ent Assignmen... Dashboard | Khan... Untitled document - Solid SLUOTES LOILTOTT RecomTTTTETNauuS Skupials 19 Language alls You have prizes to revea Eighth grade AA.3 Solve a system of equations by graphing: word problems W9J Christine is comparing the cost of a fresh lobster dinner at two different restaurants. The first restaurant charges $30 for the meal, plus $3 per pound for the lobster she picks. At the second restaurant, Christine would pay $2 per pound for the lobster, in addition to $50 for the meal. Christine realizes that, in theory, dinner at both restaurants could cost the same amount if the lobster had a certain weight. How much would Christine pay for her dinner? Write a system of equations, graph them, and type the solution.
Answers
Let x represent the weight of lobster in the meal for which the cost of dinner in both restaurants would be the same.
For the first restaurant, they charge $30 for the meal, plus $3 per pound for the lobster she picks. This means that if she picks x pounds of lobster at this restaurant, the cost of the dinner would be
30 + 3x
For the second restaurant, they charge $50 for the meal, plus $2 per pound for the lobster she picks. This means that if she picks x pounds of lobster at this restaurant, the cost of the dinner would be
50 + 2x
The system of equations are
y = 30 + 3x
y = 50 + 2x
y represents the cost of the dinner
Given that when she picks x pounds of lobster, the cost would be the same, it means that
50 + 2x = 30 + 3x
3x - 2x = 50 - 30
x = 20
The amount that Christin would pay for her dinner is
30 + 3 * 20
= 30 + 60
= 90
She would pay $90 for the meal.
The graph is shown below
The blue line represents y = 50 + 2x
The red line represents y = 30 + 3x
At the point of intersection, the solution is (20, 90)
Related Questions
Which data are represented by this dot plot? Student Absences in Mrs. Li's Class 0 1 2 3 4 5 6 7 8 Days O A. 2, 4, 0, 2, 4, 6, 3, 0, 7, 1, 2, 7, 8, 1, 1 O B. 0, 1, 2, 3, 4, 5, 6, 7, 8,0, 1, 2, 4, 6, 7 O C. 0, 2, 3, 0, 2, 4, 4, 5, 7, 8, 7, 2, 0, 2, 7 O D. 1, 2, 6, 4, 6, 7, 7, 2, 2, 0, 1, 0, 1
Answers
The number of dots gives the frequency of each number over which the dots appear.
The tabular representation of the dot plot is as shown below
Number | Frequency
-------------------------------------------
0 | 2
-------------------------------------------
1 | 3
-------------------------------------------
2 | 3
-------------------------------------------
3 | 1
-------------------------------------------
4 | 2
-------------------------------------------
6 | 1
-------------------------------------------
7 | 2
-------------------------------------------
8 | 1
-------------------------------------------
The only option that matches the table is option A
From the table 0 appears twice, 1 three times, 2 three times, 3 once, 4 twice, 6 once
Nevaeh earned a score of 508 on Exam A that had a mean of 500 and a standarddeviation of 40. She is about to take Exam B that has a mean of 350 and a standarddeviation of 20. How well must Nevaeh score on Exam B in order to do equivalentlywell as she did on Exam A? Assume that scores on each exam are normallydistributed
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First we must obtain the relationship between the grade, the mean and the standard deviation of exam A
[tex]\begin{gathered} z=\frac{x-\operatorname{mean}}{\sigma} \\ z_A=\frac{508-500}{40} \\ z_A=0.2 \\ \end{gathered}[/tex]Now we have to find the required score for exam B to reach the same ratio factor z
[tex]\begin{gathered} z_B=z_A \\ 0.2=\frac{x_B-350_{}}{20} \\ x_B=0.2(20)+350 \\ x_B=354 \end{gathered}[/tex]As seen in the calculations, Nevaeh must score 354 on Exam B to equal the score on Exam A
1. Find the slope of the line with the following points.A. (4,3), (6,-2)b. (7,2), (3,-4)
Answers
ANSWER:
A. - 2.5
B. 1.5
STEP-BY-STEP EXPLANATION:
The slope of a line is calculated as follows:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]A.
Replacing the points (4,3) and (6,-2):
[tex]m=\frac{-2-3}{6-4}=\frac{-5}{2}=-2.5[/tex]B.
Replacing the points (7, 2) and (3,-4):
[tex]m=\frac{-4-2}{3-7}=\frac{-6}{-4}=\frac{3}{2}=1.5[/tex]find the x and y intercept from the following equations there should be 2 ordered pairs for each solution
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in the given equation
[tex]4x+5y=-20[/tex]To find the x-intercept, substitute y by 0
[tex]\begin{gathered} y=0 \\ 4x+5(0)=-20 \\ 4x+0=-20 \\ 4x=-20 \end{gathered}[/tex]Divide both sides by 4 to find x
[tex]\begin{gathered} \frac{4x}{4}=-\frac{20}{4} \\ x=-5 \end{gathered}[/tex]Then the x-intercept is (-5, 0)
To find the y-intercept, substitute x by 0
[tex]\begin{gathered} x=0 \\ 4(0)+5y=-20 \\ 0+5y=-20 \\ 5y=-20 \end{gathered}[/tex]Divide both sides by 5, them to find y
[tex]\begin{gathered} \frac{5y}{5}=-\frac{20}{5} \\ y=-4 \end{gathered}[/tex]Then, the y-intercept is (0, -4)
Given the problem below, what is the maximum number of gallons that the storagetank can hold?The volume of water, V, in a storage tank can be modeled as a function of the number of hours since it was27full by the equation V = 55cos -1 +67, where V represents the number of gallons of water in the tank.
Answers
ANSWER:
122 gallons
STEP-BY-STEP EXPLANATION:We have the following function:
[tex]V=55\cdot\: cos\mleft(\frac{2\pi}{7}t\mright)+67[/tex]The first thing is to calculate the periodicity of the function. The value of the periodicity would be the value of x (in this case t) to calculate the value of y, that is, in this case the volume.
As follows:
[tex]\begin{gathered} p=\frac{2\pi}{\frac{2\pi}{7}}=7 \\ \text{therefore x = 7, replacing} \\ V=55\cdot\: cos(\frac{2\pi}{7}\cdot7)+67 \\ V=55\cdot\: cos(2\pi)+67 \\ V=55+67 \\ V=122 \end{gathered}[/tex]Therefore the maximum volume would be 122 gallons.
You have to Determine analytically if the following function are even, odd, or neither.
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Given the function
[tex]f(x)=2x^3-x[/tex]Using the graphical method,
The graph of the given function is shown below
From the graph of the function,
[tex]f(-x)=-f(x)[/tex]Hence, the given function is Odd
Alternatively
[tex]f(x)=2x^3-x[/tex]Replacing x with -x and solving
[tex]\begin{gathered} f(x)=2x^3-x \\ \text{where x =-x} \\ f(-x)=2(-x)^3-(-x) \\ f(-x)=2(-x^3)+x=-2x^3+x \\ f(-x)=-2x^3+x=-1(2x^3-x) \\ f(-x)=-1(2x^3-x) \\ R\text{ecall that }f(x)=2x^3-x \\ \text{Thus} \\ f(-x)=-f(x) \end{gathered}[/tex]It can be seen from the above deduction that
[tex]f(-x)=-f(x)[/tex]Hence, the function f(x)=2x³-x is odd
At what x-values do the graphs of the functions y = cos 2x and y =3cos^2x-sin^2x intersect over the interval -pi
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To find:
The x-values at the intersection of the graphs of two functions.
Solution:
Two functions are:
[tex]y=\cos2x\text{ and }y=3\cos^2x-\sin^2x[/tex]The functions are equal at the intersection. So,
[tex]\cos2x=3\cos^2x-\sin^2x[/tex]The solutions of the above equation are the x-values of the intersection.
[tex]\begin{gathered} \cos2x=3\cos^2x-\sin^2x \\ \cos^2x-\sin^2x=3\cos^2x-\sin^2x \\ 2\cos^2x=0 \\ \cos^2x=0 \\ \cos x=0 \end{gathered}[/tex]The solution to the above equation is:
[tex]x=\frac{\pi}{2}+2\pi n\text{ and }x=\frac{3\pi}{2}+2\pi n[/tex]It is given that x lies between -pi and pi. So, the value of n = 0 for the first solution and n = 1 for the second solution. Therefore,
[tex]x=\frac{\pi}{2}\text{ and }x=-\frac{\pi}{2}[/tex]Thus, options A and B are correct.
Perform the following transformations :First reflect the ABC across the y-axis ,then dilate by a factor of 1/2
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Given the triangle ABC, you have to reflect it over the y-axis and then dilate it by scale factor k=1/2
- The reflection over the y-axis is a rigid transformation (the figure changes position but it does not change shape), which means that the resulting image will be congruent to the original.
- The dilation is a nonrigid transformation, the figure changes its shape, the resulting image after dilation is similar to the original one.
Reflection over the y-axis ΔABC to ΔA'B'C'
To reflect an image over the y-axis you have to change the sign of the x-coordinate leaving the y-coordinate of each vertex equal. The rule of the reflection can be expressed as follows:
[tex](x,y)\to(-x,y)[/tex]Preimage → Image
A(-1,-4) → A'(-(-1),-4)= A'(1,-4)
B(-3,-2) → B'(-(-3),-2)= B'(3,-2)
C(-1,2) → C'(-(-1),2)= C'(1,2)
After the reflection over the y-axis, the coordinates for the triangle are A'(1,-4), B'(3,-2), and C'(1,2).
ΔABC and ΔA'B'C' are congruent.
Dilation by scale factor k=1/2 ΔA'B'C' to ΔA''B''C''
To dilate a figure by a determined scale factor, you have to multiply the coordinates of each vertex by the said scale factor, you can write the dilation rule as follows:
Dilation factor k=1/2
[tex](x,y)\to(\frac{1}{2}x,\frac{1}{2}y)[/tex][tex]\begin{gathered} \text{Preimage \rightarrow Image} \\ A^{\prime}(1,-4)\to A^{\doubleprime}(\frac{1}{2}\cdot1,\frac{1}{2}\cdot(-4))=A^{\doubleprime}(\frac{1}{2},-2) \\ B^{\prime}(3,-2)\to B^{\doubleprime}(\frac{1}{2}\cdot3,\frac{1}{2}(-2))=B^{\doubleprime}(\frac{3}{2},-1) \\ C^{\prime}(1,2)\to C^{\doubleprime}(\frac{1}{2}\cdot1,\frac{1}{2}\cdot2)=C^{\doubleprime}(\frac{1}{2},1) \end{gathered}[/tex]After the dilation, the coordinates for the new triangle are A''(1/2,-2), B''(3/2,-1), and C''(1/2,1).
ΔABC and ΔA''B''C'' are similar.
5. The point (-4,1) falls in which quadrant?O Quadrant IO Quadrant IIQuadrant IIIQuadrant IV
Answers
We are given the following point
(-4, 1)
We are asked to determine in which quadrant does the point lies.
As you can see, the x-coordinate (x = -4) of the point is negative and the y-coordinate (y = 1) of the point is positive.
Let us sketch a diagram to better understand the problem
The point falls in Quadrant II since the x-coordinate is negative and y-coordinate is positive,
A 25-foot ladder is leaning against a building. If the bottom of the ladder is 6 feet (4 pts.)
from the bottom of the building, determine the measure of the angle that is formed
by the ladder and the ground. (Round to the nearest degree.)
Answers
determine if the given triangles are similar if they are select the option that includes a similarity statement with the justifying prostulaye or theorem them they are not select option states such
Answers
We are asked to determine if the given triangles are similar or not.
Let us find the rato of the corresponding sides
[tex]\begin{gathered} \frac{GA}{BE}=\frac{GU}{EF} \\ \frac{12}{15}=\frac{16}{20} \\ \frac{4}{5}=\frac{4}{5} \end{gathered}[/tex]So, △GUA and △EFB have two equal sides since the ratio of the two corresponding sides is equal.
[tex]\begin{gathered} GA\sim BE \\ GU\sim EF \end{gathered}[/tex]Also, notice that the one corresponding angle is equal
[tex]\angle G\cong\angle E[/tex]Hence, the triangles △GUA and △EFB are similar by SAS theorem since the ratio of two corresponding sides is equal and one included angle is also equal.
Therefore, the last option is the correct answer.
FreshmenBelow, the two-way table is given for aclass of students.Sophomore Juniors SeniorsTotalMale 462 2.Female 3 46 3TotalIf a student is selected at random, find theprobability the student is a junior. Roundto the nearest whole percent.
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To the nearest percentage, the probability that the randomly selected student is a junior is 27%
Here, we want to get the probability that a randomly selected student is a junior
From what we have in the table, the total number of students will be;
4 + 3 + 6 + 4 + 2 + 6 + 2 + 3 = 30
The number of juniors we have is ;
2 + 6 = 8
So the probability is simply the number of juniors divided by the total number of students
We have this as;
[tex]\frac{8}{30}\times\text{ 100 \% = 27\%}[/tex]the price of a new 2014 jeep grand Cherokee cost about 37,000 when originally bought. today that same car is only worth 15,910. what was the percent decrease of the car
Answers
The percent decrease price is 57%.
Given:
Original cost is, C = 37000.
New cost is, N = 15910.
The objective is to find the percentage decrease of the price.
The formula to find the percentage decrease is,
[tex]\text{Percentage decrease=}\frac{N-C}{C}\times100[/tex]Now, substitute the given values in the above equation.
[tex]\begin{gathered} \text{Percentage decrease=}\frac{15910-37000}{37000}\times100 \\ =-\frac{21090}{37000}\times100 \\ =-0.57\times100 \\ =-57\text{ percentage} \end{gathered}[/tex]THe negative sign indicate the decrease in percentage.
Hence, the percent decrease price is 57%.
Identify the type of sampling method used.A trucking company places their office phone number on the back of all of their vehicles to receive comments on how well their employees are driving.
Answers
Explanation
In this sample, people elect to participate or self-select to do the survey. Often, these folks have a strong interest in the main topic of the survey.
In essence, they volunteer to inform the trucking company about the activities of their drivers. That makes this a voluntary sample.
Answer: Voluntary Sampling Method
Graph the system and find the vertices (comers of the darkest shaded area, where the lines intersect) of the region.żyfix) 53XS-2(0-3). (2.0), (0,0)(-23).(-26).(4.3)(0-3).(-2.3). (4.3)(3.-2).(-2,-6). (3.4)
Answers
Answer: (-2,3), (-2,-6), and (4,3)
Explanation:
The graph of the given system of equalities is :
Based on the graph, the vertices are (-2,3), (-2,-6), and (4,3).
in 4-6 slove each system using substitution[tex]y = \frac{1}{2}x + 4[/tex][tex]x - y = 8[/tex]
Answers
You have the following system of equations:
y = 1/2 x + 4
x - y = 8
to solve by substitution, proced as follow:
replace the expression y = 1/2 x + 4 into the second equation, and then solve for x:
x - (1/2 x + 4) = 8 eliminate parenthesis
x - 1/2 x - 4 = 8 simplify like terms left side
1/2 x - 4 = 8 add 4 both sides
1/2 x = 8 + 4
1/2 x = 12 multiply by 2 both sides
x = 12(2)
x = 24
next, replace the value x = 24 into the expression y = 1/2x + 4 to obtain y:
y = 1/2 (24) + 4
y = 12 + 4
y = 16
Hence, the solution to the given system of equations are:
x = 24
y = 16
Sarah is 13 years older than Mike. The sum of their ages is 37. How old is Sarah and how old is Mike? (awnsered in an ordered pair) (can slove it by eliminating, substituting.)
Answers
Let's define the next variables:
x: Sarah's age
y: Mike's age
Sarah is 13 years older than Mike, then:
x = 13 + y
The sum of their ages is 37, then
x + y = 37
Substituting the first equation into the second one, we get:
(13 + y) + y = 37
13 + (y + y) = 37
13 + 2y = 37
2y = 37 - 13
2y = 24
y = 24/2
y = 12
Replacing this result into the first equation:
x = 13 + 12
x = 25
Sarah is 25 years old and Mike is 12 years old
v=u+atrearrange the formula to make a the subject
Answers
Answer:
[tex]a=\frac{v-u}{t}[/tex]Explanation:
Given the equation:
[tex]v=u+at[/tex]We want to make 'a' the subject of the equation.
First, subtract u from both sides of the equation:
[tex]\begin{gathered} v-u=u-u+at \\ at=v-u \end{gathered}[/tex]Next, divide both sides by t:
[tex]\begin{gathered} \frac{at}{t}=\frac{v-u}{t} \\ a=\frac{v-u}{t} \end{gathered}[/tex]The formula rearranged with a as the subject is:
[tex]a=\frac{v-u}{t}[/tex]Identify whether each unit measures length, volume, or weight (mass).to. Mileb. CupC. Librad. Centimeterand. LiterF. Gramg. Pintah. Yardi. Kilogramj. Teaspoonfulk. Milliliter
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a. Mile length
b. Cup volume
C. Libra weight
d. Centimeter length
e. Liter volume
F. Gram weight
g. Pinta volume
h. Yard length
i. Kilogram weight
j. Teaspoonful volume
k. Milliliter volume
solve the following system algebraically using the substitution method.type the solution as an ordered pair
Answers
solve
[tex]\begin{gathered} \begin{bmatrix}6x+7y=20 \\ y=2x\end{bmatrix} \\ substituting\text{ y } \\ 6x+7(2x)=20 \\ 6x+14x=20 \\ 20x=20 \\ \frac{20x}{20}=\frac{20}{20} \\ x=1 \end{gathered}[/tex]and for y
[tex]y=2(1)=2[/tex]answer: (1,2)
Given the points. (0,3) and (-9,-7) and on a line, find its equation in the form y=mx+b.y=
Answers
First, we need to find the slope m using the following equation:
[tex]\begin{gathered} m=\frac{y2-y1}{x2-x1} \\ where: \\ (x1,y1)=(0,3) \\ (x2,y2)=(-9,-7) \\ so: \\ m=\frac{-7-3}{-9-0}=-\frac{10}{-9}=\frac{10}{9} \end{gathered}[/tex]Now, using the point-slope equation:
[tex]\begin{gathered} y-y1=m(x-x1) \\ y-3=\frac{10}{9}(x-0) \\ y-3=\frac{10}{9}x \\ Solve_{\text{ }}for_{\text{ }}y: \\ y=\frac{10}{9}x+3 \\ Answer: \\ y=\frac{10}{9}x+3 \end{gathered}[/tex]2. Jenny makes $333.75 for 25 hours of work, and Christina makes $505.75 for 35 hours of work.a. How much do Jenny and Christina each make per hour?
Answers
• We know that
,• Jenny makes $333.75 for 25 hours of work.
,• Christina makes $505.75 for 35 hours of work.
To know how much they make per hour, we just need to divide each given relation.
Jenny's earnings per hour:
[tex]J=\frac{333.75}{25}=13.35[/tex]Therefore, Jenny earns $13.35 per hour.
Christina's earnings per hour:
[tex]C=\frac{505.75}{35}=14.45[/tex]Therefore, Christina earns $14.45 per hour.
This means Christina earns more money per hour than Jenny.
Add polynomials (intro) Add. Your answer should be an expanded polynomial in standard form. (3x^3 + 4x²) + (3x^3 – 4x^2 – 9x) =
Answers
(3x^3 + 4x²) + (3x^3 – 4x^2 – 9x) =
We have to combine like terms, terms that have x raised to the same power:
First, eliminate the parenthesis:
3x^3 + 4x² + 3x^3 – 4x^2 – 9x =
We have 2 terms raised to the second power (4x^2 and -4 x^2) simply add and subtract.
3x^3+3x^3+4x^2-4x^2-9x
6x^3-9x
lYou invested S8000 between two accounts paying 4% and 8% annual interest, respectively if the total interest earned for the year was $520, how much was invested at each ratė? was invested at 4% and was invested at 8% Enter your answer in the edit fields and then click Check Answer All parts showing Clear All Check Answer
Answers
Answer:
$3000 was invested at 4% and was $5000 invested at 8%
Explanation:
The formula for calculating simple interest id expressed as;
I = I1+I2
I1 and I2 are the interest earned on both accounts'
Since I =PRT/100
520 = P1R1T1/100 + P2R2T2/100
P is the principal
R is the rate
T is the time
520 = P1(4)(1)/100 + P2(8)(1/100)
520 = (4P1+8P2)/100
4P1+8P2 = 520 *100
4P1+8P2 = 52,000 ......1
SInce the total amount invested is $8,000, hence;
P1 + P2 = 8000 .... 2
Solve 1 and 2 simultaneously;
4P1+8P2 = 52,000 ......1 ..... * 1
P1 + P2 = 8000 .... 2 .... * 4
____________________________]
4P1+8P2 = 52,000
4P1 + 4P2 = 32000
Subtract both equatons;
8P2 - 4P2 = 52000 - 32000
4P2 = 20000
P2 = 20000/4
P2 = 5000
Recall that P1 + P2 = 8000
P1 = 8000 - P2
P1 = 8000 - 5000
P1 = 3000
Hence $3000 was invested at 4% and was $5000 invested at 8%
Maia can run 4/5 of a mile in 5/3 of an hour. How far can she run in 1 hour? * 1 point O 12/15 mile O 15/20 mile 4/3 mile O 12/25 mile
Answers
Answer:
Explanation:
Maia can run 4/5 of a mile in 5/3 of an hour.
Let the mile run in 1 hour = x
We therefore have that:
[tex]\frac{\frac{4}{5}}{\frac{5}{3}}=\frac{x}{1}[/tex]Which of the following sets of numbers could not represent the three sides of a triangle? O {4, 17,23} O {14, 26,38} Submit Answer O {12, 18, 28} O {12, 19, 28}
Answers
The sum of any 2 sides must be greater than the third side. Therefore, let us test the values
[tex]\begin{gathered} \mleft\lbrace4,17,23\mright\rbrace\rightarrow4+17=21 \\ 21<23 \\ \text{this is does not represent a triangle} \end{gathered}[/tex]What amount of money will accumulate to $192,400 in 6 years and 11 months at the interest rate of 5.36% compounded semi-annually? $_______
Answers
We will have the following:
[tex]\begin{gathered} 192400=A(1+\frac{0.0536}{2})^{(11/12)(2)}\Rightarrow A=\frac{192400}{(1+0.0536/2)^{(11/12)(2)}} \\ \\ \Rightarrow A=183293.7505...\Rightarrow A\approx18329375 \end{gathered}[/tex]So, the original quantity was approximately $183 293.75.
Select the correct answer from each drop-down menu.The given equation has been solved in the table.StepStatement1= 15- - 6 =- - 6 + 6 = 15 ++4- = 21N34.2-2 - 215y = -42Use the table to complete each statement.In step 2, theIn step 4, theproperty of equality was applied.property of equality was applied.VResetNext
Answers
Solution
Step 1:
Addition Property of Equality
If two expressions are equal to each other, and you add the same value to both sides of the equation, the equation will remain equal. When you solve an equation, you find the value of the variable that makes the equation true.
Step 2
In the step 2, addition property of equality is applied.
[tex]\begin{gathered} \frac{2}{3}x\text{ - 9 =-13} \\ Apply\text{ the addition property of equality} \\ \frac{2}{3}x\text{-9 + 9=-13+9} \end{gathered}[/tex]Final answer
A) Step 2
Write a story or situation that can be represented by the given equation.4a + 5 = 12a − 11
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Let a be the cost per ticket at a cinema. Person A goes to see a movie with another 3 friends and spends 5 dollars on popcorn. On the other hand, person B goes with another 11 friends and gets a discount of 11 dollars due to the number of tickets he bought. If both people paid the same, determine the cost of one ticket.
Can someone please help me.Number 2.I just need to solve for x and y using trigonometry
Answers
Given the Right Triangle, you can identify that has two equal sides. Therefore, you can determine that it is a Right Isosceles Triangle.
By definition, a Right Isosceles Triangle has two equal sides and two equal angles, and the third angle measures 90 degrees (also called "Right Angle").
Therefore, you can determine that, in this case:
[tex]x=y[/tex]By definition, the sum of the interior angles of a triangle is 180 degrees. Then, knowing that a Right Isosceles Triangle has two equal angles and another angle that measures 90 degrees, you can set up this equation:
[tex]x+y+90\text{\degree}=180\text{\degree}[/tex][tex]x+x+90\text{\degree}=180\text{\degree}[/tex](Since "y" and "x" have the same measure, you can rewrite the equation using any of them, as you can see above)
Solving for "x", you get:
[tex]2x=180\text{\degree}-90\text{\degree}[/tex][tex]x=\frac{90\degree}{2}[/tex][tex]x=45\degree[/tex]Hence, the answer is:
[tex]x=45\degree[/tex][tex]y=45\degree[/tex]