19
A
Straight line A passes through the points (-1, 2) and (1,6)
Straight line B has equation y-x
Work out the coordinates of the point where line A crosses line B
You may use the grid to help you.
40
10
+
7
-2
14
T
6
5-
4-
3
2
O
-1-
-2-
-3
-5-
-6-
Answer (
2
3
5
6
[4 marks]
angles c and d are complementary. the measure of angle d is 15 degrees greater than the measure of angle. what is the measure of each angle.
The measure of the angles is c = 37. 5 degrees
d = 15 + 37.5 = 52. 5 degrees
How to determine the anglesTo determine the value, we need to know what complementary angles are;
Complementary angles are defined as pair of angles whose sum is equal to 90 degrees
From the information given, we have that;
Angle c and d are both complementary angles
Also, the measure of angle d is 15 degrees greater than the measure of angle c
Then, we have;
d = 15 + c
Substitute the values
c + 15 +c = 90
collect like terms
2c = 90 - 15
2c = 75
Divide both sides by the coefficient
c = 37. 5 degrees
Substitute the value for angles d
d = 15 + 37.5 = 52. 5 degrees
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Which of the following functions is graphed below? HELP
The solution is: Piece-wise function
f(x)=x+6 , x≤1
f(x) = x^2 + 3 , x>1, the following functions is graphed below.
Option C is correct.
Explanation:
We are given a graph of piece-wise function which break at x=1
We need to choose correct option for graph.
Function is break at x=1.
We will get two function
For x≤1 and x>1
As we can see x≤1, graph is linear and x>1 graph is parabolic.
Equation of linear graph, x≤1
Take two point of graph (0,6) and (-6,0)
Equation of line:
y-y1/y2-y1 = x-x1/x2-x1
y = x+1
f(x)=x+6 , x≤1
Equation of parabolic graph, x>1
f(x) = x^2 + 3
Piece-wise function
f(x)=x+6 , x≤1
f(x) = x^2 + 3 , x>1
Please see the attached figure.
Hence, The option C is correct.
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Will Give Brainliest Please Help!
Question 11
Explanation, step-by-step
You would need two angles to know the lines are parallel
simplify 28 divided by 0
Answer: Infinity
Step-by-step explanation: Since 0 doesn't have a measurable amount of times it can go into 28 the answer is infinity.
Please Help Im stuck
Answer: The last one is the right one
Step-by-step explanation:
So first solve for n
1/2n+3<5
1/2n<2, multiple by 2 on both sides to remove fraction
n<4
the circle will be at 4, and since n<4, n is less than 4, so your line must also be less that 4.
William throws a football in the air from a height of 4 feet with an initial upward velocity of 96 feet per second.
Write a rule in the form of h=at^2+bt+c that models the height h of the football after t seconds.
Answer:
Step-by-step explanation:
its 123 jd
Let f(x) = 5 sin(x). Describe the graph of each of the following in terms of the graph off.
1. g(x) = 5 sin(x) + 4
2. h(x) = 5 sin(x + 1)
3. k(x) = 20 sin(x) + 10
4. m(x) = 5 sin(4x - 1)
I
The graph of g(x) will have the same shape as f(x), but every y-coordinate will be increased by 4 units,The graph of h(x) will have the same shape as f(x), but every x-coordinate will be decreased by 1 unit,The graph of k(x) is 20 and every y-coordinate is increased by 10 units and the graph of m(x) is horizontally squeezed.
To describe the graphs of the given functions, let's first analyze the effects of the transformations applied to the original function f(x) = 5 sin(x).
1. g(x) = 5 sin(x) + 4:
The function g(x) is obtained by vertically shifting the graph of f(x) by 4 units upward. This means that the graph of g(x) will have the same shape as f(x), but every y-coordinate will be increased by 4 units.
2. h(x) = 5 sin(x + 1):
The function h(x) is obtained by horizontally shifting the graph of f(x) to the left by 1 unit. This means that the graph of h(x) will have the same shape as f(x), but every x-coordinate will be decreased by 1 unit. The period of the function remains the same.
3. k(x) = 20 sin(x) + 10:
The function k(x) is obtained by vertically stretching the graph of f(x) by a factor of 20 and then shifting it 10 units upward. This means that the amplitude of the graph of k(x) is 20 (compared to the amplitude of 5 in f(x)), and every y-coordinate is increased by 10 units.
4. m(x) = 5 sin(4x - 1):
The function m(x) is obtained by compressing the graph of f(x) horizontally by a factor of 4, reflecting it across the y-axis, and shifting it 1 unit to the right. This means that the period of m(x) is 1/4 of the period of f(x), and the graph is horizontally squeezed. The reflection across the y-axis means that the graph of m(x) will be inverted compared to f(x). The amplitude remains the same.
Remember that the graph of the original function f(x) = 5 sin(x) represents a sine wave with an amplitude of 5 and a period of 2π. Applying the transformations described above will modify the position, scale, and shape of the graph, resulting in the respective graphs for each function g(x), h(x), k(x), and m(x).
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Select the correct answer.
Which statement is true?
OA
Point estimates are used to make inferences about population parameters.
OB. When we use the population mean and proportion to summarize information about the entire population, we call them point
estimates.
OC. The population mean and proportion are always equal to their corresponding point estimates.
O D.
The sample mean and sample proportion of a population are called population parameters.
Answer:
A. Point estimates are used to make inferences about population parameters.
4.1 Find the intervals on which the function = [tex]x^{3}[/tex] −
4[tex]x^{2}[/tex]$ + 10 is increasing or decreasing.
The intervals on f(x) is increasing on (-∞, 0) and (8/3, ∞), and decreasing on (0, 8/3).
The intervals on which the function f(x) = x³ − 4x² + 10 is increasing or decreasing need to find its derivative and determine its sign.
f(x) = x³ − 4x² + 10
f'(x) = 3x² − 8x
The critical points we set f'(x) = 0 and solve for x:
3x² − 8x = 0
x(3x − 8) = 0
x = 0 or x = 8/3
These are the critical points of the function.
Now we can determine the sign of f'(x) in each interval:
Interval (-∞, 0):
Choose x = -1. f'(-1)
= 3(-1)² - 8(-1)
= 11 is positive.
So f(x) is increasing on (-∞, 0).
Interval (0, 8/3):
Choose x = 1. f'(1) = 3(1)² - 8(1)
= -5 is negative.
So f(x) is decreasing on (0, 8/3).
Interval (8/3, ∞):
Choose x = 3. f'(3) = 3(3)² - 8(3)
= 19 is positive.
So f(x) is increasing on (8/3, ∞).
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30 POINTS HELP! To analyze the change in the number of dog walks over time, draw a line to model the data. Use the connect line to draw the line.
The line of the best fit that models the data is added as an attachment
From the question, we have the following parameters that can be used in our computation:
The graph
To draw a line to model the data is to draw the line of best fit
A good line of best fit would have equal number of points on either sides
To plot the graph, we draw a line that divides the points on the graph evenly
This line when drawn on the scattered points divided the points approximately evenly
Hence, the line of the model is attached
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Which of the following function pairs are inverses?
Question 3 options:
A)
B)
C)
f (x) = x2 – 16 and g(x) = x – 4
D)
The function pairs that are inverses are:
C) f(x) = 5x - 3 and g(x) = (x + 3)/5
To determine if two functions are inverses, we need to check if applying one function and then the other function will return the original input.
Let's go through each option:
A) f(x) = -2x and g(x) = (1/2)x
To check if they are inverses, we can apply function f(g(x)) and see if it returns x:
f(g(x)) = f((1/2)x) = -2(1/2)x = -x
Since f(g(x)) = -x ≠ x, these functions are not inverses.
B) f(x) = 4x² and g(x) = √x
To check if they are inverses, we can apply function f(g(x)) and see if it returns x:
f(g(x)) = f(√x) = 4(√x)² = 4x
Since f(g(x)) = 4x = x, these functions are not inverses.
C) f(x) = 5x - 3 and g(x) = (x + 3)/5
To check if they are inverses, we can apply function f(g(x)) and see if it returns x:
f(g(x)) = f((x + 3)/5) = 5((x + 3)/5) - 3 = x + 3 - 3 = x
Since f(g(x)) = x, these functions are inverses.
D) f(x) = x² - 16 and g(x) = x - 4
To check if they are inverses, we can apply function f(g(x)) and see if it returns x:
f(g(x)) = f(x - 4) = (x - 4)² - 16 = x² - 8x + 16 - 16 = x² - 8x
Since f(g(x)) = x² - 8x ≠ x, these functions are not inverses.
Based on the analysis above, the function pairs that are inverses are:
C) f(x) = 5x - 3 and g(x) = (x + 3)/5
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The complete question:
Which of the following function pairs are inverses?
A) f(r) = -2x and g(x) = (1/2)x
B) f() = 4x² and g(x) = √x.
C) f(x) = 5x - 3 and g(x) = (x + 3)/5
D) f(x) =x² - 16 and g(x) = x - 4
car cost #450,000 and its being sold for #540,000. find the profit as a percentage of the cost price
Suppose the data represent the inches of rainfall in April for a certain city over the course of 20 years.
Determine the quartiles.
0.76
1.08
1.32
1.55
1.83
2.09
2.57
2.83
3.01
3.25
3.63
3.78
4.09
4.32
4.64
4.93
5.23
5.34
5.44
5.73
The quartiles of rainfall in April for the city are:
Q1 = 1.96Q2 = 3.44Q3 = 4.79.What are the quartiles of rainfall?The quartiles refers to the e values that split sorted data into four parts each with an equal number of observations
To determine quartiles, we first need to sort the data in ascending order which are:
[tex]0.76, 1.08, 1.32, 1.55, 1.83, 2.09, 2.57, 2.83, 3.01, 3.25,\\3.63, 3.78, 4.09, 4.32, 4.64, 4.93, 5.23, 5.34, 5.44, 5.73[/tex]
There are 20 data points, so, median (Q2) will be the average of the 10th and 11th values.
Q2 = (3.25 + 3.63) / 2
Q2 = 3.44.
Q1 = (1.83 + 2.09) / 2
Q1 = 1.96.
Q3 = (4.64 + 4.93) / 2
Q3 = 4.79.
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round 12.083 to the neatest tenth
Answer: 12.1
Step-by-step explanation: rounding 12.083 to the nearest tenth will leave you with- 12.1
hope this helps!
Write the number 6,600,000 in scientific notation.
Answer:
6.6 x 10^6
Step-by-step explanation:
please help I don’t know how to do this graph
The graph of the functions f(x) and g(x) is given below.
Given that:
Function, f(x) = x³
Translated function, g(x) = (x + 6)³
If the function is translated by 'h' units horizontally and 'k' units vertically, then x and y are replaced with (x - h) and (y - k), respectively.
The curve of the function g(x) is translated left side by 6 units.
The graph of the functions is given below.
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The length of a pen is about
Any options to pick from?
Most pens are about 13-14 cm or approx 5.5 inches.
bryan’s hockey team is purchasing jerseys the company charges 250$ for a one time set up fee and 23$ for each printed jersey which expression represents the total cost of x number of jerseys for the yeam
Answer:
23x+250 and that would equal your total cost
what is the surface area of 10 in 10 in 10in
The surface area of a three dimensional shape is the total area of all of the faces. To find the surface area of a shape, we find the area of each face and add them together. E.g. The measurements here are in centimetres so the surface area is measured in square centimetres ( c m 2 ) (cm^2) (cm2).
8) John wishes to make a line
plot of the heights in inches for a soccer team. The heights are
listed below. How many dots
would be above the greatest
height recorded?
Answer options
1
2
3
4
There are three dots above the greatest height.
We have,
The greatest height is 75
The smallest height is 62
Now,
We can make a line plot as:
* *
* * * * *
* * * * *
62 66 68 72 75
Thus,
There are three dots above the greatest height.
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This proportion can be solved to find the unknown length, x
, in the smaller triangle.
Answer:
x=3
Step-by-step explanation:
1.25/5.00=2/8=x/12=1/4
12=x×4
x=12÷4
x=3
If Hannah place is 6500 into account and a 5% interest compounded continuously how much will she have after 10 years?
¿Para qué valor de la constante "b" la función real
f(x) = 2bx³ + 2x² − 3 tiene un extremo relativo en x = -1/6
a) b=4
b) b=-4
c) c=-6
d) b=6
e) b=-3
There are 1000 cubic centimeters and 1 Liters in 1000 cubic millimeters in 1 milliliter. How many cubic millimeters are there in 1000 cubic centimeters
Answer:Set up a proportion, letting = the amount of cubic millimeters in 1,000 cubic centimeters. Solve for : 1,000,000 cubic millimeters are in 1,000 cubic centimeters.
What are the zeros of the function defined by y = x2 + 6x + 5?
What is the area of the figure?
The area of the triangular figure is 16 m²
What is the area of a triangle?The area of a triangle is given by A = 1/2bh where
b = length of base and h = height of triangleGiven the figure below, we see that it is two triangles with height, h = 2 m and base, b = 8 m.
Since the area of each triangle is A = 1/2bh, and the area of both triangles are the same, then the area of both triangles is A" = A + A
= 2A
= 2(1/2bh)
= bh
Substituting the values of the variables into the equation, we have that
A" = bh
= 8 m × 2 m
= 16 m²
The area is 16 m²
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Jonah walks 1/3 mile in 3/4 hour. What constant of proportionality relates the distance she travels to the time?
A set contains 13 elements.
a) How many subsets does it have?
b) How many proper subsets does it have?
Step-by-step explanation:
Answer and Explanation:
The set contains 13 elements here, so the total number of subsets can be calculated as 213=8192 2 13 = 8192 .
calculate for me question 4, please
Answer:
f(x) = x^2 - 5x + 6
f'(x) = 2x - 5
Since the slope of h(x) is 1/3, the slope of the tangent line to f(x) will have slope -3.
2x - 5 = -3
2x = 2, so x = 1