y = 2x – 2 y = -x + 7
Answers
Given the system of equations:
[tex]\begin{gathered} y=2x-2 \\ y=-x+7 \end{gathered}[/tex]We will find the solution of the system by the graph
To draw each line, we need to know 2 points
So, we will substitute with 2 values of x and calculate the corresponding value of y
For the first equation: y = 2x - 2
[tex]\begin{gathered} x=0\rightarrow y=2\cdot0-2=-2 \\ x=2\rightarrow y\rightarrow=2\cdot2-2=2 \end{gathered}[/tex]So, the line passes through the points ( 0, -2 ) and ( 2, 2)
For the second line: y = -x + 7
[tex]\begin{gathered} x=0\rightarrow y=0+7=7 \\ x=2\rightarrow y=-2+7=5 \end{gathered}[/tex]so, the line passes through the points ( 0, 7) and ( 2, 5)
The graph of the system will be as shown in the following figure:
As shown in the figure:
Equation 1 is the blue line
Equation 2 is the red line
The point of intersection = ( 3, 4)
So, the answer is the solution of the system = ( 3, 4 )
Related Questions
Solve the system algebraically 5 x - y = 0
Answers
Answer:
To solve the system of equations,
[tex]\begin{gathered} 5x-y=0 \\ \frac{y^2}{90}-\frac{x^2}{36}=1 \end{gathered}[/tex]Solving 1st equation we get,
[tex]y=5x[/tex][tex]\frac{y^2}{90}-\frac{x^2}{36}=1[/tex]Substitute y=5x in the above equation, we get
[tex]\frac{(5x)^2}{90}-\frac{x^2}{36}=1[/tex][tex]\frac{25x^2}{90}-\frac{x^2}{36}=1[/tex][tex]\frac{5x^2}{18}-\frac{x^2}{36}=1[/tex][tex]\frac{10x^2-x^2}{36}=1[/tex][tex]\frac{9x^2}{36}=1[/tex][tex]\frac{x^2}{4}=1[/tex][tex]x^2=4[/tex][tex]x=\pm2[/tex]when x=2, we get y=5x=5(2)=10
when x=-2, we get y=5x=5(-2)=-10
There are two solution for the given system.
[tex](2,10),(2,-10)[/tex]Answer is: x=2,y=10 and x=2,y=-10
An automotive manufacturer wants to know the proportion of new car buyers who prefer foreign cars overdomestic. Supposed a sample of 879 new car buyers is drawn. Of those sample 298 preferred foreign over domestic cars. Using the data estimate the proportion of new car buyers who prefer foreign cars. Enter your answer as a fraction or a decimal number rounded to three decimal places
Answers
ANSWER:
0.339
STEP-BY-STEP EXPLANATION:
We can determine the proportion since we know the general sample and the specific sample, just like this:
[tex]\begin{gathered} p=\frac{298}{879} \\ \\ p=0.339 \end{gathered}[/tex]The proportion is 0.339
PLEASE HELP IM DESPERATE AND NEED THE ANSWER NOW WILL GIVE BRAINLIEST 50 POINTS
△ABC has a right angle at C, BC=9.2 centimeters, and m∠A=63∘.
What is CA ?
Enter your answer rounded to the nearest tenth in the box.
Answers
Answer:
CA = 4.7 cm
Step-by-step explanation:
There're two ways to solve that
Reflect the figure over the line y = -x - 1.Plot all of the points of the reflected figure.You may click a plotted point to delete it.1098765432-10-9-8-7-6-54345 6789 10-10
Answers
We are going to determine how to reflect over the line
y = - x -1
First, if we are going to undertand how to reflect it over y = -x
What happens when y = - x?If we want to reflect the point (-4, 0) over y = -x, graphically we know that its reflection is (0, 4).
It would be tha same for any point (x, 0), its reflection would be (0, -x).
Similarly, if we want to reflect the point (0, -5) over y = -x. Its reflection would be (5,0).
It would be the same for any point (0, y), its reflection would be (-y, 0)
We can generalize it: if we have a point (x, y) its reflection over y = -x would be (-y, -x)
(x, y) → (-y, -x)
Now that we have undertood when it is reflected over y = -x. We can find how to do it over y = -x -1
Reflection over y = - x -1
Doing the same case as y = -x
If we see the figure we will observe that
(x, y) reflected point would be (- y - 1, - x -1)
(x, y) → (-y - 1, -x - 1)
Reflecting the figure
We can observe that the figure has 5 points
(-4, -1), (-4, -4), (-2, -9), (-7, -2), (-8, -8)
We are going to reflect them using the last formula
(x, y) → (-y - 1, -x - 1)
(-4, -1) → ( -(-1) - 1, - (-4) -1)
= ( 1 -1, 4 - 1) = (0, 3)
(-4, -4) → (- (-4) -1, - (-4) -1)
= (4 -1, 4 - 1) = (3, 3)
(-2, -9) → (- (-9) -1, - (-2) -1)
= (9 - 1, 2 - 1) = (8, 1)
(-7, -2) → (- (-2) -1, - (-7) -1)
= (2 -1, 7 -1) = (1, 6)
(-8, -8) → (- (-8) -1, - (-8) -1)
= (8 - 1, 8 -1) = (7, 7)
Then the new points are:
(0, 3), (3, 3), (8, 1), (1, 6), (7, 7)
If h(x)-(fog)(x) and h(x) = 4(x+1)*, find one possibility for 5 %) and g(x).f(x) = x +1O A.8(x) = 4x2O B. M(x)=(x+1)8(x)=4x2O c.f(x) = 4x2g(x) = x +1D.f(x) = 4x28(x)= (x+1)
Answers
It is given that h(x)=fog(x) and h(x)=4(x+1)^2.
So it follows:
[tex]\text{fog(x)}=4(x+1)^2[/tex]For option A, f(x)=x+1,g(x)=4x^2
So the value of fog(x) is given by:
[tex]f(g(x))=g(x)+1=4x^2+1[/tex]So A is incorrect.
For option B, f(x)=(x+1)^2,g(x)=4x^2
So the value of fog(x) is given by:
[tex]f(g(x))=g(x)+1=(g(x)+1)^2=(4x^2+1)^2[/tex]So B is incorrect.
For option C, f(x)=4x^2,g(x)=x+1
So the value of fog(x) is given by:
[tex]f(g(x))=4\lbrack g(x)\rbrack^2=4(x+1)^2[/tex]So C is correct.
The equation a +c = b+c demonstrates an examples of which property?O The distributive propertyO The addition property of equality O The commutative propertyO The associative property
Answers
The correct answer is the addition property of equality
Here, we want to select the property demonstrated by the example
The correct answer is the addition property of equality
What this is saying is that if we have two numbers, in this case represented by the variables a= c
If we add an equal number to both sides, then the results on both sides still stay the same regardless since it is the same number that we added on both ends
For each coefficient choose whether it is positive or negative.Choose the coefficient with the least value.Choose the coefficient closest to zero.
Answers
From the given graph
a)
If the coefficient is positive, then the graph is upward
If the coefficient is negative, then the graph is downward
In the first 2 figures, the graphs are upward, then
A and B are positive
In the last 2 figures, the graphs are downward, then
C and D are negative
b)
The least coefficient is the coefficient of the graph which nearest to the x-axis
Since graph C is the nearest graph to the x-axis, but we have negative values, then
The least coefficient is the coefficient of the downward graph and farthest from the x-axis, then
D is the least coefficient
c)
The closest coefficient to zero is the graph C
1. [2/3 Points)DETAILSPREVIOUS ANSWERSSALGTRIG45.4.001.MY NOTESASK YOUR TEACHERFor a function to have an inverse, it must be one-to-oneTo define the Inverse sine function, we restrict the domainDof the sine function to the IntervalXNeed Help? Paad
Answers
In the case of sine function the domain of the function is given by the limits of the range of sine function.
The limits of the range of sine function are [-1,1].
Hence, the domain of the inverse sin function is [-1,1].
luann is playing a math game . she chose three cards - first card: -12 - second card: 3- thrid card: -5 what is the sum of the value ?
Answers
we sum the values
[tex]-12+3+(-5)=-12+3-5=-14[/tex]answer: -14
The notation __1____ reads the probability of Event B given that Event A has occurred. If Events A and B are independent, then the probability of Event A occurring ___2___the probability of Event B occurring. Events A and B are independent if_3____1.A. P(AlB)B. P(BlA)C. P (A and B)2. A. Doesn't affectB. Affects3. A. P(BIA) = P(B)B. P(BIA) = P(A)C. P (BIA)= P(A and B).
Answers
P(B|A) (option B)
Doesn't affect (option A)
P(B|A) = P(B) (option A)
Explanation:1) Conditional probabilities could be in the form P(A|B) or P(B|A)
P(B|A) is a notation that reads the probability of event B given that event A has occurred.
P(B|A) (option B)
2) Independent events do not affect the outcome of each other
For event A and B to be independent, the probability of event A occurring doesn't affect the the probability of event B occurring
Doesn't affect (option A)
3) Events A and B are independent if the following are satisfied:
P(A|B) = P(A)
P(B|A) = P(B)
The ones that appeared in the option is P(B|A) = P(B) (option A)
a and b are supplementary angles. if ma=(2x-24)°and mb=(5x-27)°, find the measure for b
Answers
Supplementary angles add up 180°.
So:
M
(2x-24) + (5x-27) = 180
Solve for x:
2x - 24 + 5x - 27 = 180
Combine like terms:
2x + 5x - 24 -27 = 180
7x -51 = 180
7x = 180 +51
7x = 231
x= 231/7
x= 33
Replace x on m
m< B = 5x-27 = 5 (33) - 27 = 165-27 = 138
m
The height of a building is 1497 feet . How long would it take for an object to fall from the top
Answers
The function is given as
[tex]S=16t^2[/tex]Given that the height of the building is
[tex]S=1497ft[/tex]To calculate the value for time (t), we will substitute the value of S=1497 ft in the function above
[tex]\begin{gathered} S=16t^2 \\ 1497=16t^2 \\ 16t^2=1497 \\ \text{Divide both sides by 1}6 \\ \frac{16t^2}{16}=\frac{1497}{16} \\ t^2=93.5625 \\ \text{squareroot both sides} \\ t=\sqrt[]{93.5625} \\ t=9.67 \\ t\approx9.7\sec onds \end{gathered}[/tex]Hence,
The final answer is t= 9.7 seconds
Find the circumference and area of each. Round for the nearest tenth:
1) a circle has a radius of 2 meters
2) a circle has a diameter of 16 cm
3) a circle has a radius of 8ft
4) a circle has a diameter of 11 cm
Answers
Answers:
1) C = 12.6 m
A = 12.6 m²
2) C= 50.3 cm
A = 201.1 cm²
3) C= 50.3 ft
A = 201.1 ft²
4) C= 34.6 cm
A = 95.0 cm²
Explanation:
The circumference and area of a circle with radius r can be calculated as:
[tex]\begin{gathered} \text{Circumference = 2}\pi r \\ Area\text{ = }\pi r^2 \end{gathered}[/tex]Where π is approximately 3.1416
Then, for each option, we get:
1) Replacing the radius by 2 m, we get:
[tex]\begin{gathered} \text{Circumference}=2(3.1416)(2m)=12.6m \\ \text{Area}=(3.1416)(2m)^2=(3.1416)(4m^2)=12.6m^2 \end{gathered}[/tex]2) If the diameter is 16 cm, the radius is 8 cm because the radius is half the diameter. So, replacing r by 8 cm, we get:
[tex]\begin{gathered} \text{Circumference = 2(3.1416)(8cm) = 50.3cm} \\ \text{Area = (3.1416)(8cm)}^2=(3.1416)(64cm^2)=201.1cm^2 \end{gathered}[/tex]3) Replacing r by 8 ft, we get:
[tex]\begin{gathered} \text{Circumference = 2(3.1416)(8ft) = 50.3ft} \\ \text{Area = (3.1416)(8ft)}^2=(3.1416)(64ft^2)=201.1ft^2 \end{gathered}[/tex]4) If the diameter is 11 cm, the radius is 11/2 = 5.5 cm, so:
[tex]\begin{gathered} \text{Circumference = 2(3.1416)(5.5cm) = 34.6 cm} \\ \text{Area = (3.1416)(5.5cm)}^2=(3.1416)(30.25cm^2)=95.0cm^2 \end{gathered}[/tex]
what is the y-intercept of the function y=-¹/²cos(3/2x)
Answers
Problem
We need to find the y intercept of this function
y=-1/2cos(3/2x)
Solution
The y intercept correspond to the value of x=0 of the function and we can do this:
y= -1/2 cos (3/2 *0)
y= -1/2 cos (0) = -1/2
And then the best solution it would be:
x=0 and y= -1/2
(0,-1/2)
can you please help me
Answers
Given the equation:
[tex]\text{ 2x + 2y = -4}[/tex]don’t be slow pls i only care about the answers and the steps you did
Answers
Problem N 12
we have that
m by exterior angle
substitute
mm
Problem N 13
we have that
m by exterior angle
substitute given values
45=(1/2){arc JK-55}
90=arcJK-55
arc JK=90+55
arc JK=145 degreesProblem N 14
we have that
m by exterior angle
substitute given values
50=(1/2){110-arc JL}
100=110-arc JL
arc JL=110-100
arc JL=10 degrees3x - 5y = 2 4x + 5y = 33
Answers
the equations are,
3x - 5y = 2
4x + 5y = 33
sum the equations,
7x = 35
x = 35/7
x = 5
put x = 5 in equation 3x - 5y = 2
3(5) - 5y = 2
15 - 2 = 5y
5y = 13
y = 13/5
thus, the answer is x = 5 and y = 13/5
i have solved your problem in the answer tab.
if you have any doubt with this solution then let me know.
Two-Way Tables• Create a two-way frequency table• Draw at least 2 conclusions / inferences from the data shown
Answers
Step 1
Create a two-way frequency table.
For example, the following two-way table shows the results of a survey that asked 100 people which sport they liked best: baseball, basketball, or football. The rows display the gender of the respondent and the columns show which sport they chose
Below is the two-way frequency table.
This is a two-way table because we have two categorical variables: gender and favorite sport.
Step 2
Draw at least 2 conclusions/inferences from the data shown.
1) The probability that a survey respondent likes basketball the most, given that the respondent is male is?
[tex]=\frac{Males\text{ that like basketball}}{Total\text{ number of male}}=\frac{15}{48}=0.3125[/tex]2) The probability that a survey respondent likes baseball the most, given that the respondent is female is?
[tex]=\frac{females\text{ that like baseball}}{Total\text{ number of female}}=\frac{23}{52}=0.4423076923[/tex]i need help with this question parts f g and h
Answers
ANSWER and EXPLANATION
f) The y-intercept of a graph is the point where the graph touches/intersects the y-axis of the coordinate grid.
Therefore, the y-intercept for the given graph is:
[tex](0,-3)[/tex]g) The domain of a function is the set of all input values for which the function is valid. In other words, it is the set of all x-values of the function.
From the given graph, we have that the domain of the function is:
[tex](-\infty,\infty)[/tex]h) The range of a function is the set of all output values for which the function is valid. In other words, it is the set of all y-values of the function.
From the given graph, we have that the range of the function is:
[tex]-3\cup[0,\infty)[/tex]That is the answer.
Bought office equipment of Rs.50,000 on cash and of Rs.70,000 on cReddit from jayaram
Answers
Answer:
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36 inches 23 inches is what fraction of a yard
Answers
If a yard contains 36 inches, then 21 inches is the 7/12 fraction of a yard
A yard contains 36 inches
We know
One yard = 36 inches
Here we have to use the unitary method for the conversion
The unitary method is the method of the value of a single unit.
36 inches = 1 yard
Then one inch = 1 / 36 yard
21 inches = (1 / 36) × 21
Multiply the terms
= 21 / 36
Divide both numerator and denominator by 3
= (21 / 3) / (36 / 3)
Divide the terms
= 7 /12 yard
Hence, if a yard contains 36 inches, then 21 inches is the 7/12 fraction of a yard
The complete question is
A yard contains 36 inches. 21 inches is what fraction of a yard ?
Learn more about unitary method here
brainly.com/question/22056199
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Mark to review later..3. Javier purchased a laptop at an electronics store 57 days ago for $385. The store's policy states that items can be returnedwithin 60 days for 90% of the original purchase price. Items can still be returned after 60 days, but there is an additional restockingfee of 2%. If Javier returns the computer today, what is the total amount he will receive as a refund
Answers
Javier has purchased the laptop 57 days ago, and the store's policy for items returned within 60 days is a 90% refund of the original price. Since Javier returned the item today, which is exactly 57 days right after his purchase, the 90% refund will be made. To solve the refunded price, we just multiply the cost of the laptop by the percent refund. We have ($385) x (90%) = $346.5.
Hence, Javier gets $346.5 as a refund on returning the laptop today.
⦁ A vine called the mile-a-minute weed is known for growing at a very fast rate. It can grow up to 0.5 ft per day. How fast in inches per hour can the mile-a-minute weed grow up to? Show your work using the correct conversion factors.
Answers
Answer:
"0.5 ft * 12 = 6 inches (because there are 12 inches in 1 foot)1 day = 24 hours0.5 ft per day = 6 inches in 24 hoursInches grown in one hour = 6/24 = 0.25"
Step-by-step explanation:
Plot the points. Then identify the polygon formed.a) A(4, 1), B(4, 6), C(-1, 6), D(-1, 1)b) A(2, -2), B(5, -2), C(7, -4), D(0, -4)
Answers
a)
The points for polygon a are shown below:
From the graph we notice that this is a square.
b)
The points for polygon b are shown below:
From the graph we conclude that this is a trapezoid.
Identify all of the features of this graph;A. Amplitude of 4B. Period of 1C. This is a sine curveD. Period of 5pi/2E. Amplitude of 2F. Midline at y= -3G. Period of 2piH. Amplitude of -1I. Midline at y= -2J. This is a cosine curvecan choose more than one
Answers
EXPLANATION
As we can see in the graph:
A. Amplitude is equal to 4 (distance from valley to ridge)
G. Period is equal to 2pi (distance from valley to valley -->5pi/2-pi/2)
F. Midline at y=-3
C. This is a sine curve (Start in pi/2).
One of the largest carnivals has 25 rides and accommodates 120 people on each ride. If every ride was was completely full 4 nights this week, how many people will the carnival accommodate during those 4 nights?
Answers
The carnival has 25 rides
Each ride accomodates 120 people (when full)
Each ride was completelly booked for 4 nights .
Step one, calculate how many people can the carnival accomodate in one night by multiplying the number of people by ride by the number of rides:
120*25= 3000
This means that in one night, the carnival can accomodate 3000 people in all 25 rides.
Step two, multiply the value obtained by the number of nights the carnival will be full:
3000*4=12000
The carnival will expect to accomodate 12000 people for 4 nights with all rides full booked.
A projectile is launched from the ground at 128 feet per second and will hit the ground after a certain amount of time. It models the function g(x) = -16x2 + 128x, where x represents the time of the of the flight (in seconds) of the projectile. What is an appropriate domain for this model? 00 0
Answers
time can only take values greater than or equal to zero, so the domain starts on 0
the las point of the domain is when the projectile hit the ground, this means when g=0
now we will replace g=0 o find the last value of the domain
[tex]\begin{gathered} g=0 \\ -16x^2+128x=0 \end{gathered}[/tex]solve x to know the last time
[tex]\begin{gathered} 16x(-x+8)=0 \\ -x+8=\frac{0}{16x} \\ -x+8=0 \\ -x=-8 \\ x=8 \\ \end{gathered}[/tex]the last time in seconds of the model is 8
so the domain is
[tex]\lbrack0,8\rbrack[/tex]In an arithmetic sequence, the difference between two consecutive terms is _______.the sameonetwoalways zero
Answers
Given
In an arithmetic sequence, the difference between two consecutive terms is _______.
Find
Complete the statement
Explanation
As we know , in the arithmetic sequence , the difference between two consecutive numbers is always same.
so , the correct answer is ,.. the same
Final Answer
Therefore , the correct option is 1.
Bart has a cylindrical pitcher with a radius of 6 cm and a height of 12 cm and a height of 12 cm he pours 1,300 cubic centimeters of lemonade into the pitcher approximately how much lemonade will a pitcher hold
Answers
SOLUTION
To determine the volume of a cylinder;
Step 1:
[tex]\begin{gathered} Volume\text{ of cylinder=}\pi r^2h \\ \pi=\frac{22}{7} \\ r=6cm \\ h=12cm \end{gathered}[/tex][tex]Volume\text{ of pitcher=}\frac{22}{7}\times6^2\times12=1357.7143\approx1358cm^3[/tex]THE ANSWER IS 1358cm^3
a deep dish pizza can be classified as what 3 dimensional object
Answers
Answer:
Cylinder
Explanation:
A deep-dish pizza can be classified as a Cylinder.
Other examples of cylinders are tins of milk, pipes, etc.