Slope of lines 3x - 5y = 2 and 3x + 5y = -2 are m₁ = 3/5 and m₂ = -3/5 respectively.
What is slope of the line?The slope of a line is defined as the change in y-coordinate with respect to the change in x-coordinate of the line. The net change in the y coordinate is Δy and the net change in the x coordinate is Δx. Therefore, the change in y-coordinate for a change in x-coordinate can be written as
Line slope is a measure of the steepness or direction of a line in the coordinate plane.
m = Δy/Δx
where,m is the slope
Given,
equations of the line
3x - 5y = 2
Moving 3x to RHS
-5y = -3x + 2
y = (3/5)x - 2/5
comparing with slope intercept equation of the line y = mx + c
slope m₁ = 3/5
Now, equation
3x + 5y = -2
moving 3x to RHS
5y = -3x - 2
y = (-3/5)x - 2
comparing with slope intercept equation of the line y = mx + c
slope m₂ = -3/5
Hence, m₁ = 3/5 and m₂ = -3/5 are slope of lines 3x - 5y = 2 and 3x + 5y = -2 respectively.
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Suppose a car moving in straight line steadly increases it's speed each seconds first from 35 to 45km/h then 40 to 45 km/h then from 45 to 50km/h, What is the acceleration?
The acceleration of the car is not constant but is increasing steadily, starting at 10 km/h, decreasing to 5 km/h, and then remaining constant at 5 km/h.
To find the acceleration of the car, we need to use the formula:
acceleration = (final velocity - initial velocity) / time
Let's calculate the acceleration for each interval of time:
For the first interval, the initial velocity is 35 km/h and the final velocity is 45 km/h. The question says the speed increases each second.
Therefore, the acceleration is:
acceleration = (45 - 35) / 1 = 10 km/h
For the second interval, the initial velocity is 40 km/h and the final velocity is 45 km/h. Again, the acceleration is:
acceleration = (45 - 40) / 1 = 5 km/h
For the third interval, the initial velocity is 45 km/h and the final velocity is 50 km/h. The acceleration is:
acceleration = (50 - 45) / 1 = 5 km/h
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Mrs. Cohen purchases a motorcycle for her son, jack for $12,000. The motorcycle depreciates at a rate of 21% per year. Determine the value of the motorcycle at the end of 5 years
Answer:
$3692
Step-by-step explanation:
100-21=79
=> 0.79
12000 × 0.79^5 = $3692
Flagpole a and flagpole c are both casting a shadow that ends at point s.
The distance of (x) between the flagpole is 12 m.
The distance (y) from flagpole c to point s is 10 m.
The height of flagpole a is 4.4 m.
What is the height of flagpole c?
In linear equation, 60m is the height of flagpole c .
What in mathematics is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
Height/ Shadow
Shadow of the pole = 12 m
Height of the pole = x m
Tim's shadow = Height of the pole - Tim's distance
12 m - 10 m = 2 m
Tim's height = 2 m
Hence:
x/12 = 2/10
Cross Multiply
2x = 12 × 10
x = 120/2
x = 60 m
Approximately = 60m
Hence, the height of the flagpole = 60m
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PLEASE HELP!! im desperate A chef uses a bowl shaped like the one below to prepare her avocado lime sauce. Due to the amount of mixing involved in this recipe she does not want to fill the bowl up entirely to the top. She estimates she can only fill the bowl up to about 2/3 its capacity. What is the volume of contents the chef will be able to fill the bowl with using her estimation?
1429 cubic centimeters is the volume of contents the chef will be able to fill the bowl.
What is Three dimensional shape?a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
Given that Chef uses a bowl shape which has radius of 8cm to prepare her avocado lime sauce.
We have to find the volume of contents the chef will be able to fill the bowl with using her estimation upto 2/3.
Firstly let us find volume of bowl.
Volume=4/3πr³
=4/3×3.14×(8)³
=2143.5
To find the amount of contents the chef can fill the bowl with, we need to multiply this volume by 2/3,
So 2143.5×2/3
1429.04 cubic centimeters.
Hence, the chef will be able to fill the bowl with about 1429 cubic centimeters of avocado lime sauce.
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PLEASE HELP THIS IS S MATH TEST I NEED 4 QUESTIONS I'LL GIVE EXTRA POINTS
1 ).
Question
Select the values that are solutions of the inequality x/5≥3
2) Graph x<8
3)
Solve x−5≥1 and graph the situation
Question 4
Which graph represents the solution of 8≥x+6
Question 6
Solve 6m>24 then graph
1) values are 15, 16 and 17
2) Drawn in the graph (2)
3) [tex]x \geq 6[/tex] and graph (3)
Question 6) [tex]m > 4[/tex] and graph (6)
What is Inequality?In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa.
1)
As per the given data:
Values are: 12, 13, 14, 15, 16, 17
Given inequality:
[tex]\frac{x}{5} \geq 3\\= x \geq 5\times3\\= x \geq 15[/tex]
The values of [tex]x[/tex] greater than or equal to 15 out of the given values are:
15, 16 and 17
15, 16, 17 are the solutions of the given equality.
2)
Given inequality:
[tex]x < 8[/tex]
For making the graph, first draw the point [tex]x=8[/tex]
The region to the left of the point [tex]x=8[/tex] will represent the graph as shown in the diagram.
3)
Given inequality:
[tex]x-5\geq 1[/tex]
= [tex]x \geq 1 + 5[/tex]
= [tex]x \geq 6[/tex]
For making the graph, first draw the point [tex]x=6[/tex]
The region to the right and including the point [tex]x=6[/tex] will represent the graph as shown in the diagram.
6)
Given inequality:
[tex]6m > 24[/tex]
= [tex]m > \frac{24}{6}[/tex]
= [tex]m > 4[/tex]
For making the graph, first the plot the point m = 4.
The region to the right of the point m = 4 will represent the graph as shown in the diagram.
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what is the measure of angle L?
what is x?
what is the measure of angle M?
SHOW YOUR WORK
The value of angle L, x and angle M is 55°, 35 and 60° respectively
What is an equation?An equation is an expression that shows the relationship between numbers and variables using mathematical operators like addition, subtraction, multiplication and division. Equations can be linear, quadratic.
From the triangle:
∠OLM + ∠MLN = 180° (sum of angles in a straight line)
125 + ∠MLN = 180°
∠MLN = 55°
Also:
∠MLN + ∠MNL + ∠LMN = 180 (sum of angle in a triangle)
substituting:
55 + (2x - 10) + 65 = 180
2x + 110 = 180
2x = 70
x = 35°
∠LMN = 2x - 10 = 2(35) - 10 = 60°
The value of angle M is 60°
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Given
ℎ
(
�
)
=
4
�
+
4
h(x)=4x+4, find
ℎ
(
2
)
h(2)
Answer:
h(2)=12
Step-by-step explanation:
Given:
h(x)=4x+4
Find:
h(2)
Substitute 2 into x.
[tex]h(2)=4(2)+4[/tex]
Solve:
[tex]h(2)=12[/tex]
what is 62 kilos in pounds
62 kilograms was found to be equal to approximately 136.7 pounds using conversion formula.
To convert kilograms to pounds, the following formula is used:
Pounds = Kilograms x 2.20462
Plugging in 62 kilograms, we get:
Pounds = 62 x 2.20462
Pounds ≈ 136.7
Therefore, 62 kilograms is approximately equal to 136.7 pounds.
The pound (symbol: lb) is defined as exactly 0.45359237 kilograms, or approximately 16 ounces. There are also different types of pounds, such as the avoirdupois pound (used for general purposes) and the troy pound (used for precious metals).
The kilogram (symbol: kg) is used to measure the mass of an object or substance. For example, it can be used to measure your own body weight, the weight of a bag of groceries, or the mass of a planet. The prefix "kilo-" means "one thousand", so a kilogram is equal to 1,000 grams.
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HELPPPP PLEASEEEEEEEE
Answer:
Step-by-step explanation:
square root of 100 is 10 and the only point that is on 10 is f so f = 10 or square root of 100
square root of 80 equals about 8.9 and the only point on 8.9 d so d is equal to square root of 80
3 * pi is about 9.4 and the only option left is e so e = 3 * pi
David drove 603 miles in 9 hours.
At the same rate, how many miles would he drive in 13 hours?
Answer:871
Step-by-step explanation:If he drove 603 miles in 9 hours, he drove 67 miles per hour. So in 13 hours he will drive 67x13, which is 871.
Answer:
Step-by-step explanation:
David would drive 871 miles. This is because 603 ÷ 9 = 67.
So, you'd have to multiply 67 times 13. Because 67 is the average mph.
in the metric system each millimeter increment is equal to
In the Metric System , each millimeter increment is equal to the 1/10 or 0.1 of a centimeter .
The Metric System is defined as a standardized system of measurements which is used in many countries around the world.
In the Metric System, there are different units of length, which include millimeters (mm) and centimeters (cm).
we know that , 1 centimeter is equivalent to 10 millimeters. This means that each millimeter increment is equal to 0.1 of a centimeter.
For Example, if we measure a length of 50 millimeters, we can convert it to centimeters by dividing 50 by 10, which gives you a length of 5 centimeters.
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The given question is incomplete , the complete question is
In the metric system each millimeter increment is equal to ____ of a centimeter .
The elimination method was used to solve the following system of equations:
x2 – y = –3
x2 + y2 = 9
Which of the following is the correct y-coordinate of the solution? (5 points)
0
1
3
-4
Answer:
(c) 3
Step-by-step explanation:
You want the y-value of the solution to the equations ...
x² -y = -3x² +y² = 9EliminationWe are interested in the value of y, so it can be useful to eliminate x from the equation(s). The x² term appears in both, so it is convenient to subtract the first equation from the second.
(x² +y²) -(x² -y) = (9) -(-3)
y² +y = 12
y² +y -12 = 0 . . . . . . subtract 12
(y +4)(y -3) = 0 . . . . . factor
y = -4 or +3 . . . . . . . . values that make the factors zero
DomainSolving the first equation for y, we find ...
x² +3 = y . . . . . . . add y+3
We know that x² cannot be negative, so this tells us the values of y will be ...
y ≥ 3
Of the two solutions we found above, the value -4 is extraneous (not in the domain of y).
The y-coordinate of the solution is 3, choice C.
__
Additional comment
The solution is the point of intersection of the two curves shown in the attachment. The y-coordinate of that point is 3.
<95141404393>
A triangle has sides with lengths of 32 millimeters, 60 millimeters, and 64 millimeters. Is it a right triangle?
Answer:
Yes it is a right triangle
Step-by-step explanation:
These side lengths correspond to a Pythagorean triple, specifically 8-15-17, which is a set of three positive integers that satisfies the Pythagorean theorem. The theorem states that in a right triangle, the sum of the squares of the lengths of the two shorter sides is equal to the square of the length of the longest side, also known as the hypotenuse.
In this triangle, 32^2 + 60^2 = 8^2 + 15^2 = 17^2, which confirms that it is indeed a right triangle.
y> -2x - 3
Y <4/3x +3
The solution to the inequality is a coordinate of (-1.8, 0.6)
How to determine the solution to the inequalityFrom the question, we have the following parameters that can be used in our computation:
y> -2x - 3
Y <4/3x +3
Next, we make a plot of the system to determine the solution
The shaded area in the plot represent the solution to the inequality
In this case, the shaded area has a coordinate of (-1.8, 0.6)
Hence, the solution is (-1.8, 0.6)
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6x3+5(6-4)³-7+4² I need help
Answer:
Answer: 67
18+5x2^3-7+16
18+5x8-7+16
18+40-7+16
67
The following sample space could represent which reapeted expirement
S[WW,WL,LW,LL]
The given sample space could represent a win and loss game by flipping a coin twice, where win represent the outcome head and loss represent the outcome tail.
What is a Sample Space?A sample space is a set of all the possible outcomes in a random experiment. It is usually denoted by the letter, S.
The subset of the sample space are events.
Given sample space is S = {WW, WL, LW, LL}
This can be interpreted as the outcomes in a random experiment, which has only two possibilities, either win or loss.
Suppose that we flip a coin two times.
Possible outcomes are,
HH : head appears twice
HT : head appears at first and tail appears second
TH : tail appears first and then head appears
TT : tail appears twice
Let the outcome head represent the win and tail represent the loss.
Possible outcomes are then WW, WL, LW, LL.
Hence the given sample space can be a possible outcomes of flipping a coin twice.
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Which statements are always true about a system of linear equations?
(more than one answer)
(1) the solution of a system of linear equations is any values of the variables that satisfy any of the equations.
(2) a system of linear equations has only two equations.
(3) on a graph, the solution of a system of equations is any point on one of the lines.
(4) on a graph, the solution of a system of equations is the point where the lines intersect.
(5) a system of linear equations includes at least two linear equations.
6) the solution of a system of linear equations is any values of the variables that satisfy both equations at the same time.
Answer:
(4) on a graph, the solution of a system of equations is the point where the lines intersect.
(5) a system of linear equations includes at least two linear equations.
(6) the solution of a system of linear equations is any values of the variables that satisfy both equations at the same time.
7 x 5 im 8 in 4th grade
Answer:
35 :)
Step-by-step explanation:
Answer:
35
Step-by-step explanation:7x5=35
You need to know your multiples.
7, 14, 21, 28, 35, 42, 49, 56, and so on.......
Find area of figure with radius 20.8 ft, both terms of r and to the nearest tenth. Use 3.14 for r.
The area of this figure with radius 20.8 ft include the following: D. 432.64π ft² ≈ 1358.5 ft².
How to calculate the area of a circle?Mathematically, the area of a circle can be calculated by using this mathematical expression:
Area = πr²
Where:
r represents the radius of a circle.
By substituting the radius into the formula for the area of a circle, we have the following;
Area of circle = π × 20.8²
Area of circle = 432.64π square feet.
Area of circle = 1358.5 square feet.
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The box plot represents the number of tickets sold for a school dance.
A horizontal line labeled Number of Tickets sold that starts at 8, with tick marks every one unit up to 30. The graph is titled Tickets Sold for A Dance. The box extends from 17 to 21 on the number line. A line in the box is at 19. The lines outside the box end at 10 and 27.
Which of the following is the appropriate measure of variability for the data, and what is its value?
The IQR is the best measure of variability, and it equals 17.
The range is the best measure of variability, and it equals 4.
The IQR is the best measure of variability, and it equals 4.
The range is the best measure of variability, and it equals 17.
The correct option is C. The IQR is the best measure of variability, and it equals 4.
What is IQR (interquartile range)?The IQR (interquartile range), a measure of variability that depicts the range of the middle 50% of the data, is used in box plots. It is determined as the gap between the first and third quartiles (Q1 and Q3) (Q1). Since the box in this instance spans the numbers 17 to 21 on the number line, Q1 equals 17 and Q3 equals 21. IQR = Q3 - Q1 = 21 - 17 = 4 as a result.
The difference between the dataset's maximum and minimum values is represented by the range, another measure of variability. As a result of its sensitivity to extreme values, it is less reliable than the IQR. Although the range in this instance is equal to 27 - 10 = 17, it could not correctly reflect the variety of the data.
Therefore, the IQR is the most appropriate measure of variability for this data, and its value is 4.
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how do i solve this -> y=x+46, y=7x+16
Answer:
x=5, y=51
Step-by-step explanation:
y = x + 46
y = 7x + 16 substitute equation 1 into equation 2 to get an expression all in terms of x, then solve for x
7x + 16 = x + 46
6x = 30
x = 30/6 = 5 substitute this into either equation and solve for y
y = 5 + 46 = 51
Find the value of z
6cm 15cm and right angle in triangle
For the given right triangle, the value of z is approximately 16.155 cm.
To find the value of z in a right triangle with sides 6 cm and 15 cm, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (z) is equal to the sum of the squares of the lengths of the other two sides (6 cm and 15 cm).
So we can write the equation:
z^2 = 6^2 + 15^2
Simplifying the equation:
z^2 = 36 + 225
Adding the numbers on the right side of the equation:
z^2 = 261
Taking the square root of both sides of the equation:
z = √261
Approximating the square root:
z ≈ 16.155
Therefore, the value of z is approximately 16.155 cm.
Note: The question is incomplete. The complete question probably is: Find the value of z (hypotenuse) if the other dimensions are 6cm, 15cm and right angle in triangle.
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MARKING BRAINLIEST! please help asap, show your work then choose the correct answer, thank you
Answer:
lower right option
Step-by-step explanation:
using the properties of logarithms
• loga + logb ⇔ log(ab)
• loga - logb ⇔ log ([tex]\frac{a}{b}[/tex] )
• log[tex]x^{n}[/tex] = nlogx
• lne = 1
given
a[tex]e^{bt}[/tex] = c ( take ln of both sides )
ln a[tex]e^{bt}[/tex] = lnc
lna + ln[tex]e^{bt}[/tex] = lnc
lna + bt lne = lnc ( subtract lna from both sides )
bt = lnc - lna
bt = ln ([tex]\frac{c}{a}[/tex] ) ← divide both sides by b
t = [tex]\frac{ln(\frac{c}{a}) }{b}[/tex]
please answer this question
The domain of the relation include the following: A. {1, 2, 3, 6}.
How to determine of this relation?In Mathematics, the horizontal extent of any graph of a function represents all domain values and they are always read and written from smaller to larger numerical values, and from the left of the graph to the right.
By critically observing the graph shown in the image attached below, we can reasonably and logically deduce the following domain:
Domain = {1, 2, 3, 6}.
In conclusion, the domain of this relation are all the x-values (independent value) that are located on the x-axis of the graph, which include {1, 2, 3, 6}.
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What is the standard form for 9^2
Answer:
81
Step-by-step explanation:
A blueprint of a concrete patio has a scale of 2 inches=5 feet. Use this to answer parts a, b, and c.
Expression for actual length and actual width of the concrete patio are
30x inches and 30y inches respectively.
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).
For example, if we have a rectangle of sides 2 cm and 4 cm, we can enlarge it by multiplying each side by a number, say 2.
Given,
A blueprint of a concrete patio has a scale of 2 inches=5 feet.
2 inches = 60 inches
scale factor = 60/2 = 30
Let length of the patio on the blue print is x inches
width of the patio on the blue print is y inches
then actual length of the 30x inches
actual width of the patio = 30y inches
Hence, 30x inches is actual length and 30y inches is actual width of the concrete patio.
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The amount of corn exported by a country
increased exponentially each year between
2007 and 2016.
In 2012, the country exported 210,000 tonnes
of corn.
In 2016, the country exported 806,736 tonnes
of corn.
Work out how much corn the country exported
in 2007.
Give your answer to the nearest tonne.
PLEASE HELP ME THIS IS DUE TOMORROW AND I DONT WANT A DETENTION
Answer: corn 806,736
Step-by-step explanation:
The items a to e that follow show the number of sides of a regular polygon. For each item, find the sum and the individual value of the interior angles.
a) 15 sides
b) 20 sides
c) 3 sides
d) 4 sides
e) 100 sides
For the polygon the individual value of the interior angles.
a) 15 sides is 145°
b) 20 sides is 108°
c) 3 sides is 60°
d) 4 sides is 90°
e) 100 sides is 18°
A regular polygon is one where all sides are the same length and all interior angles are the same. The number of sides of a regular polygon can affect the value of its interior angles.
a) 15 sides: The sum of the interior angles of a regular polygon with 15 sides is equal to 2180 degrees. To find the individual value of each angle, divide the sum by the number of sides. In this case,
=> 2180 / 15 = 145 degrees per angle.
b) 20 sides: The sum of the interior angles of a regular polygon with 20 sides is equal to 2160 degrees. To find the individual value of each angle, divide the sum by the number of sides. In this case,
=> 2160 / 20 = 108 degrees per angle.
c) 3 sides: The sum of the interior angles of a regular polygon with 3 sides is equal to 180 degrees. To find the individual value of each angle, divide the sum by the number of sides. In this case,
=> 180 / 3 = 60 degrees per angle.
d) 4 sides: The sum of the interior angles of a regular polygon with 4 sides is equal to 360 degrees. To find the individual value of each angle, divide the sum by the number of sides. In this case,
=> 360 / 4 = 90 degrees per angle.
e) 100 sides: The sum of the interior angles of a regular polygon with 100 sides is equal to 1800 degrees. To find the individual value of each angle, divide the sum by the number of sides. In this case,
=> 1800 / 100 = 18 degrees per angle.
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A union is the graph of a compound inequality containing or, the solution is a solution of either inequality, but never both.
O True
O False
Answer:
True
Step-by-step explanation:
A union is the graph of a compound inequality that contains "or," meaning the solution is a solution of either inequality, but not necessarily both. The union represents all values that satisfy at least one of the inequalities in the compound inequality. The solution is shown as the shaded region on the graph that represents the union of the solutions of the individual inequalities.
47% is it growth or decay