The average rate of change of the height as a function of time from 1 to 2 is 96
Rate of change
Rate of change defines the ratio that compares the change in values of the y variables to the change in values of the x variables.
Given,
The height (in feet) of a falling object with an initial velocity of 48 feet per second launched straight upward from the ground is given by h(t) = 16t² + 48t where is time (in seconds).
Here we need to find the average rate of change of the height as a function of time from 1 to 2.
In order to find the average rate of change we need to find the value for the time 1 and time 2.
For, that we have to apply the value on the function,
First, we have to apply the value of t as 1, then we get the value of the function as,
h(1) = 16(1)² + 48(1)
h(1) = 16 + 48
h(1) = 64
Now, we have to apply the value of t as 2, then we get,
h(2) = 16(2)² + 48(2)
h(2) = (16 x 4) + 96
h(2) = 64 + 96
h(2) = 160
Therefore, the average rate of change is,
=> rate of change = (160 -64) / 2 - 1
=> rate of change = 96
Therefore, the average rate of change from 1 to 2 is 96.
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which represents a rotation of 189
degrees?
(X,y) -> (-X,-y)
(X,y) -> (X,-y)
(X,y) -> (y,X)
(X,4) -> (-X,4)
The required rotation of the 180° is given by, (X,y) -> (-X,-y), option A is correct and the required translation is given by (x + 6, y - 2), option D is correct.
Given that,
To determine which option shows the rotation of 180°, and translation of right 6 units and down 2 units.
Coordinate, is represented as the values on the x-axis and y-axis of the graph. while the coordinate x is called abscissa and the coordinate of the y is called ordinate.
Here,
For the rotation of the 180°, the given coordinate undergoes the change in direction so the required coordinate after 180° rotation is given as (-x, -y).
Now, for the translation of 6 units right we must add x with 6 and for 2 units down we must subtract y by 2, the required translation is given as(x + 6, y -2).
Thus, the required rotation of the 180° is given by, (X,y) -> (-X,-y), and the required translation is given by (x + 6, y - 2).
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Define the formula for a parabola (a quadratic function) that has horizontal intercepts (roots) at x=9.9 and x = 8.7 and passes through the point ( 0, 8.5 )
Answer:
ft HD st he do it to we if do ks do just bc
let f(x) = x-1 graph g(x)=f(3/4x)
The graph of the function g(x) after putting the value in function f(x) is attached with the answer.
What is function?
A relation b/w a collection of inputs and outputs is known as a function. A function is a relationship between inputs in which each input is connected to precisely one output.
Given function: f(x) = x-1
we have to find: g(x)=f(3/4x)
Putting the value of f(x) in g(x),
g(x) = 3/4x - 1
Now, the graph of the function (3/4)x - 1 is attached in the question.
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*URGENT + 100 POINTS*
A right triangle is shown in the graph.
right triangle on coordinate plane with hypotenuse labeled t and one endpoint of hypotenuse at r comma s and the other endpoint at x comma y, vertical line from point x comma y and horizontal line from r comma s that meet at right angle of triangle, horizontal dotted line from point r comma s to point s on y axis, horizontal dotted line from point x comma y to point y on y axis, vertical dotted line from point r comma s to point r on x axis, and vertical dotted line from right angle to point x on x axis
Part A: Use the Pythagorean Theorem to derive the standard equation of the circle with center at (r, s) and a point on the circle at (x, y). Show all necessary math work. (3 points)
Part B: If (r, s) = (7, –4) and t = 10, determine the domain and range of the circle. (4 points)
Part C: Is the point (9, 1) inside the border of the circle if (r, s) = (7, –4) and t = 10? Explain using mathematical evidence. (3 points)
Answer:
Part A
[tex](x-r)^2+(y-s)^2=t^2[/tex]
where:
(r, s) is the center of the circle.(x, y) is a point on the circle.t is the radius of the circle.Part B
Domain = [-3, 17]
Range = [-14, 6]
Part C
Point (9, 1) is inside the border of the circle.
Step-by-step explanation:
Part A[tex]\boxed{\begin{minipage}{9 cm}\underline{Pythagoras Theorem} \\\\$a^2+b^2=c^2$\\\\where:\\ \phantom{ww}$\bullet$ $a$ and $b$ are the legs of the right triangle. \\ \phantom{ww}$\bullet$ $c$ is the hypotenuse (longest side) of the right triangle.\\\end{minipage}}[/tex]
From inspection of the given triangle:
a = x - rb = y - sc = tSubstitute these values into the formula to derive the standard equation of the circle:
[tex]\boxed{ (x-r)^2+(y-s)^2=t^2}[/tex]
where:
(r, s) is the center of the circle.(x, y) is a point on the circle.t is the radius of the circle.Part BGiven the center of the circle (r, s) is (7, -4) and the radius (t) is 10.
The domain of the circle is the x-value of the center minus and plus the radius:
[tex]\begin{aligned}\implies \textsf{Domain}&=[r-t,r+t]\\&= [7-10, 7+10] \\&= [-3, 17]\end{aligned}[/tex]
The range of the circle is the y-value of the center minus and plus the radius:
[tex]\begin{aligned}\implies \textsf{Range}&=[s-t,s+t]\\&=[-4-10, -4+10]\\& = [-14, 6]\end{aligned}[/tex]
Part CSubstitute (r, s) = (7, –4) and t = 10 into the derived equation from part A:
[tex]\implies (x-r)^2+(y-s)^2=t^2[/tex]
[tex]\implies (x-7)^2+(y-(-4))^2=10^2[/tex]
[tex]\implies (x-7)^2+(y+4)^2=100[/tex]
Substitute the given point (9, 1) into the equation:
[tex]\begin{aligned}\implies (9-7)^2+(1+4)^2&=2^2+5^2\\&=4+25\\&=29\end{aligned}[/tex]
As 29 < 100, the point (9, 1) is inside the border of the circle.
Helppp!
Triangle FJE and GKH are similar right triangles. Which statements about the slopes of FE and GH is true?
Solve the following system of linear equations by graphing:
4x + 2y = -4
4x + 2y = -20
Graph the linear equations by writing the equations in slope-intercept form:
y= ___x + ___
y= ___x + ___
Identify the appropriate number of solutions. If there’s a solution, give the point.
Answer:
No solution. The lines are parallel
Step-by-step explanation:
I graphed with Desmos. It is a free.
A stockbroker charges a 1.5% commission to sell shares of a stock for a client. Find the value of stock sold by a broker if the commission was $420.
Answer:
value of stock =1.5% × 420?= 6.3
Write the equation of a sine function that has the given characteristics.
Amplitude: 4
Period: 3pie
Answer:
y = 4 sin(2x/3)
Step-by-step explanation:
The parent function for sine functions is: y = a sin b(x - c) + d
"a" defines amplitude/vertical dilation
"b" defines the change to the period/horizontal dilation
"c" defines the phase shift/horizontal translation
"d" defines the midline/vertical translation
We can already set "a = 4" because 4 is the amplitude.
However, to include the period into the function, we have to take note of the parent sine function already having a period of 2π.
This means: 2π/b = period
2π/period = b
2π/3π = b
2/3 = b
Knowing the "a" and "b" values, we can set up the equation:
y = 4 sin(2x/3)
No horizontal/vertical translations were applied, so "c" and "d" are both zero.
What is 1 2/3 of 32 in fractions?
Answer:
53 1/3
Step-by-step explanation:
[tex]1\frac{2}{3} =\frac{3+2}{3} =\frac{5}{3}[/tex]
[tex](32)(\frac{5}{3} )=\frac{(32)(5)}{3} =\frac{160}{3}[/tex]
[tex]\frac{160}{3} =53 +\frac{1}{3} =53\frac{1}{3}[/tex]
Hope this helps
The value of the expression is [tex]\frac{160}{3}[/tex].
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
[tex]1\frac{2}{3}[/tex] of 32
= [tex]\frac{5}{3}[/tex] x 32
[ 5 x 32 = 160 ]
= [tex]\frac{160}{3}[/tex]
Thus,
The value of the expression is [tex]\frac{160}{3}[/tex].
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A $26,000 car is on sale for 5% off with 3% tax. Interpret the change of the price as a percentage. Round to the nearest hundredth.
The new price of the car is $25441.
How to calculate the price?Given that the $26,000 car is on sale for 5% off with 3% tax.
The discount will be:
= 5% × $26000
= $1300
The tax will be:
= 3% × ($26000 - $1300)
= 3% × $24700
= $741
The new price will be:
= Amount - Discount + Tax
= $26000 - $1300 + $741
= $25441
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b) On the grid draw the graph of x+y=6 for values of c between -2 and 3
I don't know what I'm doing! HELP!!!
Booker's father amount of commission earned is 668.31 dollars.
Sophia needs to make sells of 16744 dollars in order to earn at least 1800 dollars in commission.
How to find how much commission Booker's father will earn?Booker's father sells computer software and earns a 4.25% commission on every software package he sells.
The amount of commission he will earn after selling a software package of $15, 725 can be calculated as follows:
amount of commission earned = 4.25% of 15725
amount of commission earned = 4.25 / 100 × 15725
amount of commission earned = 66831.25 / 100
Therefore,
amount of commission earned = 668.3125
amount of commission earned = 668.31 dollars
Sophia needs to earn at least 1800 dollars each month to cover her living expenses.
The minimum she needs to sell in order to earn at least 1800 dollars if she earns 10.75% commission can be calculated as follows:
let
x = amount she needs to sell
Therefore,
10.75% of x ≥ 1800
10.75 / 100 x ≥ 1800
multiply both sides by 100
10.75x ≥ 180000
divide both sides by 10.75
x ≥ 16744.1860465
x ≥ 16744
Therefore, she needs to sell 16744 dollars worth of goods.
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A right triangle has a leg that measures 7 in. The angle opposite this side measures
62°. What is the length of the hypotenuse of this triangle? Round to the nearest tenth.
(Remember to include the correct units in your answer)
Please help
The hypotenuse of the right triangle is 7.93 inches.
According to the question,
We have the following information:
A right triangle has a leg that measures 7 in. The angle opposite this side measures 62°.
Now, the hypotenuse can be easily found using the trigonometric function.
(More to know: in a right triangle, we can use the Pythagoras theorem. This theorem can not used in any other triangle.)
We will use sin 62 to find hypotenuse.
Sin 62 = perpendicular/hypotenuse
Hypotenuse = perpendicular/sin 62
Hypotenuse = 7/0.88295
Hypotenuse = 7.93 inches
Hence, the hypotenuse of the right triangle is 7.93 inches.
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Hi can someone please help me? Thank you so much have a good day/night! ;)
Answer:
136 cm
Step-by-step explanation:
area of rectangle-- width x length--- 112
area of triangle-- base x height divided by 2--- 24
please mark brainiest
find the values of x, y, and z.
To find x, you would do 180-36-63, which would be 81.
Then you would do 180-81 to find z, which is 99.
To find y, would do do 180-99-13, which is 68.
Answer:
x=81
y=68
Z=99
Step-by-step explanation:
to find x we have to remember the rule that all 3 angles sum up to be 180 in a triangle
So we use this to find x
180-(63+36)=x
180-99=x
81=x
Now to find z since it is on a flat plane you just subtract 81 from 180 to find z
180-81=z
99=z
Now to find y we add all the angles of the second triangle and then subtract that sum by 180
180-(13+99)=y
180-112=y
68=y
Hopes this helps please mark brainliest
PLEASE PLEASE HURRY What is −12÷2/3? Responses −36 negative 36 −24 negative 24 −18 negative 18 −8 negative 8
Answer: -18
Step-by-step explanation:
im not 100% sure but good luck :)
Answer: -12/2/3=-2
Step-by-step explanation:
A rectangular plece of carpet covers 180 yd². The width is 7 yd less than the length. Find the length and width.
Round your answers to the nearest tenth of a yard.
The length is approximately
yd.
The width?
THE LENGTH AND WIDTH WILL BE = length: 5.7 yd
width: 1.7 yd.
What is unitary method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units. What can be values and units.Let's say you go to the store to buy six apples. You are informed by the shopkeeper that he is offering 10 apples for Rs 100. In this instance, the value and the units are the price of the apples.Recognizing the units and values is crucial when using the unitary technique to a problem.Always write the items that need to be computed on the right side and the things that are known on the left side to simplify things.We are aware of the quantity of apples and the amount of money in the aforesaid problem.According to our question-
w(w +4) = 10
w² +4w = 10 . . . . . eliminate parentheses
w² +4w +4 = 14 . . . . . . add the square of half the w-coefficient to complete the square
(w +2)² = 14 . . . . . . . . . rewrite as a square
w +2 = √14 . . . . . . . . . take the square root
2 = -2 +√14 ≈ 1.7 . . . . yards (width)
Then the length is 4 more yards than this, so is ...
length = 1.7 +4 = 5.7 . . . yards
The length and width are 5.7 and 1.7 yards, respectively.
In the attached graph, we let x represent the length. As you can see, the magnitudes of the two zeros are width and length.
HENCE,THE LENGTH AND WIDTH WILL BE = length: 5.7 yd width: 1.7 yd.
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I earn $285/week. There are 4 pays in most months. So, my monthly pay is $285 x 4 or $1140 per month.
Is my calculation of my monthly income accurate? Please explain.
Answer: Yes
Step-by-step explanation: Most month have 4 weeks so your right.
Please help these lessons are confusing me
Answer: y-9 = 17(x+7)
Step-by-step explanation:
We will use the second coordinate point to use in the equation and the first coordinate (-8, -8) to figure out the slope of this line.
Answer:
y-9=17x+119
Step-by-step explanation:
given points (-8,-8) & (-7,9)
let's take (-7,9) as (x1,y1) and (-8,-8) as (x2,y2)
now for finding out equation through two points, we use
[tex] \frac{x-x_{1} }{x_{1}-x_{2} } =\frac{y-y_{1} }{y_{1}-y_{2} } [/tex]
So accordingly, we input the values
[tex] \frac{x-(-7) }{-7-(-8)} } =\frac{y-9 }{9-(-8) } [/tex]
[tex] \frac{x+7 }{-7+8} } =\frac{y-9 }{9+8 } [/tex]
[tex] \frac{x+7 }{1} } =\frac{y-9 }{17 } [/tex]
[tex] 17(x+7) = y-9 [/tex]
[tex] 17x+119 = y-9 [/tex]
How do you solve this problem step-by-step? 15(40-9)x3+6
Answer:
The answer to this problem is 1401.
Step-by-step explanation:
By using the order of operations listed here, we can solve the problem very easily.
EVALUATE IN PARENTHESES [tex]40-9[/tex]: 40 minus 9 is 31, so now the problem is 15(31) x 3 + 6
MULTIPLY/DIVIDE [tex]15(31)*3[/tex]: X times Y can be [tex]X*Y[/tex] or [tex]X (Y)[/tex]. This evaluates to [tex]15*31*3[/tex] which is 1395.
ADD/SUBTRACT: The problem now is just [tex]1395+6[/tex] which evaluates to a total of [tex]1401[/tex].
U= {2, 3, 4, 5, 7}
C= {2, 4}
D= {2, 7}
(a) (C n D)’=
(b) C’ U D=
The value of (CnD)'= {3,5} and the valueof C' U D = { 2,3,5,7}
What is complement of a set?The complement of a set is the set that includes all the elements of the universal set that are not present in the given set. Let's say A is a set of all coins which is a subset of a universal set that contains all coins and notes, so the complement of set A is a set of notes (which do not includes coins).
if U = { 2,3,4,5,7}
C= { 2,4}
D= { 2,7}
therefore (CnD)= { 2,4,7}
the complement of set (CnD) that is, (CnD)' = {3,5}
complement of set C (C')= { 3,5,7}
Therefore the union of C' and D(C' U D) = { 2,3,5,7}
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Question 10
Pollsters are concerned about declining levels of cooperation among persons contacted in surveys. A
pollster contacts 93 people in the 18-21 age bracket and finds that 79 of them respond and 14 refuse to
respond. When 251 people in the 22-29 age bracket are contacted, 219 respond and 32 refuse to respond.
Assume that 1 of the 344 people is randomly selected. Find the probability of getting someone in the 18-21
age bracket or someone who responds.
Report the answer as a percent rounded to one decimal place accuracy. You need not enter the "%" symbol.
P(18-21 or responds) =
(Hint: It might be helpful to organize the data into a table first.)
Submit Question
%
The probability of getting someone in the 18-21 age bracket or someone who responds is 28.7%.
The total number of people in the 18-21 age bracket is 93. The number of people in this bracket who responded is 79. The number of people in this bracket who refuse to respond is 14. The total number of people in the 22-29 age bracket is 251. The number of people in this bracket who responded is 219. The number of people in this bracket who refuse to respond is 32.
A person is randomly selected from all the people surveyed. We need to find out the probability of getting someone in the 18-21 age bracket or someone who responds. Let the variables E1 and E2 represent the events.
E1 is the event of getting a person from the 18-21 age bracket.
E2 is the event of getting a person who responds.
P(E1∪E2) = P(E1) + P(E2) - P(E1∩E2)
P(E1∪E2) = (93/344) + [(79 + 219)/344] - (79/93)
P(E1∪E2) = 0.27035 + 0.86628 - 0.84946
P(E1∪E2) = 0.28717
Hence, the probability of getting someone in the 18-21 age bracket or someone who responds is 28.7%.
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Question in file please help!!!!
Answer:
Step-by-step explanation:
Ok:
Area of circle:
A=πr^2
1. Apply to question!
5^2π=
25π/4: Since it is a 1/4 of the circle
6.25π
Answer: 6.25π or 6.25 pie
Answer:
about 19.63496 m^2
Step-by-step explanation:
this is 1/4 of a circle so we find the are of the full circle
pi(r)^2
pi(5)^2
pi25
78.53982
Divide by 4
78.53982/4
19.63496
Hopes this helps please mark brainliestC
The figure is cut into 12 equal pieces. Shade 2/3 of the figure.
Answer:
Step-by-step explanation:
OK:
I won't be able to draw this but if I can I will
1. Find 2/3 of the 12 pieces
2/3*12=
24/3=
8
2. Answer: Shade 8 out of 12 pieces
a store sells a $400 microscope after a markup of 32% what is the price of the microscope at the store
A 32% mark up means that the price goes up by 32 percent. The way to find this is by finding 132% of $400.
1.32 x 400 = $528.
I hope this helps!
The price of the microscope after the markup of 32% at the store will be equal to $528.
What is Percentage?The Latin term "per centum," which signifies "by the hundredth," was the source of the English word "percentage." Segments with a denominator of 100 are considered percentages. In other terms, it is a relationship where the worth of the entire is always considered to be 100.
As per the given data in the question,
Price of microscope = $400
Markup percentage = 32%
Increase in price = 400 × 32/100
= $128.
Price after markup will be,
$400 + $128 = $528.
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I need help please and thank you.
The inequality that relates [tex]LN[/tex] and [tex]OQ[/tex] is [tex]LN>OQ[/tex].
What is answer? Tell me pls :)
Answer:
when y=20
x=unknown number
x-y=16
x=16+y
x=16+20
x=36
Step-by-step explanation:
Which values from the given replacement set make up the solution set of the inequality?
2b≥6; {1, 2, 3, 4}
Responses
{1, 2, 3}
left curly bracket 1 comma 2 comma 3 right curly bracket
{1, 2}
left curly bracket 1 comma 2 right curly bracket
{3, 4}
left curly bracket 3 comma 4 right curly bracket
{2, 3, 4}
PLS HURRY AHHH
{3, 4} are the values which make up the solution set of the inequality
2b ≥ 6.
Given, an inequality
2b ≥ 6.
Now, we have to find the solution set of the given inequality,
2b ≥ 6
On dividing both the sides by 2, we get
2b/2 ≥ 6/2
b ≥ 3
So, the solution set of the given inequality, be
the values of b must be greater than or equal to 3.
So, Option (3) i.e. {3 , 4} is the solution set of the inequality.
Hence, {3, 4} are the values which make up the solution set of the inequality 2b ≥ 6.
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hi thank you for seeing this
Each pair of angles should be matched with the correct property (theorem) as follows:
e. Vertical Angles: Angles 7 and 6.
a. Alternate Exterior Angles: Angles 1 and 8.
g. Alternate Interior Angles: Angles 4 and 5.
h. Corresponding Angles: Angles 2 and 6.
d. Supplementary Angles: Angles 6 and 8.
What are parallel lines?Parallel lines simply refers to two (2) lines that always have the same or equal distance apart and never meet.
What is the alternate exterior angle theorem?The alternate exterior angle theorem states that when two (2) parallel lines are cut through by a transversal, the alternate exterior angles that are formed are congruent or angles of equal measure and magnitude such as Angles 1 and 8.
What is the alternate interior angles theorem?The alternate interior angles theorem states that when two (2) parallel lines are cut through by a transversal, the alternate interior angles that are formed are congruent such as Angles 4 and 5.
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Cheng is thinking a of a number
what number is Cheng thinking of ?
cheng thinking ;
I multiply my number by 100,hen divide by 10,then multiply by 1000.
My answer is 170'000
Is Cheng's answer is correct or incorrect
The number is 17
Let the number = x
From the question, we have
(x*100)/10*1000 = 170000
x = 17
Multiplication:
Mathematicians use multiplication to calculate the product of two or more numbers. It is a fundamental operation in mathematics that is frequently utilized in everyday life. When we need to combine groups of similar sizes, we utilize multiplication. The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are multiplied are referred to as the factors. Repeated addition of the same number is made easier by multiplying the numbers.
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