The equation is linear because it is in the form y = mx+b, which is slope intercept form
m = 2 is the slope
b = -5 is the y intercept
Graphing y = 2x-5 produces a straight line.
The equation y=2x-5 is linear because it fits the form y = a + bx, with a straight-line graph and a direct relationship between x and y.
Explanation:The equation y=2x-5 is a linear equation. In the form y = a + bx, a is the y-intercept, and b represents the slope.
Here, -5 is the y-intercept, and 2 is the slope of the equation, indicating how much y changes for each unit increase in x.
This linear equation can be graphed as a straight line.
The structure is similar to other linear equations like 7y = 6x + 8 and y + 7 = 3x, which are also represented by straight lines on a graph.
Linear relationships model a direct correlation between two variables, making them suitable for analysis with techniques like linear regression.
In practice, finding a relationship between an independent variable, such as hours worked on a car, and a dependent variable, like labor charges (y = 55x + 75), showcases a real-world example of linear equations.
Find the value of x and y
Answer:
x=90: y =43
Step-by-step explanation:
Given is a triangle. In ABC, AB = AC is given. also angle C = 47 is given.
AD is angle bisector of angle A
Since two sides are equal, ABC is isosceles. We have angle C = angle B
Hence angle B = 47 degrees.
Angle A = 180-(B+C) = 180-94 = 86
So angle y = 1/2 (86) = 43
Consider triangle BAD.
We have got two angles as 47 and 43.
Hence third angle is 180-(47+43) = 90
So x=90, y = 43
What step should you perform to bisect an angle drawn on tracing paper
Answer:
Step-by-step explanation:
• Suppose the angle is PQR where Q is the midpoint.
• Keep the compass at angle vertex Q and adjust some wide setting (the width is not important).
• Without changing the compass, draw an arc across each leg of the angle
• Now keep the compasses on the point drawn on each leg, and draw an arc in the interior of the angle.
• Using a ruler, draw a line through the vertex to the point where the arcs cross
Answer: fold the paper through the vertex so that the rays lie on top of each other.
Step-by-step explanation: apex
The multiplication of two or more quantities may be expressed as the ? of the same quantities.
Answer:
sum
Step-by-step explanation:
We have that, 'The multiplication of two or more quantities may be expressed as the repeated addition of the same quantities'.
i.e. multiplication of two or more terms is equal to adding as many copies of one of them.
i.e. a × b = a + a + ... ( 'b' number of times ) = b + b + .... ( 'a' number of times )
For example,
2 × 4 = 8
2 × 4 = 2 + 2 + 2 + 2 = 8 i.e. adding 2 four times
2 × 4 = 4 + 4 = 8 i.e. adding 4 two times
or
3 × 7 = 21
3 × 7 = 3 + 3 + 3 + 3 + 3 + 3 + 3 = 21 i.e. adding 3 seven times
3 × 7 = 7 + 7 + 7 = 21 i.e. adding 7 three times.
Hence, 'The multiplication of two or more quantities may be expressed as the repeated addition of the same quantities'.
The multiplication of two or more quantities can be expressed as the product of the same quantities in mathematics.
Explanation:Multiplication is a fundamental arithmetic operation that combines two or more numbers to find their total value. It represents repeated addition and is denoted by the "×" or "*" symbol. For example, multiplying 5 by 3 results in 5 * 3 = 15, indicating that the value is added five times.
In mathematics, the multiplication of two or more quantities may be expressed as the product of the same quantities. For example, if you multiply 2 by 3, the product is 6. This concept of multiplication applies to all quantities, whether they are numbers or variables.
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Mike has two containers, One container is a rectangular prism with width 2 cm, length 4cm, and height 10cm. The other is a cylinder with a radius of 1cm and height 10cm. Both containers sit on flat surfaces. Water has been poured into two containers so that the height of the water in two containers is 80 cubed cm, then the height of the water in each container is?
so, we know both the rectangular prism and the cylinder got filled up to a certain height each, the same height say "h" cm.
we know the combined volume of both is 80 cm³, so let's get the volume of each, sum them up to get 80 then.
[tex]\bf \stackrel{\stackrel{\textit{volume of a}}{\textit{rectangular prism}}}{V=Lwh}~~ \begin{cases} L=length\\ w=width\\ h=height\\[-0.5em] \hrulefill\\ L=4\\ w=2\\ \end{cases}~\hspace{2em}\stackrel{\textit{volume of a cylinder}}{V=\pi r^2 h}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=1 \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]
[tex]\bf \stackrel{\textit{prism's volume}}{(4)(2)(h)}~~+~~\stackrel{\textit{cylinder's volume}}{(\pi )(1)^2(h)}~~=~~80 \\\\\\ 8h+\pi h=80\implies h(8+\pi )=80\implies h=\cfrac{80}{8+\pi }\implies h\approx 7.180301999[/tex]
Final answer:
To find the height of the water in each container, we must calculate the volumes of the rectangular prism and the cylinder, set equations based on their volumes that add up to 80 cm³, and solve for the heights of the water in each container.
Explanation:
To solve this, the volume of the containers and then the height of the water in each container must be determined.
The volume of the rectangular prism can be found with the formula:
Volume = length × width × height. So, the volume = 4cm × 2cm × height of water for the rectangular prism.
The volume of the cylinder is calculated using the formula: V = πr²h, where 'r' is the radius and 'h' is the height of water for the cylinder. Given the radius is 1 cm, the formula simplifies to V = π × 1 cm × height of water.
Knowing the combined volume of the water is 80 cm³, we set up the equations considering the volume of water held by each container and solve for the heights of water in both the rectangular prism and the cylinder. The calculations will provide the individual heights of water, ensuring they add up to the total volume of 80 cm³.
hich of the following expressions is equivalent to |x + 4| < 5? A. –5 > x + 4 < 5 B. –5 < x + 4 < 5 C. x + 4 < 5 and x + 4 < –5 D. x + 4 < 5 or x + 4 < –5 Please select the best answer from the choices provided A B C D
Answer:
option B
Given : |x + 4| < 5
A. –5 > x + 4 < 5
B. –5 < x + 4 < 5
C. x + 4 < 5 and x + 4 < –5
D. x + 4 < 5 or x + 4 < –5
In general , |x|< n where n is positive
Then we translate to -n < x < n
|x + 4| < 5
5 is positive, so we translate the given absolute inequality to
-5 < x+4 < 5
So option B is correct
what is 1+2+3+4+5+6+7+8+9+10
Answer:
55
Step-by-step explanation:
Add from left to right
1+2+3+4+5+6+7+8+9+10
3 +3+4+5+6+7+8+9+10
6+4+5+6+7+8+9+10
10+5+6+7+8+9+10
15+6+7+8+9+10
21+7+8+9+10
28+8+9+10
36+9+10
45+10
55
Given the equation, y = x - 4, what is the slope and the y-intercept?
m = 4 and b = 1/3
m = -4 and b = 1/3
m = 1/3 and b = 4
m = 1/3 and b = -4
Answer:
the answer would be m=1/3 and b=-4
Step-by-step explanation:
Y=X-4
the X= 1 almost all the time in an equation unless otherwise your given an equation for "x". so x is automatically 1/3 which would be your slope, and then then looking at the equation the end part of the equation is your starting point.so you look at the end of the equation and the -4 is were youd start your point on the graph.
Which is the solution to (x-2)(x+10)=13
The solution to (x-2)(x+10)=13 is x can be either 3 or -11, therefore the problem has 2 solutions.
Answer:
x = 3 or x = -11
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What is the approximate area of the shaded sector in the circle shown below
Answers in pic
Answer:
B. 51 in²
Step-by-step explanation:
π14²= 615.752160104 (find total circle area)
30/360= 1/12 (calculate fraction size the section would be of the entire circle)
615.752160104/12= 51.3126800087 (the slice's area)
Answer:
51
Step-by-step explanation:
x − 2y = 14
x + 3y = 9
(1, 12)
(−1, −12)
(12, −1)
(12, 1)
Find the product 284 times 36
Your answer to 284*36 will be 10,224.Hope this helps!
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Answer:
10,224
I just entered 284*36 into my calculator haha
Graph the linear equation.find three points that solve the equation,then plot on the graph -3x++2y=11
[tex]-3x+2y=11\qquad\text{add 3x to both sides}\\\\2y=3x+11\qquad\text{divide both sides by 2}\\\\y=\dfrac{3}{2}x+\dfrac{11}{2}\\\\for\ x=1\to y=\dfrac{3}{2}(1)+\dfrac{11}{2}=\dfrac{3}{2}+\dfrac{11}{2}=\dfrac{14}{2}=7\to(1,\ 7)\\\\for\ x=-3\to y=\dfrac{3}{2}(-3)+\dfrac{11}{2}=-\dfrac{9}{2}+\dfrac{11}{2}=\dfrac{2}{2}=1\to(-3,\ 1)\\\\for\ x=-5\to y=\dfrac{3}{2}(-5)+\dfrac{11}{2}=-\dfrac{15}{2}+\dfrac{11}{2}=-\dfrac{4}{2}=-2\to(-5,\ -2)[/tex]
Complete the equation of the graphed linear function in point-slope form. y – (–2) = (x – ) The graph of the function goes through point 1, negative 2 and point 2, 2.
Answer:
[tex]y+2=4(x-1)[/tex]
Step-by-step explanation:
we know that
The equation of the line into point-slope form is equal to
[tex]y-y1=m(x-x1)[/tex]
Let
[tex]A(1,-2), B(2,2)[/tex]
Find the slope of the line AB
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
substitute
[tex]m=\frac{2+2}{2-1}[/tex]
[tex]m=\frac{4}{1}[/tex]
[tex]m=4[/tex]
With the point A and the slope m find the equation of the line
[tex]y-(-2)=4(x-1)[/tex]
[tex]y+2=4(x-1)[/tex]
Rule; y=5x
Table:
x | y
2
4
6
The 7th grade students at Palm Coast Middle School made some apple pies for a bake sale. The school cafeteria also donated 9 pies toward the effort. All the pies at the sale were cut into 8 pieces. If at least 224 pieces of pie were sold in all, how many pies did the students bake?
Answer:
19 i think
Step-by-step explanation:
Answer:
The students baked at least 19 pies.
Step-by-step explanation:
We know that each of the pies were cut into 8 pieces. Since the students sold at least 224 pieces of pie, we can use these equations to figure out how many pies were sold and how many were made by the students.
Total number of pies = total number of slices sold/number of slices per pie
Total number of pies = 224/8
Total number of pies = 28
Pies made by students= total number of pies-pies made by school cafeteria
Pies made by students= 28-9
Pies made by students= 19
If an object traveled 230 miles at a rate of 25 miles per hour, how long (in hours) did it take to travel this distance?
Answer:
9.2 hours for the total drive
To determine how long it took for an object to travel 230 miles at 25 miles per hour, divide the distance by the speed, which results in 9.2 hours.
This problem is a straightforward application of the formula for calculating time when distance and speed are known. The formula is Time = Distance ÷ Speed.
In this case, the distance (d) is 230 miles and the speed (v) is 25 miles per hour. Using the formula:
Therefore, it took 9.2 hours for the object to travel a distance of 230 miles at a speed of 25 miles per hour.
65% of a group of people have brown eyes.
How many people are in the group if 260 people have brown eyes?
Answer:
There are 400 people in the group
Step-by-step explanation:
people with brown eyes = people * percentage with brown eyes
We know that 65 percent have brown eyes
There are 260 people with brown eyes.
We are looking for people
260 = people * .65
Divide each side by .65
260/.65 = people
400= people
Help please?
Describe a situation that matches the equation. 34 = g + 25
A: The temperature on Monday was 25 degrees below zero and on Tuesday the temperature got up to 34 degrees. What was the increase in temperature between Monday and Tuesday?
B: The eighth-grade class has 34 students. The year before, when the students were in seventh grade, there were 25 students. How many students were added between seventh and eighth grade?
C: A person bikes 34 miles on Monday and 25 miles on Tuesday. How many miles total did the person bike?
D: Jack has 25 marbles. Mary gives him 34 marbles. How many marbles does Jack have?
Answer:
The answer is B!
Step-by-step explanation:
The equation and the equation from scenario B are both, when simplified, g = 9.
Answer:
Option B matches the equation
Step-by-step explanation:
Equation: 34 = g + 25
A:Since we are given that The temperature on Monday was 25 degrees below zero So, in given equation there should be -25 in place of 25
So, It does not matches the equation
B: The year before, when the students were in seventh grade, there were 25 students.
Let g be the no. of students added between seventh and eighth grade
So, Total students = 25+g
We are given that The eighth-grade class has 34 students.
So, equation becomes : 34=g+25
It matches the equation.
C :A person bikes 34 miles on Monday
He bikes 25 miles on Tuesday.
So, Total miles =25+34
So, It does not matches the equation
D: Jack has 25 marbles.
Mary gives him 34 marbles.
Total marbles = 25+34
So, It does not matches the equation
Hence Option B matches the equation
hawick is 15 miles south of abbostford and kelso is 17 miles east of abbotsford. what is the distance from Hawwick to kelsi?
Answer:
22.7 miles
Step-by-step explanation:
You are gonna use a^2 + b^2 = c^2 because the cities make a right triangle and you are trying to find the hypotenuse (c). C^2 ends up being 517 and the square root.
Answer:
22.7
Step-by-step explanation:
Amy has 408 beads she gives 322 beads to her sister how many beads dose amy have now
Answer:
86
Step-by-step explanation:
Subtract 322 from 408
8-2=6
we cant subtract 2 from zero so we take 1 from the next
10-2=8
3-30
86
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How do you find the domain an range and how do you graph it
Divide 46 on both sides to get f(x)=((x+2)^3-3)/46. The domain ranges from negative infinity to infinity. The range ranges from -infinity to infinity as well because the exponent is 3, so the resulting number may be negative.
Remember, when graphing cubics, there is always two turns. The following graph is from Desmos.
Fred brown and his sister, Nancy, each have $15 in the bank. Every week Nancy plans to add $3 to her account. Fred who loves to spend money when he has it, plans to add $1 to his account each week. How many weeks will it take Nancy’s account to have TWICE as much money as Fred’s account?
(Explain your thinking)
Answer:
it will take 15 weeks for Nancy’s account to have TWICE as much money as Fred’s account
Step-by-step explanation:
Fred brown and his sister, Nancy, each have $15 in the bank
Initially both Fred and Nancy have $15
Every week Nancy plans to add $3 to her account
Let 'n' be the number of weeks she plans to add in her account
for 1 week, $3
For n weeks , its 3n
So amount of money in Nancy's account after 'n' weeks = 15 + 3n
Fret plans to add $1 to his account each week
for 1 week, $1
For n weeks , its 1n
So amount of money in Fred's account after 'n' weeks = 15 + 1n
Now we need to find out 'n' when
Nancy's account = 2 times of Fred's account
15 + 3n = 2(15+1n)
Distribute 2 inside the parenthesis
15 + 3n = 30 + 2n
Subtract 2n on both sides
15 + n = 30
Subtract 15 on both sides
n = 15
Hence, it will take 15 weeks for Nancy’s account to have TWICE as much money as Fred’s account
artaud noticed that if he takes the opposite of his age and adds 40, he gets the number 28. how old is artaud?
let's say Artaud's age is "x", its opposite will then be -x, so
[tex]\bf \stackrel{\textit{opposite of his age plus 40}}{-x+40}~~\stackrel{is}{=}~~28\implies -x+40-28=0 \\\\\\ -x+12=0\implies \boxed{12=x}[/tex]
Answer:
12 years old
Step-by-step explanation:
28 - 40 = -12
Note that -12 is the opposite of 12.
Artaud is 12
If you multiply two even numbers where the product be even or odd explain with an example
Answer:
Even
Step-by-step explanation:
Any two numbers you multiply together that are both even will always result in an even number. For example 48x24=1152. You can use any two even numbers and you will always get and even product.
What is the slope of a line that is parallel to the line shown in this graph?
Answer:
The slope of the parallel line is 2/3
Step-by-step explanation:
Parallel lines have the same slope, so we need to find the slope of the line on the graph.
We can use the equation for the slope of a line
m = (y2-y1)/ (x2-x1)
=(2-0) /(3-0)
= 2/3
The slope of the line of the graph is 2/3 so
The slope of the parallel line is 2/3
The range of the following relation R:
Answer:
{- 5, - 4, 2 }
Step-by-step explanation:
the range is the corresponding values of y ( output) from the given set in ascending order without repeats
Which of the following is true about the expression given below?
9>2
A.9 is to the left of 2 on a horizontal number line.
B.9 is the opposite of 2 on a horizontal number line.
C.9 is to the right of 2 on a horizontal number line.
D.9 is at the same place as 2 on a horizontal number line.
Answer: Option 'C' is correct.
Step-by-step explanation:
Since we have given that
9 > 2
i.e. 9 is to the right of 2 on a horizontal number line
As we know that in the Cartesian plane, upper most is for y- positive coordinate, lower most is for y- negative coordinate
Similarly, right most is for x-positive coordinate and left most is for x- negative coordinate.
And we have 9>2
Both 2 and 9 are positive numbers so, both numbers must be in the right part of axis.
And 9 is always right of 2 on a horizontal number line.
Hence, Option 'C' is correct.
A rectangular playground has an area of 3,162 square meters. If the width of the rectangle is 51, find the length.
The length of the rectangular playground can be determined using the conversion of the area formula, Length = Area ÷ Width. Substituting the values provided gives us Length = 3,162 ÷ 51.
Explanation:The subject of this question is mathematics, more specifically, the topic involves calculating the dimensions of a rectangle when given the area and one side length. In this case, the student is asked to determine the length of a rectangular playground that has an area of 3,162 square meters and a known width of 51 meters.
The area of a rectangle is calculated by multiplying its length by its width, according to the formula: Area = Length x Width. This can be rearranged to find Length, resulting in: Length = Area ÷ Width.
Plugging in the values provided, we find the length by using the rearranged formula:
Length = 3,162 ÷ 51
With these calculations, we would find our answer for the length of the playground.
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what is the solution to 4(x-7)=0.3(x+2)+2.11
Expand
4x - 28 = 0.3x + 0.6 + 2.11
Simplify 0.3x + 0.6 + 2.11 to 0.3x + 2.71
4x - 28 = 0.3x + 2.71
Add 28 to both sides
4x = 0.3x + 2.71 + 28
Simplify 0.3x + 2.71 + 28 to 0.3x + 30.71
4x = 0.3x + 30.71
Subtract 0.3x from both sides
4x - 0.3x = 30.71
Simplify 4x - 0.3x to 3.7x
3.7x = 30.71
Divide both sides by 3.7
x = 30.71/3.7
Simplify 30.71/3.7 to 8.3
x = 8.3
The gasoline tank in Deborahs car holds 13.2 gallons. When her gas gauge says that the tank is 1/4 full, how many gallons of gasoline does the tank have?
Answer:
3.3
Step-by-step explanation:
To find the amount of gasoline when Deborah's tank is 1/4 full, divide the tank's full capacity (13.2 gallons) by 4, which results in 3.3 gallons of gasoline in the tank at 1/4 full.
To find out how many gallons of gasoline Deborah's car has when the tank is 1/4 full, we need to calculate 1/4 of the total capacity of the tank. Since the tank holds 13.2 gallons when full, the amount of gasoline at 1/4 full is calculated as follows:
Divide the full tank capacity by 4 to find 1/4 of the tank's capacity: 13.2 gallons / 4 = 3.3 gallons.Therefore, when Deborah's gas gauge indicates that the tank is 1/4 full, it contains 3.3 gallons of gasoline.