The cost of the file is $6.15 and the cost of the pen is $8.9
Solving word problems with systems of linear equations.The interpretation of the given word problem leads to a system of linear equations.
From the given information:
Let the file be denoted with f and the pen be denoted with pf + 3p = 32.85 --- (1)
2f + 8p = 83.5 --- (2)
From equation (1)
f = - 3p+32.85
Replace the value of f in the above equation into equation (2)
2(-3p + 32.85) + 8p = 83.5
2p + 65.7 = 83.5
2p = 83.5 -65.7
2p = 17.8
p = 17.8/2
p = 8.9
Replacing the value of p = 8.9 into f = - 3p+32.85
f = -3(8.9)+32.85
f = 6.15
Therefore, we can conclude that the cost of the file is $6.15 and the cost of the pen is $8.9.
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Tyler spent 17,700 seconds completing a 1,000 piece puzzle.
How many hours is this equivalent to? Answer choices are rounded
to the nearest hour.
O 288 hours
O 20 hours
5 hours
O124 hours
Which term describes the set of all possible input values for a function? O A. Range OB. Input O C. Output OD. Domain SUBMI
Answer:
D. domain
Step-by-step explanation:
domain is set of x-values
range is set of y-values
Input is the set of x-values, so it is the domain.
Name this triangle by its sides and angles. This is a(n) ____________________ triangle. a triangle with one right angle and three non-congruent sides obtuse, isosceles obtuse, scalene right, scalene right, isosceles
Answer:
c
Step-by-step explanation:
A garden table and a bench cost $714 combined. The garden table costs $64 more than the bench. What is the cost of the bench?
Answer:
The bench costs $325
Step-by-step explanation:
let garden table = x
let bench = y
x = y+64
x+y = 714
y+y+64 = 714 (we know, x = y+64)
2y + 64 = 714
2y = 650
y = 325
Answer:
Bench: $325
Garden Table: $389
Step-by-step explanation:
g + b = 714 Eq. 1
g = b + 64 Eq. 2
g = cost of the garden table
b = cost of the bench
Replacing Eq.2 in Eq.1
(b+64) + b = 714
2b + 64 = 714
2b = 714 - 64
2b = 650
b = 650/2
b = 325
from the Eq. 2
g = b + 64
g = 325 + 64
g = 389
Check:
from the Eq. 1
g + b = 714
389 + 325 = 714
Which of the following equations has the solution x = all real numbers?
O 4(3-x) + 7x = 4x + 12 + 2x
O 4(4-x) + 6x = x + 16 - 4x
O 3(4-x) + 6x = 4x + 12 - x
O 4(3-c) + 6x = 3x + 8x
Answer: 3(4-x) + 6x = 4x + 12 - x
Step-by-step explanation:
For the solution to be all real numbers, the left hand has to be identical to the right hand side.
1) [tex]4(3-x)+7x=12-4x+7x=12+3x[/tex], so wrong.
2) [tex]4(4-x)+6x=16-4x+6x=16+2x[/tex], so wrong.
3) [tex]3(4-x)+6x=12-3x+6x=12+3x=4x+12-x[/tex], so correct.
4) Wrong variable, so eliminate immediately.
A box with an open top is to be constructed from a 15 inch by 24 inch piece of cardboard by cutting squares of equal sides from the corners and folding up the sides. Find the dimensions of the box of the largest volume that can be constructed.
The dimensions of the box of the largest volume that can be constructed are
D=18,9,3
What are the dimensions?Generally, the equation for the lenght is mathematically given as
Lenght=(24-2x)
Widht= (15-2x)
Therefore
Volume =L*B*H
V=(24-2x)(15-2x)x
V=(360-48x-30x+4x)x
V=4x^3-78x^2+360x
Differnciating we have
dv/dx=12x^2-156x+360
put dv/dx=0
12(x^2-13x+30)=0
x^2-10x-3x+30=0
(x-10)(x-3)=0
root=10,3
Second diiferciation
d^v/dx^2=24x-156
[tex]lim _{x=3} =-84 < 0[/tex]
In conclusion,
L=24-2x
L=24-2x3
L=18in
w= 15-2x
w=15-2*3
w=9in
h=x
h=2in
Dimension=18,9,3
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7. Write a general formula to describe the variation: x varies directly with the cube of y; x = 8 when y = -8.
Answer: it should be this M=kb^3/B^2
Step-by-step explanation:
Draw a histogram and a box-and-whisker plot to represent the combined data, and answer the questions. Be sure to include the new graphs as part of your final submission.
How do the graphs of the combined data compare to the original graphs?
Compared to the original graphs, do the new graphs make it easier or more difficult to estimate the price of a book?
The new graphs would make it more difficult to estimate the price of a book.
How to create the combined graph?To do this, we simply combine the frequencies on Felix and Tyler's table.
When this is done, we have the following dataset
3,3,3,3,3,3,3,3,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7, 8,8,8,8,9,9,9,9,9,9,9,9,9,11,11,13,13,13,13,15,15,15,16,16,18,18,18,18,18,19,19,19,19,19,19,29,32,32,36,36,36,38,38,64,64,66,66,66,68,68,69,75,75,76,76,76,76,76,78,78,79,82,82,86,86,86,89,96,96,97,97,99
Next, we create the box & whisker plot and the histogram using the new dataset
(see attachment for the graphs)
The new graphs would make it more difficult to estimate the price of a book.
This is so because the dataset used to create the graphs do not come from the same source
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??????????????????????????????
[tex]\large\displaystyle\text{$\begin{gathered}\sf \frac{2x-20}{3}=2x \end{gathered}$}[/tex]
Multiply both sides of the equation by 3.
[tex]\large\displaystyle\text{$\begin{gathered}\sf 2x-20=6x \end{gathered}$}[/tex]
Subtract 6x on both sides.
[tex]\large\displaystyle\text{$\begin{gathered}\sf 2x-20-6x=0 \end{gathered}$}[/tex]
Combine 2x and −6x to get −4x.
[tex]\large\displaystyle\text{$\begin{gathered}\sf -4x-20=0 \end{gathered}$}[/tex]
Add 20 to both sides. Any value plus zero results in its same value.
[tex]\large\displaystyle\text{$\begin{gathered}\sf -4x=20 \end{gathered}$}[/tex]
Divide both sides by −4.
[tex]\large\displaystyle\text{$\begin{gathered}\sf x=\frac{20}{-4} \end{gathered}$}[/tex]
Divide 20 by −4 to get −5.
[tex]\large\displaystyle\text{$\begin{gathered}\sf x=-5 \ \ \to \ \ \ Answer \end{gathered}$}[/tex]
{ Pisces04 }[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Equation: }[/tex]
[tex]\mathbf{\dfrac{2x - 20}{3} = 2x}[/tex]
[tex]\huge\textbf{SIMPLIFY IT or DISTRIBUTE:}[/tex]
[tex]\mathbf{\dfrac{2}{3}x - \dfrac{20}{3} = 2x}[/tex]
[tex]\huge\textbf{SUBTRACT 2x to BOTH SIDES:}[/tex]
[tex]\mathbf{\dfrac{2}{3}x - \dfrac{20}{3} - 2x = 2x - 2x}[/tex]
[tex]\huge\textbf{SIMPLIFY IT!}[/tex]
[tex]\mathbf{- \dfrac{4}{3}x - \dfrac{20}{3} = 0}[/tex]
[tex]\huge\textbf{ADD }\boxed{\rm{\bf \dfrac{20}{3}}}\huge\textbf{ to BOTH SIDES:}[/tex]
[tex]\mathbf{-\dfrac{4}{3}x - \dfrac{20}{3} + \dfrac{20}{3} = 0 + \dfrac{20}{3}}[/tex]
[tex]\huge\textbf{SIMPLIFY IT!}[/tex]
[tex]\mathbf{-\dfrac{4}{3}x = \dfrac{20}{3}}[/tex]
[tex]\huge\textbf{MULTIPLY }\boxed{\rm \bf {\dfrac{3}{-4}}}\huge\textbf{ to BOTH SIDES:}[/tex]
[tex]\mathbf{\dfrac{3}{-4}\times\dfrac{-4}{3}x = \dfrac{3}{-4}\times\dfrac{20}{3}}[/tex]
[tex]\huge\textbf{SIMPLIFY IT!}[/tex]
[tex]\mathbf{x = -5}[/tex]
[tex]\huge\text{Therefore, your answer should be: \boxed{\mathsf{x = -5}}}\huge\chekmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Helppppppo points to give
a) The point (2, -7/5) is not a point on the graph?
b) The value of f(x) when x is 1 is -1/3 and the point on the graph is (1, -1/3)
c) The value of x for f(x) = 2 is 22 and the point on the graph is (22, 2)
d) The domain of x is all real values of x ≠ 10
e) The x intercept is -2
f) The y intercept is -1/5
What is a Function?Function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output and not one input for two outputs.
Analysis:
a) To test if the point (2, -7/5) is a point on the graph, we put in x = 2 into the function,
f(2) = 2+2/2-10 = 4/-8 = -1/2 ≠ -7/5. Therefore (2, -7/5) is not a point on the graph.
b) if x = 1, f(1) = 1 +2 / 1-10 = 3/-9 = - 1/3
The point on the graph is (1, -1/3)
c) if f(x) = 2, then 2 = x+2/x-10
2(x-10) = x+2
2x -20 = x+2
2x-x = 2+20
x = 22, the point on the graph is (22, 2)
d) The domain of the function is such that the denominator would not be zero.
so if x - 10 ≠ 0
Then the values of x ≠ 10 are the domain of the function.
e) The x intercept of the graph is the point at which f(x) = 0
0 = x+2/x-10
x+2 = 0
x = -2. The x-intercept is -2.
f) the y-intercept is such that x = 0
0+2/0-10 = 2/-10 = -1/5
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What the 29th square number?
Answer: 841
Step-by-step explanation:
29×29=841
Which of the following is the best buy?
a 6 oz box of rice for $0.90
a 12 oz box of rice for $1.93
a 16 oz bag of rice for $2.42
a 9 oz box of rice $1.25
The $1.25 one for 9 Oz box of rice would be the best buy.
How to find the Unit Price?To get the best buy among the given items and prices, we need to find the unit price. Thus, the formula is;
Unit price = Price/Quantity
A) Unit Price = 0.90/6 = 0.15
B) Unit Price = 1.93/12 = 0.15083
C) Unit price = 2.42/16
Unit Price = 0.15125
D) Unit Price = 1.25/9 = 0.138
The $1.25 one for 9 Oz box of rice would be the best buy.
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Which of the following could be the ratio between the lengths of the two legs of a 30-60-90 triangle?
Check all that apply.
Answer:c
options A and B
Step-by-step explanation:
the ratio between the lengths of the two legs of a 30-60-90 triangle
General ration of 30-6- 90 degrees triangle is
x : xsqrt(3) : 2x
When x=1 the ratio becomes 1 : 1 sqrt(3)
when x= 2sqrt(3) the ratio becomes
It becomes
Two sides of 30-60-90 triangle cannot be equal
so option c and option D are not possible
sqrt(2) is also not possible because we have sqrt(3) in general ratio
PLS MARK ME AS BRAINLIEST.
in the x-y plane, what is the y- intercept of the graph of the equation y=6 (x-1/2) (x+3)
The y-intercept on the x-y plane is (0, -9).
How to get the y-intercept?To get the y-intercept we just need to evaluate in x = 0.
Here we have:
y = 6*(x - 1/2)*(x + 3)
Evaluating the given equation in x = 0 we get:
y = 6*(0 - 1/2)*(0 + 3) = -9
Then the y-intercept on the x-y plane is (0, -9).
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Answer:
-9
Step-by-step explanation:
John deposits a certain amount that is compounded continuously at 8% interest. Find the number of years it takes to double the amount.
Answer:
about 8.66 years
Step-by-step explanation:
The multiplier of account value when interest is compounded continuously is ...
k = e^(rt)
where r is the annual interest rate, and t is the number of years.
SetupWe want to find t when k=2 and r=0.08. Putting these values in the formula gives ...
2 = e^(0.08t)
SolutionTaking logs of both sides, we have ...
ln(2) = 0.08t
t = ln(2)/0.08 = 0.693147/0.08 ≈ 8.66
It takes about 8.66 years to double the amount.
__
Additional comment
If the interest rate is expressed in integer numbers of percentage points (R%), then the doubling time is ...
t = 100·ln(2)/R ≈ 69.3147/R
Here, that is 69.3147/8 ≈ 8.66.
The "rule of 72" is used to estimate the doubling time for periodically compounded interest at rate R%. That rule tells you the time is t ≈ 72/R. For most interest rates and compounding frequencies in a reasonable range, this gives a time within a reasonable amount of error.
For continuously compounded interest, we have shown the doubling time in years is 69.3147/R. (The exact value of the constant is 100·ln(2).) For the purpose here, a constant of 69.3 gives an estimate accurate to 3 sf.
Choose the equation for the graph.
a) y = -x - 4 + 1
b) y=-x-4) - 1
c) y = -x + 4 + 1
d) y = -x + 4) - 1
e) y =
|x4| +1
Answer:
a
Step-by-step explanation:
The vertex is at (4,1).
Eliminate b, c, dAlso, the graph opens down, so this eliminates e.
So, the answer is a.
in a random sample of 36 criminals convicted of a certain crime, it was determined that the mean length of sentencing was 50 months, with a standard deviation of 5 months. construct and interpret a 90 % confidence interval for the mean length of sentencing for this crime.
The answer is 90% of the crime is between 48.63 and 51.37
How to solve for the confidence intervalThe sd = 5 months
n = 36
Mean length = 50
1- 0.90
= 0.1
Critical value = alpha/2 = 1.645
Margin of error
E = 1.645 x 5/√36
= 1.37
The upper and lower limits are50 - 1.37 + 50 + 1.37
= (48.63, 51.37)
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PLS HELP ME 17 MIN LEFT Solve the following equation: one third plus one third equals
one third,
two sixths,
two thirds,
or three thirds.
A bus covered a distance of 331.25 km in 25 L of diesel. Find the distance covered by the bus in 1 L of diesel . please do answer in copy
Answer:
13.25km
Step-by-step explanation:
25 Litres = 331.25km
1 Litre =
[tex] \frac{331.25}{25} \\ = 13.25km[/tex]
Answer:
13.25 km
Step-by-step explanation:
25 litres = 331.25 km
1 litre =
331.25
25
=13.25 km
One jar filled with honey weighs 120 grams and one empty jar with half filled honey jar weighs 150 grams what is the weight of the jar
Answer:
90 grams
Step-by-step explanation
Full = 120
half filled + empty = 150
half of 120 = 60
Therefore, a jar weighs 150 - 60
= 90 grams
Peter received a $15 tip on a meal that cost $130. What percent of the meal cost was the tip?
11.5%
21%
18.5%
14%
The ratio of the weight of an object on Planet A to the weight of the same object on Planet B is 100 to 3. If an elephant weighs 3200 pounds on Planet A, find the
elephant's weight on Planet B.
The elephant's weight on Planet B is….. lb.
A ratio shows us the number of times a number contains another number. The elephant's weight on Planet B is 96 pounds.
What is a Ratio?A ratio shows us the number of times a number contains another number.
The ratio of the weight of an object on Planet A to the weight of the same object on Planet B is 100 to 3.
Weight on Planet A/ Weight on planet B = 100 / 3
Now, the weight of the elephant on planet A to Planet B will be,
elephant's weight on Planet A/elephant's weight on Planet B = 100 / 3
elephant's weight on Planet B = (3 ×3200)/100
elephant's weight on Planet B = 96 pounds
Hence, the elephant's weight on Planet B is 96 pounds.
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15. Which one of the following is a geometric sequence?
O A. 0, 1, 2, 3,...
O B. 2, -3, 92, -18/4
O C. -7, 10, 23, 36, ...
O D. 8, 4, 2, 1, 1/2, ¹/4....
Find the y intercept of the line on the graph
Answer: y = -1
Step-by-step explanation:
When x = 0, y = -1
Also, you can think about it as when the graph of the line passes the y axis
how much is 0.54/0.2
Answer:
2.7 is the answer!!
Step-by-step explanation:
hope this helps :)
What is this expression in simplified form?
Answer:
See below
Step-by-step explanation:
= (-7)(11)(√(3*10) ) = - 77 √(30)
Which of the following equations have complex roots?
Answer:
D
Step-by-step explanation:
Subtracting 2 from both sides and then dividing both sides by 3 gives that x² = -2/3, which indicates the roots are complex.
Complete the table below to solve the equation 2.5x − 10.5 = 64(0.5x).
x f(x) = 2.5x − 10.5 g(x) = 64(0.5x)
2
3
4
5
6
A newspaper started an online version of its paper 14 years ago. In a recent presentation to stockholders, the lead marketing executive stated, “The revenues for online ads are more than double that of the revenues for printed ads.”
Use the graph below to justify the lead executive’s statement.
Determine the approximate year that the two ad revenues were equal.
See Text Version
Two ocean beaches are being affected by erosion. The table shows the width, in feet, of each beach measured at high tide where 1995 is represented by year 0:
Year number Western Beach width (in feet) Dunes Beach width (in feet)
0 100 20
5 90 45
10 80 70
11 78 75
12 76 80
15 70 95
Describe the patterns shown by the erosion data measurements shown for each of the beaches in the table.
Between which years will the beaches have approximately the same width?
Assuming these rates remain constant, what can you do to get a better approximation of when the two beaches will have the same width?
The answers are as follows:
What is data?Data is information that has been translated into a form that is efficient for movement or processing.
1. By substituting the values x= 1, 2, 3..
We get the point where f(x)= g(x)
So, f(5)= g(5) =2
Hence, the value of x is 5.
2. As per the given data, during year 14,
revenue from online ads is approximately $4.2 million, whereas revenue from online ads is double than revenue from printed ads.
Also, both line intersect inbetween 7 and 8th year and both online ads and printed ads generated an approximate revenue of $2.2 million.
3. Western Beach erodes from 100 ft to 70 ft.
So, rate of erosion = 30 ft/15 yr = 2 ft/yr.
and, Dunes Beach builds up from 20 ft to 95 ft.
So, rate of buildup = 75 ft/15 yr = 5 ft/yr.
Hence, Dunes beach gets 5 feet every year, and every 5 years the beach loses 25 feet.
b) From the table, beaches will have the same width sometime in year 11 (2006).
c) If the rate remains constant then there is no same width cause of decrease in western beach and increase dunes beach.
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The following table shows the data collected from a random sample of 100 middle school students on the number of hours they do household chores every week:
Weekly Duration of Household Chores
Time (in hours) 0–1 2–3 4–5 6–7
Number of Students 32 64 3 1
There are 1,500 students in the school. Based on the sample proportion, how many students in the school would be expected to do household chores for at least two hours every week?
A 480
B 960
C 1020
D 1440
The students in the school would be expected to do household chores for at least two hours every week with 1020 students.
We have given
Time (in hours) 0– 1 2–3 4–5 6–7
Number of Students 32 64 3 1
What is the random sample?A simple random sample is a subset of a statistical population in which each member of the subset has an equal probability of being chosen.
The keyword is at least, this means anything under that number will not qualify.
So that leaves 68 out of the 100 sample students.
So if you want to have the same thing but with 1,500 students.
Take off the 2 zeros at the end of 1500 and multiply by 68 to get your answer.
This is because there are 2 zeros in 100, so to cancel out the 2 zeros in 100, take out the 2 zeros in 1500 making it a lot easier.
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Please help!!! Suppose we have two functions...
Answer:
4
Step-by-step explanation:
To find f(-1)g(-1) which is f(-1)*g(-1), first, we must find what are values of f(-1) and g(-1) first which can be found by substituting x = -1 in both functions.
[tex]\displaystyle{f(-1)=(-1)^2+1}\\\\\displaystyle{f(-1)=1+1 = 2}[/tex]
Now we know that f(-1) is 2, next, we find g(-1).
[tex]\displaystyle{g(-1) = 3(-1)+5}\\\\\displaystyle{g(-1)=-3+5 = 2}[/tex]
Now we know that g(-1) is 2 too. Since the question wants to find f(-1)g(-1), therefore 2*2 = 4.
Hence, the answer is 4.
Answer:
D) 4
Step-by-step explanation:
Given functions:
f(x) = x² + 1
g(x) = 3x + 5
Here, we're asked to find the value of both functions when the value of x is -1. Then, we multiply the functions in order to find the value of f(-1)•g(-1).
Note: f(-1) • g(-1) is equivalent to (f • g)(-1).
Method 1: f(-1) • g(-1)
Find the value of each function when x = -1.
f(-1) = (-1)² + 1 ⇒ f(-1) = 1 + 1 ⇒ f(-1) = 2
g(-1) = 3(-1) + 5 ⇒ g(-1) = -3 + 5 ⇒ g(-1) = 2
Multiply the functions together.
f(-1) • g(-1) ⇒ 2 • 2 ⇒ 4
Method 2: (f • g)(-1)
First, multiply the functions.
⇒ (x² + 1) • (3x + 5) [ Simplify using the Distributive Property: (a + b) • (c + d) = ac + ad + bc + bd. ]
⇒ x²(3x) + x²(5) + 1(3x) + 1(5)
⇒ 3x³ + 5x² + 3x + 5
Now, substitute -1 as the value of x.
⇒ 3(-1)³ + 5(-1)² + 3(-1) + 5 [ Exponents first. }
⇒ 3(-1) + 5(1) -3 + 5 [ Multiply the numbers. ]
⇒ -3 + 5 - 3 + 5 [ Simplify. ]
⇒ 4
Therefore, the product of both functions when x = -1 is 4.
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