The equation of line parallel to the given equation and goes through the given point is y = 7x - 26.
What is the equation of line parallel to the given equation and goes through the given point?Given the data in the question;
Equation: y = 7x + 3Point: (-4,-2)First, we determine the slope by comparing the equation with the slope intercept formula ( y = mx + b )
y = 7x + 3
Hence,
Slope m = 7
Next, we use the point-slope formula y-y₁ = m( x-x₁ ) to determine the equation of the line parallel.
Note that, the slopes must equal.
Given that; slope m = 7, Point: (-4,-2)
Plug into the point-slope formula and simplify.
y-y₁ = m( x-x₁ )
y - (-2) = 7( x - (-4) )
y + 2 = 7( x + 4 )
y + 2 = 7x + 28
y = 7x + 28 - 2
y = 7x - 26
Therefore, the equation of line parallel to the given equation and goes through the given point is y = 7x - 26.
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6 Sasha thinks of a number.
She adds 1 to her number then multiplies the result by 5.
a Use a mapping to write this as a function.
The answer Sasha gets is 11.
b Use inverse functions to work out the number Sasha thought of in the beginning.
Show all your working.
Find a*b
a = 4i + 8j
b = -2i + 3j
i think i know the answer but i still need help…
The solutions for 'u' are u ≤ -5 and u ≤ 1
How to solve the inequality
Given the inequalities;
-3u ≤ 15 2u - 1 ≤ 1Let's solve for u in the expression
-3u ≤ 15
Make 'u' the subject
-3u/3 ≤ 15/ -3
u ≤ -5
Let's solve for 'u' in the expression
2u - 1 ≤ 1
collect like terms
2u ≤ 1 + 1
Add like terms
2u ≤ 2
Make 'u' the subject
u ≤ 2/ 2
u ≤ 1
Thus, the solutions for 'u' are u ≤ -5 and u ≤ 1
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Write an equation of the line through each pair of points in slope-intercept form.
(0,5) and (3,3)
The equation of line is y = (-2/3)x + 5
Given the points:
(x₁, y₁) = (0, 5)
(x₂, y₂) = ( 3, 3)
The slope-intercept form:
y = mx + b
Where, m is the slope and b is the y-intercept, that is (0, b)
The formula for slope:
m = (y₂ – y₁) / (x₂ – x₁)
We have given
x₁ = 0
x₂ = 3
y₁ = 5
y₂ =3
So,
m = (3 – 5) / (3 – 0) = -2/3
here, we have b = 5
Therefore we have the equation of the line as:
y = mx + b
That is the equation of line is y = (-2/3)x + 5
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A number line can represent positions that are north and south of a truck stop on a highway
Positive positions are north of the truck stop and negative positions are south of the truck stop. What is the value, in miles, of each position on a number line?
1. The truck stop ______
2. 5 miles north of the truck stop _____
3. 3.5 mlles south of the truck stop ____
WILL GIVE BRAINLIEST, TYYY !
Using integer numbers, the values of the positions in this problem are given as follows:
1. 0.
2. 5.
3. -3.5.
What are integer numbers?Integer number are numbers that can have either positive or negative signal, but are whole numbers, meaning that they have no decimal part.
In the context of each problem, integer numbers may have different representations, and for this problem, we have that:
The truck stop is the origin, that is, position zero.Positions north of the truck stop will be represented by positive values.Positions south of the truck stop will be represented by negative values.Hence:
5 miles north is represented by the integer 5.3.5 miles south is represented by the integer -3.5.Hence the values of the positions in this problem are given as follows:
1. 0.
2. 5.
3. -3.5.
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PLEASE HELP!!!!!!!!!!
Answer:
m∠ FHC = 87°
Step-by-step explanation:
Hello!
Angle EHD and FHC are vertical angles, meaning they are non-adjacent angles formed by intersecting lines.
The two intersecting lines are EF and DC, and angles EHD and FHC are formed as non-adjacent angles.
Vertical Angles are congruent in measure.
Therefore, Angle FHC is also 87°.
Which set of numbers are irrational number
Answer:
numbers like 9.58596638927, pi, square root of 2, or square root of 11
One of the planet Saturn's rings has a diameter of approximately 2.5 × 105
kilometers. What is the diameter of the ring, in kilometers, written in standard
notation?
A.
2,500
B.
25,000
C. 250,000
D. 2,500,000
The diameter of the ring, in kilometers, written in standard notation is 250000 kilometers
What is the diameter of the ring, in kilometers, written in standard notation?The given parameters are:
Diameter = 2.5* 105 kilometers
Rewrite properly as
Diameter = 2.5* 10^5 kilometers
Express 10^5 as 100000
So, we have:
Diameter = 2.5* 100000 kilometers
Evaluate the product
Diameter = 250000 kilometers
Hence, the diameter of the ring, in kilometers, written in standard notation is 250000 kilometers
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13. What is the mean of the data set in the box below? −8, −6, −2, 0, −6, −8, 4, −7, −8, 1 A. −8 C. −6 B. −7 D. −4
Answer: D. -4
Step-by-step explanation:
-8 + -6 + -2 + 0 + -6 + -8 + 4 + -7 + -8 + 1= - 40
-40 divided by 10= -4
(You're dividing by 10 because there are 10 numbers that you added up)
The mean is -4.
How to draw 2 number lines that show 0.200 and 1/5 are equivalent
We create a number line with a range from 0 to 1.0 and divide it into 5 equal segments to demonstrate the equality between 0.200 and 1/5.
What is a Number Line?The visual representation of numbers on a straight line, either horizontally or vertically, is known as a number line. When numbers are written down on a number line, it is straightforward for humans to compare them and perform basic arithmetic operations on them. One might assume that a number line starts at zero (0). There are only negative numbers to the left of zero and only positive numbers to the right of zero. In other words, as we move to the right on a number line, the value of the numbers increases. This shows that the numbers on the right are more numerous than those on the left.
We create a number line with a range from 0 to 1.0 and divide it into 5 equal segments to demonstrate the equality between 0.200 and 1/5.This line will include points at 0.2, 0.4, 0.6, 0.8, and 1.0.Next, we create a second number line that has five equally spaced segments and ranges from 0 to 5/5.This line will have the following points: 1, 2, 3, 5, 4, and 5/5.These values of 0.200 and 1/5 will be equivalent, as demonstrated by the equal segments.To know more about the number line, visit:
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Determine a base area and height for each shape
You have to show the picture of what your talking about. Please do so if you want someone to answer your question.
Solve the equation. Check your solution.
8.32=4.1z+10.5
Pls help.
Answer:
z = -0.5317073
Step-by-step explanation:
Get variable on left and all constants on right
-4.1z = 10.5 - 8.32
-4.1z = 2.18
Divide both sides by -4.1
z = -0.5317073
To check:
8.32 = 4.1(-0.5317073) + 10.5
Mayumi rides her bike around a park . each lap around the park is two/ three . mayumi rides of total of three. how many laps around the park mayumi ride ? write your answer as a whole number of laps plus a fraction of a lap you can use the model to help.
Two expression with equal sign in between is equation. If Mayumi rides her bike around a park . each lap around the park is two/ three . Mayumi rides of total of three. Then 4 1/2 laps around the park mayumi ride.
What is Equation?
Two expression with equal sign in between is called as Equation.
Mayumi rides her bike around a park . each lap around the park is two/ three . mayumi rides of total of three. The number of laps around the park mayumi ride be x.
We convert this given data as a expression as given
2x/3=3
Apply cross multiplication.
2x=9
x=9/2,
We need to write answer as a whole number of laps plus a fraction of a lap.
x=4 1/2
Therefore 4 1/2 laps around the park mayumi ride.
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Answer: Mayumi Rides 4 whole laps, plus 1/2 of a lap.
Step-by-step explanation:
3/7 divided by 11/21 = 3/7 x
The solution to the given equation 3/7 divided by 11/21 = (3/7)x is x = 21/11.
What is the solution to the given equation?Given the equation in the question;
3/7 divided by 11/21 = 3/7 x
3/7 ÷ 11/21 = (3/7)x
To divide two fractions, multiply the first fraction by the reciprocal of the second fraction.
3/7 ÷ 11/21 = (3/7)x
3/7 × 21/11 = (3/7)x
( 3 × 21 )/( 7 × 11 ) = (3/7)x
63/77 = (3/7)x
Remove the parenthesis
63/77 = (3/7) × x/1
63/77 = ( 3 × x )/( 7 × 1)
63/77 = 3x/7
Cross multiply
63 × 7 = 3x × 77
441 = 231x
231x = 441
Divide both sided by 231
231x/231 = 441/231
x = 441/231
x = 21/11
The solution to the given equation 3/7 divided by 11/21 = (3/7)x is x = 21/11.
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Caroline is the youngest of four siblings whose ages are consecutive odd integers. If the sum of their ages is 9696, find Caroline's age.
Answer:
2421 or 21
Step-by-step explanation:
Hello!
Consecutive odd integers are set of odd integers that come right after each other.
Let "C" be Caroline's age. Caroline's next older sibling would be C + 2, as odd integers come to every two numbers, and the next would be C + 4, and finally C + 6.
If we add up all the expressions, we should get 9696.
Solve for CC + C + 2 + C + 4 + C + 6 = 96964C + 12 = 96964C = 9684C = 2421The solution to this question does not seem reasonable. I assume that the correct sum of the age should be 96, given 9696.
If this is the case, then Caroline's age would be 21, using the same general logic.
Find the arithmetic mean a n of the given terms. a n₋₁ = r, a n₊₁=s
The arithmetic mean a n of the given terms a n₋₁ = r, a n₊₁=s is
[tex]a_{n}[/tex] = [tex](a_{n+1} - a_{n-1})/2[/tex].
What is arithmetic mean?a n₋₁ = r, a n₊₁=s is
[tex]a_{n}[/tex] = [tex](a_{n+1} - a_{n-1})/2[/tex]
The arithmetic mean is the most straightforward and widely used method of calculating a mean or average. It only requires adding up a group of figures, then dividing the result by the entire amount of figures in the series. Consider the numbers 34, 44, 56, and 78 as an example. It totals 212.
The mean or arithmetic average are other names for the arithmetic mean. It is determined by adding up each number in a particular data set, then dividing the result by the overall number of items in the data set. For uniformly distributed integers, the middle number serves as the arithmetic mean (AM).
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Beau buys a 3-pound of trail mix for a hike. he wants to make one-ounce bag of trail mix for his friends with whom he is hiking how many one-ounce bags can he make?
Using conversion, Beau can make 48 one-ounce bags of trail mix from the 3-pound trail mix he bought for the hike.
To know how much one-ounce bags of trail mix can he make from the 3-pound trail mix, convert first the amount of trail mix in pounds to ounce.
In mathematics, conversion is the process of changing the value of one form or unit to another. It can be changing ones unit of length, weight, volume or even currency to another.
Converting pounds to ounce,
1 pound = 16 ounces.
If Beau has 3 pounds of trail mix, equivalently, converting pounds to ounces, he has:
1 pound = 16 ounces
3 pounds = 3(16 ounces)
3 pounds = 48 ounces
If he wants to make one-ounce bag of trail mix from the 3-pound of trail mix (= 48 ounces), divide it by one ounce to get how many bags he can make.
number of one-ounce bag = 48 ounces/1 ounce
number of one-ounce bag = 48
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A women's coat comes in sizes 4,6,8 , or 10 in black, brown, ivory, and cinnamon. How many different coats could be selected?
As women's coat comes in sizes 4,6,8 , or 10 in black, brown, ivory, and cinnamon , possibility of selection of different coats is equal to 16.
As given in the question,
Availability of size number in women's coat = 4, 6, 8, or 10
⇒N(S) =4
Availability of color in women's coat = black, brown, ivory, and cinnamon
⇒ N(C) =4
Possibility of selection of different women's coats = N(S) × N (C)
=4 × 4
=16
Therefore, the possibility of selection of different coats is equal to 16 as per the availability of women's coat sizes and colors.
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Find the distance between each pair of points.
A(14,-3), B(9,-9)
Answer: (24, -12)
because 14 + 9 is 24 ob. and -3 + -9 will be 3+9 with the - so it's -12
C=(r+z / 3) h
what does r equal
Answer:
r= 3C/h - z
Explanation:
divide each side to isolate the variable.
Complete the statement.
7-(-4) is
direction.
units from 7 in the
7-(-4) is 4 units from 7 in the negative direction.
The number line keeps going both ways. You can include 6, 7, and so on, all the way up to the hundreds, thousands, and beyond, because the set of natural numbers only extends to the right.
A number line is a diagram that shows numerical values along a straight line that can be drawn either horizontally or vertically. It's simple for us to compare and compute basic arithmetic operations on numbers when they are written down on a number line. A number line's origin is typically thought to be zero (zero). There are only positive numbers to the right of zero and only negative numbers to the left of zero.
therefore,
7 - (-4)
= 7 + 4
= 11
when we simplify the expression we get the answer as 11 units
the result is that 11 units is 4 units away from 7 in a negative direction.
Hence we get the complete sentence.
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If the sum of 12 numbers is 480 then what is their mean? (a) 20 (b)40 (c) 30 (d)24
Answer:
A
Step-by-step explanation:
40 x 12 = 480
The table shows information about the
faces, edges and vertices for some
pyramids.
Shape of Faces Edges Vertices
base
Triangle 4
Square 5
Pentagon 6
Hexagon
7
6
8
10
12
Formula:
Write a formula that connects the
number of sides of the base, S,
with the number of faces, F.
Hence, work out the number of faces a
pyramid with a 20-sided base has.
4
5
6
7
Faces:
Formula:
E = 2S is the equation that links the base's S number of sides to its F number of faces.
E = 2S
S is the number of sides on a base.
E equals the number of edges.
Triangle (1)
3 and S are the base side counts.
edges equal 6, hence the answer is E.
E = 2S
Table 2
Base has four sides, hence the response is S.
edge count = E (8 edges)
E = 2E
3rd Pentagon
S is equal to the five sides of the base.
The letter E is equivalent to 10 edges.
S = 2E
4) A hexagon
S is equal to the six sides of the base.
Edge count: 12 equals E.
E = 2S
Thus, it is shown that E = 2S.
The 30 sides of the pyramid foundation.
The answer is S since the base has 20 sides.
The number of edges is E = 2S = 20 x 2 = 40 edges.
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A trapezoidal deck has dimensions as shown.
a. What is a formula for the area of this trapezoid?
What is the Area of Trapezoid?
The area of a trapezoid is the total space covered by its sides. An interesting point to be noted here is that if we know the length of all sides we can simply split the trapezoid into smaller polygons like triangles and rectangles, find their area, and add them up to get the area of the trapezoid. However, there is a direct formula that is used to find the area of a trapezoid if we know certain dimensions.
Area of Trapezoid Formula :
The area of a trapezoid can be calculated if the length of its parallel sides and the distance (height) between them is given.
The formula for the area of a trapezoid is expressed as,
A = 1/2 (a +b) h
where (A) is the area of a trapezoid, 'a' and 'b' are the bases (parallel sides), and 'h' is the height (the perpendicular distance between a and b)
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Simplify 5x√3x − 2x√3x − x√3x
Answer:
2√3 х^2 this solution
Step-by-step explanation:
I checked everything is correct
You find 400 mg of a substance that has a half-life of 20 days. What is it's daily rate of decay? Round answers to four decimal places.
The daily rate of decay is approximately equal to 0.0347 days⁻¹.
What is the rate of decay of a substance?
According to the statement, we find that a substance is under a decay process, whose differential equation is introduced below:
dm(t) / dt = - k · m(t) (1)
Where:
m(t) - Current mass of a substance, in miligrams.k - Rate of decay, in 1 / day.The half-life of the substance is the time needed for a substance to decrease its mass by half. The rate of decay can be found in terms of half-life:
k = (㏑ 2) / t' (2)
Then, the daily rate of decay of the substance is:
k = (㏑ 2) / (20 days)
k ≈ 0.0347 day⁻¹
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Tyrone says it is not possible to show that Δ A D E ≅ Δ A C B . Lorenzo disagrees, explaining that since ∠A D E ≅ ∠A C B , and ∠ A ≅ ∠ A by the Reflexive Property, ΔA D E ≅ ΔA C B . Is either of them correct? Explain.
We can conclude that ΔADE ≅ ΔACB under AA condition.
What exactly does the term "triangle congruency" mean?When the three corresponding sides and angles of two triangles are the same size, they are said to be congruent.These triangles can be moved, rotated, flipped, and turned to appear identical.If they are moved, they will coincide.When two triangles satisfy the five congruence conditions, congruence exists.They are the side-side-side (SSS), side-angle-side (SAS), angle-side-angle (ASA), angle-angle-side (AAS), and right angle-hypotenuse-side (RHS).So,
To prove that: ΔADE ≅ ΔACB
∠A ≅ ∠A = Given∠ADE ≅ ∠ACB = Given∠AED ≅ ∠ABC = AA condition proves that triangles are congruent, so these 2 angles will also be identical.Therefore, ΔADE ≅ ΔACB under AA condition.
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What is the answer to the following questions: 2 x 5
Answer:10
Step-by-step explanation:
Answer:
2x5=10 . .............
A group of friends wants to go to the amusement park. They have $89.50 to spend on parking and admission. Parking is $7.75, and tickets cost $27.25 per person, including tax. Write and solve an equation which can be used to determine pp, the number of people who can go to the amusement park.
Answer:
7.75 +27.25p = 89.50p = 3; 3 people can go the the amusement parkStep-by-step explanation:
Given parking costs $7.75 and admission costs $27.25, you want an equation and its solution for the number of people (p) who can go to the amusement park for $89.50.
EquationThe equation relates the total of costs to the total of funds available. The cost will be the total of 7.75 for parking and 27.25p for admission for p people.
7.75 +27.25p = 89.50
SolutionThis 2-step equation is solved by subtracting 7.75, then dividing by the coefficient of p.
7.75 +27.25p = 89.50 . . . . . equation
27.25p = 81.75 . . . . . . . . . . . subtract 7.75
p = 3 . . . . . . . . . . . . . . . . . . . divide by 27.25
3 people can go to the amusement park for $89.50.
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Solve each system by elimination.
4x+2y = 4 , 6x + 2y = 8
By elimination, the solution of the system of equations, 4x + 2y = 4 and 6x + 2y = 8, is (2 , -2).
A system of equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy all the equations.
There are three methods that can be used to solve system of equations.
1. Elimination
2. Substitution
3. Graphing
Using the elimination method, given two equations in x and y, a variable should be eliminated by adding/subtracting the two equations.
Subtracting the two equations will eliminate the variable y.
6x + 2y = 8 (equation 2)
4x + 2y = 4 (equation 1)
2x + 0y = 4
x = 2
Substitute the value of x to any of the two equations and solve for y.
6x + 2y = 8 (equation 2)
6(2) +2y = 8
2y = 8 - 12
2y = -4
y = -2
Hence, the solution of the system of equations is (2 , -2).
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