Find the equation of the line that is parallel to the line y = 3x - 8 and passes through the point (-8,-3). Write the equation in point-slope form.
Answers
Substituting for x and y in the equation y = 3x + c
results in -3 = 3 x -8 + c
-3 = -24 + c so c must equal -3 + 24 = 21
The required line has the equation y = 3x + 21
Related Questions
In a freefall skydive, a skydiver begins at an altitude of 10,000 feet. during a freefall, the skydiver drops toward earth towards earth at a rate of 175 ft per second. the height of the skydiver from the ground can be modeled using the function H(t)=10,000-175t.
What is the domain of the function for this situation?
Answers
Answer:
{\(t|0\leq t\leq 50\)}
Step-by-step explanation:
We are given that
In a freefall skydive, a skydiver begins at an altitude during free fall =10,000 feet
The skydiver drops towards earth at a rate=175 ft/s
The height of the skydiver from the ground can be modeled using the function
\(H(t)=10000-175t\)
We have to find the domain of the function for this situation.
When t=0
Then ,\(H(0)=10,000 feet\)
From given graph we can see that the value of t lies from 0 to 50.
Therefore, the domain of the function for this situation is given by
{\(t|0\leq t\leq 50\)}
the manager of a computer retails store is concerned that his suppliers have been giving him laptop computers with lower than average quality. his research shows that replacement times for the model laptop of concern are normally distributed with a mean of 3.7 years and a standard deviation of 0.6 years. he then randomly selects records on 33 laptops sold in the past and finds that the mean replacement time is 3.5 years.assuming that the laptop replacement times have a mean of 3.7 years and a standard deviation of 0.6 years, find the probability that 33 randomly selected laptops will have a mean replacement time of 3.5 years or less.
Answers
The probability of 33 randomly selected laptops having a mean replacement duration of 3.5 years or fewer is roughly 0.0287, or 2.87%.
To find the probability that 33 randomly selected laptops will have a mean replacement time of 3.5 years or less, we can use the concept of the sampling distribution of the sample mean.
Given that the population means replacement time is 3.7 years and the standard deviation is 0.6 years, and assuming that the distribution is approximately normal, we can use the formula for the standard error of the mean:
Standard Error (SE) = σ / √n
where n is the sample size and σ is the population standard deviation.
In this case, σ = 0.6 years and n = 33. Plugging these values into the formula, we get:
SE = 0.6 / √33 ≈ 0.1045
Next, we need to calculate the z-score for the sample mean of 3.5 years. The z-score formula is:
z = (x - μ) / SE
where x represents the sample mean, μ represents the population mean, and SE represents the standard error.
Plugging in the values, we have:
z = (3.5 - 3.7) / 0.1045 ≈ -1.91
Now, we can use a standard normal distribution table to find the probability associated with this z-score. The probability represents the area under the curve to the left of the z-score.
Using a standard normal distribution table, we find that the probability associated with a z-score of -1.91 is approximately 0.0287.
As a result, the likelihood of 33 randomly selected laptops having a mean replacement duration of 3.5 years or fewer is roughly 0.0287, or 2.87%.
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yakubu and bello owned a business in which the ratio of their shars was 3:5, respectively. if yakubu later sold 3/4 of his share to bello for N180000, what is the value of the business?
Answers
The value of the yakubu and bello business is N80,000.
Let's start by determining the original value of Yakubu and Bello's shares in the business before the sale took place.
The ratio of their shares is given as 3:5, which means Yakubu owns 3 parts and Bello owns 5 parts out of a total of 3+5 = 8 parts.
Now, let's assume the value of the business is represented by "V" (to be determined).
Since Yakubu later sold 3/4 of his share to Bello, this means he sold 3/4 * 3 = 9/4 parts of the business to Bello.
The value of 9/4 parts of the business is N180,000, so we can set up the following equation:
(9/4) * V = N180,000
To solve for V, we multiply both sides of the equation by 4/9:
V = (4/9) * N180,000
V = N80,000
Therefore, the value of the business is N80,000.
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Use cramers rule to find the solution to the following system of linear equations.
Answers
The solution of the system of equations using Cramer's rule is x = 37/39 and y = 9/39.
What is the solution of the equations?The solution of the system of equations using Cramer's rule is calculated as follows;
The given equations are as follows;
9x - 2y = -9
-3x - 8y = 1
The determinant of the coefficient matrix is calculated as;
D = [9 -2]
[-3 -8]
D = -8(9) - (-3 x - 2)
D = -72 - 6 = -78
The x coefficient is calculated as;
Dx = [-2 -9]
[ -8 1]
Dx = -2(1) - (-8 x -9)
Dx = -2 - 72 = -74
The y coefficient is calculated as;
Dy = [9 -9]
[ -3 1]
Dy = 9(1) - (-3 x -9)
Dy = 9 - 27 = -18
The x and y values is calculated as;
x = Dx/D = -74/-78 = 74/78 = 37/39
y = Dy/D = -18/-78 = 18/78 = 9/39
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A cylinder has a volume of 400 cubic feet. If the height of the cylinder is 25 feet, what is the radius of the cylinder? Use 3.14 for π and round to the nearest hundredth.
Answers
Answer:
2.26 feet
Step-by-step explanation:
400/25=16
16/3.14=5.0955
5.0955^2=2.257
Sam figures that he also earns about $2.50 in tips for each person he serves.
Sam works 4 hours on a particular day.
If n represents the number of people Sam serves that day, which of the
following functions could Sam use to figure E, his total earnings for the day?
An+ 10
Answers
Option c is the correct answer. Sam's total earning for the day is equal to
E(n) = 2.5n + 24
Given data
Sam earning per hour = $6
Sam earning on tips per person = $2.5
Sam's total hour per day =4
How to find the function for Sam's total earningsSam's daily earning excluding tips = Sam earning per hour * Sam's total hour per day
= $6 * 4 hours = $24
If n represents the number of people Sam serves that day, then Sam's earnings on tips in a day = $2.5 * n = $2.5n
The function for Sam's total earning is given by E(n)
E(n) = Sam's daily earning excluding tips + Sam's earnings on tips in a day
E(n) = $24 + $2.5n
this is re arranged as
E(n) = 2.5n + 24
Therefore we can say that Sam's total earning for the day is equal to
E(n) = 2.5n + 24
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Complete question
Sam is a waiter at a local restaurant where he earns wages of $6 per hour. Sam figures that he also earns about $2.50 in tips for each person he serves. Sam works 4 hours on a particular day. If n represents the number of people Sam serves that day, which of the following functions could Sam use to figure E, his total earnings for the day?
A. E(n) = 2.5n
B. E(n) = 4n + 10
C. E(n) = 2.5n + 24
Finding all real answers i need help for both please and thank you
Answers
done,
hope this helps
.......
A negatively charged balloon moves close to another balloon. They then repel each other. What can be said about the other balloon? (2 points)
A: Both balloons have a positive charge.
B: It has a negative charge.
C: The balloon is uncharged.
D: There is a positive charge.
Answers
The repulsion between two negatively charged objects is an indication that the other object must be negatively charged. Thus, the correct answer is B: It has a negative charge.
This is due to the fact that like charges repel each other, while opposite charges attract each other. In this case, the negatively charged balloon repels the other balloon, indicating that the other balloon is also negatively charged. So, the correct answer is B).
The other options are incorrect. Option A is incorrect because both balloons cannot be positively charged as they would attract each other, not repel. Option C is incorrect because an uncharged object would not repel a negatively charged object. Option D is incorrect because a positively charged object would attract the negatively charged balloon, not repel it.
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The graph below shows a company’s profit f(x) in dollars depending on the price of pens x, in dollars, sold by the company What do the x-intercepts and maximum value of the graph represent? What are the intervals where the function is increasing and decreasing and what do they represent about the sale and profit? What is an aproxímate average rate of change of the graph from x=3 to x=5 and what does this rate represent?
Answers
Solution:
Given:
\(\begin{gathered} f(x)=profits \\ x=price\text{ of pens} \end{gathered}\)From the graph, the x-intercept exists at (0,0) and (6,0).
The maximum value is (3,120).
The x-intercept represents the break-even points. The company was not in profit or loss when no pen was sold and when 6 pens were sold, the profit was $0 at these two points.
The maximum value of the graph represents the maximum profit made by the company. The company made a maximum profit of $120 when 3 pens were sold.
The interval where the function is increasing is from negative infinity to x = 3. This shows that the more pen sold, the higher the profit made.
The interval where the function is decreasing is from x = 3 to positive infinity. This shows that the less pen sold, the lower the profit made.
The approximate average rate of change of the graph from x = 3 to x = 5 is;
\(\begin{gathered} ARC=\frac{f(x_2)-f(x_1)}{x_2-x_1} \\ where: \\ x_1=3 \\ x_2=5 \\ f(x_1)=120 \\ f(x_2)=60 \\ \\ Hence, \\ ARC=\frac{60-120}{5-3} \\ ARC=\frac{-60}{2} \\ ARC=-30 \end{gathered}\)The rate represents a decrease of $30 for every pen sold across the decreasing interval.
The MTC Theater holds 250 people, and last night’s performance sold out! Students paid $2.00 per ticket, while adults paid $4.00 per ticket. Last night’s show brought in $780. How many adult tickets were sold? How many students?
Answers
Answer:
110 students and 140 adults
Let adults be x and students be y
make equations:
1) x + y = 250
2) 2y + 4x = 780
make x the subject in equation 1:
x + y = 250x = 250 - yinsert this in equation 2:
2y + 4(250 - y) = 7802y + 1000 - 4y = 7802y - 4y = 780 - 1000-2y = -220y = 110So, there were total 110 students.
Find for x:
x = 250 - 110x = 140So, there were total 140 adults.
Help, brainlest if best explained
Answers
Answer:
The correct answer is the first choice.
Step-by-step explanation:
Let's solve your inequality step-by-step.
−2x>6
Step 1: Divide both sides by -2.
\(\frac{-2x}{-2}\) > \(\frac{6}{-2}\)
x < −3 <== this equation matches the graph
a square of side length 11 and a circle of radius \dfrac{\sqrt{3}}{3} 3 3 share the same center. what is the area inside the circle, but outside the square?
Answers
The area inside the circle but outside the square is approximately 0.0474 square units.
To find the area inside the circle but outside the square, we first need to calculate the area of both the circle and the square.
The area of a square is given by the formula: side length squared. So, for a square with a side length of 11, the area would be 11^2 = 121 square units.
The area of a circle is given by the formula: pi times the radius squared. In this case, the radius is √3/3. Plugging this value into the formula, we get pi * (√3/3)^2.
Simplifying this, (√3/3)^2 = 3/9 = 1/3. Therefore, the area of the circle is pi * (1/3).
To find the area inside the circle but outside the square, we subtract the area of the square from the area of the circle. So, the required area is pi * (1/3) - 121.
Calculating this, we get the final answer as approximately 0.0474 square units.
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the equation of a line is y equals 4 x plus 3 over 2. what is the slope of a line that is perpendicular to this line?
Answers
Therefore, the slope of a line perpendicular to the given line is -1/2.
The given equation of the line is y = (4x + 3) / 2.
To find the slope of a line perpendicular to this line, we need to determine the negative reciprocal of the slope of the given line.
The slope-intercept form of a line is y = mx + b, where m represents the slope of the line.
Comparing the given equation y = (4x + 3) / 2 with the slope-intercept form, we can see that the slope of the given line is 4/2, which simplifies to 2.
The negative reciprocal of 2 is -1/2.
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uppose m professors randomly choose from n time slots to hold their final exams. If two professors pick the same time slot, we say that they are in conflict. (If three professors all pick the same time slot, that gives three pairs of professors in conflict.) What is the expected number of pairs of professors in conflict? Your answer should depend on m and n.
Answers
The expected number of pairs of professors in conflict is given by (m choose 2) * 1/n.
It can be calculated using the principle of linearity of expectation. We can first calculate the probability that any two professors pick the same time slot, which is 1/n. Then, we can count the number of pairs of professors, which is given by the binomial coefficient (m choose 2) = m(m-1)/2. Therefore, the expected number of pairs of professors in conflict is:
Expected number of pairs in conflict = (m choose 2) * 1/n
This formula holds when the selection of time slots by each professor is independent of the choices made by all other professors. Note that this formula assumes that each professor selects only one time slot, and does not consider the possibility of a professor selecting multiple time slots. If professors are allowed to select multiple time slots, then the formula would need to be modified accordingly.
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Graph the following inequalitiesy < 2/5x - 3
Answers
Given the following question:
\(y<\frac{2}{5}x-3\)The following inequality is graphed as followed:
The point A is shown on the unit grid below the point B is 2surd 5 units from A and lies on the intersection of 2 grid lines write the coordinates of both possible positions for B
Answers
The coordinates of the two possible positions for B are:
(2, 1+√5) and (2, 1-√5).
Find coordinates of 2 points B.Since point B is 2√5 units from A and lies on the intersection of two grid lines, it can be located at two possible positions by moving 2 units in the positive or negative direction on the x-axis and 1 unit in the positive or negative direction on the y-axis.
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Olivia spent $20.00 on pencils and pens. Each pencil cost $2.00, and each pen cost $2.50.
Which equation represents the number of pencils, x, and the number of pens, y, Olivia could have bought?x+y=20
x + y = 20 ,
x+y=4.50
x + y = 4.50 ,
2x+2.50y=20
2 x + 2.50 y = 20 ,
2.50x+2y=20
Answers
Answer:
2x + 2.50 y = 20
Step-by-step explanation:
pencil =x, pen =y
Each pencil cost $2.00, and each pen cost $2.50.
x * 2 + y * 2.50 =
Olivia spent $20.00 on pencils and pens.
2x + 2.50 y = 20
A rectangular parking lot is surrounded on its perimeter by a fence that is 1,200 feet long. If the length of the rectangular parking lot is 5 times its width, w, which equation can be used to find the width of the parking lot? Ow+ (w+5) = 1,200
Answers
Answer:
w+5w=1200
Step-by-step explanation:
what theorem can be used to prove these triangles are congruent?
Answers
Answer:
B. HL
Step-by-step explanation:
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Each year you sell 3,000 units of a product at a price of $29.99 each. The variable cost per unit is $18.72 and the carrying cost per unit is $1.43. You have been buying 250 units at a time. Your fixed cost of ordering is $30. What is the economic order quantity? A) 342 units B) 329 units OC) 367 units D) 355 units E) 338 units
Answers
The economic order quantity is approximately 355 units, which corresponds to option D) 355 units.
To find the economic order quantity (EOQ), we can use the following formula:
EOQ = sqrt((2 * Annual Demand * Fixed Ordering Cost) / Carrying Cost per Unit)
Given information:
Annual Demand = 3,000 units
Fixed Ordering Cost = $30
Carrying Cost per Unit = $1.43
Substituting the values into the formula:
EOQ = sqrt((2 * 3,000 * 30) / 1.43)
EOQ = sqrt(180,000 / 1.43)
EOQ = sqrt(125,874.125)
EOQ ≈ 354.91
Rounding the EOQ to the nearest whole number, we get:
EOQ ≈ 355 units
Therefore, the economic order quantity is approximately 355 units, which corresponds to option D) 355 units.
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2. What is the best first step in solving the equation below? * 15
(1 Point)
(2x - 3)2 + 5 = 20
Take the square root of both sides of the equation
Subtract 20 from both sides of the quatic
O Subtract 5 from both sides of the equation
O Divide by 2 on both sides of the equation
Answers
Answer:
subtract 5 from both sides of the equaton
Step-by-step explanation:
(2x - 3)^2 + 5 = 20
(2x-3)^2 =25
which of the following calculations multiplies 23 by 0.01? =23% =23 =23+.01 =24-.01
Answers
The correct calculation that multiplies 23 by 0.01 is 23 * 0.01. This will give you the ans.23.0
1. 23%: This represents 23 percent of a whole. To convert a percentage to a decimal, you divide it by 100. So, 23% is equal to 0.23. This is not the correct calculation.
2. 23: This is simply the number 23 without any multiplication or division. This is not the correct calculation.
3. 23 + 0.01: This equation adds 23 and 0.01 together. The result is 23.01. This is not the correct calculation.
4. 24 - 0.01: This equation subtracts 0.01 from 24. The result is 23.99. This is not the correct calculation.
In summary, to multiply 23 by 0.01, you would use the equation 23 * 0.01, which equals 0.23.
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HELP PLEASEE, ILL BRAINLIST!!
Answers
Answer:
(a) To find the missing angle, we would do inverse tan.
\(angle =tan^{-1}\frac{opp}{adj}\)
\(angle = tan^{-1}\frac{17}{21}\)
angle= 39.0 degrees or 0.7 radians
(b) To find the missing angle, we would do inverse sin.
\(angle= sin^{-1}\frac{opp}{hyp}\)
\(angle= sin^{-1}\frac{12.7}{22.1}\)
angle= 35.1 degrees or 0.6 radians
Use synthetic division to divide x4 – 5x3 + 2x2 + 6x + 6 by x – 2.
Answers
x3 - 3x2 - 4x - 2 + 2/x-2
In ΔMNO, the measure of ∠O=90°, the measure of ∠M=13°, and OM = 9. 6 feet. Find the length of MN
Answers
In a right triangle, the right angle is marked as 90°. Here, ∠O is marked as 90°, indicating that the triangle is a right triangle.
Moreover, the length of OM is given as 9.6 feet. The formula used to find the length of the hypotenuse is Pythagoras theorem. The formula is given as c² = a² + b². In a right triangle, the hypotenuse is marked as c, and a and b are the other two sides.
Let's use Pythagoras theorem to find the length of the hypotenuse, MN. MN is the hypotenuse.c² = a² + b²c² = 9.6² + 13²c² = 92.16 + 169c² = 261.16The square root of 261.16 is 16.16. Therefore, the length of MN is 16.16 feet. This is the required solution. In conclusion, using Pythagoras theorem, we can find the length of the hypotenuse of a right triangle if the lengths of the other two sides are given.
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Why is he using an open circle for x > 4 ?
We want to include 4 in our solution set
or
We do not want to include 4 in our solution set
Answers
An open circle is used to represent x > 4 as we do not want to include 4 in our solution set.
How to graph inequalities?Treat the <, ≤, >, or ≥ as a = sign when putting an inequality on a graph. Graph the equation as a dotted line if the inequality is either or. Graph the equation as a solid line if the inequality is either or. The xy plane is split along this line into two regions: one that fulfils the inequality and the other that does not.
Using the open instructions when we plot the inequality we see that x > 4 has an open circle at 4.
This indicates that we do not want to include 4 in our solution set.
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Draw the graphs of the lines below on the same grid to find the coordinates of the point of intersection. y=2x+3 y−1/2x−2
Answers
Answer:
(2, 2)
Step-by-step explanation:
The point of intersection is at (2, 2)
A linear equation is given by:
y = mx + b;
where y, x are variables, m is the slope of the line and b is the y intercept.
Given the line with equations:
y = 3 x − 4 and y = 1/ 2x + 1
Plotting the graphs using geogebra online tool, the point of intersection is at (2, 2)
One day, the Early Bird Restaurant used
15 dozen eggs for 200 breakfast
customers. At this rate, approximately
how many dozen eggs are needed for 300
breakfast customers?
E. 20
F. 23
G. 25
H. 30
Answers
Answer:
F. 23
Step-by-step explanation:
15/2 = 7.5
7.5 dozen eggs per 100 customers
15 + 7.5 = 22.5 which can be rounded to 23
= 23
17. AMUSEMENT PARK The graph shows the
relationship between the number of Fun
Pass tickets sold and the total value of the
sales. Use the graph to estimate the x- and
y-intercepts of the function, where the
function is positive and negative, and
interpret the meanings in the context of the
situation. (Lesson 2-3)
Fun Pass Sales
(hundreds of $)
Value of Sales
25
20
15
10
O
20 40 60 80 100
Number Sold
Answers
The x- and y-intercepts of the function both are zero which represents when sold 0 tickets are, the value of sales is 0 and when the value of sales is 0, the number is 0.
What is a graph?
A graph can be defined as a pictorial representation or a diagram that represents data or values.
The relationship between the quantity of Fun Pass tickets sold and the amount of the overall sales are represented on the given graph.
Positive and negative functions are performed here, and the meanings are interpreted in the context of the situation.
Therefore, the x- and y-intercepts of the function are zero which represents when sold 0 tickets are, the value of sales is 0 and when the value of sales is 0, the number is 0.
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What is the total surface area of a triangular prism.
Answers
3 (hight) × 8 (base) = 24
24 ÷ 2 = 12 (area of triangle)
12 × 2 = 24 (because there are 2 triangles)
5 × 7 = 35 (because length times width)
35 × 2 = 70 (because there are 2 rectangles)
8 × 7 = 56 (because of the base)
ANSWER24 + 12 + 24 + 35 + 70 + 56 = 221