The linear relationship must follow the general rule:
[tex]y=m\cdot x+b[/tex]where m is the slope of the linear relationship and b is called the y-intercept
if b = 0, so, it will be a proportional relationship
So, if we have a graph, the graph will be a line
The slope of the line will be = rise/run
Where rise = the difference between y-coordinates
And the run will be = the difference between x-coordinates
If we have a table, we will find the slope using two points from the table with the ordered pair (x1, y1) and ( x2, y2 ) as follows:
[tex]slope=\frac{y_2-y_1}{x_2-x_1}[/tex]The ratio must be constant between any two points from the table
Finally, if we have an equation, it must be like the general form or can be converted to the general form
In general, the linear equation has a degree of 1
- School is 2 miles from home along a
straight road. The table shows your
distance from home as you walk home
at a constant rate. Give the constant of proportionality as a decimal.
Time (min)= Distance from home (mi)
10 min =1.5 miles
20 min= 1 mile
30 min= 0.5 miles
The most appropriate choice for proportion will be given by -
the constant of proportionality is 0.05
What is proportionality?
Suppose there are two quantities. Proportion indicates that if there is a change in the value of one quantity, the value of other quantity also changes but maintaining a constant ratio
Proportion can be direct or inverse
Direct proportion
Two quantities are said to be in direct proportion if on increasing the value of one quantity, the value of other quantity also increases and vice versa.
For example cost of a commodity and quantity of a commodity are in direct proportion
Inverse proportion
Two quantities are said to be in inverse proportion if on increasing the value of one quantity, the value of other quantity decreases and vice versa.
For example Number of men and number of days taken by those men to complete a job.
Here,
Distance from home is not proportional to time
Distance of school from home = 2 miles
For distance from school = 2 - 1.5 = 0.5 miles, time taken is 10 min
For distance from school = 2 - 1 = 1 mile, time taken is 20 min
For distance from school = 2 - 0.5 = 1.5 miles, time taken is 30 min
Let [tex]d = k \times t[/tex], where k is the constant of proportionality.
Putting d = 0.5, t = 10,
[tex]0.5 = k\times 10\\k = \frac{0.5}{10}[/tex]
k = 0.05
Putting d = 1, t = 20,
[tex]1 = k\times 20\\k = \frac{1}{20}[/tex]
k = 0.05
Putting d = 1.5, t = 30,
[tex]1.5 = k\times 10\\k = \frac{0.5}{30}[/tex]
k = 0.05
So the constant of proportionality is 0.05
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the heigh of a rocket, h, is increasing at a constant rate of 18 feet per second. If it's height at five seconds is 118 feet, then write a linear equation for h as a function of time, t, in seconds since it was fired
A linear equation for h as a function of time, t, in seconds since it was fired is; h(t) = (18t + 28) ft
How to find a Projectile equation?
We are given that the Rate of increasing of height is 18 ft/s
We are told that at t = 5 seconds, the height is 118 feet,
This means that;
h(5) = 118 ft
We know that height of rocket is increasing 18 ft for every second passed, and it will also have an initial height.
Thus;
h(t) = 18t + h₀
where;
h₀ is the initial height
Plugging in the relevant values for a height of 5 seconds gives;
118 = (18 * 5) + h₀
h₀ = 118 -90
h₀ = 28 ft
Thus, the equation for the height is;
h(t) = (18t + 28) ft at a time t seconds.
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Plllllz help
A candy company sells peanut brittle and almond bark. The information for both types of candy is shown.
graph labeled Peanut Brittle with x axis labeled weight in ounces and y axis labeled cost in dollars with a line from point 0 comma 0 going through 10 comma 10
Determine how much more one candy costs per ounce than the other candy.
Almond bark costs $0.38 more per ounce than peanut brittle.
Peanut brittle costs $0.38 more per ounce than almond bark.
Almond bark costs $0.60 more per ounce than peanut brittle.
Peanut brittle costs $0.60 more per ounce than almond bark.
Answer:
THE ANSWER IS C.
I also took the test.
owen made a scale drawing of a city. in real life a neighboorhood park is 170 yards long. it is 17 inches long innthe drawing. what scale did owen use for the drawing
1 inch : ____ yards
Answer:
1 inch: 10 yards
Step-by-step explanation:
170/17 = 10
Divide the actual scale by the drawn scale to find how many yards is represented by an inch.
Pepe Garza, sales leader for the past month, earned 47 one-point certificates. If he earned a total of 68 points, how many three-point certificates did he earn?
We know Pepe earned a total of 68 points, 47 of which were earned by one point certificates. That means that 68-47=21 points were earned by 3 points certificates.
Therefore he earned 21/3=7 three point certificates.
Solve for b and graph the solution.
5=1b-51
Answer:
b = 56
Step-by-step explanation:
Answer:B =46
Step-by-step explanation:
Given the base band height hof a triangle, calculate the area A using the formula for the area of a triangle: A = 1/2 bh Calculate A when b 17 feet and h = 6 feet. what is the answer
The area of the triangle of base (b) and a height (h) is A
[tex]A=\frac{1}{2}\cdot b\cdot h[/tex]Given: b = 17 feet and h = 6 feet
So, the area will be :
[tex]A=\frac{1}{2}\cdot17\cdot6=17\cdot3=51ft^2[/tex]so, the answer is : the area of the triangle = 51 square feet.
The graph shows the scores of an exam. About what percent of students scored above 86%?
Attach shows the scores of students in an exam
[tex]\begin{gathered} \text{(students scored above 86\%) = }\frac{\text{ number of students score above 86\%}}{\text{Total scored }}\text{ x }\frac{100}{1} \\ \text{(students scored above 86\%) = }\frac{\text{8+5.9+2.2+2}}{1.4+2.2+4.5+6.2+8.5+16.5+18+16.3+8+8+5.9+2.2+2}X\frac{100}{1} \\ \\ \text{(students scored above 86\%) = }\frac{18.1}{99.7}\text{ X }\frac{100}{1} \\ \text{(students scored above 86\%) = }18.15\text{ \%} \\ \text{(students scored above 86\%) = 18\%} \end{gathered}[/tex]Hence the correct answer = 18% Option A
Start with 16÷8. Rewrite as an equivalent multiplication expression using the multiplicative inverse of 8.
The equivalent multiplication expression using the multiplicative inverse of 8 is 16 x ¹/₈ or 16 x 8⁻¹.
What is the multiplicative inverse?The multiplicative inverse is the reciprocal of a number.
The multiplicative inverse can be used to replace the division operation.
It is a simpler way that supplies the equivalent multiplication result in place of the division operation.
Check:
16÷8 = 2
Similarly, 16 x ¹/₈ = 2
Thus, instead of 16÷8, we can also use the multiplication inverse of 8 which is 16 x ¹/₈.
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what is the whole number, improper fraction and fraction 10/10
An improper fraction has the top number bigger or equal to the bottom one.
Therefore in this case 10/10 is an improper fraction.
This can be written as 1, then the whole number representation is 1.
Find the values of x, y, z, A, and B in the image below. List the facts that both triangles have 90° angles and that the triangles are similar. What is the value of A and B in degrees? What is the measure of y and z?
Answer:
[tex]\begin{gathered} A=36.87\text{\degree} \\ B=53.13\text{\degree} \\ x=12 \\ y=10.15 \\ z=6.25 \end{gathered}[/tex]Step-by-step explanation:
First, we'll work on the triangle that's on the left side. We'll find the values of A,B and x.
Using the law of sines, we'll have that:
[tex]\frac{\sin(90)}{15}=\frac{\sin(A)}{9}[/tex]Solving for A,
[tex]\begin{gathered} \frac{\sin(90)}{15}=\frac{\sin(A)}{9} \\ \\ \rightarrow\sin(A)=\frac{9\sin(90)}{15} \\ \\ \rightarrow\sin(A)=\frac{3}{5} \\ \\ \rightarrow A=\sin^{-1}(\frac{3}{5}) \\ \\ \Rightarrow A=36.87\text{\degree} \end{gathered}[/tex]Now, since we know that the sum of the interior angles of a triangle is 180°, we'll have that:
[tex]\begin{gathered} 90+A+B=180 \\ \rightarrow B=180-A-90 \\ \rightarrow B=180-36.87-90 \\ \\ \Rightarrow B=53.13\text{\degree} \end{gathered}[/tex]Using the law of sines again, we'll get that:
[tex]\frac{x}{\sin(B)}=\frac{15}{\sin(90)}[/tex]Solving for x,
[tex]\begin{gathered} \frac{x}{\sin(B)}=\frac{15}{\sin(90)} \\ \\ \rightarrow x=\frac{15\sin(B)}{\sin(90)}\rightarrow x=\frac{15\sin(53.13)}{\sin(90)} \\ \\ \Rightarrow x=12 \end{gathered}[/tex]Now, we'll work on the triangle that's on the right side. We'll find the values of y and z.
Since this is a right triangle (it has a 90° angle), we can say that:
[tex]\cos(38)=\frac{8}{y}[/tex]Solving for y,
[tex]\begin{gathered} \cos(38)=\frac{8}{y}\rightarrow y\cos(38)=8\rightarrow y=\frac{8}{\cos(38)} \\ \\ \Rightarrow y=10.15 \end{gathered}[/tex]We can also state that:
[tex]\tan(38)=\frac{z}{8}[/tex]Soving for z,
[tex]\begin{gathered} \tan(38)=\frac{z}{8}\rightarrow z=8\tan(38) \\ \\ \Rightarrow z=6.25 \\ \end{gathered}[/tex]This way, we can conclude that:
[tex]\begin{gathered} A=36.87\text{\degree} \\ B=53.13\text{\degree} \\ x=12 \\ y=10.15 \\ z=6.25 \end{gathered}[/tex]a 6 inch cube has the same volume as a box with a base 8in by 9in how tall is the box
Answer: 3 inches tall
Step-by-step explanation:
The formula for the volume of a cube is a to the power of 3
Substitute a with 6 and you get 6^3. 6 X 6 X 6 = 216 so the volume is 216 inches cubed.
The formula for the volume of a rectangular prism is length X width X height. If we substitute the length and with with 8 and 9, we get 8 X 9 X height = 216 (since the volume is the same.)
72 X height = 216. Divide both sides by 72 and you get 3 as an answer.
These marbles are placed in a bag and twoof them are randomly drawn.What is the probability of drawing two yellowmarbles if the first one is NOT placed back intothe bag before the second draw?
Given the figure of marbles:
As shown, the number of marbles = 10
Two marbles are randomly drawn
We will find the probability of drawing two yellow marbles
The probability the first marble is yellow:
The number of yellow marbles = 2
so, the probability the first marble is yellow = 2/10 = 1/5
The first one is NOT placed back into the bag before the second draw
So, the number of marbles = 10 - 1 = 9
The number of yellow marbles = 2 - 1 = 1
So, the probability the second marble is yellow = 1/9
So, the probability of drawing two yellow =
[tex]\frac{1}{5}\times\frac{1}{9}=\frac{1}{45}[/tex]So, the answer will be 1/45
11 Evaluate d-fif d = 7 and f = -15.
Answer:
22
Step-by-step explanation:
= 7 − (−15)
= 7 + 15
= 22
Please please please help I’m dialing
Write another valid congruency statement:
Step-by-step explanation:
I need help with 1&2 they are one whole question
1. From the graph we see that the x-intercept occurs at the points: (3,0) and (-4,0).
Therefore, the factored form of the equation is given by:
[tex]\begin{gathered} x=3 \\ x-3=3-3 \\ x-3=0 \end{gathered}[/tex]or
[tex]\begin{gathered} x=-4 \\ x+4=-4+4 \\ x+4=0 \end{gathered}[/tex]So, the factored form is:
[tex](x-3)(x+4)[/tex]Answer: B. (x - 3)(x + 4)
help pls thank you ….
PART A
1 ounces of chlorine(y) = 0.0078 gallons(x)
y = 0.0078x
PART B
21500 gallons per water = 2.795 ounces of chlorine
What is the formula for converting ounces to gallons?The conversion factor from ounces to gallons is 1 fluid ounce = 0.0078125 gallons.
Given: 0.585 ounces of chlorine
4500 gallons per water
PART A
We know that,
1 ounces of chlorine(y) = 0.0078 gallons(x)
So the equation becomes,
y = 0.0078x
PART B
0.585 ounces of chlorine = 4500 gallons per water
z ounces of chlorine = 21500 gallons per water
z = (21500 × 0.585)/4500
= 2.795
∴ 21500 gallons per water = 2.795 ounces of chlorine
Therefore, the answers of both parts are as follows:
PART A
1 ounces of chlorine(y) = 0.0078 gallons(x)
y = 0.0078x
PART B
21500 gallons per water = 2.795 ounces of chlorine
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The scores on the test for a sample of 39 students are summarized in the following table. Fine the mean score. Round your answer to at least one decimal place
To find the mean of the sample we will sum all the scores and divide by the number of students, therefore
[tex]\begin{gathered} \text{ mean }=\frac{9\cdot90+18\cdot80+12\cdot70}{39} \\ \end{gathered}[/tex]Now, let's use a calculator to solve it, we get
[tex]\text{mean }=\frac{3090}{39}[/tex]And then
[tex]\text{ mean = }79.23[/tex]Therefore, the mean of the sample is 79.23
what is the length of the marked portion of each line segment? Copy the segment onto your paper before finding the missing length. Assume that the entire line segment is sub divided into equal sections.
The length of the marked portion of line segment A is 25, B is 45 and C is 30.
What is line segment?
A line segment in geometry is a section of a straight line that is enclosed by two clearly defined end points and contains all of the points on the line that lie inside those endpoints. The distance between two ends of a line segment is its length. Half-open line segments contain exactly one of the endpoints while other end point is open, while closed line segments have both the endpoints closed. Open line segments do not contain any of the endpoints.
Calculation of line segment A,
75 ÷ 3 = 25
25 × 1 = 25
Therefore, the length of the marked portion of line segment A is 25
Calculation of line segment B,
75 ÷ 5 = 15
15 × 3 = 45
Therefore, the length of the marked portion of line segment B is 45
Calculation of line segment C,
50 ÷ 5 = 10
10 × 3 = 30
Therefore, the length of the marked portion of line segment C is 30
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What is the value of x in the equation x-2/3 + 1/6 = 5/6
The value of x in the equation (x - 2)/3 + 1/6 = 5/6 is: x = 4
How to Solve an Equation?To solve a given equation, find the value of the variable in the equation by isolating the variable to one side using the necessary properties of equality.
Given the equation, (x - 2)/3 + 1/6 = 5/6:
(x - 2)/3 + 1/6 = 5/6
Subtract both sides by 1/6:
(x - 2)/3 + 1/6 - 1/6 = 5/6 - 1/6 (subtraction property of equality)
(x - 2)/3 = 4/6
Multiply both sides by 3:
(x - 2)/3 × 3 = 4/6 × 3 (multiplication property of equality)
x - 2 = 2
Add both sides by 2:
x - 2 + 2 = 2 + 2 (addition property of equality)
x = 4
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three fifths of the t-shirt shop are blue. five eighths of those t-shirts are on sale. One third of the blue t-shirts that are eon sale are size medium. What fraction of the shop's t-shirts are blue t-shirts that are on sale and are size medium? explain
Fraction, A number that is stated mathematically as a quotient, where the numerator and denominator are divided. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.
Blue t-shirts that are on sale and are in the medium size make up 1/8 of the speakers in the store.
Detailed explanation:Let T represent the quantity of T-shirts in the store.
In a store selling t-shirts, blue dominates by three to one.
3/5 of the blue T-shirts were worn.
These blue t-shirts, 5/8 of them, are on sale.
The amount of blue T-shirts for sale is equal to 5/8 × 3/5 T, or 3/8 T.
The majority of the blue t-shirts for sale are size medium,
The number of medium-sized blue t-shirts available for purchase is equal to 1/3 × 3/8 T = 1/8 T.
Blue t-shirts in size medium that are on sale make up 1/8 of the store's speakers.
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Can someone please help me?
I will give brainliest
We can find the QS side that is missing by using the proportions (C) QS/SR = PO/OR.
What do we mean by proportions?A proportion is an equation that equalizes two ratios.You could, for instance, write the ratio as follows: 1: 3 in the case of 1 boy and 3 girls (for every one boy there are 3 girls)The proportion formula is used to determine whether two ratios or fractions are equal.We can find the missing value by dividing the given values.The proportion formula can also be written as a: B::C:D = a/b = c/d, where a and d are the extreme terms and b and c are the mean terms.So, a proportion that is used to determine the QS's missing side
(A) QS/OR = PO/SR
Not possible, and the bases in the denominator have the wrong base positions.(B) PR/PO = QS/QR
Not possible because the order of the lines does not allow for the measurement of line length. QS/SR = PO/OR.(C) QS/SR = PO/OR
Given that the sides and base are both perfectly positioned within the fractions, this ratio can be used to determine the length of line QS.Therefore, we can find the QS side that is missing by using the proportions (C) QS/SR = PO/OR.
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help i am on limited time
The slope intercept equation of the graph f is y = -1/3x + 5
Slope intercept equation:
The general for of the slope intercept equation is,
y = mx + b
Here,
(x, y) = Every point on the line
m = Slope of the line
b = y-intercept of the line
Given,
Here we have the point (-9, 8) and the line of the graph is perpendicular to the x intercept 6 and y intercept -18.
Now we need to find the slope intercept equation for the graph f.
From the given details, we know that,
The x intercept point (6,0)
Y intercept point (0,-18)
So you are looking for a line perpendicular to a line that passes through the points (6,0) and (0,-18)
The slope of the line going through these points is:
m=(y1-y2)/(x1-x2)
slope of this line = 18/6 = 3
the slope of line perpendicular to this line will have slope of -1/3
( negative reciprocal)
Therefore, the point (-9, 8 ) has the slope = -1/3
Now we can use this slope and the given point (-9,8) to find the y-intercept (b)
y = mx + b
8 = (-1/3)(-9) + b
8 = 9/3 + b
b = 8 - 3
b = 5
Therefore, the equation of the line in point intercept form is:
y = -1/3x + 5
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Solve the following system of inequalities graphically on the set of axes below. State the coordinates of a point in the solution set.y < -x - 1y < 1/5x + 7
SOLUTION
Given the question, the following are the solution steps to answer the question.
STEP 1: Write the given inequalities
[tex]\begin{gathered} y<-x-1 \\ y<\frac{1}{5}x+7 \end{gathered}[/tex]STEP 2: Plot the graph of both inequalities
For the first inequality
For the second inequality
STEP 3: Plot the two inequalities on the graph to get the solution set.
The coordinates of a point in the solution set can be given as:
[tex](-10,1)_{}[/tex]can you show me the format to get the answer to m/3 +4=7
can you show me the format to get the answer to m/3 +4=7
we have
[tex]\frac{m}{3}+4=7[/tex]solve for m
that means
isolate the variable m
so
step 1
subtract 4 both sides
[tex]\begin{gathered} \frac{m}{3}=7-4 \\ \frac{m}{3}=3 \end{gathered}[/tex]step 2
multiply by 3 both sides
[tex]\begin{gathered} m=3\cdot3 \\ m=9 \\ \\ \\ \end{gathered}[/tex]therefore
the answer is
m=9we have thatstep 1is equal to
m/3 +4-4=7-4
step 2is equal to
m/3=3
step 3is given
step 4is given
Part 2Let
n------> number of hours
y -----> the total charge
Remember that
The linear equation in slope intercept form is equal to
y=mx+b
where
m is the slope or unit rate
b is the y-intercept or initial value
In this problem
y=mn+b
where
m=$25 per hour
b=$50
so
y=25n+50
For y=$125
Find out the number of hours
substitute the value of y in the equation and solve for n
125=25n+50
25n=125-50
25n=75
n=3 hours
therefore
the answers are
the total charge's equation is (25n+50)
the number of hours are 3
WA Alvin used 1/2 of a cup of frosting to decorate some cupcakes. He divided all the frosting equally among 5 cupcakes. How much frosting did Alvin use on each cupcake? Write your answer as a fraction or as a whole or mixed number. cups Submit
1) Gathering the data
1/2 a cup of frosting equally divided by 5
2) Let's divide the
Directions: Raise the powers of all variables and numbers indicated, and then turn the following expressions in radical form into exponential expressions in rational form. You do not need to evaluate or solve any of the expressions, just put them in simplest exponential form.
The value of the exponents in simple exponential form is [tex]x^{\frac{44}{5}}[/tex] .
The mathematical operation of exponentiation, written as bⁿ, involves the base number (b) and the exponent (or power) number (n). The way to say this word is "b (elevated) to the (power of) n."
Exponentiation corresponds to repeated base multiplication when n is a positive integer since bⁿ is the outcome of multiplying n bases. The exponent is often displayed to the right of the base as a subscript.The phrase "b to the nth power" or simply "b to the nth" is used to refer to bn. Other variations are "b (raised) to the power of n," "the nth power of b," and "b to the power of n" and "b to the nth power,"The properties of exponents tell us that when the bases are equal then on multiplication the powers are added and on division the powers are subtracted.
[tex]\sqrt[5]{5^y} \cdot(5^4)^3 = 5^{\frac{y+60}{5} }[/tex]
[tex]\sqrt[5]{5^x} \cdot(5^4)^3 = 5^{\frac{x+60}{5} }[/tex]
Therefore the properties of exponents can be used to find the exponential solutions.
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The outside temperature decreases by 7 degrees in 3 1/2 hours. How would you represent the temperature change as a unit rate?
In each hour the outside temperature decreases by 2°C/hr.
What is a unitary method?A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.
Given the outside temperature decreases by 7 degrees in 3 1/2 or 7/2 hours.
The representation for the change in temperature as a unit rate will be.
= 7/(7/2) degrees.
= 7×2/7 degrees.
= 2 degrees.
So, The representation of the temperature change as a unit rate will be 2°C/hr.
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Graph the function g(x). I have a picture of the problem.
Let's begin by listing out the given information
[tex]\begin{gathered} g\mleft(x\mright)=\frac{3}{2}x-7 \\ g(x)=y \\ y=\frac{3}{2}x-7 \end{gathered}[/tex]We will proceed to assume values for x to obtain the y-values (x = -2, 0, 4, 8)
[tex]\begin{gathered} y=\frac{3}{2}x-7 \\ x=-2 \\ y=\frac{3}{2}(-2)-7=-3-7=-10 \\ x=0 \\ y=\frac{3}{2}(0)-7=0-7=-7 \\ x=4 \\ y=\frac{3}{2}(4)-7=6-7=-1 \\ x=8 \\ y=\frac{3}{2}(8)-7=12-7=5 \\ (x,y)=(-2,-10),(0,-7),(4,-1),(8,5) \end{gathered}[/tex]We will plot these points on the graph. We have:
Stock on the new york stock exchange opened at 52$ on Monday morning. The table shows the store's value change for each day that week. What was the stock worth at the close of business on Friday?
SOLUTION:
To get the value of the stock at the close of business on Friday, we get the initial value and add the whole daily changes to it;
[tex]\begin{gathered} 52-2+1+3-1-4 \\ \\ =\text{ \$}49 \end{gathered}[/tex]Therefore, on the close of business on Friday, the stock was worth $49
