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The smaller side of the triangle from missing sides is 63cm.

What is a triangle?

In Geometry, triangles are the type of polygons, which have three sides and three vertices. This is a two-dimensional figure with three straight sides. A triangle is considered a 3-sided polygon. The sum of all the three angles of a triangle is equal to 180°. The triangle is contained in a single plane. Based on its sides and angle measurement, the triangle has six types.

Based on the sides of a triangle, a triangle is classified into 3 types, namely:

Scalene Triangle – All the sides are of different measures.

Isosceles Triangle – Two sides of a triangle are of the same measure and the remaining side has a different measure.

Equilateral Triangle – All the 3 sides of a triangle are of the same measure.

Based on the angles of a triangle, a triangle is classified into 3 types, namely:

Acute Angle Triangle – All the angles of a triangle is less than 90°.

Obtuse Angle Triangle – One of the angles of a triangle is greater than 90°.

Right Angle Triangle – One of the angles of a triangle is equal to 90°.

Now,

According to Pythagorean theorem,

H^2=P^2+B^2

Where H=hypotenuse, B=base, P=Perpendicular

Given base=16

let perpendicular=x then hypotenuse=x+2 as  The lengths of the other two sides are consecutive odd integers

Therefore, (x+2)^2=x^2+16^2

x^2+4+4x=256+x^2

x=63 and x+2=65

Hence,

          The smaller side of the triangle from missing sides is 63cm.

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Answer:

ask your teacher it's the best answer

The length of the hypotenuse is: 8.64 meters

The length of the hypotenuse of a right triangle can be found using the Pythagorean theorem, which states that;

In any right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

The Pythagorean theorem can be defined as; fundamental theorem in mathematics that relates to right triangles.

In this case, the two shorter sides have lengths 8.49 meters and 1.61 meters, so the length of the hypotenuse can be found by calculating the square root of the sum of the squares of these lengths:

i.e.  √(8.49^2 + 1.61^2) = √(72.0201 + 2.5881) = √74.6082 = 8.64 m

So, the length of the hypotenuse is approximately 8.64 meters.

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Answer:

The equation of the line is y = -3x + 5.

Step-by-step explanation:

y - y1 = m(x - x1)     where m = the slope and (x1, y1) is the given point

So here we have:

y - (-1) = -3(x - 2)

y + 1 = -3x + 6

y = -3x + 5.

Therefore , the solution of the given problem of input and output comes out to be methods for Fixing an Input-Output Table begin with the very first input.

The function generates an output value by using an input value, such as x = 3, as an example. If you substitute 3 for the number x in the equation y = x + 5 y = x + 5, you get y = 3 + 5 = 8 y = 3 + 5 = 8. So, y = 8.

Here,

The output value is as follows.

Both the value of the final goods and services produced and the value added at each stage of production can be used to calculate total output.

An input-output table's governing principle is the mathematical operation or operations that are applied to the input to yield the desired output. The rule can be very basic, like adding 1, or quite complex, like squaring the amount and taking 17 out.

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Answer:

$75

Step-by-step explanation:

3/4 -tuition

4/4-3/4=1/4 1/3×1/4=1/12 -books

1/12+1/4=1/3 1-1/3= 2/3 -left which is equal to $50

2/=$50

1=

1×3/2×$50= $75

After 3 years, Beth's investment will be worth $1,281.216.

What is percentage ?

A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used.

The formula to calculate the future value of an investment is:

FV = PV * (1 + r/n)^(nt)

where:

PV = present value = $1,000

r = annual interest rate = 8.25%

n = number of compounding periods per year = 12 (monthly)

t = number of years = 3

FV = $1,000 * (1 + 0.0825/12)^(12 * 3)

Plugging in the values and using a calculator, we get:

FV = $1,000 * (1 + 0.0825/12)^(12 * 3) = $1,000 * (1.006866)^36 = $1,000 * 1.281216 = $1,281.216

So after 3 years, Beth's investment will be worth $1,281.216.

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The equality held at the value t is equal to 2.4494.

In mathematics, equality is a relationship that states that two quantities have the same value or that two mathematical expressions reflect the same mathematical object. A = B is the symbol for the equality of A and B, and it is also pronounced as A = B. The "equals sign" is the symbol "=". It is claimed that two objects are distinct if they are not equal.

Example- The perimeter of a square is equal to four times its side length, i.e. P = 4 x side.

Equations in one variable: 4x + 26 = 6x + 10.

The given equality is-

[tex]< t^3-6t,0.33333t^2+4 > = < 0,6 > \\\\t^3-6t=0\\0.333333t^2+4=6\\\\t^3=6t\\t^2=6\\\\0.333333(6)+4=6\\2+4=6\\6=6\\\\t^2=6\\\\t=\sqrt6[/tex]

Hence, the equality held at the value t is equal to 2.4494.

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Answer:

If you have one x2-block and 2n x-blocks, you need to add (2n)^2 1-blocks to form a square. The dimensions of the square will be (x2-block + 2n x-blocks) x (x2-block + 2n x-blocks) = (2n+2) x (2n+2) = (2n + 2)^2.

Answer: 191.8 feet

Step-by-step explanation:

The equation for the ball's height h at time t seconds after launch is h(t) = -16t^2 + 1.6t + 190.4.

To find the maximum height the ball achieves before landing, we need to find the maximum value of h(t). To do this, we need to find the vertex of the parabola represented by the equation. The vertex of a quadratic equation in the form of y = a(x-h)^2 + k is (h, k), where h is the x-coordinate of the vertex and k is the y-coordinate of the vertex.

We can find the x-coordinate of the vertex by using the formula:

h = -b/2a

Here, a = -16, b = 1.6, and c = 190.4

Plugging these values into the formula:

h = -1.6/2*(-16) = 1/8

The x-coordinate of the vertex is 1/8 of a second, which is the time at which the ball reaches its maximum height.

To find the y-coordinate of the vertex, we can plug in the value of t = 1/8 into the equation for h(t):

h(1/8) = -16(1/8)^2 + 1.6(1/8) + 190.4

This gives us the maximum height that the ball achieves before landing, which is approximately 191.8 feet.

The number of 0.001 inches present in one inch is 1000.

Unit conversion is a process with multiple steps involving multiplication or division by a numerical factor, particularly a conversion factor. The procedure may also demand the selection of the correct number of substantial digits and rounding. Different units of conversion are used to calculate different parameters.

We convert the units of any quantity to understand better. For example, the length of a table is measured in inches; on the other hand, the length of a garden is measured in yards to make it simple to comprehend. We cannot calculate the length of a finger in miles.

Let x be the 0.001 inches present in 1 inch

Therefore, 0.001x = 1

x = 1/0.001

x = 1000

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(a)The percentage error is 0.123%.

(b)The percentage error is 0.049%.

Find the equation of the tangent line at the point (0,f(0)),

⇒ f(x)  = exp(x/500)
⇒ f'(x) = 1/500 exp(x/500)

⇒ f(0) = exp(0/500)

          = 1

So the equation of the tangent line at x = 0 is,

⇒ y = f(0) + f'(0)(x - 0) y

      = 1 + 1/500x y

      = x/500 + 1

Find the equation of the tangent line at the point (100,f(100)),

⇒ f(x)  = exp(x/500)

⇒ f'(x) = 1/500 exp(x/500)

⇒ f(100) = exp(100/500)

             = exp(1/5)

So the equation of the tangent line at x = 100 is,

⇒ y = f(100) + f'(100) (x - 100)

⇒ y = e^(1/5) - (1/500)(x - 100)

⇒ y = -x/500 + exp(1/5) + 1

Now we can use these two equations to approximate the function f(x) for 0 < x < 100.

For example, when x = 25

⇒ y = x/500 + 1

⇒ y = 25/500 + 1

⇒ y = 1.05

And the actual value of f(25) is,

⇒ f(25) = exp(25/500)

⇒ f(25) = exp(1/20)

⇒ f(25) ≈ 1.0513

So the percentage error is,

⇒ |1.05 - 1.0513| / 1.0513 x 100% ≈ 0.123%

We can repeat the process for x = 50 and find that the percentage error is 0.049%.

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The business records related amounts in their respective accounts known as ledger accounts.

All such accounts are assembled in a book or collection called the

ledger.

All the accounts, including assets, liabilities, equity, revenues, and expenses, that are required to adequately portray a company's financial operations are included in the General Ledger.

Financial statements like the balance sheet, income statement, and cash flow statement are created from the accounts in the general ledger and offer an overview of the company's financial situation.

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Answer: x1= -3, x2=3

Step-by-step explanation:

3xlxl=8+1

3xlxl=9

lxl=3

x=3

=-3

solution

x1= -3, x2=3

Hamilton led the Annapolis Convention in 1786 to adopt the United States Constitution in place of the Articles of Confederation.

Alexander Hamilton and George Washington spent years working near to one another, but they never grew close friends because of their respective roles and personalities. They exchanged gifts, nevertheless, that may have been of more value.

The popular Broadway musical Hamilton has been added to Disney+'s streaming library. Since then, the hip-hop and rap-infused history lesson has become more and more well-known. Alexander Hamilton's tale, along with that of other significant American Revolutionary War figures, is told in Hamilton.

In an effort to restore his political standing, Hamilton published a pamphlet to deny the charges of speculation but publicly admitted to the affair in what would be the first major American political sex scandal.

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The solution of the given differential equation is [tex]y=2e^x-1[/tex].

A differential equation in mathematics is an equation that includes one or more functions and their derivatives. The rate of change of a function at a place is determined by the derivatives of the function. It is mostly employed in disciplines like physics, engineering, biology, and others. Studying equation-satisfying solutions and the solutions' characteristics is the main goal of differential equations.

We have the differential equation -

[tex]\frac{dy}{dx}-y=1\\\\\frac{dy}{1+y}=dx\\\\log(1+y)=x+c\\1) y(0)=1\\log2=c\\\\1+y=e^{x+c}\\y=2e^x-1[/tex]

2)

y(1)=0

log(1+0)=1+c

c=-1

[tex]y=e^{x-1}\\[/tex]

3)

y(0)=6

log7=c

[tex]y=e^{x+log7}-1\\y=7e^x-1[/tex]

4)

c=log5

[tex]y=5e^x-1[/tex]

The complete question is-

The given differential equation is [tex]\frac{dy}{dx}-y=1[/tex],

find the particular solution on ivp y(0)=1,y(1)=0 ,y(0)=6 and y(0)=5

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The area of the cylinder is 3, 399. 74 square centimeters

The formula for calculating the area of  a cylinder is expressed with the equation;

A = 2πrh + 2πr²

Given that the parameters are;

From the information given, we have that;

Radius, r = 13.4 centimeters

Height, h = 27 centimeters

Now, subsitute the values, we get;

Area = 2× 3.14 × 13. 4× 27 + 2× 3.14 × (13.4)²

expand the bracket

Area = 2272. 104 + 1127.64

Add the values

Area = 3, 399. 74 square centimeters

Hence, the value is 3, 399. 74 square centimeters

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The singular matrix that differs from a by the smallest possible amount is [σ1   σ2]

The term called matrix is defined as a set of numbers arranged in rows and columns so as to form a rectangular array.

Here we have know that suppose a is a 2 x 2 nonsingular matrix with singular values σ1 > σ2 > 0.

Here we have also know that In particular if some row or column has all its entries equal to zero and then its determinant is zero.

In those cases here we have the whole matrix is called singular.

As we all know that if X is a non-singular matrix which means that if none of its entries are zero then the determinant of X will not be zero.

So, the singular form of the matrix is written as,

=> [σ1   σ2]

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The area of the triangle spanned by the vectors u and v can be calculated by taking the magnitude of the cross product of the two vectors. The cross product of u and v is (6, 4, -8) and the magnitude of this vector is 10, so the area of the triangle is 10.

The area of a triangle spanned by two vectors u and v can be calculated by taking the magnitude of the cross product of the two vectors. To calculate the cross product of two vectors u and v, we use the formula u x v = (u2v3 - u3v2, u3v1 - u1v3, u1v2 - u2v1). For our vectors, u = (1, 2, -2) and v = (0, -1, 3), the cross product is (6, 4, -8). We then calculate the magnitude of the cross product, which can be done using the formula |u x v| = √(u2v3 - u3v2)2 + (u3v1 - u1v3)2 + (u1v2 - u2v1)2. Substituting in the values for our vectors gives |u x v| = √62 + 42 + (-8)2, which is equal to 10. Therefore, the area of the triangle spanned by the vectors u and v is 10.

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Step-by-step explanation:

8/2 = 48/b

4=48/b

b=48/4

b=12

Answer:

Step-by-step explanation:

8/2 = 48/b

b = 48×2/8

b = 12

Answer:

y = x + 14

Step-by-step explanation:

plug any two x and y coordinates into y = mx + b, then simplify

=> 14 = m(0) + b => b = 14

=> 15 = m(1) + b => 15 = m + b

solve for m by plugging b

=> 15 = m + 14 => m = 1

plug in the values of b and m into y = mx + b, then simplify

=> y = (1)x + 14 => y = x + 14

The number of fifty dollar bill is 15

Let a represent the number of twenty dollar bill
Let b represent the number of fifty dollar bill

a + b= 46.......equation1

20a + 50b= 1370..........equation 2

From equation 1

a + b= 46

a= 46-b

Substitute 46-b for a in equation 2

20(46-b) + 50b= 1370

920 - 20b + 50b= 1370

30b= 1370-920

30b= 450

b= 450/30

b= 15

Substitute 15 for b in equation 1

a + 15= 46

a= 46-15

a= 31

Hence the number of fifty dollar bill is 15

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Answer:

[tex]\frac{1}{4y^9}[/tex]

Step-by-step explanation:

using the rule of exponents

• [tex]\frac{a^m}{a^n}[/tex] = [tex]\frac{1}{a^{(n-m)} }[/tex]

[tex]\frac{y^{-3} }{4y^{6} }[/tex]

= [tex]\frac{1}{4}[/tex] × [tex]\frac{y^{-3} }{y^6}[/tex]

= [tex]\frac{1}{4}[/tex] × [tex]\frac{1}{y^{(6-(-3))} }[/tex]

= [tex]\frac{1}{4}[/tex] × [tex]\frac{1}{y^{(6+3)} }[/tex]

= [tex]\frac{1}{4y^9}[/tex]

Answer:

x = -6

Step-by-step explanation:

x/15 + 3/15 = -1/5

x/15 + 1/5 = -1/5

x/15 = -2/5

x = -6

Let's check

-6/15 + 3/15 = -1/5

-3/15 = -1/5

-1/5 = -1/5

So, x = -6 is the correct answer.

A non-fruitful function which makes a turtle draw an equilateral triangle is given in the explanation.

Here is an example of a non-fruitful function in Python that takes a turtle object and a size as arguments and makes the turtle draw an equilateral triangle:

import turtle

def draw_triangle(some_turtle, some_size):

   for i in range(3):

       some_turtle.forward(some_size)

       some_turtle.left(120)

# Create a turtle object

t = turtle.Turtle()

# Call function to draw an equilateral triangle of size 100

draw_triangle(t, 100)

# Hide turtle and exit the turtle window

turtle.done()

This function makes the turtle move forward by some_size units and turn left by 120 degrees three times, resulting in a triangle with three equal sides and three 60-degree angles.

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830.72 sq in of wrapping paper does Tiana need to buy.

What is surface area of a cylinder?

The formula for the surface area of a cylinder is

SA = 2πr^2 +2πrh = 2πr(r +h)

To find the total area of wrapping paper needed for one box, Tiana needs to add up the area of each of the six sides. The area of the top and bottom is,

22.2 inches * 4.8 inches = 106.56 square inches.

The area of each of the four sides is 14 inches * 22.2 inches = 308.8 square inches.

So, the total area of wrapping paper needed for one box is,

106.56 + 308.8 = 415.36 square inches.

Since, Tiana needs to wrap 2 boxes, she needs to buy twice that amount, which is 2 * 415.36 = 830.72 square inches.

Rounding to the nearest hundredth, Tiana needs to buy 830.72 sq in of wrapping paper.

Hence, 830.72 sq in of wrapping paper does Tiana need to buy.

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The vertices of the image of the quadrilateral after rotation are C'(-6, 6), D'(-8, 6), E'(-10, 8) and F'(-8, 10).

Rotation is a kind of geometric transformation where a figure or point is rotated by a certain degrees about a given point.

Given that,

The coordinates of the vertices of quadrilateral CDEF are C(6, 6), D(6, 8), E(8, 10), and F(10, 8).

This is rotated 90° about the origin.

Any point (x, y) after a rotation of 90° about the origin changes to the point (-y, x).

C(6, 6) changes to C'(-6, 6)

D(6, 8) changes to D'(-8, 6)

E(8, 10) changes to E'(-10, 8)

F(10, 8) changes to F'(-8, 10)

Hence the coordinates of the vertices of the image are C'(-6, 6), D'(-8, 6), E'(-10, 8) and F'(-8, 10).

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[tex]$\frac{2}{7}[/tex] fraction of the total distance to her grandmother’s house traveled on Sunday.

Joanie's family traveled [tex]$\frac{2}{7}[/tex] of the distance to her grandmother’s house on Saturday.

They traveled [tex]$\frac{2}{5}[/tex] of the remaining distance on Sunday.

Let us consider the total distance to be 1.

Then subtract the distance traveled on Saturday from the total distance to calculate the remaining distance.

On subtracting we get the remaining distance:

Remaining distance = [tex]$\frac{7}{7} - \frac{2}{7}[/tex]

Remaining distance = [tex]$\frac{5}{7}[/tex]

Here we have to determine the fraction of the total distance to her grandmother’s house traveled on Sunday.

They traveled [tex]$\frac{2}{5}[/tex] of the remaining distance on Sunday.

To calculate the [tex]$\frac{2}{5}[/tex] fraction of the remaining distance we have to multiply both the fractions.

On multiplying we get:

[tex]$=\frac{5}{7} \times \frac{2}{5}[/tex]

[tex]$= \frac{2}{7}[/tex]

Therefore the distance traveled on the Sunday is  [tex]$\frac{2}{7}[/tex] a fraction.

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According to elementary algebra, time t has values of 3 and 1 seconds, respectively.

Polynomial equations are those created by combining variables, exponents, and coefficients. The higher exponent, known as the degree of the equation, might have several exponents.

A polynomial expression equal to 0 is the basis of a polynomial equation. For instance, since 3x² - 5 is a polynomial expression, 3x² - 5 = 0 is a polynomial equation.

Quadratic equations are two-variable, degree-two polynomial equations of the form f(x) = [tex]ax^{2}[/tex] + bx + c = 0 and with the variables a, b, c, and R R and a = 0.

With "a" denoting the leading coefficient and "c" denoting the absolute term of f, it is a quadratic equation in its general form (x).

Knowing that h = 15 m, we can enter that number into the equation to find t:

15 = 20t - [tex]5t^{2}[/tex]   Let's set the equation equal to 0 to solve

-[tex]5t^{2}[/tex] + 20t - 15 = 0 Let's factor out a -5 to simplify the equation

-5(t2 - 4t + 3) = 0  0/-5 is still 0

[tex]t^{2}[/tex] - 4t + 3 = 0   Let's find factors for this solution

(t -3)(t - 1) = 0   We have 2 solutions for this equation

t = 3, t = 1

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