Answer:
y = mx + c
8 = 2x + 2
4. The chart below represents the kinematics of a freely falling body.
Time
(seconds t)
Total Distance
meters d (t)
1
5
2
20
45
80
125
3
4
5
a. Is the relationship between time and distance an arithmetic sequence?
Explain.
b. The total distance a freely falling body covers in time, t, is given by the equation d(t)=1/2 gt2, where g is constant at 10 m/s². Show, in terms of n, the distance a falling body covers in t = n seconds of movement.
a. The given sequence is not an arithmetic sequence.
b. The distance a falling body covered in t = n seconds of movement is 5n²meters.
What is the distance?
Distance is a measurement of how far apart two things or points are, either numerically or occasionally qualitatively. The distance can refer to a physical length in physics or to an estimate based on other factors in common usage.
Here, we have
a. A sequence can be said arithmetic sequence if the difference between any two consecutive terms remains the same.
In this case, the difference between 20 and 5 is 15, and the difference between 45 and 20 is 25, this shows that the difference between two consecutive terms is not the same.
Hence, it can be said that the given sequence is not an arithmetic sequence.
b. To evaluate the distance covered by the body in “n” seconds, Substitute t=n in d(t) then d(n) will represent the distance covered by the body in “n” seconds
d(n)=1/2 g(n)²
d(n) = 1/2(10)(n)²
d(n) = 5n²meters
Hence, the distance a falling body covered in t = n seconds of movement is 5n²meters.
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Jimmy, Johny, and Jolly worked part-time on the weekend to earn some extra money. Three of them together earned $57. If Johny earned twice as much as Jolly did and Jimmy earned $3 less than Johny did, how much did Jimmy earn?
On solving the provided linear equation question - Jolly = $17.4, Jimmy =2x-30 =4.8 and Johnny = 2x=34.8
What is a linear equation?A linear equation has the algebraic form y=mx+b. where m is the slope and b is the y-intercept, consisting of a first-order (linear) term and a constant. If x and y are variables, the above is sometimes called a "two-variable linear equation".
Take Jolly's expenditure as x.
Jimmy would have spent twice as much as Jolly.
Johnny Equals 2x-30 if Johnny spent $30 less than Johnny.
Total amount spent: $57
Therefore,
[tex]x+ (2x-30) + 2x = 57\\ x+ 2x -30 +2x =57.\\ 5x = 57+ 30\\[/tex]
x = 87/5
x= 17.4
Now take is that - X= 17.4.
Jolly is that - x= $17.4
Jimmy is that - =4.8
Johnny is that = =34.8
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when $n$ is divided by $8$, the result is greater than $5$. what is the least possible integer value of $n$?
when N is divided by 8, the result is greater than 5 the least possible integer value of N is 48.
Zero, a positive natural number, or a negative integer with a minus sign are all examples of integers. The additive inverses of the positive numbers are the negative numbers. The boldface Z is frequently used in mathematics to denote the set of integers.
Positive integers: If a number is greater than zero, it is positive. Example: 1, 2, 3 . . .Negative integers: If a number is less than zero, it is negative. Example: -1, -2, -3 . . .Zero cannot be thought of as either a negative or a positive integer. It's an entire number.the least possible integer greater than 5 is 6,
and when 6 × 8 = 48 thus,
the least possible integer value of N is 48.
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If Harry travels 4 and 6/8 of a mile in 5 hours on his broomstick. How far will he travel in 1 hour?
Answer:
Step-by-step explanation:
Use the given functions to set up and simplify 6/8.
4 =
6/8 = 3/4
1/5 mi/hr mulitplied by 1 hr = 1/5 mi
The average mass of 5 boys is 50 kilograms. Another boy’s mass is added and the average goes to 40 kilograms. What was the mass of the sixth boy?
The mass of the sixth boy is 80 kilograms.
What was the mass of the sixth boy?It's important to note that a mean simply means the average of a set of numbers that are given. In this situation, the average mass of 5 boys is 50 kilograms. The total mass will be:
= 50 × 5
= 250 kilograms
In this case, when another boy’s mass is added and the average goes to 55 kilograms. The total mass will be:
= 55 × 6
= 330 kilograms.
The average mass of the last boy will be:
= 330 - 250
= 80 kilograms
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Complete questions
The average mass of 5 boys is 50 kilograms. Another boy’s mass is added and the average goes to 55 kilograms. What was the mass of the sixth boy?
Mrs. Evans is taking 9 students to an amusement park. Mr. Sanchez is taking 14 students to a water park. Each student will buy a ticket to the appropriate park and pay for a ride fee. Admission to the amusement park is 2 times that of the water park's admission as shown in the table. The total cost is the same for both groups of students.
Amusement Park
Water Park
Admission: $2x per student
Admission: $x per student
Ride Fee: $3.00
Which equation represents the problem?
Ride Fee: $4.50
O A) 9(x + 4.50) = 14(2x + 3.00)
O B) 9(x + 3.00) = 14(2x + 4.50)
O C) 9(2x + 4.50) = 14(x + 3. 00)
O D) 9(2x + 3. 00) = 14(x + 4.50)
The equation the represent the event of taking Mrs. Evans taking 9 students to an amusement park and Mr. Sanchez is taking 14 students to a water park is
D) 9(2x + 3.00) = 14(x + 4.50)How to find the expression that represent the problemThe problem is solved using simultaneous equation, the equations required is derived as follows:
Amusement park
Admission: $2x per student
Ride Fee: $3.00
Mrs. Evans is taking 9 students to an amusement park
9($2x + $3.00)
Water park
Admission: $x per student
Ride Fee: $4.50
Mr. Sanchez is taking 14 students to a water park
14($x + $4.50)
The total cost is the same for both groups of students
9($2x + $3.00) = 14($x + $4.50)
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Show the work please! Thanks!!
Simplifying
2x + 5y = 2
Solving
2x + 5y = 2
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-5y' to each side of the equation.
2x + 5y + -5y = 2 + -5y
Combine like terms: 5y + -5y = 0
2x + 0 = 2 + -5y
2x = 2 + -5y
Divide each side by '2'.
x = 1 + -2.5y
Simplifying
x = 1 + -2.5y
Simplifying
5X + 10y = 17
Solving
5X + 10y = 17
Solving for variable 'X'.
Move all terms containing X to the left, all other terms to the right.
Add '-10y' to each side of the equation.
5X + 10y + -10y = 17 + -10y
Combine like terms: 10y + -10y = 0
5X + 0 = 17 + -10y
5X = 17 + -10y
Divide each side by '5'.
X = 3.4 + -2y
Simplifying
X = 3.4 + -2y
Josefina ate 3/8 of the pizza and Leando ate 4/16. How much did they eat between the two of them?
To calculate how much they ate between the two of them, the amounts each ate must be added:
[tex]\begin{gathered} \sf \frac{3}{8} + \frac{4}{16} = \\ \\ \sf\frac{16 \div 8 \times 3 + 16 \div 16 \times 4}{16} = \\ \\ \sf\frac{6 + 4}{16} = \\ \\ \sf \frac{10}{16} = \red {\boxed{ \sf \frac{ \green5}{ \green8} }}\end{gathered}[/tex]
Therefore, between the two of them they ate five eighths of pizza.
To add heterogeneous fractions, fractions with different denominators, follow these steps:
Find the common denominator, which is the least common multiple of the denominators.Divide the common denominator by the other denominator and multiply by the numerator.Write the results obtained above as numerators with the sign of the sum between them.Add the numerators.Simplify the result if possible.Merry Christmas and Happy New Year
The Alpha.To calculate how much they ate between the two of them, the amounts each ate must be added:
[tex]\begin{gathered}\begin{gathered} \bold{ \frac{3}{8} + \frac{4}{16}} \\ \\ \bold{\frac{16 \div 8 \times 3 + 16 \div 16 \times 4}{16}} \\ \\ \bold{\frac{6 + 4}{16}} \\ \\ \bold{ \frac{10}{16} }= {\boxed{ \sf \frac{ \bold5}{ \bold8} }}\end{gathered}\end{gathered} [/tex]
[tex]\therefore[/tex] Between the two of them they ate five eighths of pizza.
To add heterogeneous fractions, fractions with different denominators, follow these steps:
Find the common denominator, which is the least common multiple of the denominators.
Divide the common denominator by the other denominator and multiply by the numerator.
Write the results obtained above as numerators with the Sign of the sum between them.
Add the numerators.Simplify the result if possible.which of the following sets of data represent valid functions?
Answer:
b
Step-by-step explanation:
-8p^4 +12p^3 +4p^4 -8p^2 +3p^2
Answer:
-4[tex]p^{4}[/tex] + [tex]12p^{3}[/tex] - 5[tex]p^{2}[/tex]
Step-by-step explanation:
[tex]-8p^{4}[/tex] + [tex]12p^{3}[/tex] + [tex]4p^{4}[/tex] - [tex]8p^{2}[/tex] + [tex]3p^{2}[/tex] Combine the terms with the same exponents
([tex]-8p^{4}[/tex] + [tex]4p^{4[/tex]) + [tex]12p^{3}[/tex] + ([tex]-8p^{2}[/tex] + [tex]3p^{2}[/tex])
[tex]-4p^{4}[/tex] + [tex]12p^{3}[/tex] - [tex]5p^{2}[/tex]
Danny opened a savings account and deposited $100.00. The account earns 2% interest,
compounded annually. If he wants to use the money to buy a new bicycle in 3 years, how
much will he be able to spend on the bike?
nt
P(1 + 1)^²₁. where A is the balance (final amount), P is the principal
Use the formula A = P 1 +
(starting amount), r is the interest rate expressed as a decimal, n is the number of times per
year that the interest is compounded, and t is the time in years.
Round your answer to the nearest cent.
Answer: f = p * (1 + r) ^ n
f is the future value.
p is the present value.
r is the interest rate per time period.
n is the number of time periods.
time periods are months.
rate is the percent divided by 100.
p = 100
r = 6% per year / 12 = .5% per month / 100 = .005 per month.
n = 2 years * 12 = 24 months.
formula becomes f = 100 * (1 + .005) ^ 24
solve for f to get:
f = 112.7159776 = 112.72
that's how much Danny will be able to spend on the bike in 2 years.
Step-by-step explanation:
Select yes or no to state if the expression is equivalent to -2 + 5
A. 5 - 2 yes or no
B. -2 - (-5) yes or no
C. -2 - 5 yes or no
D. 5 + (-2) yes or no
Answer:
a) yes
b) yes
c) no
d) yes
Step-by-step explanation:
-2 + 5 = 3
5-2 = 3
-2 - (-5) = -2 + 5 = 3
-2 - 5 = -7
5 + (-2) = 5-2 = 3
PLEASE HELP ASAP!!!!!! I WILL GIVE BRAINIEST!!!!! I only need 2 and 3. Please explain your answer so I can understand this!!
The least expensive per pound is Customer A.
How to illustrate the expression?It should be noted that expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.
The rate for the first customer will be:
= $14.50 / 1.75
= $8.29 per pound.
The second Customer rate will be:
= $26.25 / 2.5
= $10.5 per pound
The third Customer will be:
= $5.50 / 0.375
= $14.47 per pound.
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Graph the solution to this inequality on the number line. 1/2x−3<−1 3/8
The solution to the inequality, 1/2x - 3 < -1 3/8, is x < 13/4. See the graph below.
How to Graph the Solution of an Inequality on a Number Line?Given the inequality, 1/2x - 3 < -1 3/8, solve to find the value of x, which is the solution to the inequality.
1/2x - 3 < -1 3/8 [given]
1/2x - 3 < -11/8
Add 3 to both sides of the equation:
1/2x - 3 + 3 < -11/8 + 3 [addition property of equality]
1/2x < 13/8
Multiply both sides by 2:
1/2x * 2 < 13/8 * 2 [multiplication property of equality]
x < 13/4
The solution to this inequality, x < 13/4 is given in the graph below.
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choose the best graph to match the given expression.
F(x)= [x+1]
Answer:
Step-by-step explanation:
I don't see a graph from which to choose. Are the brackets in "[x+1]" supposed to be parentheses, or are they absolute value signs?
The graph of functions
(F(x) = (x+1), and
(F(x) = |x+1| are both attached.
Ahmad jogged a distance of 3200 m on Saturday and a distance of 1.8 km on Sunday.
(a) Express the distance he jogged on Saturday as a percentage of the total distance jogged on both days.
(b) Find the percentage decrease in the distance he jogged from Saturday to
Sunday.
Answer:
a) 4,000 meters
b) - 56.25% (or -56% with 2 sig figs
Step-by-step explanation:
Calculate the total distance Ahmad jogged on both days. This will require a conversion unit to make the distances the same units.
Sat.: 3200 m
Sun: 1.8 km
(1,000m/km)
(1.8km)*(1,000 m/km) = 1,800 m jogged on Sunday
Total distance jogged = 3,200 m + 1,800 m = 4,000 meters total jogged
a) Percentage jogged on Saturday:
(3,200 m)/(4,000 m) = 0.80 or 80%
b) Percentage Decrease (From Saturday to Sunday):
Sat: 3200 m
Sun: 1800 m
Difference = 1400 m (decrease)
Percentage Decrease = (1800/3200) = 56.25%
Ahmad's distance on Sunday was a 56.25% decrease from Saturday.
if you have a learner's license, how many hours of driving experience are required to earn the class e license?
If you currently hold a learner's permit, you must complete 50 hours of practice driving under supervision, including at least 15 hours after dusk, before you may take a road test to get a class e license.
Explain the term learner's license?The candidate receives a learner's license after passing a written or online exam that assesses his understanding of traffic laws.
You may practice driving the public roads after receiving a learner's permit as long as you are supervised by someone who has a valid driving license.Before being permitted to receive a full driver's license, first-time drivers must first obtain a driver's permit, sometimes referred to as a learner's permit, driver's licence license, or provisional license. Prior to passing your driving test, you are able to drive (with some restrictions) if you obtain a driver's permit. Each state has a different minimum age requirement for obtaining a driver's license.Thus, if you currently hold a learner's permit, you must complete 50 hours of practice driving under supervision, including at least 15 hours after dusk, before you may take a road test to get a class e license.
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The square root of (-2x)^2 for which values of x does the expression makes sense?
Answer: [tex]x\leq 0[/tex]
Step-by-step explanation:
The first thing we need to do is to make the argument or the number inside the square root equal or larger than zero:
-2x ≥ 0
x ≤ 0/-2
x ≤ 0
So the given expression only makes sense for x that is less than or equal to zero.
Find the slope (rate of change) of a line that passes through (-2, -3) and (1, 1).
1. 1/3
2. 1
3. 2
4. 4/3
Answer:
4. 4/3
Step-by-step explanation:
(-2, -3) (1,1)
1+3/1+2=
4/3
Write an equation for (k) and (t)
Required equation of points plotted on graph relating range gain(k) and charging time(t) is k=4t.
What is linear equation in two variables?A two-variable linear equation is one in which both variables have exponent 1.
What is straight line?An object in geometry known as a line is simply one that is described as being straight, thin, one-dimensional, zero width, and extending on both sides to infinity.
In essence, a straight line is just a line devoid of any bends.
Additionally, we can state that any line that crosses two certain points on the same plane will be singular.
Straight line form
m= y 2. – y 1/x 2-x 1
y-y 1=m (x-x 2)
A (0,0) and B (5,20)
([tex]x_{1}[/tex],[tex]y_{1}[/tex] ) = (0,0) and ([tex]x_{2}[/tex],[tex]y_{2}[/tex]) = (5,20)
m = 20-0/5-0
= 20/5
= 4
([tex]x_{1}[/tex],[tex]y_{1}[/tex] ) =(0,0)
y-0=4(x-0)
y=4x
Replace y with k and x with t
k=4t
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A package of 6 pair of inulated glove cot $47. 94 what i the unit price of the pair of glove?
Therefore the solution for this question is the unit price of each pair of gloves is $7.99.
What is division?One of the four fundamental arithmetic operations, or the process by which two or more numbers are added together to create a new number, is division. Multiplication, addition, and subtraction round out the list of operations.
Here,
The cost of 6 pairs of gloves = $47.94
Now, the unit price = Price per unit of the given item
Let x be the unit price of the glove
thus
x=47.94/6
x=7.99
or it can be written as price of glove=$7.99
Therefore, Unit price of the glove = $7.99
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What is the slope of line a?
13
12
11
10
6
do
9
is
-
(5.7)
(x,y)
11
a
Answer:
Your question choices are messed up fix and I can help
Step-by-step explanation:
:)
At a football stadium, 25% of the fans in attendance were teenagers. If there were 10 teenagers at the football stadium, what was the total number of people at the stadium?
Answer:
40 people
Step-by-step explanation:
25% = 10
50% = 20
100% = 40
Jaylen bought 5 pounds of apples for 12.99 and 4 cupcakes for 2.99 each. He went to the store with $48. How much did Jaylen have left after his shopping trip?
23.05
37.94
10.06
24.95
Answer:
$24.95
Step-by-step explanation:
2.99 times 4 is 11.96, and you would add that with 12.99 to get 24.95.
Answer:
Jaylen have left 23.05 $
Step-by-step explanation:
5 pounds of apples = 12.99 $
4 cupcakes = 2.99 $/apple
Total money = 48 $
All the cupcakes costs = 4*2.99 = 11.96 $
Then she bought in total:
48 -(12.99 + 11.96)
48 - 24.95 = 23.05
Using the unit circle, on what interval is the cosine function increasing? (0, startfraction pi over 2 endfraction) (0, pi) (startfraction pi over 2 endfraction, startfraction 3 pi over 2 endfraction) (pi, 2 pi)
The interval where the cosine function is increasing is (π, 2π).
Finding the value of the cosine function in different intervals:The cosine function for the interval (0, π/2) gives
cos(x) = cos(0) = 1
cos(x) = cos(π/2) = 0
So, the value of the function is decreasing in this interval.
Then, for the interval (0, π), it gives
cos(0) = 1; cos(π) = -1
So, the value of the cosine function is decreasing in this interval.
Then, for the interval (π/2, 3π/2), it gives
cos(π/2) = 0
cos(π) = -1
cos(3π/2) = 0
So, the value of the function decreases up to x = π and then increases up to the same value as before i.e., cos(π/2) = cos(3π/2).
Then, for the interval (π, 2π), the cosine function gives
cos(π) = -1
cos(2π) = 1
Thus, the cosine function in this interval increase from -1 to 1.
Therefore, in the interval (π, 2π), the cosine function is increasing.
This is explained by using a unit circle below:
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Answer:
D
Step-by-step explanation:
got it right
Harmony pays $64.00 per month for a base cable package and an additional amount for on-demand programming. Last month, Harmony received a $67.36 cable bill.
$64.00 + x = $67.36
Ignoring sales tax and additional fees, how much did she spend for on-demand programming?
A) $3.36
B) $6.36
C) $70.72
D.) $131.36
There are 75 fifth graders and 125 fourth graders. They are going to be grouped in teams for Field Day with the same number of students on each team. If there must be the same number of fifth graders on each team, how many teams can there be at most?
Answer:25
Step-by-step explanation:
3
5
standard equation of a parabola with a vertex of (0,0) and a focus of (-8,0)
Answer:
(x + 8)^2 + y^2 = (x - 8)^2
Step-by-step explanation:
A store ships books by weight a small box can hold 4 to 6 pounds while a large box can hold 8 to 9 pounds how much can each box hold
Small box= 4 to 6 lbs
Large box= 8 to 9 lbs
Book weights large 3.1 lbs
Small 2.4 lbs
Answer:
The small box can hold 4 to 6 lbs, so it can hold the 3.1 lb book and 2.4 lb book. The large box can hold 8 to 9 lbs, so it can hold the 3.1 lb book, but not the 2.4 lb book.
Step-by-step explanation:
Simplify the expression below
7/2h - 3(5h - 1/2)
step by step please
Answer: [tex]-\frac{23}{2}h+\frac{3}{2}[/tex]
Step-by-step explanation:
[tex]\frac{7}{2}h-15h+\frac{3}{2}\\\\\frac{7}{2}h-\frac{30}{2}h+\frac{3}{2}\\\\-\frac{23}{2}h+\frac{3}{2}[/tex]