Answers
In the given Geometric shape/figure ∠1=∠4 i.e. C.
What are geometric shapes?
In Mathematics, Geometric shapes are the figures which demonstrate the shape of the objects we see in our everyday life. In geometry, shapes are the forms of objects which have boundary lines, angles and surfaces. There are different types of 2d shapes and 3d shapes.
Shapes are also classified with respect to their regularity or uniformity. A regular shape is usually symmetrical such as a square, circle, etc. Irregular shapes are asymmetrical. They are also called freeform shapes or organic shapes. For example, the shape of a tree is irregular or organic.
In plane geometry, the two-dimensional shapes are flat shapes and closed figures such as circles, squares, rectangles, rhombus, etc. In solid geometry, the three-dimensional shapes are cube, cuboid, cone, sphere and cylinder. We can observe all these shapes in our daily existence also. For example books (cuboid shape), glasses (cylindrical shape), traffic cones (conical shape) and so on.
Now,
As we know, If two lines intersect and make an angle, say X=45°, then its opposite angle is also equal to 45°.
The same theorem is applied here
hence
The opposite angles ∠1 and ∠4 equal.
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Related Questions
write a non-fruitful function draw triangle(someturtle, somesize) which makes a turtle draw an equilateral triangle.
Answers
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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(1 point) for what value(s) of t does the equality ⟨t3−6t,0.333333t2 4⟩=⟨0,6⟩ hold true?
Answers
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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Find a linear approximation to the function f(x)= e^(x/500)
for the range of values O< x <100. Do this by making the linear approximation equal to the function at the end points x=0 and x=100.
Find the percentage error in the approximation when
(a) x = 25
(b) x = 50
Answers
(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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HELP!!! ASSIGNMENT DUE SOON
order from least to greatest
Answers
(2, -1) with a slope of -3
Answers
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.
14. equation from exercise 2; y(0) = 1, y(1) = 0, y(0) = 6, y(0) = 5.
Answers
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 two shorter sides of a right triangle have lengths 8.49 meters and 1.61 meters. what is the length of the hypotenuse?
Answers
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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if beth makes an initial investment of $1,000, how much will it be worth after three years if her average return is 8.25 percent (compounded monthly
Answers
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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(strang 7.2.19) suppose a is a 2-by-2 nonsingular matrix with singular values σ1 > σ2 > 0. how would you create a singular matrix that differs from a by the smallest possible amount?
Answers
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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A convention manager find that he ha $1370, made up of twentie and fiftie. She ha atotal of46bill. How many fifty-dollar bill doe the manager have?
Answers
The number of fifty dollar bill is 15
How to calculate the number of fifty dollar bill?
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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a student spends 3/4 of his money on tuition and 1/3 of what remains on books. if he has $50 dollars left, how much money did he start with?
Answers
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= $75
"It appears, moreover, that on the 25th of July last the Mail of the United States, on the road from Pittsburgh to Philadelphia, was
stopped by two armed Men, who cut it open, and took out all the letters, except those contained in one packet: these armed men, from
all the circumstances which occurred, were manifestly acting on the part of the Insurgents.
The declared object of the foregoing proceedings, is to obstruct the execution and compel a repeal of the laws... on spirits distilled
within the United States and upon Stills."
-Alexander Hamilton, A Letter to George Washington, August 5, 1794
What event is Alexander Hamilton describing in his letter to Washington AND what caused this event?
Answers
Hamilton led the Annapolis Convention in 1786 to adopt the United States Constitution in place of the Articles of Confederation.
What incident AND what reason(s) is Alexander Hamilton describing in his letter to Washington?Alexander Hamilton and George Washington spent years working near to one another, but they never grew close friends because of their respective roles and personalities. They exchanged gifts, nevertheless, that may have been of more value.
The popular Broadway musical Hamilton has been added to Disney+'s streaming library. Since then, the hip-hop and rap-infused history lesson has become more and more well-known. Alexander Hamilton's tale, along with that of other significant American Revolutionary War figures, is told in Hamilton.
In an effort to restore his political standing, Hamilton published a pamphlet to deny the charges of speculation but publicly admitted to the affair in what would be the first major American political sex scandal.
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Joanie' family traveled 2/7 of the ditance to her grandmother’ houe on Saturday. They traveled 2/5 of the remaining ditance on Sunday. What fraction of the total ditance to her grandmother’ houe wa traveled on Sunday?
Answers
[tex]$\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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Suppose you have a table
with constant differences. The input 2 gives the
output 11. The input 3 gives the output 14. What is
the output for the input 7?
Answers
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.
What are the input and output rules?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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x/15 + 3/15 = -1/5
the solution is x =
Answers
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.
Select the correct answer from each drop-down menu.
In which accounts does the business record the amounts, and where are these accounts assembled?
The business records related amounts in their respective accounts known as
____
accounts. All such accounts are assembled in a book or collection called the
____
.
Answers
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.
What is the general 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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The length of the smallest side of a right triangle is 16. The lengths of the other two sides are consecutive odd integers. Use the Pythagorean theorem to solve for the smaller of the two missing sides
Answers
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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Help me please
Thank you
Have a great day :)
Answers
I need help with this one asap
Answers
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]
. Ryan bought cans of soup on sale for $1.30 each and paid with a $20 bill. If he received at least $5 but no more than $10 back, which inequality represents c. the number of cans he purchased?
Answers
Answer:
[tex]5 \leqslant 20 - 1.3x < 10[/tex]
What is the solution to the equation? 3|x| − 1 = 8
Answers
Answer: x1= -3, x2=3
Step-by-step explanation:
3xlxl=8+1
3xlxl=9
lxl=3
x=3
=-3
solution
x1= -3, x2=3
How many .001 inches are there in one inch?
a. 1
b. 100
c. 1,000
d. 10,000
Answers
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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You have one x2-block and 2n x-blocks (where n is a positive whole number). How many 1-blocks do you need to form a square? What are the dimensions of the square? Express your answer in terms of n.
Answers
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.
A punter kicks a football, it has a vertical speed of 70 m/s, and a height, h, in meters after t seconds can be modeled by the equation h = 70t - 5t 2
What is the maximum height of the football?
How long does it take to reach maximum height?
How long is the football in the air?
Answers
According to elementary algebra, time t has values of 3 and 1 seconds, respectively.
What is meant by polynomial equation?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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Tiana needs to wrap 2 gifts with no overlap. The boxes are shaped as right
rectangular prisms. The length of each box is 22.2 in, the width is 4.8 in, and the
height is 14 in. How much wrapping paper does Tiana need to buy? Round to the
nearest hundredth. Leave out units.
A
Answers
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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help me please i beg of you
Answers
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
If the cylinder has a radius of 13.4 centimeters and a height of 27 centimeters, what is the area of the cross section?
Answers
The area of the cylinder is 3, 399. 74 square centimeters
How to determine the area of the cylinderThe formula for calculating the area of a cylinder is expressed with the equation;
A = 2πrh + 2πr²
Given that the parameters are;
A is the area of a cylinderπ takes the value of 22/7 or 3.14h is the height of the cylinderr is the radius of the cylinderFrom 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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Solve the proportion.
8/2 = 48/b
b = ___
(Help please )
Answers
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
A ball is launched from a 190.4-foot tall platform. The equation for the ball's height h at time t seconds after launch is h (t) = - 16t? 1.6t + 190.4, where h is in feet. What is the maximum height the ball achieves before landing?
Answers
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.
HELP ASAP WILL MARK THE BRAINLIEST
Answers
Answer:
Second choice : -3, 11, -45, 179
Step-by-step explanation:
First term: a₁ = - 3
Second term a₂ = -4a₁ -1 = (-4)(-3) - 1 = 12 - 1 = 11
There are only two options with 11 as the third term, Options 2 and 4 look the same but the fourth option has curly braces around the numbers making it a set rather than a sequence
If you wanted to be sure and compute the third term to see if it matches
a₃ = -4a₂ - 1 = -4(11)- 1 = -44 - 1 = -45
