Answer:
[tex]\huge\boxed{x^3-y^3=508}[/tex]
Step-by-step explanation:
[tex]\underline{+\left\{\begin{array}{ccc}x+y=10\\x-y=6\end{array}\right}\qquad|\text{add the sides of the equations}\\.\qquad2x=16\qquad|\text{divide both sides by 2}\\.\qquad\boxed{x=8}\\\\\text{Substitute it to the first equation}\\8+y=10\qquad|\text{subtract 8 from both sides}\\\boxed{y=2}\\\\x^3-y^3=8^3-2^3=512-8=504[/tex]
Mrs. Greene wants to plant a vegetable garden in her yard. She purchased a package containing 30 sections of fencing, each 1-foot long If she uses all 30 sections to create rectangular space, how many different arrangements are possible? What is the largest area she can enclose for her garden with this fencing?
Answer:
The largest area she can enclose for her garden with this fencing is [tex]56 ft^2[/tex]
Step-by-step explanation:
Suppose the rectangular space Mrs. Greene wants to plant has dimensions x feet and y feet.
Since each section of fencing is 1-foot long, both x and y must be integer numbers.
The perimeter of the rectangular space is calculated as:
P = 2x + 2y
And we know she uses all 30 sections of fencing, thus:
2x + 2y = 30, where x, y are integers and positive.
Simplifying by 2:
x + y = 15
Solve for x:
x = 15 - y
This equation doesn't have infinitely many solutions, since both numbers must be integers and positive. Suppose we start by setting y=1, then x=14. That is a possible arrangement for the garden.
Another valid option is for y=2, x=13
Continuing with these patterns, we find the maximum value for y is 7, x=8, because if we set y=8, x=7, this is the same condition as y=7, x=8.
Thus, from y=1 to y=7, there are 8 possible combinations for the arrangement of the garden.
The area of a rectangle is
[tex]A=x\cdot y[/tex]
Testing some possible arrangements:
y=1, x=14
[tex]A=1\cdot 14= 14 ft^2[/tex]
y=2, x=13
[tex]A=2\cdot 13= 26 ft^2[/tex]
y=3, x=12
[tex]A=3\cdot 12= 36 ft^2[/tex]
We can notice the combination y=7, x=8 has an area of:
[tex]A=7\cdot 8= 56 ft^2[/tex]
This is the largest possible area of all combinations, thus:
The largest area she can enclose for her garden with this fencing is [tex]56 ft^2[/tex]
Eight rolls of paper towels cost $4.80. At the same unit rate, how much will six rolls of paper towels cost? Describe the steps that you took to determine your answer.Eight rolls of paper towels cost $4.80. At the same unit rate, how much will six rolls of paper towels cost? Describe the steps that you took to determine your answer.
Answer:
$3.6Step-by-step explanation:
Given that 8 rolls cost $4.80
let us compute how much 1 roll will cost (that is the unit cost of a roll)
so 8 rolls cost $4.80
1 roll will cost x
x= 4.8/8
x=$0.6
so the paper tower cost $0.6 per roll (this is the rate)
therefore 6 rolls will cost
=6*0.6
=$3.6
Determine the slope of the line that passes through the points M(-3, 5) and N(1, 8). Represent the slope in decimal form.
Answer:
The slope of the line that passes through the points M(-3, 5) and N(1, 8) in decimal form is 0.75
Step-by-step explanation:
The given points are M(-3, 5) and N(1, 8)
The formula for finding the slope, m, given the coordinates of two points on the line is given as follows;
[tex]Slope, \, m =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Where, (x₁, y₁) = (-3, 5), and (x₂, y₂) = (1, 8), we have;
[tex]Slope, \, m =\dfrac{8-5}{1-(-3)} = \dfrac{3}{4} = 0.75[/tex]
The slope, m = 0.75
The slope of the line that passes through the points M(-3, 5) and N(1, 8) in decimal form = 0.75.
When electrons flow with little resistance through a conductor it is called a
Answer:
The answer is free electrons
Step-by-step explanation:
When electrons flow with little resistance through a conductor, then it is called a Electricity.
What are electrons?"The electron is a subatomic particle whose electric charge is negative one elementary charge."
What is resistance?"Resistance is a measure of the opposition to current flow in an electrical circuit."
What is conductor?"A conductor, or electrical conductor, is a substance or material that allows electricity to flow through it. "
What is Electricity?The steady flow of electrons through a conductor is called electricity
Hence , if electrons are flowing that means they conducts electricity.
Learn more about electricity here
https://brainly.com/question/8971780
#SPJ2
10 Brynlee's monthly cell phone bill
is $60 a month plus $2.50 per
gigabyte used. Raylin's cell phone bill is $450
per month plus $3.25 per gigabyte used.
Determine after how many gigabytes used
would the cell phone plans cost the same
for the month what is the answer??
Answer:
20 gigabytes
Step-by-step explanation:
Let n represent the amount of gigabytes used.
First make an equation for each senario, Brynlee's would be 60+2.50n and Raylin's would be 45+3.25n.
Set them to equal each other, 60+2.50n=45+3.25n.
Then isolate for n.
60-45=3.25n-2.50n
15=0.75n
Divide both sides by 0.75 to get 20
Holden wants to earn money teaching kids how to skate. It costs him $250 to advertise his new skate school. He charges students $16 and hour to learn how to skate. How many hours does he have to teach in order to make $768, the amount needed to
buy a new gaming system?
Create an equation where r represents the
number of hours Holden needs to work.
Answer:
16r - 250 = 768
Step-by-step explanation:
First, create a term that represents his revenue:
Since he charges students $16 per hour, the amount of money he makes from this can be represented by 16r.
Then, subtract the advertising cost of $250 from this.
Set it equal to 768, because that is how much the gaming system costs.
16r - 250 = 768 will be the equation
can someone answer this and explain? and the one below, will mark brainlest
Step-by-step explanation:
there were 50 boxes of gum
each box had 36 packs of gum
in each pack were 15 pieces of gum
so total pieces of gum:
for one box of gum total pieces= 15*36= 540 pieces
for 50 boxes= 540*50= 27000 pieces of gum in total
number sentence:
15*36=540
540*50= 27000
bonus question:
27 gums in 1 day
27000 gums in x days
27000/27= 1000 days
Answer:
540 pieces x 50
27000/27=1000 days
aleena bought 15 kg of fruits she brought 3kg 750 g of apples 4kg 250g of mangoes and rest were oranges find the weight of oranges
pls urgent will surely mark u the brainliast
Answer:
8.950 kg
Step-by-step explanation:
Lemme know if incorrect
An alloy is a mixture of metals. Suppose that a certain alloy is made by mixing 50 g of an alloy containing 12% copper with 78 g of an alloy containing 92% copper how many grams of copper are in the resulting mixture what percentage of the resulting mixture is copper
Given :
An alloy is a mixture of metals. Suppose that a certain alloy is made by mixing 50 g of an alloy containing 12% copper with 78 g of an alloy containing 92% copper.
To Find :
How many grams of copper are in the resulting mixture what percentage of the resulting mixture is copper.
Solution :
Mass of copper in 50 gm alloy = [tex]50\times 0.12 = 6\ gram[/tex].
Mass of copper in 78 gm alloy = [tex]78\times 0.98 = 76.44\ gram[/tex].
Total mass of copper, ( 6 + 76.44 ) gm = 82.44 gram.
Percentage of copper in resulting mixture :
[tex]\%=\dfrac{82.44}{50+78}\\\\\%=64.4\ \%[/tex]
Hence, this is the required solution.
The formula for the volume of a rectangular prism is V = lwh. Which is the equivalent equation solved for h?
Answer:
V /(lw) = h
Step-by-step explanation:
V = lwh
Divide each side by lw
V/ ( lw) = lwh/(lw)
V /(lw) = h
V /(lw) = h
V = lwh
Divide each side by lw
V/ ( lw) = lwh/(lw)
V /(lw) = h
A and \angle B∠B are supplementary angles. If m\angle A=(5x-19)^{\circ}∠A=(5x−19)
∘
and m\angle B=(2x+10)^{\circ}∠B=(2x+10)
∘
, then find the measure of \angle B∠B.
Answer: 52
Step-by-step explanation:
4x+8 = 5x-3 by the Vertical Angles Theorem that states the vertical angles are congruent.
Subtract 4x from both sides and get:
8=1x -3
Add 3 to both sides:
11= 1x
if x =11, plug that in to angle A.
4x+ 8 becomes 4(11)+8 =
44+ 8=
52
solve for t. 79t=14 write your answer here
Answer: im pretty sure its 14 divided by 79 soo 0.17?
if not im sorry
use your brain tho:)
hope this helps you
If B = 3x^2-x+3and A=x-6, find an expression that equals 2B+3A in standard form?
Answer:
[tex]6x^{2} +x-12[/tex]
Step-by-step explanation:
All you need to do is multiply equation B by 2 and multiply equation A by 3, then put an addition sign between them and combine like terms after you've distributed what you needed for each one.
Nool is a computer repairman, To fix a computer,
he charges a customer X per hour, plus a fired
lee of $15 for the service call, as represented by
the equation below
y = 40x + 15
In the equation, what is represented by the variable
A the number of hours Noel worked
the amount Noel charged per hour
C, the fixed fee for the service call
D. the total cost of the repair job
Can someone
If f(x)=4x-3 and the domain of f is {0,5,10}, what is the range of f?
Ron Alotte and Dee Selerate ran a 20 km. Race. Dee made three 10 minute stops during the race to fix her shoes and rest and yet the two racers finished in a tie. If Ron ran the race at a constant speed of 8 km. Per hour, find Dee's average speed when running.
Answer:
10km/hr
Step-by-step explanation:
Given that:
Distance covered by both Dee and Ron= 20km
Ron's speed = 8km/hr
Dee made three 10 minute stops during the race.
Time it took Ron to cover 20km
Time = distance / speed
20km / 8km/hr = 2.5 hours = 150 minutes
Since they both tied ;
Running time of Dee = (150 - (3*10)) = 120 minutes = 2 hours
Ron's speed = distance / time
Speed = 20 km / 2hours
Speed = 10km/hr
Someone please help! Asap
Multiply. Use the greatest common factor to write each answer in simplest form. 8/21 x 7/10
Answer:
56/210---> 8/30---> 4/15
Step-by-step explanation:
Which sequences of transformations confirm the congruence of shape II and shape I?
a reflection of shape I across the x-axis followed by a 90° clockwise rotation about the origin
a reflection of shape I across the x-axis followed by a 90° counterclockwise rotation about the origin
a reflection of shape I across the y-axis followed by a 90° counterclockwise rotation about the origin
a reflection of shape I across the y-axis followed by a 90° clockwise rotation about the origin
a reflection of shape I across the x-axis followed by a 180° rotation about the origin
A,B,C
Step-by-step explanation:
Answer:
A, B and C
Step-by-step explanation:
Simplify the following expression.
(5^3)^5
Answer:
5 ^15
Step-by-step explanation:
(5 ^3)^5 =5 ^(3×5)=5 ^15
The rule used is (a^b)^c = a^(b*c)
If you raise some exponential expression to another exponent, then you multiply the exponents. You keep the base the same.
In this case, a = 5, b = 3, c = 5.
Using a calculator,
5^15 = 30,517,578,125
But it's likely your teacher will want you to keep the answer in exponential form since it's easier to work with.
Jenny works mowing lawns and babysitting. She earns $8.80 an hour for mowing and $7.70 an hour for babysitting. How
much will she earn for 1 hour of mowing and 3 hours of babysitting?
Answer:
$31.90
Step-by-step explanation:
Hope it helps :)
Have a good day/night
Brainliest pls?
Which equation shows an example of the associative property of addition?
A. (–4 + i) + 4i = –4 + (i + 4i)
B. (–4 + i) + 4i = 4i + (–4i + i)
C. 4i × (–4i + i) = (4i – 4i) + (4i × i)
D. (–4i + i) + 0 = (–4i + i)
Answer:
I am pretty it's A
Step-by-step explanation:
Basically the Associative Law of Addition means that the order that the numbers are added does not matter.
Answer:
A. (–4 + i) + 4i = –4 + (i + 4i)
Step-by-step explanation:
edge2020
Have a great day y'all :)
What is the value of n in the equation -1/2 (2n + 4) + 6 = -9 + 4(2n + 1)?
n =
Answer:
n=1
Step-by-step explanation:
Answer:
n=1
Step-by-step explanation:
The standard height from the floor to the bull's-eye at which a standard dartboard is hung is 5 feet 8 inches. A standard dartboard is
18 inches in diameter.
Suppose a standard dartboard is hung at standard height so that the bull's-eye is 11 feet from a wall to its left.
Samuel throws a dart at the dartboard that lands at a point 11.5 feet from the left wall and 5.5 feet above the floor.
Does Samuel's dart land on the dartboard?
Answer:
Yes, Samuel dart does land on the dart board
Step-by-step explanation:
The given parameters are;
The height from the floor to the bulls eye = 5 feet 8 inches
The size of the standard board = 18 inches diameter
The distance of the bulls eye from the wall to the left = 11 feet
The distance the dart Samuel throws land from the left wall = 11.5 feet
The distance above the ground, the dart Samuel throws land = 5.5 feet
Whereby Samuel throws the dart directly at the dartboard, we have;
The location of the bulls eye = (11, 5.67)
The equation of the circle representing the dart board = (x - 11)² + (y - 5.67)² = 0.75² = 0.5625
The unit of the radius is in feet
The position of Samuel's dart is represented by the coordinate, (11.5, 5.5)
Plugging in the coordinates of the position of Samuel's dart into the equation of the circle of the dart board gives;
(11.5 - 11)² + (5.5 - 5.67)² = 0.2789 ≈ 0.528²
Therefore, given that the square of the distance of the position of Samuel's dart is less than the square of the radius of the dart board, we have;
Yes, Samuel dart does land on the dart board.
From the parameters given to find out if Samuel's dart landed on the dartboard, we can say that;
Samuel's dart does not land on the dartboard.
We are given;
Height from the floor to the bulls eye = 5 ft 8 in = 5.67 ft
Diameter of the standard dartboard = 18 in = 1.5 ft
Thus, radius; r = 1.5/2 = 0.75 ft
Distance of the bulls eye from the wall to the left = 11 ft
Distance of dart thrown by Samuel from the left wall = 11.5 ft
Height of dart thrown by Samuel above the ground = 5.5 ft
We know that general equation of a circle is;
(x - a)² + (y - b)² = r²
Since Height from the floor to the bulls eye is 5.67ft,then a = 5.67 ft
And also since Distance of the bulls eye from the wall to the left = 11 ft, then b = 11 ft
Thus;
(x - 11)² + (y - 5.67)² = 0.75²
(x - 11)² + (y - 5.67)² = 0.5625
Now, since he throws a dart at the dartboard that lands at a point 11.5 feet from the left wall and 5.5 feet above the floor. Thus;
r² = (11.5 - 11)² + (5.5 - 5.67)²
r² = 0.2789
r² of 0.2789 gotten here is lesser than 0.5625 gotten earlier, we can conclude that Samuel's dart does not land on the dart board.
Read more at; https://brainly.com/question/18430680
Given: ΔABC, where AB = BC Prove: m∠BAC = m∠BCA Statement Reason 1. Let ΔABC be an isosceles triangle with AB = BC. given 2. Create point D on side so bisects ∠ABC. constructing an angle bisector 3. M∠ABD = m∠CBD definition of angle bisector 4. BD = BD Reflexive Property of Equality 5. ΔABD ≅ ΔCBD 6. M∠BAC = m∠BCA Corresponding angles of congruent triangles have equal measures. What is the reason for statement 5 in this proof? A. ASA B. SSS C. AAS D. SAS
Answer:
D. SAS
Step-by-step explanation:
Given: ΔABC
Bisecting <ABC to create point D implies that BD is a common side to ΔABD and ΔCBD.
Also,
m<ABD = m<CBD (angle bisector)
BA = BC (given property of the isosceles triangle)
Therefore,
ΔABD ≅ ΔCBD (Side Angle Side)
The reason for statement 5 in this proof is that ΔABD ≅ ΔCBD by SAS (Side-Angle-Side) relations of the congruent triangles.
Answer:
Option D is correct trust me
Step-by-step explanation:
y=2x-3 in standard form. I’ll give brainliest if you answer it right. But hurry. It’s for my missing assignment.
Answer:
It would be 2x-y=3.
The sum of three consecutive even numbers is 66. Find the numbers
Answer:
20, 22, and 24
Step-by-step explanation:
hope this helps. can I also have brainliest please :)
Answer:
BRAINLIEST PLZZ
Step-by-step explanation:
The other 2 numbers are (x + 2) and (x + 4)
Their sum is 66:
x + (x + 2) + (x + 4) = 66
x + x + 2 + x + 4 = 66
3x + 6 = 66
3x = 60
x = 20
2nd number = x + 2 = 20 + 2 = 22
3rd number = x + 4 = 20 + 4 = 24
Answer: The numbers are 20, 22 and 24
PLEASE HELP ANYONE:))
Answer:
3 million dollars
Step-by-step explanation:
i just did this and got it right
Help! look at the image of the table of values below. Over which interval of x is the average rate of change the largest?
Answer:
A
Step-by-step explanation:
There is no way to tell a pattern.
The shampoo Eva likes to use costs $6 for a 24-ounce bottle. The conditioner she likes to use costs $12 for a 30-ounce bottle. How much more per ounce does her conditioner cost than her shampoo? $ per ounce
Answer:
0.15
Step-by-step explanation:
6 divided by 24 equals 0.25
12 divided by 30 equals 0.4
0.4 minus 0.25 is 0.15
$0.15 more per ounce does her conditioner cost than her shampoo.
Given that, the shampoo Eva likes to use costs $6 for a 24-ounce bottle.
What is the unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
The conditioner she likes to use costs $12 for a 30-ounce bottle.
Cost of shampoo per ounce =Total cost/Number of ounce
= 6/24
= $0.25 per ounce
Cost of conditioner per ounce =Total cost/Number of ounce
= 12/30
= $0.4 per ounce
Difference =0.4-0.25
= $0.15
Therefore, $0.15 more per ounce does her conditioner cost than her shampoo.
To learn more about the unitary method visit:
brainly.com/question/22056199.
#SPJ2