Which system of equations is satisfied by the solution shown on the graph?
Answer:
D
Step-by-step explanation:
To find the system of equations that is satisfied by the solution shown on the graph, we will simply need to find the equations of our two lines.
So, we will begin by finding the slope of each line and then proceed to find the entire equation.
Red Line:
To find the slope, we will first pick any two points from the red line.
Two sample points include (-5, 5) and (-4, 6).
The slope formula is given by:
[tex]\displaystyle m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Lett (-5, 5) be (x₁, y₁) and (-4, 6) be (x₂, y₂). Substitute:
[tex]\displaystyle m=\frac{6-5}{-4-(-5)}=\frac{1}{1}=1[/tex]
Hence, the slope of the red line is 1.
Now, we can find the entire equation. We will use the slope-intercept form:
[tex]y=mx+b[/tex]
Where m is the slope and b is the y-intercept.
We know that the slope m is 1. Hence:
[tex]y=x+b[/tex]
We need to find our y-intercept b. For the red line, we know that when x is -5, y is 5. Hence:
[tex](5)=(-5)+b[/tex]
Solving for b yields:
[tex]b=10[/tex]
Therefore, our entire equation is:
[tex]y=x+10[/tex]
Blue Line:
Again, we will find the slope first.
Picking two points, we get (0, 6) and (1, 5).
Using the slope formula by letting (0, 6) be (x₁, y₁) and (1, 5) be (x₂, y₂), we acquire:
[tex]\displaystyle m=\frac{5-6}{1-0}=\frac{-1}{1}=-1[/tex]
Hence, the slope of the blue line is -1.
Again, we can use the slope-intercept form:
[tex]y=mx+b[/tex]
Fortunately, we already know the y-intercept in this case. Since we have the point (0, 6), the y-intercept b is 6.
Therefore, our equation is:
[tex]y=-x+6[/tex]
So, our two equations are:
[tex]y=x+10\text{ and } y=-x+6[/tex]
Our answers are in standard form, so we will convert the two equations to standard form. Standard form is given by:
[tex]Ax+By=C[/tex]
Where A, B, and C are integers and A is positive.
For the first equation, we can subtract x from both sides to get:
[tex]-x+y=10[/tex]
Since A should be positive, we multiply both sides to get:
[tex]x-y=-10[/tex]
For the second equation, we can add x to both sides:
[tex]x+y=6[/tex]
Hence, our two equations in standard form is:
[tex]x+y=6\text{ and } x-y=-10[/tex]
Therefore, our final answer is D.
Answer: D x + y = 6 and x − y = -10
Step-by-step explanation:
A container has 12 1/2 cups of pancake mix. A serving uses exactly 1 1/2
cups
• How many full servings are in the container?
• How many cups of pancake mix are left over?
Enter each answer on a separate line.
Answer:
8 full servings
Step-by-step explanation:
1/2 cup of mix left
.In the recipe of a ban cake 3 cups of water is needed for 6 cups of flour .
How many cup of water is needed for 12 cups of
Answer:
6 cups of water
Step-by-step explanation:
3 cups of water = 6 cups of flour.
12 ÷ 6= 2
3 x 2= 6
3/6 -> 6/12
- I hope this helps have a great day
Which function represents the sequence -5.5, -4.75 -4,-3.25... ?
Geometry
Please help !
Would the answer be z is 64?
The graph of a Function f(x) is shown below:
What is the domain of f(x)?
Answer:
69
no
U will not get answers on a test noob
Answer:
Step-by-step explanation:
domain includes alll values of x so are from -1 to 2 except 0
[-1, 0) ∪ (0, 2]
Which of the following relations describes a function?
OA. {(-3,-4), (-4,-3), (3, 4), (4,3)}
OB. {(3,-1), (3, 1), (4, -1), (4, 1) }
OC. {(3, 3), (3, 4), (4,3), (4,4)}
OD. {(0,0), (0, 3), (3, 0), (3, 3) }
Answer:
{(-3,-4), (-4,-3), (3, 4), (4,3)}
Step-by-step explanation:
{(-3,-4), (-4,-3), (3, 4), (4,3)}
because x should not be the same in more than one pair
A parking lot is constructed in the shape of a parallelogram. A construction company needs to pave the parking lot, which will cost $3 per square foot. What is the total cost to pave the parking lot.
Answer:
[tex]\$3A[/tex]
[tex]A[/tex] denotes area of a parallelogram
Step-by-step explanation:
Given: A parking lot is in the form of a parallelogram. Per square foot cost to pave the parking lot is [tex]\$3[/tex].
To find: Total cost to pave the parking lot
Solution:
Let [tex]A[/tex] denotes area of a parallelogram.
Also,
Per square foot cost to pave the parking lot is [tex]\$3[/tex].
So,
Total cost to pave the parking lot [tex]=\$3A[/tex]
Anyone know the answer??
Help!! Please and thank you
Answer:
110.9 cm³Step-by-step explanation:
[tex]V=\frac13\cdot A_b\cdot H[/tex]
[tex]A_b[/tex] - Base Area
H - Height of the pyramid
Base is regular triangle: [tex]A_b=\dfrac{8^2\sqrt3}4[/tex]
The volume:
[tex]V=\dfrac13\times \dfrac{8^2\sqrt3}4\times 12=64\sqrt3\approx110.9[/tex]
How many terms are in the expression 4x2 + y - 0 ?
help pleaseeee
Answer:
3 I did the test to btw
Step-by-step explanation:
did the test
20% off $115 7.5% sales tax what is the final price of the coffee table
Answer:
Therefore the final price of the table coffee which is on sale by 20% with a sales tax of 7.5% is $98.9
Step-by-step explanation:
it is $98.9
Answer:
$98.9
Step-by-step explanation:
what is the y-intercept of the line shown ?
(+8) + (+6) + (+2) =
Answer:
0
Step-by-step explanation:
Multiply − 1 by − 6 . − 8 +6 + 2
Add − 8 and 6 . − 2 + 2
Add − 2 and 2 .
0
what is y-5=3(x+2) in slope intercept form
Answer:
y=3x=11 .
Step-by-step explanation:
Because this y=mx+b converted in Intercept form is the answer i already gave you :).
Liam had \$250$dollar. Then, he and his classmates bought a present for their teacher, evenly splitting the \$ p cost among the 24
of them.
Answer:
20
Step-by-step explanation:
Ricardo open a savings account with an initial deposit of $560 and will not make any additional deposits or withdrawals . The account earns 1% simple interest. What is the total amount that Ricardo will have in his account at the end of 3 years ?
A:$168.00
B:$56.00
C:$576.80
D:$565.60
Answer:
C
Step-by-step explanation:
Savannah and Reagan both work in a grocery store. They each stocked the same number of shelves last Saturday, but it took Reagan less time. They've been told that they'll spend their entire 4-hour shifts next Saturday stocking shelves. If their average speeds are consistent, who will likely stock more shelves next Saturday?
HELP!
Answer:
Reagan
Explanation:
Since Reagan is able to stock the same number of shelves as Savannah while spending less time to do so, it means that Reagan is able to stock shelves faster than Savannah, thus Reagan is able to stock more shelves than Savannah given that their average speeds are constant and that they both work under 4-hour shifts.
Hope this helps :)
One angle is five degrees less than three times the degree measure of another angle. Together, the angles measures have a sum of 143°. What is the measure of each angle?
Answer:
a
Step-by-step explanation:
HELPPPP PLEASEEEE dfuij bfsv
Answer:
7
Step-by-step explanation:
16+5+16+5+16+5
Answer: 6.875 If it aks you to round it is 7 gallons.
Step-by-step explanation:
Which expression is equivalent to 5p2+ 3p2 - 6p?
a. 2p2
b. 14p2
C. 8p2 - 6p
d. p(5p + 3p - 6)
Answer:
is c or d i think
How many numbers can fit in a number place?
Given side lengths 4 units, 8 units, and x units, determine the range in which x must lie in order for a triangle to exist.
A)
X > 12
B)
0
C)-4
D)
4
Answer:
4 < x < 12
Took the test
pleasee help!! im confused
Answer:
28k + 68
Step-by-step explanation:
7(8 + 4k) + 12
first, you use the distributive property on the parentheses
56 + 28k + 12
then you add like term, 56 + 12 = 68
68 + 28k
numbers with variables go first
28k + 68
Use long division to calculate 276 ÷ 15
Answer:
18.4
Step-by-step explanation:
Drag and drop numbers into the equation to complete the equation of the line in slope-intercept form.
The line passes through (7, 13) and (4,1).
The equation of the line is y =
X +
15
-15
4
Answer:
y = 4x - 15
Step-by-step explanation:
Find slope (m) using of the line that passes through (7, 13) and (4, 1).
[tex] slope (m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{1 - 13}{4 - 7} = \frac{-12}{-3} = 4 [/tex]
Find y-intercept (b) by substituting x = 4, y = 1, and m = 4 in y = mx + b.
Thus:
1 = (4)(4) + b
1 = 16 + b
Subtract 16 from each side
-15 = b
b = -15
substitute m = 4, and b = -15 in y = mx + b, to get the equation.
The equation of the line would be:
✅ y = 4x + (-15)
y = 4x - 15
Which of the following is the point-slope equation of the line that passes through
(4,-2) and has a slope of 1/2?
Answer: y + 2= 0.5(x - 4) Is this good?
Step-by-step explanation:
Write the equation of the line given the following: Passes through (-2, 7) and is parallel to the graph y=-8x-2.
Answer:
y = -8x+9
Step-by-step explanation:
7 = -8(-2) - b
7 = 16 - b
-9 = -b
b = 9
y = -8x+9
How many tables that seat eight are required to provide places for 62 people at a banquet
Answer:
8
Step-by-step explanation:
62 divided by 8 is 7.75
you can't cut people so round it up and you get 8
Write 12 1/3 as an improper fraction.
Answer: 37/3
Step-by-step explanation:
12 1/3 = 12*3+1/3 = 37/3
Answer:
[tex]\frac{37}{3}[/tex]
Step-by-step explanation:
[tex]12\frac{1}{3}[/tex]
When converting mixed numbers (such as the one above), to improper fractions, we must first multiply the whole number by the denominator:
[tex]12*3=36[/tex]
Then, add the numerator the the product:
[tex]36+1=37[/tex]
Now, put the sum over the denominator to get your solution:
[tex]\frac{37}{3}[/tex]
-
To check your work, you can convert the improper fraction to a mixed number to make sure you will end up with [tex]12\frac{1}{3}[/tex].
Divide [tex]37[/tex] into [tex]3[/tex]:
[tex]12[/tex] with a remainder of [tex]1[/tex]
Put the remainder over the denominator:
[tex]12\frac{1}{3}[/tex]
Therefore, our solution is correct!