Answer:
F(3,3)
Step-by-step explanation:
The coordinate of F is (3, 3).
GivenThree vertices of parallelogram DEFG are D(0, 2), E(-1, 5), and G (4, 0).
What is the formula to find the midpoints?Diagonals of a parallelogram bisect each other, meaning they divide each other into equal parts.
The formula is used to find the midpoints are as follows;
[tex]\rm \dfrac{x_1+x_2}{2} , \ \dfrac{y_1+y_2}{2}[/tex]
Let (x, y) = coordinates of vertex F.
DF and EG are diagonals of parallelogram DEFG, therefore:
The midpoint of DF = midpoint of EG
Then,
The midpoint of D(0, 2) and F(x, y) is;
[tex]\rm \dfrac{x_1+x_2}{2} , \ \dfrac{y_1+y_2}{2}\\\\\dfrac{0+x}{2}, \ \dfrac{2+y}{2}[/tex]
The midpoint of E(-1, 5) and G(4, 0) is;
[tex]\rm \dfrac{x_1+x_2}{2} , \ \dfrac{y_1+y_2}{2}\\\\\rm \dfrac{-1+4}{2} , \ \dfrac{5+0}{2}\\\\\dfrac{3}{2}, \dfrac{5}{2}[/tex]
Comparing the equation;
[tex]\rm \dfrac{0+x}{2} = \dfrac{3}{2}\\\\\dfrac{x}{2} = \dfrac{3}{2}\\\\x=3[/tex]
[tex]\rm \dfrac{2+y}{2} =\dfrac{5}{2}\\\\2+y =5\\\\y = 5-2\\\\y =3[/tex]
Hence, the coordinate of F is (3, 3).
To know more about Midpoints click the link given below.
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y = 2x – 4
y = -x + 5
Answer:
(3, 2)
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Algebra I
Solving systems of equations using substitution/eliminationStep-by-step explanation:
Step 1: Define Systems
y = 2x - 4
y = -x + 5
Step 2: Solve for x
Substitution
Substitute in y: 2x - 4 = -x + 5Add x to both sides: 3x - 4 = 5Add 4 to both sides: 3x = 9Isolate x: x = 3Step 3: Solve for y
Define equation: y = -x + 5Substitute in x: y = -3 + 5Add: y = 2what two numbers' sum=-4 and product=-2
Let a and b be the two numbers. Then
a + b = -4
a b = -2
Solve the second equation for b :
b = -2/a
Substitute this into the first equation:
a - 2/a = -4
Multiply both sides by a :
a² - 2 = -4a
Move 4a to the left side:
a² + 4a - 2 = 0
Use the quadratic formula to solve for a :
a = (-4 ± √(4² - 4(-2))) / 2
a = -2 ± √6
If a = -2 + √6, then
-2 + √6 + b = -4
b = -2 - √6
In the other case, we end up with the same numbers, but a and b are swapped.
A bee flies at 6 feet Per second directly to a flower bed from its hive. The bee stays at the flower bed for 19 minutes, and then flies directly back to the hive at 4 ft per second. Is away from the high for a total of 24 minutes. What equation can used to find the distance of the flower bed from the hive? How far is the flower bed from the hive?
Answer:
720 feet
Step-by-step explanation:
We can Find the travelling time. We know that the bee spends 19 minutes hunting down the nectar in the flowerbed. But was away from the hive for a total of 24 minutes, then the travelling time becomes(24min - 19min) = 5 min
Then let us Convert to seconds vfir consistency
1 minute = 60 seconds
5 minutes = (5×60 )= 300 seconds.
Then the travelling time becomes 300 seconds
We can Find the time each way, since we know that the total time is 300 seconds, though not evenly divided
Let us denote the time there = t
the time back = (300 - t)
But the distances are the same.
r = 6 m/s and r1 = 4 m/s
t1 = t and t2 = (300 - t)
Let dthere = dback
Where, d =( rate × time)
(6× t )= 4 (300 - t)
6t= 1200 - 4t
10t=1200
t=120 seconds
To Find the distance?
d =( rate × time)
d = ? r = 6 m/s and t = 120 second
d = r*t
d = 6 × 120
= 720 feet
Hence, instance of the flower bed from the hive is 720 feet while the equation is ( d = r*t)
The slope of the line below is 2. Which of the following is the point-slope form of the line?
The correct point-slope form of the line is A. y + 1 = 2(x - 1).
The point-slope form of a linear equation is given by y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line.
Given that the slope of the line is 2 and the point on the line is (1, -1), we can substitute these values into the point-slope form to find the correct equation.
Using the point-slope form, we have:
y - (-1) = 2(x - 1)
Simplifying the equation, we get:
y + 1 = 2(x - 1)
Now we compare this equation to the answer choices:
A. y + 1 = 2(x - 1)
B. y - 1 = -2(x + 1)
C. y + 1 = -2(x - 1)
D. y - 1 = 2(x + 1)
Comparing the equation y + 1 = 2(x - 1) to the given point-slope form, we see that they match.
In this equation, the point (1, -1) lies on the line, and the slope of the line is 2. The equation represents a line with a slope of 2 that passes through the point (1, -1).
For more such questions on point-slope form
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Use the table to write the rule (equation) for the relationship between x
and y.
х
у
0
4
1
5
2.
6
Answer:
y = x + 4 or x - y + 4 = 0
Step-by-step explanation:
The relation between "x" and "y" is linear.
Slope of the line m = [tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex] = [tex]\frac{6-5}{2-1}[/tex] = 1
Coordinates of y-intercept of the line (0, b) = (0, 4)
Slope-intercept form of a line equation is y = mx + b
The rule (equation) of line is y = x + 4
or x - y + 4 = 0 (in standard form)
the perimeter of a isosceles triangle is 5(2+root2) find the area
Answer:
12.5
Step-by-step explanation:
If an isosceles right triangle as the length of the equal sides is a , then the length of the hypotenuse will be a2–√ (using pythogoras theorem.
Hence the perimeter will be a+a+a2–√=a(2+2–√)
Hence the equal sides of the triangle in question has the length of a=5
Area of the triangle = 12∗Height∗Base
=12∗5∗5=12.5
For a given function ƒ(x), the translation ƒ(x – 2) + 3 means the function will shift
Question 6 options:
A)
right 2 and upward 3.
B)
right 3 and upward 2.
C)
left 3 and downward 2.
D)
left 2 and downward –3.
Answer:
A
Step-by-step explanation:
Given f(x) then f(x + a) represents a horizontal translation of f(x)
• If a > 0 then a shift left of a units
• If a < 0 then a shift right of a units
Then f(x - 2) represents a shift to the right of 2 units
Given f(x) then f(x) + c represents a vertical translation of f(x)
• If c > 0 then a shift up of c units
• If c < 0 then a shift down of c units
Then f(x - 2) + 3 is shift to the right of 2 and up by 3 units
Answer:
right 2 and upward 3.
Step-by-step explanation: I took the test
Find the length of the unknown side. Round your answer to the nearest whole number.
Pls help thx 19 points
Answer:
7 inches
Step-by-step explanation:
you have to use the Pythagorean Theorem
Answer:
10 inches
Step-by-step explanation:
Assuming one of angles is 30 degrees we can use the theorem leg opposite to 30 degree angle the hypotenuse will be double than the leg measurements so it is 10 inches.
____ - 369 = 286?
help a sister out
Answer:
655
Step-by-step explanation:
655-369=286
I hope this is correct and have a great day
Pls answer I need it
With work!!! Pls...
Answer:
5
Step-by-step explanation:
g(x) = 2 - 3x
g(-1) = 2 - 3(-1)
g(-1) = 2 + 3
g(-1) = 5
James is earning money to buy a bicycle for $100. For each dollar James earns, his mother gives him $1. So far he has earned $14 mowing lawns and $7 wash cars. How much more must James earn in order to but the bike??
Answer:
James needs to earn 78 more dollars.
Step-by-step explanation:
If you add up all of the money James has earned, (1 + 7 + 14), it equals 22. If you subtract 22 from 100, it equals 78. Therefore James needs to earn 78 more dollars.
Answer:
$58
Step-by-step explanation:
$14*2=$28 as her mum gives another dollar for each dollar he earns
$7*2=$14 as her mum gives another dollar for each dollar he earns
then 28 + 14 = 42
100 - 42=$58
For a fundraiser, the Lexington High School football team is making ice cream sundaes, They can buy chocolate ice cream for $15 per gallon and vanilla ice cream for $10 per gallon. They need at least 25 gallons and have a budget of $300. The lines x + y = 25 and 15x +10y= 300 are graphed in the coordinate plane below where and represent the number of gallons of chocolate and vanilla ice cream, respectively.
Which region represents all the numbers of gallon of each flavor that the team could buy?
Region A
Region B
Region C
Region D
Answer:
region D
Step-by-step explanation:
all other regions are higher than $300
Answer:
C
Step-by-step explanation:
because its either A or C and when I did it I picked C and it was wrong.
¯\_(ツ)_/¯
Long division 4/8,728
Answer:
0.0004582951
Step-by-step explanation:
I just put this equation into a calculator to solve.
Complete the table below for the function y 3.2 0. 0 1 2 3
What is the solution set of the quadratic inequality x^2-5<_0
Answer:
b
Step-by-step explanation:
edg
Answer:
B
Step-by-step explanation:
right on edge 2021
please help, im desperate
Answer:
i think 124...is the answer
Due tonight! PLEASE HELP The graph of a quadratic function has a domain of (-∞, ∞) and range of [4, ∞). In two or more complete sentences, explain how the given range of the function can help you to determine whether the graph opens up or down.
Answer:
Opens upStep-by-step explanation:
The range is:
[4, oo)It means the lowest point is 4 and all the other points are greater than 4
Point 4 is the y-coordinate of the vertex and the graph opens up.
JT has coordinates J (-2,-5) and T (2,3). The segment is rotated 180° about the origin to form J'T'. Then J'T' is translated 6 units to the right and 3 units down to form J''T''. What are the coordinates of J'T' and J''T''?
Answer:
(2,5)) ,(-2,-3),(8,2),(4,-6)
Step-by-step explanation:
it is rotated by 180 degree so evrything becomes positve beside the -6
What is the slope of a line with points -5,7 and 1,1
Answer
6/-11
Step-by-step explanation:
use the slope formula m= [tex]\frac{y 2-y 1}{x 2-x 1}[/tex]
then sub in numbers m=[tex]\frac{7-1}{-5-1}[/tex]
now subtract numerator and the denominator
[tex]7-1= 6[/tex] and
[tex]-5-6=-11[/tex] this now looks like [tex]\frac{6}{-11}[/tex]
Carmen is playing draw & compare decimals with her partner. Carmen drew 4,7,6,0, and 2 and has to use three of the cards to make a decimal less then 1. If they are playing for "more" what decimal should Carmen make? If they are playing "less" what decimal should Carmen make?
Answer:
For more;
4.76
for less;
0.46
Step-by-step explanation:
Here, we intend getting the decimals that Carmen should make in her game given the numbers she drew
She has two types to make; a decimal less than 1 and a decimal more than 1
If the decimal should be less than 1, the number zero should lead;
And since she is using three of the numbers, we can have something like;
0.46
To make a decimal more than one, she could actually start with any of the numbers other than zero
we can have something like 4.76
Write two like terms using whatever variable(s) you'd like. Explain why these are like terms.
The equation for the cost in dollars of producing computer chip is y = .000015x^2 - .03x +35. Where X is the number of chips produced. Find the number of chips that minimizes the cost. What is the cost for that number of chips?
Answer:
The equation for the cost in dollars of producing computer chips
The equation for the cost in dollars of producing computer chips is C = 0.000015x^2 - 0.03x + 35, where x is the number of chips produce. Find the number of chips that minimizes the cost.
Step-by-step explanation:
7 inches of snow in 7 hours rate and unit rate
Answer:
unit rate: (1,1)
Step-by-step explanation:
How much will her mother donate
Determine if the triangles below are similar or not
Answer:
I dont see them
Step-by-step explanation:
can someone help me (3.7x10-8)(2.9x10⁶
Andrew ate 2/3 of the desert. cassandra ate 5/16 of the desert. what portion of the desert did andrew and cassandra eat altogether?
Answer:
Concept: Fractions
A ate 2/3 and C ate 5/16Let us find a common denominator Let 48 be our common DHence 32/48+ 15/48 = 47/48Answer:
The portions added together make 47/48 of the dessert.
Step-by-step explanation:
To find the total amount that Andrew and Cassandra ate of the dessert, we have to add the two fractions together:
[tex]\frac{2}{3} + \frac{5}{16}[/tex]
[tex]\frac{32}{48} + \frac{15}{48}[/tex]
[tex]\frac{47}{48}[/tex]
Hence, Andrew and Cassandra almost ate up all of the dessert, clocking in at 47/48 of the dessert.
Hope this helped!
what is x? please help!
Answer:
x is 10x-33
Step-by-step explanation:
I need help with my math homework. It would mean a lot to me if someone coupd explain it. Ill type the directions. It says: Using the graphs below, write the linear equation of the line in slope intercept form (use format: no spaces, y=mx+b) ansaers and earn pixels for correct answers. Answer all 18 problems correctly to reveal the pixel art image. Here are the graphs I need to do. Please help me out if you can. I will make another question on my account so I can add more pictures of the graphs because I can only do five on here.
how to solve
[tex] \sqrt{4} x {}^{2} = x + 2[/tex]
Answer:
➩ [tex]x=2,-\frac{2}{3}[/tex]
Step-by-step explanation:
[tex]\sqrt{4x^2}=x+2[/tex]
➨ We can also solve by completing both squares, however. Since we can pull out the square root.
[tex]\sqrt{4x^2}=|2x|[/tex] ➩ Define of Absolute Value/Square Root
➩ [tex]\sqrt{x^2}=|x|[/tex]
Thus, our new equation is ➩ [tex]|2x|=x+2[/tex]
To solve an absolute-value equation, let there be two conditions.
➨ Where x ≥ 0
[tex]2x=x+2\\[/tex]
Move x to another side
[tex]2x-x=2\\x=2[/tex]
➨ Where x < 0
[tex]-2x=x+2\\-2x-x=2\\-3x=2\\x=\frac{2}{-3}\\x=-\frac{2}{3}[/tex]