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A pair of linear equations is shown: y = −x + 1 y = 2x + 4 Which of the following statements best explains the steps to solve the pair of equations graphically? On a graph, plot the line y = −x + 1, which has y-intercept = −1 and slope = 1, and y = 2x + 4, which has y-intercept = 2 and slope = 4, and write the coordinates of the point of intersection of the two lines as the solution. On a graph, plot the line y = −x + 1, which has y-intercept = 1 and slope = 1, and y = 2x + 4, which has y-intercept = 1 and slope = 4, and write the coordinates of the point of intersection of the two lines as the solution. On a graph, plot the line y = −x + 1, which has y-intercept = 1 and slope = −1, and y = 2x + 4, which has y-intercept = −2 and slope = 2, and write the coordinates of the point of intersection of the two lines as the solution. On a graph, plot the line y = −x + 1, which has y-intercept = 1 and slope = −1, and y = 2x + 4, which has y-intercept = 4 and slope = 2, and write the coordinates of the point of intersection of the two lines as the solution.
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Answer:
The last option is correct:
"On a graph, plot the line y = −x + 1, which has y-intercept = 1 and slope = −1, and y = 2x + 4, which has y-intercept = 4 and slope = 2, and write the coordinates of the point of intersection of the two lines as the solution."
Step-by-step explanation:
We have a pair of equations of lines:
y=-x+1
y=2x+4
The equation of a line can be written as follows:
y=mx+b
Where m is the slope and b is the y-intercept.
Following the form of both lines, we can conclude that:
The first line has slope -1 and y-intercept 1
The second line has slope 2 and y-intercept 4.
To solve the system of equations graphically, we must plot both lines and write the coordinates of the point of intersection of the lines as the solution.
The only option which has all the correct information is the last one:
"On a graph, plot the line y = −x + 1, which has y-intercept = 1 and slope = −1, and y = 2x + 4, which has y-intercept = 4 and slope = 2, and write the coordinates of the point of intersection of the two lines as the solution."
The fourth option is correct which is : On a graph, plot the line y = −x + 1, which has y-intercept = 1 and slope = −1, and y = 2x + 4, which has y-intercept = 4 and slope = 2, and write the coordinates of the point of intersection of the two lines as the solution.
For plotting the graph of a line we compare the given equation of the line to the standard equation: y = mx + c
where m = slope of the lie
c = intercept on y- axis
(i) y = -x + 1
comparing with y = mx + c we get,
slope m = -1
y-intercept c = 1
(ii) y = 2x + 4
comparing with y = mx + c we get,
slope m = 2
y-intercept c = 4
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Consider f(x) = mx + b where m and b are both non-zero constants. The function g(x) is the inverse of f(x). Which of the following functions is g(x)? Use composition of functions to check your answer.
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Answer:
2x-54n
Step-by-step explanation:
1. Factor the expression completely 20x^4+80x^3-5x^2-20x
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Answer:
5x(x+4)(2x+1)(2x−1)
Step-by-step explanation:
Can some one PLEASE answer these for me? (I’ll also mark you brainliest!)
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Answer:
0.83
Step-by-step explanation:
Answer:
0.83 A
Step-by-step explanation:
find the number of point p that is 1/4 of the way from a to b.
A__________________B
-15 33
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Answer:12
Step-by-step explanation:33 + 15=48 48/4=12
8+9 divided by 3 in algebraic expression
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Answer:
(8 + 9) ÷ 3 = x
Step-by-step explanation:
You first need to add 8+9, so you put them in parenthesis for PEMDAS
Then you divide them by 3
Finally, you make the answer a variable as an algebraic expression involves variables and the answer is not given
In Level 1, Nora earned 16 points because her bridge passed inspection. Then, she lost 25 points because part of her bridge collapsed! What was Nora's score at the end of Level 1?
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Answer:
-9 points
Step-by-step explanation:
A taco stand sells tacos for $3.50 each. The stand's expenses for the day are
$180. How many tacos do they need to sell in a day in order to make a profit?
Write and solve an equation.
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52 tacos
3.5x<180
Step-by-step explanation:
it would be bigger than symbol because the minimum they need to sell is 52 but they could sell more
Simplify: –3(y + 2)2 – 5 + 6y
What is the simplified product in standard form?
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Answer:
-17
Step-by-step explanation:
[tex] - 3{(y + 2)}^{2} - 5 + 6y \\ - 3(y + 2)(y + 2) - 5 + 6y \\ ( - 3y - 6)(y + 2) - 5 + 6y \\ - 3 {y}^{2} - 6y - 6y - 12 - 5 + 6y \\ - 3 {y}^{2} - 12y - 12 - 5 + 6y \\ - 3 {y}^{2} - 12y + 6y - 12 - 5 \\ - 3 {y}^{2} - 6y - 17[/tex]
Answer[tex]-3y^{2}-6y-17[/tex]
slope line in simplest form
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Answer:
y=-2/3x
I think that's the simplest form
Patty needs a total of $80 to buy a bicycle. She has already saved $35. If she saves $10 a week from her earnings, what is the least number of weeks she must work to have enough money to buy the bicycle?
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Answer:
5 weeks
Step-by-step explanation:
She would need to work at least 8 weeks because the bicycle is $80 and she has $35.
Answer:
5 weeks
Step-by-step explanation:
i took 80 - 35 to get 45 (money she still needs)
then took 45 divided by 10 to get 4.5 ( how many weeks till she has the money)
and if you get 10 dollars per week and its asking how many weeks
you have to up the 4 by one because it has a .5
so it would be 5 weeks
Given f(x)=3x2+7 and g(x)=5x-4 solve f(5) btw in the problem the 2 is on top of the X
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Answer:
f(5) = 82
Step-by-step explanation:
To evaluate f(5) substitute x = 5 into f(x) , that is
f(5) = 3(5)² + 7 = 3(25) + 7 = 75 + 7 = 82
BRAINLIST!!!!!!!!!
which one is a function???
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Answer: C
i hope this helps
2 + 6x equals 1 - x
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Answer:
x = -1/7
Step-by-step explanation:
simplify by bringing all the x to the left and all the constants to the right:
6x + x = 1 - 2
7x = -1 (divide by 7)
x = -1/7
x=1/5
Step-by-step explanation:
2+6x= 1-x
=> Transfer the same algebraic terms in one side
2-1 = -x+6x
{things get negavtive sign when they are transfered to another side}
1=5x
x=1/5
Please help look at the screenshot
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Answer:
Step-by-step explanation: 40 newtons to the right
number 3 pls!!! I need help with figuring it out
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Answer:
C. Angle MNP
Step-by-step explanation:
Check the corresponding equal sides with congruent angles
Answer: Third choice. [tex]\angle MNP[/tex]
=======================================================
Explanation:
We want to find something congruent to angle ABC.
With angle ABC, we have
A firstB secondC thirdThe order is important.
Looking at the triangle on the right, we see that
angle A has three arc marksangle B has one arc markangle C has two arc marksThe sequence of arc markings can be written as 3,1,2
Now focus your attention on the triangle on the left. Start with the triple arc angle, move to the single arc angle, then go to the double arc angle. You should trace out M, N then P in that exact order.
Therefore [tex]\angle ABC \cong \angle MNP[/tex]
Note how M is first, N is second, then P is third.
This lets us form these pairs of congruences
A = M (first letters; triple arc marking)B = N (second letters; single arc marking)C = P (third letters; double arc marking)what is the relationship between the radius and diameter of a circle?
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The relationship between the radius and diameter of a circle is that the diameter is twice the length of the radius.
In other words, the diameter of a circle is equal to 2 times the radius. Mathematically, this relationship can be expressed as:
Diameter (D) = 2 * Radius (r)
This relationship is consistent for all circles. No matter the size of the circle, the diameter will always be exactly twice the length of the radius. The radius is the distance from the center of the circle to any point on the circle's circumference, while the diameter is the distance from one point on the circumference to another, passing through the center. Understanding this relationship is essential in various geometrical calculations and formulas involving circles.
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A government is investing Heavily in many different industries. It is improving roads to allow companies to ship their products more easily, making sure high speed Internet is available at a low cost, and loaning money to start up companies. It is also increasing funding for education to make sure the next generation of workers as the skills that needs to be productive. Which macroeconomic goal is this government trying to achieve?
A. Decreasing per capita GDP
B. Reducing unemployment
C. Reducing inflation
D. Increasing GDP
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What the government is trying to achieve is to incease the output within the borders of the country which will result to: D. increasing GDP.
What is GDP?GDP stands for gross domestic product. It is the monetary value of of goods and services produced in a country over a period of time by the final user.
GDP aacounts for all output that are generated within a country's border.
Therefore, the macroeconmic goal that the government aims to achieve through its given actions is: D. increasing GDP.
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Answer:reducing unemployment
Step-by-step explanation:just took test
Which of the following is both a perfect square and a perfect cube?
64
16
81
1,000
I know the answer is 64, but how? Can someone please explain me to me how to work this out?
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A survey of 500 college students moving into their dorm revealed that 425 brought a microwave, 380 brought a
video game console, and 50 brought neither a microwave nor a game console. A survey participant is randomly
selected. Let M be the event that the participant brought a microwave and let C be the event that the participant
brought a video game console. Organize these events in a two-way table. What is the probability that the participant
brought both a microwave and a console, P(M and C)?
0.65
0.71
0.76
0.90
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Answer:
The answer is B. 0.71
Step-by-step explanation:
The probability that the participant brought both a microwave and a console is 0.65.
Since a survey of 500 college students moving into their dorm revealed that 425 brought a microwave, 380 brought a video game console, and 50 brought neither a microwave nor a game console, to determine what is the probability that the participant brought both a microwave and a console the following calculation must be performed:
500 = 425 1 = X 425/500 = X 0.85 = X 380/500 = X 0.76 = X 0.85 x 0.76 = X 0.646 = X
Therefore, the probability that the participant brought both a microwave and a console is 0.65.
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Solve the power equation
x to the 1/2 power + 3=5
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Answer:
x = 4
Step-by-step explanation:
Solve for x by simplifying both sides of the equation, then isolating the variable.
At a fabric store, fabrics are sold by the yard. A dressmaker spent $36.35 on 4.25 yards of silk and cotton fabrics for a dress. Silk is $16.90 per yard and cotton is $4 per yard. Here is a system of equations that represent the constraints in the situation. x + y = 4.25 16.90x + 4y = 36.35 Find the solutions to the system of equations. Explain or show your reasoning
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Given:
The system of equations that represent the constraints for the given situation is
[tex]x+y=4.25[/tex]
[tex]16.90x+4y=36.35[/tex]
To find:
The solution of given system of equations.
Solution:
We have,
[tex]x+y=4.25[/tex] ...(i)
[tex]16.90x+4y=36.35[/tex] ...(ii)
Multiply equation (i) by 4.
[tex]4x+4y=17[/tex] ...(iii)
Subtracting (iii) from (ii), we get
[tex]16.90x+4y-(4x+4y)=36.35-17[/tex]
[tex]16.90x+4y-4x-4y=19.35[/tex]
[tex]12.90x=19.35[/tex]
Divide both sides by 12.90.
[tex]x=\dfrac{19.35}{12.90}[/tex]
[tex]x=1.5[/tex]
Put this value in (i).
[tex]1.5+y=4.25[/tex]
[tex]y=4.25-1.5[/tex]
[tex]y=2.75[/tex]
The solution of system of equations is x=1.5 and y=2.75. It means, the yards of silk are 1.5 and yards of cotton are 2.75.
1. The first step to solving a 2-Step Equation, like in the problem below, is
to: *
2 points
-3x + 5 = 12
Division: Divide both sides by -3 to isolate the variable.
Addition: Add 3 to both sides to isolate the variable.
Subtraction: Subtract 5 from both sides to isolate the variable term.
Multiplication: Multiply by the common denominator 60.
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Answer:
addition add 3 to both sides to isolate the variable term
decimal equivalent 9 1/3
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The decimal equivalent to 9 1/3 is
SBS: step multiply whole number 1:9 x 3=27 step add product 2: 27+1=28 step 3 divide: 28 ÷ 3= 9.333333
Final answer in decimal form: 9.33
Therefore, the answer is C
The equivalent from of [tex]9\frac{1}{3}[/tex] ⇒ 9.
The given mixed fraction is,
[tex]9\frac{1}{3}[/tex]
Now to convert it into decimal form
First of all convert it into simple fraction
So numerator of [tex]9\frac{1}{3}[/tex] is formed by multiplying 3 with 9 then add 1
and denominator remains same as 3
Therefore,
Simple fraction be
[tex]9\frac{1}{3}[/tex] ⇒ (9x3 + 1)/3
= 28/3
Now divide 28 by 3
we get,
9.333333
Here,
It is non terminating number
And 3 is repeating after decimal
therefore,
The decimal form of [tex]9\frac{1}{3}[/tex] ⇒ 9.[tex]\frac{}{3}[/tex]
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Which describes the graph of y = (x - 5)2 - 4?
O A. Opens up with a vertex at (5, -4)
B. Opens down with a vertex at (-5,-4)
ting
C. Opens up with a vertex at (-5,-4)
O D. Opens down with a vertex at (5,-4)
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Answer:
A. Opens up with a vertex at (5,-4)
Step-by-step explanation:
Apex
Answer: A. Opens up with a vertex at (5,-4)
Step-by-step explanation:
$30 for 2 1/2 hours of work
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Answer:
$75
Step-by-step explanation:
30*2.5 = 75
Mrs. Lowry drove 20 miles in 25 hour. What is Mrs. Lowry’s speed in miles per hour?
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Answer:
Mrs. Lowry is driving 0.8 mph.
Step-by-step explanation:
If she is going 20 miles per 25 hours you would set up the problem as 20/25 or 20 ÷ 25. This is because you need to get down to how many miles she is traveling per 1 hour. So, 20 ÷ 25 = 0.8. Therefore she is going 0.8 miles per 1 hr.
Given the following roots x = 2, -3, 4. Write a polynomial function p(x)
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Answer:
[tex]x^3-3x^2-10x+24[/tex]
Step-by-step explanation:
The first thing that you have to do is take the roots that you're given and write binomial products.
[tex]x= 2, -3, 4[/tex]
[tex](x-2)(x+3)(x-4)[/tex]
Remember that a root is the value of "x" in a binomial expression, so the binomial expression itself will have the opposite sign of the root.
The next thing you have to do is multiply the roots together. A good way to do this is the "box method."
(See attachment below for the multiplication of [tex](x-2)[/tex] and [tex]x+3[/tex]. )
Next, multiply your new trinomial by your remaining binomial. (See additional attachment below for the multiplication of [tex](x^2+x-6)[/tex] and [tex](x-4)[/tex])
The resulting polynomial is [tex]x^3-3x^2-10x+24[/tex].
A newborn baby has about 26,000,000,000 cells. An adult has about 1.9 X 10^3 times as many cells as a newborn. About how many cells does an adult have? Write your answer in scientific notation.
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Answer:
1900
Step-by-step explanation:
26,000,000,000 cells = 2.6 x 10^10 (baby cells)
An adult has about 4.94 times 10 to the thirteenth power
(4.94 x 10^13)/(2.6 x 10^10) = 1.9 x 10^3 = 1900
Rewrite the expression using the distributive property: 3(2r + 2)
Answers
Answer:
3(2r+2) = 6r + 6
Step-by-step explanation:
Three times to is six just add the ''r'' to the six and you have six ''r'' then youdo three times two which is six