Answer:
-7x-3y
Step-by-step explanation:
5x-7y+4y-12x
Collect like terms
-7x-7y+4y
Connect like terms
-7x-3y
Three vertices of parallelogram DEFG are D(-4, - 2), E(-3, 1) and F(3, 3). Find the coordinates of G.
Given:
The three vertices of parallelogram DEFG are D(-4, - 2), E(-3, 1) and F(3, 3).
To find:
The coordinates of vertex G.
Solution:
Let the coordinates of vertex G are (a,b).
We know that, diagonal of parallelogram bisect equal other. It means, the midpoints of both diagonals are same.
Midpoint formula:
[tex]Midpoint=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)[/tex]
Two diagonals of the parallelogram DEFG are DF and EG.
[tex]\text{Midpoint of DF}=\text{Midpoint of EG}[/tex]
[tex]\left(\dfrac{-4+3}{2},\dfrac{-2+3}{2}\right)=\left(\dfrac{-3+a}{2},\dfrac{1+b}{2}\right)[/tex]
[tex]\left(\dfrac{-1}{2},\dfrac{1}{2}\right)=\left(\dfrac{-3+a}{2},\dfrac{1+b}{2}\right)[/tex]
On comparing both sides, we get
[tex]\dfrac{-3+a}{2}=-\dfrac{1}{2}[/tex]
[tex]-3+a=-1[/tex]
[tex]a=-1+3[/tex]
[tex]a=2[/tex]
And,
[tex]\dfrac{1+b}{2}=\dfrac{1}{2}[/tex]
[tex]1+b=1[/tex]
[tex]b=1-1[/tex]
[tex]b=0[/tex]
Therefore, the coordinates of vertex G are (2,0).
The coordinates of vertex G of parallelogram DEFG is: (2, 0).
Recall:
Diagonals of a parallelogram bisects each other, meaning they divide each other into equal parts.Midpoint formula = [tex](\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2})[/tex]The given vertices of parallelogram DEFG are:
D(-4, - 2), E(-3, 1) and F(3, 3)
Let (x, y) = coordinates of vertex G.
DF and EG are diagonals of parallelogram DEFG, therefore:
midpoint of DF = midpoint of EGFind midpoint of D(-4, - 2) and F(3, 3) using [tex](\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2})[/tex]:
[tex](\frac{-4 + 3}{2}, \frac{-2 + 3}{2}) = (\frac{-1}{2}, \frac{1}{2})[/tex]
Find midpoint of E(-3, 1) and G(x, y) using [tex](\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2})[/tex]:
[tex](\frac{-3 + x}{2}, \frac{1 + y}{2})[/tex]
Make the midpoint of DF equal to the midpoint of EG, then solve for x and y.
[tex]\frac{-1}{2}, \frac{1}{2} = \frac{-3 + x}{2}, \frac{1 + y}{2}[/tex]
Solve for x:[tex]\frac{-1}{2} = \frac{-3 + x}{2}[/tex]
Cross multiply[tex]2(-1) = 2(-3 + x)\\\\-2 = -6 + 2x\\\\-2 + 6 = 2x\\\\4 = 2x\\\\\mathbf{x = 2}[/tex]
Solve for y:[tex]\frac{1}{2} = \frac{1 + y}{2}[/tex]
Cross multiply[tex]2(1) = 2(1 + y)\\\\2 = 2 + 2y\\\\2 - 2 = 2y\\\\0 = 2y\\\\\mathbf{y = 0}[/tex]
Therefore, the coordinates of vertex G of parallelogram DEFG is: (2, 0).
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What is AD/AB in simplest form?
A. 10/3
B. 1/3
C.17/5
D. 3
Find the onginal price
Discount 20%
Sale price $75
Answer:
Original price: $
75
Discount percentage:
20
%
Results
Discount:
$15.00
Final Price:
$60.00
Step-by-step explanation:
Simplify the expression
14(n − 3) + 5(n - 6)
[tex]\bold{14(n-3)+5(n-6) }[/tex]
[tex]\sf{[(14\times n)-(14\times 3)]+[(5\times n)-(5\times 6)] }[/tex]
[tex]\longrightarrow \bold{14n-42+5n-30 }[/tex]
[tex]\longrightarrow \bold{ 14n+5n-42-30 }[/tex]
[tex]\longrightarrow \bold{19n-42-30 }[/tex]
[tex]\dashrightarrow\bold{19n-72 }[/tex]
5d
P= 15 +
12
what is d
Answer:
Step-by-step explanation:
10
An open-top box with a square base is to be constructed from 120 square centimeters of material. What dimensions will produce a box with the largest possible volume
Answer:
Maximum length and breadth of the box is 6.32 cm and the height of the box is 3.16 cm
Step-by-step explanation:
Surface area of box
[tex]4xy+x^2=120\\\Rightarrow y=\dfrac{120-x^2}{4x}[/tex]
Volume of box is
[tex]V=x^2y\\\Rightarrow V=x^2\times \dfrac{120-x^2}{4x}\\\Rightarrow V=\dfrac{120x-x^3}{4}\\\Rightarrow V=30x-\dfrac{1}{4}x^3[/tex]
Differentiating with respect to [tex]x[/tex]
[tex]\dfrac{dV}{dx}=30-\dfrac{3}{4}x^2[/tex]
Equating with zero
[tex]30-\dfrac{3}{4}x^2=0\\\Rightarrow x^2=\dfrac{30\times 4}{3}\\\Rightarrow x^2=40\\\Rightarrow x=6.32[/tex]
Double derivative of the volume
[tex]\dfrac{d^2V}{dx^2}=-\dfrac{6x}{4}=-\dfrac{6\times 6.32}{4}=-9.48<0[/tex]
So, the volume is maximum at [tex]x=6.32[/tex]
[tex]y=\dfrac{120-x^2}{4x}=\dfrac{120-40}{4\times \sqrt{40}}\\\Rightarrow y=3.16[/tex]
So, the maximum length and breadth of the box is 6.32 cm and the height of the box is 3.16 cm.
Which is a solution of the equation y=2x+5
Answer:
y=2x+5
0=2x+5
-2x=5
x=-2.5
Factorise fully 3m+12
Answer:
The answer is 3(m+4)
hope it helps..
Answer:
Step-by-step explanation:
3(m+4)
For which value of x is the relation not a function? \ (0,1),(x,0),(3,5)\ 2,6\ }
Answer:
Please check the explanation.
Step-by-step explanation:
We know that a function is a relation where each input or x-value of the X set has a unique y-value or output of the Y set.
In other words, we can not have duplicated inputs as there should be only 1 output for each input.
In our case, we need to determine the value of x so that we can have repeated or duplicated inputs or x-values because duplicated inputs mean the relation would not be a relation.
Given
{(0, 1), (x, 0), (3, 5), (2, 6)}
Now, if we put x = 3, the relation would become:
{(0, 1), (3, 0), (3, 5), (2, 6)}
Here, x = 3 is repeated twice, and we can not have duplicated inputs as there should be only 1 output for each input.
Therefore,
For the value of x = 3, the relation would not be a function.
Note: The same can be said about the values of x = 0, or x = 2 because then the the dupilcated values be x = 0 or x = 2 respectively.
Study the pattern in the equations. Use your observations to solve the equation for a. Express your answer in terms of
log4x 2^a = 3
Answer:
(log64x³) / 2 log = a
Step-by-step explanation:
Given the equation :
log4x 2^a = 3
Recall: If :
loga b = c becomes ; a^c = b
log4x 2^a = 3 ; becomes ; (4x)^3 = 2^a
4^3 * x^3 = 2^a
64x^3 = 2a
log64x³ = log 2a
log64x³ = 2 log a
Divide both sides by 2 log
(log64x³) / 2 log = 2 log a / 2 log
(log64x³) / 2 log = a
There are 9 boys and 11 girls in a math class. Which ratios compare the number of girls to the number of
boys in the class?
Select all that apply.
9:11, 11 to 9, 11:20, 9/11, 11:9, and 11/9
Answer:
b & e
Step-by-step explanation:
tell me if I am right :)
Can I please have help real answers only
Answer:
Sure.
Step-by-step explanation:
ok, so you basically just count from 0 going left three spaces. and the same going 5 spaces. For positive numbers you go (starting at 0) from left to right. for negative numbers (starting from 0 on the line) you go right to left.
I will make a G for where the green dot goes and a P for the pink dot.
<--I--I--I--I--I--I--I--I--I--I--I--I--I--I--I--I-->
P G 0 3 5
Hope this helps.
- Mach Speed.
Five friends earn a total of $50 doing yard work in their neighborhood. Each friend earns the same amount. Use the equation 5f = 50 to find f, the amount that each friend earns. _______________________
Answer:
Each friend earned 10 dollars. 50÷5=10
Henry and Holly Hitch are a couple, who like to eat out and go to the theater. In addition to the money it takes for these activities, they must get a babysitter for each evening out, which is done through their babysitting cooperative. During the coming year, they will have $12,000, and 300 hours of babysitting credits, to use for their dining out and theater visits. Each dinner evening takes 3 hours and costs $150, while each evening at the theater also takes 3 hours and costs $100. Use x to denote the number of dinners out and y to denote the number of theater visits. Write down Henry and Holly's time budget constraint and money budget constraint.
Answer:
See step-by-step explanation
Step-by-step explanation:
Table
To eat out ( x ) cost 150 $ and need 3 hours
To go to the theater ( y ) cost 100 $ and need 3 hours
Therefore Budget constraint:
150 * x + 100 * y ≤ 12000
And time constraint is:
3 * x + 3* y ≤ 300
General constraints x ≥ 0 y ≥ 0 and must be integer
please help! im failing and i really need help!
A bag of candy containing 320 pieces is to be divided up into 18 smaller bags for distribution with fourteen left over. How many pieces will go in each bag?
Answer:
17
Step-by-step explanation:
A bag of candy contains 320 pieces
It is to be divided into 18 smaller bags with fourteen left over
Therefore the pieces that will go in each bag after the distributorn can be calculated as follows
= 320/18
= 17 remainder 14
Hence 17 pieces of candy will be in each bags
Write a function rule for "The output is half of the input x."
Answer:
[tex]y = \frac{x}{2}[/tex]
Step-by-step explanation:
Functions:
Functions have the following format:
y = f(x)
In which y is the output, x is the input, and f is the relation between them.
In this question:
The output is half of the input x. This means that:
[tex]y = \frac{x}{2}[/tex]
Functions can be represented using equations and mathematical statements
The function rule is y = 0.5x
The statement is given as:
The output is half of the input x."
Let the output be y.
So, we have:
y = 0.5 * x
Evaluate the product
y = 0.5x
Hence, the function rule is y = 0.5x
Read more about function rules at:
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2. The population of a school is 800 students and is increasing at a rate of 2% per year. Write an
exponential growth function
Answer:
400
Step-by-step explanation:
Whats 900 x 30 it would be extremly helpful for my upcoming test
Answer:
27000
Step-by-step explanation:
Answer:
its 27,000
Step-by-step explanation:
hope it helps ;)
Katia has 7 chairs she wants to paint. If it takes 2/3 can of spray
paint to paint a chair, how many cans of spray paint does Katia
need?
Answer:
4 2/3
Step-by-step explanation: You would do 7 × 2/3, but you cannot do that so you have to make the 7, 7/1 and than it is 7/1 × 2/37/1 × 2/3 =First step: Multiply the top: 7 × 2 = 14Second step: Multiply bottom: 1 × 3 = 3Answer: 14/3 and than you simplify to 4 2/39
Use the expression 43 + 8 – to find an example of
y
each kind of expression.
Kind of expression Example
Quotient
y
9
Sum
у
Variable
43 + 8
Answer:
quotient: 9y
sum: 4³+8
variable is y
Two angles are supplementary if the sum of their measures is 180∘. If the measure of one angle is 4 x degrees, represent the measure of its supplement as an expression of x
100 points for answer. please help
Answer:
19.09
Step-by-step explanation:
4x÷3+8x÷3
4x+8x÷3×3
12x²÷6
x²=6/12
x²=3/6
3/6x²
√3/6
Answer:
19.09
Step-by-step explanation:
4x10 26 [87.96 x 10 6]
Answer:
remember that you start in the [ ] and work your way out
Step-by-step explanation:
HELP ILL GIVE U BRAINLIEST 10 POINTSQuestion 9 (1 point)
Fill in the blanks to create an equation that matches the graph.
Fence Installation
om/
450
400
350
A 300
250
Cost in $)
✓
200
150
100
50
5
10 15 20 25 30 35
Linear Feet
X +
y =
Blank 1:
Blank 2:
Answer:4
Step-by-step explanation:
Find a solution to the linear equation y=6x−18 by filling in the boxes with a valid value of x and y.
Pietro is given a test question asking him to show that the sum of two odd integers is
always an even integer. Which choice is the best proof of his conjecture?
Answer: second option Let (2a +1) be an odd number. Let (2b +1) be a different odd number. Because the sum of these two numbers, 2(a + b + 1), is a multiple of 2, it is an even number.
B. Let (2A + 1) and (2B + 1) are different odd numbers. sum of these odd number is 2(A+ B +1) is a multiple of 2.
What is even and odd number?Whole numbers in mathematics can also be divided into even and odd numbers. There isn't a single number that can be both even and odd, making odd and even numbers distinct sets of numbers. A number can be either even or odd. Odd numbers are ones that are not entirely divisible by two, whereas even numbers are entirely divisible by two.
Let (2A + 1) and (2B + 1) are different odd numbers. the sum of these odd numbers is 2(A+ B +1) is a multiple of 2. furthermore, let 2a and 2b be two even numbers so the sum of those two will also be an even number. Therefore the sum of two odd numbers is always even.
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#SPJ2
pleaseeeeeee helppppppp
Answer:
what is the substitution method???
Step-by-step explanation:
The profileration of the internet has given rise to a new method of advertising, called spamming, that essentially is a more cost-effective method of the telephone solicitations method known as cold calling. If a company buys three mailing list with 2,500, 3,500, and 4,000 email addresses respectively and spam them with promotional material, how many potential customers has it reached?
A. 5,000
B. 10,000
C. 15,000
D. 20,000
Answer:
10,000
Step-by-step explanation:
2500 + 3500 + 4500 = 10,000
A local stadium seats 27,250 fans. For a special event, 12% of the seats were reserved for students. What
was the total number of seats reserved for students?
Answer:
3270
Step-by-step explanation: