Answers
= 4.865
a = 2.2 to nearest tenth.
Answer: a = 2.2
Given that: b = 4.0, c = 3.7, A=33.
The law of cosine is:
[tex]a^2=b^2+c^2-2bccosA\\a^2=4.0^2+3.7^2-2(4.0)(3.7)cos(33)\\a^2=4.86535118882\\a=\sqrt{4.86535118882}\\a=2.20575410888\\a=2.2[/tex]
So a = 2.2
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Related Questions
A line passes through the ordered pairs (4,1) and (2,8) . What is the slope? Please help
Answers
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.
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?
Answers
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.
Osman broke the unusually shaped picture window and his parents living room. The figure shows the dimensions of the window. replacement glass cost $8 per square foot, and there will be a $35 installation fee. Find the cost to replace the window to the nearest cent.
Answers
Osman can calculate the cost to replace the unusually shaped picture window by determining its area and then using the formula C = (Area of the window × $8) + $35 to find the total cost. The final total should be rounded to the nearest cent. However, without the window's dimensions, an exact cost cannot be calculated.
Explanation:To calculate the cost to replace the unusually shaped picture window in Osman's parents' living room, we must first determine the area of the window to find out how many square feet of glass are needed. Once we have the area, we can multiply by the cost per square foot and add the installation fee. Unfortunately, the question does not provide the necessary dimensions of the window, so we cannot proceed with the exact calculations. However, I will provide a general formula that Osman could use to calculate the replacement cost.
Let's assume that the dimensions of the window are provided and that we have managed to calculate the area, A, in square feet. The cost of the replacement glass will then be A × $8. After calculating this, Osman would need to add the installation fee, which is $35. So the total cost to replace the window, C, would be calculated using the formula:
C = (A × $8) + $35
Once Osman replaces the window, if the total calculated cost is not a whole number, he should round it to the nearest cent.
Judy squeezes 140 mm of lemonade to make 1 liter of lemonade how many millimeters of lemon juice are in 2 L of lemonade
Answers
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.
Answers
S = 2(LW +H(L +W))
S = 2((4 cm)*(4 cm) +(6 cm)*(4 cm +4 cm))
S = 2(16 cm² +48 cm²)
S = 2*64 cm² = 128 cm²
The surface area of the prism is 128 cm².
Q # 6 find the measure please
Answers
angle AEB=180°-127°=53°
We can conclude that the measure of angle AEB is 53°
Angles AEB and BEC are examples of supplementary angles. Supplementary angles are two angles whose measures add to a sum of 180 degrees. This can be represented using the following formula:
A1 + A2 = 180
In this case, the formula can be rewritten to state the following:
∠AEB + ∠BEC = 180
Insert any values given in the problem above:
∠AEB + 127 = 180
Now subtract 127 from both sides of the equation:
∠AEB = 53
We have now proven that ∠AEB has a measure of 53 degrees.
I hope this helps!
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.
Answers
because s= r × angle measurement in radian
we have s= arc , r = radian so we got the value
hey can you please help me posted picture of question
Answers
A. y=(x-2)^2-4
1. As you can see in the figure attached, the red parabola has the function f(x)=x^2. This is the patern function. By definition, which is the most basic function of the quadratics functions.
2. The blue parabola is shifted 2 units at x axis and 4 units in the -y axis. Therefore, the correct function that represents this parabola is the function of the option A.
3. If you want to verify it, you can give values to x and plot each point on a graph.
Mias dog weighs 32.6 pounds. Letties dog weighs 3.8 times as much as Mias you. What does Letties dog weigh in pounds?
Answers
We are given the weight of Mia's dog and told to find the weight of Lettie's dog based on the known relationship. Using these given values, we can create the following equation (let "w" represent the total weight of Lettie's dog):
w = 32.6(3.8)
Simplify the right side of the equation:
w = 123.88
We have now proven that Lettie's dog weighs 123.88 lbs.
I hope this helps!
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.
What is the answer to the problem i am very confused...
Answers
h(0) = -3(0 - 3)² + 108
Parenthesis first
h(0) = -3(-3)² + 108
Exponents next
h(0) = -3(9) + 108
Multiplication
h(0) = -27 + 108
Combine like terms
h(0) = 81: The height of the hovercraft at the time of takeoff is 81 meters!
Hope this helps :)
Solve the system using the substitution method
2x+y=6
3x+5y=9
branliest offered
Answers
lori is 3 times as old as 7 more than ron's age if ron is a years old how old is lori
Answers
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?
Answers
y = 10x + 20
We are to calculate the amount of charity if 50 cars are washed. Number of cars are represented by x, so by substituting x = 50 in above equation we can find the amount of charity that is earned by washing 50 cars.
y = 10(50) + 20 = $ 520
Thus, the charity can earn $520 if 50 cars come in for a wash.
hey can you please help me posted picture of question
Answers
The x and y values are flipped when finding an inverse.
So, if in the inverse function a y value is paired with more than one x values, this will mean that in the function an x-value was paired with more than one y-values.
Looking at the graph we can say that no y-value in the inverse is paired with more than one x values, so the original relation would be a function.
So the answer is TRUE
who help me is a genius
Answers
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
Answers
in a right triangle
Applying the Pythagoras Theorem
c²=a²+b²
in this problem
c=√87 yd
a=√23 yd
b=?
so
b²=c²-a²-----> b²=(√87)²-(√23)²----> b²=87-23----> b²=64----> b=8 yd
the answer is
8 yd
we have 8 yards of wrapping paper if we use two feet for each present how many presents can we wrap
Answers
Mulitply 8 × 3 = 24
You have 24 feet of wrapping paper.
Divide 24 by 2 = 12
You can wrap 12 presents.
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! :)
Answers
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.
y = |x| translated half a unit to the left
Answers
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
which situation is represented by the following equation?45w+123.95=753.95
Answers
subtract 123.95 from both sides
45w+123.95-123.45=753.95-123.95
simplifying gives us:
45w=630
multiply both sides by 1/45
1/45×45w=630×1/45
simplifying we get
w=14
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
Answers
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.
The mean of a normal distribution is 12.3 with the standard deviation is 1.7. find the 73th percentile
Answers
If two cylinders are similar and the ratio between the lengths of their edges is 2:5 what is the ratio of their volumes
Answers
[scale factor] is equal to the ratio between the lengths of their edges
so
scale factor=2/5
volume smaller cylinder/volume larger cylinder=[scale factor]³
volume smaller cylinder/volume larger cylinder=[2/5]³---> 8/125
the answer is
8/125
Answer: Thou answer shalt be Le letter B. 8:125
i need help finding the perimeter of a rectangle
Answers
L= length
W= width
Plug in the width and length into the formula above to solve for perimeter.
Hope this helps! :)
Experts/ace/geniuses helppp
Answers
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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
Answers
Your answer for that equation is x = 2/3
Not sure what you mean by "decompose" though.
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?
Answers
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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Find the solutions for a triangle with a =11.4, b =13.7, and c =12.2.
Answers
The solutions for the triangle are: ∠A = 51.833...° , ∠B = 70.880...° and ∠C = 57.286...°
Explanation
For finding the unknown angles, we need to use Cosine rule. The formulas are...
[tex]cos A = \frac{b^2+c^2-a^2}{2bc} \\ \\ cos B= \frac{a^2+c^2-b^2}{2ac}\\ \\ cos C= \frac{a^2+b^2-c^2}{2ab}[/tex]
Given that the length of three sides of the triangle as : [tex]a= 11.4, b= 13.7[/tex] and [tex]c=12.2[/tex]
Thus,
[tex]cosA= \frac{(13.7)^2+(12.2)^2 -(11.4)^2}{2(13.7)(12.2)} \\ \\ cosA= \frac{206.57}{334.28} \\ \\ cosA= 0.61795... \\ \\ A= cos^-^1 (0.61795...)= 51.833... degree\\ \\ \\ \\ cos B= \frac{(11.4)^2+(12.2)^2 -(13.7)^2}{2(11.4)(12.2)}\\ \\ cos B= \frac{91.11}{278.16} \\ \\ cos B= 0.3275...\\ \\ B= cos^-^1 (0.3275...)= 70.880... degree \\ \\ \\ \\ cos C= \frac{(11.4)^2+(13.7)^2 -(12.2)^2}{2(11.4)(13.7)}\\ \\ cos C= \frac{168.81}{312.36} \\ \\ cos C= 0.54043...\\ \\ C= cos^-^1 (0.54043...)= 57.286... degree[/tex]
Answer
To simplify the answer above this one, it is
C) A=51.8 B=70.9 C=57.3
Step-by-step explanation:
I got it right on edge
PLEASE Help!! What is the solution of the equation? Eliminate any extraneous solutions.
Answers
sq rt of 3x+28-8=x
add 8 to both sides
sq rt of 3x+28 = x+8
square both sides of the equation
3x + 28 = x^2 + 16x + 64
subtract x^2+16x+64 from both sides
group common terms
-13x-36-x^2=0
rearrange and put in quadratic form
x= -13 +/- sq rt of 13^2-4(1)(36) over 2(1)
subtract 169 by 144
x= -12 +/- sq rt of 25 over 2
solve for both sides
x = -13+5 over 2
=-4
x= -13-5 over 2
= -9
now plug in x
sq rt of 3(-4)+28 -8=-4
sq rt of 3(-9)+28 -8= -9
-4 = -4
but
-7 does not = -9
so -4 is the solution
The lengths of the base of a trapezoid is 12ft and 5ft the height is 96 in what is the area of the trapezoid
Answers
A = (1/2)(b₁ +b₂)h
Substitute the given information and evaluate. (Make sure all dimensions have the same units.)
A = (1/2)(12 ft +5 ft)(8 ft)
A = 68 ft²
The area of the trapezoid is 68 square feet.
Answer:
the area is 816
Step-by-step explanation:
Step-by-step
12 + 5 = 17
17 / 2 = 8.5
8.5 * 96 = 816
the area is 816