Step-by-step explanation:
f(x) = 0
-2x + 2x is always 0.
so, g(x) + f(x) = g(x) + 0 = g(x) = 2x.
long proof :
g(x) + f(x) = 2x + -2x + 2x = 2x
Lauren received a box of 12 identical-looking truffles for Valentine's Day. 3/4 of them have a fruit filling and 2/3 of the remaining are coffe-flavored. 1/3 of the fruit-filled ones have raspberry filling and 1/6 of the remaining fruit-filled truffles have strawberry flavor. What is the probability that she will draw a flavor she doesn't reconize.
A. 1/3
B. 2/5
C. 1/2
D. 3/4
C. 1/2
9 of the truffles are fruit-filled. 2 are coffee-flavored. one is unaccounted for.
Of the 9 fruit-filled ones, 3 are raspberry and one is strawberry. 5 are unaccounted for.
Putting together the ones we don't know, we get 6 unknown ones. 6/12, or 1/2, is the answer.
How do I determine z ∈ C:
[tex](\frac{3-2i}{1+i} - \frac{5+3i}{1+2i} )z = \frac{1}{2} - \frac{2}{5}i[/tex]
Simplify the coefficient of z on the left side. We do this by rationalizing the denominators and multiplying them by their complex conjugates:
[tex]\dfrac{3-2i}{1+i} - \dfrac{5+3i}{1+2i} = \dfrac{3-2i}{1+i}\cdot\dfrac{1-i}{1-i} - \dfrac{5+3i}{1+2i}\cdot\dfrac{1-2i}{1-2i}[/tex]
[tex]\dfrac{3-2i}{1+i} - \dfrac{5+3i}{1+2i} = \dfrac{(3-2i)(1-i)}{1-i^2} - \dfrac{(5+3i)(1-2i)}{1-(2i)^2}[/tex]
[tex]\dfrac{3-2i}{1+i} - \dfrac{5+3i}{1+2i} = \dfrac{3 - 2i - 3i + 2i^2}{1-(-1)} - \dfrac{5 + 3i - 10i - 6i^2}{1-4(-1)}[/tex]
[tex]\dfrac{3-2i}{1+i} - \dfrac{5+3i}{1+2i} = \dfrac{3 - 5i + 2(-1)}2 - \dfrac{5 - 7i - 6(-1)}5[/tex]
[tex]\dfrac{3-2i}{1+i} - \dfrac{5+3i}{1+2i} = \dfrac{1 - 5i}2 - \dfrac{11 - 7i}5[/tex]
[tex]\dfrac{3-2i}{1+i} - \dfrac{5+3i}{1+2i} = \dfrac{1 - 5i}2\cdot\dfrac55 - \dfrac{11 - 7i}5\cdot\dfrac22[/tex]
[tex]\dfrac{3-2i}{1+i} - \dfrac{5+3i}{1+2i} = \dfrac{5 - 25i - 22 + 14i}{10}[/tex]
[tex]\dfrac{3-2i}{1+i} - \dfrac{5+3i}{1+2i} = -\dfrac{17 + 11i}{10}[/tex]
So, the equation is simplified to
[tex]-\dfrac{17+11i}{10} z = \dfrac12 - \dfrac{2i}5[/tex]
Let's combine the fractions on the right side:
[tex]\dfrac12 - \dfrac{2i}5 = \dfrac12\cdot\dfrac55 - \dfrac{2i}5\cdot\dfrac22[/tex]
[tex]\dfrac12 - \dfrac{2i}5 = \dfrac{5-4i}{10}[/tex]
Then
[tex]-\dfrac{17+11i}{10} z = \dfrac{5-4i}{10}[/tex]
reduces to
[tex]-(17+11i) z = 5-4i[/tex]
Multiply both sides by -1/(17 + 11i) :
[tex]\dfrac{-(17+11i)}{-(17+11i)} z = \dfrac{5-4i}{-(17+11i)}[/tex]
[tex]z = -\dfrac{5-4i}{17+11i}[/tex]
Finally, simplify the right side:
[tex]-\dfrac{5-4i}{17+11i} = -\dfrac{5-4i}{17+11i} \cdot \dfrac{17-11i}{17-11i}[/tex]
[tex]-\dfrac{5-4i}{17+11i} = -\dfrac{(5-4i)(17-11i)}{17^2-(11i)^2}[/tex]
[tex]-\dfrac{5-4i}{17+11i} = -\dfrac{85 - 68i - 55i + 44i^2}{289-121(-1)}[/tex]
[tex]-\dfrac{5-4i}{17+11i} = -\dfrac{85 - 68i - 55i + 44(-1)}{410}[/tex]
[tex]-\dfrac{5-4i}{17+11i} = -\dfrac{41 - 123i}{410}[/tex]
[tex]-\dfrac{5-4i}{17+11i} = -\dfrac{41 - 41\cdot3i}{410}[/tex]
[tex]-\dfrac{5-4i}{17+11i} = -\dfrac{1 - 3i}{10}[/tex]
So, the solution to the equation is
[tex]z = -\dfrac{1-3i}{10} = \boxed{-\dfrac1{10} + \dfrac3{10}i}[/tex]
Please help I do not understand thanks
A bicycle has a listed price of $660.95 before tax. If the sales tax rate is 7.25%, find the total cost of the bicycle with sales tax included.
Round your answer to the nearest cent, as necessary
9514 1404 393
Answer:
$708.87
Step-by-step explanation:
The price with tax included is ...
660.95 + 0.0725×660.95 = 660.95(1 +0.0725) = 708.87
The total cost of the bicycle with tax is $708.87.
Answer:
$ 708.87
Step-by-step explanation:
Think that, a bicycle has listed price of $ 100,
Listed price Tax rate Total cost of the bicycle with sales tax
$ 100 7.25 107.25
$ 660.95 x
Let the Total price of the bicycle be x
Now you can create a equation like this,
[tex]\frac{100}{660.95}=\frac{107.25}{x}[/tex]
Use cross multiplication, and find out the total cost of the bicycle with sales tax.
[tex]100x=660.95*107.25[/tex]
[tex]100x=70886.8875[/tex]
[tex]\frac{100x}{100} =\frac{70886.8875}{100} \\[/tex]
[tex]x=708.8688[/tex]
Therefore, the total cost of the bicycle with sales tax is,
≈ $ 708.87
Hope this helps you.
Let me know if you have any other questions :-)
A stockbroker estimates that at the end of the year, there is a 40% chance a stock will be worth $50,
a 35% chance it will be worth $60 and a 25% chance it will be worth $70. What expected value
does this broker assign to this stock's end-of-the-year price?
The expected value that this broker assign to this stock's end-of-the-year price is $58.50.
Using this formula
Expected value=Stock worth at $50+ Stock worth at $60+ Stock worth at $70
Where:
Stock worth at $50=40% chance
Stock worth at $60=35% chance
Stock worth at $70=25% chance
Let plug in the formula
Expected value=(40%×$50)+($35%×$60)+($25%×$70)
Expected value=$20+$21+$17.5
Expected value=$58.50
Inconclusion the expected value that this broker assign to this stock's end-of-the-year price is $58.50.
Learn more here:
https://brainly.com/question/12834805
Find the sum of 5x + 6 and -11x - 9
solve the equation 5/x+3 + 4/x+2 = 2
Answer:
5 + 4 = 9
x × x = X2
3 + 2 = 5
9/x + 5 = 2
Answer:
5/x+3+4/x+2=2
=9/x+5=2
9/x=-3
Multiply both sides by x
9= -3x
Divide by -3
Answer x= -3
Hope this helps
An aircraft factory manufactures airplane engines. The unit C(the cost in dollars to make each airplane engine) depends on the number of engines made. If x engines are made , then the unit cost is given by the function C (x) = 0.9x^2-306x+34,590. What is the minimum unit cost?
If an item is $6.49 for 36 ounces, then it is $
Answer:
0.18
Step-by-step explanation:
i'll mark brainliest, thanks in advance!
Answer:
not enough information.
Step-by-step explanation:
We know one side and the vertical angle. We do not have enough information to determine if the triangles are congruent.
40 out of 50 birds are female. total number of birds is 1,120, how many of them would be female
Answer:
896
Step-by-step explanation:
40/50 = 80%
80% of 1120 is 896
If i have a silver necklece at the price of 26 $ and its 50 percent of what was the orginal price.
50%=100%/2
26*2 = 52
Original price is 52 dollas
Answer:
52
Step-by-step explanation:
please mark brainlest
no link no bot right please
Answer:
27pi in^3
Step-by-step explanation:
the volume for a cone is (1/3)pi*r^2*h. r=3in, h=9in. so the volume is (1/3)*pi*3^2*9=27pi
An experiment is given together with an event. Find the (modeled) probability of each event, assuming that the dice are distinguishable and fair, and that what is observed are the numbers uppermost.
Two dice are rolled; the numbers add to 11.
Answer:
A woman wants to measure the height of a nearby building. She places a 7 ft pole in the shadow of the building so that the shadow of the pole is exactly covered by the shadow of the building. The total length of the building's shadow is 184 ft, and the pole casts a shadow that is 5.5ft long. How tall is the building? Round your answer to the nearest foot. (The figure is not drawn to scale.)
Step-by-step explanation:
A woman wants to measure the height of a nearby building. She places a 7 ft pole in the shadow of the building so that the shadow of the pole is exactly covered by the shadow of the building. The total length of the building's shadow is 184 ft, and the pole casts a shadow that is 5.5ft long. How tall is the building? Round your answer to the nearest foot. (The figure is not drawn to scale.)A woman wants to measure the height of a nearby building. She places a 7 ft pole in the shadow of the building so that the shadow of the pole is exactly covered by the shadow of the building. The total length of the building's shadow is 184 ft, and the pole casts a shadow that is 5.5ft long. How tall is the building? Round your answer to the nearest foot. (The figure is not drawn to scale.)
helppppppppp
what is -12x<60
Answer:
x > -5
Step-by-step explanation:
-12x < 60
To solve the equation for x, we want x to be by itself on one side. Let's start by dividing both sides by -12:
-12x/-12 < 60/-12
When dividing or multiplying by a negative number, we have to turn around the inequality sign, so now we have:
x > 60/-12
And 60/-12 = -5, so:
x > -5
A recipe for pasta dough says, “Use 150 grams of flour per large egg.”
How much flour is needed if 6 large eggs are used?
How many eggs are needed if 450 grams of flour are used?
Answer:
1. 900 grams
2. 3 eggs
Step-by-step explanation:
1. 150 x 6 = 900
2. 450 / 150 = 3
Answer:
900 grams of flour are needed if six eggs are used. 3 eggs are needed if 450 grams of flour are used.
Step-by-step explanation:
First, multiply the number of large eggs by grams per large egg: 150×6=900
Next, divide the number of grams of flour by grams per large egg: 450/150=3
Select the correct answer.
Which point is a reflection of T(-6.5, 1) across the x-axis and the y-axis?
A. point U
B. point V
C. point W
D. point X
Answer:
the answer is A. point U
or it's point W
A baseball pitcher has made 53 pitches in the first four innings of a baseball game and plans to pitch 3 mote innings. The manager of the team has committed to allowing his pitcher to throw, at most, pitches during the game. Write an inequality to find the average number of pitches the pitcher can throw over the next three innings Solve the inequality from Part 1. What is the maximum number of pitches the pitcher can make in cach of the next 3 innings ? Graph your solution from Part 2 on a number line and explain what your solution means. If the pitcher threw just 6 pitches in the fifth inning, what is the greatest number of pitches the pitcher can throw per inning he wishes to pitch nine innings? Write and solve an inequality to answer this part.
Answer:
at most 17 pitches per inning
Step-by-step explanation:
It is given that a baseball pitcher makes 53 pitches in the first 4 innings of a game and plans to pitch in the next 3 innings.
We need to write and solve an inequality to find the possible average pitches per inning the pitcher made in the next 3 innings if the pitcher is assigned a maximum of 105 pitches.
From part (a) we know 3 p + 53 3p+53 represents the total number of pitches made if the pitcher makes an average of p pitches per inning in the next 3 innings.
If the pitcher can make at most 105 pitches, then:
3 p + 53 ≤ 105 3p+53≤105
To solve the inequality, first subtract 53 on both sides of the inequality to isolate the variable term:
3 p + 53 − 53 ≤ 105 − 53 3 p ≤ 53
3p+53≤105 [tex]p\leq 17\frac{1}{3}[/tex]
at most 17 pitches per inning
(Hope this helps can I pls have brainlist (crown)☺️)
help 1234567891011121314151617181920
Solve the given equation. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to three decimal places where appropriate).
4 sin(2θ) − 2 sin(θ) = 0
Answer:
θ = πk, 1.318+2πk, 4.965+2πk
Step-by-step explanation:
4sin(2θ) − 2sin(θ) = 0
8sin(θ)cos(θ) - 2sin(θ) = 0
2sin(θ)[4cos(θ)-1] = 0
2sin(θ) = 0
sin(θ) = 0
θ = πk
4cos(θ)-1 = 0
4cos(θ) = 1
cos(θ) = 1/4
θ ≈ 1.318+2πk, 4.965+2πk
Therefore, θ = πk, 1.318+2πk, 4.965+2πk
Is this statement true or false:
a - b = b - a
True
False
Answer:
False
Step-by-step explanation:
positive A and negative B does not equal positive B and negative A
Answer:
FALSE
Step-by-step explanation:
Marking as brainliest rn ! Write the congruent statement
Answer:
Same thing here as the last question, just matching congruent angles.
1. ΔXZY ≅ ΔQRP
2. ΔQRS ≅ ΔSCD
3. ΔGHI ≅ ΔGHT
Step-by-step explanation:
hope this helps. . .<3
good luck! UwU
Answer:
1.) ΔXZY ≅ ΔQRP
2.) ΔQRS ≅ ΔSCD
3.) ΔGHI ≅ ΔGHT
Hope this helps!
f(x)=ax^2 +bx +c solve: heigh 275 width 290
Answer:
800 i think
Step-by-step explanation:
What is the equation in point-slope form of a line that passes through the points (−4, −1) and (5, 7) ?
y−1=8/9(x−4)
y+1=8/9(x+4)
y+4=9/8(x+1)
y+1=8/7(x+4)
Answer:
y+1=8/9(x+4)
Step-by-step explanation:
Tell me if you want one!
Last month 288 people attended the monthly bingo night. This month 243 people attended bingo night. To the nearest tenth of a percent, what is the percent decrease in attendance from last month to this month? Enter your answer as a decimal in the box. %
Answer:
15.625
Step-by-step explanation:
old number = 288
new number = 243
percent decrease = (old - new / new ) * 100
= (288 - 243 / 288) * 100
= 45 / 288 * 100
= 15.625
Answer:
15.6 (rounded)
Step-by-step explanation:
I took the test
Someone pls help me with these worksheets >.<
(Please answer properly, if u don't know, just ignore so someone who knows can answer)
Answer:
gsdddddddddddddddddddddddddddd
Step-by-step explanation:
Peter Morris wants to verify the amount
deposited to his savings account. His new balance is $729.49,
his previous balance was $680.50, interest earned on his
account was $3.25, and withdrawals totaled $222.06. Find the
amount deposited to his savings account.
Answer:324.24??? Not sure just a guess.
Step-by-step explanation:
Consider the functions f(x) and g(x). The function f(x)=2x-5 and g(x)= -f(x+1)+3. Describe the three transformations that are performed on f(x) to create g(x).
A.
1.
2.
3.
B. Sketch a graph of g(x):
Answer: 3
Step-by-step explanation:
what is the measure of line CD. explain
Number of Bars
1
Analyze A store sells variety packs
of granola bars. The table shows
the types of bars in each pack.
Mason says that for every 7 bars in
a pack, there is 1 cinnamon bar.
Do you agree? Explain.
Type
Cinnamon:1
Honey:4
Peanut Butter:3
Answer: Disagree. 1 in 8 bars are cinnamon.
Step-by-step explanation:
There are a total of 8 bars in the pack. Cinnamon is 1 of the 8. Therefore, for every 8 bars, one is cinnamon.