Solution:
Given the expression:
[tex](12-6i)(3-10i)[/tex]To simplify in the form:
[tex]a+bi[/tex]step 1:
Multiply the terms in the second parenthesis by each term in the first parenthesis.
Thus,
[tex]\begin{gathered} 12(3-10i)-6i(3-10i) \\ \Rightarrow36-120i-18i+60i^2 \end{gathered}[/tex]step 2:
Collect like terms.
[tex]\begin{gathered} 36-120i-18i+60i^2 \\ \text{but } \\ i^2=-1 \\ \text{thus,} \\ 36+60(-1)-120i-18i \\ \Rightarrow36-60-120i-18i \\ =-24-138i \\ \Rightarrow-24+(-138)i \end{gathered}[/tex]Hence, the expression is simplified as
[tex]-24+(-138)i[/tex]In the group of ordered pairs shown, the x-values are inputs and the y-values are outputs. Select all the statements that are true.
(2, 4), (6, 3), (5, 4), (7, 3), (8, 2)
A. There is only one input for every output.
B. There is only one output for every input.
C. There is more than one output for some inputs.
D. There is more than one input for some outputs.
E. The group of ordered pairs represents a function.
Since in this group of ordered pairs shown above, the x-values are inputs and the y-values are outputs, all the statements that are true include the following:
A. There is only one input for every output.
B. There is only one output for every input.
What is an ordered pair?An ordered pair can be defined as a pair of two (2) elements or points that are commonly written in a fixed order within parentheses as (x, y), which represents the x-coordinate or x-axis (abscissa) and the y-coordinate or y-axis (ordinate) on the coordinate plane of any graph.
Generally speaking, the values on the x-coordinate or x-axis (abscissa) of any graph represents all of the input values while the values on the y-coordinate or y-axis (ordinate) of any graph represents all of the output values.
In this context, we can reasonably and logically deduce that there is a unique input for every output and a unique output for every input.
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The following data are the ACT score of all student in the history class
The frequency means how many times specific data shows up in a set of values.
Score Frequency
1-6 2
7-12 4
13-18 5
...
And so on.
What is an equivalent expression to 20x - 45y
Equivalent linear expressions are expressions that have the same value. That is, if you have two linear expressions that are equivalent to one another, and you plug the same value in for the variable in each of them, you will get the same result in each of them.
In the case of this question, the equaivalent expression can be gotten by factorizing the expression
[tex]undefined[/tex]Peter's farm has 160 meters of fencing, and he wants to fence a rectangular field thatborders a straight river. He needs no fence along the river side. Find the largest areaof Peter's farm that can be fenced.
ANSWER
3200 m²
EXPLANATION
Peter wants to build a fence around a rectangular field, except for one side because the river is there,
So, the total perimeter of the fence is,
[tex]P=W+W+L=2W+L[/tex]And this is equal to 160 m. Solving for L,
[tex]160=2W+L\text{ }\Rightarrow\text{ }L=160-2W[/tex]The area of this field is,
[tex]A=WL[/tex]Replace L with the expression we found from the perimeter,
[tex]A=W(160-2W)=160W-2W^2[/tex]The area is given by a quadratic function whose leading coefficient is negative, which means that the graph is a downward parabola and, therefore, the vertex is the maximum value of the area.
The x-coordinate of the vertex is given by,
[tex]f(x)=ax^2+bx+c\text{ }\Rightarrow\text{ }x_{vertex}=\frac{-b}{2a}[/tex]In this case, x is W, a = -2, and b = 160, so the width of the field for the maximum area is,
[tex]W_{vertex}=\frac{-160}{2(-2)}=\frac{160}{4}=40m[/tex]And the length when W = 40 is,
[tex]L=160-2W=160-2\cdot40=160-80=80m[/tex]And the area is,
[tex]A=WL=40m\cdot80m=3200m^2[/tex]Hence, the largest area of Peter's farm that can be fenced is 3200 square meters.
PLEASEEEEEEEE HELPPP
If Greg has 1 1/2 servings of cereal for breakfast each day, he can consume 8 breakfasts from a box of cereal.
The price of one breakfast from a regular-sized box of cereal is $0.54 if the box costs $4.29.
Greg could consume 4 additional breakfast portions from a single family-sized box.
How to find unit rate of Greg's breakfast?A regular-sized box of cereal = 12 servings
If Greg eats 1 1/2 servings for breakfast every day
Number of breakfast Greg can eat in a regular-sized box = A regular-sized box of cereal / servings of breakfast eaten everyday
= [tex]\frac{12}{\frac{11}{2} }[/tex]
=[tex]\frac{12}{\frac{3}{2} }[/tex]
multiply by the reciprocal of [tex]\frac{3}{2}[/tex]
= 12 × [tex]\frac{2}{3}[/tex]
= [tex]\frac{24}{3}[/tex]
= 8 breakfast
Cost of regular-sized box of cereal = $4.29.
Cost of one breakfast from a regular-sized box of cereal = Cost of regular-sized box of cereal ÷ Number of breakfast Greg can eat in a box
= [tex]\frac{4.29}{8}[/tex]
= 0.53625
Approximately,
$0.54 per breakfast
If Greg purchased the family-sized box of cereal that contains 18 servings
Family-sized box of cereal divided by the daily serves of breakfast is the number of breakfasts Greg can consume.
= 18 servings / [tex]\frac{11}{2}[/tex]
= 18 ÷[tex]\frac{3}{2}[/tex]
= 18 × [tex]\frac{2}{3}[/tex]
= [tex]\frac{36}{3}[/tex]
= 12 servings
Consequently, the number of additional breakfasts Greg may consume from a single family-sized package
= Number of breakfast Greg can eat in a family-sized box - Number of breakfast Greg can eat in a regular-sized box
= 12 servings - 8 servings
= 4 servings
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Mrs. long bought 4 types of fruits at the market. she bought 2 cantaloupes that weighed 2.3 pounds each 6 peaches that weighed a total of 1.7 pounds 4 apples that weighed a total of 1.25 pounds and 3 pounds and 3 pounds of grapes. what was the total weigh of the four fruits she bought?
Mrs. long bought 4 types of fruits at the market:
- 2 cantaloupes that weighed 2.3 pounds each:
that is, a total of 2.3x2 = 4.6
- 6 peaches that weighed a total of 1.7 pounds.
- 4 apples that weighed a total of 1.25 pounds.
- and 3 pounds of grapes.
The total weight of the four fruits is:
4.6 + 1.7 + 1.25 + 3 = 10.55 pounds.
The area of a trapezoid is given by the formula A = (a + b). Solve the formula for b.
Starting from the given formula:
[tex]A=\frac{h}{2}(a+b)[/tex]Multiply both sides of the equation by 2:
[tex]\begin{gathered} \Rightarrow2\times A=2\times\frac{h}{2}(a+b) \\ \Rightarrow2A=h(a+b) \end{gathered}[/tex]Divide both sides by h:
[tex]\begin{gathered} \Rightarrow\frac{2A}{h}=\frac{h(a+b)}{h} \\ \Rightarrow\frac{2A}{h}=a+b \end{gathered}[/tex]Substract a from both sides of the equation:
[tex]\begin{gathered} \Rightarrow\frac{2A}{h}-a=a+b-a \\ \Rightarrow\frac{2A}{h}-a=b \end{gathered}[/tex]Therefore:
[tex]b=\frac{2A}{h}-a[/tex]HELP ASAP
Solve 21 ≤ −4z − 21.
z ≤ −10.5
z ≥ −10.5
z ≤ 0
z ≥ 0
[tex]21 + 21 \leqslant - 4z \\ - 4z \geqslant 42 \\ \frac{ - 4z}{ - 4} \geqslant \frac{42}{ - 4} \\ z \leqslant - 10.5[/tex]
ATTACHED IS THE SOLUTION
BE AWARE THE SIGNS <> ONLY CHANGE SIGN WHEN YOU MULTIPLY OR DIVIDE BY A NEGATIVE NUMBER.
A relationship between two expressions or values that are not equal to each other is called 'inequality. Z≤ -10.5 is the solution for inequality 21 ≤ −4z − 21.
What is Inequality?A relationship between two expressions or values that are not equal to each other is called 'inequality.
The given inequality is twenty one lesser or equal to minus four z minus twenty one.
21 ≤ −4z − 21.
We need to solve for z
Let us add twenty one on both sides
21+21≤ −4z − 21+21
42≤ −4z
Divide both sides by 4
10.5≤ -Z
-10.5≥Z
Z≤ -10.5
Hence Z≤ -10.5 is the solution for inequality 21 ≤ −4z − 21.
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help plwsty Graph the equation: y-1 = 2/3(x-3)?
The given expression : y-1=2/3(x-3)
Simplify the equation :
[tex]\begin{gathered} y-1=\frac{2}{3}(x-3) \\ y=\frac{2}{3}x-\frac{2}{3}(3)+1 \\ y=\frac{2}{3}x-2+1 \\ y=\frac{2}{3}x-1 \end{gathered}[/tex]for the graph we need atleast two coordinates
Let at x=0 then
y=2/3(0)-1
y=-1
Cooridnate = (0,-1)
Now, let x=9 then
y=2/3(9)-1
y=2(3)-1
y=5
Coordinate =(9,5)
Plot these point (0,-1) & (9,5)on the graph and join them by staright line
The graph will be ;
Jaylen's beta fish holds 4 1/2 gallons of water. It takes him 1 7/8 minutes to fill. What is the flow rate of the water in gallons per minute? show your work.
Let's begin by listing out the information given to us:
Jaylen's beta volume = 4 1/2 gallons = 4.5 gal
Time taken = 1 7/8 minutes = 1.785 min
[tex]Flowrate=\frac{volume}{time\text{ taken}}=\frac{4.5}{1.875}=2.4\text{ gal/min}[/tex]Flow rate = volume / Time taken = 4.5 / 1.875 = 2.4 gal/min
can you draw a quadrilateral with 2 pairs of congruent parallel sides and 4 right angles
ANSWER and EXPLANATION
We want to draw a quadilateral that has 2 pairs of congruent parallel sides and 4 right angles.
There are 2 quadilaterals that fit this description:
A square and a rectangle
What is the next fraction in the sequence 19/20,4/5,13/20,1/2
The monthly mortgage loan payment on the Flynn's home is $609. Additionally, they pay $1,080 in annual real estate taxes and $799 per year in homeowner's insurance.
What is the total amount of their monthly payment?
How to do this? Primary math please teach me
By using products and percentages, the grandson had the amount of $ 225 before to buy foods and beverages.
How much money did the grandson have at first?In accordance with the statement, the grandson spent 80 % of all his amount to buy some food, later 40 % of the remaining money to buy some beverages and there was $ 27 remaining. We need to determine the amount that the grandson had initially. Then, the situation can be described by the following mathematical expression:
(1 - 80 / 100) · (1 - 40 / 100) · x = 27
(20 / 100) · (60 / 100) · x = 27
(1200 / 10000) · x = 27
(12 / 100) · x = 27
12 · x = 2700
x = 2700 / 12
x = 225
By means of percentages, the grandson had an amount of $ 225 before buying foods and beverages.
RemarkThe name of the grandson cannot be added due to profanity detector.
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Use the given values to write an equation that relates x and y.
We are given that "x" and "y" vary inversely. This means that the variables follow the next relationship:
[tex]y=\frac{k}{x}[/tex]Where "k" is a constant to be determined. To determine "k" we will use the given values:
[tex]\begin{gathered} x=3 \\ y=6 \end{gathered}[/tex]Now, we plug in the values:
[tex]6=\frac{k}{3}[/tex]Now, we solve for "k" by multiplying both sides by 3:
[tex]\begin{gathered} 6\times3=\frac{k}{3}\times3 \\ \\ 18=k \end{gathered}[/tex]Therefore, the value of "k" is 18. Now, we substitute in the relationship:
[tex]y=\frac{18}{x}[/tex]And thus we get the equation.
1. Solve the Systemy = 2x - 6y = -6x - 14
x = -1
Explanation:The given equations:
y = 2x - 6
y = -6x - 14
Since both equations are equal to y, we will equate the right hand side of both equations.
y = y
2x - 6 = -6x - 14
collect like terms:
2x + 6x = -14 + 6
8x = -8
divide both sides by 8:
8x/8 = -8/8
x = -1
Given that F( x) = x + 2, evaluate F(2)
Answer:
f(2) = 4
Step-by-step explanation:
Hello!
We can find f(2) by substituting 2 for x in the equation.
Evaluate f(2)f(x) = x + 2f(2) = 2 + 2f(2) = 4The value of f(2) is 4.
Function Notation - Transformationsill send a picture of the question
Let's see how two points on the left are mapped to their corresponding points on the right:
Point A has a corresponding point at A'. We have:
f(A) = A'
f(-6, -3) = (2, 4)
Point B has a corresponding point at B'. We have:
f(B) = B'
f(-4, -1) = (4, 6)
Now, notice that:
2 = -6 + 8
4 = -3 + 7
So, for (x, y) = (-6, -3), we have:
f(x, y) = (2, 4) = (x + 8, y + 7)
Notice that the same happens to the mapping of the other point:
4 = -4 + 8
6 = -1 + 7
So, for (x, y) = (-4, -1), we have:
f(x, y) = (4, 6) = (x + 8, y + 7)
Therefore, the rule for the transformation is
f(x, y) = (x + 8, y + 7)
The cost of mailing a package is proportional to the weight of the package. The proportional relationship can be represented with the equation c = 0.4w, where c represents the total cost and w represents weight in ounces. A graph for the equation is shown.
graph with x axis labeled weight in ounces and y axis labeled cost in dollars, with a line from 0 comma 0 going through 2 comma 0.8
Which of the following statements is true about the graph shown?
The graph is incorrect and the line should go through the point (0.4, 1).
The equation c = 0.4w is correctly represented by the graph.
The x-axis and y-axis are labeled incorrectly.
The graph does not show a proportional relationship.
The statement which is true about the graph shown is that: B. The equation c = 0.4w is correctly represented by the graph.
How to determine the equation of a proportional relationship?Mathematically, a proportional relationship can be modeled by the following linear equation:
y = kx
Where:
y and x are the variables.k represents the constant of proportionality.Next, we would determine the constant of proportionality (k) for this graph:
k = y/x
k = 0.8/2
k = 0.4.
In this context, the proportional relationship which models the cost of mailing a package to the weight of the package is given by this linear equation:
c = 0.4w
where:
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Answer:
Step-by-step explanation:
The statement which is true about the graph shown is that: B. The equation c = 0.4w is correctly represented by the graph.
How to determine the equation of a proportional relationship?
Mathematically, a proportional relationship can be modeled by the following linear equation:
y = kx
Where:
y and x are the variables.
k represents the constant of proportionality.
Next, we would determine the constant of proportionality (k) for this graph:
k = y/x
k = 0.8/2
k = 0.4.
In this context, the proportional relationship which models the cost of mailing a package to the weight of the package is given by this linear equation:
c = 0.4w
where:
c is the total cost.
w is weight in ounces.
Ekua designs and sells T-shirts for $1 13 each. Ekua has to spend $280 per month, $9.50dollar per T-shirt ordered.
As Ekua has to spend $280 per month and the cost of each sheet is $9.50 / dollar. The inequality followed is T≤29.
What is inequality?It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.
For the inequality, we have to apply the arithmetic operation in which we do the multiplication of x and apply the inequality for the given data.
To ascertain the maximum or lowest values of a scenario with many restrictions, a system of linear inequalities is frequently utilized. Inequalities reflect a limit of what is permitted or achievable rather than a precise quantity.
It is given that Ekua designs and sells T-shirts for $1 13 each. Ekua has to spend $280 per month, $9.50 dollar per T-shirt ordered.
We have to find the maximum number of T-shirts she can buy,
⇒ $280 / $9.50
⇒ 29.47 ≅29
Thus, Ekua has to spend $280 per month and the cost of each sheet is $9.50 / dollar. The inequality followed is T≤29.
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On Mrs. Sean's desk,there are pink and yellowmarkers. The ratio of pinkmarkers to total markersis 1:3. If there are 16yellow markers, then howmany markers are pink?
We know that the ratio of pink markers to total markers is 1:3.
This means that for every 3 markers, one of them is pink. The other 2 will be yellow markers.
We can write that the ratio of pink markers to yellow markers is 1:2, based on the last sentence. This means that if we have N yellow markers, we will have N/2 pink markers.
Then, if we have 16 yellow markers, then we will have 16/2=8 pink markers.
A florist has 60 tulips and 72 daffodils. The florist will make bouquets with the same number of tulips and the same number of daffodils in each, using all the flowers.
What is the greatest number of bouquets the florist can make?
Enter the correct answer in the box.
The greatest number of bouquets that the florist can make is 12.
What is the greatest number of bouquets that the florist can make?The greatest number of bouquets that the florist can make can be determined by calculating the highest common factor of 60 and 72. The factor of a number is the number that divides another number without any remainder. The highest common factor of two or more numbers is the highest factor that is common to two or more numbers.
Factors of 60 =1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.
Factors of 72 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36 and 72.
Highest common factor = 12
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Julia sells subs for $6 each. How many subs will she need to sell to break even each month based on the costs listed below?
Labor costs (management & workers) = $11,000
Insurance = $400
Rent = $1300
Utilities = $300
Average cost of ingredients/packaging for each sub = $1.32
Answer:
2777.7777... subs
Step-by-step explanation:
11000+400+1300+300=13000
6-1.32=4.68
13,000/4.68
=2777.777777...
55 miles per hour Anserw
Answer: Uhm hold on
Step-by-step explanation:
A change in temperature of 6°C is equivalent to achange in temperature of•F
A change in temperature of 6°C is equivalent to a
change in temperature of 10.8°F
Explanations:From the table drawn:
A change in temperature of 1°C is equivalent to 1.8°F
A change in temperature of 2°C is equivalent to 3.6°F
Following the relationships above, we can conclude that the relationship between °C and °F is:
°F = 1.8 °C
Therefore, a change in temperature of 6°C will be equivalent to:
°F = 1.8 °C
°F = 1.8 x 6
°F = 10.8°F
El 30 % de que numero es el 30 % del 10 % de 700
Answer:
70
Step-by-step explanation:
[tex]\frac{(700)(0.1)(0.3)}{0.3}=70[/tex]
A new cream was developed to reduce the irritation caused by poison ivy. To test the effectiveness, researchers placed an ad online asking for volunteers to participate in the study, and 100 subjects replied. They are informed that one group of 50 will receive a new cream and the remaining group of 50 will receive a cream with no active ingredient. The subjects are numbered 1–100 and these numbers are put into a random number generator. The first 50 unique numbers will represent the subjects that will receive the new cream and the remaining 50 subjects will receive the inactive cream. All subjects are exposed to poison ivy and given their cream. They are asked to return in three days and report their level of irritation. The average scores for each cream are compared.
Does this procedure describe a completely randomized design for this experiment?
Yes, the subjects will be exposed to the poison ivy.
Yes, the subjects are randomly assigned to each treatment.
No, the subjects are asked to return in three days. It is possible that some of them may not return, which will introduce bias into the results.
No, the subjects are randomly assigned to the two treatment groups, but the groups are not guaranteed to have 50 subjects in each.
The procedure describe a completely randomized design for this research as B. Yes, the subjects are randomly assigned to each treatment.
How to illustrate the information?In a randomized block design, the experimental units are divided into groups that we refer to as blocks. The experimental units inside each of the blocks will then be randomly assigned treatments.
As we can see from the question, they were divided into Blocks based on how much sun exposure they received while engaging in outdoor activities. After that, random treatments are assigned to each group.
Here, the participants are divided into groups based on their sun exposure, and then both treatments are distributed at random among the groups.
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Find the first 5 terms of the following sequence. For the first term let a_1=1. Round your answer to the nearest hundredth.a_n= \frac{2^n}{n^2} 1st term = Answer2nd term = Answer3rd term = Answer4th term = Answer5th term = Answer
1st term
Given:
[tex]a_1=1[/tex]With the formula of the sequence:
[tex]\begin{gathered} a_1=\frac{2^1}{1^2}=\frac{2}{1}=2 \\ \\ a_1=2 \end{gathered}[/tex]________
Second term:
[tex]\begin{gathered} a_2=\frac{2^2}{2^2}=\frac{4}{4}=1 \\ \\ a_2=1 \end{gathered}[/tex]____________
Third term:
[tex]\begin{gathered} a_3=\frac{2^3}{3^2}=\frac{8}{9}\approx0.89 \\ \\ a_3=0.89 \end{gathered}[/tex]_________
Fourth term:
[tex]\begin{gathered} a_4=\frac{2^4}{4^2}=\frac{16}{16}=1 \\ \\ a_4=1 \end{gathered}[/tex]-________________
Fifth term:
[tex]a_5=\frac{2^5}{5^2}=\frac{32}{25}=1.28[/tex]Find the average rate of change of k(x) = 4x + 11 over the interval [-19, -17].
Step 1:
Concept:
Use the rate of change formula below.
[tex]\begin{gathered} \text{Rate of change = }\frac{k(b)\text{ - k(a)}}{b\text{ - a}} \\ k(x)\text{ = 4x + 11} \\ a\text{ = -19} \\ b\text{ = -17} \end{gathered}[/tex]Step 2
Find k(a) and k(b)
[tex]\begin{gathered} k(-19)\text{ = 4(-19) + 11 = -76 + 11 = -65} \\ k(-17)\text{ = 4(-17) + 11 = -68 + 11= - 57} \end{gathered}[/tex]Step 3:
[tex]\begin{gathered} \text{Rate of change = }\frac{-57\text{ - (-65)}}{-17\text{ - (-19)}} \\ =\text{ }\frac{-57\text{ + 65}}{-17\text{ + 19}} \\ =\text{ }\frac{8}{2} \\ =\text{ 4} \end{gathered}[/tex]of one hundred and forty two students attending college , 23 are criminal justice majors. if 9 are selected at random, determine the probability each 9 criminal justice major. set up the problem as if it were to be solved but don't solve.
The probablity that first one selected is a criminal justice major is,
[tex]P_1=\frac{23}{142}[/tex]Now, the probablity that second one is a criminal justice major is when selected without replacement,
[tex]P_2=\frac{22}{141}[/tex]Simirally,
[tex]\begin{gathered} P_3=\frac{21}{140} \\ P_4=\frac{20}{139} \\ \ldots.\text{.} \end{gathered}[/tex]Thus, using the multiplication theorem,
[tex]\begin{gathered} P=P_1\times P_2\times\ldots\ldots.P_9 \\ =\frac{23}{142}\times\frac{22}{141}\times\frac{21}{140}\times\ldots\ldots\ldots\ldots\ldots\frac{15}{134} \end{gathered}[/tex]Thus, the above equation gives the requried probablity.