Lesson 10 Practice Problems
1. Andre bought a new bag of cat food. The next day, he opened it to feed his cat. The
graph shows how many ounces were left in the bag on the days after it was bought.
a. How many ounces of food were in
the bag 12 days after Andre bought
it?
b. How many days did it take for the
bag to contain 16 ounces of food?
c. How much did the bag weigh before
it was opened?
d. About how many days did it take for
the bag to be empty?
ounces of cat food
Answers
Using a linear function, it is found that:
a) 36 ounces of food were there after 12 days.
b) It took 24 days for the bag to contain 16 ounces of food.
c) The bag weighed 56 ounces before it was opened.
d) It took about 33 days for the bag to be empty.
What is the definition of a linear function?A linear function is defined according to the following rule:
y = mx + b
In which:
m is the slope of the function, also called the rate of change of the function, given by the change in y divided by the change in x.b is the y-intercept of the function, which is the the value of y when the function crosses the x-axis(x = 0).From the graph of the function, we have that:
The intercept is of b = 56.The slope is of m = -40/24 = -1.6667, as in 24 days, the amount of food decayed from 56 ounces to 16 ounces, that is, it decayed 40 ounces.Hence the function for the amount of food after t days is given by:
A(t) = 56 - 1.6667t.
After 12 days, the amount is given by:
A(12) = 56 - 1.6667(12) = 36 ounces.
From the graph, we have that:
It took 24 days for the bag to contain 16 ounces of food.The bag weighed 56 ounces before it was opened. (y-intercept of the function = initial value).It took about 33 days for the bag to be empty. (x-intercept of the function).What is the missing information?The graph of the function is missing, and is given at the end of the answer.
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Related Questions
Select the row of Pascal's triangle that is used to expand the binomial expression (22³ + 3y²)².
1
11
121
1331
14 641
1
5 10 10 5 1
1 6 15 20 15 6 1
1 7 21 35 35 21
35 21 7 1
1 8 28 56 70 56 28 8 1
M
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Answers
We will select the third row from the pascal triangle to expand the binomial expression (22³ + 3y²)² which is equal to
(22³ + 3y²)² = 22⁶ + 63888y² + 9y⁴
We know that when we need to expand the expression (a + b)² we select the coefficients from the row of triangle beginning with 1,2 which is (1,2,1).
And when we write the expansion we note that with each new term we decrease the power of a and increase the power of b.
Thus the expansion can be written as
(a + b)² = 1a² + 2ab + 1b²
which we normally write as
(a + b)² = a² + 2ab + b² (1)
According to the question we have been the expression as
(22³ + 3y²)² which is equal to the above expression where,
a = 22³ and b = 3y²
Putting the required values in equation (1) we get
(22³ + 3y²)² = (22³)² + 2(22³)(3y²) + (3y²)²
= 22⁶ + 63888y² + 9y⁴
Hence we will select the third row from the pascal triangle to expand the binomial expression (22³ + 3y²)² which is equal to
(22³ + 3y²)² = 22⁶ + 63888y² + 9y⁴
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Help pls . Math people
Answers
3(121) -5
363-5
358
[tex]f(x)=3x^2-5[/tex]
Substitute x = -11 in the equation.
[tex]f(-11)=3(-11)^2-5\\f(-11)=3(121)-5\\f(-11)=363-5\\f(-11)=358[/tex]
Thus, the answer is 358 aka the second choice.
can someone help me with these two please
Answers
Answer:
1) y=1/2x+4 and y=-2x-4
2) y-9 = -2(x+7)
Step-by-step explanation:
1) Perpendicular lines must have reciprocal slopes. So, the sign must be switched and the numerator and denominator must be switched.
2) Point-slope form is [tex]y-y_{1} = m(x-x_{1})[/tex]
So plug the slope and point in.
y - 9 = -2 (x - (-7))
y-9=-2(x+7)
What is a pendulum?
Answers
Answer:
A pendulum is a weight suspended from a pivot so that it can swing freely. When a pendulum is displaced sideways from its resting, equilibrium position, it is subject to a restoring force due to gravity that will accelerate it back toward the equilibrium position
EXAMPLES:
the tick in a grandfather clock, a wrecking ball suspended by a chain or link
Step-by-step explanation:
hope this helps! please mark brainliest:)
A pendulum is a simple device consisting of a weight suspended from a fixed point, allowing it to swing back and forth under the force of gravity
Pendulum: A pendulum is a simple device consisting of a weight suspended from a fixed point, allowing it to swing back and forth under the force of gravity. The bob is typically attached to a string, rod, or wire that allows for free movement.
When a pendulum is set in motion, it swings back and forth in a regular and repetitive pattern.
The motion of a pendulum is governed by several factors, including the length of the pendulum, the mass of the bob, and the gravitational acceleration.
The swinging motion of a pendulum is influenced by two fundamental principles:
1. Period: The period of a pendulum is the time it takes for the pendulum to complete one full swing from one side to the other and back. The period depends on the length of the pendulum and is not affected by the mass of the bob. A longer pendulum will have a longer period, while a shorter pendulum will have a shorter period.
2. Oscillation: The pendulum oscillates due to the force of gravity acting on the bob. As the pendulum swings to one side, it gains potential energy, which is then converted into kinetic energy as it swings back. This energy transfer causes the pendulum to continue swinging back and forth.
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What is the surface area of the cylinder with height g in and radius 4 in? Round your
answer to the nearest thousandth.
Answers
Answer:
if you want ans area of cylider is 2πrh+2πr2
Step-by-step explanation:
need thanks and make me brainiest if it helps you
HELP I HAVE 5 MINUTES
Answers
Answer:
24
Step-by-step explanation:
4x6
The value of y is directly proportional to the value of x. If y = 35 when X = 140, what is the
value of y whenx=70?
Answers
Answer:
17.5
Step-by-step explanation:
soln:
given,
since, x and y are directly proportional
and x=140, y=35
dividing x by y we get,
x/y=140/35
or,x/y=4/1
or,x=4y
when x=70,
x=4y
or,70=4y
•°•y=17.5
Tammy made a recipe that called for 3/4 teaspoon of salt. If the recipe is cut in half, how much salt is needed?
Answers
Answer:
answer is A your welcome
Answer:
If the recipe is cut in half, 3/8 teaspoon of salt is needed.
Step-by-step explanation:
Since the recipe is cut in half, we need to find 1/2 of 3/4. This means we need to multiply 1/2 times 3/4. For the numerator, 1 times 3 equals 3. For the denominator, 2 times 4 equals 8. The fraction is 3/8.
HELP ASAP I DONT HAVE TIME AND IT ALSO DETECTS IF ITS RIGHT OR WRONG
Answers
Answer:
I think it's 1,920
Step-by-step explanation:
Multiply 320 × 6 which would give you 1,920!
how do i evaluate l18l
Answers
Answer:
18
Step-by-step explanation:
It is asking for the absolute value of 18. The absolute value is the units away from 0 the number is, so the answer is 18.
Answer: the answer is 1^19 (one to the power of 19)
Step-by-step explanation:
l^18 multiplied by l^1 = l^(18 + 1) = l^19
(1 to the power of 18 multiplied by 1 to the power of 1 equals 1 to the power of (18 + 1) equals 1 to the power of 19)
for f(x) = 1/3x +5
f(3) =
Answers
Answer:
f(3) = 6
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Function NotationStep-by-step explanation:
Step 1: Define
f(x) = 1/3x + 5
f(3) is x = 3
Step 2: Evaluate
Substitute: f(3) = 1/3(3) + 5Multiply: f(3) = 1 + 5Add: f(3) = 6On a coordinate plane, a point is 7 units up on the y-axis. Which of the statements are true? On a coordinate plane, a point is 7 units up on the y-axis.
Which of the statements are true? Select all that apply.
The point is located at (7, 0).
The point is located at (0, 7).
The point is on the y-axis.
The point is on the x-axis.
The point is at the origin.
Answers
Answer:
The second one
The third one
Step-by-step explanation:
Answer:
the point is located at 7,0. the point is on the y-axis.
Step-by-step explanation:
U= {1,2...,10}
A= {2,3,5,7}
B= {2,4,5,7}
D= {1,2,5,7}
Find:
1. A U B U D
2. A n B n D
Answers
Answer:
1) {5,7}
2) {1,2,5,7}
Step-by-step explanation:
1) A union B union C
means you take common contents in all A,B,C
2) A and B and C
means you take all the contents of all A,B,C and combine
complete the table and then find the function rule. Remember to put in the y=mx+b form
Answers
Answer:
1. 81 2. -20 3. 168 4. -24
Step-by-step explanation:
I hope this is right :)
Bike sprockets and chain.
A gear ratio is the ratio of the teeth on the front sprocket and the teeth on the rear sprocket. If a bike has 36 teeth on the front sprocket and 12 teeth on the rear sprocket, what is the gear ratio for the bike?
Answers
Answer: 3:1
Step-by-step explanation:
From the question, we are informed that a gear ratio is the ratio of the teeth on the front sprocket and the teeth on the rear sprocket.
We are further told that the bike has 36 teeth on the front sprocket and 12 teeth on the rear sprocket.
Based on the explanation given in the question, the gear ratio for the bike would be the ratio of 36 to 12. This will be:
= 36:12
Since 12 is a common factor. It can be further reduced to 3:1.
Therefore, the gear ratio is 3:1
Answer:
[tex]\frac{3}{1}[/tex]
Step-by-step explanation:
That's the answer
7x+8(x+1/4)=3(6x-90-8
Answers
Answer:
exact form 296/3 decimal form 98.6666666 mixed number form 98 2/3
Step-by-step explanation:
Answer:
First result: X = 248/3 or 82.67 Second result: X = 260/3 or 86.57
Step-by-step explanation:
1st one: 7x + 8(x + 1/4) = 3(6x - 90 - 8)
7x + 8x + 2 = 18x - 270 - 24
15x + 2 - 2 = 18x - 246 - 2
15x - 18x = 18x - 18x -248
-3x = 248 --> -3x/3 = 248/3
X = 248/3 or X = 82.67
2nd one: 7x + 8(x+1/4) = 3(6x - 90) - 8
7x + 8x + 2 = 18x - 270 - 8
15x + 2 - 2 = 18x - 262 - 2
15x - 18x = 18x -18x - 260
-3x = 260 --> -3x/3 = 260/3
X = 260/3 or X = 86.67
Sorry if none of these are the answer!
15 POINTS FOR THIS MATH QUESTION!
A teacher’s monthly gross pay is $5,321. The federal government withholds 15% of the teacher’s monthly gross pay for income taxes. How much does the teacher pay in income tax every month?
Answers
Answer:
798.15
Step-by-step explanation:
5321 x .15 = 798.15
(I think)
Answer:
798.15
Step-by-step explanation:
Nathen packs 25 boxes in 2 hours. How many boxes can he pack in his 8 hour shift?
Answers
PLEASE HELP ASAP
during the first home game, the eagle's soccer team had a total of 90 fans. by the second game, this number increased to 150 fans. What was the percent increase in attendance between the first and second games of the season?
A)55%
B)66.7%
C72%
D75.5%
Answers
Answer:
The answer is A.
Step-by-step explanation:
I hope that help's??
B
What is the value of x in the solution to this system of equations?
4x−7y=105
y=−3x+10
Enter your answer in the box.
Answers
Answer:
Y=7y=105
Step-by-step explanation:
Answer:
x = 7
y= -11
Step-by-step explanation:
athletic shoes: $79.99
discount: 40%
Answers
Answer:
48$ -specific (not rounded)
Step-by-step explanation:
There could be other solutions that can work. Such as counting the 79.99 to just 80. But for the very SPECIFIC value, you have to find 40% of 79.99 by multiplying it by .4 . 79.99*.4 = 31.99. After that, you would subtract 79.99 and 31.99 which would get you to 48.
Answer:
$47.99
Step-by-step explanation:
79.99*40/100
79.99*0.4
40% of $79.99 = $32.00 ( rounded )
79.99 - 32 = $47.99
What is the quotient?
Answers
Answer:
just post them all in one question instead of a ton of different questions. it's annoying.
Step-by-step explanation:
Square number (2x+5y)(3x^2-4xy+2y^2)
Answers
Answer: 6x³+7x²y-16xy²+10y³
Step-by-step explanation:
( 2x + 5y )( 3x² - 4xy + 2y²)
⇒ (2x * 3x² ) = 6x³
⇒ (2x * - 4xy) = -8x²y
⇒ (2x * 2y² ) = 4xy²
⇒ (5y * 3x² ) = 15x²y
⇒ (5y * - 4xy) = -20xy²
⇒ (5y * 2y² ) = 10y³
( 2x + 5y )( 3x² - 4xy + 2y²) = 6x³-8x²y+4xy²+15x²y-20xy²+10y³
= 6x³+7x²y-16xy²+10y³
what is the maximum value of the derivative of f(x)= 3x^2+x^3
Answers
Answer:
Maximum Value: ∞
General Formulas and Concepts:
Calculus
Basic Power Rule:
f(x) = cxⁿ f’(x) = c·nxⁿ⁻¹Step-by-step explanation:
Step 1: Define
f(x) = 3x² + x³
Step 2: Find Derivative
Basic Power Rule: f'(x) = 2 · 3x²⁻¹ + 3 · x³⁻¹Simplify: f'(x) = 6x + 3x²Step 3: Analyze
We see that our derivative is the graph of some sort of parabola. The parabola would be opening upwards.
Therefore, the maximum value of the derivative would be ∞, as the parabola's output y infinitely increases.
Can someone please help me with proofs
Answers
3) Triangle AED is congruent to triangle CFD (SAS)
Help me out it’s for geometry thank you
Answers
Answer:
7
Step-by-step explanation:
11x-2 = 75
+2. +2
---------------
11x = 77
/11. /11
56 divided by 9,072 long form
Answers
Answer:
0.0061728395
Step-by-step explanation:
BOOM
evaluate v(x) = 14 - 3x when x = -3,0, and 4.
Answers
Answer:
v(-3)=23
v(0)=14
v(4)=2
Step-by-step explanation:
t= u+v/2 for u
•u= 2t+v
•u= 2t/v
•u= 2(t-v)
•u= 2t-v
Answers
Answer:
u=2t-v
Step-by-step explanation:
t=(u+v)÷2 |×2
2t=u+v
-u=v-2t |:(-1)
u=-v+2t
u=2t-v
How many portions of 8 ¾ ounces each can be made from a boneless roast weighing 28 pounds?
Answers
Number of portions of 8 ¾ ounces each can be made from a boneless roast weighing 28 pounds is 51 7/35.
Here,
A boneless roast weighing = 28 pounds
Each portion = 8 3/4 ounces
We have to find the number of portion.
What is Division method?
Division method is used to distributing a group of things into equal parts.
Now,
Since, 1 pound = 16 ounces
Hence, 28 pound = 28 x 16 = 448
So, Number of portions = 448 ÷ 8 ¾ = 448 ÷ 35/4 = 51 7/35
Therefore, Number of portions of 8 ¾ ounces each can be made from a boneless roast weighing 28 pounds is 51 7/35.
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