The table can be completed as follows x = 0, 2, 4 we get y = 1, 2, 3 for the linear equation [tex]y = \frac{1}{2}x + 1[/tex].
What is a Linear Equation ?If an equation is written in the form ax + by + c=0, where a, b, and c are real integers and the coefficients of x and y, i.e., a and b, respectively, are not equal to zero, then it is said to be a linear equation in two variables.
Examples of two-variable linear equations are 10x+4y = 3 and -x+5y = 2.
Such an equation has a pair of numbers as its solution, one for x and one for y, which further equalises the two sides of the equation.
A specific point on the graph represents the solution of a linear equation in two variables, ax+by = c, where the total of these two values will equal c when the x-coordinate is multiplied by a and the y-coordinate by b.
Basically, there are infinitely many solutions to a linear equation with two variables.
The equation is :
[tex]y = \frac{1}{2}x + 1[/tex]
So, when x = 0
y = 1,
when x = 2
y = [tex]\frac{1}{2}*2 + 1[/tex] = 1 + 1 = 2
and , when x = 4
y = [tex]\frac{1}{2}*4 + 1[/tex] = 2+ 1 = 3
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The two polygons are similar. Solve for x
Determine if the triangles are similar by Angle-Angle similarity
The triangles are similar by Angle-Angle similarity since they are congruent.
What is Angle-Angle Similarity?According to the Angle-Angle Similarity Theorem, if two angles in one triangle are equal to two angles in another triangle, the triangles are similar. The triangles are similar if two pairs of corresponding angles in a pair of triangles are congruent. We know this because if two angle pairs are equal, then the third pair must be equal as well.
Two triangles with two angles, starting with Triangle 1, one measuring 47 degrees and the other measuring 53 degrees, are congruent to two angles in Triangle 2. Following the AA similarity theorem, it is assumed that Triangle 1 is similar to Triangle 2.
In this case, angle MNP = angle QPL (corresponding angles, //lines) (A)
angle QLP is common angle (A)
By AA, the 2 triangles are similar.
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I need help with number nine please
On #9:
Slope-intercept form is y = mx + b
Based on the graph, the slope is -4/3 and the y-intercept is (0,0).
The answer is y = –4/3 x.
You could add "+0" at the end to have y = –4/3 x +0, but since adding 0 doesn't change it, it's usually left off.
Answer:
y = -4/3x + 0 or just y = -4/3
Step-by-step explanation:
you just find the slope by doing rise over run, and find the y-intercept by looking at what number the line hits on the y-axis.
NOT MANY POINTS BUT I NEED HELP ON MY FINAL
A linear pair's total angles are always equal to 180°. Hence ∠ HJL is 94°
What is a Linear Pair of Angles?When two lines cross at one point, a linear pair of angles is created. If the angles follow the intersection of the two lines in a straight line, they are said to be linear. A linear pair's total angles are always equal to 180°.Those two neighboring angles whose sum is 180° are referred to as a linear pair of angles. They are represented by a ray that serves as a common arm between the angles and is drawn on a straight line.The name "linear" comes from the standard illustration of a linear function in one dimension: a line drawn through the origingiven
∠HJL and ∠LJK are linear pair
∠ HJL = ?
∠HJL + ∠JLK =180
x + x -8 = 180
2x -8 =180
x = 188/ 2 = 94°
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slope of (-3,-2) and (-1,-5)
Answer: Slope of [tex](-3, -2)[/tex] and [tex](-1, -5)[/tex] is [tex]-1.5[/tex].
Step-by-step explanation:
The slope of a line is given by, [tex]m=\frac{y_2-y_1{} }{x_2-x_1}[/tex]
Here we have,
[tex](x_{1}, y_{1}) = (-3, -2)[/tex] and [tex](x_{2}, y_{2}) = (-1, -5)[/tex]
Now put the known values in the slope formula we get,
[tex]m=\frac{(-5) -(-2) {} }{(-1) -(-3)}[/tex]
[tex]m=\frac{(-3) {} }{2}[/tex]
Slope (m) = 1.5
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Maths qs
Dot diagram and mean mass
Answer:
mean 33.214
Step-by-step explanation:
465/14= 33.214
Does this given information represent a function?
Please answer fast lots of points!!!!
Answer:
Step-by-step explanation:
Sidney bought two magazines that
were each $4.95. If Sidney paid a total of
$10.59 for the two magazines with tax,
what percent tax did she pay for her s
purchase?
Answer:
Step-by-step explanation:
0.69
Five times a number increased by 5 is equal to 25, find the number.
Answer: the number is 4
Step-by-step explanation:
5x+5=25 is the equation
solve for x by isolating x
5x+5-5=25-5
5x=20
divide both sides by 5 to isolate x
x=4
Answer: 4
Step-by-step explanation:
5x + 5 = 25 this is what the equation is!
Then we subtract 5 on both side
5x = 20
Then divided by 5 on both side
x= 4
solve for x please I'm having a hard time on this one
Answer:
divide 2x by 2, that gives you x, then divide 104 by 2 and that gives you the answer to x
Is 38 / 53 and simplest form explain? Why t? Or or why not
yes 38/53 is the simplest form
Step-by-step explanation:
The fraction is already reduced.
Sergio has p paintings in his art collection. He and other local painting collectors agreed to donate a total of 48 paintings to the local museum. Each of the 12 collectors will donate the same number of paintings.
Write an equation for this problem.
The equation for this problem will be 12x = 48.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
Sergio has p works of art in his craft assortment. He and other nearby canvas gatherers consented to give a sum of 48 compositions to the neighborhood historical center. Every one of the 12 authorities will give a similar number of artistic creations.
Let 'x' be the number of donations by each. The equation for this problem is given as,
12x = p
12x = 48
The equation for this problem will be 12x = 48.
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A marble is launched from a ledge at a height of 2.8 m with a velocity of 3.27 m/s. How far from the ledge will the marble land
All objects fall at the same rate in a vacuum as long as the only force acting on them is gravity.
How height is the ledge from the ground?King employs a first person narrator and opens with the protagonist, a retired pro tennis star named Stan Norris, in the clutches of a wealthy, A horizontal projection forming a narrow shelf on a wall. A ledge is created when the working length can no longer be negotiated and the original pathway of the canal has been lost.The magnitude of the velocity of the ball is 26.3 m/s for the parabolic motion just before it hits the ground and this greater than the 17.1 m/s for the velocity of the ball that falls straight downward.Hence, the height of the ledge from the ground is 1.25m.
3.27m/s
Given parameters:
Initial velocity = 3.27m/s
Height of fall = 2.8m
Unknown:
Final velocity = ?
To solve this problem, we have to look at our given parameters and compare to the appropriate motion equation.
we have been given; u (initial velocity) and height of fall (h)
Since this body falls under acceleration due to gravity, g = 9.8m/s²
Now, we use;
V² = U² + 2gh\
where V is the final velocity
Input the parameters and solve;
V² = 3.27m/s + (2 x 9.8 x 2.8)
V = 65.4m/s
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if my grade is a 92.30% and i got 70% on something that counted for 20% of my grade, what would the final grade be?
If you got a score of 90 percent on the test and the test is worth 20 percent of your overall grade, you would multiply 90 by 0.2 for a value of 18 points out of the possible 20 points.
Is 70 percent a failing grade?
The standard range for grades is 55 to 100. As seen in the chart below, number grades correspond to letter grades. The required passing score is 70. (C). Failure grades are any grades between 55 and 69 (D and F), for which no unit credit is granted.
A Passed grade requires a C or higher; a C- or worse results in a Not Passed mark. Many prerequisites (such as those for General Education and Electives) may be satisfied by a grade of C-, but neither credit nor requirements will be satisfied by a grade of Not Passed.
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The length of a rectangular drainage pond is changing at a rate of 8 ft/hr and the perimeter of the pond is changing at a rate of 24 ft/hr. At what rate is the width changing?
The rate of width changing will be;
⇒ 4 feet/hour
What is mean by Rectangle?
A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.
Given that;
The length of a rectangular drainage pond is changing at a rate of 8 ft/hr and the perimeter of the pond is changing at a rate of 24 ft/hr.
Now,
We know that;
⇒ Perimeter of rectangle = 2 (Length + Width)
Substitute al the values, we get;
⇒ 24 = 2 (8 + x)
⇒ 12 = 8 + x
⇒ x = 12 - 8
⇒ x = 4
Thus, The rate of width changing will be;
⇒ 4 feet/hour
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Draw and label a coordinate plane so that the x-axis extends from -9 to 9 and the y-axis
extends from -6 to 6. Represent each of these points with a dot, and label the point using
its letter name.
The required given Co-ordinates are plotted in graph below.
What are Co-ordinates?The numbers on a direction lattice are utilized to find focuses. Each point can be recognized by an arranged sets of numbers; that is, a number on the x-axis called a x-coordinate, and a number on the y-hub called a y-coordinate. Requested matches are written in enclosures (x-coordinate, y-coordinate).
Explain graph.Graph is characterized as to make an outline that shows a connection between at least two things. An illustration of diagram is to make a progression of bars on charting paper
According to question:coordinates plane so that the x-axis extends from -9 to 9 and the y-axis
extends from -6 to 6
Plotted points on the graph are shown in image below.
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Given that the equation of line one (L1) is 2x-y=3 and equation of line two (L2) is kx+2y=3 where k is a constant.
(a) Find the value of k such that L1 and L2 are parallel.
(b) Find the value of k such that L1 and L2 are perpendicular.
This question is related to Linear functions, Answers: (a) k = -4, (b) k=1. Someone pls tell me how to get there though
Answer:
see explanation
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
(a)
given the equation of L1 is
2x - y = 3 ( subtract 2x from both sides )
- y = - 2x + 3 ( multiply through by - 1 )
y = 2x - 3 ← in slope- intercept form
with slope m = 2
• Parallel lines have equal slopes
then slope of L2 is m = 2
given the equation of L2 is
kx + 2y = 3 ( subtract kx from both sides )
2y = - kx + 3 ( divide through by 2 )
y = - [tex]\frac{k}{2}[/tex] + [tex]\frac{3}{2}[/tex] ← in slope- intercept form
with slope m = - [tex]\frac{k}{2}[/tex]
since slope of L1 and L2 are equal, both 2 , then
- [tex]\frac{k}{2}[/tex] = 2 ( multiply both sides by 2 to clear the fraction )
- k = 4 ( multiply both sides by - 1 )
k = - 4
----------------------------------------------
(b)
given the slope of a line is m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{2}[/tex]
Then
for L2 to be perpendicular to L1
- [tex]\frac{k}{2}[/tex] = - [tex]\frac{1}{2}[/tex] ( multiply both sides by - 1 )
[tex]\frac{k}{2}[/tex] = [tex]\frac{1}{2}[/tex] , thus
k = 1
Aubrey and Charlie are driving to a city that is 120 mi from their house. They have already traveled 15 mi, and they are driving at a constant rate of 65 mi/h. Complete the function that models the distance they drive as a function of time. Then complete a reasonable domain for this situation.
Therefore, the solution of this problem is the domain would be
0 < t ≤ 1.61.
What is domain?A function's domain is the set of possible values that can be entered. This set reflects the values of x in a function like f. (x). Its range refers to the set of possible values that a function can accept. These are the values that are returned by the function when we enter an x value.
Here,
The remaining distance that would result from multiplying the speed by the time t will be added to the 20 miles that make up the total distance. The formula for the equation would be as follows:
120 = 15 + 65t
It would be 0 hours at the very least. When the entire 120-mile distance has been accomplished, the time limit is reached.
t ≤ (120 - 15)/65
t ≤ 1.61 hours
Therefore, the solution is the domain would be 0 < t ≤ 1.61.
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Solve for r in terms of q, s, and r. S=-qtr
To isolate a certain variable in an equation, we must perform inverse operations on both sides of the equal sign to cancel out values.
Solving the Question[tex]S=-qtr[/tex]
⇒ Right now, r is being multiplied by q and t. Divide both sides by qt to cancel these values out:
[tex]\dfrac{S}{qt}=\dfrac{-qtr}{qt}\\\\\dfrac{S}{qt}=-r[/tex]
⇒ Now, to remove the negative symbol, multiply both sides by -1:
[tex]r=-\dfrac{S}{qt}[/tex]
Answer[tex]r=-\dfrac{S}{qt}[/tex]
The volume of water in a rectangular, in-ground, swimming pool is given by V(x ) =x3 + 11x2 + 24x where V (x) is the volume in cubic feet when the water is x ft high
What is the dimension of the base of the pool? (a) x + 3 and x + 8 (b) x + 4 and x + 7 (c) x + 4 and x + 8(d) x + 3 and x + 7 What is the volume of the pool when x = 3 ft?
(a) 298 ft3 (b) 148 ft3 (c) 268 ft3 (d) 198 ft3
If the volume is 100 ft3 of water, what is the height x ? (a) 2 ft (b) 3 ft (c) 4 ft (d) 5 ft
If the maximum capacity of the pool is 520 ft3 what is the maximum depth? (a) 2 ft (b) 3 ft (c) 4 ft (d) 5 ft
1) The dimension of the base of the pool is; (x + 3) and (x + 8)
2) The volume of the pool when x = 3 ft is; 198 ft³
3) If the volume is 100 ft³ of water, the height x is; 2 ft
4) If the maximum capacity of the pool is 520 ft³, the maximum depth is; 5 ft
How to find the volume of a cuboid?We are given that the volume of water in a rectangular, in-ground, swimming pool is; V(x) = x³ + 11x² + 24x
where;
V(x) is the volume in cubic feet when the water is x ft high
1) V(x ) =x³ + 11x³ + 24x
V(x) is the volume in cubic feet when the water is x ft high
Factorizing the polynomial into its' factors gives;
V(x) = x(x² + 11x + 24)
V(x) = x(x + 8)(x + 3)
The water is x ft high and so the dimensions of the base of the pool are (x + 3) and (x + 8)
2) We want to find the volume of the pool when x = 3 ft. Thus;
V(3) = 3(3 + 8)(3 + 3)
V(3) = 3 (11)(6)
V(3) = 198 ft³
3) If the volume is 100 ft³ of water, the height x is calculated as;
x(x + 8)(x + 3) = 100
Solving for x gives us;
x = 2 ft
4) If maximum capacity of the pool is 520 ft³, then the maximum depth is;
x(x + 8)(x + 3) = 520
Solving for x gives us;
x = 5 ft
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slope of the line that passes through (10, 4) and (5, 13). as a integer
The slope of the line that connects (10,4) and (5,13) is -9/5.
What is a slope?The slope of a line indicates its steepness. Slope is calculated mathematically as "rise over run" (change in y divided by change in x).Here given,
The two points are (10,4) and (5,13).
We have to find the slope that passes through the given points,
The formula to find slope(m) is,
The slope of the line that passes through (x1 , y1) and (x2,y2) is,
Slope(m) = y2 - y1 / x2 - x1
By substituting the values in x and y
Slope = 13 - 4 / 5 - 10
= 9 / -5
Slope = -9/5
= -1.8
Therefore the slope of line that passes through (10,4) and (5,13) is -9/5.
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(a) Write 7.97 x 10 ^-6 as an ordinary number.
Answer:
0.00000797
Step-by-step explanation:
C is directly proportional to D, when C-125 and D=5. Work out the value of C when D = 6. Work out the value of D when C = 4725
Answer:
d=189 when c=4725
Step-by-step explanation:
c:d
125:5
divide by 5 to find the value of c when d=1
25:1
multiply by 6 to find the value of c when d=6
150:6
4725:?
4725/25=189
189*1=189
Ellen wants to build a sidewalk of uniform width around her pool. Her pool is rectangular,
and its dimensions are 60 feet by 50 feet. She has enough pavers to cover 1000 square
feet and wants to use all the pavers.
Complete the following statement. Round to the nearest tenth
Ellen should make the width of the sidewalk
feet.
Answer:
she should just divide the dimensions by 3
Step-by-step explanation:
Find the measure of each acute angle in a right triangle where the measure of one acute angle is 8 times the measure of the other acute angle
The measure of the acute angles in the right triangle are 10 and 80 degrees.
How to find the angle of a right angle triangle?A right angle triangle is a triangle that has one of its angles as 90 degrees. The sides of a right angle triangle can be named base on the position of the angles. The sides includes hypotenuse side, opposite side and adjacent side.
The sum of angles in a right angle triangle is 180 degrees.
The other measures of the right triangle are acute angles.
Any angle that measures greater than 0° and less than 90° is called an acute angle.
Hence, let's find the measure of the acute angles
let
x = measure of one acute angle
Hence,
x + 8x + 90 = 180
9x = 180 - 90
9x = 90
x = 90 / 9
x = 10
Therefore, the measure of the acute angles are 10 and 80 degrees.
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What is 2/9 to the 4th power?
Answer:
[tex]\frac{16}{6561}[/tex]
Step-by-step explanation:
[tex]\frac{2x2x2x2}{9x9x9x9}[/tex] = [tex]\frac{16}{6561}[/tex]
i need answers now pls asap im going to fail I will pay someone on pay pal
The next day Patsy have t choose between cheerleading and play practice is 17th September
How to find the next day Patsy will choose between cheerleading and play practiceTo solve the problem of calculating the next day Patsy will have the events of cheerleading and school play same day, we find the lowest common multiple of the intervals of the occurrence of the two events
The interval of the events are:
cheerleading - 4th day
school play - 6th day
The Lowest common multiple of 4 and 6 is calculated to be 12
If the two events occurred on 5th September the next will on
= 5 + 12
= 17
The next time to choose between the two will be on 17th September
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*URGENT* I need help with 5,6,7 please answer correctly and quickly
Answer:
Step-by-step explanation:
(5). ( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] )
y - [tex]y_{1}[/tex] = m( x - [tex]x_{1}[/tex] )
~~~~~~~~~~~~~~~~~
( 4 , 8 )
y = [tex]\frac{1}{7}[/tex] x - 5 ; slope m = [tex]\frac{1}{7}[/tex]
Slope of line ⊥ to the given line is opposite reciprocal to [tex]\frac{1}{7}[/tex] and equal to ( - 7)
y - 8 = - 7( x - 4 )
(6).
( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] )
( [tex]x_{2}[/tex] , [tex]y_{2}[/tex] )
m = [tex]\frac{ y_{2} -y_{1} }{ x_{2} -x_{1} }[/tex]
y = mx + b
~~~~~~~~~~~~
( 4 , 3 )
( 5 , 1 )
m = [tex]\frac{1-3}{5-4}[/tex] = - 2
y - 3 = - 2( x - 4 )
y = - 2x + 11
(7). y = - [tex]\frac{1}{2}[/tex] x + 2
The table how the amount of time, in minute, it take to walk a given ditance, in mile, along each path. Complete the table to how the average walking rate, in mile per hour, for each path
The data posted at the conclusion of the answer provides the finished table with the average walking rates.
What is unitary method ?Area is the total amount of space that an object's shape or a flat (2-D) surface occupy.
Create a square on paper by using a pencil. Two dimensions make it up. A shape's area on paper is the space it takes up.
Imagine that your square is made up of smaller unit squares.
The area of a figure is equal to the number of unit squares required to completely cover the surface area of a particular 2-D shape. Square cms, square feet, square inches, square meters, etc. are a few common units for measuring area.
To get the area of the square figures presented below, draw unit squares with 1-centimeter sides. Therefore, the shape will be measured
According to our question-
The velocity in this problem is the average walking speed, hence the distances in the table are calculated by dividing the time in the same row by the velocity.
The velocity is reported as follows for the first row:
2.5 miles per hour is equal to v = 0.5/(12/60) = 0.5/0.2.
The minutes are split by 60 because the time is in hours.
The velocity is stated as follows for the second row:
1.5 x 4/3 divided by 45/60 equals 2 miles per hour, or v.
The velocity is given as follows for the third row:
v = 0.75 x 4 x (15/60) = 4 miles per hour.
Hence, 4 miles per hour.
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