Answer:
Use identities:
(a + b)² = a² + 2ab + b²i² = -1Simplify:
(x + (3 + 5i))² = x² + 2x(3 + 5i) + (3 + 5i)² = x² + 6x + 10xi + 9 + 30i - 25 = x² + 6x + 10xi + 30i - 16Identity used:-
[tex]\boxed{\sf (a+b)^2=a^2+b^2+2ab}[/tex]
Now
[tex]\\ \sf\longmapsto (x+(3+5i))^2[/tex]
[tex]\\ \sf\longmapsto x^2+2x(3+5i)+(3+5i)^2[/tex]
[tex]\\ \sf\longmapsto x^2+6x+10xi+3^2+2(3)(5i)+(5i)^2[/tex]
i^2=-1[tex]\\ \sf\longmapsto x^2+6x+10xi+9+30i-25[/tex]
[tex]\\ \sf\longmapsto x^2+6x+10xi+30i+9-25[/tex]
[tex]\\ \sf\longmapsto x^2+6x+10xi+30i-16[/tex]
When Asia was young, her father marked her height on the door frame every month. He noticed that between the ages of one and three, he could predict her height (in inches) by taking her age in months, adding 75 inches, and multiplying the result by one-third.
Create an equation linking her predicted height, h, with her age in months, m, and solve to find when her height will be 30 inches.
Answer:
15 months old.
Step-by-step explanation:
Let m = months and h = height:
h = 1/3(m + 75) ⇔ h = 1/3m + 25
Let h = 30:
[tex]30=\frac{1}{3}m+25\\5=\frac{1}{3}m\\15=m[/tex]
Therefore, when Asia is 30 inches tall, she will be 15 months old.
Find the value of x in each case:
9514 1404 393
Answer:
x = 45°
Step-by-step explanation:
The triangle interior angle at I will be the supplement of the angle marked 2x. The triangle interior angle at G will be equal to x, the alternate interior angle with respect to transversal GI crossing the parallel lines.
The angle marked 3x is the sum of these "remote" interior angles:
3x = 180 -2x +x
4x = 180 . . . . . . . . . add x; next, divide by 4
x = 180/4 = 45 . . . . . degrees
x = 45°
Find the missing side of the triangle
Answer:
x = 7[tex]\sqrt{2}[/tex]
Step-by-step explanation:
Pytago:
[tex]7^2 + 7^2 = x^2\\x = \sqrt{7^2 + 7^2} \\x = 7\sqrt{2}[/tex]
Step-by-step explanation:
In a right triangle, you can find the leg of the triangle by using the Pythagorean theorem.
[tex]a^2+b^2=c^2[/tex]
In this case, we have [tex]7^2+7^2=c^2[/tex], or
[tex]c^2=98[/tex]
[tex]\sqrt{98}[/tex]≅[tex]9.9[/tex]
Which of the following show the factored equivalent of
f(x) = (2x^2 +7x + 3)(x - 3) and its zeros?
Answer:
the answer is "D"
(2x+1)(x+3)(x-3) //// -3,-.5,3
Step-by-step explanation:
Factored Form: y= (2x+1)(x+3)(x-3)
Answer:
D
Step-by-step explanation:
[tex]f(x) = (2x^2 +7x + 3)(x - 3)[/tex] is factored into: [tex]f(x)= (2x+1)(x+3)(x-3)[/tex]
That takes out the choices B and C.
The roots are -0.5, 3, and -3.
Therefore, the answer is D.
I hope this helps!
pls ❤ and mark brainliest pls!
A poll of 400 people from Dobbs Ferry showed 250 preferred chocolate raspberry coffee while 170 out of 350 in Irvington preferred the same flavor. To test the hypothesis that there is no difference in preferences in the two villages, what is the alternate hypothesis
Answer: The alternate hypothesis would disprove the null hypothesis and state that there are a significant difference in preferences/proportions between the two villages.
For instance, let's say:
p₁ = proportion of preference from Dobbs Ferryp₂ = proportion of preference from IrvingtonThe null hypothesis would be that p₁ = p₂, while the alternative hypothesis would be that p₁ ≠ p₂.
Find the length of the arc. Round your answer to the nearest tenth
Answer:
12.6 mi
Step-by-step explanation:
Arc length = 2πr (Θ/360)
2π(12) (60/360)
= 12.6 mi
Answered by g a u t h m a t h
Each machine at a certain factory can produce 90 units per hour. The setup cost is 20 dollars for each machine and the operating cost is 26 dollars per hour (total, not 26 dollars per machine per hour). You would like to know how many machines should be used to produce 40000 units, with the goal of minimizing production costs.
First, find a formula for the total cost in terms of the number of machines, n:_______
TC = ______
machines for a total cost of The minimum total cost is achieved when using dollars.
Answer:
a) [tex]Total Cost=20n+\frac{(\frac{40000}{90}*26)}{n}[/tex]
b) [tex]n=24[/tex]
Step-by-step explanation:
From the question we are told that:
Rate r=90 units per hour
Setup cost =20
Operating Cost =26
Units=40000
Generally the equation for Total cost is mathematically given by
[tex]Total Cost=20n+\frac{(\frac{40000}{90}*26)}{n}[/tex]
[tex]T_n=20n+\frac{11556}{n}\\\\T_n=\frac{20n^2+11556}{n}.....equ 1[/tex]
Differentiating
[tex]T_n'=\frac{n(40n)-(40n^2+11556)}{n_2}\\\\T_n'=\frac{20n^2-11556}{n^2}.....equ 2[/tex]
Equating equ 1 to zero
[tex]0=\frac{20n^2+11556}{n}[/tex]
[tex]n=24[/tex]
Therefore
Substituting n
For Equ 1
[tex]T_n=\frac{20(24)^2+11556}{24}[/tex]
F(n)>0
For Equ 2
[tex]T_n'=\frac{20(24)^2-11556}{24^2}[/tex]
F(n)'<0
Does the function ƒ(x) = (1∕2) + 25 represent exponential growth, decay, or neither?
A) Exponential growth
B) Impossible to determine with the information given.
C) Neither
D) Exponential decay
Answer:
A) Exponential growth
Step-by-step explanation:
Hello I'm new can anyone help me with this question?
Thank you so much! <3 xoxo
What is 21 1/8 minus 14 1/8
Answer:
8.75
Step-by-step explanation:
211/8 = 26.375
141/8 = 17.625
now,
211/8-141/8
26.375-17.625
8.75
find the length of the arc . round your answers to the nearest tenth
Answer:
10.2
Step-by-step explanation:
Length of arc=(2*pi*r)*(theta/360)
Length of arc=(2*pi*3)*(195/360)=10.2
There are nickles and quarters worth $2.20 in total. If there are 28 coins, how many nickels are there?
A 7% acid solution will be mixed with a 15% acid solution. 20 L of a 12% acid solution needs to be made.
Identify the two variables in the problem by completing the following statements: * Let r represent: Let y represent:
Answer:
Let r = amount of the 7% solution
y represent the amount of the 15 percent solution
r =7.5 L
y = 12.5 L
Step-by-step explanation:
Let r = amount of the 7% solution
y represent the amount of the 15 percent solution
.07r + .15 y = (r+y) .12
r+y = 20
y = 20-r
.07r + .15 (20-r) = (20) .12
0.07r+0.15(20-r)=2.4
.07r+ 3 - .15r = 2.4
-.08r = 2.4-3
-.08r = -.6
Divide by-.08
r =7.5
y = 20-7.5
y = 12.5
In Waterville, the average daily rainfall in July is 10 mm with a standard deviation of 1.5 mm. Assume that this data is normally distributed. How many days in July would you expect the daily rainfall to be more than 11.5 mm
Answer:
You should expect 5 days in July with daily rainfall of more than 11.5 mm.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
In Waterville, the average daily rainfall in July is 10 mm with a standard deviation of 1.5 mm.
This means that [tex]\mu = 10, \sigma = 1.5[/tex]
Proportion of days with the daily rainfall above 11.5 mm.
1 subtracted by the p-value of Z when X = 11.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{11.5 - 10}{1.5}[/tex]
[tex]Z = 1[/tex]
[tex]Z = 1[/tex] has a p-value of 0.84.
1 - 0.84 = 0.16.
How many days in July would you expect the daily rainfall to be more than 11.5 mm?
July has 31 days, so this is 0.16 of 31.
0.16*31 = 4.96, rounding to the nearest whole number, 5.
You should expect 5 days in July with daily rainfall of more than 11.5 mm.
Use the equation d=z–9 to find the value of d when z=10.
d=
Step-by-step explanation:
d = z - 9
d = 10 - 9 ----> substitute
d = 1
(A) The weight of cans of vegetables is normally distributed with a mean of 1380 grams and a standard deviation of 80 grams. What is the probability that the sample mean of weight for 15 randomly selected cans is more than 1410
Answer:
7.35%
Step-by-step explanation:
μ = 1380
σ = 80
n = 15
P(x>1410)
= (1410-1380)/((80)/(sqrt(15)))
= 1.4524
P(z>1.4524) = 0.4265 (from the graph)
P(z>1.4524) = 0.5 - 0.4265 = 0.0735
A macaroni and cheese recipe calls for 2/5 of a 2 1/2 pound a block of cheese. How many pounds are needed?
I
2/5 of 2.5. = 2x2.5 / 5x1 = 5/5 = 1 pound
Move the numbers to the lines to order them from least to greatest.
least
greatest
67.98
68.6
68.11
Please answer ASAP
Answer:
67.98,68.11, 68.6
In the picture below, which lines are lines of symmetry for the figure?
A. none
B. 1, 2, and 3
C. 1 and 3
D. 2 and 4
Answer:
i gues none... bcuz its irregular symmetry shape
Answer:
1 because it takes a full rotation to get back to a symmetrical shape. or 2 because it is the same halfway around.
Question 3 plz show ALL STEPS
Answer:
7,0, -1 and -2
Step-by-step explanation:
Just substitute the values,
a. f(g(7))=f(-1) [g(7)=-1 given]
=7 [f(-1)=7 given]
b.f(g(-1))=f(3)=0 [g(-1)=3 Given]
c.g(f(-1))=g(7)=-1 [f(-1)=7 given]
d.g(f(7))=g(5)=-2 [f(7)=g(5) given]
Which expression is equivalent to (b^n)m?
Step-by-step explanation:
By the law of exponent :
(a^n)^m=a^n×m
Option C
b^n×m is the correct answer...
hope it helps
what’s the formula to find the shaded area?
shaded area = area of outer figure - area of inner figure........
The profit earned by a hot dog stand is a linear function of the number of hot dogs sold. It costs the owner $48 dollars each morning for the day’s supply of hot dogs, buns and mustard, but he earns $2 profit for each hot dog sold. Which equation represents y, the profit earned by the hot dog stand for x hot dogs sold? y=48x−2 y=48x+2 y=2x−48 y=2x+48
Answer:
c. y=2x−48
Explanation:
It is telling us that it costs $48 each morning to buy the day's supply of hot dogs, so we must subtract that from our pay, and it will be our y intercept
It also says he earns $2 per hot dog, so that will be our slope (rate of change)
Hope it helps! :]
y = 2x - 48 equation represents the profit earned by the x hot dog sold.
What is linear equation?A linear equation is an algebraic expression in which highest power of the given variable is equals to one.
Given that, the profit earned by a hot dog stand is a linear function of the number of hot dogs sold.
It costs the owner $48 dollars each morning for the day’s supply of hot dogs, buns and mustard, but he earns $2 profit for each hot dog sold.
We need to establish an equation that represents the total profit,
According to the question,
x represents the number of hot dogs sold
y represents the total profit earned
Cost required for supply = $48
Profit on each hot dog sold = $2
As per the condition given, the required linear equation is =
y = 2x - 48
Hence, y = 2x - 48 equation represents the profit earned by the x hot dog sold.
Learn more about linear equation here :
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IF YOU DONT ANSWER THIS AND GET IT RIGHT YOUR MOM IS PREGO WITH YOUR KID a store sells pencils pens and markers that sells two times as many markers as pencils and three times as many pens as pencils is the store sells a total of 1950 pencils and pens and markers in a week how many of each were sold
Answer:
Pencils = 325 ; Pens = 975 ; Markers = 650
Step-by-step explanation:
Let :
Number of Pencils = x
Number of pens = y
Number of markers = z
2 times as many markers as pencils
z = 2x
3 times as many pens as pencils
y = 3x
x + y + z = 1950
Write z and y in terms of x in the equation :
x + 3x + 2x = 1950
6x = 1950
Divide both sides by 6
6x / 6 = 1950 / 6
x = 325
Number of pencils = 325
Pens = 3 * 325 = 975
Markers = 2 * 325 = 650
Pencils = 325 ; Pens = 975 ; Markers = 650
find the measure of a
Answer:
C
Step-by-step explanation:
e = 20 ° angles subtended by the same arc are equal
d = 20° opp base angles of an isosceles are equal
a+d =90° angles subtended by a diameter = 90°
a+20=90°
a=70°
The sum of the interior angles of a regular nonagon (9-gon) is equal to
The sum of the interior angles is 1260°
given the series 1+2+3+4+5+6+...+5000. Write the series in sigma notation if all the powers of 4 are removed from the series.
We have 4⁶ = 4096 and 4⁷ = 16,384, which is to say that the given sum only contains the first six powers of 4.
Now,
[tex]\displaystyle 1+2+3+\cdots+5000 = \sum_{k=1}^{5000}k[/tex]
and you subtract the sum of the first six powers of 4 to get the sum S that you want,
[tex]\displaystyle S = \boxed{\sum_{k=1}^{5000}k - \sum_{k=1}^64^k}[/tex]
a bag contains 7 red chips and 11 blue chips. two chips are selected randomly without replacement from the bag. what is the probability that the two chips are NOT the same coler
Answer:
77/306 or around 25.2%
Step-by-step explanation:
[tex]\frac{7}{18} *\frac{11}{17}[/tex] section 1/total * section 2/(total-1) since there is no replacement
just solve and you get 77/306
I need some help please!!!
9514 1404 393
Answer:
13 < √181 < 14
Step-by-step explanation:
Apparently, you're supposed to know that ...
13² = 169
14² = 196
so √181 will lie between 13 and 14.
13 < √181 < 14
The lines shown below are parallel. If the green line has a slope of 5, what is a
the slope of the red line?
Answer:
A. 5
Step-by-step explanation:
Parallel lines have the same slope.
Answer:
5
Step-by-step explanation:
