the height will be 50 ft after 0.575 seconds and after 5.424 seconds.
At what time(s) is the ball 50 feet above the ground?The equation that models the height is:
h(t) = 96*t - 16*t^2
Here we want to find the time such that the height is 50ft, then we need to solve the equation:
h(t) = 50 = 96*t - 16*t^2
Now we can solve that for t, we have the quadratic equation:
50 = 96*t - 16*t^2
0 = -16*t^2 + 96*t - 50
Then the solutions are:
t = (-96 ± √(96*96 - 4*(-50)*(-16))/(2*-16)
t = (-96 ± 77.6)/(-32)
The two solutions are:
t = (-96 + 77.6)/(-32) = 0.575t = (-96 - 77.6)/(-32) = 5.424This means that the height will be 50 ft after 0.575 seconds and after 5.424 seconds.
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HELP PLEASE!!!!!! Anaya bought a sweater that was on sale. The sweater originally cost $34.50 but was purchased for $27.60. What percentage of the original price was the discount?
Answer: 80%. Hope this helps, please consider making me Brainliest.
Step-by-step explanation:
To find the percentage, divide the sale cost by the original cost:
27.60/34.50
Let's multiply both sides by 10 to make the operation easier:
27.6/34.5 ( I eliminated the zero's because they kind of have no use) -->
276/345, now solve:
276/345 = 0.8
0.8 = 80%
The percentage is 80%.
I don’t get it and it’s confusing me I need help
Simplify negative 2 and 3 over 5 minus 6 and 2 over 7.
negative 12 and 1 over 2
negative 8 and 31 over 35
negative 8 and 6 over 35
12 and 6 over 35
The value of the expression is -8 31/35
How to simplify the given expression?The expression is given as:
negative 2 and 3 over 5 minus 6 and 2 over 7.
Rewrite properly as
- 2 3/5 - 6 2/7
Express as improper fraction
-13/5 - 44/7
Take the LCM
(-13 * 7 - 44 * 5)/35
Evaluate the difference of products
-311/35
Express as mixed fraction
-8 31/35
Hence, the value of the expression is -8 31/35
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Answer:
B
Step-by-step explanation:
Last week, a chocolate shop sold 9 ounces of white chocolate. It sold 9 9/10 times as much milk chocolate as white chocolate. How many ounces of milk chocolate did the shop sell?
please answer asap
Solving the Question
We're given:
9 ounces of white chocolate sold[tex]9\dfrac{9}{10}[/tex] times as much milk chocolate as white chocolate soldIf the shop sold " [tex]9\dfrac{9}{10}[/tex] times as much milk chocolate as white chocolate", we must multiply [tex]9\dfrac{9}{10}[/tex] by the amount of white chocolate sold to find the amount of milk chocolate sold.
Multiply [tex]9\dfrac{9}{10}[/tex] by 9 ounces:
[tex]9\dfrac{9}{10}\times9[/tex]
Convert the fraction into an improper fraction:
[tex]=\dfrac{99}{10}\times9[/tex]
Multiply:
[tex]=\dfrac{891}{10}[/tex]
AnswerThe shop sold [tex]\dfrac{891}{10}[/tex] ounces of milk chocolate.
f(x) = 2x - 4
f(3) = [?]
Answer: f(3)=2
Step-by-step explanation:
f(x) = 2x - 4
f(3) =2(3) - 4
f(3) = 6-4
f(3)=2
78/99 simplified to the smallest form
Answer:
The simplest form of
78/99
is
26/33
.
Given a graph for the transformation of f(x) in the format g(x) = f(x) + k, determine the k value.
Ok = -3
Ok = 1
Ok = 4
Ok=5
-8 -7
f(x)
-6 -5
y¹¹
-10
g(x)
4-
-3 -2 -1 0
-4-
-2
-3
-4
-5
Answer:
4
Step-by-step explanation:
g(x) is the graph of f(x) shifted up 4 units.
Joshua purchased a game card for the arcade for a total of $20. He played three basketball hoop games for $2.25 each and two rounds of air hockey for $1.75 each. How much did he have left on the game card?
1.)$ 13.50
2.)$ 10.25
3.)$ 9.75
4.)$ 6.75
Answer:
b
Step-by-step explanation:
Joshua had $9.75 left on the game card (option 3).
Joshua's expenses on the game card can be calculated as follows:
Cost of playing three basketball hoop games = 3 games * $2.25/game
Cost of playing three basketball hoop games = $6.75
Cost of playing two rounds of air hockey = 2 rounds * $1.75/round
Cost of playing two rounds of air hockey = $3.50
Total expenses = $6.75 + $3.50
Total expenses = $10.25
Joshua originally had $20 on the game card, and he spent $10.25. To find out how much he had left, subtract his expenses from the original amount:
Amount left = $20 - $10.25
Amount left = $9.75
So, Joshua had $9.75 left on the game card.
The correct answer is 3.) $9.75.
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solve: let f(x)=2x-1 and g(x)=x^2-4. find g(f(x))
Work Shown:
g(x) = x^2 - 4
g(f(x)) = ( f(x) )^2 - 4
g(f(x)) = ( 2x-1 )^2 - 4
g(f(x)) = (2x-1)(2x-1) - 4
g(f(x)) = 4x^2-2x-2x+1 - 4
g(f(x)) = 4x^2 - 4x - 3
A rectangular piece of metal is 5 in. longer than it is wide. Squares with sides 1 in. long are cut from the four corners, and the
flaps are folded upward to form an open box. Which equation indicates that the volume of the box is 56 in.³?
The equation which shows the volume of rectangular box is w² + 5w - 56 = 0.
What is defined as the rectangle?A rectangle is a two-dimensional (2D) shape with opposite sides that are parallel as well as equal to each other and four right angles.
The breadth (width) of a rectangle is the shorter side, and the length is the longer side.
The metal's length is 5 inches longer than its width. However, we fold up 1-inch flaps on every side, resulting in a 1-inch box height and an 2-inch decrease in length and width (1 inches on each side). Because the length and width both decrease in the same amount, the length remains 5 inches longer than that of the width.Then, the equations are as follows:
l = w + 5
The height of the box will be 1 inch which is cut and folded upward.
vol = l x w x h = 56 in³
Substitute the value of l in the equation.
56 = (w + 5)(w)(1)
56 = w² + 5w
w² + 5w - 56 = 0
Therefore, the equation which represent the volume of the rectangular box on 56 in.³ is w² + 5w - 56 = 0.
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Mark all of the statements that are true.
A. The domain for this function is the set {-5).
B. All real numbers are in the range of this function.
C. The domain for this function is all real numbers.
D. The range for this function is the set {-5).
E. This graph is not a function because the value of y is the same for every value of x
Option E:
This graph is not a function because the value of y is the same for every value of x
Solution :
Domain:
The domain of a function is the set of its possible inputs, i.e., the set of input values where for which the function is defined. In the function machine metaphor, the domain is the set of objects that the machine will accept as inputs.
For example, when we use the function notation f:R→R, we mean that f is a function from the real numbers to the real numbers. In other words, the domain of f is the set of real number R (and its set of possible outputs or codomain is also the set of real numbers R).
relation represents y as a function of x
1) is NOT a function of if there are two or more points with the same − , but
− .
2) is a function of if each has a different
There is a technique called the vertical line test that is often used to determine if a graph represents y
as a function of x
In this question only a horizontal line is present.
Option E:
This graph is not a function because the value of y is the same for every value of x
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Write an inequality and then solve.
9. A freight elevator can safely hold no more
than 2200 pounds. An elevator operator must
take 60-pound boxes to a storage area. If the
operator weighs 155 pounds, how many boxes
can be safely moved at one time?
Let the number of boxes be x.
The total weight of the boxes is 60x.
Adding the operator, the total weight is 60x+155, which is no more than 2200.
[tex]60x+155 \leq 2200 \\ \\ 60x \leq 2045 \\ \\ x \leq 34.08333... \\ \\ \lfloor x \rfloor =\boxed{34}[/tex]
In a salad recipe, the ratio of carrots to broccoli must remain constant. The table below shows some possible combinations of carrots and broccoli.
Salad Ingredients
Carrots
Broccoli
3
9
4
12
6
18
7
21
If only whole vegetables can be used, what is the fewest number of vegetables that can be used to make this salad?
A.1
B.3
C.4
D.12
Answer:
Evaluate the numerical expression. 1/4 - (- 5/8)
Step-by-stepexplanation:
Answer: pretty sure 4
Step-by-step explanation:
took test
yeaswass
49.95 pair of shoes;5% tax
the price of the computer is 899$ the tax rate is 7% what is the sales tax on this computer in dollars and cents
The sales tax on this computer in 62 dollars and 93 cents
What is the sales tax on this computer in dollars and cents?The given parameters
Price = $899
Tax rate = 7%
The sales tax on this computer in dollars and cents is calculated as
Sales tax = Price * Tax rate
This gives
Sales tax = $899 * 7%
Evaluate
Sales tax = $62.93
Hence, the sales tax on this computer in 62 dollars and 93 cents
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The governor of state A earns $54,900 more than the governor of state B. If the total of their salaries is $310,850, find the salaries of each.
need to find a and b
Answer:
$127975, $182875
Step-by-step explanation:
Let the salary in state A be x. Then, the salary in state B is x+54900.
[tex]x+x+54900=310850 \\ \\ 2x=255950 \\ \\ x=127975 \\ \\ x+54900=182875[/tex]
New Jersey transit claims that it’s 8:00 AM train from Princeton to New York has probability 0.9 of arriving on time. I assume for now that this claim is true. Explain what probability 0.9 means in the setting
It means there's a 90 percent chance that 8:00 AM train from Princeton to New York will arrive on time, and 10 percent chance it’s 8:00 AM train from Princeton to New York will not arrive on time.
Probability refers to possibility. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Knowing the total number of outcomes is necessary before we can calculate the likelihood of a particular event happening.
It means there's a 90 percent chance that 8:00 AM train from Princeton to New York will arrive on time, and 10 percent chance it’s 8:00 AM train from Princeton to New York will not arrive on time.
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HELP ASAP!!!
Determine the direction in which the graph of the function f(x)=x^2+x-2 opens.
A.upward
B.downward
C.to the left
D.to the right
Answer:
A
Step-by-step explanation:
Since the leading coefficient of the function is greater than 0, then it opens upward.
O-13
13
O-5
O 5
Simplify 9-(-4)=
Answer:
B. 13
Step-by-step explanation:
[tex]Rule:a-\left(-b\right)=a+b\\=9-\left(-4\right)=9+4\\=9+4\\=13[/tex]
S= 1/2( a + b + c) solve for b
The solution of the equation for b is b = 2s - a - c
How to solve for b in the equation?The equation is given as
s= 1/2(a + b + c)
Multiply through by 2
So, we have
2s = a + b + c
Subtract a and c from both sides of the equation
b = 2s - a - c
Hence, the solution of the equation for b is b = 2s - a - c
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What is the slope of y = arcsin(x) when x=0.4?
(You can compute arcsin(x) = sin-1(x) by pressing the “inverse” or “second function key”then pressing the “sin" key. Do this calculation in degrees, so arcsin(1)=90.)
Answer: about 0.41
Step-by-step explanation:
Use calculator
[tex]arcsin=sin^{-1}x\\\\\boxed{sin^{-1}(0.4) = 0.41151684}[/tex]
For the equation, find three ordered pair solutions by completing the table. Then use any two of the ordered pairs to graph the equation.
For the linear function x - y = 3, three ordered pairs are given as follows:
x = 3, y = 0.x = 1, y = -2.x = 0, y = -3.Using points (3,0) and (0,-3), the graph of the function is given at the end of the problem.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.In this problem, the function is:
x - y = 3.
In standard notation:
y = x - 3.
Hence three pairs of points are given as follows, replacing the value of x in the equation to find y.
x = 3, y = 0.x = 1, y = -2.x = 0, y = -3.The graph of the function is given at the end of the answer.
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whats the distance between points p1=(-3,5) P2=(4,2)
Step-by-step explanation:
First, find the vector.
= (4,2) - (-3,5)
= (4-(-3),2-5)
= (7,-3)
And then, find the distance.
= √(7² + (-3)²)
= √(49 + 9)
= √58 ✓
Select all that apply to a segment bisector.
A segment bisector intersects anywhere.
A segment bisector intersects at the midpoint.
A segment bisector cuts the segment into two equal pieces.
A segment bisector can bisector line.
The statements that apply to a segment bisector are:
A segment bisector intersects at the midpoint.A segment bisector cuts the segment into two equal pieces.What does a segment bisector do?A segment bisector intersects the midpoint of a segment such that it is able to divide/ cut the segment into two equal pieces.
This means that a segment bisector can also be said to create two congruent segments. A segment bisector would also be perpendicular to the segment.
In conclusion, a segment bisector intersects at the midpoint and cuts a segment into equal pieces.
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The temperature drops to 15 degrees below zero. What is a real world example to make 0 in this situation?
Here are the examples that combine to make zero:
Two month ago, the temperature was 15 degrees. This morning, the temperature dropped to 15 degrees below zero.
Michael has $0 in his account. He makes a purchase of $75. Later in the day, he deposits 75 in the account.
An elevator rises to the ninth floor and she then takes the elevator from the ninth floor to the ground floor.
The parking garage is located 4 floors below ground level. But, her office is 4 floors above ground level.
What are the real world examples?
In order for the examples to combine to make zero, there has to be a positive number and a negative number. A positive number is a number that is greater than zero. A negative number is a number that is less than zero.
In order for the positive and negative number to make zero, they have to be added together. Addition is determining the total value or summing two or more numbers. Addition is one of the four basic operations in mathematics.
Two month ago, the temperature was 15 degrees. This morning, the temperature dropped to 15 degrees below zero. -15 + 15 = 0
Michael has $0 in his account. He makes a purchase of $75. Later in the day, he deposits 75 in the account. - 75 + 75 = 0
An elevator rises to the ninth floor and she then takes the elevator from the ninth floor to the ground floor. + 9 - 9 = 0
The parking garage is located 4 floors below ground level. But, her office is 4 floors above ground level. = -4 + 4 = 0
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The histogram shows the number of miles driven by a sample of automobiles in New York City. What is the class width
The class width of the histogram is 5000.
What is class width?It should be noted that the class width is the distance that can be found between the lower limits of consecutive classes.
The range is the difference between the maximum and minimum data entries.
class width of a histogram is given by the equation
Therefore, class width:
= maximum of a class - minimum of a class
In the given histogram, first-class start at 2500 and ends at 7500..Therefore considering first class,.minimum =2500 and maximum=7500.
Therefore, class width will be:
= 7500-2500
= 5000
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Suppose you have $5000 to invest. A certificate of deposit (CD) earns 6% annual interest, while bonds are much riskier,
earn 8% annual interest. You decide to invest $2000 in a (CD) and the balance in bonds. How much interest would you have
earned at the end of one year? How much interest would you have earned compounded annually after 2 years?
Get the first year interest. Also, calculate the second year interest then add it to the first to get total interest after 2 years.
Remember: Interest - Principal x Rate x Time
A. $360, $794.40
B. $120, $240
C. $360, $746.40
Answer:
b
Step-by-step explanation:
earned at the end of one year? How much interest would you have earned compounded annually after 2 years?
Get the first year interest. Also, calculate the second year interest then add it to the first to get total interest after 2 years.
Remember: Interest - Principal x Rate x Time
a repair bill for your ebike is $188. the parts costs $73 dollars and the cost of the labor is $46 per hour.
a. write an equation that represents this situation.
b. how many hours dud the repair take?
Answer:
188 = 46x + 73
It took 2 1/2 or 2.5 hours to complete.
Step-by-step explanation:
There is a one time cost of 73 for the parts, but the hours will be 46 per hour. I know the total cost, so we need to solve for x which is the hours.
188 = 46x + 73 Subtract 73 from both sides of the equation
115 = 46x Divide both sides of the equation by 46
2.5 = x
Somebody know what’s the endpoint and midpoint?
Answer:
The point in the middle/center of the line joining two points (also known as endpoints) is called a midpoint. Given one endpoint and a midpoint, the other midpoint can be calculated using the midpoint formula.
Step-by-step explanation:
The point in the middle/center of the line joining two points (also known as endpoints) is called a midpoint. Given one endpoint and a midpoint, the other midpoint can be calculated using the midpoint formula.
a 42 inch string is to be cut so that one piece is 7 inches longer than the other. what is the length of the shorter piece?
Answer:
17.5 inches
Step-by-step explanation:
Let the length of the shorter piece be x
Shorter piece + Longer piece = Whole string
x + (x + 7) = 42
x + x + 7 = 42
Both sides minus 7 to remove the 7 from the left side of the equation.
2x + 7 - 7 = 42 - 7
2x = 35
x = 17.5 inches
Hope this helped! ^^