 2ft and height 8ft is shown. Find the volume of the cone in cubic feet. Round your answer to the nearest hundredth
How do I find the hypotenuse of a triangle when given 90 degrees and one side length?
Answers
The direct answer to your question is that you can't.
Q #7 please solve the equation
Answers
a = 640s
where,
a = number of acres
s = number of square miles
We are to find the number of acres for 7.5 square miles.
This means, s = 7.5
Using the value in the formula, we get:
a = 640 x 7.5 = 4800 acres
So the answer to this question is option B
please show all possible solution by graphing a linear inequality
Answers
x = the number of adult tickets
y = the number of children's tickets
We write the inequality:
8x + 6y <= 172
The solution is the set of points that belong to the region shaded in the graph.
Answer:
8x + 6y <= 172
see attached image.
x = the number of adult tickets
y = the number of children's tickets
Then write the inequality:
8x + 6y <= 172
Answer:
8x + 6y <= 172 so the solutions of this equation are those who are in the shaded part of the graph.
Of all rectangles with area 9 which one has the minimum perimeter
Answers
write 3.6 as a mixed number in the simplest form
Answers
(sorry if it's wrong)
enter the ordered pair that is the solution to the system of equations graphed below please :]
Answers
Since (1, -2) is the point of intersection, then it is the solution to the system of equations. Let's test our answer to see if it's correct:
[tex]-2 = -4(1) + 2 -2 = -4 + 2 -2 = -2[/tex]
But that's only for the first one, let's test for the second one:
[tex]-2 = 1 - 3 -2 = -2[/tex]
This is how we know that (1, -2) is the solution to the system of equations. Hope I helped! :3
The half-life of cobalt-60 is 5.20 yr. how many milligrams of a 2.000-mg sample remains after 6.55 years?
Answers
Answer:
0.835 mg of a 2.000-mg sample remains after 6.55 years.
Step-by-step explanation:
We are given that The half-life of cobalt-60 is 5.20 yr.
Formula of half life : [tex]N(t) = N(0)e^{\frac{-0.693t}{t\frac{1}{2}}}[/tex]
Where N(0) = Initial amount
N(t) = Quantity remaining after time
t = time
[tex]\frac{t}{2} =\text{half life}[/tex]
So, N(0) = Initial amount = 2 mg
t = time = 6.55 years
[tex]\frac{t}{2} =\text{half life} = 5.20 yr [/tex]
Substitute the values in the formula
Therefore,
[tex]N(t) = 2 e^{\frac{-0.693 \times 6.55}{5.20}}[/tex]
[tex]N(t) =0.835[/tex]
Hence 0.835 mg of a 2.000-mg sample remains after 6.55 years.
A straight line has the equation 2y-8x=5x-12. If point C, (4, n) lies on this straight line, find n.
Answers
2y-8x=5x-12----> 2y=13x-12
we know that
If point C, (4, n) lies on this straight line
so
in the straight line
for x=4
the value of y must be n
2y=13x-12-----> 2y=13*4-12----> 2y=52-12----> 2y=40----> y=20
the value of n must be 20
the answer is
n is 20
A 4-foot tall person standing with her back to the sun casts an 6-foot long shadow.
To the nearest degree, what angle does the sun make with the ground?
Answers
Tan (x) = (4/6)
Clearing the angle we have:
x = Atan (4/6)
x = 33.69006753
Rounding off we have:
x = 34 degrees
Answer:
The angle that sun makes with the ground is:
x = 34 degrees
1.
Find the annual percentage rate, using the annual percentage rate table.
Amount Financed: $2,650
Finance Charge: $484.69
Number of Payments: 36
Answers
Finance Charge: $484.69
Number of Payments: 36
(Finance Charge)/(Amount Financed)*100$=($484.69)/($2,650)*100$
(Finance Charge)/(Amount Financed)*100$=(0.1829)*100$
(Finance Charge)/(Amount Financed)*100$=$18.29
In the row of number of Payments 36, we look for:
(Finance Charge)/(Amount Financed)*100$=$18.29, and we see to which annual porcentage rate it corresponds in the first row
Answer: 11.25%