Todd's conclusion is therefore incorrect, not all linear relationships are proportional, they can be represented by a linear equation but they don't need to have a constant ratio between the two variables.
What is a linear relationship?
A linear relationship is a relationship between two variables in which the change in one variable is directly proportional to the change in the other variable. Linear relationships can be represented by a linear equation, which is an equation that can be written in the form of y = mx + b, where m and b are constants.
Proportional relationships also have a constant ratio between the two variables, but the relationship between the variables is not always linear. Proportionality can be represented by the equation y = kx, where k is a constant.
In general, it is not true that all linear relationships must be proportional. While it is true that a proportional relationship will always result in a linear graph, there are also many other types of linear relationships that do not fit this definition. For example, the equation y = 2x + 3 describes a linear relationship, but it is not proportional because the ratio between y and x is not constant.
Hence, Todd's conclusion is therefore incorrect, not all linear relationships are proportional, they can be represented by a linear equation but they don't need to have a constant ratio between the two variables.
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IMPORTANT: Given the triangles below are similar, find the missing side length. Show the work that
Answer:
x=15
Step-by-step explanation:
6(5)=30
3(5)=15
The length of the missing side Triangle is 3
As it is given that the given triangle is similar which shows all three sides of both the triangle will be in the same ratio by CPST (corresponding parts of similar Triangles).
so
15/x=30/6 ................. the ratio of two sides of the triangle
x = 15*6/30
x= 3
here the value of x is 3.
Also, the ratio of the side comes out to be 5:1 as 6 and 30 are the length so the first triangle has a side of 15 and the length of another triangle will be 3 to make the ratio 5:1.
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Two angles are complementary to each other. One angle measures 18°, and the other angle measures (8x − 28)°. Determine the value of x.
Since one angle measures 18°, and the other angle measures (8x − 28)°, the value of x is equal to 12.5.
What is a complementary angle?In Mathematics, a complementary angle can be defined as two (2) angles or arc whose sum is equal to 90 degrees (90°).
Mathematically, a complementary angle can be calculated by using this mathematical expression:
Q + R = 90°
Where:
Q and R are measure of the angles subtended.
Substituting the given parameters into the complementary angle formula, the sum of the angles is given by;
(8x - 28)° + 18° = 90°
8x - 10 = 90
8x = 90 + 10
8x = 100
x = 100/8
x = 12.5
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if one bird requires half square foot or six square inches of space during brooding how much space is required in total for 30 Birds
Answer: 6 or 7 square inches
Step-by-step explanation: Chicks need enough space under the brooder so that they can keep warm without crowding, piling up or smothering. Under normal conditions, each replacement chick needs about 6 or 7 square inches of brooder space
Which of the arithmetic mean, median, mode, and geometric mean are resistant measures of central tendency?
a) The arithmetic mean and median only.
b) The median and mode only.
c) The mode and geometric mean only.
d) The arithmetic mean and mode only.
The median and mode only are resistant measures of central tendency.
The correct option is B.
Statistics that are resistant to outliers don't change as a result. We assert that the median is a resistive measure of centre, in contrast to the mean, which is not. In a way, the median is able to reject distant values whereas the mean is drawn to them. It cannot withstand the impact of excessive values. The measurement that is least subject to sample variation is the median, which is defined as the middle of ranking data, where 50% of values are above it and 50% below it. As a result, the extreme figures have no bearing on the median. For symmetric data, nonresistant measures perform better because they are less affected by skewness and outliers. Resistant measures can be used since they are less negatively influenced.
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Rearrange this expression into quadratic form, 2++=0 , and identify the values of , , and . 0.20=2/75−x
Rearranging the given expression into quadratic form gives x² + 0.2x - 15 = 0.
The values of a, b, and c include the following:
a = 1
b = 0.2
c = -15
What is a quadratic function?In Mathematics, the standard form of a quadratic function is given by this mathematical expression;
ax² + bx + c = 0
Where:
a and b represents the coefficients of the first and second term in the quadratic function. c represents the constant.Next, we would multiply both sides of the quadratic function by (75 - x) as follows;
0.20 × (75 - x) = x²/(75 - x) × (75 - x)
0.20 × (75 - x) = x²
By applying the distributive property to the mathematical expression, we have the following:
0.20(75) - 0.20(x) = x²
15 - 0.2x = x²
By rearranging the mathematical expression, we have the following:
x² + 0.2x - 15 = 0
Therefore, the quadratic function is equal to x² + 0.2x - 15 = 0.
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If the mean time between unscheduled maintenance of LCD displays in a hospital's CT scan facility is 4,000 operating hours, what is the probability of unscheduled maintenance in exactly 5,000 hours?
The probability of unscheduled maintenance in exactly 5,000 hours is 4/5.
What is the probability?
We know that the probability deals with the fact that an event may or many not occur. It deals with a chance event. In this case, we have been told that the hospital's CT scan facility is 4,000 operating hours.
We know that the probability can be obtained from;
P = Number of unscheduled maintenance hours/Total operating hours
This would now give us that;
P = 4000/5000
P = 4/5
Hence, there is a probability of 4/5.
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1 week is 5 miles 2 weeks is 6 miles 3 weeks is 7 miles 4 weeks is 8 miles write an equation while w is weeks and m is miles m=w...
The automobile travels at an average speed of 65.71 mph.
Find the car's average speed ?Put r = d/t to use.You are moving at a rate of 12 miles per hour since 24 miles are multiplied by two hours.Become familiar with the distance formula, a Pythagorean theorem application that can be used to determine the separation between two places.
Sal Khan and the CK-12 Foundation created it.
The car's average speed is 65.71 miles per hour.
the settings provided;Initially, the automobile is traveling at 50 mph.
motion time, t = 3 hours
v = 70 mph is the motion's final speed.
motion time, t = 11 hours
The following formula is used to determine the car's average speed:
average speed = total distance /total speed
Total distance traveled divided by total motion duration equals average speed.
The entire distance is equal to 920 miles (50 x 3 + 70 x 11).
The duration of the motion was (3 + 11) hours, or 14 hours.
The car's typical speed is;
Consequently, the car's average speed is 65.71 mph.
average speed =920/14
= 65.71 mph.
Find out more here:The automobile travels at an average speed of 65.71 mph.
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Please please please help. I'm in honor's geometry and if I don't get my grade at least to a C, I'm going to fail
In the diagram below, m is the perpendicular bisector of BC.
If BK = 5x, AC = 6x + 7, CP = 4x, AB = 9x – 14. Find BC
Answer:
BC = 56 units
Step-by-step explanation:
since the main diagonal AK bisects the diagonal BC , then the figure is a kite.
• the disjoint pairs of consecutive sides are congruent in a kite, that is
AB = AC and BK = CK
using the pair AB = AC to solve for x
9x - 14 = 6x + 7 ( subtract 6x from both sides )
3x - 14 = 7 ( add 14 to both sides )
3x = 21 ( divide both sides by 3 )
x = 7
Since m bisects BC , then
CP = PB and
BC = CP + PB = 4x + 4x = 8x
then
BC = 8x = 8 × 7 = 56
What is the value of the expression d (20+d) d when =8
36
84
168
224
Answer:
Option D: 224
Step-by-step explanation:
[tex] \sf (20 + d)d[/tex]
Insert the value d = 8
[tex] \sf(20 + 8)8[/tex]
Add
[tex] \sf (28)8[/tex]
multiply
[tex] \sf 224[/tex]
The registration fee for a used car is 0.8% of the sale price of $5,900. How much is the fee? (Simplify your answer.)
the water tank of mang peter was full with 10000 liters of water on monday. he used 1500 liters that day.How much water was left on tuesday?
Therefore , the solution of subtraction after subtraction, amount of water left on Tuesday is 98500 liters.
What is difference?One of the most crucial mathematical operations, which is obtained by removing two numbers, produces difference in mathematics. It reveals how much one number deviates from another. To determine how many numbers are between the two given numbers is the goal of finding the difference in math.
Here,
Given:
Amount of water on Monday=10000
Amount of water used=1500
Water left on Tuesday=10000-1500=98500
Thus , amount of water left on Tuesday is 98500 liters.
Therefore , the solution of subtraction after subtraction, amount of water left on Tuesday is 98500 liters.
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Complete a table for the rule y = 3-x
a. Draw a complete graph (4 quadrants) for this rule. Either
use a growth triangle or a table to help you.
b. Is (32,-29) a point on this graph? Explain why or why not
a. Drawn a complete graph in the attachment. (32,-29) is a point on this graph.
What is graph?A graph is a mathematical diagram that shows the correlation between two or more sets of numbers or measurements. It is a diagram that shows the relationship between various sets of numbers or quantities using a series of dots, lines, etc., plotted in reference to a set of axes.
a. Using rule y = 3-x
When x = 3
y = 3-(4)
y = -1
A(4, -1)
Using rule y = 3-x
When x = 2
y = 3-(2)
y = 1
B(2, 1)
Using rule y = 3-x
When x = -2
y = 3-(-2)
y = 5
C(-2, 5)
b. Lets put (32,-29) on the rule
-29 = 3 - 32
-29 = -29
Thus, (32,-29) is a point on this graph
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Anything would be great
PLEASE THIS ONE'S EASY BUT I'M JUST stu--It's Due Now!
A. The range of the function y = 3x - 2, considering the domain {-1, 2,4}, is given as follows:
Range: {-5, 4, 10}.
B. The set of ordered pairs that represent the function is given as follows:
{(-1,-5), (2,4), (4,10)}
How to obtain the range of the function?The function for this problem is given as follows:
y = 3x - 2.
The domain of the function is given as follows:
{-1, 2,4}.
The range of the function is composed by the numeric values of the function assumed for these input values.
The numeric values of the function are found replacing the lone instance of x by their input values, as follows:
y = 3(-1) - 2 = -5.y = 3(2) - 2 = 4.y = 3(4) - 2 = 10.Hence the range is the set composed by -5, 4 and 10.
An ordered pair has the following format:
(x,y).
In which y is the numeric value of the input x.
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The midpoint of the segment joining points (a, b) and (j, k) is:
The midpoint of the segment joining points (a,b) and (j,k) is, (a+j)/2, (b+k)/2)
The midpoint of the segment joining two points (x1, y1) and (x2, y2) is given by the point ((x1 + x2)/2, (y1 + y2)/2).
So, to find the midpoint of the segment joining the points (a, b) and (j, k), we need to take the average of the x-coordinates and the average of the y-coordinates:
((a + j)/2, (b + k)/2)
So the midpoint of the segment joining points (a,b) and (j,k) is (a+j)/2, (b+k)/2).
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Which equation is represented by the graphed line? (Image: graph of a line) y = x + 5 y = 5x y = x - 5
The graphed line is y = 5x passing through points (0, 0) and (1, 5)
What is an equation?An equation is an expression that shows the relationship between variables and numbers.
The linear equation is in the form:
y = mx + b
where m is the rate of change and b is the y intercept.
The graphed line passes through (0, 0) and (1, 5), hence the equation is:
y - 0 = [(5-0)/(1 - 0)](x - 0)
y = 5x
The graphed line is y = 5x.
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Joe pushes a 200 kg car with a force of 125 N. In what scenario
would Joe not be doing work or the car?
O when the car moves
O when the car does not move
O when there is no friction
O when the power is too large
9 This is a required question
The chart below shows the force applied on four different
2 pol
Joe pushes a 200 kg car with a force of 125 N, In the scenario when the car does not move, Joe not be doing work or the car.
Which four types of friction are there?Static friction, sliding friction, rolling friction, and fluid friction are the four main categories of friction. Normal force and friction are independent of the hardness of the contacting surfaces and are directly proportional to the contacting surfaces.
How is the friction work calculated?The tiny bumps push against each other as two surfaces slide over one another. A surface is subject to a force from friction equivalent that opposes the direction of the surface's motion. Application of lubricants can reduce friction.
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If Jill makes $90 commission on $300 in sales, at the same commission rate,
how much will she make on $480 in sales?
The commission made by Jill for a $480 sale at the rate of commission 30% is $144.
What is meant by the rate of commission?
A commission is a payment made to a salesperson by a company in exchange for his or her assistance in facilitating or closing a sale. The design of the underlying commission agreement determines how a sales commission is calculated.
The rate of commission is a percentage or fixed sum that is linked to a specific amount of sales.
Given,
Sales = $300
Commission = $90
Then, rate of commission = (Commission/ sales) * 100
= ( 90/300) * 100 = 30%
For this rate of commission, the commission she makes for a $480 sale is
= 480 * (30/100) = 480 * 0.3 = $144
Therefore, the commission made by Jill for a $480 sale at the rate of commission 30% is $144.
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A bag contains 3 blue marbles, 10 green marbles,
4 yellow marbles, and 8 red marbles. A marble is chosen at random,
replaced, then another marble is chosen. Find each probability of getting
a green then a yellow.
8/125
24/625
12/625
6/125
On solving the provided question, the equation will be and the factors - This cannot be determined from the information given
what is parabola?When points on a curve are equally spaced from a fixed point and line, the curve is said to have a parabola as its equation. The parabola's fixed point is referred to as the focus, and its fixed line is referred to as the directrix. Remember that the fixed point is not on the fixed line as well. A parabola is the locus of any point that is equidistant from both a focus and a straight line. A conical curve of interest in coordinate geometry is a parabola.
The equation will be
=> 4x+9 = 20x - 2.3y
x = 989-32y
y = 5.4x - 10
Factors - This cannot be determined from the information given
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The table shows the points scored by a community football team during two seasons. Use the mean and standard deviation to determine during which season the team scored more consistently.
Last Season: 10, 3, 20, 27, 35, 17, 20, 13, 17
This Season: 23, 17, 28, 16, 23, 16, 16, 10, 13
The season the team scored more consistently will be this season because the Standard deviation is less.
What are statistics?Statistics is the study of collection, analysis, interpretation, and presentation of data or discipline to collect and summarise the data.
Last Season: 10, 3, 20, 27, 35, 17, 20, 13, 17
The mean is given as,
Mean = (10 + 3 + ...... + 17) / 9
Mean = 18
Then the standard deviation is given as,
Standard deviation = [(10 - 18)² + (3 - 18)² + ...... + (17 - 18)²] / 9
Standard deviation = 8.78
This Season: 23, 17, 28, 16, 23, 16, 16, 10, 13
The mean is given as,
Mean = (23 + 17 + ... + 13) / 9
Mean = 18
Then the standard deviation is given as,
Standard deviation = (23 - 18)² + (17 - 18)² + ...... + (13 - 18)²
Standard deviation = 5.29
The season the team scored more consistently will be this season because the Standard deviation is less.
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What is the equivalent of 3(x - 6)
Answer:
3x-18
Step-by-step explanation:
Inga is solving 2x2 + 12x – 3 = 0. Which steps could she use to solve the quadratic equation? Select three options. 2(x2 + 6x + 9) = 3 + 18 2(x2 + 6x) = –3 2(x2 + 6x) = 3 x + 3 = Plus or minus StartRoot StartFraction 21 Over 2 EndFraction EndRoot 2(x2 + 6x + 9) = –3 + 9
(2x + 3)(x - 1) = 0
x = (-b ± √(b^2 - 4ac))/ 2a, where a = 2, b = 12, and c = -3.
2x^2 + 12x = 3
(6/2)^2 = 9
2x^2 + 12x + 9 - 9 = 3 - 9
factor out the 2x^2 + 12x + 9 = 0
a cube has 6 faces top bottom and all 4 sides.
The perimeter of a triangular park shown on the right is 11x-6.
What is the missing angle ?
The missing length of the right-angle triangle will be 6x - 3.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.
The perimeter of the triangle is determined by adding together all of its sides.
The third side of the triangle is given as,
11x - 6 = H + 4x + 2 + x - 5
H = 11x - 6 - 4x - 2 - x + 5
H = 6x - 3
The missing length of the right-angle triangle will be 6x - 3.
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The complete question is given below.
Question 3 of 10
What is the value of x?
37⁰
75"
The value of x in the figure is 40°.
What is linear pair?When two lines meet at a single point, a pair of linear angles is created. If the angles follow the point where the two lines cross, they are considered to be linear. A linear pair's angles add up to 180° in every case. These angles are additionally referred to as. A linear pair is made up of two angles that are next to one another and whose non-common sides form a line. All angles that create a linear pair are supplementary, however not all supplementary angles have to be linear pairs.In a linear pair, the total of two angles is always 180°. All neighboring angles are linear pairs, however not all adjacent angles are linear pairs.
∠DBA + ∠ABC = 180° ( ∵ linear pair)
∠100° + ∠ABC = 180°
∠ABC = 180° - 100°
∠ABC = 80°
The sum of angles of a triangle is 180° .
So, in triangle ABC
∠A + ∠B + ∠C = 180°
x + 80 + 60 = 180°
x + 140 = 180°
x = 180° - 140°
x = 40°
So, ∠A = x = 40°
The complete question is,
Find the value of x in the figure below :
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Roman and Sienna are comparing the number of pages they’ve each read over the Winter Break. Roman said he read 40% of his book, which has a total of 200 pages. Sienna’s book has a total of 400 pages, and she read of it. Without calculating, who do you predict has read more pages of their book? Explain 1/5 your reasoning.
In linear equation, 53% is predict has read more pages of their book .
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.
Total pages = 400
Remaining pages to be read after Monday = 400 - 200 = 200
40% of 200 = 200 × 40/100 = 80
Remaining pages to be read after Tuesday = 400 - 80 = 320
600 × x/100 = 320
Let the remaining percentage of pages remain to be read be x,
so, 600 × x/100 = 320
x = 320/6 = 53.33333% = 53%
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Which graph shows the solution to the system of linear inequalities?
x – 4y < 4
y < x + 1
Answer: we have
--------> inequality A
--------> inequality B
Using a graphing tool
the solution of the inequality A is the shaded area above the dashed line
see the attached figure N
the solution of the inequality B is the shaded area below the dashed line
see the attached figure N
therefore
the solution of the compound system of inequalities is the shaded area between the two dashed lines
see the attached figure N
therefor
the answer in the attached figure N
The cylindrical and the cuboidal containers shown below have the same height. the same amount of water was poured into each container. The water filled 1/2 of the cylindrical container and 1/3 of the cuboidal container. If the base are of the cylindrical container is 154 sq cm, what is the base area of the cuboidal container?
Note that where the cylindrical and the cuboidal containers shown below have the same height. the same amount of water was poured into each container. The water filled 1/2 of the cylindrical container and 1/3 of the cuboidal container. If the base area of the cylindrical container is 154 sq cm, the base area of the Cuboidal Container is 15.2
What is the justification for the above?Let the height of the cylinder and cuboidal container be h m
We know that the base of the cylinder container is given as: 154 sq cm.
Recall that the volume for a cylinder is = Base x Height
That means in this case:
The volume for the cylinder is = 154 x Height
Thus,
1/2 * 154h = 1/3h³
77h = 1/3h³; divide both side by h to get
77 = 1/3h²
Collecting like terms and make h subject of the formula, we have;
h² = 77 * 3
h² = 231
h = √231
h= 15.1986841536
h = 15.199 or [tex]\approx[/tex] 15.2
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6 times a number plus 22 is greater than 7
Answer:X>=5/2;
Step-by-step explanation:
(6*5/2)+22>7
Answer:
True
Step-by-step explanation:
(6*5/2+22) it gives you the correct amount. You also need to pay attention to the greater then and less than signs so that you don’t get confused.
→ < >
Therefore, this is true
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You are pulling a kite back to the ground at a rate of 2 feet per second.
After 4 seconds, the kite is 16 feet above the ground.
a. Write an equation that represents the height y (in feet) above the
ground after x seconds.
b. At what height was the kite when you started pulling it in?
c. When does the kite touch the ground?
The slope of line exists -2 then the value of x is 12 seconds.
What is meant by point-slope form?The simplest definition of point-slope form is a line equation expressed using a single line point and the line's slope. The slope is the ratio of the change in the y values over the change in the x values, or the rise over run, and the point form is written as (x, y).
The relationship between x and y is linear because the rate at which the kite is being drawn in is constant. The height reaches 16 feet after 4 seconds, making the point (4, 16) on the line. After 5 seconds, the height is 14 feet since the kite is being dragged in at a rate of 2 feet per second. Therefore, (5, 14) is another point on the line.
slope of line = (16-14)/(4-5) = -2
Using the point-slope form, an equation of the line exists:
y - 16 = -2(x - 4)
y - 16 = -2x + 8
y = -2x + 24
To estimate the original height,
Let x = 0: y = -2(0) + 24 = 24 feet
The kite hits the ground when y = 0:
0 = -2x + 24
x = 12 seconds
Therefore, the value of x = 12 seconds.
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