The equation of the line, with slope equal to 5 and passing through the point located at (0 , 2), is 5x - y = -2.
The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.
The standard form of an equation of a line is expressed as ax + by = c, where a and b, if all possible must be integers, are the coefficients of variable x and y, respectively, and c is a constant. Meanwhile, slope-intercept form is given by the formula y = mx + b, where m is the slope of the line and b is the y- intercept. On the other hand, given the slope m and a point on the line (x , y), we can express the equation in point-slope form, (y - y1) = m(x - x1).
Using the point slope form, plug in the values to set up the equation.
(y - y1) = m(x - x1)
where m = 5 and (x1 , y1) = (0 , 2)
(y - 2) = 5(x - 0)
y - 2 = 5x
In slope-intercept form, the equation of the line is:
y - 2 = 5x
y = 5x + 2
In standard form, the equation of the line is:
y = 5x + 2
5x - y = -2
To learn more about equation of line: brainly.com/question/19417700
#SPJ4
what is 109 x 3= the answer is
327
Answer:
109 x 3 = 327
Step-by-step explanation:
How does the First Amendment to the Constitution affect American society?
The right to bear arms means many Americans own guns for protection.
The right to bear arms means many Americans own guns for protection.
The right to due process gives Americans a strong sense of ownership of their personal property.
The right to due process gives Americans a strong sense of ownership of their personal property.
The right to a jury trial has created a strong sense of fairness in the criminal justice system among Americans.
The right to a jury trial has created a strong sense of fairness in the criminal justice system among Americans.
The right to a free press allows Americans to have access to many independent sources of news and information.
The First Amendment to the Constitution affect American society as D. The right to a free press allows Americans to have access to many independent sources of news and information.
What is Constitution?It should be noted that Constitution simply refers to the rules and laws that guide a group of people especially a country.
In this case, the First Amendment to the Constitution affect American society as The right to a free press allows Americans to have access to many independent sources of news and information.
In conclusion, the correct option is D.
Learn more about Constitution on:
brainly.com/question/453546
#SPJ1
The correct answer is "The right to a free press allows Americans" to have access to many independent sources of news and info
Explanation:
The First Amendment to the constitution was ratified in 1791, in this it was established government could not interfere in the right to exercise religion or assemble as well as the rights of freedom of speech and freedom of the press. This last aspect implies the government cannot interfere in the circulation of information, according to this, citizens have the right to create sources of news and information to report news or express opinions. Thus, the First Amendment affects American society because "the right to a free press allows Americans to have access to many independent sources of news and info".
Help me Pleaseee this has to be turned in by tomorrow I am a 7th grader for tips to get an accurate answer
Answer:
Parallelogram S: b = 7, h = 6
Parallelogram T: b = 3, h = 6
Area of Parallelogram S = 42
Area of Parallelogram T = 18
Step-by-step explanation:
The bases and heights of each parallelogram are given by the arrows, just count the number of boxes you see.
Area = base × height, so you just multiply these numbers. Area of parallelograms is found the same way as area for squares/rectangles.
7 × 6 = 42 and 3 × 6 = 18
Y=35x1 where x is distance and y is height
The average rate of change of the equation is 35
How to determine the average rate of change?The equation is given as
y = 35x^1
Evaluate the quotient x^1
So, we have
y = 35x
The above equation is a proportional linear equation
A proportional linear equation is represented as
y = mx
Where
m represents the average rate of change
By comparison, we have
m = 35
Hence, the average rate of change of the equation is 35
Read more about average rate of change at
https://brainly.com/question/11524125
#SPJ1
Complete question
Given the equation y = 35x^1 where x is distance and y is height, calculate the average rate of change
what is a vonoroi diagram in SIMPLE terms please help!
Answer:
Image result for what is a voronoi diagram in SIMPLE terms please help!
In mathematics, a Voronoi diagram is a partition of a plane into regions close to each of a given set of objects. In the simplest case, these objects are just finitely many points in the plane (called seeds, sites, or generators)
Step-by-step explanation:yes
Determine whether set of numbers can be the measures of the sides of a triangle. If so, classify the triangle as acute, obtuse, or right. Justify your answer. 7,24,25
Given set of numbers 7, 24, 25 represent a right triangle.
By the triangle inequality theorem , the sum of the lengths of any two sides should be greater than the length of the third side.
Since the sum of the lengths of any two sides is greater than that of the third side, the set of numbers are the measures of a triangle.
Now we find the type of triangle.
We find the sum of the squares of the two smaller sides, and compare the sum to the square of the largest side.
the sum of the squares of the two smaller sides is,
= 7² + 24²
= 49 + 576
= 625
= 25²
Since the sum of the squares of the two smaller sides is equal to the square of the largest side, by Pythagoras theorem the triangle must be right triangle.
Therefore, given set of numbers 7, 24, 25 represent a right triangle.
Learn more about the triangle inequality theorem here:
https://brainly.com/question/1163433
#SPJ4
Find the center and the radius of each circle. x²+2 x+1+y²=4
The center and radius of the circle given by the equation x^2 + 2x + 1 + y^2 = 4 is (-1 , 0) and 2, respectively.
The standard form of the equation of circle is given by
(x - h)^2 + (y - k)^2 = r^2
where (h , k) is the location of the center and r is the radius of the circle.
On the other hand, the general form of the equation of circle is given by
x^2 + y^2 + Dx + Ey + F = 0
where D = -2h, E = -2k, and F = h^2 + k^2 -r^2.
If the equation of the circle in general form is x^2 + 2x + 1 + y^2 = 4, then the coefficients are:
D = 2
E = 0
F = 1 - 4 = -3
If D = -2h and D = 2, then
2 = -2h
h = -1
If E = -2k and E = 0, then
0 = -2k
k = 0
If F = h^2 + k^2 -r^2 and F = -3, then
-3 = (-1)^2 + 0^2 - r^2
r^2 = 1 + 0 + 3
r^2 = 4
r = 2
Learn more about equation of a circle here: brainly.com/question/1559324
#SPJ4
10 = z/2 + 7 what is 10
Answer:
19
I first do plus 2and 7 and 10=z
line k passes through the points (-12, 10) and (6, 1) line l is perpendicular to line k with y-intercept 6 find the x-intercept of line l
The line l which is perpendicular to line k has an x intercept of -3.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The standard equation of a line is:
y = mx + b
where m is the slope and b is the y intercept.
Line k passes through the points (-12, 10) and (6, 1), hence:
Slope = (1 - 10) / (6 - (-12)) = -1/2
Two lines are perpendicular if the product of their slopes is -1. Line L is perpendicular to line k, with y-intercept 6. hence:
Slope of line l = 2
Equation of line l is:
y = 2x + 6
At y = 0:
0 = 2x + 6
x = -3
The line l which is perpendicular to line k has an x intercept of -3.
Find out more on equation at: https://brainly.com/question/13763238
#SPJ1
Which step is included in the graph of the function f(x)=[x-17?
O y=-5 for-4≤x<-3
O y=-2 for -2≤x<-1
O y=-2 for -2
O y=-5 for -4
Answer:
y = -2 for -2 < x ≤ -1
Step-by-step explanation:
Ceiling function
[tex]f(x) = \left\lceil x \right\rceil[/tex]
The least integer that is greater than or equal to x.
Given ceiling function:
[tex]f(x) =\left\lceil x-1 \right\rceil[/tex]
Evaluate values in the given intervals.
[tex]\boxed{-4 \leq x < -3}[/tex]
[tex]\implies f(-4) =\left\lceil -4-1 \right\rceil=\left\lceil -5 \right\rceil=-5[/tex]
[tex]\implies f(-3.1) =\left\lceil -3.1-1 \right\rceil=\left\lceil -4.1 \right\rceil=-4[/tex]
[tex]\boxed{-2 \leq x < -1}[/tex]
[tex]\implies f(-2) =\left\lceil -2-1 \right\rceil=\left\lceil -3 \right\rceil=-3[/tex]
[tex]\implies f(-1.1) =\left\lceil -1.1-1 \right\rceil=\left\lceil -2.1\right\rceil=-2[/tex]
[tex]\boxed{-2 < x \leq -1}[/tex]
[tex]\implies f(-1.9) =\left\lceil -1.9-1 \right\rceil=\left\lceil -2.9 \right\rceil=-2[/tex]
[tex]\implies f(-1) =\left\lceil -1-1 \right\rceil=\left\lceil -2 \right\rceil=-2[/tex]
[tex]\boxed{-4 < x \leq -3}[/tex]
[tex]\implies f(-3.9) =\left\lceil -3.9-1 \right\rceil=\left\lceil -4.9 \right\rceil=-4[/tex]
[tex]\implies f(-3) =\left\lceil -3-1 \right\rceil=\left\lceil -4\right\rceil=-4[/tex]
Therefore, the step that is included in the graph of the given ceiling function is: y = -2 for -2 < x ≤ -1.
Graph of the parent ceiling function f(x) = ⌈x⌉
The graph of the parent function has open dots at (x, x+1) and closed dots at (x, x). Each segment is joined with a horizontal line (step).
The open dot means the value is not included, whereas the closed dot means the value is included.
To graph the given ceiling function f(x) = ⌈x - 1⌉
(See attachment).
The y-value is 1 less than the parent function, therefore place open dots at (x, x) and closed dots at (x, x-1). Join each segment with a line (step).From inspection of the attached graph of the given ceiling function:
The step for y = -5 is -5 < x ≤ -4 (shown in blue).The step for y = -2 is -2 < x ≤ -1 (shown in red).This proves that the only step that is included in the graph of the given ceiling function from the given answer options is:
y = -2 for -2 < x ≤ -1On a coordinate graph, your house is located at the origin (0,0) You leave your house and walk 6 blocks north. Then you turn and walk 22 blocks west. Since it is getting late, you decide to walk straight back home. How many blocks is it to walk straight back to your house? Round your answer to the nearest tenth
Answer:
22.8 blocks
Step-by-step explanation:
We can think of your path as traveling on a coordinate plane. You start by walking 6 units in the positive y direction, then 22 units in the negative x direction, then walking from this point (-22, 6) back to (0, 0)
This path draws a right triangle. The shorter leg is 6 units long, and the longer end is 22 units long. You want to find the hypotenuse of this triangle.
The hypotenuse is found using the Pythagorean theorem:
[tex]a^2+b^2=c^2[/tex]
A and B represent the sides of the triangle, and c represents the hypotenuse!
Before plugging in the functions, isolate c, since that's the answer we're looking for:
[tex]a^2+b^2=c^2\\c=\sqrt{a^2+b^2}[/tex]
Now, plug in the side lengths of the triangle:
[tex]c=\sqrt{6^2+22^2}[/tex]
Now simplify!
[tex]c=\sqrt{36+484} \\x=\sqrt{520} x=22.8[/tex]
It is 22.8 blocks back to your house! Hope this helps!
Identify a pattern and find the next three numbers in the pattern.
3,6,10,15, . . .
The pattern exists described as a sequence of repeating objects, shapes, or numbers. Patterns can also occasionally be referred to as a series.
The pattern follows the rule = Σn+(n+1)
The next three numbers in the pattern be 3, 6, 10, 15, 21, 28, 36.
What is meant by pattern?A recurring arrangement of numbers, forms, colors, and other elements constitutes a pattern in mathematics. The pattern can be connected to any kind of occasion or thing. When a group of numbers are arranged in a particular way, the arrangement is referred to as a pattern. Patterns can also occasionally be referred to as a series.
Let the numbers in the pattern be 3,6,10,15, . . .
t1 = 1 + 2 = 3
t2 = 3 + 3 = 6
t3 = 6 + 4 = 10
t4 = 10 + 5 = 15
t5 = 15 + 6 = 21
t6 = 21 + 7 = 28
t7 = 28 + 8 = 36
The pattern follows the rule = Σn+(n+1)
Therefore, the next three numbers is 21, 28, 36.
To learn more about identifying patterns, refer to:
brainly.com/question/24565868
#SPJ4
Polygon Q is a scaled copy of Polygon P using a scale factor of
1/2 Polygon Q's area is what fraction of Polygon P's area?
Polygon Q is a scaled replica of Polygon P with a factor of half. The area of Polygon Q is a proportion of the area of Polygon P= 1/4
Polygons described as:A polygon is a plane figure characterized by a fixed amount of straight-line segments joined to form a closed polygonal chain. A polygon is a bounded plane region, a bounding circuit, or both. The segments of such a polygonal circuit are referred to as its edges or sides.
What is an example of a polygon?Polygons are made up of triangles, hexagons, pentagons, and quadrilaterals. The name indicates how many sides the form has. A triangle, for example, has three sides, whereas a quadrilateral has four.
According to the given data:We are aware of this.
If the areas of two figures were similar, the ratio of their areas equals the scale factor squared.
Let
z → the scale factor
x → polygon q’s area
y → polygon p’s area
So,
Z² = x/y
Z is given as = 1/2
Putting value we get:
(1/2)² = x/y
(1/4) = x/y
x = 1/4(y)
The fraction of Polygon P's area = 1/4
To know more about polygon visit:
https://brainly.com/question/24464711
#SPJ9
The city of San Diego has an average monthly rainfall of 0.87 inches per month. Brick reports that the average rainfall for the first three
months was 2.02 inches per month and that the average rainfall for the next 7 months was 0.25 inches.
What does the average rainfall for the rest of the year need to be per month so that San Diego meets its average monthly rainfall
marks for the year? Round your answer to the nearest hundredth
The average rainfall for the rest of the year need to be per month is 1.31 inches per month.
According to the statement
We have to find that the average rainfall for the rest of the year.
So, For this purpose, we know that the
The average value in a set of numbers is the middle value, calculated by dividing the total of all the values by the number of values.
From the given information:
an average monthly rainfall of 0.87 inches per month. and the average rainfall for the first three months was 2.02 inches per month and that the average rainfall for the next 7 months was 0.25 inches.
Then
An average monthly rainfall per month = 0.87 inches
An average monthly rainfall per year = 0.87 *12
An average monthly rainfall per year = 10.44 inches
Then
The average rainfall for the first three months was 2.02 inches per month
The average rainfall for the first three months = 2.02 *3
The average rainfall for the first three months = 6.06
And
The average rainfall for the next seven months = 0.25*7
The average rainfall for the next seven months = 1.75
Then
The remaining average rainfall in one year = average monthly rainfall per year - (average rainfall for the first three months + average rainfall for the next seven)
The remaining average rainfall in one year = 10.44 - (6.06 + 1.75)
The remaining average rainfall in one year = 10.44 - (7.81)
The remaining average rainfall in one year = 2.63
And then
The remaining average rainfall in 2 months = 2.63
The remaining average rainfall in 2 months per month = 2.63/2
The remaining average rainfall in 2 months per month = 1.31.
So, The average rainfall for the rest of the year need to be per month is 1.31 inches per month.
Learn more about average value here
https://brainly.com/question/20118982
#SPJ9
Sketch the solid that results when the region enclosed by the given equations is revolved about the x -axis.
y = x²
y = 2x
y = x² , y = 2 x are the region enclosed by the given equations is revolved about the y -axis.
What exactly is a closed area?
All space between a floor and ceiling that is enclosed on all sides by solid walls or windows, except doors that stretch from the floor to the ceiling, is referred to as an enclosed area.
What do you mean by the region that a closed curve encloses?
The sum of all infinitely thin rectangles with height f(x), enclosed by the curve y=f(x), and the x-axis between x=a and x=b, is what we mean when we write baf(x)dx.
Whether contained or not?
Use enclosed at all times. No longer regarded as a regular variety, enclosed would even be mistaken for another word by many readers.Use enclose, encloses, and enclosing rather than inclose for other words that are similar to enclosed.The graph is attached in equation y = x² , y = 2 x
Learn more about enclosed region
brainly.com/question/15517451
#SPJ4
How many solutions does each of the following equations have?
3(x-7)+4=x-1
Answer:
1
Step-by-step explanation:
It is a linear equation, so it has 0 or 1 solution (or infinitely many).
You could view this one as the intersection of line y=3(x-7)+4 and the line y=x-1. There is one intersection, and it is at x=8.
Find the coordinates of point I so Δ I K L is the indicated type of triangle. Point J has coordinates (0,0) and point K has coordinates (2 a, 2 b) .
isosceles triangle
The coordinate of the point L is such that ΔL K L is an isosceles triangle that will be either (0,y) or (2a,y).
It is given that in ΔL K L , J has coordinates (0,0) and K has coordinates (2 a, 2 b) .
We have to find the coordinates of point L so that , ΔL K L is an isosceles triangle.
What is a triangle ?
A triangle is a 3-sided shape. There are three sides and three angles in every triangle, some of which may be the same.
As per the question ;
The ΔL K L is an isosceles triangle,
J has coordinates (0,0)
K has coordinates (2 a, 2 b) .
The possible coordinate of the point L will be (0,y) or (2a,y).
Let's check it.
Using the distance formula ;
JK = [tex]\sqrt{(2a-0)^2 + (2b -0)^2}[/tex]
JK = [tex]\sqrt{(4a^2 + 4b^2)}[/tex]
JK = [tex]2\sqrt{a^2 + b^2}[/tex]
Similarly ;
JL = [tex]\sqrt{0^2 + y^2}[/tex]
JL = y
And
KL = [tex]\sqrt{4a^2 + (2b - y)^2}[/tex]
Let's say two sides JK and KL are equal at any value of a , b and y.
Then ;
The two sides are of equal length , so , we can conclude that this is an isosceles triangle.
Thus , the coordinate of the point L is such that ΔL K L is an isosceles triangle that will be either (0,y) or (2a,y).
To learn more about triangles click here ;
https://brainly.com/question/2773823
#SPJ4
Summarize the possible relationships for the y -intercepts, slopes, and number of solutions in a system of two linear equations in two variables.
A consistent system of equations has at least one solution.
A consistent system is considered to be an independent system if it has a single solution, such as the example we just explored. The two lines have different slopes and intersect at one point in the plane.
A consistent system is considered to be a dependent system if the equations have the same slope and the same y-intercepts. In other words, the lines coincide so the equations represent the same line. Every point on the line represents a coordinate pair that satisfies the system. Thus, there are an infinite number of solutions.
Another type of system of linear equations is an inconsistent system, which is one in which the equations represent two parallel lines. The lines have the same slope and different y-intercepts. There are no points common to both lines; hence, there is no solution to the system.
For more information on slopes click on the link below:
https://brainly.com/question/3493733
#SPJ4
If 35% of a number is 63 and 60% of the same number is 108, find 25% of that number.
Answer:22.05
hope it help
and have a good day
Answer:
45
Explanation
35% is 63
so 5% is 9
so 100% is 180 cuz 5 multiplied by 20 is 100
so 25 % is 25 divided by 100 is 0.25×180 which is 45
hope that helps
Can somebody please Help me please!!!and thank you!!!!!!!
Answer:
17.25 < 17.252
Step-by-step explanation:
17.25 means 17.250. So, 17.250 is less than 17.253, which is correct. The other answer choices are incorrect because the sign is pointed the wrong way. 29.60 is not greater than 29.65, so that's incorrect. 21.51 is greater than 21.49. That is not an answer choice though, so that answer choice is incorrect. 7.602 is not greater than 7.612, so that is incorrect.
Hope this helps! :)
Somebody help me ASAP
Answer:
⬤ = 8
⬛ = 6
Step-by-step explanation:
⬤ = x
⬛ = y
x + y = 14
x - y = 2
add the numbers on top of each other together:
add x to x = 2x , y + -y = 0 , 14 + 2 = 16
2x = 16
divide both sides by 2
x = 8, plug this back into the equation
8 + y = 14
8 - y = 14
y = 6
Name the property of real numbers illustrated by each equation.
(2√7) . √3 = 2(√7 . √3)
Associative Property Of Addition illustrated by each equation.
(2√7) . √3 = 2(√7 . √3)
What is Associative Property Of Addition?The total of three or more integers is constant according to the associative property of addition, regardless of how the numbers are arranged.The grouping of numbers does not alter their sum, according to the associative characteristic of addition. For instance, 75 + (81 + 34) = 75 + 115 = 190; and 75 + (81 + 34) = 75 + (81 + 34) = 156 + 34 = 190.According to the associative property, no matter how the addends are grouped, the total or product of adding or multiplying three or more integers will always be the same (or the multiplicands).This law essentially asserts that you can rearrange the numbers in a problem without changing the solution when adding or multiplying them.To know more about Associative Property Of Addition, refer to the following link:
https://brainly.com/question/2843406
#SPJ4
The formula for converting degrees Celsius to degrees Fahrenheit is F=-C+32. Solve this formula for C.
Answer:
C = 32 - F
Step-by-step explanation:
that is the solution above
1. Find an equivalent ratio to 12:9 such that the second number is 3.
O a. 6:3
O b. 4:3
O c. 9:3
Answer:
B. 4:3
Step-by-step explanation:
Divide both by 3:
12/3 = 4
9/3 = 3
4:3
a. 0.7 ÷ 2 = whattttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttt
Answer:
0.7/2=0.35
Step-by-step explanation:
Determine whether -FG is tangent to ®E . Justify your answer.
Line segment FG is not tangent to circle E.
What is Tangent:
The tangent is defined as a line touching circles or an ellipse at only one point. Suppose a line touches the curve at P, then the point “P” is called the point of tangency. In other words, it is defined as the line which represents the slope of a curve at that point.
What is Line Segment:
A line segment has two definite endpoints in a line. The length of the line segment is fixed, which is the distance between two fixed points. The length here can be measured by metric units such as centimeters (cm), millimeters (mm) or by conventional units like feet or inches.
Now, According to the problem
The tangent line to a circle makes an angle of 90 degrees with the radius.
If |FG| is tangent to circle E.
then,
30^2 = 26^2 + 17^2
which is not true.
Therefore, line segment FG is not tangent to circle E.
To know more about "Tangent and Line Segment"
Refer this link:
https://brainly.com/question/8788771
#SPJ4
please help me witht this math problum.
Answer: 1/3
Step-by-step explanation:
Translate the sentence into an equation.
Five less than the product of 3 and a number equals 6.
Use the variable b for the unknown number.
Answer:
3b - 5 = 6
Step-by-step explanation:
3b - 5 = 6
Find the center and the radius of each circle. x²+y²-6 x-2 y+4=0
The equation of the circle x^2 + y^2 - 6x - 2y + 4 = 0 has a radius of √6 and a center located at (3 , 1).
The standard form of the equation of circle is given by
(x - h)^2 + (y - k)^2 = r^2
where (h , k) is the location of the center and r is the radius of the circle.
On the other hand, the general form of the equation of circle is given by
x^2 + y^2 + Dx + Ey + F = 0
where D = -2h, E = -2k, and F = h^2 + k^2 -r^2.
If the equation of the circle in general form is x^2 + y^2 - 6x - 2y + 4 = 0, then the coefficients are:
D = -6
E = -2
F = 4
If D = -2h and D = -6, then
-6 = -2h
h = 3
If E = -2k and E = -2, then
-2 = -2k
k = 1
If F = h^2 + k^2 -r^2 and F = 4, then
4 = 3^2 + (1)^2 - r^2
r^2 = 9 + 1 - 4
r^2 = 6
r = √6
Learn more about equation of a circle here: https://brainly.com/question/1559324
#SPJ4
The amount of a commission is directly proportional to the amount of a sale. A realtor received a commission of 48,000 on the sale of an 800,000 house. How much would the commission be on a 650,000 house?
How much would the commission be on a 650,000 house? $39,000
Given:
Rate of the house 1= $8,00,000
Commission for the house 1=$48,000
Rate of the house 2= $6,50,000
Commission for the house 2=x
What is the commission for the house 2?
8,00,000 ⇒48,000
6,50,000 ⇒ x (directly proportional)
On cross multiplication,
[tex]8,00,000 *x= 48,000*6,50,000\\\\x=\frac{48,000*6,50,000}{8,00,000} =39,000[/tex]
Commission for the house 2 = $39,000
To learn more about direct proportionality , refer:
https://brainly.com/question/25773497
#SPJ4
