a) The vertex-form definition of the quadratic function is given as follows: y = 1/3(x - 3)² + 5.
b) The rider's minimum height above the ground is of: 5 meters,
c) The horizontal distance is given as follows: x = 0 m and x = 6 m.
How to obtain the features?The quadratic function in the context of this problem is defined as follows:
y = x²/3- 2x + 8.
In which:
x is the horizontal distance.y is the vertical distance.The coefficients are given as follows:
a = 1/3, b = -2, c = 8.
The x-coordinate of the vertex is given as follows:
x = -b/2a = -(-2)/(2/3) = 3.
Hence the y-coordinate of the vertex is given as follows:
y = (3)²/3 - 2(3) + 8 = 5 meters.
Hence the vertex-form definition of the equation is given as follows:
y = 1/3(x - 3)² + 5.
As the function is concave up, the minimum height is of 5 meters.
For the horizontal distance at a height of 8m, we have that:
x²/3 - 2x + 8 = 8
x²/3 - 2x = 0
x(x/3 - 2) = 0.
Hence:
x = 0 m and x = 6 m.
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-A student is chosen randomly from the group. What is the probability that the student ONLY takes History Class?
-A student is chosen randomly from the group. What is the probability that the student takes BOTH History and Biology?
-A student is chosen randomly from the group. What is the probability that the student does NOT take History or Biology?
-A student is chosen randomly from the group. What is the probability that the student takes Biology class?
Help me, please
To find the probability that the student ONLY takes History Class, we need to divide the number of students taking only History (37) by the total number of students (150).
What is probability?Probability is the measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. Probability can be used to analyze and make predictions about a wide range of situations, including games of chance, weather patterns, financial markets, and more.
Here,
Using the given numbers, we can calculate the probabilities as follows:
To find the probability that the student ONLY takes History Class, we need to divide the number of students taking only History (37) by the total number of students (150):
P(ONLY History) = 37/150 = 0.2467 or approximately 24.67%
To find the probability that the student takes BOTH History and Biology, we need to divide the number of students taking both (25) by the total number of students (150):
P(History AND Biology) = 25/150 = 0.1667 or approximately 16.67%
To find the probability that the student does NOT take History or Biology, we need to add the number of students taking neither History nor Biology (21) to the number of students taking only Biology (17), and then divide by the total number of students:
P(Neither History nor Biology) = (21 + 17)/150 = 0.2533 or approximately 25.33%
The complement of this event (i.e., the probability of taking either History or Biology) is:
P(History or Biology) = 1 - P(Neither History nor Biology) = 1 - 0.2533 = 0.7467 or approximately 74.67%
To find the probability that the student takes Biology class, we need to add the number of students taking both History and Biology (25) to the number of students taking only Biology (17), and then divide by the total number of students:
P(Biology) = (25 + 17)/150 = 0.2133 or approximately 21.33%
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WILL GIVE brainliest HELP ASAP
Answer:
E,B are the answers.
Step-by-step explanation:
Como despejar x en y = 10x - 1
Answer:
x= y+1/10
Step-by-step explanation:
y = 10x-1
y+1 = 10x
y+1/10 = x
y+1/10
Step-by-step explanation:
1. Add 1
2.divide by 10
What is the measure of ABE
If <A = 51° then the measure of angle ABE be 39°.
What is meant by right angled triangle?The term "right triangle" refers to a triangle with an interior angle of 90 degrees. The hypotenuse, the side that faces the right angle and is also the side with the longest side in a right triangle, and the height and base are the two arms of the right angle.
It is 90 degrees at a right angle. Angles smaller than 90 degrees are considered sharp angles. More over 90 degrees is considered an obtuse angle. Additionally, these angles aid in categorizing the various triangular varieties.
ΔABE = 180 degree
Let the equation be
∠A + ∠B + ∠E = 180 degree
simplifying the above equation, we get
51° + ∠B + 90° = 180°
∠B = 180° - 90° - 51°
∠B = 39°
Therefore, the measure of angle ABE be 39°.
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Which equation represents a function?
Responses
A y = ±2x + 3y = ±2x + 3
B x2
+ y2
= 16x 2 + y 2 = 16
C y = ±3x+8−−−−−√
y = ± 3 x + 8
D y2
= -5x - 8y 2 = -5x - 8
E x = 4y + 7
Option (A) (y = ±2x + 3) represents a function. In this equation, for every value of x, there is only one corresponding value of y, which satisfies the equation.
A function is a relation between two variables where each input is associated with exactly one output. To determine if an equation represents a function, we can use the vertical line test.
Out of the given options, only equation A (y = ±2x + 3) represents a function. In this equation, for every value of x, there is only one corresponding value of y, which satisfies the equation. When plotted on a coordinate plane, a vertical line will intersect the graph at most once for every value of x.
Equations B[tex](x^2 + y^2 = 16)[/tex], C[tex](y = \pm3x + 8)[/tex], D [tex](y^2 = -5x - 8)[/tex], and E [tex](x = 4y + 7)[/tex] do not represent functions. In these equations, a vertical line will intersect the graph more than once for some values of x, meaning that there are multiple outputs for a single input, which violates the definition of a function.
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If a battery has a radius of 4 millimeters and a height of 32 millimeters, approximately what is the area of the surface to be covered by the label? Use 3.14 for and round to the nearest hundredth.
The surface area to be covered by the label is 904.32 mm²
Assuming the shape of the battery is cylindrical.
The dimensions of the cylindrical battery:
radius r = 4 millimeters
height h = 32 millimeters
We know that the formula for the surface area of cylinder is:
A = 2πrh + 2πr²
where r is the radius of the cylinder and h is the height of the cylinder
Using this formula of surface area of cylider, the surface area to be covered by the label would be,
A = 2πr(h + r)
A = 2π × 4 × (32 + 4)
A = 2 × 3.14 × 4 × 36
A = 904.32 mm²
Thus, the required area = 904.32 sq. mm.
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how many hip-hop songs does the streaming music channel play for every 12 pop songs? plot a point on the graph to model this relationship
For every 12 pop songs played on the streaming music channel, there are 8 hip-hop tracks.
How do you write the relationship of a graph?After that, the algebraic relationship is denoted by the equation y = mx + b, where y stands for the distance, x for time, m for the slope, and b for the y-intercept. Distance = (2m/s)time - 1m is the relationship we infer from the graph.
The association between two quantitative variables measured for the same individuals is displayed in a scatterplot. One variable's values are shown on the horizontal axis, and the other variable's values are shown on the vertical axis. Each individual in the data is represented by a point on the graph.
As the values of the independent variables rise, a linear connection shows as a straight line, rising or dropping. A direct relationship is shown by a rising line to the right. If the line curves right, there is an inverse relationship.
For every 12 pop songs played on the streaming music channel, there are 8 hip-hop tracks.
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solve the following systems of linear equations by graphing
x=4 and y=-3/2x - 2
Answer: -8
Step-by-step explanation: I did long division for 3/2 = -1.5 now I have to mutiply -1.5 x 4 = -6 - 2 = -6 + (-2) which now eqauls negative 8
what is another term for the average value of a distribution?
The another term for the average value of a distribution is "mean."
The mean is a commonly used measure of central tendency that represents the average value of a set of data. It is calculated by summing up all the values in a dataset and dividing by the total number of observations. The mean is a useful tool for summarizing the general tendency of a dataset and is used as a basis for other statistical calculations such as variance and standard deviation.
However, the mean is sensitive to outliers, meaning that a few extreme values in a dataset can greatly affect the mean. For this reason, it's sometimes necessary to use other measures of central tendency, such as the median or mode, to get a better understanding of the central tendency of a dataset.
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charlie drove to the mountains last weekend. there was heavy traffic on the way there, and the trip took hours. when charlie drove home, there was no traffic and the trip only took hours. if his average rate was miles per hour faster on the trip home, how far away does charlie live from the mountains?
If his average rate was miles per hour faster on the trip home, Charlie lives 480 miles from the mountain.
Let s = his speed to the mountains,
(s+20) = his return speed
The distance each way is the same,
Using the formula,
Distance = speed * time
12s = 8(s+20)
12s = 8s + 160
12s - 8s = 160
4s = 160
s = 160/4
s = 40 mph
So his speed to the mountain is 40mph
then,
Putting the values of speed and times we get,
40 * 12 = 480 miles to the mountains
Therefore, distance between charlie and the mountains is 480 miles.
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what are the coordinates to graph y=-2x-2
Answer: the y intercept is (0,-2)
Step-by-step explanation:
Step-by-step explanation:
it is a line.
so, you need 2 points of the line that you can then connect via a ruler and a pen.
you get a point by picking a value for x and calculate the corresponding y.
like x = 0, y = -2×0 - 2 = -2
or x = -2, y = -2×-2 - 2 = 2
If a two system of equation passes to the origin (0,0), How many solutions does it have?
A) One solution
B) infinity many solution
C) No solution
D) none of the above
Which model shows and angle that appears to represent 45/360 of a circle
A protractor is a tool used for measuring and drawing angles. It is typically a semi-circular piece of plastic or metal with a degree scale marked along its curved edge.
The scale typically ranges from 0 to 180 degrees, which covers half a circle. To measure or draw an angle of 45 degrees, you would line up the protractor's baseline with one arm of the angle and use the degree scale to find 45 degrees. If you are drawing the angle, you would then use a straightedge to extend the other arm of the angle from the point where it intersects the 45-degree mark on the protractor.
It's important to note that the 45-degree angle represents 45/360 of a full circle, which is equal to one-eighth of a full rotation. This means that if you were to rotate the angle around its vertex, it would make one-eighth of a full circle before aligning with its original position.
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x − y = 8 x + 4 y = 13
Answer:
x=9, y=1
Step-by-step explanation:
Give brainlist, please
if i'm given 3 points and found a vector projected onto another vector, how do i know those 3 points lie on the same line?
If you have three points in space , we can use direction vector , check if vectors are collinear or proportional to know those 3 points lie on the same line.
If you have three points in space and you find a vector that is projected onto another vector from each of these three points, it is possible to determine if the three points lie on the same line. Here's how you can do it:
Find the direction vector: Calculate the direction vector from one of the points to the other two points.
Check if the projection vectors are collinear: If the projection vectors from all three points are collinear, it means that they are all pointing in the same direction and are proportional to each other.
Check if the projection vectors are proportional: If the projection vectors are proportional, it means that they are all pointing in the same direction, and the three points are on the same line. Note that in order to determine if the projection vectors are proportional, you would need to know the magnitude of the projection vectors.
If the three points do lie on the same line, the direction vector found in step 1 will be proportional to the projection vectors found in step 2 and step 3, and all three points will lie on the same line in space.
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When switching x and y, the result is always an inverse ________(relation or function).
function is the answer of this question
What rule would you allow to test whether (x,y) is on line l
The slope of the line will be 5 / 4 for the given graph.
What is a slope?Slope or the gradient is the number or the ratio which determines the direction or the steepness of the line. The slope of the line is defined as the ratio of the rise o the line to the run of the line.
Given that the line is passing through points ( 4,5) and ( 8, 10). The slope of the line will be calculated as:-
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
Slope = ( 10 - 5 ) / ( 8 - 4 )
Slope = 5 / 4
Hence, the slope of the line is equal to 5 / 4.
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A scuba diver is hired to take underwater photos. He begins swimming straight downward from an elevation of -5 meters relative to sea level. His elevation changes at a constant rate of 2.5 meters per minute. When he stops, his camera is still in a safe depth for use. For how many minutes could he have been swimming? Graph the solution set. Show your work.
Step-by-step explanation:
The scuba diver's elevation after t minutes can be represented by the equation y = -5 + 2.5t. The camera is in a safe depth for use when y is greater than or equal to 0, so we want to find the value of t when y is equal to 0.
Solving for t:
0 = -5 + 2.5t
5 = 2.5t
t = 5/2.5
t = 2
So the scuba diver could have been swimming for 2 minutes.
The graph of the solution set would be a line with slope 2.5 and y-intercept of -5, and the x-axis (y = 0) would be the line where the diver's depth is equal to sea level. The solution to the problem would be the point on the graph where y = 0 and x = 2.
a bike tire was 1/2 full it took a small air compressor 3 1/3 seconds to fill it up how long would it have taken to fill a empty tire
Answer:7 seconds
Step-by-step explanation:
it would take 7 seconds second to fill in a inTIRE empty bike
3 1/2 *2=7
3. Write an exponential function for each set of points.
a. (0, 3), (1, 12), (2, 48), (3, 192), and (4, 768)
The exponential function for each set of points is y = 3 * 2ˣ,
What is the exponential function?
An exponential function is a Mathematical function in form f (x) = ax, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0. The most commonly used exponential function base is the transcendental number e, which is approximately equal to 2.71828.
The exponential function can be described as y = 3 * 2ˣ,
where,
x is the input value
and y is the output value.
This function says that for every increase in x by 1 unit, the value of y will be multiplied by 2, starting from an initial value of 3.
For example, when x = 0, y = 3 * 2⁰ = 3, and when x = 1, y = 3 * 2¹ = 12.
Hence, the exponential function for each set of points is y = 3 * 2ˣ,
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A)How much material does he need to cover the one rectangular side of the tent with the rip? Justify your answer using equations/formulas, models, and/or words to explain your mathematical reasoning.
Answer:
B)If David’s dad wanted to recover the whole tent including the bottom, how much material would he need? Justify your answer using equations/formulas, models, and/or words to explain your mathematical reasoning.
Answer:
C)What is the volume of the tent? Justify your answer using equations/formulas, models, and/or words to explain your mathematical reasoning. (You need to find the area of one of the triangular bases, and then you can take that measurement and multiply it with the height of the entire prism. ) V=Bh, where B = area of one of the triangular bases
Answer
He would need 54 ft² material to cover the one rectangular side of the tent with the rip and 213 ft² to recover the whole tent including the bottom. The volume of the tent is 189 ft³.
Part A
He would need 54 ft² material to cover the one rectangular side of the tent with the rip. As we have to find the area of a rectangular side of a rectangle we will use the formula Area= Length × Width
∴ Area of a Rectangle = length of the rectangle × width of the rectangle
A = 9 × 6
A = 54 ft²
Part B
David's dad would need 213 ft² material to recover the whole tent including the bottom. We know that the 2 sides of the tent are 54 ft² each. So, the total is 54 × 2 = 108 ft².
We will now find the area at the bottom of the tent
A = 7 × 9
A= 63 ft²
We will now find the area of the triangular sides
Triangle Area = 1÷2 × b×h
A = 1÷2 × 7 × 6
A = 1÷2 × 42
A = 21 ft²
As there are 2 triangular sides so we have to multiply it by 2
∴ 21 × 2 = 42 ft²
Add all the sides together 108 63 + 42 = 213 ft²
Part C
The volume of the tent is 189 ft³. It can be found by applying the formula V= b×h
Triangle area = 1÷2 × bh
A = 1÷2 ×7 × 6
A= 1÷2 × 42
A= 21
With a=21 as B and h= 9ft and applying the formula v=Bh
We have,
v = 21 × 9
v = 189 ft³
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which of the following compound conditions are equivalent to the following nested conditionals? if (x > 200): if (y < 200): i. ((x > 200) and (y < 200)) ii. (x > 200 and y > 200) iii. not ((x
the expression are equivalent compound condition for the nested conditionals is (x > 200) and (y < 200).
ii. The equivalent compound condition for the nested conditionals is not (x > 200 and y > 200).
iii. The equivalent compound condition for the nested conditionals is not ((x ≤ 200) or (y ≥ 200)).
The equivalent compound conditions for the given nested conditionals are as follows:
i. The compound condition (x > 200) and (y < 200) is equivalent to the nested conditionals if (x > 200): if (y < 200). This is because the compound condition requires both conditions to be true for the condition to be satisfied.
ii. The compound condition not (x > 200 and y > 200) is equivalent to the nested conditionals if (x > 200): if (y < 200). This is because the compound condition requires both conditions to be false for the condition to be satisfied.
iii. The compound condition not ((x ≤ 200) or (y ≥ 200)) is equivalent to the nested conditionals if (x > 200): if (y < 200). This is because the compound condition requires both conditions to be false for the condition to be satisfied.
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a) Complete the table of values for y = x^2 - 4 x
b) Which of the three curves drawn matches the graph of y = x^2 - 4x
On solving the provided question, we can say that from the graph[tex]y = x^2 - 4x[/tex], x = 0, y = 0 and x =2, y = 0
What is graphs?Mathematicians use graphs to logically convey facts or values using visual representations or charts. A graph point will typically reflect a relationship between two or more things. Nodes, or vertices, and edges make form a graph, a non-linear data structure. Glue together the nodes, often referred to as vertices. This graph has vertices V=1, 2, 3, 5, and edges E=1, 2, 1, 3, 2, 4, and (2.5), (3.5). (4.5). Statistical charts (bar charts, pie charts, line charts, etc.) graphical representations of exponential growth. a logarithmic graph in the shape of a triangle.
from the graph,
[tex]y = x^2 - 4x[/tex]
so,
x = 0, y = 0
x = -1,
y = 5
and x =2, y = 0
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If $100 is increased by 15% it then becomes?
Answer:
$115
Step-by-step explanation:
If $100 is increased by 15%, it becomes $100 + 0.15 * $100 = $100 + $15 = $115.
Answer: 115
Step-by-step explanation:
100 x 0.15 = 15 so, 100 + 15 = 115
(PLS HELP!!!)
The medians of ADEF are DK, EL, and FJ. They meet at a single point M.
(In other words, M is the centroid of ADEF.)
Suppose EL=24, DM = 12, and FM = 6.
Find the following lengths.
Note that the figure is not drawn to scale.
Answer:
DK = 18
MJ = 3
ML = 8
Step-by-step explanation:
In this problem, we need to use the Median of a Triangle Formula. This formula states that EM/EL = FM/JF = DM/DK = 2/3. To implement this into our question, we can write ML/EL = 1/3, so we get that ML = 24/3 = 8. We also know that MJ/FM = 1/2, so MJ = 6/2 = 3. Finally, DM/DK = 2/3, so DK = (12*3)/2 = 18. Hope this is correct.
I want to build a rectangular garden so that the length is 45 meters more than twice the width. I have 1350 meters of fencing available. What dimensions should I make the garden?
Answer:
Step-by-step explanation:
Let's start by defining the variables for the problem. Let's say that:
w = the width of the rectangular garden (in meters)
l = the length of the rectangular garden (in meters)
We know that the length is 45 meters more than twice the width, so we can write:
l = 2w + 45
We also know that we have 1350 meters of fencing available to enclose the rectangular garden. The perimeter of the rectangular garden is equal to the sum of the lengths of all four sides. Since there are two sides of length w and two sides of length l, we can write:
Perimeter = 2w + 2l
Substituting the expression for l that we derived earlier, we get:
Perimeter = 2w + 2(2w + 45)
Perimeter = 6w + 90
We know that the perimeter of the rectangular garden is equal to 1350 meters, so we can write:
1350 = 6w + 90
Solving for w, we get:
6w = 1260
w = 210
Now that we know the value of w, we can use the expression for l that we derived earlier to find the length:
l = 2w + 45
l = 2(210) + 45
l = 465
Therefore, the dimensions of the rectangular garden should be 210 meters by 465 meters.
Chloe has already read 50 pages of a book and reads 40 additional pages per hour. Write the equation of the line that represents the number of pages read y in x hours. Plus sign Minus sign Multiplication sign Division sign Big fraction Superscript (Ctrl+Up) Square root Root Equals sign Not equal to Less-than sign Greater-than sign Less-than or equal to Greater-than or equal to Parentheses Pi
In the given situation, the required equation will be 40x + 50 = P where P is the total pages read and x is the number of hours read.
What is an equation?A mathematical equation, such as 6 x 4 = 12 x 2, states that two amounts or values are equivalent a meaningful noun.
An equation is used when two or more factors must be considered jointly in order to understand or explain the whole situation.
So, in the question we have:
50 pages of the book already read by Chole.
He reads 40 pages every hour.
He reads for more x hours.
Then, accordingly, the equation will be:
40x + 50 = P
Where x is the number of hours read and P stands for the total pages read.
Therefore, in the given situation, the required equation will be 40x + 50 = P where P is the total pages read and x is the number of hours read.
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9. In June, Maxwell's father
comes to live in their home and
can count as Maxwell's
dependent. What steps does
Maxwell need to take next? *
Income
ТІР: Те
is
(c) ift
(b) Us
rom all of these jo
married filing joint
(a) Us
There are no steps Maxwell needs to
take
DO O
are Information o
Submit a new W-4
also
Com
home for your
Add to Step 3 so that Maxwell claims
an additional $500 for a dependent
om with
- ON:
Verbally tell the HR department at Big
City Office Furniture
Maxwell's father comes to live with him in his house, and his number of dependents has now increased.
Maxwell can count his father as his dependent if his father is not able to earn his own livelihood. Maxwell should submit a new W4 form clearly mentioning his father as his dependent.
A W4 form is used to inform employers about withholding correct federal income tax on the employee pay.
This is based on the allowances deducted for the dependents and then the income left is subject to tax.
Maxwell can claim an allowance for his father. The correct option is to Submit a new W4 form.
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(In a survey of a group of 180 students, 50 students like cricket game only, 30 students like basketball game only and 50 students do not like both games.): i)Represent the above information in a Venn-diagram. ii)Find the ratio of the students who like cricket game and basketball game.
Answer:
Ratio of cricket to basketball = 5:3
Venn diagram attached below
Step-by-step explanation:
Ratio =
50 people like cricket
30 people like cricket
50:30
simplified
= 5:3
A bricklayer needs to order 6300 kg of building sand.
a) Write 6300 kg in grams, giving your answer in standard form.
One grain of this sand approximately weighs 7 x 10*g.
b) How many grains of sand are there in 6300 kg of sand?
Give your answer in standard from.
The standard form of 6300 kg in grams is 0.63 x [tex]10^7[/tex] g.
There are 90000 grains in 6300 kg of sand.
What is unit conversion?It is the conversion of one unit to another unit with its standard conversion.
Example:
1 minute = 60 seconds
1 km = 1000 m
We have,
6300 kg
Now,
1 kg = 1000 g
So,
6300 kg = 6300 x 1000 g
6300 kg = 63 x [tex]10^5[/tex] g
6300 kg = 0.63 x [tex]10^7[/tex] g
Now,
One grain = 7 x 10 g
So,
Number of grains in 0.63 x [tex]10^7[/tex] g.
= 0.63 x [tex]10^7[/tex] ÷ 7 x 10
= 90000
Thus,
0.63 x [tex]10^7[/tex] g is the standard form.
90000 grains.
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