A line passes through the ordered pairs (4,1) and (2,8) . What is the slope? Please help
Final answer:
The slope of the line that passes through the points (4,1) and (2,8) is calculated using the slope formula and results in a slope of -3.5.
Explanation:
To find the slope of a line passing through the ordered pairs (4,1) and (2,8), you can use the slope formula:
m = (y2 - y1) / (x2 - x1). Here, (x1, y1) is the first point (4,1) and (x2, y2) is the second point (2,8).Plugging in the values, we get:
m = (8 - 1) / (2 - 4) = 7 / (-2) = -3.5Therefore, the slope of the line that passes through the points (4,1) and (2,8) is -3.5.
The slope of the line passing through the given points is -3.5.
Let’s find the slope of the line passing through the points (4, 1) and (2, 8).
The slope of a line can be calculated using the following formula:
[tex]\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
where:
• [tex](x_1) and (y_1)[/tex] are the coordinates of the first point (in this case, (4, 1)).
• [tex](x_2) and (y_2)[/tex] are the coordinates of the second point (in this case, (2, 8)).
Let’s compute the slope:
1. Difference in (x)-coordinates: [tex](x_2 - x_1 = 2 - 4 = -2)[/tex]
2. Difference in (y)-coordinates:[tex](y_2 - y_1 = 8 - 1 = 7)[/tex]
Now, calculate the slope:
[tex]\text{slope} = \frac{7}{-2} = -3.5[/tex]
Therefore, the slope of the line passing through the given points is -3.5.
Hey can you please help me posted picture of question
lori is 3 times as old as 7 more than ron's age if ron is a years old how old is lori
A local company employs a varying number of employees each year, based on its needs. The labor costs for the company include a fixed cost of $41,949.00 each year, and $28,826.00 for each person employed for the year. For the next year, the company projects that labor costs will total $1,483,249.00. How many people does the company intend to employ next year?
Answer:
50
Step-by-step explanation:
Let
x = number of employees each yeary = labor costsThe relationship between x and y can be represented through a linear equation.
y = a . x + b
where,
a is the slope
b is the y-intercept
The slope represents the cost per each person employed, that is, a = $28,826.00/person.
Then,
y = ($28,826.00/person) . x + b
Even if no person is hired (x = 0), there is a fixed cost of $41,949.00 (y = $41,949.00).
$41,949.00 = ($28,826.00/person) . 0 + b
b = $41,949.00
The final equation is
y = ($28,826.00/person) . x + $41,949.00
If the company will spend $1,483,249.00 (y = $1,483,249.00.),
$1,483,249.00 = ($28,826.00/person) . x + $41,949.00
1,441,300 = ($28,826.00/person) . x
x = 50 person (50 people)
The company intends to employ 50 people next year.
£54 in the ratio 5:4
hey can you please help me posted picture of question
y = |x| translated half a unit to the left
Answer:|
y=|x+.5|
Step-by-step explanation:
I found my answer by drawing a graph and then moving 2 spaces left then you need to do absolute values
you also need to plot some points on the graph to see where there is a straight line
I hope this helps
A sandwich shop offers the following toppings. How many two topping sandwiches can you make? -lettuce -tomato -bacon -cheese -mustard
A) 8
B) 10
C) 12
D) 20
Please include steps or explain how you got your answer! :)
The correct answer is: B) 10
Step 1:
To calculate the number of two-topping sandwiches you can make from the given toppings, you can use the combination formula:
[tex]\[C(n, k) = \frac{n!}{k!(n-k)!}\][/tex]
Where:
- [tex]\(n\)[/tex] is the total number of toppings available (5 in this case).
- [tex]\(k\)[/tex] is the number of toppings you want to choose (2 in this case).
- [tex]\(C(n, k)\)[/tex] represents the number of combinations.
Step 2:
Substituting the values:
[tex]\[C(5, 2) = \frac{5!}{2!(5-2)!}\][/tex]
[tex]\[C(5, 2) = \frac{5!}{2!3!}\][/tex]
[tex]\[C(5, 2) = \frac{5 × 4}{2 × 1}\][/tex]
[tex]\[C(5, 2) = \frac{20}{2}\][/tex]
[tex]\[C(5, 2) = 10\][/tex]
So, you can make [tex]\(10\)[/tex] two-topping sandwiches from the given toppings.
ASAP
The equation of the linear regression line represents the relationship between the number of cars washed for charity, x, and the amount earned for charity, y. yˆ=10x+20 How much money can the charity expect to earn if 50 cars come in for a wash?
Determine the measure of an angle (in radians) that cuts off an arc length of 6.4 inches in a circle with a 6.4 inch radius.
Solve the system of equations algebraically 5x - 3y = 6 6x - 4y = 2
Answer:
[tex]x=9[/tex] and [tex]y=13[/tex]
Step-by-step explanation:
We have been given a system of equations. We are asked to solve our given system algebraically.
[tex]5x-3y=6...(1)[/tex]
[tex]6x-4y=2...(2)[/tex]
From equation (1), we will get:
[tex]x=\frac{6+3y}{5}[/tex]
Upon substituting this value in equation (2), we will get:
[tex]6(\frac{6+3y}{5})-4y=2[/tex]
[tex]\frac{36+18y}{5}-4y=2[/tex]
[tex]\frac{36+18y}{5}-\frac{5*4y}{5}=2[/tex]
[tex]\frac{36+18y-20y}{5}=2[/tex]
[tex]\frac{36-2y}{5}=2[/tex]
[tex]\frac{36-2y}{5}*5=2*5[/tex]
[tex]36-2y=10[/tex]
[tex]36-36-2y=10-36[/tex]
[tex]-2y=-26[/tex]
[tex]\frac{-2y}{-2}=\frac{-26}{-2}[/tex]
[tex]y=13[/tex]
Upon substituting [tex]y=13[/tex] in equation (1), we will get:
[tex]5x-3(13)=6[/tex]
[tex]5x-39=6[/tex]
[tex]5x-39+39=6+39[/tex]
[tex]5x=45[/tex]
[tex]\frac{5x}{5}=\frac{45}{5}[/tex]
[tex]x=9[/tex]
hey can you please help me posted picture of question
I need help on this please
which situation is represented by the following equation?45w+123.95=753.95
My son is trying to figure out how to decompose 8/12 and what he has to work with is x/2 + x/2 =8/12
Find the sum of the first 10 terms for the sequence {21, 63, 189, . . . }.
5.2 × 1010
620,004
206,661
2730
The sum of the first 10 terms for the sequence given is 620,004.
What is Geometric sequence?A geometric sequence, is a sequence of non-zero numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.
Given is a geometric sequence, 21, 63, 189, . . . we need to find the sum of the first 10 terms,
Sum of n terms of GP = aₙ = arⁿ-1 / r-1,
a₁ = 21
r = 3
So,
a₁₀ = 21 × 3¹⁰-1 / 3-1
a₁₀ = 21 × 29,524
a₁₀ = 620,004
Hence the sum is 620,004.
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Two cable ferries start moving towards each other from shores A and B. When the pass each other for the first time the distance to shore B is 100 meters. Once they reach their destinations and start traveling back at the same time. When they meet for the second time, the distance to shore A is 50 meters. What is the distance between the shores Aand B?
The first meeting point of the ferries represents half of the total roundtrip, while the second meeting point represents a quarter of it. Knowing this proportion and the distances at which the meetings happen, we conclude that the distance between shores A and B is 200 meters.
Explanation:This problem can be solved using rates and proportions. Consider the total round trip of each ferry. The first meeting is at 100 meters from shore B and the second meeting is 50 meters from shore A.
Imagine a full roundtrip travel, from A to B and back to A. When the ferries meet for the first time, they have collectively completed one full round trip (distance A to B and B back to A). At their second meeting, they have collectively made two full round trips.
This means that the first meeting happened at 1/2 of the round trip distance and the second meeting happened at 1/4 of the round trip distance, meaning that the second meeting point was half the distance of the first meeting point. Based on where the second meeting point is (50 meters from shore A), we know that the first meeting point (100 meters from shore B) is twice the distance of the second meeting point from shore A.
Now, we understand the distances as follow: the total distance from shore A to shore B is the sum of the distance from the first meeting point to shore B (100 meters) and twice the distance from the second meeting point to shore A (2*50 meters), which sums up to 200 meters. Therefore, the distance between shores A and B is 200 meters.
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Judy squeezes 140 mm of lemonade to make 1 liter of lemonade how many millimeters of lemon juice are in 2 L of lemonade
How many different ways can a family visit Philadelphia, Baltimore, and Washington? 3 6 12
Answer:
Answer is 6 ways
Step-by-step explanation:
Given that a family wants to visit three different places as Philadelphia, Baltimore, and Washington.
We have to find the number of ways these three can be visited.
Here this is a question of permutation since order matters.
There are 3 cities and these can be visited in 3P3 ways =3!
=3x2x1 =6 ways
There are in total 6 different ways that the family can visit three different places as Philadelphia, Baltimore, and Washington.
If two cylinders are similar and the ratio between the lengths of their edges is 2:5 what is the ratio of their volumes
Answer: Thou answer shalt be Le letter B. 8:125
Hey can you please help me posted picture of question
we have 8 yards of wrapping paper if we use two feet for each present how many presents can we wrap
Bianca and Dave are a married couple filing a joint tax return. They have a combined gross income of $81,031 and claim four exemptions. They can make an adjustment of $2,914 for business expenses, an adjustment of $1,939 for business losses, a deduction of $4,140 for medical expenses, an adjustment of $4,825 for contributions to their retirement fund, and a deduction of $2,420 for charitable donations. If exemptions are worth $3,650 apiece and the standard deduction for a joint return is $8,350, what is their total taxable income?
a.
$50,193
b.
$41,843
c.
$48,403
d.
$52,793
Answer:
C
Step-by-step explanation:
Gross income(81,031) - adjustments(9,678) - exemptions(3,650•4 = 14,600) - STANDARD deduction(8,350)
$81,031 - $2,914 - $1,939 - $4,825 - $14,600 - $8350 = $48,403
itemized deductions = $6,560 which is less than the Standard deduction of $8,350, so you would use the Standard deduction
The total taxable income is b. $41,843..
To find Bianca and Dave's taxable income, we'll follow these steps:
Calculate the Total Exemptions:
They have 4 exemptions worth $3,650 each.
Total exemptions = 4 × $3,650 = $14,600.
Calculate Adjustments and Deductions:
Business Expenses: $2,914 Business Losses: $1,939 Medical Expenses: $4,140 Retirement Contributions: $4,825 Charitable Donations: $2,420Total adjustments and deductions = $2,914 + $1,939 + $4,140 + $4,825 + $2,420 = $16,228.
Determine the Standard Deduction:
For married filing jointly, the standard deduction is $8,350.
Calculate Adjusted Gross Income (AGI):
AGI = Combined Gross Income - Adjustments
AGI = $81,031 - (Business Expenses + Business Losses + Retirement Contributions)
AGI = $81,031 - ($2,914 + $1,939 + $4,825) = $81,031 - $9,678 = $71,353.
Calculate Total Deductions:
In this case, we will take the higher of the total adjustments/deductions calculated or the standard deduction.
Total official deductions = max(Total adjustments and deductions, Standard Deduction)
Total deductions = max($16,228, $8,350) = $16,228.
Calculate Taxable Income:
Taxable Income = AGI - Total Deductions - Total Exemptions
Taxable Income = $71,353 - $16,228 - $14,600
Taxable Income = $71,353 - $30,828 = $40,525.
Mias dog weighs 32.6 pounds. Letties dog weighs 3.8 times as much as Mias you. What does Letties dog weigh in pounds?
Final answer:
Lettie's dog weighs 123.88 pounds, calculated by multiplying Mia's dog's weight of 32.6 pounds by 3.8.
Explanation:
Calculating Lettie's Dog's Weight:
To find out how much Lettie's dog weighs, we need to perform a simple multiplication calculation because we are told Lettie's dog weighs 3.8 times as much as Mia's dog. Mia's dog weighs 32.6 pounds, so the weight of Lettie's dog will be:
32.6 pounds × 3.8 = 123.88 pounds.
It's important to remember that when we're dealing with measurements such as weight, we need to ensure that we stick to the same unit for a proper comparison. Given that we're talking about the weight of dogs, the pound is the most suitable unit of measurement for this context. Thus, we would not be using ounces or tons here, as those units are suitable for much lighter or heavier items, respectively.
Solve the system using the substitution method
2x+y=6
3x+5y=9
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Q # 6 find the measure please
i need help finding the perimeter of a rectangle
PLEASE HELP
1. What is the length of the unknown leg in the right triangle? with sides
sqrt 23yd and sqrt 87 yd
a. 8yd
b. sqrt 110yd
c. 64 yd
d. sqrt 7040yd
who help me is a genius
Find the surface area of regular prism with height 6 cm, if the base of the prism is a Regular quadrilateral with side 4 cm.