Answer:
The cost of 80 oranges = 480 nairas
Step-by-step explanation:
Given
The cost of 5 oranges = 30 naira
Determine
The cost of 80 oranges
Given that the cost of 5 oranges = 30 naira
so,
Unit rate = 30 nairas / 5 oranges
= 6 nairas per orange
∴ The cost of 1 orange = 6 nairas
As the cost of 1 orange = 6 nairas
Thus,
The cost of 80 oranges = 6 × 80 = 480 nairas
Hence,
The cost of 80 oranges = 480 nairas
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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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
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3(9+c+b) if c=13 and b=4
Answer:
78
Step-by-step explanation:
Hope this helped. Pls mark brainliest
Answer:
78
Step-by-step explanation:
3(9+13+4)
9+13+4 = 26
3(26) = 78
5d
P= 15 +
12
what is d
Answer:
Step-by-step explanation:
10
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.
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 :)
9
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
1. Use the figure below to answer the questions.
(a) Solve for x.
Answer:205
Step-by-step explanation:This is an hexogon so you would do
720-118-112-131-154
At Happy Harry’s Laundromat, the dryer costs $1.50 for 10 minutes. At Jolly Judy’s Laundromat the dryer costs $2.25 for 15 minutes. Which laundromat offer the better deal?will giv brainly if correct
Happy Harry’s Laundromat
Jolly Judy’s Laundromat
They charge the same amount.
heeeeeeeeeeeeeeeeeeeeeeeeeeeeeelllllllllllllllllllllllllllppppppppppppppp
Answer: They charge the same amount.
Step-by-step explanation:
which number is equivalent to 47/9
Answer:
94/18
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 ;)
4x10 26 [87.96 x 10 6]
Answer:
remember that you start in the [ ] and work your way out
Step-by-step explanation:
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
4. What is the volume of a rectangular prism that has the following
dimensions?
Length - 5 inches
Width - 7.5 inches
Height - 12 inches
Answer:
450cm3 or 450 cube cm.
Step-by-step explanation:
Formula = Length x Width x Height
So,
5 x 7.5 x 12 = 450cm3
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
Jonnell has finished 20% of an art project that taken him a total of 3 hours so far. If he continues to work at the same rate, how many hours will it take for him to complete the entire project?
A rectangular prism is 12 cm long 6 cm wide and 5 cm high what is the volume of the rectangular
9514 1404 393
Answer:
360 cm³
Step-by-step explanation:
The volume is the product of the given dimensions:
V = LWH
V = (12 cm)(6 cm)(5 cm) = 360 cm³
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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4x² - 5x + 3y + 6
The coefficient in the first term is __?
The constant is __?
There are __? terms in this expression.
The variable in the third term is __?
Answer:
The coefficient in the first term is 4
The constant is 6
There are 4 terms in this expression
The variable in the third term is y
Step-by-step explanation:
The constant is 6 because it is the only term without a variable, therefore the one term that will stay the same/remain constant.
The first term is 4x^2, the second term is -5x, the third term is 3y, and the fourth term is 6.
The variable in the first term is x^2, therefore the coefficient of x^2 is 4.
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:
I can quite figure out how to go about this problem l, we are writing equations by defining a variable, writing an equation, then solving
Answer:
14 ft
Step-by-step explanation:
Let x represent the number of segments of the divided wood beam
Let y represent the total length of the wood beam.
Given that each segment measures 3.5, the equation to express this scenario is given as
y = 3.5x
Thus, to find the length of the wood beam, substitute x = 4 into the equation.
We would have:
y = 3.5(4)
y = 14
Length of the wood beam = 14 ft
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:
Which is a solution of the equation y=2x+5
Answer:
y=2x+5
0=2x+5
-2x=5
x=-2.5
Find out how much paint is in each jar
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:
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 2/32. 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:
What is AD/AB in simplest form?
A. 10/3
B. 1/3
C.17/5
D. 3
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.