Answer:
(1)
Karen: [tex]y = 2x +3[/tex]
Alice: [tex]y = 2x +1[/tex]
(2): Slope is 2
(3) y intercept
[tex]b = 3[/tex] --- For Karen
[tex]b = 1[/tex] --- For Alice
(4) They do not intersect
(5) No solution
(6) No
Step-by-step explanation:
Given
[tex]x = loaves[/tex]
[tex]y = amount[/tex]
Solving (1): Complete the equation.
For Karen:
[tex]m = 2[/tex] --- the rate
[tex]b = 3[/tex] --- additional spendings
For Alice:
[tex]m = 2[/tex] --- the rate
[tex]b = 1[/tex] --- additional spendings
The general equation is;
[tex]y = mx +b[/tex]
For Karen, it becomes
[tex]y = 2x +3[/tex]
For Alice, it is:
[tex]y = 2x +1[/tex]
(2): The slopes.
In (1), we have:
[tex]m = 2[/tex] --- the rate (for both Karen and Alice).
This rate implies the slope.
Hence, the slope is 2
(3): The y intercept.
The additional spendings in (1) means the y intercept.
So, we have:
[tex]b = 3[/tex] --- For Karen
[tex]b = 1[/tex] --- For Alice
(4) Because they have the same slope, they do not intersect
(5) Number of solutions.
[tex]y = 2x +3[/tex]
[tex]y = 2x +1[/tex]
Subtract both equations
[tex]y-y = 2x-2x +3-1[/tex]
[tex]0 = 2[/tex]
This means there is no solution
(6) Can they spend the same amount on the same number of loaves
In (5), the equations have no solution
Hence, it is not possible to spend the same amount for the same number of loaves
Ezra’s dad is building a cover for his sandbox. The sandbox is in the shape of a kite as shown.
A kite has a width of 6 feet and a height of 4 feet.’
What is the area of the sandbox cover?
6 square feet
12 square feet
18 square feet
24 square feet
Answer:
12
Step-by-step explanation:
its either 12 or 18 try 12 first
The unit prices and quantities for two goods for two years
are shown in the table below. Assume that consumers are
purchasing 8 units of water and 10 loaves of bread. Also
assume that Year 1 is the base year.
Year
Price of Water Price of Bread
(dollars) (dollars)
$1.00
$2.00
1
2
2.00
3.00
Answer: $28
Step-by-step explanation:
The price of water in Year 1 is $1 per unit. There are 8 units so their value is:
= 8 * 1
= $8
Price of a loaf of bread is $2. The basket contains 10 loaves of bread. Value is:
= 10 * 2
= $20
Total value of the basket in year 1 is:
= 20 + 8
= $28
If (a+b)² =10 and ab=1 then find a²+b²
Answer:
8
Step-by-step explanation:
so openeing the parenthesis we get
a2+2ab+b2=10
a2+2(1) +b2=10
a2+2+b2= 10
a2+b2=8
if my answer helps please mark as brainliest
a truck just left the weigh station on interstate 40. it weighted 6 tons 500 pounds and had a load of 1,200 pounds. How much would the transfer truck alone weigh?
Answer:
The weight limit on the bridge is75,500 pounds. ... In pounds, how much cargo can the truck carry and still be ... Helllppp pleaseeee A rancher has a three sided plot of ..
Please help me, I think this is easy but I just don't get it...
Answer:
the last one?
Step-by-step explanation:
i dont know, but that one seems like it would
Answer:
answer is A if only one can be chosen. if more than one can be, b might be an answer as well, but not c and d.
Step-by-step explanation:
think of a 3 4 5 triangle for answer a.
just remembered this method, do Pythagorean theorem for each answer. that will tell you which equals a triangle. answer a foe sure is one cmbecuase of a 3 4 5 triangle.
20) Write a division number story with an answer of 1/4.
Be sure to ask a question.
Answer:
Story: Mr. Lanre bought 8 apples for $2. What is the cost of each apple.
Step-by-step explanation:
Given
[tex]Answer = \frac{1}{4}[/tex]
Required
Write a division story
A division story could be:
Mr. Lanre bought 8 apples for $2. What is the cost of each apple.
Solving the above problem, we have:
[tex]Apples = 8[/tex]
[tex]Total\ Cost =\$2[/tex]
The cost of each is:
[tex]Each = \frac{Total\ Cost}{Apples}[/tex]
[tex]Each = \frac{2}{8}[/tex]
Simplify fraction
[tex]Each = \frac{1}{4}[/tex]
According Two data from the 2010 United States Census 83.7% of Americans lived in the metropolitan area suppose maria researcher takes a random sample of 125 Americans and find that 98 live in the Metropolitan area let P hat represent the sample proportion of Americans that live in a metropolitan area what are the mean and standard deviation of the sampling distribution of P hat provide your answer rounded to three decimal places
Answer:
Mean is 83.7%
And, the standard deviation is 0.033
Step-by-step explanation:
The computation of the mean and the standard deviation is as follows:
Let us assume the P be the sample proportion
Mean is 83.7%
And, the standard deviation is
[tex]= \sqrt{\frac{p(1-p)}{n} } \\\\=\sqrt{\frac{0.837(1-0.837)}{125} }[/tex]
= 0.033
Write an
equivalent expression using the distributive property.
1/4(4x - 6)
Answer:
Step-by-step explanation:
Distributive property: a*(b + c)= (a*b) + (a*c)
[tex]\frac{1}{4}(4x - 6) = 4x*\frac{1}{4} - 6*\frac{1}{4}\\\\[/tex]
[tex]= x -3*\frac{1}{2}\\\\=x - \frac{3}{2}[/tex]
PLEASE HELP ITS REALLY URGENT
A car dealership decreased the price of a certain car by 14%. The original price was $48,200.
(a) Fill in the blank to write the new price in terms of the original price.
Write your answer as a decimal.
New price = { x Original price
(b) Use your answer in part (a) to determine the new price.
New price: $0
Answer:
a) New price = 0.86 * Original price
b) New price = 0.86 * 48200 = $41452
Step-by-step explanation:
The statement "one-eighth the age, a" can be expressed algebraically as ?
Answer:
1/8a
Step-by-step explanation:
Pls hurry and help!!!!! 3х + 3 = Зу
2x – 6у = 2. Solve the equations by using elimination (adding) show work
Answer:
Step-by-step explanation:
3x - 3y = -3
2x - 6y = 2
-6x + 6y = 6
2x - 6y = 2
-4x = 8
x = -2
-4 - 6y = 2
-6y = 6
y = -1
(-2, -1)
If 2.22 moles of ammonia (NH3 ) decomposes according to the reaction shown, how many moles of hydrogen (H2 ) are formed? A. 1.11 moles of H2 B. 3.33 moles of H2 C. 6.66 moles of H2 D. 2.22 moles of H2
Answer:
C. 3.33 moles
Step-by-step explanation:
Ammonia decomposes
[tex]2NH_3\rightarrow N_2+3H_2[/tex]
We have to find the moles of hydrogen formed in 2.22 moles of ammonia.
From the reaction
2 moles of ammonia gives 3 moles of hydrogen
1 mole of ammonia produce hydrogen=3/2 moles
2.22 moles of ammonia produces hydrogen=[tex]\frac{3}{2}\times 2.22[/tex] moles
Number of moles of hydrogen formed by decomposition of 2.22 moles of ammonia
=[tex]\frac{6.66}{2}=3.33[/tex]moles
Hence, 3.33 moles of hydrogen are formed in 2.22 moles of ammonia.
Option C is true.
C. 3.33 moles
A restaurant needs to plan seating for a party of 150 people. Large tables seat 10 people and small tables seat 6. Let x represent the number of large tables and y represent the number of small tables. The expression 10A + 6B, which represents the total number of people you can seat using A large tables and B small tables, is called a linear combination. For instance, 150 people could be seated using 6 large tables and 15 small tables. Use that expression to enter an equation in standard form that models all the different combinations of tables the restaurant could use. Then identify at least one possible combination of tables other than (6, 15).
The equation is . Another possible combination is
Answer:
15
Step-by-step explanation:
Which of the following linear equations below is equivalent to 10x−5y=−15?
a. y = 3x + 2
b. y = 2x + 3
c. y = 3x - 2
d. y = 2x - 3
Answers:
B. y = 2x + 3
hope this helps
trapezoid.mp4
Find the value of x and y.
Rek2
20
x
12
Y
x =
y =
9514 1404 393
Answer:
x = 12y = 20Step-by-step explanation:
The figure only makes sense as a kite, in which case left sides are equal and right sides are equal.
x = 12
y = 20
Solve 4x+x+4 = 8x -3x + 4
Answer:
x ∈ R
Step-by-step explanation:
4x+x+4=8x−3x+4
Combine 4x and x to get 5x.
5x+4=8x−3x+4
Combine 8x and −3x to get 5x.
5x+4=5x+4
Subtract 5x from both sides.
5x+4−5x=4
Combine 5x and −5x to get 0.
4=4
Compare 4 and 4.
True
This is true for any x.
x ∈ R
Hello, please help.
Find the value of x:
x^2 + 3x^3 - 2x + 9 = 24 + 54x + 92x^2 - 2x^3
Answer:
-91x² + 5x³ - 56x -15 = 0
Step-by-step explanation:
x² + 3x³ - 2x + 9 = 24 + 54x + 92x² - 2x³
x² + 3x³ - 2x + 9 - 92x² = 24 + 54x + 92x² - 2x³ - 92x²
-91x² + 3x³ - 2x + 9 + 2x³ = 24 + 54x -2x³ + 2x³
-91x² + 5x³ - 2x + 9 - 54x = 24 + 54x - 54x
-91x² + 5x³ - 56x + 9 - 24 = 24 - 24
-91x² + 5x³ - 56x -15 = 0
Hope this helps!
Maybe brainliest?
Use the graph to write a linear function that relates y to x.
The linear function is y=?
Answer:
identify the value that is intercepting y-axis !!
Step-by-step explanation:
in this case it is 1
What's the slope of -x+2y=5
Answer:
Slope = (1/2)
Step-by-step explanation:
Rearrange the equation into the y = mx + b format.
-x + 2y = 5
2y = x + 5
y = (1/2)x + (5/2)
m represents slope, which is (1/2) in this question.
Is AABC-ADEF? If so, identify the similarity postulate or theorem that applies 30- A
Answer:
C. Similar - AA
Step-by-step explanation:
From the diagram given, we know that all 3 angles of ∆ABC are congruent to all corresponding 3 angles of ∆DEF.
If we know just two of the angles of the two triangles given are equal to each other, it is enough information for us to prove that they are similar to each other based on the AA Similarity theorem.
The corresponding three angels of both triangles are equal, therefore, based on AA, they are similar to each other.
Which statement describes the graph
Answer:
Your answer is A
Step-by-step explanation:
I hope I helped :)
When a commodity is sold for x dollars per item, the number of items sold is f(x). The item costs 5 dollars to make. The item costs 3 dollars to make.
Required:
a. Express the total profit P in terms of x (the answer has been partially filled in for you).
b. What is the rate of change of the total profit as x changes?
c. If 3000 items sell when the price is 45 dollars and if the number of items that are sold decreases by 600 for every 1 dollar increase in price, find the rate of change of the profit when the item price is 45 dollars.
In this exercise we will use the differential equations to calculate finances, we find that:
a) [tex]Profit = (x - 3)f(x)[/tex]
b) [tex]P' = f(x) + (x - 1) f'(x)[/tex]
c) [tex]P' = 29400[/tex]
The cost of producing the items is the total expenses of production while the revenue is the amount of money generated from selling the item.
a)Then using the given formula and substituting for the known values we find that;
[tex]Cost = \ cost \ of \ producing \ one \ item * number \ of \ items \ produced\\Cost = $3 * f(x) = 3f(x)\\Revenue = selling \ price \ of \ one \ item * number \ of \ items \ produced\\Revenue = x * f(x) = xf(x)\\Profit = Revenue - Cost = xf(x) - 3f(x)\\Profit = (x - 3)f(x)[/tex]
b) Applying knowledge of differential equations we find that:
[tex]P' = d/dx(xf(x) - 3f(x) )\\P' = f(x) + xf'(x) - f'(x)\\P' = f(x) + (x - 1) f'(x)[/tex]
c)Substituting the known values into the formula given above, we find that:
[tex]f(x) = 3000, x = $45, f'(x) = -600 items / 1$\\P' = 3000 + (45 - 1)(-600)\\P' = 3000 + 26400\\P' = 29400[/tex]
See more about differential equations at brainly.com/question/25731911
Phyllis invested 32000 dollars, a portion earing a simple interest rate of 5 percent per year and the rest earning a rate of 6 percent per year. After
one year the total interest earned on these investments was 1820 dollars. How much money did she invest at each rate?
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Answer:
$10,000 at 5%$22,000 at 6%Step-by-step explanation:
Let x represent the amount invested at 6%. Then 32000-x is the amount invested at 5%, and the total interest earned is ...
0.06x +0.05(32000 -x) = 1820
0.01x +1600 = 1820 . . . . simplify
0.01x = 220 . . . . . . . . . . subtract 1600
x = 22,000 . . . . . . . . . . . multiply by 100
32000 -x = 10,000
Phyllis invested $22,000 at 6% and $10,000 at 5%.
What is tan K? help pleasee
8/15
Hope this helps!
Answer:
[tex]\frac{8}{15}[/tex]
Step-by-step explanation:
[tex]Tan(k)=\frac{24}{45} =\frac{8}{15}[/tex]
Classify the following polynomials by the number of terms and degrees
-2x^3 +5x
Answer:
A third degree binomial
Step-by-step explanation:
The highest power is 3 hence the 3rd degree
and there are 2 terms hence the bi-nomial
Solve the system of linear equations by graphing
Answer:
Place one dot at (0,-2) and another point at (-1,-1) then draw a line through it. Then place a dot at (0,3) and (1,0) And draw a line through those two points. Wherever those two lines intercept will be your answer.
Step-by-step explanation:
can anyone pls help me with this question I'm stuck
Answer:
I think 24
let b=3
l=4
and h=2
Answer:
864
Good luck!
Security A rounds every 2 minutes and 20 seconds in the gate 1. Security B rounds every 1 minute and 40 seconds in the gate 2. If they conduct rounds at the same time. After how many minutes they will rounds together again?
Answer:
[tex]Time = 11\frac{2}{3}\ min[/tex]
Step-by-step explanation:
Given
[tex]Security\ A = 2\ mins, 20\ secs[/tex]
[tex]Security\ B = 1\ mins, 40\ secs[/tex]
Required
After how many minutes, will they round together
First, convert the given time to minutes
[tex]Security\ A = 2\ mins, 20\ secs[/tex]
[tex]Security\ A = 2\ mins+ 20\ secs[/tex]
[tex]Security\ A = 2\ mins+ \frac{20}{60}\ min[/tex]
[tex]Security\ A = 2\ mins+ \frac{1}{3}\ min[/tex]
[tex]Security\ A = 2\frac{1}{3}\ min[/tex]
[tex]Security\ B = 1\ mins, 40\ secs[/tex]
[tex]Security\ B = 1\ mins+ 40\ secs[/tex]
[tex]Security\ B = 1\ mins+ \frac{40}{60}\ min[/tex]
[tex]Security\ B = 1\frac{2}{3}\ min[/tex]
So, we have:
[tex]Security\ A = 2\frac{1}{3}\ min[/tex]
[tex]Security\ B = 1\frac{2}{3}\ min[/tex]
List out the multiples of the time of both security personnel take round.
[tex]Security\ A = 2\frac{1}{3}min,\ 4\frac{2}{3}min,\ 7min,\ 9\frac{1}{3}min,\ 11\frac{2}{3}min...[/tex]
[tex]Security\ B = 1\frac{2}{3}min,\ 3\frac{1}{3}min,\ 5min,\ 6\frac{2}{3}min,\ 8\frac{1}{3}min,\ 10min\ ,11\frac{2}{3}min,...[/tex]
In the above lists, the common time is:
[tex]Time = 11\frac{2}{3}\ min[/tex]
This implies that they go on round after [tex]11\frac{2}{3}\ min[/tex]
Which pair of ratios forms a proportion?
A 7 15
10 18
B 5 15
9 27
C 3 15
10 25