Sylvie finds the solution to the system of equations by graphing.
y = A system of equations. y equals StartFraction 2 over 3 EndFraction x plus 1. y equals negative StartFraction 2 over 3 EndFraction x minus 1x + 1 and y = x – 1
Which graph shows the solution to Sylvie’s system of equations?
A coordinate grid with 2 lines. The first line passes through the points (negative 1.7, 1.57), (0, negative 1), and (2, negative 4). The second line passes through the points (negative 1.7, 1.57), (0, 1), and (3, 0).
A coordinate grid with 2 lines. The first line passes through the points (negative 1.02, 0.63), (0, negative 1), and (2, negative 4). The second line passes through the points (negative 1.02, 0.63), (0, 1), and (3, 2).
A coordinate grid with 2 lines. The first line passes through the points (negative 1.5, 0), (0, negative 1), and (3, negative 3). The second line passes through the points (negative 1.5, 0), (0, 1), and (3, 3).
A coordinate grid with 2 lines. The first line passes through the points (negative 1.71, 0.14), (0, negative 1), and (3, negative 3). The second line passes through the points (negative 1.71, 0.14), (0, 1), and (2, 2).
Answers
Answer:
The correct answer is:
A coordinate grid with 2 lines. The first line passes through the points (negative 1.5, 0), (0, negative 1), and (3, negative 3). The second line passes through the points (negative 1.5, 0), (0, 1), and (3, 3).
Step-by-step explanation:
We are given the system of equations as:
[tex]1.\ y=-\dfrac{2}{3}x-1\\2.\ y=\dfrac{2}{3}x+1\\[/tex]
We have 2 equations here with variables x and y so we use coordinate grid with 2 lines having axis as x and y.
As per the given options, we can see that coordinate of one point has y = 0 and other point has x = 0.
So, let us put y = 0 and x =0, in both the equations one by one and have a look at the value of x coordinate.
y = 0, Equation (1) becomes:
[tex]0=-\dfrac{2}{3}x-1\\\Rightarrow 1 =-\dfrac{2}{3}x\\\Rightarrow x = - 1.5[/tex]
So, one coordinate is (-1.5, 0)
x = 0, Equation (1) becomes:
[tex]y=-\dfrac{2}{3}\times 0-1\\\Rightarrow y =-1[/tex]
So, other coordinate is (0, -1)
And the point (3, -3) also satisfies the given equation.
y = 0, Equation (2) becomes:
[tex]0=\dfrac{2}{3}x+1\\\Rightarrow 1 =-\dfrac{2}{3}x\\\Rightarrow x = - 1.5[/tex]
So, one coordinate is (-1.5, 0)
x = 0, Equation (2) becomes:
[tex]y=\dfrac{2}{3}\times 0+1\\\Rightarrow y =1[/tex]
So, other coordinate is (0, 1)
And the point (3, 3) also satisfies the given equation.
Please refer to the attached graph and points on lines.
So, correct answer is:
A coordinate grid with 2 lines. The first line passes through the points (negative 1.5, 0), (0, negative 1), and (3, negative 3). The second line passes through the points (negative 1.5, 0), (0, 1), and (3, 3).
Answer:
D
Step-by-step explanation:
trust
Related Questions
he salad contains fruits and vegetables. There are at most 8 pounds of fruits and vegetables in the salad. Write the system of inequalities to represent this situation.
Answers
Answer:
The system of inequalities to represent this situation is [tex]x+y \leq 8[/tex]
Step-by-step explanation:
Let the amount of fruits be x pounds
Let the amount of vegetables be y pounds
We are given that There are at most 8 pounds of fruits and vegetables in the salad.
This means that there are less than or equal to 8 pounds of fruits and vegetables in the salad.
So,[tex]x+y \leq 8[/tex]
Hence the system of inequalities to represent this situation is [tex]x+y \leq 8[/tex]
The point $(p,9)$ lies on line $k$ shown here. What is the value of $p$?
Answers
Answer:
(10,9) P=10
Step-by-step explanation:
find the slope first: y2-y1/x2-x1=(3-1)/1-(-2)=2/3
y=2/3x+b
find b:
3=2/3(1)+b
b=3-2/3
b=7/3
now we find P
(p,9) input the y in the equation
y=2/3 x+7/3
9=2/3x+7/3
9-7/3=2/3x
x=10
**BRAINLIEST IF ANSWERED*****
Circle P has a radius of 5.
What is its exact circumference?
5pi
10 pi
15pi
20pi
Answers
Answer:
The answer is 10piStep-by-step explanation:
Circumference of a circle is 2πr
where r is the radius
radius = 5
Circumference of circle P is
2π × 5
= 10πHope this helps you
x=4y+7 2x-6y=12 System of equations using substitution
Answers
Answer:
x=3, y=-1
Step-by-step explanation:
We are already given an equation solved for x, making substitution much easier. We know x=4y+7, meaning we can put 4y+7 whenever we see x in the second equation
2x-6y=12
We substitute 4y+7 in place of x
2(4y+7)-6y=12
Now we only have one variable to work on, distribute the 2
8y+14-6y=12
Combine similar terms, 8y-6y=2y
2y+14=12
Subtract 14 from both sides
2y=-2
y=-1
Now we plug in -1 for y in the first equation to find x
x=4(-1)+7
x=-4+7
x=3
The required solution of the given system of equations are x = 3 and y = -1.
What is the equation?The term "equation" refers to mathematical statements that have at least two terms with variables or integers that are equal.
The given system of equations is below as:
x = 4y + 7 ....(i)
2x - 6y = 12 ....(ii)
To solve the equations, use the substitution method.
Substitute the value of equation x = 4y+7 in (ii), and solve for y
2(4y + 7) - 6y = 12
8y + 14 - 6y = 12
8y - 6y = 2y
2y + 14 = 12
Subtract 14 from both sides of the equation
2y = -2
y = -1
Substitute the value of y = -1 in (i), and solve for x
x = 4(-1) + 7
x = -4 + 7
x = 3
Thus, the required solution of the given system of equations are x = 3 and y = -1.
Learn more about the equation here:
brainly.com/question/10413253
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What are the zeros of f(x) = x(x - 9)?
A. X = 0 only
B. X = 0 and x = -9
O
C. x = 9 only
O D. x = 0 and x = 9
Answers
Explanation:
x(x-9) = 0
=> x = 0
=> x-9 = 0
=> x = 9
A piece of aluminum with a mass of 100.0 g has a temperature of 20.0°C. It absorbs 1100 J of heat energy. What is the final temperature of the metal?
Answers
Answer:
31.81°CStep-by-step explanation:
Using the formula for calculating heat energy H = mcΔT
m = mass of the aluminum (in g/kg)
c = specific heat capacity of aluminum
ΔT = change in temperature = T - Ti (in °C)
T is the final temperature
Ti is the initial temperature
Given m = 100.0g, c = 0.931096J/g °C, Ti = 20°C, H = 1100J T = ?
Substituting the given values into the formula;
1100 = 100*0.931096 (T - 20)
1100 = 93.1096T - 1862.192
93.1096 T = 1100+1862.192
93.1096 T = 2962.192
T = 2962.192/93.1096
T = 31.81°C
The final temperature of the metal is 31.81°C
Answer:
31.81c
Step-by-step explanation:
1100 = 100*0.931096 (T - 20)
1100 = 93.1096T - 1862.192
93.1096 T = 1100+1862.192
93.1096 T = 2962.192
T = 2962.192/93.1096
T = 31.81°C
translate into an algebraic expression: x is increased by 50% and decreased by 30% . What is the result?
Answers
Answer:
x+4/5x
Step-by-step explanation:
x is increased by 80% 0f it self
80%of x= 4/5x
... x+4/5x
1.
Which of the following equations is equivalent to 1.43p + 2.2= -4.001 use photo for choices
Answers
Answer:
1430p + 2200 = -4001
Step-by-step explanation:
The graphs show the distances traveled by two people walking at constant rates. Drag to the table the unit rate that matches each graph.
Answers
Answer:
from left: 220, 177
Step-by-step explanation:
unit rate = first derivative = slope
first graph;
slope = (880-660)/(4-3) = 220 ft/min
2nd graph;
slope = (177-0)/(1-0) = 177 ft/min
Create a rectangle around the parallelogram. The dimensions of this rectangle are .
Find the area of the four right triangles surrounding the parallelogram. The total area of the triangles is square units.
Subtract the triangle areas from the area of the rectangle to obtain the area of the parallelogram. The area of parallelogram ABCD is square units.
Answers
Answer:
First drop down: 11 by 20
Second drop down: 110
Third drop down: 110
The new coordinates of the rectangle will be A'(-3, 9), B'(8, 9),C'(8, -11), and D'(-3, -11) .
What is a parallelogram?A quadrilateral with the opposing sides parallel is called a parallelogram (and therefore opposite angles equal). A parallelogram with all right angles is known as a rectangle, while a quadrilateral with equal sides is known as a rhombus.
Given, a parallelogram with the dimension of A(-3, -1), B(7, 9), C(8, -1), and D(-2, -11)
The rectangle around the parallelogram will cover the parallelogram with horizontal and vertical lines,
Thus the new coordinates of the rectangle will be:
A'(-3, 9), B'(8, 9),C'(8, -11), and D'(-3, -11) as shown in the figure,
Learn more about parallelograms here:
https://brainly.com/question/29147156
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Complete question:
What is the area of triangle qrs?
Answers
Answer:
area=HbB/2
hope you understand
Please answer this question fast in two minutes
Answers
Answer:
(8, -7)
Step-by-step explanation:
QR, R= (-2, -1)
M= (3, -4)
Q= ?
--------
3= (-2+x)/2 ⇒ x= 6+2= 8-4= (-1+y)/2 ⇒ y= -8+1= -7Q= (8, -7)
Determine the unknown side lengths’ to the nearest tenth. for the first question and also please help with question 6
Answers
Answer:
z =15cm and
y=9.0cm
Step-by-step explanation:
Use sine rule
12/ sin53 = z / sin 90
Z = 12 x sin 90 / sin 53
Z = 15cm
To find y the angle opposite to y will be 180-(90+53)=37º
So
15/sin 90= y/sin37
y= 15 x sin37 /sin 90
y = 9.0cm
Can someone explain this to me I need help T_T
Answers
Answer: 6,800,000 people
Step-by-step explanation:
We are looking for the number of people, not the percentage of wealth that has been made up by the people.
2% of the people are the richest in the United States, and there are 340,000,000 people in total in the United States.
2% = 0.02
340,000,000 * 0.02 = 6,800,000
I hope this was helpful! :)
What is the equivalent radian measure of 540°?
1
radians
3
radians
radians
3
3x radians
DONE
Answers
Answer: 3π
I don't see 3π in your answer choices, but I'm assuming the "3x" is supposed to be 3π.
Step-by-step explanation:
To convert from degrees to radians, you multiply by π/180.
[tex]540*\frac{\pi }{180} =3\pi[/tex]
Whic transformation could.be performed to show that triangle abc is similar to triangle a”b”c”
Answers
Answer:
Its a dilation, either a big dilation or small dilation, a b c is the pre image and a"b"c" is the image :O
Step-by-step explanation:
The velocity of an object in meters per second varies directly with time in seconds since the object was dropped, as represented by the table.
The acceleration due to gravity is the constant of variation. What is the acceleration due to gravity of a falling object?
Answers
The answer is 9.8 m/s2
Answer:
B. 9.8 m/s^2
Step-by-step explanation:
I got it correct on edg2020
rearrange to make x the subject t=bx/3
Answers
Answer:
x = 3t/b
Step-by-step explanation:
Step 1: Multiply both sides by 3
t = bx/3
3t = bx
Step 2: Divide both sides by b
3t/b = x
???????????????????????
Answers
Answer:
D is the answer
Step-by-step explanation:
because it has high probability of success 70 %
so
8 of 8
Find the product of 505 and 68
Answers
Answer:
Step-by-step explanation:
505 × 68 = 34340
Answer:
34340
Step-by-step explanation:
Plz mark me brainliest!
Find m∠V. Struggling in geometry! Help plz :/
Answers
Answer:
16 degrees
Step-by-step explanation:
74 + 90 = 164
180-164 = 16
Both triangles are congruent so that means Angle T is 74 degrees. There is also a right angle which means there is 90 degrees in that angle. A triangle always has 180 degrees so add 74+90 which is 164. Then subtract 180-164=16
Good luck :)
if you graph the system of Inequalities given below, which points would lie in the solution set? Select all the correct answers.
x-y2-4
2x-ys 5
2y+ x>1
Answers
Answer:
(-1,3)
Step-by-step explanation:
we need to replace the values x and y for every point and see if the point satisfies all the inequations.
Point (-2,3):
x - y ≥ -4
-2 - 3 ≥ -4
-5 ≥ -4
Then, -5 is not greater than -4, so that point is not a solution.
Point (-1,3):
x - y ≥ 4 2x - y ≤ 5 2y + x > 1
-1 - 3 ≥ 4 2(-1) - 3 ≤ 5 2(3) + (-1) > 1
-4 ≥ -4 -5 ≤ 5 5 > 1
Then, (-1,3) is a solution
Point (0,0):
x - y ≥ 4 2x - y ≤ 5 2y + x > 1
0 - 0 ≥ 4 2(0) - 0 ≤ 5 2(0) + (0) > 1
0 ≥ -4 0 ≤ 5 0 > 1
Then, 0 is not greater than 1, so that point is not a solution.
Point (2,-2):
x - y ≥ 4 2x - y ≤ 5
2 - (-2) ≥ 4 2(2) - (-2) ≤ 5
4 ≥ -4 6 ≤ 5
Then, 5 is not greater than 6, so that point is not a solution.
If f(x) = x^2 is translated 3 units to the right to form g(x), which of the following equations best represents the new graph? g(x) = x^2 - 3 g(x) = (x - 3)^2 g(x) = x^2 + 3 g(x) = (x + 3)^2
Answers
Answer:g(x) = (x + 3)^2
Step-by-step explanation:
It is translated 3 units to the right so it is the only one that makes sense!
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α' β
5. A quadratic equation 2x2 = 6x + 3 has two roots p and q. Find the quadratic equations with
roots p2q and pq2?
Answers
Answer:
8x² +36x -27=0
Step-by-step explanation:
2x²= 6x +3
Let's rewrite the equation into the form of ax²+bx+c= 0.
2x² -6x -3=0
Thus, a= 2
b= -6
c= -3
Sum of roots= [tex] - \frac{b}{a} [/tex]
Since your roots are p and q, sum of roots= p +q
p +q= [tex] - (\frac{ - 6}{2} )[/tex]
p +q= 6 ÷2
p +q= 3
Product of roots= [tex] \frac{c}{a} [/tex]
pq= [tex] - \frac{3}{2} [/tex]
Quadratic equations:
x² -(sum of roots)x +(product of roots)= 0
Thus, we have to find the sum and the product of the new roots, p²q and pq².
p +q= 3
pq= -3/2
Product of new roots
= (p²q)(pq²)
= p³q³
= (pq)³
[tex] = ( - \frac{3}{2} )^{3} \\ = - \frac{27}{8} [/tex]
sum of new roots
= p²q +pq²
= pq(p +q)
= (-3/2)(3)
= -9/2
Thus, the quadratic equation with roots p²q and pq² is
x² -(-9/2)x -27/8 = 0
[tex]x ^{2} + \frac{9}{2} x - \frac{27}{8} = 0[/tex]
Multiply by 8 throughout:
[tex]8 {x}^{2} + 36x - 27 = 0[/tex]
A company that sells widgets has to pay 1000 in one-time equipment fees and then it costs $\$0.50$ for each widget it makes. It sells widgets at a price of $2.75 per widget. What is the least number of widgets the company has to sell in order to make a profit?
Answers
Answer:
[tex]445[/tex]
Step-by-step explanation:
[tex]\text{Profit}=\text{Price}-\text{Cost}\\\text{Profit}=2.75-50=2.25\\\text{In order to make back the starting amount we need to sell n lots of widgets.}\\2.25n\geq 1000\\n\geq \frac{1000}{2.25}\\n\geq 444.444444\\\text{You can't sell a fraction of products, so you need to round it up to the nearest number.}\\n=445[/tex]
Answer:
12 widgets
Step-by-step explanation:
A hemisphere is exactly one-half of a sphere. Find the volume of a hemisphere where the radius is 6 m. (Round to the nearest tenth)
Answers
Answer:
144π or 452.4
Step-by-step explanation:
Volume of a Sphere Formula: V = 4/3πr³
Step 1: Plug in 6 for r
V = 4/3π(6)³
V = 288π
Step 2: Divide by 2
V = 288π/2
V = 144π
HELP ASAP FUNCTIONS!!!!
Answers
Answer: A) y is less than or equal to 5
Step-by-step explanation:
This graph portrays a ray that starts at five and moves down forever. It never stops decreasing, so there is no limit to how low it can go. It also never goes above five, thus the <5
Answer:
A. y (is less than or equal to 5)
Step-by-step explanation:
The point starts at y-5 and there is a ray going downwards. the y value will never be greater than 5 if the line is going down.
What is the order of this from least to greatest. 4.37, 5.844, 5 21/25,117/20
Answers
Find m
A. 46
B. 23
C. 69
D. 167
Answers
Answer:
69, nice
Step-by-step explanation:
118-49=69
Answer:
i think its 69, but i think im wrong
Step-by-step explanation:
Bubba Bulldog and all of his dog friends love to hide bones! Bubba hid 444 bones, Barry hid 555 bones, Larry hid 101010 bones, and Goby hid 131313 bones. Find the mean number of dog bones. 20 POINTS PLEASE HELP
Answers
Answer:
58,330.5
Step-by-step explanation:
To get the mean of something, you add all the numbers then divide it by the number of things added. I added them all, then divided by 4 to get 58,330.5
Hope this helps GL on the rest of your Khan Academy! :)
Answer:
The correct answer is 8
Step-by-step explanation: