We have two points of the line, and we have to find the equation of the line in the slope-intercept form:
\(y=mx+b\)First, we find the slope as:
\(m=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}=\frac{9-3}{4-1}=\frac{6}{3}=2\)With the value of the slope, we can calculate b replacing the values of x and y with one of the know points:
\(\begin{gathered} y=mx+b \\ y=2x+b \\ 3=2\cdot1+b \\ 3=2+b \\ b=3-2 \\ b=1 \end{gathered}\)Now, we have the two parameters (slope and y-intercept) to define the line, and we can write the equation as:
\(y=2x+1\)A plumber charges $70 per hour plus $40 for the call. What does he charge for 4 hours of work? Use x to represent the hours of work.
Answer:
Step-by-step explanation:
70x4 is 280 plus 40 is 320.
Answer:
$320
Step-by-step explanation:
(4 x $70) + $40 is the equation
$280 + $40 = $320
$320
Anyone can help with this answer please
please hurry A side of the triangle below has been extended to form an exterior angle of 133°. Find the value of xx.
Solution:
Note that:
x + 108 + (180 - 133) = 180Simplify the equation to find x.
=> x + 108 + (180 - 133) = 180=> x + 108 + (47) = 180=> x + 155 = 180=> x = 180 - 155 = 25°→ x + 108 + (180 - 133) = 180°
→ x + 108 + (47) = 180°
→ x + 155 = 180°
→ x = 180 - 155 = 25°
4. Xander pays $8 for 10 skateboard stickers. There is a proportional relationship between the number of stickers Xander buys, x, and the total cost, y. Equation:
Answer:8x=10y
Step-by-step explanation:
A proportional relationship between the number of stickers Xander buys, x, and the total cost, y is 8x=10y.
Given that, Xander pays $8 for 10 skateboard stickers.
What is a proportional relationship?Proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value times the other. That constant is know as the "constant of proportionality".
Given, the number of stickers Xander buys, x, and the total cost, y.
Now, 8x=10y
⇒ x/y = 10/8
Therefore, a proportional relationship between the number of stickers Xander buys, x, and the total cost, y is 8x=10y.
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Use the method of direct proof to prove the following statement.
If two integers have the same parity, then their sum is even. (Try cases.)
In both cases, if two integers have the same parity, then their sum is even. Therefore, the statement is true.
To prove the statement "If two integers have the same parity, then their sum is even," we will use the method of direct proof.
Let's assume that there are two integers a and b with the same parity. This means that both a and b are either even or odd.
Case 1: Both a and b are even.
If both a and b are even, then we can write them as a=2m and b=2n for some integers m and n. Their sum is:
a+b = 2m + 2n = 2(m+n)
Since m and n are integers, m+n is also an integer. Therefore, a+b is even.
Case 2: Both a and b are odd.
If both a and b are odd, then we can write them as a=2m+1 and b=2n+1 for some integers m and n. Their sum is:
a+b = (2m+1) + (2n+1) = 2(m+n) + 2
Since m and n are integers, m+n is also an integer. Therefore, a+b is even.
In both cases, we have shown that if two integers have the same parity, then their sum is even. Therefore, the statement is true.
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BRAINIEST AND A LOT OF EXTRA POINTS FOR A SURE AND CORRECT ANSWER
Using the arithmetic operations, the total change in her monthly electric bill over 5 months is +$10.58
For the past 5 months,
The change in her July electric bill = +$18.02
The change in her August electric bill = +$1.03
The change in her September electric bill = -$0.44
The change in her October electric bill = -$6.84
The change in her November electric bill = -$1.19
The total change in her monthly electric bill over 5 months = Sum of all changes in her electric bill over 5 months
= +18.02+1.03-0.44-6.84-1.19
= +$10.58
Hence, the total change in her monthly electric bill over 5 months is +$10.58
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Which coordinates represent a translation of B(1, 2) 3 units to the left and 2 units up?
B′(–2, 0)
B′(–2, 4)
B′(4, 4)
B′(4, 0)
Answer:
(-2,4)
Step-by-step explanation:
B(1,2)
(x-3, y+2)
1-3=-2
x=(-2)
2+2=4
y=4
Hope this helps! :)
Answer:
B'(-2, 4)
Step-by-step explanation:
If it goes 3 units left, that means you're doing x - 3.
If it goes 2 units up that means you're doing y + 2 This would be:
(1 - 3, 2 + 2)
(-2, 4)
can anyone help and explain why this is either proportional or not? urgent!! (it needs an explanation too)
Answer:
The answer is that the table is not a proportional relationship.
Step-by-step explanation:
It's not a proportional relationship because the number was not a constant variable.In order for the table to have a proportional relationship the number has to be the same for all of the ratios.
Proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value times the other. That constant is know as the "constant of proportionality".
Hope this helps!!
A random survey asked two samples of 100 high school students how much time they spend on homework each night. A 4-column table with 2 rows.
The time categories are divided into "<1 hour," "1-2 hours," "2-3 hours," and ">3 hours."
What does the frequency distribution in the table reveal about the homework habits of the two samples of high school students?
The frequency distribution in the table provides insights into the distribution of homework habits among the two samples of high school students. By examining the frequency counts in each time category, we can determine the proportion of students spending different amounts of time on homework each night. This information helps identify patterns and differences in homework habits between the two samples, allowing for a comparison of their study behaviors.
Here is an example of a 4-column table with 2 rows representing the results of a random survey asking two samples of 100 high school students about the amount of time they spend on homework each night:
Sample 1:
Sample 1 Number of Students
Time Frequency
<1 hour 20
1-2 hours 40
2-3 hours 30
>3 hours 10
Sample 2:
Sample 2 Number of Students
Time Frequency
<1 hour 30
1-2 hours 35
2-3 hours 20
>3 hours 15
In this table, each sample represents a different group of 100 high school students, and the frequency of students spending a particular amount of time on homework each night is recorded. The time categories are divided into "<1 hour," "1-2 hours," "2-3 hours," and ">3 hours." The table provides an overview of the distribution of homework time among the two samples of high school students.
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For every 3 apples in a
bowl there is 1 banana. If
there are 18 apples, how
many bananas will there
be? First person gets a 5star review!!
Answer:
18 apples equals 6 bananas
Answer:
There will be 6 bananas in that bowl
What is 7/56 simplified
Answer:
1/8
Step-by-step explanation:
BOOM!
Answer:
1/8
Step-by-step explanation:
broken down into fractions 1/8 is the simplest answer
Question
Enter a recursive rule and an explicit rule for the arithmetic sequence. Then, find the 20th term of the
sequence
55, 65, 75, 85,-
The recursive rule is f(1) =
f(n)=f(?
+
The explicit rule is f(n) =
+
?
f(20) =
Answer:
The recursive rule is \(f(1)\) = first term; \(f_({n})\) = \(f_({n-1})\) + d
f(1) = 55; \(f_{20}\) = \(f_{19}\) + 10
The explicit rule is f(n) = f(1) + (n - 1)d
f(20) = 245
Step-by-step explanation:
The recursive rule of the arithmetic sequence is
\(a_{1}\) = first term; \(a_{n}\) = \(a_{n-1}\) + d
Where:
\(a_{1}\) is the first term in the sequence \(a_{n}\) is the nth term in the sequence \(a_{n-1}\) is the term before the nth term n is term number d is the common difference.The explicit rule of the arithmetic sequence is
\(a_{n}=a_{1}+(n-1)d\)
where:
\(a_{1}\) is the first term in the sequence \(a_{n}\) is the nth term in the sequence n is term number d is the common difference∵ The first 4 terms of the sequence are 55, 65, 75, 85
∴ \(a_{1}\) = 55
∵ d = 65 - 55
∴ d = 10
∵ We need to find the 20th term
∴ n = 20
∵ The recursive rule is \(f(1)\) = first term; \(f_({n})\) = \(f_({n-1})\) + d
→ Substitute the values of \(a_{1}\), n, and d in recursive rule
∴ f(1) = 55; \(f_{20}\) = \(f_{19}\) + 10
∵ The explicit rule is f(n) = f(1) + (n - 1)d
→ Substitute the values of n and d to find it
∴ f(20) = 55 + 19(10) = 245
∴ f(20) = 245
Find the equation of the line below.
-10
-10-
(1,-4)
(2,-8)
O A. y--¹x
B. y = 4x
OC. y=-4x
D. y - x
10
The equation of the line is y = 4x. Option B
How to determine the valueFirst, we need to know that the general equation of a line is expressed as;
y = mx + c
Such that the parameters of the formula are expressed as;
y is a point on the y-axis of the linem is the slope of the linex is a point on the x-axis of the linec is the intercept of the lineFrom the information given, we have that the points in the line are;
(1,-4)
(2,-8)
Now, let us determine the slope of the line, we have to take the change in the value of the points
Slope, m = -8 -(-4)/2-1
expand the bracket
Slope, m = 4
Then, the intercept is;
-8 = 4(2) + c
c = 0
Equation of the line would be;
y = 4x
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Matt ate 0.45 of his birthday cake. Convert the amount of cake Matt consumed into a fraction in simplest form.
Answer: 9/20
Step-by-step explanation:
45/100 ÷ 5/5 = 9/20
To convert 0.45 into a fraction, we can consider it as 45/100. Then to get the simplest form of the fraction, we divide both the numerator and denominator by their greatest common factor which is 5. So, the simplest form of the fraction is 9/20. Therefore Matt ate 9/20 of his birthday cake.
Let's see what it would take to win that trip to Hawaii.
Remember that you think you'll respond to 12 questions and hope to score 600 points to win,
although it's possible to score even more points or many fewer (including negative scores!) on
the show.
Here are the equations you wrote to model your winning scenario:
x+y=12
100x - 200y = 600
Are the boundaries of the first equation viable in the second equation? What does this
suggest about your plan to score 600 points?
Select the two correct statements.
Answer:
A and D choices (Plato)
Step-by-step explanation:
The upper boundary of the first equation is at x = 12, y = 0. With these values, this is the second equation:
100(12) − 200(0) = 1,200.
The lower boundary of the first equation is at x = 0, y = 12. With these values, this is the second equation:
100(0) − 200(12) = -2,400.
Both of these scores are possible in the game, so they are both viable.
Because the upper boundary is greater than 600, it suggests that you can still score 600 points and win the game even if you get one or two of the questions incorrect.
In fact, you could give 10 correct and 2 incorrect answers to score 600 points and still beat the champion, Kimberly, assuming she answers 15 correct and 5 incorrect to score 500 points.
Compare the expression 3 8 and 3 5 x 3 3 using the properties of multiplication what do you notice
Using the properties of multiplication to compare the expressions 3 to the eighth power and 3 to the fifth power x 3 to the third power, it can be seens that that the two expressions are equal to each other.
The properties of multiplication state that when multiplying two expressions with the same base, we can add their exponents together. This means that 3 to the fifth power x 3 to the third power is equal to 3 to the eighth power.
In mathematical notation, this looks like:
3^8 = 3^5 x 3^3
Using the properties of multiplication, we can add the exponents together:
3^8 = 3^(5+3)
Simplifying the exponent:
3^8 = 3^8
This shows that the two expressions are equal to each other. Therefore, we can conclude that 3 to the eighth power and 3 to the fifth power x 3 to the third power are the same value.
Note: The question is incomplete. The complete question probably is: Use the properties of multiplication to compare the expressions 3 to the eighth power and 3 to the fifth power x 3 to the third power.
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Keisha had $405 in her bank account. Over the summer, she made 4 withdrawals of $45 each a) What is the balance in Keisha's account? * b) Write an integer expression to represent this problem. Solve the problem. *
Answer:
see below
Step-by-step explanation:
The amount she withdrew is 45*4 =180
405 - 4*45=
405 -180 =225
There is 225 in the account
Answer: a) $225
Step-by-step explanation:
405 - 45 (4) = x
405 - 180 = x
225 = x
PLEASE HELP!!! I WILL GIVE BRAINLIEST!! HURRY PLEASE!!
You have 4 1/4 yards of ribbon to tie the goodie bags. You will need 1/8 of
a yard for each goodie bag. Will you have enough ribbon to tie a
goodie bag for each persn at the party? Explain!
24 people.
Answer:
Yes, you will have enough ribbon
Step-by-step explanation:
16/4 divided by 1/8
32 people will get ribbon
Answer:
Yes you have enough
Step-by-step explanation:Multiply 1/4 times 2 that is 2/8, Already 2 people done.22 people are left and 4 whole yards of ribbon are left too, for every yard of ribbon you have right now its 8 people so , 4 times 8 is 32.So you have enough.
Identify the constant of proportionality from the graph. 9 0 15 3 A2
To find the constant of proportionality:
We can see that for every 1 unit we move to the right on the x- axis (positive), the line moves up 2 units.
Divide the change on y by that change on x:
2/1=2
The constant of proportionality is 2. (option a)
A spinner is divided into blue,green,red and yellow parts. George spins the spinner 500 timesu
George spun the spinner 500 times.
Since the spinner has four equal parts, each color has a 25% chance of being landed on. To find out how many times each color was landed on, we can multiply 500 by 0.25.
- Blue: 500 x 0.25 = 125 times
- Green: 500 x 0.25 = 125 times
- Red: 500 x 0.25 = 125 times
- Yellow: 500 x 0.25 = 125 times
Therefore, we can conclude that George landed on each color 125 times out of 500 spins.
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can anyone help me with this question?
Answer:
45 and 13…......
Step-by-step explanation:
devide
if the diameter of a circle double, the circumference of the larger circle is how many times the circumference of the original circle?
The circumference of the larger circle is 2 times the circumference of the original circle.
What is the circumference and area of a circle?Let r be the radius of the circle.
Then the area of the circle will be
A = πr² square units
The circumference of the circle will be
C = 2πr units
If the diameter of a circle doubles, the circumference of the larger circle.
Let d be the diameter of the circle.
Then the diameter of the small circle is d and the diameter of the other circle is 2d.
Then the ratio of the circumference of the circles will be
⇒ 2πr₂ / 2πr₁
⇒ 2r₂ / 2r₁
⇒ 2d / d
⇒ 2
The circumference of the larger circle is 2 times the circumference of the original circle.
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need help ASAP and pls hurry
10 pts + brainliest
Answer:
r=0318
0Step-by-step explanation:
that what i think
Answer:
i agree
Step-by-step explanation:
5/x+3 take away 1/x-2 equals to 1. solve two possible answers for x
Answer:
Solution:-First write the given equation\(\qquad{:}\longrightarrow\)\(\sf \dfrac {5}{x+3}-\dfrac{1}{x-2}=1 \)
\(\qquad{:}\longrightarrow\)\(\sf \dfrac {5 (x-2)-1 (x+3)}{(x+3)(x-2)}=1\)
\(\qquad{:}\longrightarrow\)\(\sf \dfrac {5x-10-x }{x^2-6x-6} =1\)
use cross multiplication method\(\qquad{:}\longrightarrow\)\(\sf 5x-x-10=x^2-6x-6 \)
\(\qquad{:}\longrightarrow\)\(\sf x^2-6x-6=4x-10 \)
\(\qquad{:}\longrightarrow\)\(\sf x^2-6x-4x-6+10=0 \)
\(\qquad{:}\longrightarrow\)\(\sf x^2-10x+4=0\)
use quadratic formula\(\qquad{:}\longrightarrow\)\(\sf x=\dfrac {-b\underline{+}\sqrt {b^2-4ac}}{2a}\)
\(\qquad{:}\longrightarrow\)\(\sf x=\dfrac {10\underline{+}\sqrt {(-10)^2-4×1×4}}{2×1}\)
\(\qquad{:}\longrightarrow\)\(\sf x=\dfrac {10\underline{+}\sqrt{100-16}}{2}\)
\(\qquad{:}\longrightarrow\)\(\sf x=\dfrac {10\underline{+}\sqrt {84}}{2}\)
\(\qquad{:}\longrightarrow\)\(\sf x=\dfrac {10+\sqrt {84}}{2}\quad or\quad x=\dfrac {10-\sqrt{84}}{2}\)
Which of the following best explains the value of Sine StartFraction pi Over 3 EndFraction on the unit circle below?
A unit circle is shown. A radius with length 1 has an angle measure of StartFraction pi Over 3 EndFraction
sine StartFraction pi Over 3 EndFraction = StartFraction opposite Over hypotenuse EndFractionEquals StartFraction opposite Over 1 EndFraction Equals opposite
The length opposite the angle is the vertical distance from the x-axis on the graph.
sine StartFraction pi Over 3 EndFraction = StartFraction adjacent Over hypotenuse EndFraction = StartFraction adjacent Over 1 EndFraction Equals adjacent
The length adjacent to the angle is the vertical distance from the x-axis on the graph.
Sine StartFraction pi Over 3 EndFraction = StartFraction opposite Over hypotenuse EndFraction = StartFraction opposite Over 1 EndFraction Equals opposite
The length opposite the angle is the horizontal distance from the y-axis on the graph.
Sine StartFraction pi Over 3 EndFraction = StartFraction adjacent Over hypotenuse EndFraction = StartFraction adjacent Over 1 EndFraction Equals adjacent
The length adjacent to the angle is the horizontal distance from the y-axis on the graph.
Answer:
a. sine StartFraction pi Over 3 EndFraction = StartFraction opposite Over hypotenuse EndFractionEquals StartFraction opposite Over 1 EndFraction Equals opposite
The length opposite the angle is the vertical distance from the x-axis on the graph.
Step-by-step explanation:
sin (π/3) = opposite/hypotenuse = opposite/1; The length opposite the angle is the vertical distance from the x-axis on the graph.
What is the trigonometric ratio of unit circle?
Unit circle is a circle centered at the origin, (0,0) with radius(r) i.,e r= 1.
The angle π/3 forms an arc of length S and the x-axis and y-axis divide the coordinate plane and the unit circle as it is centered at (0.0).
Also, the terminal side intersect the circle at (x, y). Thus;
sin (π/3) = opposite/hypotenuse = opposite/1
Thus;
sin (π/3) = opposite
Also, the length opposite the angle is the vertical distance from the x-axis on the graph.
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sam walks from home to his school which is 0.75 miles away in 12 minutes. how fast was he walking?
Answer:
3.75mph, or 0.0625 miles a minute
Step-by-step explanation:
12 times 5 is 60
.75 times 5 is 3.75
so he was walking mathematically 3.75 miles per hour
Answer:
3.75 mph
Step-by-step explanation:
12 minutes is 0.2 hours
0.75/0.2 = 3.75 mph
A point starts at the location (6,0) and travels 16.8 units CCW along a circle with a radius of 6 units that is centered at (0,0). Consider an angle whose vertex is at (0,0) and whose rays subtend the path that the point traveled. Draw a diagram of this to make sure you understand the context. a. What is the radian measure of this angle? radians Preview b. What is the degree measure of this angle? degrees Preview
The radian measure of the angle is 2.8 radians, and the degree measure is approximately 160.918 degrees.
What is the radian measure of the angle formed by the point's path of 16.8 units along a circle with a radius of 6 units?To understand the context and visualize the situation, let's draw a diagram:
```
6
/
/
(6,0) o (0,0)
```
The point starts at (6,0) and travels along a circle with a radius of 6 units centered at (0,0). It moves counterclockwise (CCW) for a distance of 16.8 units. We need to find the radian and degree measures of the angle formed by the path traveled by the point.
a. Radian Measure:
The circumference of a circle is given by the formula C = 2πr, where r is the radius of the circle. In this case, the radius is 6 units, so the circumference is C = 2π(6) = 12π units.
Since the point traveled 16.8 units, we can find the fraction of the circle's circumference it covered by dividing the distance traveled by the circumference:
Fraction of circumference traveled = 16.8 / 12π
To find the radian measure of the angle, we need to multiply the fraction of the circumference traveled by 2π, as a complete circle corresponds to 2π radians:
Radian measure = (16.8 / 12π) * 2π = 16.8 / 6
Simplifying, we get:
Radian measure = 2.8 radians
b. Degree Measure:
To convert radians to degrees, we use the fact that 1 radian is equal to 180/π degrees.
Degree measure = (2.8 radians) * (180/π degrees)
Simplifying, we get:
Degree measure ≈ 160.918 degrees (rounded to three decimal places)
Therefore, the radian measure of the angle is 2.8 radians, and the degree measure is approximately 160.918 degrees.
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At a carnival, food tickets cost $2 each and ride tickets cost $3 each. A total of $1,240 was collected at the carnival. The number of food tickets sold was 10 less than twice the number of ride tickets sold.
The system of equations represents x, the number of food tickets sold, and y, the number of ride tickets sold.
2x + 3y = 1240
x = 2y – 10
How many of each type of ticket were sold?
180 food tickets and 293 ride tickets
180 food tickets and 350 ride tickets
293 food tickets and 180 ride tickets
350 food tickets and 180 ride tickets
Answer:
D on edg
Step-by-step explanation:
Answer:d on ed
Step-by-step explanation:
(im giving brainliest for real answer)
The constant of proportionality of y and x in the graph is given as follows:
k = 3/4.
How to obtain the constant of proportionality?In a proportional relationship, the ratio between the output variable y and the input variable x is constant, and is called constant of proportionality, given as follows:
k = y/x.
A proportional relationship is a special case of a linear function, which has an intercept of zero, as is the case for the graph in this problem.
The marked point on the graph has the coordinates given as follows:
(4,3).
Meaning that the constant of proportionality of y and x in the graph is calculated as follows:
k = y/x = 3/4.
(division of the value of the y-coordinate by the value of the x-coordinate).
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Which equation of a line of best-fit reflects a negative correlation?.
The equation of a line of best-fit that reflects a negative correlation is y = mx + b, where the slope m is negative.
When analyzing a scatter plot, a negative correlation indicates that as the independent variable increases, the dependent variable decreases. In the equation y = mx + b, the negative slope m represents the rate of decrease in the dependent variable for each unit increase in the independent variable. A negative slope means that as the x-values increase, the corresponding y-values decrease. The y-intercept b represents the value of the dependent variable when the independent variable is zero. Thus, the equation y = mx + b with a negative slope indicates a negative correlation between the variables being studied.
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"What is the equation of the line of best fit that represents a negative correlation between two variables?"