The equation of the line that passes through (6,-3) and is parallel to the line y = -2/3 x + 5 is y = - 2 / 3 x + 1.
How to write equation of a line?The equation of a line can be represented in slope-intercept form as follows:
y = mx + b
where
m = slope of the lineb = y-interceptTherefore, the equation of the line passes through (6,-3) and is parallel to y = -2/3 x + 5.
Parallel lines have the same slopes.
Therefore, the slope of the line is - 2 / 3.
Hence, let's find the y-intercept of the line using (6, -3).
Therefore,
y = - 2 / 3 x + b
-3 = - 2 / 3 (6) + b
-3 = -12 / 3 + b
b = -3 + 4
b = 1
Therefore, the equation of the line is y = - 2 / 3 x + 1.
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What is the image of (-5, -1) after a reflection over the y-axis?
Answer:
5, -1
Step-by-step explanation:
Hope it helps! =D
A man is x years old and his son is y years old. what is their average age
Answer:(x+y)/2
Step-by-step explanation:
xiv 2. Complete the table. Make drawings if needed. a. b. C. d. e. Rectangle Length: 4 cm Width: 2 cm Length: 3 cm Width: 2 cm Length: 5 cm Width: 4 cm Length: 6 cm Width: 3 cm Length: 7 cm Width: 6 cm 0 1 2 3 Perimeter Area Enlarge by: 2 times Length: Width: 3 times Length: Width: 4 times Length: Width: 2 times Length: Width: 3 times Length: Width: 4 5 6 7 8 9 Perimeter Are 10 11 12
Answer:
bsbsnhs
Step-by-step explanation:
gsgdhbdjdnndnsnnsbsbdnhidfgdhhdjjdndjsjkekkekekekkekkekejekkdir
What is the general form of linear equation class 10?.
The general form of linear equation is expressed in the form of ax+b=0 where a and b are the integers and X is the variable and has the only one solution and the general form of a linear equation in two variables is ax + by + c = 0, where a and b cannot be zero simultaneously.
An equation is a statement that two mathematical expressions having one or more variables are equal And the equations in which the powers of all the variables involved are one are called linear equations. The degree of a linear equation is always one.
Define Linear Equation in One Variable
A linear equation with one variable is one with a single variable of order 1 or less. Where x is the variable, it has the form a x +b = 0.
There is just one solution to this equation. Examples include:
3x = 1
22x-1=0
4x+9=-11
A simple equation is deemed to be a linear equation of two variables when it is given the form ax+by+c=0, according to the Linear Equations in Two Variables CLass 10 textbook. A, B, and C in this scenario should all be constants or real integers, such 2, 3, 4, etc. The a and b coefficients of x and y in this situation shouldn't be equal to zero. Given that a, b, and c are real values, the two unknown variables in this case would be x and y. An illustration of a two-variable linear equation is 4x+5y+3=12.
therefore , the general form of linear equation in one variable and intwo variable are ax+b=0 and ax+by+c=0
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What is the length of the side opposite?.
A right triangle's hypotenuse is its longest side, its "opposite" side is the one that faces a certain angle, and its "adjacent" side is the one that faces the angle in question.
The side opposite the right angle is always the hypotenuse of a right triangle. In a right triangle, it is the longest side. The opposing and neighboring sides are the other two sides. The labels on these sides relate to an angle.
One side is opposite the other at a specific angle. The non-hypotenuse side that lies next to a particular angle is known as the neighboring side. The terms hypotenuse, opposite, and adjacent are used to define the trigonometric functions sine, cosine, and tangent.
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A city double it ize every 24 year. If the population i currently 145,000, what will the population be in 48 year?
The population in 48 year becomes 580,000.
what is Doubling ?
Doubling or Double numbers or doubles simply represent twice the given amount or number.
To double means to add an amount equal to what you already have. An example: If you have one bottle of coke, and you get one more bottle, you have two bottles of coke. Two is the double of one, because, which means you have doubled the amount of coke you had.
As given, if the current population is = 145,000
and after 24 year, it will double its size = 145,000×2 = 290,000
and then in the next 24 years i.e. (48 years later) = 290,000×2 = 580,000
Therefore, the population in 48 year becomes 580,000.
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The store is selling lemons at $0.60 each. Each lemon yields about 2 tablespoons of juice. How much will it cost to buy enough lemons to make four 9-inch lemon pies, each requiring half a cup of lemon juice?
Answer:
$9.60
Step-by-step explanation:
This is a tricky question because it uses different units.
Let's first convert everything to one unit to make things simpler
1 cup = 16 tablespoons
1/2 cup = 8 tablespoons
Each lemon yields 2 tablespoons of juice
Each lemon pie requires 1/2 cup of juice = 8 tablespoons of juice
4 lemon pies will require 4 x 8 = 32 tablespoons of juice
To get 32 tablespoons at 2 tablespoons per lemon we will require 32/2 = 16 lemons
16 lemons at $0.60 per lemon will cost 16 x 0.60 = $9.60 ANS
Why do we use log log?.
Data is displayed in two dimensions using log-log graphs, where both axes have logarithmic scales.
A straight line is depicted on a log-log graph when one variable varies as a constant power of the other. We can determine that X and Y do not have a power law connection if the data points do not form a straight line.
The linear function is equivalently written as log Y = log k + n log X. The statement by John Tukey that "the best thing about being a statistician is that you get to play in everyone's backyard" is amply illustrated by this example.
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80x
/
A company sells shirts for $10 each. Its revenue function is r(x) = 10x.
Its costs are $3 per shirt plus $9,000 of fixed costs. Its cost function is
c(x) = 3x + 9000. Use this information for Problems 13-15. The first
one is done for you.
13. Find the company's revenue and costs if it sells 2000 shirts.
Revenue = $20,000; costs = $15,000
14. Profit equals the difference between revenue and cost. Write the
function, p(x), for this company.
15. In 2012, the company sold 5000 shirts. Find its profit.
in Hercourt Additions and changes to the original content are the respon
a) To find the company's revenue and costs if it sells 2000 shirts, we can substitute 2000 for x in the given revenue and cost functions:
What does a math equation mean?
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
Revenue: r(x) = 10x, so r(2000) = 10(2000) = $20,000
Costs: c(x) = 3x + 9000, so c(2000) = 3(2000) + 9000 = $15,000
b) The profit function, p(x), is the difference between the revenue function and the cost function. So, the profit function for this company is:
p(x) = r(x) - c(x) = 10x - (3x + 9000) = 7x - 9000
c) To find the company's profit in 2012, when it sold 5000 shirts, we substitute 5000 for x in the profit function:
p(5000) = 7(5000) - 9000 = $20,000
So, the company had a profit of $20,000 in 2012 when it sold 5000 shirts.
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The moon is approximately 240,000 miles from earth. What is the distance between the earth and the moon in km?
Answer:
390,000
Step-by-step explanation:
Write an expreion to repreent the um of three time the quare of a number and -7. In your expreion, what i the value of the contant?
The given expression is expressed in an algebraic expression as: 3x^2 - 7 and the value of the number is √7/3
What is an equation?
An equation is the equality between two algebraic expressions, which have at least one unknown or variable.
In mathematics, when we express "square" we mean an exponent equal to two. So the expression “the square of a number ” is represented by:
x^2
When we express “three times” we mean a multiplication by three. So the expression "three time the square of a number" is represented by:
3x^2
When we express “sum” we mean an addition. So the expression "the um of three time the square of a number and -7" is represented by:
3x^2 + ( - 7)
The complete expression "the um of three time the square of a number and -7" in an algebraic expression represented by: 3x^2 - 7 = 0
Finding the value of the constant we get:
3x^2 - 7 = 0
3x^2 = 7
x^2 = 7/3
x = √(7/3)
x = 1.53
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Correctly written question:
Write an expression to represent the sum of three time the square of a number and -7. In your expression, what is the value of the constant?
A farmhouse shelters 11 animals. Some are goats and some are ducks. Altogether there are 34 legs. How many of each animal are there?(with work)
Answer: 6 Goats and 5 Ducks
Hope this helps :)
Step-by-step explanation:
6 goats (4 legs) = 24 legs
5 ducks (2 legs) = 10 legs
6 * 4 = 24
5 * 2 = 10
24 + 10 = 34
6 + 5 = 11
Answer:
6 goats and 5 ducks
Step-by-step explanation:
Given: g+d=11
Goats have 4 legs. Ducks have 2 legs. For total of 34 legs.
Use the word problem to create equation: 4g+2d=34
We can solve for either, we'll solve for g(goat) first:
4g+2d=34
2d=34-4g
d=17-2g
Plug what we found for d into other equation:
g+d=11
g+(17-2g)=11
-g+17=11
-g=-6
g=6
Plug what we found for g into equation to solve for d(duck):
g+d=11
6+d=11
d=5
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Evaluate the expression when a = -5, b = 7, c = -2, and d = 3.2. a-2-b+ (4.7 -d) - c
The value of the expression is -10.5 .
What is expression?
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. Unknown variables, integers, and arithmetic operators are the components of an algebraic expression. There are no symbols for equality or inequality in it.
Here the given expression is ,
a-2-b+(4.7-d)-c
Now put a=-5, b=7 , c=-2 and d=3.2 then
=> -5-2-7+(4.7-3.2)-(-2)
=> -14+(1.5)+2
=> -14+3.5
=> -10.5
Hence the value of the expression is -10.5 .
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How do you find the points of intersection when given a quadratic function and a line?.
When given a quadratic function and a line, the points of intersection can be found by solving for x using the Quadratic Formula.
The Quadratic Formula states that:
x² + ax+ b = 0
where the constants are a, b, and c. We utilise this equation to solve for x in order to determine the places of intersection. In order to accomplish this, we must be aware of both the line's slope and the quadratic function's y-intercept.
The slope of the line can be found by dividing the y-intercept by the distance between the points of intersection (x1 and x2), and then multiplying that number by the slope of the line (y/x).
The y-intercept can be found by simply plugging in x1 into the equation above. Once we have these two pieces of information, we can solve for x using algebraic equations.
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help me solve this quick please
the questions are
1-reflection about the x-axis
2-reflection about the y axis
3- vertical shift upwards by 10
4-vertical shift downward by 10
5-horizontal shift to the right by 10
Answer:
1- Reflection about the x-axis: The equation for this transformation would be: f(x) = -(-5^x + 10) = 5^x - 10. This flips the graph of the original function over the x-axis.
2- Reflection about the y axis: The equation for this transformation would be: f(x) = -(5^x + 10) = -5^x -10. This flips the graph of the original function over the y-axis.
3- Vertical shift upwards by 10: The equation for this transformation would be: f(x) = 5^x +10 + 10 = 5^x + 20. This shifts the graph of the original function upward by 10 units on the y-axis.
4- Vertical shift downward by 10: The equation for this transformation would be: f(x) = 5^x + 10 - 10 = 5^x. This shifts the graph of the original function downward by 10 units on the y-axis.
5- Horizontal shift to the right by 10: The equation for this transformation would be: f(x) = 5^(x-10) + 10. This shifts the graph of the original function to the right by 10 units on the x-axis.
Answer:1- Reflection about the x-axis: The equation for this transformation would be: f(x) = -(-5^x + 10) = 5^x - 10. This flips the graph of the original function over the x-axis.
2- Reflection about the y axis: The equation for this transformation would be: f(x) = -(5^x + 10) = -5^x -10. This flips the graph of the original function over the y-axis.
3- Vertical shift upwards by 10: The equation for this transformation would be: f(x) = 5^x +10 + 10 = 5^x + 20. This shifts the graph of the original function upward by 10 units on the y-axis.
4- Vertical shift downward by 10: The equation for this transformation would be: f(x) = 5^x + 10 - 10 = 5^x. This shifts the graph of the original function downward by 10 units on the y-axis.
5- Horizontal shift to the right by 10: The equation for this transformation would be: f(x) = 5^(x-10) + 10. This shifts the graph of the original function to the right by 10 units on the x-axis.
Step-by-step explanation:
Hello, can someone help me with this?
Answer:
use the graph
Step-by-step explanation:
PLSSS HELP IF YOU TURLY KNOW THISSS
The answer for algebraic expression is Option B 3(-3)
What is Algebraic expression?A mathematical expression made up of variables, coefficients, constants, and operations like addition, subtraction, multiplication, and division is called an algebraic expression. In general, something is considered equal if two of them are the same. Similar to this, analogous expressions in mathematics are those that hold true even when they appear to be different. However, both forms provide the same outcome when the values are entered into the formula.
Given
9-12+(-2)+3(-3)
Subtract: 9 - 12 = -3
Add: the result of step No. 1 + (-2) = -3 + (-2) = -5
Multiple: 3 * (-3) = -9
Add: the result of step No. 2 + the result of step No. 3 = -5 + (-9) = -14
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Scale factor = 2/5
15inches high; 35 inches length
What is the dimensions?
The new dimensions are height is 6 inches and length is 14 inches.
What is scale factor?A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).
The basic formula to find the scale factor of a figure is expressed as,
Scale factor = Dimensions of the new shape ÷ Dimensions of the original shape.
Given that, scale factor = 2/5, 15 inches high and 35 inches length.
Here, height is
2/5 = New height/15
New dimension =30/5
= 6 inches
Length of a shape is
2/5 =New length/35
= 70/5
= 14 inches
Therefore, the new dimensions are height is 6 inches and length is 14 inches.
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Answer in simplest radical form if necessary (NO DECIMALS!). Copy and paste this symbol if needed: √
The value of x from the given figure is 12 units.
What are similar triangles?Two triangles are similar if the angles are the same size or the corresponding sides are in the same ratio. Either of these conditions will prove two triangles are similar.
From the given figure,
Consider ΔDEF and ΔEGF,
∠F=∠F (Reflex property)
EF=EF (Reflex property)
∠DEF=∠EGF=90°
By AA similarity, ΔDEF ~ ΔEGF
So, DF/EF = EF/GF
12/x = x/2
x²=12×2
x=2√6 units
Therefore, the value of x from the given figure is 2√6 units.
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Which angle has sides DB and DC? Select all that apply.
No, rectangle DABC is not the result of a dilation of rectangle HEFG with a center of dilation at the origin.
What is dilation?Dilation is a geometrical transformation that changes the size of a shape or figure. It is one of the four basic transformations of geometry alongside translation, rotation, and reflection. Dilation involves resizing a shape by a scale factor and keeping its overall shape intact. The scale factor is the ratio of the size of the image to the size of the original figure.
Dilation involves a scaling of a shape, where each point on the shape is moved away from or closer to the center of dilation, proportional to its distance from the center. In this case, the angles of rectangle DABC are different from the angles of rectangle HEFG, so it is not the result of a dilation. The angles of rectangle HEFG are ∠2, ∠33, ∠EDC, whereas the angles of rectangle DABC are ∠ADB, ∠BDC, and ∠CDB.
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Please help. I need a response in 48 mins (will give 30 pts)
Answer: 8/17
Step-by-step explanation:
sinA = opp.side/hypotenuse
= BC/AB
= 8/1
If Jon runs 35 miles a week, and Jacky runs 57 miles a week, how much more does Jacky run than Jon?
Answer:
22 miles
Step-by-step explanation:
trust
Find the Average Rate of Change from Equations
According to the given information in the question the average rate of change is 3.
What is average rate of change of a function?Examples of average rates of change include: 80 kilometres per hour is the average speed of a bus. At a pace of 100 each week, a lake's fish population grows. For every 1 volt drop in voltage, the current in an electrical circuit reduces by 0.2 amps.
The average rate at which one item is changing in relation to another is known as the average rate of change. An average rate of change function, put simply, is a calculation that divides the amount of change in one thing by the corresponding amount of change in another.
The formula R = D/T, or rate of change equals the distance travelled, can be used to address rate of change problems in general.
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(1 point) A data set consists of the data given below plus one more data point. When the additional point is included in the data set the sample mean of the resulting data set is 27.917. What is the value of the additional data point?
Note: the additional data point is an integer. If the mean contains decimals, it may be a rounded value.
21, 24, 19, 36, 52, 15, 40, 47, 19, 20, 30
The value of the additional data point is equal to 12.0
What is a sample mean?In Mathematics, a sample mean is sometimes referred to as an arithmetic average and it can be defined as a ratio of the sum of the total number in a data set (population) to the frequency of the data set.
How to calculate the sample mean for the set of data points?Mathematically, the sample mean for this set of data points can be calculated by using the following formula:
Mean = [F(x)]/n
Note: Let the variable x represent the additional data point.
For the total data points, we have;
F(x) = 21 + 24 + 19 + 36 + 52 + 15 + 40 + 47 + 19 + 20 + 30 + x
F(x) = 323 + x.
Now, we can determine the additional data point as follows;
27.917 = 323 + x/12
323 + x = 335.004
x = 335.004 - 323
x = 12.004 ≈ 12.0
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what’s x. please find x for me
Answer:
x = 77°
Step-by-step explanation:
When an angle has its vertex on a circle, the arc that gets cut by sides is double the angle.
So arcDF is double angleEFD.
angleEFD = 74°
arcDF = 148°
arcFH is double angleD.
angleD = 29°
arcFH = 58°
All the arcs of the circle all add up to 360°
arcDF + arcFH + arcDH = 360°
148° + 58° + arcDH = 360°
206 + arcDH = 360°
subtract 206
arcDH = 154°
Again, the arc is double the angle, or the angle is half the arc.
arcDH = 154°
angleDFH = 77°
x = 77°
see image.
How do you find Z score with mean and standard deviation in R?.
A z-score can be calculated using the formula z = (x-)/, where x is the raw score, the mean of the population, and the standard deviation of the population.
The z-score is simply the raw score minus the mean of the population divided by the standard deviation of the population, as the formula demonstrates.
How can I use R to convert data to z-scores?Typically, z-scores, or standardized scores, are calculated by dividing the mean of all data points by the standard deviation of all data points, then subtracting the mean from each individual data point. Again, using scale(), this can be done in one call.
On a TI 84, how can the mean and standard deviation be used to calculate the z-score?Press EDIT after pressing Stat. Press Enter after highlighting L2 and entering the formula (L1-10) / 5.558. In column L2, the z-score for each individual value will be displayed automatically: Note: Press 2 and then 1 to enter "L1" into the formula.
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7. Determine if each sequence represents a function. Explain why
or why not. If it is a function, identify its domain and range.
Create a mapping to verify your answer.
a. 2, 4, 6, 8, 10, ...
b. 1, 0, 1, 0, 1, ...
c. 0, 5, 10, 15, 20, ...
Only a and c represent function
How is a sequence defined?
In mathematics, a sequence is a list of items that is in order (or events). It has members and is similar to a set (also called elements, or terms). The number of ordered elements determines the length of the sequence (potentially infinite).
a. The sequence 2, 4, 6, 8, 10, ... represents a function. The domain of the function is the set of natural numbers, and the range is the set of even natural numbers. We can create a mapping by using the rule "multiply by 2" to match each input value of the domain with its corresponding output value in the range. For example, 2 maps to 4, 4 maps to 8, 6 maps to 12, and so on.
b. The sequence 1, 0, 1, 0, 1, ... does not represent a function. The reason is that for any given input value, the output value is not unique. For example, the input value of 1 maps to both 1 and 0, which means that the function is not well-defined.
c. The sequence 0, 5, 10, 15, 20, ... represents a function. The domain of the function is the set of natural numbers, and the range is the set of multiples of 5. We can create a mapping by using the rule "multiply by 5" to match each input value of the domain with its corresponding output value in the range. For example, 0 maps to 0, 1 maps to 5, 2 maps to 10, and so on.
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i have an axis of symmetry of x= -1 what am i?
The parabola has an axis of symmetry at x= -1.
Step-by-step explanation:
PLEASE HELP I WILL MARK BRAINIEST
Answer:
y = 8
Step-by-step explanation:
The angle represented by (8x - 31)° = angle represented by (6x + 3)° since they are alternate interior angles
8x - 31 = 6x + 3
=> 8x-6x = 3 + 31
2x = 34
x = 17
Angles (8x - 31) and (5y + 35) are adjacent linear angles - they lie on the same straight line. their sum must equal 180
8x - 31 + 5y + 35 = 180
Plugging x = 17
8(17) -31 + 5y + 35 = 180
5y + 140 = 180
5y = 180 - 10 = 40
y = 40/5 = 8
Can you find the sin of a right angle?.
Sine of a right-angled triangle is 1 i.e., sin 90°=1
One of the three fundamental functions in trigonometry, along with cosine and tan functions, is the sine function. The ratio of the opposite side of a right triangle to its hypotenuse is known as the sine x or sine theta.
Let the base of the triangle be ‘x’ and the perpendicular be ‘y’ and θ be the angle
Sine acts as the ratio of the lengths of the opposing side and the hypotenuse side for any right-angled triangle measured from any angle.
sin θ =y/1
When the angle measurement hits the positive y-axis, it will have reached 90°, starting with the first quadrant. Since it now contacts the circle's rim, the value of y changes to 1. Consequently, y's value is changed to 1.
sin θ =y/1=1/1
Therefore, sin 90°=1/1
or, sin 90°=1
Hence, proved.
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