Answer:
[tex]\frac{28-3i}{26}[/tex]
Step-by-step explanation:
For #2, remember that [tex]i=\sqrt{-1}[/tex], so [tex]i^{2}=-1[/tex] Also, (a+b)(a-b), where a and b are any numbers, (a+b)(a-b)=[tex]a^2-b^2[/tex]. Now, to simplify, or radicalize, a number with surds in the denominator, you have to multiply the denominator by its conjugate. If there is a complex number [tex]a+bi[/tex], where a and b are any numbers, the conjugate is always [tex]a-bi[/tex]. Lets apply these rules. The conjugate of 4+6i is 4-6i, so do this:
[tex]\frac{5+6i}{4+6i}=\frac{(5+6i)(4-6i)}{(4+6i)(4-6i)}=\frac{20+24i-30i+36}{16+36}=\frac{56-6i}{52}=\frac{2(28-3i)}{2(26)}=\frac{28-3i}{26}[/tex]
Our answer is (28-3i)/(26)!
One type of firework splits 5 times after it is fired into the air. The number of new bursts after each split can be modeled by the function f (x ) = 2x where x is the number of times the firework splits. What is the domain of f ( x) in this context
Answer:
All positive integers less than or equal to 5
(Imagine Math)
The domain of f(x) is all the positive integer values up to 5
What is a function?A function is defined as a relation between a set of inputs having one output each.
What is domain?The domain of a function is the set of all possible inputs for the function.
How to find what is the domain of f ( x) in the problem?According to the problem,
One type of firework splits 5 times after it is fired into the air.The number of new bursts after each split can be modeled by the function f (x ) = 2x where x is the number of times the firework splits.So, the values of x will be all the positive integer values up to 5 , as the maximum number of splits is 5.
∴ we can write , x∈ {1 , 5}
This is the domain of f(x)
Find out more about "Domain of a Function" here: https://brainly.com/question/1942755
#SPJ2
Find the sum of 10x squared -x+1 and x squared-10x-7
Answer:
11x^2 - 11x - 6
Step-by-step explanation:
I'm guessing you mean:
(10x^2 - x + 1 ) + (x^2 - 10x - 7)
First you combined like terms:
Such as :
10x^2 + x^2
-x - 10x
1 - 7
There's your answer.
11x^2 - 11x - 6
A standard deck of cards has 52 cards divided into 4 suits, each of which has 13 cards. Two of the suits ( and , called 'hearts' and 'diamonds') are red, the other two ( and , called 'spades' and 'clubs') are black. The cards in the deck are placed in random order (usually by a process called 'shuffling'). In how many ways can we pick two different cards? (Order matters, thus ace of spades followed by jack of diamonds is different than jack of diamonds followed by ace of spades.)
When the order of something happens it is a permutation.
There are a total of 52 cards and you want to pick 2 different cards.
The equation for this is:
52! / (52 - 2!)
Simplified becomes 52! / 50!
Answer = 2,652 ways.
To find the number of ways to pick two different cards from a deck where order matters, we calculate the permutations, resulting in 52 times 51, which equals 2652 ways.
The question asks for the number of ways to pick two different cards from a standard deck of 52 cards considering that the order of selection matters. To calculate this, we use permutations. For the first card, there are 52 options; for the second card, since one card has already been picked, there are 51 options left. The number of permutations for two cards from a deck of 52 is therefore calculated as 52 × 51. This results in 2652 different permutations or ways to select two different cards where order is significant.
The probability that a student at certain high school likes art is 36%. The probability that a student who likes art also likes science is 21%. Find the probability that a student chosen at random likes science given that he or she likes art. Round to the nearest tenth of a percent.
Answer: Probability that a student chose at random likes science given that he or she likes art is 58%.
Step-by-step explanation:
Since we have given that
Probability that a student at certain high school likes art =[tex]P(A)[/tex] = 36%
Probability that a student who likes art also likes science= [tex]P(A\cap S)[/tex] = 21%
We need to find the value of probability that a student chosen at random likes science given that he or she likes art.
As we know the formula for "Conditional Probability" :
[tex]P(S\mid A)=\frac{P(A\cap S)}{P(A)}\\\\P(S\mid A)=\frac{21}{36}\\\\P(S\mid A)=0.58\\\\P(S\mid A)=58\%[/tex]
Hence, Probability that a student chose at random likes science given that he or she likes art is 58%.
Answer with explanation:
A= Art
S= Science
P(A)= 36%
P (A ∩ S)=21%
We have to find ,[tex]P(\frac{S}{A})[/tex].
[tex]P(\frac{S}{A})=\frac{P(S\cap A)}{P(A)}\\\\P(\frac{S}{A})=\frac{\frac{21}{100}}{\frac{36}{100}}\\\\P(\frac{S}{A})=\frac{21}{36}=\frac{7}{12}[/tex]
In terms of Percentage , Required Probability
[tex]=\frac{7}{12}\times 100\\\\=58.34[/tex]
= 58.34 %
The diameter at the center of the tower is_ meters. The center of the tower is _meters above the ground
Answer:
think 5 meters
Step-by-step explanation:
Answer:
The diameter at the center of the tower is 4 meters. The center of the tower is 8 meters above the ground.
Step-by-step explanation:
4x^2-y^2+16y-80=0
Completing squares in variable "y": Common factor -1:
4x^2-(y^2-16y)-80=0
4x^2-[(y-16/2)^2-(16/2)^2]-80=0
4x^2-[(y-8)^2-(8)^2]-80=0
4x^2-[(y-8)^2-64]-80=0
Eliminating the brackets:
4x^2-(y-8)^2+64-80=0
Adding like terms (constants):
4x^2-(y-8)^2-16=0
Adding 16 both sides of the equation:
4x^2-(y-8)^2-16+16=0+16
4x^2-(y-8)^2=16
Dividing all the terms by 16:
4x^2/16-(y-8)^2/16=16/16
Simplifying:
x^2/4-(y-8)^2/16=1
The hyperbola has the form:
(x-h)^2/a^2-(y-k)^2/b^2=1
Then:
h=0
k=8
a^2=4→sqrt(a^2)=sqrt(4)→a=2
The diameter (d) at the center of the tower is:
d=2a→d=2(2)→d=4 meters
The center of the tower is 8 (k) meters above the ground.
the force on an object is given by the equation f=ma. in this equation, F is the force, m is the mass, and a is the acceleration. which answer hows this equation solved for mass?
A. m=a/f
B. m=fa
C. m=f/a
D. m= m/f
Answer:
C. mass = force / accellaration
Step-by-step explanation:
NEED HELP!! 30 POINTS! HAS TO BE CORRECT AND NEED THE ANSWER NOOW!
Answer: options b and c
Step-by-step explanation:
∠ACD is supplementary to ∠ACE given
∠ACD is supplementary to ∠BCD given
⇒ ∠ACE is supplementary to ∠BCD transitive property
∠ACD ≅ ∠BCE given
⇒ ∠BCE is supplementary to ∠ACE substitution
and ∠BCE is supplementary to ∠BCD substitution
********************************************************************************
multiple choice options:
a) ∠ACE is supplementary to ∠BCD False
b) ∠BCE is supplementary to ∠ACE TRUE
c) ∠BCD is supplementary to ∠BCE TRUE
d) ∠ACE ≅ ∠BCE False
e) ∠BCD ≅ ∠ACE False
Cyclists were 2/3 finished with their ride when they reached the 18 kilometer mark how long was the ride
Answer:
Yes that is the correct answer, good job
What is the solution set of the equation j+4/j+2=2−1/j ? Note: j≠0, −2
Answer:
values of j are: 2 , -1
Step-by-step explanation:
In the given case, The solutions are j = -4 and j = 1, and the solution set is {-4, 1}.
The given equation is:
j+4/j+2=2−1/j
We can solve for j by cross-multiplying:
(j+4)(j) = (j+2)(2-1/j)
Expanding the left side and right side, we get:
[tex]j^2 + 4j = 2j + 4 - 2/j[/tex]
Moving all the terms to the left side of the equation, we get:
[tex]j^2 + 2j - 4 = 0[/tex]
We can factor the left side of the equation as:
(j+4)(j-1) = 0
Therefore, the solutions are j = -4 and j = 1.
Note that the given equation is defined when j ≠ 0 and j ≠ -2. Therefore, the solutions are j = -4 and j = 1, and the solution set is {-4, 1}.
Here is a step-by-step solution:
n first move the constant term to the right side of the equation.
j² + 2j = 4
We can then factor the left side of the equation.
(j+4)(j-1) = 0
The solutions are j = -4 and j = 1.
We check that these solutions are valid by substituting them back into the original equation.
j+4/j+2=2−1/j
When j = -4, the left side of the equation is 0/-2 = 0, and the right side of the equation is 2 - 1/-4 = 2 + 0.5 = 2.5.
The equation is satisfied.
When j = 1, the left side of the equation is 5/3, and the right side of the equation is 2 - 1/1 = 2 - 1 = 1. The equation is satisfied.
Therefore, the solutions are j = -4 and j = 1, and the solution set is {-4, 1}.
Learn more about solving equations here:
https://brainly.com/question/19297665
#SPJ3
If leo is 6 years old and max is 12 years, how many years would it be until max is 3 times as old as leo
Answer:
Step-by-step explanation: max is already 3 times older than max. 6*3=18 and 6+12=18
Final answer:
Max cannot be 3 times as old as Leo based on the given information.
Explanation:
To find out how many years it will be until Max is 3 times as old as Leo, we can set up an equation.
Let's assume that it takes x years for Max to be 3 times as old as Leo.
So, Max's age in x years will be 12 + x, and Leo's age in x years will be 6 + x. According to the problem, Max will be 3 times as old as Leo, so we can write the equation as: 12 + x = 3(6 + x).
To solve for x, we can start by simplifying the equation: 12 + x = 18 + 3x. Now, let's isolate the variable x by moving all the x terms to one side and the constant terms to the other side. Subtracting x from both sides gives us: 12 = 18 + 2x. Subtracting 18 from both sides gives us: -6 = 2x. Finally, dividing both sides by 2 gives us: -3 = x.
This means that it will take -3 years for Max to be 3 times as old as Leo. However, since time cannot be negative, we can conclude that it is not possible for Max to be 3 times as old as Leo based on the given information.
George desposited 2000 in his bank, which offers 5% compoud interest annually. What would be the principla amount available in georges account at the and of two years
Write the first five terms of the the sequence defined by the explicit formula an=72(1/3)^n-1
[tex]a_n=72\left(\dfrac{1}{3}\right)^{n-1}\\\\\text{Put}\ n=1,\ n=2,\ n=3,\ n=4,\ n=5\ \text{to the equation}:\\\\n=1\to a_1=72\left(\dfrac{1}{3}\right)^{1-1}=72\left(\dfrac{1}{3}\right)^0=72(1)=72\\\\n=2\to a_2=72\left(\dfrac{1}{3}\right)^{2-1}=72\left(\dfrac{1}{3}\right)^1=72\left(\dfrac{1}{3}\right)=\dfrac{72}{3}=24\\\\n=3\to a_3=72\left(\dfrac{1}{3}\right)^{3-1}=72\left(\dfrac{1}{3}\right)^2=72\left(\dfrac{1}{9}\right)=\dfrac{72}{9}=8\\\\n=4\to a_4=72\left(\dfrac{1}{3}\right)^{4-1}=72\left(\dfrac{1}{3}\right)^3=72\left(\dfrac{1}{27}\right)=\dfrac{72}{27}=\dfrac{8}{3}\\\\n=5\to a_5=72\left(\dfrac{1}{3}\right)^{5-1}=72\left(\dfrac{1}{3}\right)^4=72\left(\dfrac{1}{81}\right)=\dfrac{72}{81}=\dfrac{8}{9}\\\\Answer:\ \boxed{72,\ 24,\ 8,\ \dfrac{8}{3},\ \dfrac{8}{9}}[/tex]
Answer:
The first five terms are as follows:
72, 24, 8, 2.66, 0.88
Step-by-step explanation:
1) Explicit formula:
[tex]72 * 1/3^{n-1}[/tex]
2) Simply replace "n" with 2,3,4 and 5 in order to find the numbers associated with these terms.
a(1) = 72
a(2) = 24
a(3) = 8
a(4) = 2.66
a(5) = 0.88
Note:
In the explicit formula the first term is already provided, so you do not have to find the first term if it has already been given.
the center of a circle is at (-2, - 7) and its radius is 36 what is equation of the circle
A, (x-2)^2 +(y, - 7)^2 = 6
B, (x+2)^2 +(y, + 7)^2 = 6
C, (x-2)^2 +(y, - 7)^2 = 1296
D, (x+2)^2 +(y, + 7)^2 = 1296
Based on the table of values below, find the slope between points where x = 3 and where x = 7.
x y
3 1
4 6
7 9
Answers
−4
1/4
1
2
Answer:
d) 2
Step-by-step explanation:
let's take the points (3, 1) and (7, 9)
Slope formula (m) = (y2 - y1)/(x2 - x1)
Here x1 = 3, y1 = 1 , x2 = 7 and y2 = 9
Now plug in these values in the formula, we get
slope (m) = (9 -1) / (7 -3)
= 8/4
Slope = 2
Answer: d) 2
Thank you.
Find a polynomial f(×) with leading coefficient 1 such that the equation f(×)=0 has The given roots and no others . Root 1, -5 multiplicity 2,1
Answer:
[tex]x^{3} +3x^{2}-9x+5 = 0[/tex]
Step-by-step explanation:
We are given that the only roots of the given polynomial f(x) are 1 and -5 with multiplicity (the number of times the roots are repeating) 2 and 1 respectively.
Also, it is provided that the function satisfy that f(x)=0.
So, comparing the two information we have that,
f(x) = 0 and 1, -5 are the roots of f(x),
i.e [tex](x-1)^{2} \times (x+5) = 0[/tex]
i.e. [tex](x^{2} +1-2x) \times (x+5) = 0[/tex]
i.e. [tex]x^{3} +3x^{2}-9x+5 = 0[/tex]
Also, we can see that ths polynomial has leading co-efficient 1 i.e. the co-efficient of highest degree variable i.e. x^{3}.
Hence, the polynomial having leading co-efficient 1 and roots 1, -5 is [tex]x^{3} +3x^{2}-9x+5 = 0[/tex].
Johns house is 12 miles away from school he is 2/3 the way there how many miles has he walked
It takes Francisco 15 minutes to ride his bicycle 4km ,which is the distance from home to school . What is the average speed
Answer:
16 KMH is the correct answer
Step-by-step explanation:
What is the solution to 4+5e^(x+2)=11?
(Answers Below)
Answer:
x = ln (7/5) - 2
Step-by-step explanation:
4+5e^(x+2)=11
Subtract 4 from each side
4-4+5e^(x+2)=11-4
5e^(x+2)=7
Divide by 5 on each side
5/5e^(x+2)=7/5
e^(x+2)=7/5
Take the natural log on each side
ln (e^(x+2))= ln (7/5)
x+2 = ln (7/5)
Subtract 2 from each side
x = ln (7/5) - 2
Answer:
option 1
Step-by-step explanation:
Celeste wants to have her hair cut and permed and also go to lunch she knows she will need $50 the perm cos twice as much as her haircut and she needs $5 for lunch how much does the permcost
Answer:
$30
Step-by-step explanation:
Lets use x as the price for the haircut.
If the perm is 2 * the amount of the haircut, this can be shown by 2x (2 times the value of x which is the haircut price).
We know the price for lunch so we simply need to subtract this value from 50:
50 - 5 = 45
So 45 is the total price for the perm and haircut.
Now we can add 2x (price of perm) and x (price of haircut):
2x + x = 3x
So 3x = 45
Divide both sides by three to get x:
x = 15
So if the perm is 2x the cost of the haircut, and the haircut costs 1x which is 15, then we can multiply thise value by 2:
15 * 2 = 30
So the perm cost $30!
If I could have help on this that would be great.
Answer: Choice C) Harold
Darren is correct because he subtracted c from both sides
Julie is correct because she multiplied both sides by H, and then divided both sides by L
Brenda is correct because she multiplied both sides by r
Harold is not correct. We can see this with a counter example. If A = 7 and h = 1, then the first equation Harold wrote leads to b = 14. Now plug those same values into the second equation and we get h = 2b/A turning into 1 = 2*14/7 and that simplifies to 1 = 4, which is a false statement. This contradiction is one example why the two equations Harold wrote aren't equivalent.
Answer:
C.
Step-by-step explanation:
Juile, Brenda, and Darren are all incorrect.
There are 3 white marbles and 7 blue marbles in a bag. Jamie will randomly pick two marbles out of the bag without replacing the first marble chosen. What is the probability of Jamie's picking 2 white marbles?
A) 1/15
B) 1/18
C) 1/20
D) 1/7
Answer:
1/7 is the probability hope this helps
Answer:
A) 1/15
Step-by-step explanation:
The probability of picking a white marble is 3/10. Then 2 of the remaining 9 marbles are white, so the probability of picking one is 2/9.
The joint probability is (3/10)·(2/9) = 6/90 = 1/15
Given the table below, determine if the data represents a linear or an exponential function and find a possible formula for the function.
Answer:
Option a is correct
given data in the table represents an exponential function
The possible formula for the function is, [tex]y = f(x) = 12.5 (1.10)^x[/tex]
An exponential function is in the form of [tex]f(x) = ab^x[/tex] where a is the initial value and b ≠ 0 , b> 1.
Consider any two points from the table as shown;
(0, 12.5) and (1, 13.75)
Substitute these in [1] we have;
For (0, 12.5)
where x = 0 and f(x) = 12.5 in [1]
[tex]12.5 = ab^0[/tex]
12.5 = a
For (1, 13.75)
[tex]13.75 = ab^1[/tex]
13.75 = ab
Substitute the value of a =12.5 we have;
13.75 = 12.5b
divide both sides by 12.5 we get;
[tex]b = \frac{13.75}{12.5} = 1.10[/tex]
since, y =f(x)
therefore, we have the following exponential function as:
[tex]y= 12.5 (1.10)^x[/tex]
The length of a rectangle is three times its width. The perimeter of the rectangle is at most 112cm. Which inequality models the relationship between the width and the perimeter of the rectangle.
Answer: w ≤ 14 cm , L ≤ 42 cm
Step-by-step explanation:
width (w): w
Length(L): 3w
Perimeter (P) = 2w + 2L
P ≤ 112
2w + 2L ≤ 112
2(w) + 2(3w) ≤ 112
2w + 6w ≤ 112
8w ≤ 112
w ≤ 14
Elena mixes 5 cups of apple juice with 2 cups of sparkling water to make sparkling apple juice for a party she wants to make 35 cups of sparkling apple juice. how much of each ingredient should Elena use?
Answer: 25 cups of apple juice and 10 cups of splarking water.
Step-by-step explanation:
1. You have the following information given in the problem:
- She mixes 5 cups of apple juice with 2 cups of sparklin.
- She wants to make 35 cups of sparkling apple juice.
2. Then:
[tex]5cups+2cups=7cups[/tex] (Each lot of sparkling apple juice has 7 cups).
3. As she needs 35 cups, she needs to make 5 lots of sparkling apple juice, because:
[tex]\frac{35}{7}=5lots[/tex]
4. Therefore, you must multiply 5 lots by 5 cups of apple juice and 5 lots by 2 cups of sparkling apple juice. Then, she should use:
[tex]A.juice=5*5cups=25cups\\S.water=5*2cups=10cups[/tex]
5. The answer is:
25 cups of apple juice and 10 cups of splarking water.
To make 35 cups of sparkling apple juice, Elena will need to mix 25 cups of apple juice with 10 cups of sparkling water. This is because the initial quantity ratio is 5:2 for apple juice to sparkling water. Thus, to make a larger quantity, these original quantities are multiplied by a common factor.
Explanation:The goal here is to get the quantities of apple juice and sparkling water that Elena should use to prepare 35 cups of sparkling apple juice. In the original mix, Elena combines 5 cups of apple juice with 2 cups of sparkling water to make 7 cups of the juice. This mix is thus in a ratio of 5:2 in favor of apple juice to water.
Given that the total quantity she now wants to prepare is 35 cups, which is 5 times the original quantity (because 35/7 = 5), you would multiply the quantities of each of the components (apple juice and sparkling water) by 5. This implies:
Apple juice: 5 cups x 5 = 25 cupsSparkling water: 2 cups x 5 = 10 cupsTherefore, Elena will need 25 cups of apple juice and 10 cups of sparkling water to make 35 cups of sparkling apple juice.
Learn more about Ratio here:https://brainly.com/question/32531170
#SPJ12
20 POINTS!!!! MATH HELP PLEASE I WILL BE MARKING BRAINLY PLEASE SHOW ALL OF YOUR WORK
Answer:
Letter A:
There is a 42.857143% chance of picking a black marble out of the bag. This is because there are 7 marbles total and 42.857143% of them(3/7) are black, so that is the probability.
Letter B:
There is a 14.285714% chance of picking this. The chance of picking a black black marble first is 3/7, which you multiply by the chance of picking a marble out on your second try without putting the first black marble back in ,which is 1/3. That gives you 1/7, or the percent above.
Letter C:
The probability of picking a black marble, replacing it, then picking another black marble is 18.367347%, or 9/49. You take the probability of picking out a black marble first, 3/7, and multiply it by the chance of picking another black marble after replacing the first one, which is also 3/7.
Letter D:
The probability is different for B and C because in B the chance for the second one is less because for the second pick there are less marbles and a third of them are black. In C the chance of picking a black marble in the second is the same as in the first because you are putting the original back in.
in 2 years i will be twice as old as i was 20 years ago how old am I?
Answer:
I am 42 years old
Step-by-step explanation:
Given : In 2 years i will be twice as old as i was 20 years ago.
To Find : Current age
Solution :
Let the current age be x years.
After two years i will be (x+2) years
20 years ago i was (x-20)years
Since we are given that in 2 years i will be twice as old as i was 20 years ago.
⇒[tex]x+2 = 2 (x-20)[/tex]
⇒[tex]x+2 = 2x-40[/tex]
⇒[tex]40+2 = 2x-x[/tex]
⇒[tex]42 = x[/tex]
Thus my current age 'x' = 42 years.
Hence i am 42 years old
30 POINTS!!!
Select ALL of the expressions that are equivalent to 4 square root of 5.
A. 2 square root of 20.
B. 6^1/2-5^1/2
C. 3*5^1/2+5^1/2
D. 4* 5^1/2
E. 2 square root of 10
F. 3*5^1/2
Answer:
A, C, & D
Step-by-step explanation:
A square root has the form [tex]\sqrt[2]{x} = x^{1/2}[/tex] and can be represented in exponential form. Let's convert all the expressions to [tex]\sqrt{x}[/tex] this form. 4 square root 5 is [tex]4\sqrt{25} =\sqrt{16*5}=\sqrt{80}[/tex]
A. [tex]2\sqrt{20} =\sqrt{4*20}=\sqrt{80}[/tex]
B. [tex]6^{1/2}-5^{1/2} =\sqrt{6}-\sqrt{5}[/tex]
C. [tex]3*5^{1/2}+5^{1/2} =3\sqrt{5}+\sqrt{5}=4\sqrt{5}=\sqrt{16*5}=\sqrt{80}[/tex]
D. [tex]4*5^{1/2}=4\sqrt{5}=\sqrt{16*5}=\sqrt{80}[/tex]
E.[tex]2\sqrt{10} =\sqrt{4*10}=\sqrt{40}[/tex]
F. [tex]3*5^{1/2}=3\sqrt{5}=\sqrt{9*5}=\sqrt{45}[/tex]
Danny was was 184.56 pounds last week. He is on a special weight gain program with a trainer. What was his average daily gain?
184.56:7≈26.37 pounds
Function g is transformed to obtain function h as shown. h(x) =g(x+2)-5 Which statement describes how the graph of h is different from the graph of g?
Answer:
Translation 2 units to the left and 5 units down.
Step-by-step explanation:
Consider the parent function [tex]y=g(x)[/tex] and its graph.
1. The translation 2 units to the left forms from the graph of the parent function the graph of the function [tex]y=g(x+2).[/tex]
2. Then the translation 5 units down forms from the graph of the function [tex]y=g(x+2)[/tex] the graph of the function [tex]h(x)=g(x+2)-5.[/tex]
Answer:
the answer is d for plato users
Step-by-step explanation:
A recursive rule for a geometric sequence is a1=3;an=1/2an−1.
What is the explicit rule for this sequence?
Enter your answer in the box.
[tex]\text{The explicit rule of geometric sequence}\\\\a_n=a_1 r^{n-1}\\------------------------------\\\text{We have the recursive form}\ a_1=3,\ a_n=\dfrac{1}{2}\cdot a_{n-1}.\\\\\text{Therefore}\ r=\dfrac{1}{2}.\ \text{Substitute:}\\\\\boxed{a_n=3\left(\dfrac{1}{2}\right)^{n-1}}[/tex]