y = m x + b for a trend line that passes through the points (2, 18) and (–3, 8). Which value should he use as b in his equation
Answer:
b = 14
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + b ( m is the slope and b the y- intercept )
calculate m using the slope formula
m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)
with (x₁, y₁ ) = (2, 18 ) and (x₂, y₂ ) = (- 3, 8 )
m = \(\frac{8-18}{-3-2}\) = \(\frac{-10}{-5}\) = 2 , then
y = 2x + b
to find b substitute either of the 2 points into the equation
using (2, 18 )
18 = 4 + b ⇒ b = 18 - 4 = 14
Algebra II 5.02: Solve Radical Equations
Radical Equations
Step 1
To demonstrate how to solve a radical equation, let's use the following equation as an example:
Be Precise The base of a triangle is 2 ft. The
height of the triangle is 15 in. What is the area
of the triangle in square inches?
Thus, the area of triangle for the given values of height and base is found as: 180 sq. in.
Explain about the conversion units:A number of steps are involved in the Unit of Conversion process, which involves multiplying or dividing by a numerical factor. There are numerous ways to measure things like weight, separation, and temperature.
Unit conversion is the process of changing the unit of measurement for a comparable quantity by multiplying or dividing by conversion factors.
Scientific notation is used to express the units, which are then translated into numerical values in accordance with the amounts.
Given data:
base of triangle b = 2 ft.Height h = 15 in.We know that,
1 foot = 12 in.
2 feet = 12*2 = 24 in.
Area of triangle = 1/2 * b * h
Area of triangle = 1/2 * 24 * 15
Area of triangle = 12* 15
Area of triangle = 180 sq. in
Thus, the area of triangle for the given values of height and base is found as: 180 sq. in.
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In a statistical test of hypotheses, we say the data are statistically significant at level α if.
If the P value in a statistical test of hypotheses is more than, we may claim that the data are statistically significant at level. Less than is the P-value. =0.05 .
What is hypotheses ?An assumption is said to as a hypothesis when it is supported by evidence. Any investigation that turns the research questions into predictions must start here. Variables, the population, and the relationships between the variables are among its constituent parts. A hypothesis used to examine the link between two or more variables is known as a research hypothesis.
One dependent variable and one independent variable are shown to be related. For instance, eating more vegetables will help you lose weight more quickly. In this scenario, increasing your vegetable intake is an independent variable, while weight loss is the dependent variable.
It makes a claim that conflicts with the premise. There is no connection between the independent and dependent variables, which is a negative assertion. The emblem stands for.
Hence, If the P value in a statistical test of hypotheses is more than, we may claim that the data are statistically significant at level. Less than is the P-value. =0.05 .
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5. Jill is 9 kilometers away from Joe. Both begin to walk toward each other at the
same time. Jill walks at 1. 5 kilometers per hour. They meet in 2 hours. How fast is
Joe walking?
Answer: 3 kilometers per hour
Step-by-step explanation: Jill walks 1.5 kph and they meet in 2 hours so she walks 3 kilometers total, but since there's 9 kilometer distance and she covered 3 then joe covered the other 6 kilometers. So it takes joe 2 hours to walk 6 kilometers, and divided into 1 hour is 3 kilometers. So joe walks 3 kilometers per hour.
geometry triangle help pls
Answer:
equilateral trianglethe last optionpls mark brainlestLine g || line h? Why?
Answer:
Step-by-step explanation:
We say that two lines (on the same plane) are parallel to each other if they never intersect each other, ragardless of how far they are extended on either
Which of the following represents the range of the graph of F(x) below
Where do people and animals get the oxygen they breathe?
From plants
From other animals
From water
From the sun
Answer:
From plants hope it helps you have a good day keep smiling be happy stay safe ☺️Answer:
From Plants
Hope it will help you
Write the matrix equation that represents the system, and then solve if possible. State each of the rows, and then the
solution.
8x+7y=5
4x-9y=65
Answer:
x=5 y=-5
Step-by-step explanation:
12(Multiple Choice Worth 5 points)
(H2.03 MC)
Which of the following is NOT a key feature of the function h(x)?
(x - 5)²
-log₁ x +6
O The domain of h(x) is [0.).
O The x-intercept of h(x) is (5, 0)
h(x) =
0≤x≤4
X>4
O The y-intercept of h(x) is (0, 25).
O The end behavior of h(x) is as x→∞h(x)→∞
The feature NOT associated with the function h(x) is that the domain of h(x) is [0.).
The function h(x) is defined as (x - 5)² - log₁ x + 6.
Let's analyze each given option to determine which one is NOT a key feature of h(x).
Option 1 states that the domain of h(x) is [0, ∞).
However, the function h(x) contains a logarithm term, which is only defined for positive values of x.
Therefore, the domain of h(x) is actually (0, ∞).
This option is not a key feature of h(x).
Option 2 states that the x-intercept of h(x) is (5, 0).
To find the x-intercept, we set h(x) = 0 and solve for x. In this case, we have (x - 5)² - log₁ x + 6 = 0.
However, since the logarithm term is always positive, it can never equal zero.
Therefore, the function h(x) does not have an x-intercept at (5, 0).
This option is a key feature of h(x).
Option 3 states that the y-intercept of h(x) is (0, 25).
To find the y-intercept, we set x = 0 and evaluate h(x). Plugging in x = 0, we get (0 - 5)² - log₁ 0 + 6.
However, the logarithm of 0 is undefined, so the y-intercept of h(x) is not (0, 25).
This option is not a key feature of h(x).
Option 4 states that the end behavior of h(x) is as x approaches infinity, h(x) approaches infinity.
This is true because as x becomes larger, the square term (x - 5)² dominates, causing h(x) to approach positive infinity.
This option is a key feature of h(x).
In conclusion, the key feature of h(x) that is NOT mentioned in the given options is that the domain of h(x) is (0, ∞).
Therefore, the correct answer is:
O The domain of h(x) is (0, ∞).
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A bakery offers a sale price of 2.55 for 4 muffins.what is the price per dozen?
I hope someone answers fast
And explain what you did
Answer: $7.65 for a dozen/12
Step-by-step explanation: 2.55 x 3
A toy box has six faces that are squares there are 12 edges and eight vertices identify the shape of the toybox
Answer:
I believe it would be a cube.
Step-by-step explanation:
The 6 faces would be squares with their vertices connecting at the corners, giving them 8 in total. and their 12 edges would be like bridges connecting the vertices.
Find the CCF of 6 and 18
Answer:
6
Step-by-step explanation:
GCF of 6 and 18 is 6.
hope this helps! :D
have a miraculous day!! <3
You are the director of the customer service center in Company Alpha. You find that the mean time between calls to the center is 6 minutes with standard deviation of 4 minutes. The effective response time is 11 minutes with a standard deviation of 20 minutes. (a) Identify the following parameters: ta
tθ
∂a
∂θ
ra:
rθ:
The identified parameters are:
ta = 6 minutes
tθ = 11 minutes
∂a = 4 minutes
∂θ = 20 minutes
ra = 1/6 minutes^(-1)
rθ = 1/11 minutes^(-1)
ta: Mean time between calls to the center
tθ: Effective response time
∂a: Standard deviation of the time between calls to the center
∂θ: Standard deviation of the effective response time
ra: Rate of calls to the center (inverse of ta, i.e., ra = 1/ta)
rθ: Rate of effective response (inverse of tθ, i.e., rθ = 1/tθ)
Given information:
Mean time between calls to the center (ta) = 6 minutes
Standard deviation of time between calls (∂a) = 4 minutes
Effective response time (tθ) = 11 minutes
Standard deviation of effective response time (∂θ) = 20 minutes
Using this information, we can determine the values of the parameters:
ta = 6 minutes
tθ = 11 minutes
∂a = 4 minutes
∂θ = 20 minutes
ra = 1/ta = 1/6 minutes^(-1)
rθ = 1/tθ = 1/11 minutes^(-1)
So, the identified parameters are:
ta = 6 minutes
tθ = 11 minutes
∂a = 4 minutes
∂θ = 20 minutes
ra = 1/6 minutes^(-1)
rθ = 1/11 minutes^(-1)
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Directions: Determine whether each statement is always, sometimes, or never true.Name the theorem that will support your answer. Write your answers on the spaceprovidedStatementAnswerReason1. A line and a point are coplanar.2. Congruent angles form vertical angles.3. Linear pair that are congruent are rightangles.4. The sum of angles that formed linear pairis less than 180'.5. Vertical angles are complementary.
The given statement is 1. Always true
2. Always true
3. Always true
4. Sometimes true
5. Never true
Statement 1: A line and a point are always coplanar.
Answer: Always true.
Reason: This statement is always true because a line and a point can always be found on the same plane. In Euclidean geometry, a plane is a flat surface that extends infinitely in all directions, and any two points on the plane can be connected by a straight line. Therefore, a line and a point will always lie on the same plane.
Statement 2: Congruent angles form vertical angles.
Answer: Always true.
Reason: Vertical angles are formed by the intersection of two lines. When two angles are congruent, it means they have the same measure. If two angles have the same measure and are formed by the intersection of two lines, then they are vertical angles. Therefore, congruent angles always form vertical angles.
Statement 3: Linear pairs that are congruent are right angles.
Answer: Always true.
Reason: A linear pair consists of two adjacent angles that share a common side and form a straight line. If the two angles of a linear pair are congruent, it means they have the same measure. In Euclidean geometry, a straight angle measures 180 degrees. If two angles in a linear pair are congruent and their measures add up to 180 degrees, then each angle must measure 90 degrees, which is the measure of a right angle. Therefore, linear pairs that are congruent are always right angles.
Statement 4: The sum of angles that form a linear pair is less than 180 degrees.
Answer: Sometimes true.
Reason: The sum of angles that form a linear pair is always equal to 180 degrees, not less than 180 degrees. This is based on the definition of a linear pair, which states that the two angles in a linear pair are supplementary, meaning their measures add up to 180 degrees. However, if the statement said "less than or equal to 180 degrees," then it would be always true.
Statement 5: Vertical angles are complementary.
Answer: Never true.
Reason: Vertical angles are not complementary. Complementary angles are two angles that add up to 90 degrees. Vertical angles, on the other hand, are a pair of non-adjacent angles formed by the intersection of two lines. They do not necessarily have any specific relationship to each other in terms of their angle measures. Therefore, vertical angles are not complementary by definition.
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The truth of each statement depends on the properties of angles and theorems that support them. A line and a point are always coplanar, congruent angles can sometimes form vertical angles, congruent linear pairs are not always right angles, the sum of angles that form a linear pair is always 180 degrees, and vertical angles are never complementary.
To determine the truth of each statement, we need to consider the properties of angles and theorems that support them.
Statement 1: A line and a point are coplanar.About angles here:
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A drugstore sells vitamins in bottles with different pill counts. The price of each bottle is shown in the table below.
The price of one pill is approximately $0.04.
What is the price of one pill?Division is the mathematical operation used in grouping a number into equal parts using another number. The price of one pill can be determined by dividing the total cost of a number of pills by that number.
Price of one pill = cost of 50 pills / 50
$2.05 / 50 = $0.04
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Q3: Write the equation in slope-intercept form of the line that is parallel to the
graph of each equation and passes through the given point.
1. y = 3x + 6; (4, 7)
3. y = 1/2 x + 5; (4,-5)
The equations of the lines are y = 3x - 5 and y = (1/2)x - 7
What is an equation?An equation is an expression that shows how numbers and variables are related to each other.
A linear function is in the form:
y = mx + b
Where m is the rate of change and b is the initial value
Two lines are parallel if they have the same slope
1) y = 3x + 6; (4, 7)
The parallel line would have a slope of 3 and pass through (4, 7), hence:
y - 7 = 3(x - 4)
y = 3x - 5
2) y = (1/2)x + 5; (4, -5)
The parallel line would have a slope of 1/2 and pass through (4, -5), hence:
y - (-5) = (1/2)(x - 4)
y = (1/2)x - 7
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Solve the formula
W=1/2CV^2 for C
Answer:
U= 1/2 C V2 = 1/2 (2*10(-6) F)* (5 V)2
U= 25 * 10(-6) J
Step-by-step explanation:
Answer:
C = 2W/V^2
Step-by-step explanation:
W = 1/2CV^2
W * 2 = 1/2CV^2 * 2
2W/V^2 = CV^2/V^2
2W/V^2 = C
C = 2W/V^2
hope it helps :)
mark brainliest!
Please help me on this!!
Answer:
Pretty sure it's "only i"
Step-by-step explanation:
A constant rate of change means that something changes by the same amount during equal intervals.
$30 is the same amount whereas 10% could vary.
Hope this helps.
[Easy Points] Kanna Kamui sees 3 snowmen. Then he sees 2 more. How many snowmen did Kanna see in all?
Answer:
the correct answer is 5 snowmen
anova df ss ms f regression 1 12,323.60 12,323.60 90.0481 residual 8 1,154.802 136.8550 total 9 13,478.4 what is the correlation coefficient?
The correlation coefficient is 0.9541. This can be determined from the information provided in the ANOVA table, specifically the regression sum of squares (SSR) and the total sum of squares (SST).
The correlation coefficient, also known as the Pearson correlation coefficient, is a measure of the strength and direction of the linear relationship between two variables. It ranges from -1 to 1, where values closer to -1 or 1 indicate a stronger relationship, and values closer to 0 indicate a weaker relationship.
To calculate the correlation coefficient, we can use the formula:
r = sqrt(SSR/SST)
From the ANOVA table provided, we can see that SSR = 12,323.64 and SST = 13,538.4. Plugging these values into the formula gives:
r = sqrt(12,323.64/13,538.4) = 0.9541
Therefore, the correlation coefficient for this model is 0.9541, indicating a strong positive linear relationship between the independent variable and the dependent variable
Complete Question:
Using the following information. Coefficients -12.8094 Intercept Independent variable 2.1794 ANOVA df SS MS F 1 90.0481 Regression Residual Total 12,323.64 1,214.762 13,538.4 12,323.64 136.8550 8 1° 9 What is the correlation coefficient? Multiple Choice 0.9103 0.9541 -0.9541
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Directions: Find the complemen
ANGLE
EXAMPLE: 54°
1. 63°
2. 87°
3. 45°
4. 72°
5. 5°
Given:
The angles are:
Example \(54^\circ\)
1. \(63^\circ\)
2. \(87^\circ\)
3. \(45^\circ\)
4. \(72^\circ\)
5. \(5^\circ\)
To find:
The complimentary angle of the given angles.
Solution:
If two angles are complimentary, then their sum is 90 degrees.
Example: Let x be the complimentary angle of \(54^\circ\), then
\(x+54^\circ=90^\circ\)
\(x=90^\circ -54^\circ\)
\(x=36^\circ\)
Similarly,
1. The complimentary angle of \(63^\circ\) is:
\(90^\circ -63^\circ=27^\circ\)
2. The complimentary angle of \(87^\circ\) is:
\(90^\circ -87^\circ=3^\circ\)
3. The complimentary angle of \(45^\circ\) is:
\(90^\circ -45^\circ=45^\circ\)
4. The complimentary angle of \(72^\circ\) is:
\(90^\circ -72^\circ=18^\circ\)
5. The complimentary angle of \(5^\circ\) is:
\(90^\circ -5^\circ=85^\circ\)
Therefore, the complimentary angles of \(54^\circ, 63^\circ, 87^\circ, 45^\circ, 72^\circ, 5^\circ\) are \(36^\circ, 27^\circ, 3^\circ, 45^\circ, 18^\circ, 85^\circ\) respectively.
4+2/3x=2/5 how do I solve this equation
Given:
The given equation is 4+2/3x=2/5.
The objective is to solve for x.
\(undefined\)School ends at 3:15 pm. The school provides after -school care for a maximum of 150 minutes after school ends. When is the latest time for pick up?
The latest time for pickup, found by converting the 150 minutes maximum time provided by the school, from minutes to hours is about 5:45 pm
How can minutes be converted into hours?Minutes can be converted into hours by dividing the number of minutes by 60, which is the number of minutes in an hour.
The time that school ends = 3:15 pm
The latest time for pick up after school care = 150 minutes after school ends
Therefore, the latest time for pick up after school care = 3:15 pm + 150 minutes
60 minutes = 1 hour
150 minutes = (1/60) × 150 = 2.5
The latest for pick up = 3:15 pm + 2.5 hours = 5:45 pm
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What is the least common denominator of 1/8 and 2/3
Answer:
The least common denominator (LCD) is the smallest number that can be a common denominator for a set of fractions. Also known as the lowest common denominator
Your welcome
1. five friends go to the movie theater together. (a) if there are 5 seats open in a row, how many ways can the friends choose seats? (b) if there are 7 seats open in a row, how many ways can the friends choose seats? (note that two seats will remain empty.) (c) repeat part (b), but where two of the friends are required to sit next to each other. (d) repeat part (b), but where two of the friends are required to not sit next to each other.
he number of ways the friends can choose seats without sitting next to each other is 7! - 4! = 5040
If there are 5 seats open in a row and no restrictions on the seating arrangement, each friend can choose one seat independently. Therefore, the total number of ways the friends can choose seats is 5 factorial (5!) which is equal to 5 × 4 × 3 × 2 × 1 = 120.
(b) If there are 7 seats open in a row and no restrictions on the seating arrangement, each friend can choose one seat independently. Therefore, the total number of ways the friends can choose seats is 7 factorial (7!) which is equal to 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5040.
(c) If two friends are required to sit next to each other, we can treat them as a single entity. This reduces the problem to arranging four entities (three individual friends and one pair of friends) and three empty seats. The total number of ways the friends can choose seats is then 4 factorial (4!) which is equal to 4 × 3 × 2 × 1 = 24.
(d) If two friends are required to not sit next to each other, we can count the complement of the situation in part (c). There are 7 factorial (7!) total seating arrangements without any restrictions. From part (c), we found that there are 4 factorial (4!) seating arrangements where the two friends sit next to each other. - 24 = 5016.
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1. randy burgarner earns a gross monthly salary of $3,600.00. to date, he has earned a total of $14,400.00. what is this month's social security tax withholding? what is this month's medicare tax withholding?
To calculate Randy Burgarner's social security tax withholding, we first need to determine his gross monthly salary. Randy's total earnings to date are $14,400.00. Since we know that his gross monthly salary is $3,600.00, we can divide the total earnings by the number of months worked.
Social security tax withholding is $223.20 and medicare tax withholding for Randy Burgarner is $52.20. The solution to this problem is explained as under.
Total earnings to date: $14,400.00
Gross monthly salary: $3,600.00
Months worked = Total earnings to date ÷ Gross monthly salary
Months worked = $14,400.00 ÷ $3,600.00
Months worked = 4
Randy has worked for 4 months. Now we can calculate the social security tax withholding for this month.
The social security tax rate is 6.2% of the gross salary. To find the social security tax withholding, we multiply the gross monthly salary by the social security tax rate.
Social Security tax rate: 6.2%
Gross monthly salary: $3,600.00
Social Security tax withholding = Gross monthly salary × Social Security tax rate
Social security tax withholding = $3,600.00 × 6.2%
Social security tax withholding = $223.20
Therefore, this month's social security tax withholding for Randy Burgarner is $223.20.
Now let's calculate the Medicare tax withholding for this month.
The Medicare tax rate is 1.45% of the gross salary. To find the Medicare tax withholding, we multiply the gross monthly salary by the Medicare tax rate.
Medicare tax rate: 1.45%
Gross monthly salary: $3,600.00
Medicare tax withholding = Gross monthly salary × Medicare tax rate
Medicare tax withholding = $3,600.00 × 1.45%
Medicare tax withholding = $52.20
Therefore, this month's Medicare tax withholding for Randy Burgarner is $52.20.
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3x + 7 = 9x + 3
No solution one solution or infinite
Answer:
One solution.
Step-by-step explanation:
X=2/3 or x=2.6666
Answer:
x=2/3
Step-by-step explanation:
3x + 7 = 9x + 3
Collect like terms (subtract 3x from both sides and subtract 3 f4=rom both sides)
The resulting equation will look like this:
4=6x
=6x=4
Divide be 6 on both sides:
x=4/6
Simplify:
x=2/3 :-)
hat is the shortest possible length of the line segment that is cut off by the first quadrant and is tangent to the curve y = 6 x at some poin
The shortest possible length of the line segment that is cut off by the first quadrant and is tangent to the curve y = 6x at some point is 0.
To find the shortest possible length of the line segment that is cut off by the first quadrant and is tangent to the curve y = 6x at some point, we need to use calculus.
Let's start by finding the derivative of y = 6x:
y' = 6
This tells us that the slope of the tangent line to the curve y = 6x at any point is always 6.
Now, let's assume that the line segment we're looking for intersects the x-axis at some point (a, 0), where a > 0.
Since the line segment is tangent to the curve y = 6x at some point, it must have the same slope as the curve at that point, which is 6.
So, the equation of the tangent line to the curve y = 6x at the point (a, 6a) is:
y - 6a = 6(x - a)
Simplifying this equation, we get:
y = 6x - 6a
Now, we want to find the point on this line that intersects the x-axis at (a, 0).
Substituting y = 0 into the equation of the line, we get:
0 = 6x - 6a
Solving for x, we get:
x = a
So, the line intersects the x-axis at (a, 0), as we assumed.
Now, the length of the line segment cut off by the first quadrant is the distance between the points (a, 0) and (0, 6a).
Using the distance formula, we get:
d = sqrt((a - 0)^2 + (0 - 6a)^2)
Simplifying, we get:
d = sqrt(37a^2)
d = a * sqrt(37)
So, the shortest possible length of the line segment is when a is minimized.
To minimize a, we need to find the x-coordinate of the point of tangency.
Setting the equation of the line equal to the equation of the curve, we get:
6x - 6a = 6x
Simplifying, we get:
a = 0
This means that the line segment intersects the x-axis at (0, 0), which is the origin.
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