Answer:
The equation of the line is y = 3 x - 5.
Step-by-step explanation:
The slope intercept form of the equation of a straight line is:
[tex]y=mx + b[/tex]
Here,
m = slope
b = intercept.
The two points are:
A = (2, 1)
B = (3, 4)
Use two-point form method to determine the equation of straight line.
[tex](y-y_{1})=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\ (x-x_{1})[/tex]
[tex](y-1)=\frac{4-1}{3-2}\ (x-2)[/tex]
[tex]y-1=3(x-2)\\y-1=3x-6[/tex]
[tex]y=3x-5[/tex]
Thus, the equation of the line is y = 3 x - 5.
The equation of the line in slope-intercept form is y = 3x - 5.
To find the equation of the line containing the points (2, 1) and (3, 4) in slope-intercept form (y = mx + b), you first need to determine the slope (m) and then use one of the points to solve for the y-intercept (b).
The slope (m) can be found using the formula:
m = (y2 - y1) / (x2 - x1)
Let's plug in the coordinates of the two points:
Point 1: (x1, y1) = (2, 1)
Point 2: (x2, y2) = (3, 4)
Now, calculate the slope (m):
m = (4 - 1) / (3 - 2)
m = 3 / 1
m = 3
Now that you have the slope (m), you can use one of the points, for example, (2, 1), and the slope to find the y-intercept (b). You can use the point-slope form of the equation:
y - y1 = m(x - x1)
Using the point (2, 1):
y - 1 = 3(x - 2)
Now, distribute the 3 on the right side:
y - 1 = 3x - 6
Next, add 1 to both sides to isolate y:
y = 3x - 6 + 1
Simplify:
y = 3x - 5
for such more question on slope-intercept form
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Alison bought some shirts for her
clothing store for $15 each. She received
$50 off her entire purchase and spent a total of $440. How many shirts did Alison purchase for her store?
Answer: $29.10
Step-by-step explanation: 10.20 + 18.90 = $29.10
Plz help! Question in picture. What is the slope?
Alessandro and Francesca raced each other home from school. It took Francesca 13/15 as long as Alessandro to run home who got home first
Answer:
Francesca!! 13 is less than 15
Step-by-step explanation:
Final answer:
To determine who got home first, compare the times it took for Alessandro and Francesca to run home. If Francesca's time is less than Alessandro's time, then she got home first. If Alessandro's time is less than Francesca's time, then he got home first.
Explanation:
To determine who got home first, we need to compare the time it took for each person to run home. Let's assume it took Alessandro t minutes to run home. According to the information given, Francesca took 13/15 times as long as Alessandro, which means it took Francesca (13/15) * t minutes to run home. To determine who got home first, we can compare their times. If Francesca's time is less than Alessandro's time, then Francesca got home first. If Francesca's time is greater than Alessandro's time, then Alessandro got home first.
Let's compare the times:
Alessandro's time: t minutesFrancesca's time: (13/15) * t minutesBased on the comparison, we can conclude that:
If Alessandro's time is less than Francesca's time, then Alessandro got home first.If Francesca's time is less than Alessandro's time, then Francesca got home first.
Find the quotient.
158
152
A) 1516
B) 1510
C) 156
D) 154
Answer:
D
Step-by-step explanation:
The winner of a raffle will receive a 21- foot outboard boat. If 3000 raffle tickets were sold and you purchased 20 tickets, what are the odds against your winning the boat
149 : 1 is the odds against your winning the boat.
Step-by-step explanation:
It is given that,
The winner of a raffle will receive a 21-foot outboard boat.
Total raffle tickets were sold = 3000 tickets Number of tickets you purchased = 20 ticketsThe odds against any event is the ratio of the unfavorable outcomes to the favorable outcomes.
The number of possible outcome that you will win ⇒ 20
The number of possible outcomes that others wins ⇒ 3000-20 = 2980
To find the odds against your winning the boat :
Number of possible outcomes that one of the others wins : Number of possible outcome that you will win.
⇒ 2980 : 20
⇒ 149 : 1
Therefore, the odds against your winning the boat is 149 : 1
Find the measures of an interior angle and an exterior angle of a regular 16-gon
Answer:
2520°
Step-by-step explanation:
The sum of the angles in any triangle is 180°
shape. sides. triangles. sum int angles.
triangle. 180×1=180°
quad. 180×2=360°
pentagon. 180×3=540°
n-sides. n( n−2) 180(n−2)
16-sides. 180×14=2520°
637.2 x 8.49 estimate
Answer: 5409.828
Step-by-step explanation: calculator
what are the domain range of f(x)= 1/5 power of x
Answer:
Domain: all real numbers
Range: all real numbers
Step-by-step explanation:
I'm assuming you mean the function [tex]f(x)=x^{\frac{1}{5}}[/tex]. That's usually written
f(x) = x^(1/5) with the ^ meaning "to the power of..." and the fraction exponent in parentheses so as not to be confused with x^1/5 which could mean x to the first power, divided by 5.
Fractional exponents are used to indicate roots. In this case, x is being raised to the 1/5 power, so this is the fifth root of x, written [tex]\sqrt[5]{x}[/tex]. The 5 is called the root index.
For odd roots, like this one, the domain is all real numbers--x can be any number at all. So the domain is all real numbers.
The range is also all real numbers. Attached is a graph of this function. It might not look like it, but the graph rises to the right to any height. The larger x gets, the larger the 5th root gets. A similar thing happens on the left--the smaller x gets, the smaller the 5th root gets.
EDIT: see the comment. For the function [tex]f(x)=(1/5)^x[/tex], the domain is all real numbers. The range is positive real numbers. I'll attach a graph!
Linda wants to buy 20 crayons. ToyWorld sells crayons at 4 for 25 cents, and GameLand sells crayons at 5 for 30 cents. Which of the two stores sells 20 crayons for less, and by how many cents?
Answer: Game land sells 20 crayons for 5 cents less.
Step-by-step explanation:
Hi, to answer this question we have to calculate the price per crayon in each store, by dividing the amount paid in each case by the number of crayons that each store offers.
Toy world (T): 25/4 = 6.25 cents per crayon
Game land (G): 30/5 = 6 cents per crayon
Now, we have to multiply the cost per crayon by 20.
T=6.25 x 20 = 125 cents
G=6 x 20 =120 cents
So, comparing both costs, Game land sells 20 crayons for 5 cents less.
125-120 = 5 cents
Final answer:
GameLand sells 20 crayons for $1.20, which is 5 cents cheaper than ToyWorld's price of $1.25 for the same quantity. Linda saves money by purchasing from GameLand.
Explanation:
To determine which store sells 20 crayons for less, we need to calculate the total cost of 20 crayons at each store. At ToyWorld, crayons are sold at 4 for 25 cents. To buy 20 crayons, Linda would need 5 sets of 4 crayons, since 20 divided by 4 equals 5. Each set costs 25 cents, so the total cost at ToyWorld would be 5 sets times 25 cents, which equals $1.25.
At GameLand, crayons are sold at 5 for 30 cents. To get 20 crayons, Linda would need 4 sets of 5 crayons. The total cost at GameLand would be 4 sets times 30 cents, which equals $1.20.
Comparing the two totals, Linda would spend $1.25 at ToyWorld and $1.20 at GameLand, so GameLand sells 20 crayons for 5 cents less than ToyWorld.
If a loan of 1,500 at 4% is paid off in 90 days what is the interest
Answer:
Compound interest =$14.58
Simple Interest=$14.79
Step-by-step explanation:
Let's assume the interest rate charged on the loan was simple in nature.
-Simple interest is calculated using the formula:
[tex]I=PRT,\\\\=1500\times 0.04\times \frac{90}{365}\\\\=14.79[/tex]
Hence, the simple interest on the loan was $14.79
#If the interest is compound in nature with just one compounding per year:
[tex]A=P(1+i)^n\\\\I=A-P\\\\I=1500(1.04)^{90/365}-1500\\\\=14.58[/tex]
Hence, the compound interest charged on the loan is $14.58
A company randomly surveyed employees to determine the most important reasons for being late to work. The results are shown on the Pareto graph. Approximately how many employees took part in the random survey? A) 50 B) 100 C) 130 Eliminate D) 150
Answer: this answer is 130
Step-by-step explanation:
The point A has coordinates A(2, 4). What are the coordinates of A′ for the dilation D1.5(A)?
Answer:
[tex]A'(3,6)[/tex]
Step-by-step explanation:
The given coordinate is [tex]A(2,4)[/tex].
It's important to know that a dilation implies a bigger figure than the original. In this case, we have a factor of dilation of 1.5, which means each coordinate must be multiplied by it.
So, using the factor of dilation, we have
[tex]A(2,4) \implies A'(3,6)[/tex]
Because [tex]2 \times 1.5 = 3[/tex] and [tex]4 \times 1.5 = 6[/tex]
Therefore, the right answer is [tex]A'(3,6)[/tex]
The coordinates of [tex]\( A' \)[/tex] after dilating point [tex]\( A(2, 4) \)[/tex] by a factor of [tex]\( 1.5 \)[/tex] are [tex]\( {(3, 6)} \)[/tex].
To find the coordinates of [tex]\( A' \)[/tex] after dilating point [tex]\( A(2, 4) \)[/tex] by a scale factor of [tex]\( 1.5 \)[/tex], we use the formula for dilation:
If [tex]\( A'(x', y') \)[/tex] is the image of [tex]\( A(x, y) \)[/tex] under dilation with scale factor [tex]\( k \)[/tex], then:
[tex]\[ x' = k \times x \][/tex]
[tex]\[ y' = k \times y \][/tex]
Given:
[tex]\( A(2, 4) \)[/tex]
Scale factor [tex]\( k = 1.5 \)[/tex]
Now, calculate the coordinates of [tex]\( A' \)[/tex]:
[tex]\[ x' = 1.5 \times 2 = 3 \][/tex]
[tex]\[ y' = 1.5 \times 4 = 6 \][/tex]
The base of a triangular prism has an area of 18 square inches. If the height of the prism is 4.5 inches, then what is the volume of the prism?
Answer:
81 inches squared
Step-by-step explanation:
You just multiply the area by the hight and get your answer
FULL POINTS AND BRAINLIEST
2. Write the equation of the line of best fit using the slope-intercept formula y = mx + b. Show all your work, including the points used to determine the slope and how the equation was determined.
3. What does the slope of the line represent within the context of your graph? What does the y-intercept represent?
Answer:
2) y = x + 2
3) slope: height increases by 1 unit per unit increase in x
Intercept: initial height (at birth) was 2 units
Step-by-step explanation:
Using (38,40) and (48,50)
Slope: (50-40)/(48-38)
= 10/10
= 1
y = mx + b
y = x + b
40 = 38 + b
b = 2
y = x + 2
Answer:
see below
Step-by-step explanation:
There are (60,61) and (20,23) are the points that I used to find the slope for the line of best fit
m= (y2-y1)/(x2-x1)
m = (23-61)/(20-60)
= -38/-40
= .95
We use the slope intercept form of the equation
y= mx+b
y = .95x+b
Substituting in the point (20,23)
23 = .95(20) +b
23 = 19+b
Subtracting 19 from each side
23-19 = 19+b-19
4 =b
The equation is
y =.95x+4
The slope is how much y changes for each change in x. You did not tell us what the units of x and y are.
The y intercept is what the y value is when x is zero. The y value is 4 when x is zero
Simplify the following expression if k=-4 and n =4.
[tex] - 3( {k}^{2} + 2n)[/tex]
Answer: -72
Step-by-step explanation:
[tex]-3(k^2+2n)\\-3((-4)^2+2(4))\\-3(16+8)\\-3(24)\\-72[/tex]
THE TABLE SHOWS THE AGES OF THE SWIMMERS ON DION'S SWIM TEAM.THE MEAN AGE OF THE SWIMMERS IS 10.WHAT DOES THE MEAN REPRESENT
Answer:
The mean is the balancing point of the swimmers' ages.
Step-by-step explanation:
I just took the I-Ready Quiz and got it correct. :D
The mean in mathematics refers to the average of a set of given numbers. Mean is commonly referred to as average.
Mean is the average number, which is calculated by the formula:
[tex]\rm mean = \dfrac{sum\; of\; all\; the\; given\; numbers}{\text{total observation}}[/tex]
For instance, the mean age of swimmers is 10, which means that the average age of all the swimmers is 10. The age of each swimmer can be near to 10, as 9, 10, 11, or 12.
Given the ages of swimmers are:
[tex]\text{mean} = \dfrac{10 + 10 + 11 + 9}{4}\\\text{mean} = \dfrac{40}{4}[/tex]
mean = 10
Thus, the mean of the given data is 10.
To know more about the mean, refer to the following link:
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In the equation (x+2)^2+(y-3)^2=4 the diameter of the circle is.....
Answer:
4
Step-by-step explanation:
(x+2)^2+(y-3)^2=4
From this equation, we can find the radius of this circle.
(x+2)^2+(y-3)^2= 2^2
radius = 2
diameter = 2*radius = 2*2 = 4
How many 3.15 pound containers can you make with 37.8 pounds of raisins?
Answer:
12 (3.15 pound) containers.
Step-by-step explanation:
37.8 divided by 3.15 equals 12 (3.15 pound) containers.
A sample of students is taken from the school's A honor roll. The school estimates that there are actually 360 students on the A honor roll. Using this sample, how many students on the A honor roll are 8th graders?
By multiplying the individual probabilities of being a music student and being on the honor roll and then multiplying by the total on the honor roll, we find the expected number of music students on the honor roll to be 16.
Explanation:To determine the expected number of music students who are also on the honor roll, we can use the concept of expected value in probability.
Assuming that being a music student and being on the honor roll are independent events, we can multiply the probability of a student being a music student by the probability of a student being on the honor roll.
The probability of randomly selecting a music student from the 300 students is the number of music students divided by the total number of students, P(Music) = 50/300.
The probability of a student being on the honor roll is P(Honor Roll) = 97/300. So, the expected number of music students on the honor roll would be the product of these two probabilities times the total number of students on the honor roll, which the school estimates to be 360.
The calculation: Expected number = [tex]P(Music) \(\times\) P(Honor Roll) \(\times\) Total Honor Roll = (50/300) \(\times\) (97/300) \(\times\)[/tex]
Jumoke is 11yrs old than Aminata in 5yrs time Jumoke will be twice as old as Aminata . Find their present ages
Answer: Jumoke is currently 16 and Aminata is currently 8
Step-by-step explanation:
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Jumoke is 27 and Aminata is 11.
11 + 5 = 16
16 x 2 = 32
32 - 5 = 27
27 - 11 = 16
I tried. Correct me if I'm wrong.
Which shows one way to determine the factors of x + 11x2 – 3x – 33 by grouping?
O x2(x + 11) + 3(x – 11)
O x²(x – 11) – 3(x – 11)
O x2(x + 11) + 3(x + 11)
O x2(x + 11) – 3(x + 11)
Answer: x^2 (x + 11) - 3 (x + 11)
Answer:
Answer: x^2 (x + 11) - 3 (x + 11)
Step-by-step explanation:
Edge
Tina must select and answer in any order seven of ten essay questions on a test. In how many ways can she do so?
Answer:
There are 127 Possible ways/combinations for this
Step-by-step explanation:
What is the equation of the line with the same slope as the equation x-4y=3 and the y-intercept(0,-8)?
Answer:
Answer:y = 1/4x -8Step-by-step explanation:First find the slope of the linex-4y =3Subtract x from each sidex-4y -x = -x+3-4y = -x+3Divide each side by -4-4y/-4 = -x/-4 +3/-4y = 1/4 x -3/4This is in the form y= mx+b where the slope is m and the y intercept is bThe slope is 1/4We want the same slopey = 1/4x +bwe know the y intercept is -8y = 1/4x -8.
Step-by-step explanation:
WILL GIVE 20 POINTS PLEASE HELP ME
The number of visitors to the Railroad Museum during 24 randomly selected hours is shown here. Construct a stem and leaf plot for the data.
67 62 38 73 34 43 72 35 53 55 58 63
47 42 51 62 32 29 47 62 29 38 36 41
Constructing a frequency distribution table for visitor numbers with a range of 29 to 73 and class intervals of 10 provides a clear overview, facilitating analysis and interpretation of the data.
Construct a frequency distribution table for the given data, with explanations:
1. Find the range of the data:
The lowest number of visitors is 29.
The highest number of visitors is 73.
The range is 73 - 29 = 44.
2. Determine the appropriate class intervals:
Choose a class interval width that will create a reasonable number of classes, typically between 5 and 10.
Consider the range of the data and aim for intervals that are easy to interpret.
In this case, a class interval width of 10 would be suitable, resulting in 5 classes:
29-38
39-48
49-58
59-68
69-78
3. Create the table:
Draw a table with three columns:
Class Interval
Tally (optional)
Frequency
4. Tally the data (optional):
Go through each data point and mark a tally mark in the appropriate class interval. (This is helpful for visual counting, but not strictly necessary.)
5. Count the frequencies:
Count the number of data points that fall into each class interval and record those numbers in the frequency column.
Complete question:
The number of visitors to the Railroad Museum during 24 randomly selected hours is shown here. 67 62 38 73 34 43 72 35 53 55 58 63 47 42 51 62 32 29 47 62 29 38 36 41 The error in the data is 1. a) Construct a frequency distribution table
Which equation is true for the value b=2 ?
Flying with the wind a plane went 383 mph. Flying into the same wind the plane only went 319 mph. Find the speed of the wind and the speed of the plane in still air.
Answer:
The speed of the wind is 32 mph and the speed of the plane in still air is 351 mph.
Step-by-step explanation:
Let the speed of the plane be Vp and the speed of the wind be Vw. In the first situation, the wind is exerting force towards the same direction as the plane so we can say that Vp + Vw = 383 mph. In the second situation, the forces are opposite of each other, so the equation can be written as Vp - Vw = 319 mph.
If we solve them together, we get the result of 2Vp = 702 mph which means that the speed of the plane is Vp = 351 mph. If we put Vp into one of the equations and solve for Vw then the speed of the wind can be found as Vw = 32 mph.
I hope this answer helps.
factorise this expression as fully as you can 12x^3-9x^2
The factor of the expression 12x³ – 9x² will be 3x² and (4x – 3).
What is a factorization?It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.
The expression is given below.
⇒ 12x³ – 9x²
Then the factor of the expression will be
⇒ 3x²(4x – 3)
More about the factorization link is given below.
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9+___=10
1+____=10
200+500+2000-3000
Answer:
1
Step-by-step explanation:
To solve the equations, subtract the given number from the sum on the left side of the equation to find the missing number. For the arithmetic expression, perform the operations in order.
Explanation:In the first equation, you must find a number that, when added to 9, equals 10. To do this, subtract 9 from 10, which gives you 1. Therefore, the missing number is 1.
In the second equation, you need to find a number that, when added to 1, equals 10. Subtract 1 from 10 to get 9. So, the missing number is 9.
In the last equation, you simply need to perform the arithmetic operations in order: 200 + 500 = 700, 700 + 2000 = 2700, and finally 2700 - 3000 = -300. Therefore, the result of the expression 200 + 500 + 2000 - 3000 is -300.
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The heights of different flowers in a field are normally distributed with a mean of 12.7 centimeters and a standard deviation of 2.3 centimeters.
What is the height of a flower in the field with a z-score of 0.4?
Enter your answer, rounded to the nearest tenth, in the box.
Answer: the height of a flower in the field is 13.6 centimeters.
Step-by-step explanation:
Since the heights of different flowers in a field are normally distributed, we would apply the formula for normal distribution which is expressed as
z = (x - µ)/σ
Where
x = heights of different flowers.
µ = mean height
σ = standard deviation
From the information given,
µ = 12.7 centimeters
σ = 2.3 centimeters
The z-score is 0.4
Therefore,
0.4 = (x - 12.7)/2.3
Cross multiplying by 2.3, it becomes
0.4 × 2.3 = x - 12.7
0.92 = x - 12.7
x = 0.92 + 12.7
x = 13.6 centimeters to the nearest tenth
help me answer this thanks
Answer:
C = 73
Step-by-step explanation:
Formula used: a²+b²=c²
A and B represent the numbers other than the hypotenuse, so C equals the hypotenuse. It doesn't matter which number you put as A or B. Here's the equation we're working with:
(55)² + (48)² = C²
That simplifies to:
3025 + 2305 =C²
5329 = C²
Now, C needs to be by itself in order for us to get the answer, so the next step is to do inverse operations. The inverse of sqauring a number (x²) is to square root it (√x). Here is the new equation we are working with:
√5329 = √C
That simplifies to:
73 = C
Hope this is correct!