Simplification of Algebraic Expression.
[tex]\begin{gathered} (1+2i)(5-3i) \\ \text{First, we clear the brackets. } \\ 1(5-3i)\text{ +2i(5 - 3i)} \\ \text{Multiplying through the brackets, we get} \\ 5\text{ -}3i+10i-6(-1) \\ \text{Note: i}^2=\text{ -1} \\ 5\text{ -3i + 10i +6} \\ C\text{ollecting like terms, we get} \\ 5\text{ + 6 -3i + 10i} \\ 11\text{ +7i} \end{gathered}[/tex]Thus, the correct answer is 11 +7i ( option D )
Translate the word sentence into a number sentence5. One thousand is less than a number6. A number is greater than four-fifths7. Five and nine tenths is greater than or equal to a number8. A number is not equal to twelve hundredths 9. Eight plus four is not equal to eleven10. The sum of twelve and five is greater than a number
To translate "One thousand is less than a number" into a number, we can divide the sentence in three parts.
One thousand is less than a number
a b c
Let's translate each part:
(a) One thousand
We have to write the equivalent number: 1000.
(b) is less than
The symbol that represents it is <.
(c) a number
Since we do not know this number, let's assume it is x.
Now, we can put the parts together and write the number sentence.
1000 < x.
Answer: One thousand is less than a number is the same as 1000 < x.
The fire department is having a BBQ fundraiser. The hot dogs costs $1.50 each and cans ofsoda cost $0.75 each. The department uses the algebraic expression 1.50x+0.75y to calculatecustomers' total expenses.a. What does the x variable represent?b. What does the y variable represent?c. A family buys 7 hot dogs and 4 sodas. What are their total expenses?
a) As the expression represents the total expense for a family, the term 1.50x represents how much the familiy spends in hot dogs.
This term is the product of the price (1.50) and the number of hot dogs purchased (x).
Then, x is the number of hot dogs bought by the familiy.
b) In the same way, 0.75y represent how much the family spends in soda: 0.75 is the price and y represents the number of soda cans purchased by the family.
c) If a family buys x=7 hot dogs and y=4 sodas, we can calculate the expenses as:
[tex]\begin{gathered} E=1.50x+0.75y \\ E=1.50\cdot7+0.75\cdot4 \\ E=10.5+3 \\ E=13.5 \end{gathered}[/tex]Their total expenses are $13.5.
What is the slope of the line through (-1, -7) and (3,9)? Choose 1 answerA. -1/4B. -4C. 4D. 1/4
Answer:
C. 4
Explanation:
Given the line that passes through points (-1,-7) and (3,9):
[tex]\begin{gathered} \text{Slope},m=\frac{Change\text{ in y-axis}}{Change\text{ in x-axis}} \\ =\frac{9-(-7)}{3-(-1)} \\ =\frac{9+7}{3+1} \\ =\frac{16}{4} \\ =4 \end{gathered}[/tex]The slope of the line is 4.
The correct choice is C,
Graph two full periods, highlighting the first period using bold marking and analyze each function.Y = 2 sin (1/2 (x + pi/2) ) + 1
Given
[tex]y=2\sin(\frac{1}{2}(x+\frac{\pi}{2}))+1[/tex]
Procedure
Period: 4pi
Interval length: In the graph 2 periods 8pi
Phase shift: -pi/2
1st Per. begins: -pi/2
1st Per. ends: 7pi/2
Amplitude: 2
Domain:
(-∞, ∞)
Range:
[-1,3]
y-intercep:
(0,2.414)
x-intercept:
[tex]x=\frac{11\pi}{6}+4\pi n,\frac{19\pi}{6}+4\pi n,\text{ for any integer of n }[/tex]x-(7.65 + 3.18)=4 solve for x
Answer:
The value of x is;
[tex]x=14.83[/tex]Explanation:
Given the equation;
[tex]x-(7.65+3.18)=4[/tex]Solving for x;
[tex]\begin{gathered} x-(10.83)=4 \\ x=4+10.83 \\ x=14.83 \end{gathered}[/tex]Therefore, the value of x is;
[tex]x=14.83[/tex]what is 2*2?i dont know i in pweschool
2 x 2 is two times two
answer: 4
Solve for X Geometry, Just need a quick over view!
The value of X = 11
Step - by - Step Explanation
What to find? The value of x
To find the value of X, take the ratio of the sides.
[tex]\frac{2x+6}{32}=\frac{52.5}{60}[/tex]Cross -multiply.
[tex]60(2x+6)=52.5(32)[/tex][tex]60(2x+6)=1680[/tex]Divide both-side of the equation by 60.
[tex]\frac{\cancel{60}(2x+6)}{\cancel{60}}=\frac{1680}{60}[/tex]2x + 6 = 28
Subtract 6 from both-side of the equation.
2x + 6 - 6 = 28 - 6
2x =22
Divide both-side of the equation by 2.
[tex]\frac{\cancel{2}x}{\cancel{2}}=\frac{22}{2}[/tex]x = 11
Hence, the value of X = 11
Convert y+5=-(x+2) to the slope-Intercept (don’t put any spaces between numbers, variables, signs, or parentheses)
Given:
[tex]y+5=-(x+2)[/tex]Required:
To find the slope-Intercept form of the given equation.
Explanation:
We know that, the slope intercept form can be represented as
[tex]y=mx+b[/tex]Therefore, the given equation can be written as
[tex]\begin{gathered} y+5=-(x+2) \\ y+5=-x-2 \\ y=-x-2-5 \\ y=-x-7 \end{gathered}[/tex]Final Answer:
The slope-Intercept form of the given equation is
[tex]y=-x-7[/tex]what isk + 6 greater than or equal to 19, if k = 11
what is
k + 6 greater than or equal to 19, if k = 11
we have
[tex]\begin{gathered} k+6\ge19 \\ k\ge19-6 \\ k\ge13 \end{gathered}[/tex]For k=11
we have
[tex]\begin{gathered} 11+6\ge19 \\ 17\ge19\text{ ----}\longrightarrow\text{ is not true} \\ \text{that means-}\longrightarrow\text{ the value of k is not a solution of the inequality} \end{gathered}[/tex]Lincoln Middle School plans to collect more than 2,000 cans of food in a food drive. So far, 668 cans have been collected. Write and solve an inequality to find numbers of cans the school can collect on each of the final 7 days of the drive to meet this goal.Which inequality represents the solution to this situation?
Inequalities
Let's call c the number of cans of food.
The school wants to collect more than 2,000 cans in a food drive.
668 cans have been collected so far.
The number of cans needed to reach the goal is 2,000 - 668.
These cans will be collected in 7 days, thus:
7c > 2,000 - 668
Operating
7c > 1,332
Dividing by 7:
c > 1,332 / 7
c > 190.29
This is the average number of cans needed to collect each day.
The first choice is correct
which statement is the contrapositive of the given statement statement if you play a sport then you wear a helmet
We will have that the contrapositive statement is:
*If you do not wear a helmet, then you do not play a sport.
u want to construct an open-top box that is 6 inches deep, with a square base. it must have a volume of 864 cubic inches. You have one big piece of cardboard. You will start by cutting it down to a square, and then you will cut smaller squares out of each corner and fold up the sides.
Let's analyse each sentence:
A)
This sentence is true, because the volume of the box is given and it is 864 in³.
B)
This sentence is false, because the height of the box is given and it is 6 inches.
C)
Let's calculate the sides of the base, knowing that the length and width are the same:
[tex]\begin{gathered} V=\text{lwh} \\ 864=l\cdot l\cdot6 \\ l^2=\frac{864}{6} \\ l^2=144 \\ l=^{}12 \end{gathered}[/tex]The side of the cardboard will include the length of the base and two times the height, since it will be folded later on, so we have:
[tex]\text{cardboard side}=l+2h=12+6\cdot2=24[/tex]So the side of the cardboard needs to be 24 inches, so this sentence is false.
D)
This sentence is false, because the height is not equal the length and width.
E)
This sentence is true, because using the variable x to represent the side of the square base (that is, the length and the width), we have:
[tex]\begin{gathered} V=l\cdot w\cdot h \\ V=6x^2=864 \end{gathered}[/tex]So the correct statements are A and E.
Find the domain of f(x) = 3x/x-1 and discuss the function behavior of f near any excluded x-values.
The domains are all real numbers except the the values that makes the denominator zero
x - 1 = 0
x=1
That is; the domain is all real numbers except x=1
A class of 20 students wants to form a committee to fundraise for cancer research. If the committee is formed with four students, how many possible committees can be made?A: 116,280B: 24C: 4,845D: 9,690
1) Since there are 20 students, and each committee is formed by 4 people.
The order does not matter, and there can't be repetition. Just one person can be, let's say president, VP, secretary, and treasurer.
2) So we can write, the possibilities on the numerator of people filling in and on the denominator the number of vacancies for that committee, we can set this Combination simply as:
[tex]\frac{20}{4}\times\frac{19}{3}\times\frac{18}{2}\times\frac{17}{1}=4845[/tex]3) So there are 4845 possibilities to form a Committee with 20 people for 4 vacant lots.
Find the unknown value in the proportion. Round to the nearest tenth if needed. 4/3=12/?
Starting with the proportion:
[tex]\frac{12}{?}[/tex]Since it should be equal to 4/3, notice that if we divide both numerator and denominator by 3, then we should get 4 and 3 respectively:
[tex]\frac{12}{?}=\frac{12\div3}{?\div3}=\frac{4}{?\div3}=\frac{4}{3}[/tex]Therefore, ?÷3 is equal to 3.
Which number is equal to 3 when we divide it by 3?
That number is 9. 9÷3=3
Therefore, ?=9.
You put $400 in an account. The account earns $32 simple interest in 2 years what is the annual interest rate?
Answer
4 %
Explanation
Given:
Principal, P = $400
Interest, I = $32
Time,T = 2 years
What to find:
Annual interest rate, R
Step-by step solution:
The simple interest formula is given by:
[tex]I=\frac{\text{PRT}}{100}[/tex]Substituting P = 400, I = 32, and T = 2 into the formula:
[tex]\begin{gathered} 32=\frac{400\times R\times2}{100} \\ 800R=3200 \\ R=\frac{3200}{800} \\ R=4\text{ \%} \end{gathered}[/tex]matthew worked 20 hours ar $10 a hour. Taxes were 12%. How much money was left?
Step 1. calculate the totay pay (not including taxes)
Since he worked 20 hours with an hourly pay of $10, the total was:
[tex]20\times10=200[/tex]Step 2. Calculate the taxes
We need to calculate the 12% of $200, to find the amount that he paid in taxes. For this, we divide $200 by 100 and multiply by 12%:
[tex]\frac{200}{100}\times12[/tex]solving this operations we get:
[tex]\frac{200}{100}\times12=24[/tex]He paid $24 in taxes
Step 3. Calculate the remaining amount
We substract $24 from the initial total amount $200:
[tex]200-24=176[/tex]Answer:
How much money was left? $176
25. A group of students were asked how many movies they had watched the previous week. The results are shown below.Number of MoviesFrequency0818253547Find the mean and median for the number of movies watched per student. Round your answers to the nearest hundredth.Mean = Median =
Answer:
Explanation:
Given the results of the number of movies watched by the group of students and the frequency, we're asked to determine the mean and median for the number of movies watched per student.
We'll follow the below steps to solve for the mean and median;
1. Find the product of the number of movies and frequency;
[tex]\begin{gathered} 0\times8=0 \\ 1\times8=8 \\ 2\times5=10 \\ 3\times5=15 \\ 4\times7=28 \end{gathered}[/tex]2. Find the sum of the product of the number of movies and frequency;
[tex]0+8+10+15+28=61[/tex]3. Find the sum of the frequency;
[tex]8+8+5+5+7=33[/tex]The mean can now be determined using the below formula;
[tex]\begin{gathered} \text{Mean}=\frac{\Sigma(f\cdot x)}{\Sigma f} \\ \text{where} \\ \Sigma(f\cdot x)=\text{ sum of the product of the number of movies and frequency} \\ \Sigma f=\text{ sum of the frequency} \end{gathered}[/tex]Therefore, our mean is;
[tex]\text{Mean}=\frac{61}{33}=1.85[/tex]We can go ahead and determine the median using the below formula;
[tex]undefined[/tex]An empty tank is filled with water at a constant rate
Answer: D
Step-by-step explanation:
D is the answer because if you divide w by m, you get 16.5. Therefore 16.5 is the constant rate.
Find three consecutive odd integers that add to - 99
We will investigate how three consecutive odd numbers add up to a certain value.
We will assign a variable to the first odd number as follows:
[tex]1st\text{ : x}[/tex]The next consecutive odd number will occur two integers ahead or two integers before the first odd number. We can choose either ( ahead or before ) and express second consecutive odd number in terms of first odd number as follows:
[tex]2nd\colon\text{ ( x + 2 ) OR ( x - 2 )}[/tex]Similarly, the next consecutive odd number will occcur two integers ahead or two integer before the second odd number OR four integers ahead of for integers before the first odd number. We can choose either ( ahead or before ) and express the third consecutive odd number in terms of first or second odd number as follows:
[tex]3rd\colon\text{ ( x + 4 ) OR ( x - 4 )}[/tex]We will now sum up all three consecutive odd numbers and equate the result to ( -99 ) as follows:
[tex]\begin{gathered} (\text{ x ) + ( x + 2 ) + ( x + 4 ) = -99} \\ OR \\ (\text{ x ) + ( x - 2 ) + ( x - 4 ) = -99} \end{gathered}[/tex]Then we will solve both possibilities step by step.
[tex]\begin{gathered} 3x\text{ + 6 = -99} \\ OR \\ 3x\text{ - 6 = -99} \\ \end{gathered}[/tex]Then,
[tex]\begin{gathered} 3x\text{ = -105} \\ OR \\ 3x\text{ = -93} \end{gathered}[/tex]Next,
[tex]\begin{gathered} x\text{ = }\frac{-105}{3}\text{ = -35} \\ \\ OR \\ \\ x\text{ = }\frac{-93}{3}\text{ = -31 } \end{gathered}[/tex]For each possibilitiy the three consecutive odd numbers would be:
[tex]\begin{gathered} x\text{ = -35 , x + 2 = -33 , x + 4 = -31} \\ OR \\ x\text{ = -31 , x - 2 = -33 , x - 4 = -35} \end{gathered}[/tex]We see that both possibilities result in identical three consecutive odd numbers that would add up to a total of ( -99 ). Therefore, the three consecutive odd numbers are:
[tex]-31\text{ , -33 , -35 }\ldots\text{ Answer}[/tex]
what is 1/5 turned into a percent
7x +4 for x =9 The solution is ?
The volume of the tent is 576 cubic feet and the area of the base is 36 square feet. what is the height of the tebt
The volume of a triangular prism is: B*h. Where B is the area and h is the height.
Replacing the values in the equation we have:
V = B*h
576 = (36)*h
576/36 = h (Dividing by 36 on both sides of the equation)
16 = h (Dividing)
The answer is 16 ft.
In the gift shop of the History of Flight museum, Elisa bought a kit to make a model of a jet airplane. The actual plane is 18 feet long with a wingspan of 13.5 feet. If the finished model will be 10 inches long, what will the wingspan be?
3.75 in.
7.5 in.
24.3 in.
13.3 in.
Answer:
The answer is 24.3
Step-by-step explanation:
hope this helps you
What is the slope of the line containing (-2,5) and (4,-4)?A.3/2B.-3/2C. -2D. 2
Answer:
B.-3/2
Step-by-step explanation:
To find the slope, we need to take two points from a line. I am going to call them:
(x1,y1) and (x2,y2).
The slope is:
[tex]a=\frac{y2-y1}{x2-x1}[/tex]In this question:
(x1,y1) = (-2,5)
(x2,y2) = (4, -4)
So
[tex]a=\frac{y2-y1}{x2-x1}=\frac{-4-5}{4-(-2)}=\frac{-9}{4+2}=-\frac{9}{6}=-\frac{3}{2}[/tex]So the correct answer is:
B.-3/2
in this work today in my class want to know if am right 5w+2p for w=6 and p=2 evaluate this
Solution
For this case we have the following expression given:
5w +2p
And we have that w= 6 and p= 2
And replacing we got:
5*6 + 2*2
30 + 4= 34
• The function (x) is a transformation of the square root parent function,f(x) = V. What function is h(x)?5nuA. h(x) = v=-4B. h(c) = V - 4O C. h(z) = y +4D. h(x) = 1 + 4
we are given the following function:
[tex]f(x)=\sqrt[]{x}[/tex]The graph of h(x) is the same graph translated 4 units to the left, therefore it must be:
[tex]h(x)=f(x+4)[/tex]Replacing x for x + 4 in f(x) we get:
[tex]h(x)=f(x+4)=\sqrt[]{x+4}[/tex]Which set of parametric equations represents the function y=x^2+4x-5? Select all that apply.
Solution
- The way to solve the equation is to take the expression for x i.e. x = 2t, and substitute into the expression for y(x).
- The result must be the corresponding y-value in terms of t.
- This is done below:
Option A:
[tex]\begin{gathered} x=2t \\ y(x)=x^2+4x-5 \\ \\ \text{ put }x(t)=2t \\ \\ y(x(t))=(2t)^2+4(2t)-5 \\ y(x(t))=y(t)=4t^2+8t-5 \\ \\ \therefore y(t)=4t^2+8t-5\text{ \lparen OPTION A\rparen} \end{gathered}[/tex]Option B:
[tex]\begin{gathered} x=t+1 \\ y=x^2+4x-5 \\ \\ y(x(t))=y(t)=(t+1)^2+4(t+1)-5 \\ t^2+2t+1+4t+4-5 \\ y(t)=t^2+6t\text{ \lparen NOT IN THE OPTIONS\rparen} \end{gathered}[/tex]Option C:
[tex]\begin{gathered} x=t-3 \\ y=x^2+4x-5 \\ \\ y(x(t))=(t-3)^2+4(t-3)-5 \\ =t^2-6t+9+4t-12-5 \\ =t^2-2t-8\text{ \lparen NOT IN THE OPTIONS\rparen} \end{gathered}[/tex]Option D:
[tex]\begin{gathered} x=t^2 \\ y=x^2+4x-5 \\ \\ y(x(t))=(t^2)^2+4(t^2)-5 \\ =t^4+4t^2-5\text{ \lparen NOT IN THE OPTIONS\rparen} \end{gathered}[/tex]Option E:
[tex]\begin{gathered} x=t+1 \\ y=x^2+4x-5 \\ \\ y(x(t))=(t+1)^2+4(t+1)-5 \\ =t^2+2t+1+4t+4-5 \\ =t^2+6t\text{ \lparen OPTION E IS CORRECT\rparen} \end{gathered}[/tex]Final Answer
The answers are OPTIONS A AND E
2 Which cookie is the better deal? Oreos $2.98 for 15.5 oz O $ Chips Ahoy $2.50 for 14oz 2b-What is the Unit Price for the better deal? Round to the nearest hundredth) Put your answer in the form 0.00 or .00, so if answer is 43 cents, its 0,43 or.43, if there is a dollar amount like 1.50, do not add zeros in front) Your answer
Chips ahoy $0.18 per oz.
1) Let's write it down, since the point here is what's the best deal we need to find out the unit rate for each one. Let's set a proportion:
$2.98 ----------- 15.5 oz
x -------------- 1 oz
Cross multiplying it:
15.5x = 2.98 * 1 Divide both sides by 15.5
x= 0.192
So $0.19 per oz.
Chips Ahoy:
$2.50------------14 oz
y --------------1
14y= 2.50
y=0.1785 rounding it to the nearest hundredth 0.18
Then $0.18 per oz
So the better deal, is buying Chips Ahoy.
Elena is organizing her craft supplies. She estimatesthat her jars will fit 1,000 buttons or 50 large beads.They actually fit 677 buttons or 22 large beads. DoesElena's estimate about the buttons or her estimateabout the large beads have less percent error? To thenearest percent, how much less?
Step 1
Given;
[tex]\begin{gathered} Elena-\text{ estimates her jar will take 1000 buttons or 50 large beads} \\ Her\text{ Jar actually takes 677 buttons or 22 large beads} \end{gathered}[/tex]Required; To find if Elena's estimates have percentage error, to which percent, and how much less
Step 2
State the formula for percentage error
[tex]\text{ \% error=}\frac{|Approximate-exact|}{exact}\times100[/tex][tex]Elena^{\prime}s\text{ estimate about the button has a percentage error }[/tex][tex]\begin{gathered} For\text{ buttons} \\ Approximate=1000 \\ Exact=677 \end{gathered}[/tex][tex]\text{ \%error=}\frac{|1000-677|}{677}\times100=47.71048744\text{\%}[/tex][tex]\begin{gathered} For\text{ large beads} \\ \operatorname{\%}\text{error=}\frac{\text{\lvert50-22\rvert}}{22}\times100 \end{gathered}[/tex][tex]\text{ \% error=}\frac{28}{22}\times100=127.272727...\text{\%}[/tex]Percent errors tells you how big your errors are when you measure something in an experiment. Smaller values mean that you are close to the accepted or real value. For example, a 1% error means that you got very close to the accepted value, while 45% means that you were quite a long way off from the true value.
The percentage error for buttons with about 47.71% is less than that of the large beads which is about 127.273%.
How much less of the percentage error to the nearest percent will be;
[tex]\begin{gathered} =79.56223986 \\ \approx80\text{\%} \end{gathered}[/tex]