Answer:
y = [tex]\frac{1}{4}[/tex] x + [tex]\frac{3}{2}[/tex]
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 )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 2, 1 ) and (x₂, y₂ ) = (6, 3 )
m = [tex]\frac{3-1}{6-(-2)}[/tex] = [tex]\frac{2}{6+2}[/tex] = [tex]\frac{2}{8}[/tex] = [tex]\frac{1}{4}[/tex] , then
y = [tex]\frac{1}{4}[/tex] x + c ← is the partial equation
to find c substitute either of the 2 points into the partial equation
using (6, 3 ) , then
3 = [tex]\frac{3}{2}[/tex] + c ⇒ c = 3 - [tex]\frac{3}{2}[/tex] = [tex]\frac{3}{2}[/tex]
y = [tex]\frac{1}{4}[/tex] x + [tex]\frac{3}{2}[/tex] ← equation of line
Can someone pls help me with this and show your work it would mean a lot
Using the angle of elevation formula, the distance between John and Fred from the building is 1.2m and 1.67m.
What is the angle of elevation?The angular relationship between the horizontal plane and the line of sight for an object above the horizontal.The angle of elevation is the angle created between the line of sight and the horizontal. The angle created is an angle of elevation if the line of sight is upward from the horizontal line.You may calculate the angle of elevation, for instance, by standing on the ground and looking up at the peak of a mountain.So, the distance of the building from John and Fred is:
Let, the height of the building be QR and the distance between the building and John and Fred be PR and SR.Now, we get the formula:
Tanθ = QR/PRTanθ = QR/SRCalculate as follows:
John's distance:
Tanθ = QR/PR25 = 30/PRPR25 = 30PR = 30/25PR = 6/5Fred's distance:
Tanθ = QR/SR18 = 30/SRSR18 = 30SR = 30/18SR = 15/9SR = 1.67mTherefore, using the angle of elevation formula, the distance between John and Fred from the building is 1.2m and 1.67m.
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Students in a classroom have eaten 20% of jellybeans from a jar. There are now only 100 jellybeans left! How many jellybeans were in the jar to begin with?
Using percentages we calculate in the beginning there were 125 jellybeans in the jar.
Let the number of jellybeans in the jar was x.
Now student ate 20% of the jellybeans.
Number of jellybeans students ate = 20% of x = 0.2x
Number of jellybeans left = x - 0.2x = 0.8x
But the number of jellybeans is given as 100.
Therefore 0.8x = 100
or, x = 100 /0.8 = 125
Hence there were 125 jellybeans in the jar.
The English word "percentage" derives from the Latin phrase "per centum," which means "by the hundred." Percentages are fractions with a denominator of 100.
In other words, that is a relationship where it is always assumed that the value of the whole is 100.
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The polynomial f(x) = 2x ^ 3 + a * x ^ 2 + bx + 6 is exactly divisible by 2x - 3 and has the remainder -28 when divided by (x + 3) a) find the values of a and b. b) solve the equation f(x) = 0
The polynomial f(x) = 2x³ + ax² + bx + 6 is exactly divisible by 2x - 3. The values of a and b are a = 131/27 and b = -71/9
To solve the problem, use the polynomial remainder theorem. If a polynomial f(x) is divided by a linear function with zero x = a, then the remainder r = f(a).
The given polynomial is:
f(x) = 2x³ + ax² + bx + 6
- The polynomial is exactly divisible by (2x-3) means:
f(3/2) = 0
2. (3/2)³ + a(3/2)² + b(3/2) + 6 = 0
27 + 9a + 6b + 24 = 0
9a + 6b = - 51 (equation 1)
- f(x) divided by (x+3) has remainder -28
f(-3) = -28
2. (-3)³ + a(-3)² + b(-3) + 6 = -28
9a - 3b = 20 (equation 2)
Substract equation 2 from equation 1
9a + 6b = -51
9a - 3b = 20 _
9b = -71
b = -71/9
9a - 3(-71/9) = 20
9a = 131/3
a = 131/27
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During the problem disaggregation process, the logic trees should have branches that are?.
During the problem disaggregation process, the logic trees should have branches that are both mutually exclusive and collectively exhaustive.
Problem disaggregation refers to the process of breaking down the larger higher-level operation into smaller plans and shorter periods. It refers to the use of analysis, logic, and facts to evaluate and understand each element of the problem in terms of causes and driver of the situation using logic trees. Logic trees improve the problem definition and aid in understanding an issue in more detail. There are different types of logic trees used in the process – factor logic tree, inductive logic tree, deductive logic tree, hypothesis tree, and decision tree. The logic trees should have branches that are MECE – mutually exclusive and collectively exhaustive. It is the second and an important step in the seven steps bulletproof problem-solving process used for complex solving.
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a group of five friends goes to the state fair. each friend pays the entrance fee and buys one booklet of ride tickets and a meal ticket. the entrance fee is d dollars. a booklet of ride tickets costs 2.5 times the entrance fee. a meal ticket costs $4 less than the entrance fee.
Answer: What do you need the total or the equation? I am going to write the equation.
Step-by-Step Solution: (5)(d)+(5)(d)(2.5)+ (5)(d)-4
How much water must be added to 14 liters of a 90%
acid solution to obtain a 40% acid solution?
17.5 litres of must be added to 14 litres of a 90% acid solution to obtain a 40% acid solution.
What is percentage?A percentage is a number or ratio expressed as a fraction of 100.
Given that, there are 14 litres of a solution which is 90% acidic,
Let water added be x, then according to question,
0.90*14 = 0.40(x+14)
12.6 = 0.40x + 5.6
0.40x = 7
x = 17.5
Hence, 17.5 litres of must be added to 14 litres of a 90% acid solution to obtain a 40% acid solution.
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mike discovered that the pool in his backyard is leaking slowly. the pool holds 15,478 gallons of water, and is leaking at a rate of 11 gallons per day. if mike does not replace the water that has leaked from the pool, how many gallons of water will remain in the pool after 91 days?
The pool will have 14, 477 gallons of water.
The amount of water that has leaked in 91 days = rate of leakage × number of days
Keep the values in formula
The amount of water that has leaked in 91 days = 11 × 91
Performing multiplication
The amount of water that has leaked in 91 days = 1001 gallons
Amount of water remaining after 91 days = total amount of water - the amount of water that has leaked in 91 days
Amount of water remaining after 91 days = 15,478 - 1001
Performing subtraction
Amount of water remaining after 91 days = 14, 477 gallons
Hence, after 91 days there will be 14, 477 gallons of water in the pool.
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Graph the inequality on the axes below −2x+y≥−6
A graph of the inequality (-2x + y ≥ -6) is shown in the image attached below.
What is a graph?A graph simply refers a type of chart that is typically used for the graphical representation of data on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate and y-coordinate.
Next, we would rearrange and simplify the given equation in slope-intercept form as follows:
-2x + y ≥ -6
Adding 2x to both sides of the inequality, we have the following equation:
-2x + y + 2x ≥ -6 + 2x
y ≥ -6 + 2x
Rearranging the equation in slope-intercept form, we have the following equation:
y ≥ 2x - 6
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The graph below plots the values of y for different values of x:
plot the ordered pairs 1, 8 and 2, 3 and 3, 0 and 4, 1 and 5, 2 and 6, 1
What does a correlation coefficient of −0.2 say about this graph?
x and y have a strong, positive correlation
x and y have a weak, positive correlation
x and y have a strong, negative correlation
x and y have a weak, negative correlation
A correlation coefficient is a numerical measure of some type of correlation, meaning a statistical relationship between two variables.
Hence, the correlation coefficient is [tex]-0.9[/tex], i.e., [tex]x[/tex] and [tex]y[/tex] have a strong, negative correlation
What is a correlation coefficient?
A correlation coefficient is a numerical measure of some type of correlation, meaning a statistical relationship between two variables.
The variables may be two columns of a given data set of observations, often called a sample or two components of a multivariate random variable with a known distribution.
As we know that the correlation coefficient is a measure of the strength of the straight line or linear relationship between two variables. Correlation coefficients are expressed as values between [tex]+1[/tex] and [tex]-1[/tex].
So,
[tex](1,8),(2,3),(3,0),(4,1),(5,2),(6,1)[/tex]
As per the Excel tools i.e., CORREL function the correlation coefficient is [tex]-0.9[/tex].
Hence, the correlation coefficient is [tex]-0.9[/tex], i.e., [tex]x[/tex] and [tex]y[/tex] has a strong, negative correlation.
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Encuentre dos números positivos cuyo producto es 25 y cuya suma es un mínimo. (Especifica el valor minimo y maximo si los dos valores no son lo mismo.)
The two positive numbers are 5 , 5.
Given:
Product of two positive numbers = 25
sum of these number is minimum.
Let a and b be the two positive numbers.
a*b = 25
b = 25/a
sum s = a+b
= a + 25/a
apply derivation on both sides.
ds/da = 1 - 25/[tex]a^{2}[/tex]= 0.
1 = 25/[tex]a^{2}[/tex]
a = [tex]\sqrt{25}[/tex]
a = 5 , -5
since given are positive numbers so 5 is considered.
b = 25/5
b = 5
Therefore the two positive numbers are 5 , 5.
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how many movies did marc watch between the beginning of week 1 and the beginning of week 5? do not include the unit in your answer.
Using the concepts of straight line, we got 7 movies did marc watch between the beginning of week 1 and the beginning of week 5.
From the diagram given, we got that during the week 1 number of movies watch by marc is 2,while at the beginning of the week 5 the number of movies watch by marc is 9.
So, we need total number of movies watched by marc in between week 1 and week 9 which is given by-
Number of movies watch at the beginning of week 5-Number of movies watch at the beginning of week 1
Number of movies=9-2
=>Number of movies watched by marc=7.
Hence, the number of movies marc watch between the beginning of week 1 and the beginning of week 5 is 7.
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(Complete question)
Marc is keeping track of the total number of movies he has watched over time. The line graph below actually shows the data where the number of movies corresponds to number of movies that had been watched at the beginning of week shown on the horizontal axis.
How many movies did Marc watch between beginning of week 1 and the beginning of week 5? Do not include the unit in your answer.
Stacy bought 8.3 pounds of fruit for a class party. The class ate 7.44 pounds of the fruit. How much fruit is left?
Answer:
0.86 pounds of fruit is left.
Step-by-step explanation:
If Stacey bought 8.3 pounds and the class ate 7.44 pounds, the amount of fruit that's left is 8.3-7.44=0.86
Add. Write your answer as a fraction or as a whole or mixed number.
2 8/9 + 5 5/9 =
The required answer in mixed number for a given operation is [tex]8\frac{4}{9}[/tex]
What are mixed numbers?
A whole number and a proper fraction are both expressed together as a mixed number. A number between any two whole numbers is typically represented by it.
Given, [tex]2\frac{8}{9} + 5\frac{5}{9}[/tex]
[tex]= \frac{(2*9)+8}{9} +\frac{(5*9)+5}{9}[/tex]
[tex]= \frac{18+8}{9} +\frac{45+5}{9}[/tex]
[tex]= \frac{26}{9} +\frac{50}{9}[/tex]
[tex]= \frac{26+50}{9} = \frac{76}{9} = 8\frac{4}{9}[/tex]
Hence, the required answer for the given term is [tex]8\frac{4}{9}[/tex] .
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Radioactive elements decrease (or decay) exponentially. Suppose that 120 mg of an unknown radioactive
element decays down to 99 mg after 11 days.
(a) What is the half-life of the element? That is, how many days will it take before half of the original sample
has decayed?
half-life:
days (rounded to at least 2 decimal places)
(b) How long will it take for a sample of 99 mg in this scenario to decay to 40 mg?
days (rounded to at least 2 decimal places)
time needed:
Considering an exponential function, it is found that:
a) The half-life of the element is of 39.63 days.
b) The time needed is of 51.82 days.
What is an exponential function?A decaying exponential function is modeled by the equation presented as follows:
[tex]A(t) = A(0)(1 - r)^t[/tex]
In which the variables of the equation are:
A(0) is the initial value.r is the decay rate, as a decimal.In this problem, the parameters are given as follows, from the text:
A(0) = 120, A(11) = 99.
Hence the decay rate r is obtained as follows:
[tex]A(t) = A(0)(1 - r)^t[/tex]
[tex]120 = 99(1 - r)^{11}[/tex]
[tex](1 - r)^{11} = \frac{99}{120}[/tex]
[tex]1 - r = \sqrt[11]{\frac{99}{120}}[/tex]
[tex]1 - r = \left(\frac{99}{120}\right)^{\frac{1}{11}}[/tex]
1 - r = 0.98266367982
Hence the equation is:
[tex]A(t) = A(0)(0.98266367982)^t[/tex]
The half-life is the value of t for which:
A(t) = 0.5A(0).
Hence:
[tex]A(t) = A(0)(0.98266367982)^t[/tex]
[tex]0.5A(0) = A(0)(0.98266367982)^t[/tex]
[tex](0.98266367982)^t = 0.5[/tex]
[tex]\log{(0.98266367982)^t} = \log{0.5}[/tex]
[tex]t\log{(0.98266367982)} = \log{0.5}[/tex]
[tex]t = \frac{\log{0.5}}{\log{(0.98266367982)}}[/tex]
t = 39.63 days.
For item b, the time is obtained as follows:
[tex]A(t) = 99(0.98266367982)^t[/tex]
[tex]40 = 99(0.98266367982)^t[/tex]
[tex](0.98266367982)^t = \frac{40}{99}[/tex]
[tex](0.98266367982)^t = 0.40404040[/tex]
[tex]t = \frac{\log{0.40404040}}{\log{(0.98266367982)}}[/tex]
t = 51.82 days.
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This shows a linear function.
x y
0 15
1 25
2 35
3 45
4 55
Which equation represents the table?
A.
y = 10x + 15
B.
y = 15x + 10
C.
y = 10x
D.
y = 15x
Answer:
Option A: y = 10x + 15Step-by-step explanation:
Let's find the equation in the form of y=mx+b that fits the data. m is the slope and b is the y-intercept (the value of y when x=0). Slope, m, the the Rise/Run of the line. It can be found by taking any two points from the table. Let's choose (0,15) and (2,35), although any two will work.
x y
0 15
1 25
2 35
3 45
4 55
(0,15) (2,35)
The Rise is the change in y: (35 - 15) = 20.
The Run is the change in x for the same points: (2 - 0) = 2
The slope is the Rise/Run = (20/2) or 10.
The equation has the form y = 10x + b.
Let's find b. Just enter any of the points in the above equation and solve for b. I'll choose (3,45).
y = 10x + b
45 = 10*(3) + b
b = 45 - 30
b = 15
[Note: since b is the value of y when x equals zero, we really didn't need to calculate b as we just did. There is a data point already that tells us the value of y when x = 0: (0,15)]
The equation is y = 10x + 15Option A: y = 10x + 15whats the equation of a line that passes through the points
(12,12) and (20,6)
Pls Help Me With this
1. 2.1 x 5.12 =____ 2.12.3 x 1.6 =
Estimate______ Estimate____
3. 6.5 x 3.1 =____ 4. 51.3 x 2.7 = ____
Estimate_____ Estimate______
The corresponding estimate for numbers in 1,2,3 and 4 are 10, 24, 21 and 153
How to estimate numbers?
Estimation and approximation is the process of using rounded values when presenting numerical data and making rough calculations.
The digits 1,2,3 and are rounded down and digits 5,6,7,8 and 9 are rounded up
1. 2.1 x 5.12 = 2 x 5 = 10
Explanation: The number after the digit 2 in 2.1 is 1, we will round down 2.1 to 2. Also, the number after the digit 5 in 5.12 is 1, we will round down 5.12 to 5
2. 12.3 x 1.6 = 12 x 2 = 24
Explanation: The number after the digit 12 in 12.3 is 3, we will round down 12.3 to 12. Also, the number after the digit 1 in 1.6 is 6, we will round up 1.6 to 2
3. 6.5 x 3.1 = 7 x 3 = 21
Explanation: The number after the digit 6 in 6.5 is 5, we will round up 6.5 to 7. Also, the number after the digit 3 in 3.1 is 1, we will round down 3.1 to 3
4. 51.3 x 2.7 = 51 x 3 = 153
Explanation: The number after the digit 51 in 51.3 is 3, we will round down 51.3 to 51. Also, the number after the digit 2 in 2.7 is 7, we will round up 2.7 to 3
Therefore, the estimate for 1,2,3 and 4 are 10, 24, 21 and 153 respectively
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Decide whether events A and B are overlapping or non-overlapping, you roll a red die and a blue die. event a is that you get a sum of 9. event b is that you get a double.() overlapping ()non-overlapping
Events A and B are non-overlapping. Option(2) is correct.
When two sets A and B have at least one element in common, they are said to be overlapping.
The sets of photographs that don't overlap are the sets where no two pictures (correctly) don't overlap. They are the expansion of the cross-bifix-free sets of strings to two dimensions is called non-overlapping.
A red die and a blue die are rolled.
Assume that Event A is receiving the number 9.
Event B: You receive a double.
Whether events A and B overlap or not is what we want to determine.
When two red dice and two blue dice are thrown, a sample space is then provided by,
S = {(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2), (2,3), (2,4), (2,5), (2,6), (3,1), (3,2), (3,3), (3,4), (3,5),(3,6), (4,1), (4,2), (4,3), (4,4),(4,5),(4,6) (5,1), (5,2), (5,3), (5,4),(5,5),(5,6),(6,1), (6,2),(6,3)(6,4),(6,5),(6,6)}
The two dice are rolled, and there are a total of 36 outcomes.
n(S)=36
Assume that Event A is receiving the number 9.
The probable results for A = (3,6), (4,5), (5,5), (5,6), (6,3)
And let's say that you receive a double in Event B.
The events that may occur if B=(1,1),(2,2),(3,3),(4,4),(5,5),(6,6)
We can observe that the two events are distinct from one another since there is no overlap in the potential outcomes of the two events.
Therefore events A and B are non-overlapping
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A railroad
car container can hold 42,000 pounds.
Mr. Evans wants to ship 90 ovens and
some freezers in the same container.
If each freezer weighs 600 pounds,
how many freezers could be shipped
in the container? Explain.
40 freezers could be shipped in the container.
What is a variable?
A variable is a quality that may be measured and take on several values.
We are given that
A railroad container can hold weight=42,000 pounds
Total number of ovens for ship=90
Weight of each oven=200 lbs
Weight of each freezer=600 pounds
We have to find the number of freezers that can be shipped in the container.
Let x be the number of freezers that can be shipped in the container.
According to the question,
42000=90(200)+600x
42000=18000+600x
600x=42000-18000=24000
x=24000/600=40
Hence, 40 freezers can be shipped in the container.
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based on the graph what is the rate of the change for an airplane approaching an airport for landing
Answer:
(8, 9 000)
Step-by-step explanation:
a salesman keeps 20% of his sales as a commission. how much does he have to sell to earn $1,000?
Answer:
He has to sell 5000 to earn $1000
Step-by-step explanation:
1000/0.2 = 5000
Write the number below as a fraction in its simplest form
0.538
Answer:
0.538 as a fraction in its simplest form is 269/500
Step-by-step explanation:
We all know that 0.538 can be written as 0.538/1
Multiply the numerator and denominator by 1000 which comes out to 538/1000
Divide the numerator and denominator by 2 which comes out to 269/500
Since 269 is a prime number 269/500 is 0.538 in its simplest form
2/5 of what is 2/3? i need so much help
The answer is 4/15
2/5 * 2/3 = 2 · 2/5 · 3 = 4/15
Multiply the numerators and denominators together. Keep the result fraction to the smallest possible denominator GCD(4, 15) = 1. It cannot further simplify the fraction result by canceling in the following intermediate step.
In other words, two fifths times two thirds equals four fifteenths.
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Answer:
5/3
Step-by-step explanation:
"of" means times so so so often. It is not a hard math rule/definition. But more like a soft English-Math translation.
So, "2/5 of what"
means 2/5x (but make sure the 2/5 is a fraction beside the x, NOT the x on the bottom with the 5)
"is" means equals.
2/5x = 2/3
Multiply both sides by 5/2.
5/2 • 2/5x = 2/3•5/2
x = 2/3 • 5/2
x = 5/3
You get 5/3 either by "cancelling" the 2's OR by
fraction multiplication where you times top×top and bottom×bottom and simplify.
x = 10/6
x = 5/3
2/5 of 5/3 is 2/3.
The "what" in the question is 5/3.
a course catalog for the open university of earth lists classes via a sequence of three numbers (chosen from 0 to 9) followed by three letters in english (chosen from a to z). how many courses can be given unique catalog numbers? choose the best answer.
17576000 courses can be given unique catalog numbers.
There are three numbers and three English letters.
Each of three numbers can be chosen from 0 to 9, so the ways to choose each number is = 10
So the total number to choose three numbers = 10*10*10 = 1000
Each of letters can be chosen from A to Z.
Number of choice for the each letter = 26
So, the outcomes of letter combination = 26*26*26 = 17576
Hence the total possible catalog numbers = 1000*17576 = 17576000
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reduce with all steps
Justify each step of the solution by stating the property that was used to get to each step. (4 points - 1 point each correct answer)
Given: 2(10 - 13x) + 9x) = -34x + 60
Step 1: 20 + 26x + 9x = -34x + 60
Step 2: -17x = -34x + 40
Step 3: 17x = 40
Step 4: x = 40/17
Sample Answer
Step 1: _____ property
Step 2: ______ property
Step 3: ______ property
Step 4: ______ property
A blue whale weighs about 200 tons. It eats only small sea creatures called krill. The blue whale
eats 2% of its body weight each day. How many tons of krill does the blue whale eat each day?
Explain your thinking.
Answer:
4 tons of its body weight
Step-by-step explanation:
In this situation you must find 2% of 200. This is simply 4.
Answer: 4 tons
Step-by-step explanation:
the whale eats 2% of itself everyday, so it would be x/200= 2/100 and the whale would eat x tons, which equals 4 so it eats 4 tons of krill a day
What is this shape ?
Answer:
Decagon
Step-by-step explanation:
Because it has 10 sides.
Answer:
Its a Decagon
Step-by-step explanation:
Equation of a line in point- slope form, that passes through (1,-7) and has a slope of -2/3?
The equation of a line in point- slope form, that passes through (1, -7) and has a slope of -2/3 is (y + 7) = -2/3 (x - 1)
How to determine the equation of a line in point- slope formInformation gotten from the question include
a slope of -2/3
points (1, -7)
What is linear function ?A linear function consists of functions where the variables has exponents of 1.
The equation of a line in point- slope form is expressed in the form.
(y - y₁) = m (x - x₁)
Definition of variables
(y and y₁) = refers to variables in the y direction
m = slope
x and x₁ = refers to variables in the x direction
substituting into the slope and point (1, -7) equation gives
()y + 7) = -2/3 (x - 1)
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Aiden ha $3 worth of dime and quarter. He ha 2 more dime than quarter. Determine the number of dime and the number of quarter that Aiden ha
The number of dime and the number of quarters that Aiden have are 10 and 8 respectively.
How to find the number of dime and quarter?Aiden ha $3 worth of dime and quarter. Aiden has 2 more dime than quarter. The number of dime and the number of quarter that Aiden has can be calculated as follows:
let
x = number of quarter
y = number of dime
Therefore,
y = 2 + x
y - x = 2
0.1y + 0.25x = 3
Multiply equation(ii) by 10
y - x = 2
y + 2.5x = 30
subtract equation(i) from equation(ii)
3.5x = 28
x = 28 / 3.5
x = 8
Hence,
y = 2 + 8
y = 10
Therefore,
number of dime = 10
number of quarters = 8
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