The slope of the line is 150.
It is given the number of songs (in million) downloaded from the internet in 2006 and 2004.
We actually need to graph this data which will be a straight line. We try to find two points in this graph using the given data.
Represent the years as x coordinates and the number of songs as y coordinates. Also take 2006 as 6 only and 2004 as 4 only for convenience.
Now we get two points [tex](x_1,y_1)[/tex] = (4, 200) and [tex](x_2,y_2)[/tex] = (6, 500)
Slope of the line = [tex]\frac{y_2-y_1}{x_2-x_1} = \frac{500-200}{6-4}[/tex] = 300/2 = 150
Here the slope is positive, which means that the number of downloads are increasing with increase in years. The rate of change in number of downloaded songs from internet is 150 million in two years.
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On a number line, suppose point E has a coordinate of -1, and EG=11. What are the possible coordinates of point G?
On a number line, the possible coordinates of point E are: 10 or -12.
How to Find the Possible Coordinate of a Point on a Number Line?Given that point E on a number line has a coordinate of -1, and also, we know that the distance from point E to point G is 11 units, we would determine the possible coordinates of point G as explained below:
11 units from point E is: -1 + 11 = 10
11 units towards point E is: -1 - 11 = -12
Therefore, on a number line, the possible coordinates of point E are: 10 or -12.
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Compare and contrast function notation and vector notation for translations.
The comparison and contrast function notation and vector notation for translations are-
A transformation can be described using either notation. A equation to obtain the image from such a general point is shown in function notation. The vector notation indicates which direction to move in and the distance to move.What is termed as function notation?Function notation is a method for writing functions that are simple to comprehend and read.
When we employ function notation, the independent variable is typically x, as well as the dependent variable is F. (x). To use function notation to write a relation or equation, we must first ascertain if the relation is a function.What is termed as vector notation?Whenever a vector is simply a list of numbers, it can be represented by an arrow in space.
We divide the vector by its magnitude to discover a unit vector with the same direction as just a given vector. Consider the magnitude of a vector v = (1, 4) with a magnitude of |v|. When we divide evey component of vector v by |v|, we get the unit vector uv, which is oriented in the same direction as vector v.To know more about vector notation, here
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MP.7 Use Structure Sue and Jonah
chose numbers for a place-value game.
Sue chose the number one hundred
fifty-two thousand. Jonah chose five
million for his number. Who chose the
greater number? Explain.
Jonah has chosen the greater number.
Given, Sue and Jonah chose numbers for a place value game.
As a way to express numbers, a number system is a way of expressing them. It is a method of describing numbers from a particular set mathematically by consistently employing digits or other symbols. Every number is given a distinct representation, and the figures' algebraic and mathematical structures are also shown.
Sue chose the number = one hundred fifty two thousand
= 152000
= 1.52 lakhs
Jonah chose the number = five million
= 5,000,000
we know that 10 lakhs = 1 million = 1,000,000
therefore, 5 million = 5 × 10 lakhs
= 50 lakhs
50 lakhs > 1.5 lakhs
the greater number is 5 million.
Therefore , the greater number chose by Sue and Jonah is of Jonah's that is 5 million.
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Which of the following is equal to 7^1/4?
A. 4√7
B.√7.4
C. 7^4
D. √7
An exchange student is moving back to Italy, and her homeroom class wants to get her a going away present. The teacher takes a survey of the class of 32 students and finds that 10 people chose a card, 12 chose a T-shirt, 6 chose a video, and 4 chose a bracelet. If the teacher randomly selects the present, what is the probability that the exchange student will get a card or a bracelet?
According to the question, the homeroom class wants to get a present for a student. From [tex]32[/tex]students, [tex]10[/tex] choose cards, [tex]12[/tex] choose t-shirts, [tex]6[/tex] choose a video and the remaining choose a bracelet.
Now, calculate the probability that the exchange students should get a card or a bracelet.
Let us assume, ‘C’ represents the card and ‘B’ represents the bracelet.
Using standard probability formula:
P (C or B) = P(C)+P(B) = [tex]\frac{10}{32} + \frac{4}{32} = \frac{14}{32} = \frac{7}{16} = 43.8%[/tex]
Therefore, the probability to get a card or a bracelet is [tex]43.8[/tex] percent.
What is Probability?
The term probability means the study of the occurrence or the outcomes of the event. It is the measurement of the events that occurred during events. And many uncertain events cannot be measured.
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please help asap!!!!!!!!!!!!!!!!!!!!!!!
Answer:
MP = NQ = 5 units=====================
Given pointsM = (3, 2), N = (3, -1), P = (7, - 1), Q = (7, 2)Use distance formulaThe distance between points (x₁, y₁) and (x₂, y₂) is:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Apply this to segments MP and NQ[tex]MP=\sqrt{(7-3)^2+(-1-2)^2}=\sqrt{4^2+(-3)^2}=\sqrt{16+9} =\sqrt{25}=5[/tex][tex]NQ=\sqrt{(7-3)^2+(2-(-1))^2}=\sqrt{4^2+3^2}=\sqrt{16+9} =\sqrt{25}=5[/tex]So we have both segments with same length of 5 units
Sven is trying to find the maximum amount of time he can spend practicing the five scales of piano music
he is supposed to be working on. He has 80 minutes to practice piano and would like to spend at least 45
minutes playing songs instead of practicing scales. So, Sven sets up the following inequality, where t is
the number of minutes he spends on each scale, and solves it.
80-5t < 45
-5t -35
t≥7
Step-by-step explanation:
i thank the answer is 10.5 thanks for your question
Find the geometric mean between pair of numbers.
√20 and √80
The geometric mean between pair of numbers √20 and √80 is 6.32
We know that for a sequence of numbers x1, x2,.., xn
The formula of geometric mean is,
[tex]\Pi=\sqrt[n]{x_1.x_2.x_3...x_n}[/tex]
In this question, we have been given two numbers √20 and √80
We need to find the geometric mean between pair of numbers, √20 and √80
Using the formula for the geometric mean,
[tex]\Pi=\sqrt[n]{x_1.x_2.x_3...x_n}[/tex]
In this question, we have two numbers.
So, the value of n is 2.
[tex]\Pi=\sqrt{\sqrt{20}\times \sqrt{80} }\\\\ \Pi=\sqrt{\sqrt{1600} }\\\\ \Pi=\sqrt{40}\\\\ \Pi=6.32[/tex]
Therefore, the geometric mean between pair of numbers √20 and √80 is 6.32
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Solve the equation
2x^2 + 8x - 1 = 0
by completing the square.
Give your answers correct to 2 decimal places.
26 divided by 5 1/5 Help!!
You bought a total of 6 pens and pencils for 4 . If each pen costs 1 and each pencil costs .50 , how many pens and pencils did you buy?
I bought 2 pens and 4 pencils from given amount.
Let us represent the number of pens and pencils as x and y respectively. Forming the equation as per the given information -
Equation representing total number of pens and pencils bought
x + y = 6 - Equation 1
Rearranging the equation 1 as per the variable x
x = 6 - y - Equation 2
Equation representing cost of bought pens and pencils
1x + 0.5y = 4 - Equation 3
Keep the value of x from Equation 2 in Equation 3
1 (6 - y) + 0.5y = 4
6 - y + 0.5y = 4
Rearranging the equation for positive sign on each side -
y - 0.5y = 6 - 4
Performing subtraction on Right Hand Side of the equation to find the value of y
0.5y = 2
Shifting 0.5 to Right Hand Side of the equation and performing division
y = 2 ÷ 0.5
y = 4
Calculating the value of x by keeping the value of y in Equation 2
x = 6 - 4
x = 2
Hence, I bought 2 pens and 4 pencils from given amount.
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If a 45° -45° - 90° triangle has a hypotenuse length of 9 , find the leg length.
The leg length is 9/ root2
Here we are given a right angle triangle , and in a right triangle , sum of squares of sides is equal to the square of hypotenuse.
[tex]a^{2}+b^{2} =c^{2}[/tex]
This is right angle scalene triangle as the two angles other than right angle are 45° each.
Hence ,
In this case we have
[tex]a^{2}+a^{2} =c^{2}[/tex]
[tex]2a^{2}=c^{2}[/tex]
[tex]a^{2}=\frac{c^{2} }{2}[/tex]
Taking square roots on both sides
[tex]a=\frac{c}{\sqrt{2} }[/tex]
Here we have hypotenuse c given as 9
Hence, the leg length is [tex]a =\frac{9}{\sqrt{2} }[/tex]
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In the figure below, m ∠4=49. Find m ∠1, m ∠2, and m ∠3
Answer:
∠ 1 = 131° , ∠ 2 = 49°
Step-by-step explanation:
∠ 1 and ∠ 4 are a linear pair and sum to 180° , that is
∠ 1 + ∠ 4 = 180°
∠ 1 + 49° = 180° ( subtract 49° from both sides )
∠ 1 = 131°
∠ 2 and ∠ 4 are vertically opposite angles and are congruent , so
∠ 2 = 49°
BN.
Anna, Bob and Chris did will not disclose their weights but agree to be weighed in pairs. Anna and Bob together weigh 226 pounds. Bob and Christ together weigh 210 pounds. Anna and Chris together weigh 200 pounds. How
does each student weigh?
Anna , Bob , Chris weigh 108 pounds , 118 pounds , 92 pounds respectively .
Solve a linear equation in three variables by completing the following steps: Take any two equations and solve them for one variable Again, take two more pairs of equations and solve for the same variables. We have two systems of equations with two unknown variables. solve two equations Again, substitute the calculated values of the variables into one of the original equations and solve for the unknown variables.Let the Anna weigh = x pounds
Let the Bob weigh = y pounds
Let the Chris weigh = z pounds
According to the question Anna and Bob together weigh 226 pounds which can be written as [tex]x+y=226[/tex] ..(1)
According to the question Bob and Christ together weigh 210 pounds. which can be written as [tex]y+z=210[/tex] ...(2)
According to the question Anna and Chris together weigh 200 pounds. which can be written as [tex]x+z=200[/tex] ..(3)
From equation (1) [tex]y=226-x[/tex] putting this value in equation (2) , we get
[tex]226-x+z=210\\16=x-z\\16+z=x[/tex] ..(4)
Putting above value in equation (3) , we get
[tex]16+z+z=200\\2z=184\\z=92[/tex]
Putting z = 92 in equation (4) , we get
[tex]x=16+92\\x=108[/tex]
Putting x = 108 in equation (1) , we get
[tex]y=226-108\\y=118[/tex]
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The graph models the linear relationship between temperatures in degrees Fahrenheit and temperatures in degrees Celsius.
What is the rate of change of the temperature in degrees Fahrenheit with respect to the temperature in degrees Celsius?
According to the question, the model has linear relationship between the temperatures which are in degree Fahrenheit and in Celsius.
Now, to calculate the rate of change of the temperature which is defined in the ratio of y-axis and x-axis. Therefore, the expression can be written as:
Rate of change of the temperature = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
From the graph model, the coordinate values are (0,32) and (30,86)
[tex]x_{2} = 30; x_{1}=0; y_{2}=86; y_{1}=32[/tex]
Substituting the given values in the standard expression to calculate the rate of change of the temperature:
Rate of change of the temperature = [tex]\frac{86-32}{30-0}=\frac{54}{30} =\frac{9}{5}[/tex]
Hence, the rate of change of the temperature is 9/5.
What is rate of change in the graph?
In the graph, the rate of change of a quantity defines the relationship between the two quantities. The calculated values are either positive, negative or zero. It is a slope of a line in the form of ratio of vertical to horizontal axis.
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A closed tin of milk has diameter 12cm and height 8cm. Find the total surface area of the tin (take π=22÷7)
The total surface area of the closed milk tin is 528 cm²
The shape of the closed tin of milk is cylinder.
The formula for calculating the total surface area of cylinder is the curved surface area of the cylinder + the area of the two circles(on the top and the bottom) which equals to 2πr(r+h), where r is the radius of the cylinder and h represents the height of the cylinder.
The diameter of the cylinder is 12cm and the height of the cylinder is 8cm.
The radius of the cylinder is half of the diameter of the cylinder which is 12/2=6cm
By putting the values, we get = 2×22/7×6(6+8)
= 264/7(14)
= 264(2)
= 528 cm²
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Evaluate the indicated function for f(x) = x2 − 1 and g(x) = x − 3 algebraically. If possible, use a graphing utility to verify your answer. (fg)(4t2)
STEP 1: Apply the definition of the product of two functions.
(fg)(4t2) =
STEP 2: Replace the f and g expressions in your answer to Step 1 with expressions involving only t.
(fg)(4t2) =
STEP 3: Expand your answer from Step 2.
(fg)(4t2) =
The value of the indicated function would be (fg)(4t2) = (64t⁶ - 48t⁴ - 4t² + 3)
How to solve for the functionThe question has that
f(x) = x² - 1
f(g) = x -3
We have to find (fg)(4t²)
(fg)(4t²) = f(4t²) (g(4t²)
= (4t²)²-1) (4t² - 3)
we have to expand the bracket
(16t⁴ - 1) (4t² - 3)
= (64t⁶ - 48t⁴ - 4t² + 3)
Hence we can say that the value of
(fg)(4t2) = (64t⁶ - 48t⁴ - 4t² + 3)
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Write the equation of the line in slope-intercept form.
2x-4y=10
The equation of the line in slope-intercept form is y = (1/2)x + (-5/2) .
The equation of a line in slope-intercept form can be written as follows,
y = mx + c equation 1
m in the above equation represents slope of the line and c represents the intercept.
The given equation is 2x - 4y = 10 .
To get the equation of the line in slope-intercept form we need to convert the given equation in the format of equation of a straight line i.e., equation1. So, now we will rearrange the given equation as
2x - 4y = 10
⇒ 4y = 2x -10
Now on dividing this equation by 4 on both sides, we will get
y = (1/2)x + (-5/2) equation 2
On equating equation 1 and equation 2, we will get
Slope of the line = m = 1/2.
Intercept = c = -5/2
The equation of the line in slope-intercept form is y = (1/2)x + (-5/2) .
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question in the picture
The salary after 6 years is $83,000.
The salary after tt years is 53,000 + 5000tt.
What is her total salary?The equation that can be used to determine Aisha's salary after a period of time can be represented by a linear equation. This is because that her salary increases by a constant rate each year.
A linear function represents a straight line when drawn on a coordinate plane. A linear function is a function that has a single variable raised to the power of 1. An example is y + 2. The variable y is raised to the power of 1. 2 is the constant term.
Total salary = beginning salary + (rate of increase x number of years)
Salary after 6 years: 53,000 + (5,000 x 6)
= 53,000 + 30,000 = $83,000
Salary after tt years: 53,000 + (5,000 x tt)
53,000 + 5000tt
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Shawn surveyed his homeroom class to find out how many of his classmates have at least 1 sibling. Of the 32 people in his homeroom, 25 have at least one sibling.
(a) If there are 470 students in Shawn's school, write a proportion that could be used to predict the number of students in the school who have at least one sibling.
A proportion exists in an equation in which two ratios stand set equivalent to each other. 367 students in his school have at least one sibling.
What is meant by proportion?A proportion exists an equation that sets two ratios at the same value. A mathematical comparison of two numbers is called a proportion. In terms of proportion, two sets of given numbers are said to rise or decrease in the same ratio if they are directly proportionate to one another.
Let the number of students be x, then
25/32 = x/470
simplifying the above equation, we get
25(470) = 32x
32x = 11750
Dividing both sides of the equation by 32, we get
32x / 32 = 11750 / 32
x = 367
The value of x = 367.
Therefore, 367 students in his school have at least one sibling.
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solve each equation(with explanation please)
-4+p=-7
x/10=-6
4-3(8n - 4) = -104
Answer:
1: P = -3
2: X = -60
3: N = 5
Step-by-step explanation:
Ok, for number one you are going to add 4 on the -4 canceling that out, and adding 4 on the -7 making that -3.
Number 2 you times 10 on the x/10 to cancel out the 10 (making it x) then you do -6 times 10, and then you get -60
Last one is a little tricky here's the equations I used to get the last one
-3 x 8n = -24x
New equation: 4-24x=-104
+4 + 4
___________________________
-24x = -100
___ ___
-24 -24
_
so the answer would be x = 5
An 18-foot ladder is placed against the side of a house. The base of the ladder is positioned 8 feet from the house. How high up on the side of the house, to the nearest tenth of a foot, does the ladder reach?
A. 10.0 ft
B. 16.1 ft
C. 19.7 ft
D. 22.5 ft
E. 26.0 ft
b ≈ 16.1 is high up on the side of the house, to the nearest tenth of a foot, does the ladder reach.
What are examples of linear equations?
Ax+By=C is the usual form for two-variable linear equations. A standard form linear equation is, for instance, 2x+3y=5. When an equation is given in this format, finding both intercepts is rather simple (x and y). When attempting to solve systems involving two linear equations, this form is also quite helpful.8² + b² = 18²
64 + b² = 324
b² = 260
b ≈ 16.1
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A coin is filmed using stop-motion animation so that it appears to move.
a. Describe the translation from A to B in function notation and in words.
The translation from A to B is described as-
In notation: From x = -3 to x = 0, the coin travels through y = (2/3)x + 1.In words: From A to B, the coin shifts three spaces to a right and then two spaces up.What is meant by translation?In mathematics, a translation is the movement of a shape to the left or right and/or up or down. The translated shapes appear to be the exact size as that of the original shape, therefore the shapes are congruent.
Replace x with x - k whenever a shape is moved to the left by k units.Replace x with x + k whenever a shape is moved to the right by k units.Replace y with y + k whenever a shape is moved up by k units.Replace y with y - k whenever a shape is moved down by k units.Now, according to the question.
Consider the equation for the shifting from A to B as y = k x+b
The coordinates of the location A and B are-(see the diagram)
A(-3,-1) and B(0,1)
Thus, A, B into y = k x+b
Substitute the value of A in the equation;
-1 = -3k + b
b = 1
So, k = 2/ 3
Put value of k in 'y'.
Hence, AB ; y = (2/3)x + 1
Thus, the coin moves thought y = (2/3)x + 1 from x = -3 to x = 0.
In words; Shifting from A to B, the coin moves 3 spaces to the right after that moves 2 space up.
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-3(x + 2) > 15 or x-3 <-1
Answer:
-7
Step-by-step explanation:
-3x-6>15
-3x/-3>21/-3=-7
x<-1+3
x<2.
What is the value of x in the equation 6(x-4)=3 x ?
The value of x in equation is 8
To find the value of x, we will solve the given mathematical expression based on the sequence of signs and placement of bracket. Firstly bracket will be solved followed by subtraction or addition.
Rewriting the equation -
6(x - 4) = 3x
Performing multiplication on Left Hand Side of the equation to find the value of x
6x - 24 = 3x
Shifting 3x and 24 to other side of equation
6x - 3x = 24
Performing subtraction on Left Hand Side of the equation
3x = 24
Shifting 3 to other side of equation as denominator
x = 24 ÷ 3
Performing division on Right Hand Side of the equation
x = 8
Hence, the value of x is 8.
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Find the 17 th term of each sequence. a₁₈ = 32, d=-4
36 is 17th term of sequence a₁₈ = 32, d=-4
Given the 18th term and the common difference, we subtract the common difference from the 18th term to determine the 17th term:
a₁₇ = a₁₈ - d
= 32 - (-4)
= 36
How to solve an equation?To solve linear equations, utilize the steps that are provided below.
Remove parentheses from each side of the equation and combine similar terms to make it simpler.To separate the variable term on one side of the equation, use addition or subtraction.To find the variable, use division or multiplication.The common denominator can be multiplied by each side of the equation to eliminate fractions.Lets take an example of solve z for 7z – (3z – 4) = 12
Here is no multiplication or division, so this will be easy to solve
⇒ 7z – (3z – 4) = 12
⇒ 7z – 3z + 4 = 12
⇒ 4z = 12 – 4
⇒ 4z = 8
⇒ z = 8/4
⇒ z = 2
See, that was so simple, using the mentioned methods, every linear equation can be solved easily.
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what is the minimum value of g?
The quadratic opens upwards, so the minimum is at the vertex.
We can see that the minimum value of g is y = -1.
What is the minimum value of g?By looking at the given graph, can see that g(x) is a quadratic equation.
If the quadratic equation has a positive leading coefficient (it opens upwards) the minimum of the quadratic is on the vertex, and there is no maximum (as the function end behavior tends to infinity)
If the quadratic equation has a negative leading coefficient (it opens downwards). The maximum is at the vertex, and there is no minimum (similar like the case above).
Here we can see that the quadratic opens upwards, thus, the minimum is at the vertex, which we can see is located at x = 3 and y = -1, then the minimum value of the function g(x) is y = -1
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Write an equation for each vertical translation of y=f(x) .
2 units up.
The equation for the vertical translation of y=f(x). 2 units up is y=f(x)+2.
Using equations of the form y=f(x), you may be able to modify the graph in various ways. For example, you can move the chart up, down, left, or right, flip it around the x or y-axis, or stretch or shrink it vertically or horizontally. Understanding these transformations makes it easy to graph different functions. Start with a "basic model" and apply a series of transformations/modifications to change it to the desired function.
A point on the graph of y=f(x) has the shape (x,f(x)).
The points on the graph of y=f(x)+2 are of the form (x,f(x)+2).
So, the graph for y=f(x) +2 is the same as the graph for y=f(x) shifted up by 2 units.
The new equation is:
y=f(x)+2
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Please! Determine which system below will produce infinitely many solutions.
A. 2x + 5y = 24
2x + 5y = 42
B. 3x - 2y = 15
6x + 5y = 11
C. 4x - 3y = 9
-8x + 6y = -18
D. 5x - 3y = 16
-2x + 3y = -7
Answer:
System C
Step-by-step explanation:
When we multiply both sides of the equation 4x - 3y = 9 by -2, we obtain
-8x + 6y = -18. So system C has infinitely many solutions.
State whether the sentence is true or false. If false, replace the underlined word or number to make a true sentence.
Angles 4 and 8 are corresponding angles.
The statement "∠4 and ∠8 are corresponding angles" is true
Given,
The angles = ∠4 and ∠8
Here, ∠4 and ∠8 are lies same side of the one of two lines and both are same side of the transversal
So, ∠4 and ∠8 are corresponding angles
So the given statement is true
Hence, the statement "∠4 and ∠8 are corresponding angles" is true
Complete question is :
State whether the sentence is true or false. If false, replace the underlined word or number to make a true sentence.
∠4 and ∠8 are corresponding angles.
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