Answers
The results of the equations are listed below:
T' = 20 °C A ≈ 113.097 m² A = 100 ft² s = 312.5 mi C' = $ 120 C' = $ 40 s = 27.5 mi T' = 100 °C C' = $ 60 A = 112 ft²How to use equations to find required information?
In this problem we must make use of given formulas and substitute all known variables to determine all the required information:
Case 1
The temperature in Celsius scale in terms of the temperature in Fahrenheit scale is defined by the following formula:
T' = (5 / 9) · (T - 32)
T' = (5 / 9) · (68 - 32)
T' = 20 °C
Case 2
The area of the circle in terms of its radius is presented below:
A = π · r²
A = π · (6 m)²
A ≈ 113.097 m²
Case 3
The area of the triangle as a function of its base and its height is shown in the following formula:
A = 0.5 · b · h
A = 0.5 · (8 ft) · (25 ft)
A = 100 ft²
Case 4
The traveled distance is the product of the velocity and time:
s = v · t
s = (62.5 mi / h) · (5 h)
s = 312.5 mi
Case 5
The simple interest formula is equal to the product of the invested amount, interest rate and time divided by 100:
C' = (C · r · t) / 100
C' = [(300) · (5) · (8)] / 100
C' = $ 120
Case 6
C' = (C · r · t) / 100
C' = [(200) · (2) · (10)] / 100
C' = $ 40
Case 7
s = v · t
s = (45 mi / h) · (0.5 h)
s = 27.5 mi
Case 8
T' = (5 / 9) · (T - 32)
T' = (5 / 9) · (212 - 32)
T' = 100 °C
Case 9
C' = (C · r · t) / 100
C' = [(1200) · (2.5) · (2)] / 100
C' = $ 60
Case 10
The area of the rectangle is equal to the product of its base and its height:
A = b · h
A = (14 ft) · (8 ft)
A = 112 ft²
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Related Questions
Laci and leon are saving money to go to an amusement park. laci has $1 more than 4 times the amount of money leon has. together, they have $76. write an equation to determine how much money they have together. 4x 1 = 76 x 4x − 1 = 76 4x − 1 = 76 x 4x 1 = 76
Answers
Answer:
Leon has $15 and Laci has $61
Step-by-step explanation:
Let x = the amount Leon has. So 4 times that plus $1 would be 4x+1. Our equation is:
x + (4x+1) = 76
Combine like terms
5x + 1 = 76
Subtract 1 from both sides
5x = 75
Divide both sides by 5
x = 15. This is Leon. Laci is 4(15) +1, or 61.
Equivalent expression
4 x 6 x 7
Answers
Answer:
168
Step-by-step explanation:
4x6=24
24x7=168
What did lambert call the difference between the angle-sum of a triangle and 180 degrees?
Answers
Lambert calls the difference between the angle-sum of a triangle and 180 degrees the defect.
Who is Lambert?Johann Heinrich Lambert (26 or 28 August 1728 – 25 September 1777) was a polymath from the Republic of Mulhouse, generally referred to as either Swiss or French, who made significant contributions to mathematics, physics (particularly optics), philosophy, astronomy, and map projections. Lambert pioneered the use of hyperbolic functions in trigonometry. He also proposed theories about non-Euclidean space. Lambert is credited with being the first to demonstrate that is irrational by employing a generalized continued fraction for the function tan x. Euler believed the conjecture but was unable to prove it was irrational, and it is speculated that Aryabhata believed it as well in 500 CE. Lambert also developed theorems about conic sections that simplified the calculation of comet orbits.Lambert refers to the defect as the difference between the angle-sum of a triangle and 180 degrees.Therefore, Lambert calls the difference between the angle-sum of a triangle and 180 degrees the defect.
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At Zoe's Beading Boutique, 15 out of the 20 beads on clearance are plastic. What percentage
of beads on clearance are plastic?
Write your answer using a percent sign (%).
Submit
+
Work it out
Answers
Answer:
75%
Step-by-step explanation:
15 over 20 is equal to 3/4 and 3/4 is 75%
A survey from the Department of Motor Vehicles was given to residents in the city of Smallville. The results showed that 80% held a valid driver’s license. Of the individuals who held a value driver’s license, 10% has at least one traffic violation, whereas 30% who did not have a valid driver’s license has at least one traffic violation. What percent of Smallville residents have at least one traffic violation?
A. 14%
B. 28%
C. 38%
D. 40%
Answers
Percent of residents have at least one traffic violation with 80% held a valid driver’s license,10% has at least one traffic violation and 30% does not have valid license is 14%.
As given,
A=Person has a driver license
A'=Person does not have a driver license
P(A)=0.80
P(A')=0.20
For A, 10% has at least one traffic violation
For A', 30% had at least one traffic violation.
Probability with at least one traffic violation
=Probability of( A and one traffic violation +A' and one traffic violation)
=0.80(0.10)+0.20(0.30)
=0.08+0.06
=0.14
=14%
Therefore, percent of the residents with at least one traffic violation is 14%.
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Write an equation and solve.
For a ride on a rental scooter, Justin paid a $2 fee to start the scooter plus 12 cents per
minute of the ride. The total bill for Justin's ride was $20.84. For how many minutes did
Justin ride the scooter?
Answers
Answer:
2+0.12x=time on scooter bill
x is minutes and x is 157 minutes on the scooter
Step-by-step explanation:
can someone help me with 13 and 14 please and fast
Answers
Answer:
24 25 26
Step-by-step explanation:
guess and check..................
Continuation of Qn on part ii)
Answers
Answer:
Step-by-step explanation:
-7,5 + 4,2 =?
-0,9 * 2,7 =?
Answers
[tex]-7,5 + 4,2 = -3.3[/tex]
[tex]-0,9 \cdot 2,7 = -2.43[/tex]
Graph the following system of equations.
3x + 6y = 6
2x + 2y = 6
What is the solution to the system?
A)There are infinitely many solutions.
B)There is one unique solution, (4, -1).
C)There is one unique solution, (6, -2).
D)There is no solution.
Answers
The solution for the system of equations 3x + 6y = 6 and 2x + 2y = 6 is
B) There is one unique solution, (4, -1).
What is a solution for a system of equations?The solutions for a system of equation is the intersecting points between them
We know that system of equations has an infinite number of solutions when they coincide with each other as every point of a line falls into another line.
Systems of equations have a unique solution when they intersect each other and that intersecting point is the solution.
The system of equations has no solution when they are parallel to each other.
So, now we'll graph this system of equations and observe where they lie in XY coordinate.
Observing the graphs of both of these equations we can conclude that they have a unique solution (4,-1).
We can also solve these equations by multiplying equation(ii) by 3 and subtracting it from equation(i) and obtaining the values of (x,y).
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On a map with a scale 1 : 100,000, the distance between two cities is 12 cm. What would be the distance between these two cities on a different map with a scale 1 : 300,00?
Answers
Answer:
36 cm
Step-by-step explanation:
L is the midpoint of JM. K is the midpoint
of JL. JL = 1. What is the length of KM?
Answers
Answer:
KM = 1.5
Step-by-step explanation:
The first piece of info we get is that L is the midpoint of JM. This means that L = JM/2. The second piece of information provided is that K is the midpoint of JL, which means K = JL/2. We know that JL = 1, so we can plug it into the equation to help us figure out the problem. You can also illustrate to solve this problem, as I do here.
Since JL = 1...
K = 1/2, K = 0.5
________________________________________________
J K(0.5) L M
___________ __________
0.5 0.5
Now with this information, we know that 0.5 represents the distance of 1/4 of JM. We know that KM is 3/4 of the number line, and we know that 1/4 of the line is 0.5. We multiply 0.5 * 3 to get our final answer.
FINAL ANSWER: KM = 1.5
Use the trapezoidal rule, the midpoint rule, and simpson's rule to approximate the given integral with the specified value of n. (round your answers to six decimal places.) 4 6 ln(x) dx, 1 n = 6
Answers
The specified value of n for trapezoidal rule, the midpoint rule, and simpson's rule is 10.36 , 10.72 and 10.52.
Trapezoidal Rule: In Calculus, “Trapezoidal Rule” is one of the important integration rules. The name trapezoidal is because when the area under the curve is evaluated, then the total area is divided into small trapezoids instead of rectangles. This rule is used for approximating the definite integrals where it uses the linear approximations of the functions.
The trapezoidal rule is mostly used in the numerical analysis process. To evaluate the definite integrals, we can also use Riemann Sums, where we use small rectangles to evaluate the area under the curve.
Midpoint rule : In mathematics, the midpoint rule, also known as the midpoint Riemann sum or midpoint method, is a method of estimating the integral of a function or the area under a curve by dividing the area into rectangles of equal width. The midpoint rule formula is. The midpoint method formula works by summing the areas of each of the rectangles to produce an estimate for the area under a curve.
Simpson's Rule: Simpson's rule is used to find the value of a definite integral (that is of the form b∫ₐ f(x) dx) by approximating the area under the graph of the function f(x). While using the Riemann sum, we calculate the area under a curve (a definite integral) by dividing the area under the curve into rectangles whereas while using Simpson's rule, we evaluate the area under a curve is by dividing the total area into parabolas. Simpson's rule is also known as Simpson's 1/3 rule (which is pronounced as Simpson's one-third rule).
Now,
a=1,b=4,Δx =(b-a)/n =3/6 =1/2
f(x)=4√(ln(x))
trapezoidal rule:
∫4√(ln(x)) dx =(Δx /2)[f(1)+2*[f(1.5)+f(2)+f(2.5)+f(3)+f(3.5)]+f(4)]
∫4√(ln(x)) dx =((1/2) /2)[4√(ln(1)) +2*[4√(ln(1.5)) +4√(ln(2)) +4√(ln(2.5)) +4√(ln(3)) +4√(ln(3.5))] +4√(ln(4))]
∫4√(ln(x)) dx =10.365336
midpoint rule :
∫4√(ln(x)) dx =(Δx)[f(1.25)+f(1.75)+f(2.25)+f(2.75)+f(3.25)+f(3.75)]]
∫4√(ln(x)) dx =(1/2)[4√(ln(1.25)) +4√(ln(1.75)) +4√(ln(2.25)) +4√(ln(2.75)) +4√(ln(3.25)) +4√(ln(3.75)) ]
∫4√(ln(x)) dx =10.724182
simpsons rule:
∫4√(ln(x)) dx =(Δx /3)[f(1)+4*f(1.5)+ 2*f(2)+ 4*f(2.5)+ 2*f(3)+ 4*f(3.5)]+f(4)]
∫4√(ln(x)) dx =((1/2) /3)[4√(ln(1)) +4*4√(ln(1.5)) + 2*4√(ln(2)) +4*4√(ln(2.5)) +2*4√(ln(3)) + 4*4√(ln(3.5)) +4√(ln(4))]
∫4√(ln(x)) dx =10.527905
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8th grade Mathematics
A line has a slope of -3 and a y-intercept of 3.
What is the slope of the line?
O. -9
O. -1
O. 1
O. 9
I appreciate all of your answers even if they are wrong, thanks!! :)
Answers
Answer:
1
Step-by-step explanation:
i’m not sure on how to solve this equation. 10(2y+2)-y=2(8y-8)
Answers
Answer:
-12
Step-by-step explanation:
Distribute
20y+20-y=16y-16
Combine like terms
19y+20=16y-16
subtract 16y from 19y and subtract 20 from -16
3y=-36
Divide by 3
y=-12
A square room has a floor area of 144 square feet. the hieght of the room is 6 feet what is the area of one wall
Answers
The area of one wall of the room is 72 square feet.
What is the area of a square?The area of a square is given by -
A{S} = a²
where -
{a} is side of square.
Given is a square room has a floor area of 144 square feet. The height of the room is 6 feet.
It is given that -
floor area = 144
a² = 144
a = √(144)
a = √(12 x 12)
a = 12
The area of the wall will be equivalent to -
A{W} = h x a
A{W} = 6 x 12
A{W} = 72 square feet.
Therefore, the area of one wall of the room is 72 square feet.
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1. Find the sum.
76,749
5 565
23
+
The sum is
(Simplify your answer. Type a whole number.)
Answers
Answer:
82,337
Step-by-step explanation:
76,749
5565
+ 23
82,337
Hope it helps!!!
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Help please :)
create your own unit rate example in which you have to determine the unit rate of two fractions with different units. explain what the two fractions are, write the scenario, and calculate the unit rate. do not forget your units and remember to show your work!
no trolling!
Answers
Mansi can cover 1 mile of the distance in just 12 minutes.
How to calculate the unit rate?The unit rate can be expressed in any unit for instance minute per mile, miles/hour, etc
There is independent quantity, and a quantity which depends on it (dependent quantity). When independent quantity moves by a unit measurement (single unit increment), the increment in dependent quantity is called rate of increment of dependent quantity per unit increment in independent quantity.
Lets consider Mansi covers 3 miles in 36 minutes, her unit rate in minutes per mile is expressed as:
Unit rate = 36min/3miles
Unit rate = 12 minutes/mile
Here,
This shows that Mansi can cover 1 mile of the distance in just 12 minutes.
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What is the value of a?
Answers
Answer:
15 units
Step-by-step explanation:
By using the Pythagoras Theorem,
C^2 = A^2 + B^2
Substitute in the given values,
25^2 = a^2 + 20^2
625 = a^2 + 400
625 - 400 = a^2 + 400 - 400
a^2 = 225
[tex]a = \sqrt{225} [/tex]
= 15
Hope this too helped! ^^
I'd recommend watching a video or two on the topic of Pythagoras Theorem, if this explanation isn't clear enough.
HELP ME PLEASE TY
Abraham needs one-half of a point to get an A– in Math. What rational number can be used to represent the number of points needed for Abraham to get an A–?(1 point)
Answers
In order for Abraham to receive an A, he will need to earn a total of 1.5 points, which is the rational number that may be used to represent that amount.
Explain the concept of rational numbers.?It is important to keep in mind that a number is considered rational if it can be expressed in the form of a fraction.
It is possible when decimals and numbers have worked effectively.
In light of the fact that Abraham must get a grade of A– in mathematics in order to achieve an A, the rational number that can be used to symbolize the number of points that Abraham must earn in order to get an A will be the number 1.5.
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h is a trigonometric function of the form h(x)=a\cos(bx+c)+dBelow is the graph of h(x)h(x)h, left parenthesis, x, right parenthesis. The function has a maximum point at (-2\pi,3) and a minimum point at(− 2 π ,−4). Find a formula for h(x). Give an exact expression.
Answers
Answer is h(x) =[tex]\frac{1}{2}[/tex] cos ([tex]\frac{2}{3}[/tex]π +[tex]\frac{2}{3}[/tex]π ) - [tex]\frac{1}{2}[/tex]
∵The maximum point (- 2π. 3 )
minimum point (- π / 2 , - 4)
and h(x) = a cos (b x + c)+ d
∴ a + d = 3 d = - 1/ 2
⇒
-a + d = -4 a = 7 / 2
{solve the equation}
and -2πb + c = 0 b = 2 / 3
⇒
- ( π/ 2) b + c = λ c = 4 / 3 π
∴ h(x) =[tex]\frac{1}{2}[/tex] cos ([tex]\frac{2}{3}[/tex]π +[tex]\frac{2}{3}[/tex]π) - [tex]\frac{1}{2}[/tex]
Trigonometric functions are also known as Circular Functions can be simply defined as the functions of an angle of a triangle. It means that the relationship between the angles and sides of a triangle are given by these trig functions. The basic trigonometric functions are sine, cosine, tangent, cotangent, secant and cosecant
here detail explanation:
Sine Function
Sine function of an angle is the ratio between the opposite side length to that of the hypotenuse. From the above diagram, the value of sin will be:
Sin a =Opposite/Hypotenuse = CB/CA
Cos Function
Cos of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse. From the above diagram, the cos function will be derived as follows.
Cos a = Adjacent/Hypotenuse = AB/CA
Tan Function
The tangent function is the ratio of the length of the opposite side to that of the adjacent side. It should be noted that the tan can also be represented in terms of sine and cos as their ratio. From the diagram taken above, the tan function will be the following.
Tan a = Opposite/Adjacent = CB/BA
Also, in terms of sine and cos, tan can be represented as:
Tan a = sin a/cos a
Secant, Cosecant and Cotangent Functions
Secant, cosecant (csc) and cotangent are the three additional functions which are derived from the primary functions of sine, cos, and tan. The reciprocal of sine, cos, and tan are cosecant (csc), secant (sec), and cotangent (cot) respectively. The formula of each of these functions are given as:
Sec a = 1/(cos a) = Hypotenuse/Adjacent = CA/AB
Cosec a = 1/(sin a) = Hypotenuse/Opposite = CA/CB
cot a = 1/(tan a) = Adjacent/Opposite = BA/CB
Note: Inverse trigonometric functions are used to obtain an angle from any of the angle’s trigonometric ratios. Basically, inverses of the sine, cosine, tangent, cotangent, secant, and cosecant functions are represented as arcsine, arccosine, arctangent, arc cotangent, arc secant, and arc cosecant.
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How much will a person pay for 6.8 pounds of bananas at a price of $0.79 per pound?
Answers
Answer:
A person will pay $5.37
Step-by-step explanation:
6.8 pounds of bananas x $0.79 per pound = $5.37.
I hope this helps and have a blessed day! :)
The lines 4x+6y-5=0 and 2x+4y-3=0 intersect at N. Find the equation of the line through N perpendicular to the line x+2y=0.
Answers
4x+6y=5 and 2x+4y=3 are the 2 supplied lines. We must solve two simultaneous equations in order to determine the location at where these two lines cross.
When we multiply the second equation by two, we obtain the result 4x+8y=6. Next, we subtract this from the first equation to get -2y = -1, which equals y=1/2. N's coordinates are therefore (+1/2, +1/2).
The line we need to identify now goes through this point and is perpendicular to the line x+2y=0; its slope is -1/2 (the slope of the line [tex]ax+by+c=0[/tex] is -a/b). With m1*m2=-1, the line perpendicular to this one has a slope of 2. Consequently, the line that we must identify The slope of the equation is 2, and it goes through N. In order to simplify the equation, (y-1/2) = 2*(x-1/2), which results in 2y-1 = 2*(2x-1) and 2y-1 = 4x-2 and 4x-2y-1=0. The necessary equation is as follows.
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PLS EXPLAIN THIS ITS URGENT HOW DO YOU DO THISSSS
Answers
Answer:
It means you will have to match the name with the correct numbers on the right hand side.example:Animal bread
food dog
answeranimal— dog
food — bread
The real question answer:Zero slope — ( 16,3), (16,-80)Negative slope — (-5,-20), (-11,-20)undefined slope— (-1000,2500), (500,4000)Positive slope— (0,4,25), (1,25,1,75)Incase you aren't still convinced, you can try using the slope formula to solve it yourself .
slope = Y2 - Y1
————
X2 - X1
Hope this helpsGood luck ✅
A woman has a total of $9,000to invest. She invests part of the money in an account that pays7%per year and the rest in an account that pays9%per year. If the interest earned in the first year is$710, how much did she invest in each account? She invested $___ at 7% and $___ at 9%.
Answers
She invested $5,000 at 7% and $4,000 at 9%
How much is invested at each rate of return?
The amount invested at 7% can be assumed to be x, such that the amount invested at 9% would be total investment of $9000 minus x, which has been invested at the initial rate of 7%
total interest at 7%=interest rate*amount invested
interest rate=7%
amount invested=x
total interest at 7%=7%*x=0.07x
total interest at 9%=9%*(9000-x)
total interest at 9%=810-0.09x
total interest on both accounts=0.07x+810-0.09x
total interest on both accounts=810-0.02x
total interest earned=$710
710=810-0.02x
0.02x=810-710
0.02x=100
x=100/0.02
x=amount invested in the account which earns 7%=$5,000
amount invested at 9%=$9000-$5000
amount invested at 9%=$4,000
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the formula for the circumference of a circle is c equals 2 pi r. if the circumference is31.4 centimeters, what is the diameter of the circle? (let pi equals 3.14)
Answers
Answer: Substitute this value to the formula for circumference: C = 2 * π * R = 2 * π * 14 = 87.9646 cm. You can also use it to find the area of a circle: A = π * R² = π * 14² = 615.752 cm². Finally, you can find the diameter - it is simply double the radius: D = 2 * R = 2 * 14 = 28 cm.
Step-by-step explanation:
The equation for line r can be written as y= 1/2 x+8. Line s, which is perpendicular to line r, includes the point (2, – 7). What is the equation of line s?
Answers
Answer:
y = -2x - 3
Step-by-step explanation:
The slopes of two perpendicular lines are negative reciprocals of each other. So slope of s is -2
using m = -2, x = 2, y = -7
y = mx + b
-7 = (-2)(2) + b
-7 = -4 + b
b = -3
y = -2x - 3
I need help on my math
1/5 of x is 14
What is the x
Answers
Need an explanation, thx
Answers
Answer:
see explanation
Step-by-step explanation:
calculate the slope m using the slope formula and equate to the given slope
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
(a)
(x₁, y₁ ) = (- 3, - 4 ) and (x₂, y₂ ) = (0, y )
[tex]\frac{y-(-4)}{0-(-3)}[/tex] = [tex]\frac{y+4}{0+3}[/tex] = [tex]\frac{y+4}{3}[/tex] , then
[tex]\frac{y+4}{3}[/tex] = 2 ( multiply both sides by 3 )
y + 4 = 6 ( subtract 4 from both sides )
y = 2
ordered pair is (0, 2 )
(b)
(x₁, y₁ ) = (- 2, 2 ) and (x₂, y₂ ) = (x, 5 )
[tex]\frac{5-2}{x-(-2)}[/tex] = [tex]\frac{3}{x+2}[/tex] , then
[tex]\frac{3}{x+2}[/tex] = [tex]\frac{3}{7}[/tex] ( cross- multiply )
3(x + 2) = 21 ( divide both sides by 3 )
x + 2 = 7 ( subtract 2 from both sides )
x = 5
ordered pair is (5, 5 )
(c)
(x₁, y₁ ) = (x, 5 ) and (x₂, y₂ ) = (1, - 5 )
[tex]\frac{-5-5}{1-x}[/tex] = [tex]\frac{-10}{1-x}[/tex] , then
[tex]\frac{-10}{1-x}[/tex] = [tex]\frac{-5}{2}[/tex] ( cross- multiply )
- 5(1 - x) = - 20 ( divide both sides by - 5 )
1 - x = 4 ( subtract 1 from both sides )
- x = 3 ( multiply both sides by - 1 )
x = - 3
ordered pair is (- 3, 5 )
(e)
(x₁, y₁ ) = (- 6, y ) and (x₂, y₂ ) = (8, 2 )
[tex]\frac{2-y}{8-(-6)}[/tex] = [tex]\frac{2-y}{8+6}[/tex] = [tex]\frac{2-y}{14}[/tex] , then
[tex]\frac{2-y}{14}[/tex] = - [tex]\frac{1}{7}[/tex] ( cross- multiply )
- 7(2 - y) = 14 ( divide both sides by - 7 )
2 - y = - 2 ( subtract 2 from both sides )
- y = - 4 ( multiply both sides by - 1 )
y = 4
ordered pair is (- 6, 4 )
8xy(x^3 y) fully simplify
Answers
Answer:
8x^4y^2
Step-by-step explanation:
Just plug it in to the calculator and that will be your result.
