The triangle has three side x,y and √(x²+y²), the slope of x is zero, the slope of y is undefined, the slope of √(x²+y²) is tanα. The coordinate of the midpoint of x is x/2,0 and y is 0, y/2
how to determine the length and slope of the side of a triangle?suppose the triangle is right-angled and the sum of other two angles are also 90 degrees. we know that the side opposite to the right angle is called hypotenuse. let the other two side is denoted by x and y. Now, x is the base of triangle, and the rest of the side is y. The angle between hypotenuse and base is denoted by α . As per Pythagorean theorem, hypotenuse = √(x²+y²).
slope can be calculated by tanα or using the formula (y₂-y₁)/(x₂-x₁)
according to trigonometric ratio, tanα = opposite side/base = x/y
tanα is the slope of hypotenuse.
the side length x is along the horizontal axis, so its y coordinate is zero and slope is also zero.
the side length y is along the vertical axis whose x coordinate is zero that means slope is undefined.
When does a slope is defined?As per the formula (y₂-y₁)/(x₂-x₁) used to calculate slope, whenever x coordinate is zero the result is written as undefined.
hence, the triangle is right-angled, and the biggest side has a slope only.
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question in the photo
The compositions of the functions are given as follows:
(f ∘ g)(0) = 0.(g ∘ f)(1) = -2.The domain and the range of the functions are given as follows:
Domain of g(x) = {-4, -3, 0, 1}.Range of f(x) = {0, 1, 2}.How to obtain the composite functions?The representation of the composite function is that the output of the inner function works as the input to the outer function, as follows:
(f ∘ g)(x) = f(g(x)).
Hence, at x = 0, the composite function is given as follows:
(f ∘ g)(0) = f(g(0)) = f(1) = 0.
At x = 1, the composite function is given as follows:
(g ∘ f)(0) = g(f(0)) = g(1) = -2.
How to obtain the domain and the range?The definitions of the domain and of the range of a function are given as follows:
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Bryan was selling tickets for a school play. Adult tickets cost $10 and children's tickets cost $5. If Bryan madea total of $310 in one day of sales write an equation that could represent the number of adult's
(a) tickets and children's tickets sold.
Answer:
Step-by-step explanation:
10(a)+5(c)=310
a= number of adult
c= number children
1. The graph below shows the number of children's and adult tickets sold each day of a performance.
(a) What is the slope of the line? Show your work.
(b) What is the equation of the line in point-slope form?
(c) What is the equation of the line in slope-intercept form?
(d) What is the equation of the line in standard form? Show your steps in converting to standard form.
Answer:
(a) -2
(b) y -120 = -2(x -10)
(c) y = -2x +140
(d) 2x +y = 140
Step-by-step explanation:
Given a graph with y-intercept 140 and x-intercept 70, you want the slope and various equations describing the graph.
(a) SlopeThe line drops from a y-value of 140 to 0 as x increases from 0 to 70. The slope is ...
m = rise/run = -140/70 = -2
The slope of the line is -2.
(b) Point-slope equationThe point-slope equation of the line with slope m through point (h, k) is ...
y -k = m(x -h)
We have a line with slope -2 that goes through the point (10, 120), so we can write the equation as ...
y -120 = -2(x -10)
(c) Slope-intercept formIn part (a) we identified the y-intercept as 140, so we can write the equation as ...
y = mx + b . . . . . line with slope m and y-intercept b
y = -2x +140 . . . . . . line with slope -2 and y-intercept 140
(d) Standard formThe slope-intercept equation can be converted to standard form by adding the opposite of the x-term to both sides.
y +2x = -2x +2x +140 . . . . . 2x added to both sides
2x +y = 140 . . . . . . . . . standard form equation of the line
Line d has a slope of 6/7. line e is parallel to line d. what is the slope of line e?
Parallel lines have the same slope.
If one line has a slope of 6/7, then the other line also has a slope of 6/7.
The sum of two numbers is 43 . One number is 19 more than the other.find the numbers
PLEASE HURRY
Solve the following equation:
5- (4x+3)= 1/2 (8x - 12)
Please solve for x
Answer:
x=1
Step-by-step explanation:
---------- -----------
x =1
Isolate the variable by dividing each side by factors that don't contain the variable.
Write an equation whose solution is the number of months, x it takes for the account
balance to reach $2000.
An equation whose solution is the number of months, m, it takes for the account balance to reach $2000 would be the initial balance minus the monthly rent times the number of months equals $2000.
$4800-$400m=$2000
Given:
initial balance : $4800
removed from the account each month for rent : $400
Since the account starts with $4,800 and decreases by $400 each month, there will be 4800−400m dollars left in the account after m months have passed.
The question asks us to set up an equation representing the number of months that pass before this quantity equals 2,000, and so the desired equation is
4800−400m=2000.
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A salesperson's weekly paycheck is 15% less than a second salesperson's paycheck. The two paychecks total $1675. Find the amount of each paycheck. (Round your answers to the nearest cent.)
The amount of paycheck of Salesperson 1 and Salesperson 2 is $770 and $905 respectively.
What is Percentage?
The percentage is one of the most used methods to portray statistics. Percentage simply means "per hundred," and the sign for percentage is%. One percent (or 1%) is one hundredth of a total or whole number and is computed by dividing the whole or entire number by 100.
Solution:
Given: Paycheck of Salesperson 1 = 85% of Salesperson 2
Let, Paycheck of Salesperson 2 = x
So, paycheck of Salesperson 1 = 85/100 x
According to the question,
85/100 x + x = 1675
185/100x = 1675
x = 167500 / 185
x = 905.4$ = 905$
Salesperson 1 = 770$
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Robert had 362 in his bank account. He first spent 54 and then 82 how much money does Robert have left
If Robert had 362 in his bank account. If he first spent 54 and then 82 then the amount left in Robert bank account is $226.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given that the amount in Roberts bank account is $362.
He first spent 54 and then 82
We need to find the amount left in Robert account.
This we can find by finding the total amount he spent and removing total amount spent from the total amount he has in his account.
The total amount he spend=54+82
Fifty four plus eighty two
136
One hundred thirty six.
The amount left we calculate by subtracting 136 from 362.
362-136
We get 226.
Hence, the amount left in Robert bank account is $226.
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AreaABC Corp bought a production machine on January 1, 2019 for $31,250. The company did not elect Section 179 expensing and elected out of claiming bonus depreciation in 2019, and is depreciating the machine using the MACRS accelerated depreciation tables for 5-year property, half-year convention. What is the 2021 depreciation (Year 3) deduction for the machine?
2018 depreciation (year 3) deduction for the machine is $6000 when ABC Corp spent $31,250 on a production machine on January 1, 2019.
Given that,
ABC Corp spent $31,250 on a production machine on January 1, 2019. The corporation is depreciating the equipment using the MACRS accelerated depreciation tables for 5-year property, half-year convention, and has chosen not to exercise Section 179 expensing or to claim bonus depreciation in 2019.
We have to find what is the machine's Year 3 depreciation deduction for 2021.
We know that,
Computation of 2018 depreciation (year 3) deduction for the machine using MACRS accelerated depreciation table for 5 year property.
Name of the asset is production machine
Basis of machine is $31,250
MACRS Percentage from MACRS Percentage Table A-1 by IRS Publication 946 for 5 year property using half year convention for 3rd year is 19.20%
2018 depreciation (year 3) deduction for the machine is
$31,250×19.20%=$6,000
Therefore, 2018 depreciation (year 3) deduction for the machine is $6000 when ABC Corp spent $31,250 on a production machine on January 1, 2019.
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2) Explain how graphing these equations can help find the solution to the system.
Graphing these equations can help find the solution to the system by unique solution, no solution and infinite number of solution.
Define equation.A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.
Given
Graphing these equations can help find the solution to the system by,
There are three possible outcomes when two equations with two variables are considered in a two-dimensional plane.
1.Unique solution: A point will be where the graphs of the two lines connect.
The One equation's coefficient of variation and constant will not be proportionate to another equation's coefficient of variation and constant.
2. No Solution: The two lines run parallel to one another.
While constants are not proportional, the coefficient of variables of one equation will be related to the coefficient of variables of another equation.
3, Infinite number of Solution: The two lines will coincide.
One equation's coefficient of variation and constant will be proportional to another equation's coefficient of variation and constant.
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Wilson bought a bus ticket to travel 22 miles to his friend's house. The ticket price was $5.00 for the first 10 miles and $0.50 for each additional 1/2 mile.
How much did Wilson pay for his bus ticket?
Answer:
$7.25.
Step-by-step explanation:
To find the cost of Wilson's bus ticket, we first need to determine how many additional miles he traveled beyond the first 10 miles. Since the ticket price was $0.50 per 1/2 mile, we can divide the number of additional miles by 0.5 to find the number of additional 1/2 miles. For example, if Wilson traveled 12 miles, he would have traveled 2 miles beyond the first 10 miles. Dividing 2 by 0.5, we get 4, so he would have traveled an additional 4 1/2 miles.
Once we know the number of additional 1/2 miles, we can multiply that number by the ticket price per 1/2 mile to find the cost of the additional portion of the ticket. For example, if the ticket price was $0.50 per 1/2 mile and Wilson traveled an additional 4 1/2 miles, the cost of the additional portion of the ticket would be 4.5 * $0.50 = $2.25.
Finally, we can add the cost of the initial portion of the ticket, which was $5.00 for the first 10 miles, to the cost of the additional portion to find the total cost of the ticket. For example, if the initial portion of the ticket was $5.00 and the additional portion was $2.25, the total cost of the ticket would be $5.00 + $2.25 = $7.25.
In conclusion, to find the cost of Wilson's bus ticket, we need to divide the number of additional miles he traveled beyond the first 10 miles by 0.5 to find the number of additional 1/2 miles, multiply that number by the ticket price per 1/2 mile to find the cost of the additional portion of the ticket, and then add that amount to the cost of the initial portion of the ticket to find the total cost.
Answer:$11.00
Explanation:22-2=20
20÷5=4
4÷2=2
2×$5.00=$10
additional 2 miles
2×$0.50=$1
so
$10+$1=$11.00
A milkman had 3 1 litres of milk in the can. He sold 1 1 litres to a customer and 2 litres 423
to a hotel. How much milk is left in the can?
The amount of milk remaining after the milk is sold to the customer and hotel is 18 liters.
What is a mathematical equation and expression?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical equation is used to equate two expressions.Given is that a milkman had 31 liters of milk in the can. He sold 11 liters to a customer and 2 liters to a hotel.
Assume that the remaining milk in the container is denoted by [x]. Then, we can write -
[x] = Total milk - {milk sold to customer + milk sold to can}
[x] = 31 - {11 + 2}
[x] = 31 - 13
[x] = 18
Therefore, the amount of milk remaining in the can is 18 liters.
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Samuel wants to deposit $4,000 and keep that money in the bank without deposits or withdrawals for three years. He compares two different options. Option 1 will
pay 1.8% interest, compounded quarterly. Option 2 will pay 1.5% interest, compounded continuously.
How much interest does Option pay?
b. How much interest does Option 2 pay
Part (a)
The compound interest formula is
A = P*(1+r/n)^(n*t)
where,
A = account balance after t yearsP = deposit amountr = annual interest rate in decimal formn = number of times the money is compounded per yeart = number of yearsFor option 1, we have these values:
P = 4000r = 0.018n = 4t = 3Plug them into the formula to get:
A = P*(1+r/n)^(n*t)
A = 4000*(1+0.018/4)^(4*3)
A = 4221.4270078004
A = 4221.43
The account balance after three years is $4221.43
Then subtract off the deposit to find the interest made.
i = A - P
i = 4221.43 - 4000
i = 221.43
Answer: Option 1 pays $221.43 in interest.
====================================================
Part (b)
If n heads to infinity, then the compound interest formula is replaced with the continuously compounded interest formula.
That formula is
A = P*e^(r*t)
where the new item 'e' is a special constant.
e = 2.718...
It's similar to how pi = 3.14...
Most calculators have an "e" button, so it's best to let the calculator handle the decimal digits of "e".
For option 2, we have:
P = 4000r = 0.015t = 3So,
A = P*e^(r*t)
A = 4000*e^(0.015*3)
A = 4184.11143963493
A = 4184.11
and,
i = A - P
i = 4184.11 - 4000
i = 184.11
Answer: Option 2 pays $184.11 in interest.
Option 1 is the better choice.
PLEASE HELP IM GIVING BRAINLIEST AND ITS 15 POINTS
By solving the given expression we get sinα as a final result.
What is tanx in terms of sinx and cosx ?
Tanx can be defined as the ratio of sinx and cosx and tanx can be defined by ratio of opposite side and adjacent side also.
Given expression,
secα / (cotα+tanα)
secα can be written as 1/cosα
cotα = cosα/sinα
tanα = sinα/cosα
so,
by substituting we get,
(1/cosα ) / ((cosα/sinα) + (sinα/cosα) )
(1/cosα ) / (cos2α+sin2α)/sinαcosα
(cos square x + sin square x = 1 )
(1/cosα ) /(1/sinαcosα)
= sinα
Hence , By solving the given expression we get sinα as a final result.
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evaluate x 3 + (5x + y)2 if x= -1 and y=4
Answer:
-3
Step-by-step explanation
x^3+(5x+y)2
-1^3=-1
-1 x -1 x -1 = -1
(5x+y)2
(5(-1)+(4)2
(-5+(4))2
(-1)2 = -2
Bring -1 down from -1^3
-1-2=-3
You answer is -3
Help me please it’s due tomorrow!!!!!
Answer:
130 more dollars.
Answer:
130
Step-by-step explanation:
When ordering the Kids' Lunch at Burger Universe, the customer must choose a size, whether or not to have cheese, a side order, and a type of fruit drink. Here are the possibilities for each choice. Choice Possibilities Size Small, Large Cheese? With cheese, Without cheese Side order Fries, Onion rings Fruit drink Orange, Grape, Cherry, Lemonade How many Kids' Lunches are possible?
The possible Kids' lunches are 32.
What is a permutation?The number of possible arrangements for a given set is calculated mathematically, and this process is known as permutation. Simply said, a permutation is a term that refers to the variety of possible arrangements or orders. The arrangement's order is important when using permutations.
Using permutations:
you have
- 2 possible choices for the size (small and large),
- 2 possible choices for the cheese (with and without),
- 2 possible choices for the side order (fries and onion rings)
- 4 possible choices for the fruit drink (orange, grape, cherry and lemonade)
The total Kids' lunches possible, are the total combinations you can get, therefore:
2 × 2 × 2 × 4 = 32
There are 32 possible Kids' lunches.
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Y varies directly as x. If x=6 when y=36 find x when y=72
Answer:
x= 12
Step-by-step explanation:
Y[tex]\alpha[/tex] X
Let the constant be k
For the proportionality sign to be gone,a constant has to be introduced.
Since y varies directly,the constant ( k) will multiply x
Y= kx
Substitute for x=6 and y=36 to find k
36=6x
x = 36/6 = 6
To find the value of x,substitute for k = 6 and y = 72
72= 6x
x = 72/6
x=12
what is the slope?
Simplify Your answer and write it as a proper fraction, improper fraction, or integer
Answer: 1/2
Step-by-step explanation:
Write a numerical expression to represent the phrase "the sum of 25 and the cube of 9." Do not evaluate the expression.
Answer:
25 + 9^3
Step-by-step explanation:
In how many ways can the letters of the word ‘CAR’ be reordered to produce distinct ‘words’?
Answer:2
Step-by-step explanation:
car, and arc, however ar is also a word, not distinctly though.
The height of a cell phone tower is 200 ft tall. The tower is secured by 3 wires, stretching from the top of the tower to spots on the ground 50 ft away from the base of the tower. Each wire creates a right triangle with the tower and the ground. What is the length of each wire to the nearest foot?
Question 14 options:
42,500 ft
354 ft
3,704 ft
206 ft
Answer:
206 ft
Step-by-step explanation:
Each wire is a hypotenuse of a right triangle in which the height of the tower is one leg and the distance from the anchor of the wire to the base of the tower is the other leg.
Leg 1: 200 ft
Leg 2: 50 ft
Hypotenuse: x
200² + 50² = x²
x² = 40,000 + 2,500
x² = 42,500
x = √42,500
x = 206
Answer: 206 ft
If tan t = 4/3 in quadrant 3, find the remaining trig functions.
sin t:
cos t:
csc t:
sec t:
cot t:
Answer:
Below
Step-by-step explanation:
edited: FOR QIII (I didn't see that part)
Remember for a right triangle S-O-H-C-A-H-T-O-A
Tan is OPPOSITE LEG / ADJACENT LEG
make the right triangle with legs 3 and 4 ( in quadrant III)
then the hypotenuse is 5
sin = opp/ hyp = - 3/5
cos = - 4/5
csc = 1/sin = - 5/3
sec = 1/cos = - 5/4
cot = 1/tan = 3/4
I need help with this question
Answer:
the correct answer is 3
hope it is right
The answer to the expression is 3
Pls i need this answered fast pls anyone
The value of x in the parallel lines is 102 degrees.
How to find angles when parallel lines are cut by a transversal?When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angle, linear angles, alternate interior angles, alternate exterior angles, vertically opposite angles etc.
Therefore, let's find the value of x using the angle relationships.
Alternate exterior angles are the pair of angles on the outer side of the two parallel lines but on the opposite side of the transversal.
Therefore,
x = 102 degrees(alternate exterior angles)
Alternate exterior angles are congruent.
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Equations are given whose graphs enclose a region. Find the area of the region. (Give an exact answer. Do not round.)f(x) = x^2 + 5; g(x) = −x^2; x = 0; x = 3
The equations whose graphs encompass a region are thus provided. when the region's area is 301.5
Define area.The region that an object's shape defines as its area. The area of a figure or any other two-dimensional geometric shape in a plane is how much space it occupies. The simplest technique is to multiply the room's length and width. The floor surface area for a rectangular room is equal to the length times the width. The formula for this is area = length x width (A = lw).
Given
g(x) = x²
x = 0
x = 3
We must determine the area using the functions f(x) and g(x), which are provided.
ₐ∫ᵇ (f(x) + g(x)) dx
₀∫³ (x² + 15(x + 5)) dx
₀∫³ (x²dx + ₀∫³15(x + 5)) dx
(x³/3) + 15x²/2 + 75x
₀[x³/3]³ + ₀[15x²/2 + 75x]³
[(3 - 0)³/3] + [15(3 - 0)²/2 + 75(3 - 0)]
27/3 + 15(9/2) + 75(3)
9 + 15(4.5) + 7
76.5 + 225
301.5
The equations whose graphs encompass a region are thus provided. when the region's area is 301.5
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A clothing manufacturer made a batch of pants with a 43 inch waist. A sampling of the pants found the error factor to be 5%.
What is the smallest and largest size one can expect to find in the group.
Round the answer to two decimal places.
Smallest size= ______
Largest size= ______
Using percentage error, the error factor is ± 2.15 inches and the smallest size is 40.85 inches and largest size is 45.15 inches.
Percentage ErrorPercent error is the difference between estimated value and the actual value in comparison to the actual value and is expressed as a percentage. In other words, the percent error is the relative error multiplied by 100.
The formula of percentage error is given as
P.E = [(actual value - estimated value) / actual value] × 100
Since we know the percentage error and actual value, we can find the difference or actual error by;
5 / 100 = x / 43
0.05 = x / 43
x = 2.15
The increase of decrease in size is by a factor of ± 2.15
The smallest size = 43 - 2.15 = 40.85 in
The largest size = 43 + 2.15 = 45.15 in
The smallest and largest size are 45.15 and 40.85 inches respectively
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Math hw part 3
The graph shows the number of servings in different amounts of yogurt. Write an equation that gives the number of servings, y, in x pints of frozen yogurt. You answer must be written in the form: y=1x. NO SPACES BETWEEN EACH CHARACTER!
The equation that represents the graph that gives the number of servings, y, in x pints of frozen yogurt is: y = 3x.
How to Write the Equation that Represents a Proportional Relationship?A proportional relationship graph is a straight line graph that passes through the point of origin, (0, 0), which has an equation that can be expressed in the slope-intercept form as y = kx.
"k" is the constant of proportionality, which is the ratio of y to x. k = y/x.
Given the graph above, we need to find the constant of proportionality, k. To do this, use the coordinates of one point on the graph, say (1, 3):
Constant of proportionality, k = y/x = 3/1
k = 3
To write the equation that gives the number of servings, y, in x pints of frozen yogurt, substitute k = 3 into y = kx:
y = 3x
The equation is: y = 3x.
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Find the Area of the figure below, composed of an isosceles trapezoid and one semicircle. Rounded to the nearest tenths place
The Area of given figure is 48.28 unit² (Approx.)
How to calculate the surface area of a composite figure?Surface area are derived for some standard shapes like circle, triangle, parallelogram, rectangle, trapezoid, etc.
When some shape comes which isn't standard figure, then we find its area by slicing it (virtually, like by drawing lines) in standard shapes. Then we calculate those composing shapes' area and sum them all.
We are Given Length of parallel lines are 13 , 6 respectively
Diameter of semi-circle = 6
Height of parallelogram = 8
Area of given figure
Radius of semi-circle = Diameter of semi-circle / 2
Radius of semi-circle = 6 / 2
Radius of semi-circle = 3
Area of given figure = [1/2][Sum of parallel line][Height] + [πr² / 2]
Area of given figure = [1/2][13 + 6][8] + [(3.14)(3)² / 2]
Area of given figure = 42 + 6.28
Area of given figure = 48.28 unit² (Approx.)
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