The average rate of a function is 81 if a quadratic function with a vertex at (6, 8).
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have:
Quadratic function with a vertex at (6, 8).
It is required to find the average rate of the function:
Here the data table is not given, so we are assuming the value of a function:
At x = 13 is 196
f(13) = 144
At x = 14 is 225
f(14) = 225
The average rate of a function:
= [f(14) - f(13)]/(14 - 13)
= [225 - 144]/(1)
= 81
Thus, the average rate of a function is 81 if a quadratic function with a vertex at (6, 8).
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(06.03 HC)
Solve the following system of equations. Show all work and solutions.
y = 3x2 + 6x + 4
y = −3x2 + 4
By solving the two quadratic equations we found the values (0,-1).
What is a quadratic equation?It is a polynomial with a degree of 2 or the maximum power of the variable is 2 in quadratic equations. It has two solutions as its maximum power is 2.
Given equations are;-
y = 3x² + 6x + 4y = -3x² + 4The two equations are solved by equating them and finding the value of x.
3x² + 6x + 4 = -3x² + 4
6x² + 6x = 0
6x ( x+1 ) = 0
6x = 0 so x = 0
( x+1 ) = 0 so x = -1
Therefore solving the two quadratic equations we found the values (0,-1).
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Cheryl has a horse and cow ranch that contains 100 animals. The value of each horse is $500 and the value of each cow is $200. If the total value of the 100 animals is $31,000, how many horses and cows does Cheryl have on her ranch?
The number of the cows is 63 and the number of the horses is 37.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.
Given that:-
Cheryl has a horse and cow ranch that contains 100 animals. The value of each horse is $500 The value of each cow is $200. If the total value of the 100 animals is $31,000.The number of horses and cows will be calculated by forming the expression from the given data in the question. So the two expressions are as follows.
h + c = 100
500h + 200c = 31000
Solving the above two equations by substitution method:-
h = 100 - c
Put the value of h in the second equation:-
500 ( 100 - c ) + 200c = 31000
50000 - 500c + 200c = 31000
50000 - 300c = 31000
50000 - 31000 = 300c
c = 19000 / 300
c = 63
Put the value of c in the first equation we will get the number of the horses.
h + c = 100
h + 63 = 100
h = 100-67 = 37
Therefore the number of the cows is 63 and the number of the horses is 37.
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According to the histogram shown, how many hostel rooms are there?
Answer:
10
Step-by-step explanation:
look at the y axis for the answer to a question like this
Answer:
There are 25 hostel rooms.
Step-by-step explanation:
We simply need to add up the height of each bar.
3+5+8+6+2+1=25 hostel rooms
Find the value of x. Show each step.
0.15x+(0.15-5-x)*0.2=0.1
Answer:
-21.4
Step-by-step explanation:
0.15x + 0.2(0.15-5-x) = 0.1
0.15x + 0.03 - 1 - 0.2x = 0.1
0.15x - 0.2x = 0.1 -0.03 + 1
-0.05x = 1.07
0.05x = -1.07
x = -21.4
Evaluate each function.
14) g(x)= 3x² - 1; Find g(-3)
[tex]g(x) =3x^2 -1\\\\g(-3)=3(-3)^2 -1 \\ \\~~~~~~~~~=3(9) -1 \\\\~~~~~~~~~=27-1\\\\~~~~~~~~~=26[/tex]
Answer:
g(26)
Step-by-step explanation:
substitute -3 for x.
g(x)=3[tex]x^{2}[/tex]-1
[tex]g(-3)=3(-3)^{2} -1\\g(-3)= 3(9)-1\\g(-3)= 27-1\\g(-3)=26[/tex]
What is X of 75 degrees 13 rounded to the nearest tenth
Rewrite the expression using the distributive property and a common factor.
27x+24x
0.5n+2.5
Answer:
x(27 +24) or 3x(9 +8)0.5(n +5) or 2.5(n/5 +1)Step-by-step explanation:
The distributive property of multiplication over addition tells us that the product of a value and a sum will be the same as the sum of products of the value and the sum's addends. This property can be used to add or remove parentheses from an arithmetic expression.
a(b +c) = ab +ac . . . . expression of the distributive property
__
When applying the distributive property to a sum, the first step is to look for a factor common to the terms of the sum. That factor need not be the greatest common factor, though it is often useful if it is.
Below, we have written each expression using two different common factors.
a)27x +24x = x(27 +24) = 3x(9 +8)
__
b)0.5n +2.5 = 0.5(n +5) = 2.5(n/5 +1)
_____
Additional comment
Finding a common factor can make use of knowledge of multiplication tables, rules of exponents, and identities involving various functions used in algebraic expressions. It is sometimes useful to list the prime factors of each of the terms as an aid to finding a common one. Where fractions are involved, it is sometimes helpful to express them all using a common denominator.
The Euclidean Algorithm can also be useful for finding common factors.
What is the solution -2x+3-(5-6x).
Answer: 2(2x-1)
Range terms
Distribute
Subtract the numbers
O
O
O
-54-3 -2 -1 0 1 2 3 4 5 6 7
8
-5-4
-3 -2 -1 0 1 2 3 4 5 6 7 8
++
-5 -4
-3 -2 -1
0 1
2
3 4 5 6 7
8
+
-5 -4
-3 -2 -1 0 1
2
3
5
6
7
C
C
4
8
9 10 11 12 13
9 10 11 12 13
9 10 11 12 13
9 10 11 12 13
Step-by-step explanation:
separate the question into two inequalities then solve individually to derive at an answer then merge the two answers as one.
remember that < or > are open sets while <= or >= are closed set.
A high speed train travels a distance of 503 km in 3 hours.
The distance is measured correct to the nearest kilometre.
The time is measured correct to the nearest minute.
By considering bounds, work out the average speed, in km/minute, of the train to a suitable degree of accuracy.
You must show your working.
To gain full marks you need to give a one-sentence reason for your final answer the words 'both' and 'round' should be in your sentence.
The average speed, in km/minute, of the train is 2.79 km/minute
Calculating average speedFrom the question, we are to calculate the average speed in km/minute
From the given information,
Distance travelled = 503 km
Time taken = 3 hours = 3 × 60 minutes = 180 minutes
Using the average speed formula,
Average speed = Distance / Time
∴ Average speed of the train = 503 / 180
Average speed of the train = 2.79 km/minute
Hence, the average speed, in km/minute, of the train is 2.79 km/minute
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What expression is equivalent to the given expression?
The expression which is equivalent to the given expression is [tex]\frac{27 m^{5}}{n}[/tex]
Evaluating indicesFrom the question, we are to determine the expression which is equivalent to the given expression
The given expression is
[tex]\frac{(3m^{2}n)^{3} }{mn^{4} }[/tex]
Clearing the brackets, we get
[tex]\frac{3^{3} m^{2(3)}n^{3} }{mn^{4} }[/tex]
Simplifying, we get
[tex]\frac{27 m^{6}n^{3} }{mn^{4} }[/tex]
Then,
[tex]27 m^{6-1}n^{3-4}[/tex]
[tex]27 m^{5}n^{-1}[/tex]
= [tex]\frac{27 m^{5}}{n}[/tex]
Hence, the expression which is equivalent to the given expression is [tex]\frac{27 m^{5}}{n}[/tex]
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Dan invests £8200 into his bank account.
He receives 2% per year compound interest.
How much will Dan have after 7 years?
Give your answer to the nearest penny where appropriate.
Answer: £ 3675.79
Step-by-step explanation:
A = P(1 + r)^t
A = final amount = x
P = initial principal balance = 3200
r = interest rate = 0.02
t = number of years elapsed = 7
x = 3200(1.02)^7
x = 3200 * 1.14868567
x = 3675.79414
x = 3675.79
Which fraction names the shaded part of the set?
Answer:
Hello! Your answer is 1/2
Step-by-step explanation:
there are six cubes and three of them are shaded. That is half of the parallelograms.
So 1/4 wouldn't make sense because there are three shaded out of six.
1/6 doesn't make sense because since there is six in total for it to be 1/6 there needs to be 1 shaded out of six.
And finally 1/3 doesn't make sense because 1/3 would have to be two out of six shaded.
Have a wonderful day/night/afternoon and good luck my friend!
The triangles below are similar. Triangle Y X Z. Side Y X is 6 centimeters, X Z is 7 centimeters, and Z Y is 3 centimeters. Triangle A B C. Side A C is 14 centimeters, A B is 12 centimeters, and B C is 6 centimeters. Which similarity statement expresses the relationship between the two triangles? Triangle Z Y X is similar to triangle C A B Triangle Z Y X is similar to triangle A C B Triangle Z Y X is similar to triangle C B A Triangle Z Y X is similar to triangle A B C Mark this and return
Answer:
(c) Triangle Z Y X is similar to triangle C B A
Step-by-step explanation:
Triangles are similar when corresponding sides have the same ratio. Corresponding sides will have corresponding end point vertices. The similarity statement lists corresponding vertices in the same order.
__
corresponding sidesThe side lengths, smallest to largest, for the two triangles are ...
3 cm -- ZY6 cm -- YX7 cm -- XZAnd for the other triangle, ...
6 cm -- BC12 cm -- AB14 cm -- ACcorresponding verticesThe points joining the each side to the next one longer, in order for the two triangles, are ...
Y, X, Z and B, A, C
The vertices corresponding to ZYX in the same order are CBA.
triangle ZYX is similar to triangle CBA
Answer:
The answer is C
Step-by-step explanation:
Please help!!!!!!!!!!!!!!! i need this answer really fast!!!
Answer:
What's the question you f... you amazing human being
The function(t)--4.87+18.75 is used to model the height of an object projected in the air, where h() is the height in
meters and t is the time in seconds. What are the domain and range of the function h(0)? Round values to the nearest
hundredth.
25
20+
(1.9, 18.05)
15-
10+
st
"
The domain and range of the given function are equal to (0, 3.85) and (0, 18.75) respectively.
How to calculate the domain of the function?In this exercise, you're given the following function h(t) = -4.87t² + 18.75t. Next, we would equate the function to zero (0) to determine its domain as follows:
0= -4.87t² + 18.75t.
4.87t(-t + 3.85) = 0
t = 0 or t = 3.85.
Therefore, the domain is 0 ≤ t ≤ 3.85 or (0, 3.85).
How to calculate the range of the function?h(t) = -4.87t² + 18.75t
h(t) = -4.87(t² - 3.85t + 3.85 - 3.85)
h(t) = -4.87(t - 1.925)² + 18.05
Therefore, the range is 0 ≤ h ≤ 18.05 or (0, 18.75).
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Answer:
A on EDGE 2022
Step-by-step explanation:
Select the correct answer.
Richard reads 28.9 inches of mercury on a barometer, which is 1 inch lower than normal atmospheric pressure. The temperature is 40°F. What type of weather is most likely to occur where Richard is?
A.
fair and dry
B.
drought
C.
rain shower
D.
snowfall
The weather that is most likely to occur where Richard is is rain shower.
What type of weather is most likely to occur?
Weather is the state of the atmosphere of a particular place over a short period of time. There is low atmospheric pressure, so it is likely that it would rain. This is because when the atmospheric pressure is low, it is likely that it would rain.
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Answer:
Rain shower is most likely to occur where Richard is. (Option c)
• The air pressure is lower than the normal and that's why it suggests that the rainfall will happen in that place because rainfall generally occurs in the place where the low pressure is formed.
• And,the temperature is above than the freezing point of the water so there are no chances of the snowfall in that place.
• That's why rainfall is the most probable thing that will happen in that place.
Step-by-step explanation:
Help please and thank you !! ill give brainle and 20 points !
Answer:
G 33%
Step-by-step explanation:
17/52 = 0.32692307692
0.32692307692 is about 33 %
Have a nice day! :)
Jada fills the bathtub before taking a bath and then allows the water to drain when she is done. The graph below models the number of gallons of water, y, in the bathtub over time, t, in minutes.
On a graph, the graph increases, remains constant, and then decreases.
Is the number of gallons of water in the bathtub a function of time?
The number of gallons of water in the bathtub is a function of time. Therefore, it is true.
How to illustrate the graph?
The graph shows a curve that lets you find the number of gallons of water given any value of t betweeh 0 and 30 plus.
Hence, the number of gallons of time indeed is a function of time, in the interval shown by the graph.
The answer is true, because each t value is paired with exactly one number of gallons".
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Answer:
A
Step-by-step explanation:
What is the length of segment BC?
Answer:
[tex]BC=x=(13;+\infty)[/tex]
Step-by-step explanation:
Existence of Triangle
[tex]x-(2x-24) < x-2 < x+(2x-24)\\[/tex]
[tex]13 < x > 11[/tex]
[tex]x=(13;+\infty)[/tex]
What is the value of x in the equation shown Below?2(x+4)-4x=10x-4
Answer: 1
Step-by-step explanation:
If the quadratic equation has two rational roots,then the discriminant is_____and a perfect square
Answer:
Real and unequal
Answer:
The quadratic has two equal roots like d if it is perfect square and we may write: (x − d) 2 = x 2 − 2 d x + d 2 Then: Δ = 4 d 2 − 4 d 2 = 0 That is the discriminant is zero when the quadratic is perfect square.
Step-by-step explanation:
In a graph, x represents the number of months since a business opened, and y represents the total amount of money the business has earned. The following three points are from the graph:
The slope of the graph is 745 and the y-intercept of the graph is 500
Missing part of the questionThe following three points are from the graph: (2, 1990) (5, 4225) (9, 7205)
Find the slope and y-intercept
How to determine the slope?The points are given as:
(2, 1990) (5, 4225) (9, 7205)
The slope is calculated using:
m = (y2 - y1)/(x2 - x1)
So, we have:
m = (4225 - 1990)/(5 - 2)
Evaluate
m = 745
Hence, the slope of the graph is 745
How to determine the y-intercept?In (a), we have
m = 745
To calculate the y-intercept, we use the following points
(x1 , y1) = (0,y)
Recall that:
m = (y2 - y1)/(x2 - x1)
So, we have:
745 = (4225 - y)/(5 - 0)
Evaluate the difference
745 = (4225 - y)/(5)
Multiply both sides by 5
3725 = 4225 - y
Solve for y
y = 500
Hence, the y-intercept of the graph is 500
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Please help on this only if u know
Answer:
Option D ---> y=5x
Step-by-step explanation:
When a line is directly proportional it means it crosses the origin so has a y- and x-intercept of 0.
So if we use the format y=mx+c, it will work but our c value will be 0 as I explained above .
To work out the gradient we simply take 2 points (0,0) and (1,5)) on the graph and use the gradient formula :
m = change in y ÷ change in x
m = 5÷1
m = 5
Therefore our direct proportion equation will be y=5x
Hope this helped and have a good day
Determine x to two decimal places.
*PICTURE ATTACHED*
*TRIGONOMETRY*
This rule is applied to triangles to determine the unknown sides and angles. The value of x from the diagram is 11.78m
Trigonometry ruleThis rule is applied to triangles to determine the unknown sides and angles.
Given the following parameter
Opposite = 5m
Adjacent = x
angle = 23 degrees
According to the theorem of tangents
tan23 = opposite/adjacent
tan23 = 5/x
x = 5/tan23
x = 11.78m
Hence the value of x from the diagram is 11.78m
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Daniel runs 40/5 miles in 124/₁ minutes. What is the unit rate in terms of miles per minute? What the answer:
Using the given information, the unit rate is 0.0645 miles/minute
Calculating rateFrom the question, we are to determine the unit rate
From the given information,
Daniel runs 40/5 miles in 124 minutes
That is,
Distance = 40/5 miles = 8 miles
Time = 124 minutes
Using the formula,
Rate = Distance / Time
Rate = 8 miles / 124 minutes
Rate = 0.0645 miles/minute
Hence, the unit rate is 0.0645 miles/minute
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The unit rate is 0.0645 miles/minute
We have calculated the rate
From the question, we are to determine the unit rate
From the given information,
Daniel runs 40/5 miles in 124 minutes
Distance = 40/5 miles
Distance = 8 miles
Time = 124 minutes
What is the formula of rate?Rate = Distance / Time
Rate = 8 miles / 124 minutes
Rate = 0.0645 miles/minute
Hence, the unit rate is 0.0645 miles/minute
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Solve for x
3x-5=-x+3
Answer:
(3x - 5 = -x + 3) x = 2
Step-by-step explanation:
3x - 5 = -x + 3
3x = -x + (3 +5)
3x=-x + 8
(3x + x ) = 8
4x = 8
4/8 =2
x = 2
Glen Cove has a population of 7,200, which is decreasing at a
rate of 80 people per year. Locust Valley has a population of
5,000 and is gaining 120 people per year. In how many years
will the populations of Glen Cove and Locust Valley be the same?
Please help!!
Answer:
11 years
Step-by-step explanation:
7200 - 80x = 5000 + 120x
-5000 + 80x -5000 + 80x
2200 = 200x
11 = x
(-14,-13), (-7,-7)
Can anyone help me solve this - algebra
Answer: y=6/7x-1
Step-by-step explanation:
I am assuming you want a line formula in y=mx+b
slope (y2-y1)/(x2-x1) = -7+13/-7+14 = 6/7
y+7=6/7(x+7)
y+7 = 6/7x+6
y=6/7x-1
Solve the system using substitution.
y=-x-2,3x+3y=6
Step-by-step explanation:
x = -2-y
3(-2-y) +3y =6
-6-3y +3y=6
у=0
O=-x-2
х=-2