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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.

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.

The area of one wall of the room is 72 square feet.

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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The solution for the system of equations 3x + 6y = 6 and 2x + 2y = 6 is

B) There is one unique solution, (4, -1).

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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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:

Answer:

82,337

Step-by-step explanation:

   76,749

      5565

+         23
   82,337

Hope it helps!!!

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Answer:

36 cm

Step-by-step explanation:

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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Answer:

8x^4y^2

Step-by-step explanation:

Just plug it in to the calculator and that will be your result.

Answer:

168

Step-by-step explanation:

4x6=24

24x7=168

Answer:

75%

Step-by-step explanation:

15 over 20 is equal to 3/4 and 3/4 is 75%

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! :)

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 )

Answer:

2+0.12x=time on scooter bill

x is minutes and x is 157 minutes on the scooter

Step-by-step explanation:

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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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

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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Lambert calls the difference between the angle-sum of a triangle and 180 degrees the defect.

Therefore, Lambert calls the difference between the angle-sum of a triangle and 180 degrees the defect.

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Answer:

Animal bread

food dog

animal— dog

food — bread

slope = Y2 - Y1

————

X2 - X1

[tex]-7,5 + 4,2 = -3.3[/tex]

[tex]-0,9 \cdot 2,7 = -2.43[/tex]

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

Answer:

24 25 26

Step-by-step explanation:

guess and check..................

Mansi can cover 1 mile of the distance in just 12 minutes.

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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Answer:

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

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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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.

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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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

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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