Identify the sets of congruent angles. Explain your conclusions.

Considering the area of the rectangle, we have that the length is of 8 units and the width is of 10 units.

The area of a rectangle of length l and width w is given as follows:

A = lw.

In this problem, the area is of 80 square units, while the length and the width are consecutive even integers, hence:

Then:

l(l + 2) = 80

l² + 2l - 80 = 0

(l + 10)(l - 8) = 0.

We need the positive measure, hence:

l -  8= 0 -> l = 8 units.

w = l + 2 = 10 units.

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The force is 1.6N and the distance between them is 1.3 meters

An inverse variation from force to the square of distance is represented s:

k = Fd^2

Where k represents the variation constant

When F = 10, d = 2.

So, we have:

k = 10 * 2^2

k = 40

Substitute k = 40 in k = Fd^2

Fd^2 = 40

When d = 5, we have:

F * 5^2 = 40

This gives

25F = 40

Divide by 25

F = 1.6

Hence, the force is 1.6N

In (a), we have:

Fd^2 = 40

When F = 25, we have:

25 * d^2 = 40

This gives

25d^2 = 40

Divide by 25

d^2 = 1.6

Take the square root of both sides

d = 1.3

Hence, the distance between them is 1.3 meters

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The distance between points (- 3, 0, -7) and (- 8, - 9, - 11) is approximately 11.1 units and the midpoint is (x, y, z) = (- 5.5, - 4.5, - 9).

First, we find the vector between the two points by vector sum:

[tex]\vec r = (-8, -9, - 11) - (- 3, 0, -7)[/tex]

[tex]\vec r = (- 5, - 9, - 4)[/tex]

The distance between the two points is found by the following Pythagorean expression:

[tex]d = \sqrt{(-5)^{2}+(-9)^{2}+(-4)^{2}}[/tex]

d ≈ 11.1

And the midpoint is found by linear algebra:

[tex]\vec m = 0.5\cdot (-3, 0, -7) + 0.5 \cdot (-8, -9, - 11)[/tex]

[tex]\vec m = (- 1.5, 0, - 3.5) + (- 4, - 4.5, -5.5)[/tex]

[tex]\vec m = (- 5.5, - 4.5, - 9)[/tex]

The distance between points (- 3, 0, -7) and (- 8, - 9, - 11) is approximately 11.1 units and the midpoint is (x, y, z) = (- 5.5, - 4.5, - 9).

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The domain of the exponential function given is the set of all real numbers while the range of the exponential function is the set of all real numbers greater than zero.

As with other exponential functions, it follows that the domain of the exponential function given is the set of all real numbers while the range of the exponential function is the set of all real numbers greater than zero.

Additionally, by observation, the function has a positive variable correlation, hence;

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The equation of the line in explicit form is y = - 2 · x + 5, whose implicit form is 2 · x + y = 5. (Correct choice: D)

In this question we must find the equation of the line perpendicular to the segment BC and that goes through the point A(x, y) = (1, 3). First, the slope of the line segment BC is:

m = [1 - (- 3)]/[5 - (- 3)]

m = 4/8

m = 1/2

And the slope of the line is:

m' = - 1/(1/2) = - 2

The intercept of the line is found by using the explicit form of equation of the line, m' = - 2 and (x, y) = (1, 3):

3 = - 2 · 1 + b

b = 5

The equation of the line in explicit form is y = - 2 · x + 5, whose implicit form is 2 · x + y = 5. (Correct choice: D)

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The statements that are true about the domain and range of the functions f(x), g(x), and h(x) include:

It should be noted that a function simply means a relation between a set of inputs to a set of possible outputs.

In this case, f(x) has a domain of all real numbers as well as g(x) which also has a domain of all real numbers.

In conclusion, the correct options are A and D.

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Answer:

A and D

Step-by-step explanation:

Edge 2022

Answer:

[tex]G(x) = x^{3} -1[/tex]

Step-by-step explanation:

The red graph is the blue graph translated 1 unit down, so the answer is A.

Shyam travel total  [tex]10km 317m[/tex]  distance ,when he travelled  [tex]8 km 52 m[/tex]  by bus and [tex]2 km 265 m[/tex]  by car .

How to find the total distance travel by Shyam ?

Shyam travelled distance by bus [tex]=8 km 52 m[/tex]

Shyam travelled distance by car [tex]=2 km 265 m[/tex]

Total distance travelled by shyam is

Total distance= distance travelled by car + distance travelled by bus

Total distance

[tex]=2 km 265 m+8 km 52 m\\=(2+8)km(265+52)m\\=10km317m[/tex]

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Consider the lengths of consecutive 1-2 blocks.

block 1 - 1, 2 - length 2

block 2 - 1, 2, 2 - length 3

block 3 - 1, 2, 2, 2 - length 4

block 4 - 1, 2, 2, 2, 2 - length 5

and so on.

Recall the formula for the sum of consecutive positive integers,

[tex]\displaystyle \sum_{i=1}^j i = 1 + 2 + 3 + \cdots + j = \frac{j(j+1)}2 \implies \sum_{i=2}^j = \frac{j(j+1) - 2}2[/tex]

Now,

[tex]1234 = \dfrac{j(j+1)-2}2 \implies 2470 = j(j+1) \implies j\approx49.2016[/tex]

which means that the 1234th term in the sequence occurs somewhere about 1/5 of the way through the 49th 1-2 block.

In the first 48 blocks, the sequence contains 48 copies of 1 and 1 + 2 + 3 + ... + 47 copies of 2, hence they make up a total of

[tex]\displaystyle \sum_{i=1}^48 1 + \sum_{i=1}^{48} i = 48+\frac{48(48+1)}2 = 1224[/tex]

numbers, and their sum is

[tex]\displaystyle \sum_{i=1}^{48} 1 + \sum_{i=1}^{48} 2i = 48 + 48(48+1) = 48\times50 = 2400[/tex]

This leaves us with the contribution of the first 10 terms in the 49th block, which consist of one 1 and nine 2s with a sum of [tex]1+9\times2=19[/tex].

So, the sum of the first 1234 terms in the sequence is 2419.

Answer:

system of equation by elimination

1 write both equation in standard form

2 make the coefficient of one variable opposites

3 add the questions relating from step to eliminate one variable

4 solve for the remaining variable

5 substitute the solution from step for into one of the original equation

Answer:

The volume of the cylinder is smaller than the rectangular prism.

Step-by-step explanation:

The vertices of abc given the transition rule (x,y)-->(x,y-3) are (-6, -10), (-3, -13) and (-5, -1)

The vertices are given as:

a (-6,-7)

b(-3,-10)

c(-5,2)

The transition rule is given as

(x,y)-->(x,y-3)

So, we have

a' = (-6, -7 - 3)

a' = (-6, -10)

b' = (-3, -10 - 3)

b' = (-3, -13)

c' = (-5, 2 - 3)

c' = (-5, -1)

Hence, the vertices of abc given the transition rule (x,y)-->(x,y-3) are (-6, -10), (-3, -13) and (-5, -1)

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The correct option is (d).

The other beaker contains 17 cc (cubic centimetres) of the liquid.

The volume of a cube with dimensions of 1 cm ×1 cm× 1 cm is equal to one cubic centimetre (or cubic centimetre in US English) (SI unit symbol: cm³; non-SI abbreviations: cc and ccm). A millilitre's volume is equal to one cubic centimetre.

According to the question,

The total liquid is 32 in cubic centimetres which is stored in the two beakers.

In the first beaker the liquid stored is 15 cubic centimetres.

The second beaker will contain the liquid = total liquid stored in both beakers - liquid stored in the first beaker.

Liquid in second beaker = 32 - 15

                                        = 17

Therefore, the liquid stored in the second beaker is 17 cc (cubic centimetres).

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Answer:A or C

Step-by-step explanation: i guessed plus 19 hours ago

SOLUTION :

c² = 5² + 5²

c² = 25 + 25

c² = 50

c = √50 ft

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Using it's concepts, the domain and the range of the graph are given as follows:

In this graph, have that the function is defined for all values of x except x = -1, and assumes all real values, hence the domain and the range of the graph are given as follows:

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Mike brought $15 and Hallie brought $45 to the movie

There are many ways to define an equation. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.

The value of the variable that makes the equation a true statement is the solution to the equation.

We have to find how much money Mike and Hallie brought to the movie.

Let the money Brought by Mike be $ m and by Hallie be $ h.

Mike and hallie are going to a movie. together they bring $60 in cash

m + h = $ 60.............(1)

Hallie brings three times as much cash as mike does

h = 3 m.......... (2)

Pur the value of h from equation (2) in equation (1)

m + 3 m = $ 60

4 m = $ 60

m = $ 60/4

m = $ 15

put this value of m in equation (2)

h = 3(15)

h = $ 45

Hence we created a system of equations that models the information given in this problem and Mike brought $15 and Hallie brought $45 to the movie

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Based on the length and width of the rectangular lawn, and the percentage the man has mowed, the strip width would be 40.5 m.

first, find the area of the lawn:

= 100 x 200

= 20,000 ft²

the area mowed is:

= 40.5% x 20,000

= 8,100 ft²

the width is therefore:

= 8,100 / 200

= 40.5 m

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The coordinates of the vertex that A maps to after Daniel's reflections are (3, 4) and the coordinates of the vertex that A maps to after Zachary's reflections are (3, 2)

From the given figure, the coordinate of the vertex A is represented as:

A = (-5, 2)

The coordinates of the vertex that A maps to after Daniel's reflections

The rule of reflection across the line x = -1 is

(x, y) ⇒ (-x - 2, y)

So, we have:

A' = (5 - 2, 2)

Evaluate the difference

A' = (3, 2)

The rule of reflection across the line y = 2 is

(x, y) ⇒ (x, -y + 4)

So, we have:

A'' = (3, -2 + 4)

Evaluate the difference

A'' = (3, 4)

Hence, the coordinates of the vertex that A maps to after Daniel's reflections are (3, 4)

The coordinates of the vertex that A maps to after Zachary's reflections

The rule of reflection across the line y = 2 is

(x, y) ⇒ (x, -y + 4)

So, we have:

A' = (-5, -2 + 4)

Evaluate the difference

A' = (-5, 2)

The rule of reflection across the line x = -1 is

(x, y) ⇒ (-x - 2, y)

So, we have:

A'' = (5 - 2, 2)

Evaluate the difference

A'' = (3, 2)

Hence, the coordinates of the vertex that A maps to after Zachary's reflections are (3, 2)

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The proportion cranberry juice should be mixed with 84 ounces of apple juice 1:5 that is 1 parts of cranberry juice and 5 parts of lemon juice.

According to the question,

A punch recipe calls for mixing 2 parts of cranberry juice with 5 parts of apple juice.

84/2 = 42

5*42=210

Hence, the proportion cranberry juice should be mixed with 84 ounces of apple juice 1:5 that is 1 part of cranberry juice and 5 parts of lemon juice.

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Answer:

Step-by-step explanation:

Substitution is a method that rewrites one of the equations in terms of one variable, and substitutes that in the other equations.

We can easily rewrite x + y = 6 by subtracting y from both sides, giving us

[tex]x = -y+6[/tex]

By putting this equation in place of x in the first equation, we can solve for y:

[tex]4(-y+6)-2y=6[/tex]

[tex]-4y+24-2y=6[/tex] [Distributing 4 into the parentheses]

[tex]-6y+24=6[/tex] [Combining like terms]

[tex]-6y = -18[/tex] [Subtracting 24 from both sides]

[tex]y=3[/tex] [Dividing both sides by -6]

Since we solved for y, we can again substitute by putting it into the second equation.

[tex]x+3=6[/tex]

[tex]x=3[/tex] [Subtracting 3 from both sides]

The solution for this system of equations is (3,3).

Elimination is another method of solving systems of equations. In this method, we multiply one equation such that when both equations are combined, only one variable is left.

We can first multiply both sides of the second equation by 2.

[tex]2x+2y=12[/tex]

Now, let's add both equations to cancel out y.

[tex]4x-2y=6[/tex]

[tex]2x+2y=12[/tex]

[tex]6x=18[/tex]

Now, we can divide 6 from both sides to get the value of x.

[tex]\frac{6x}{6} = \frac{18}{6}[/tex]

[tex]x=3[/tex]

We can now substitute this value into one of the equations to get the value of y. Here, I used the second equation.

[tex]3+y=6[/tex]

[tex]y=3[/tex]

The solution to our system of equations is (3,3).

The solution to the homogenous differential equation, (11y² - xy)dx + x²dy = 0, is [tex]y = \frac{x}{11 ln (x) + C}[/tex].

A homogeneous differential equation has a homogeneous function as one of its components, if f(λx, λy) = λⁿf(x, y), for any non-zero constant λ, the function is said to be homogenous. The homogeneous differential equation's generic form is of the type f(x, y).dy + g(x, y).dx = 0. The degree of the homogeneous differential equation is the same for the equation's variables x and y.

In the question, we are asked to solve the homogeneous differential equation, (11y² - xy)dx + x²dy = 0.

The given equation can be solved as follows:

Thus, the solution to the homogenous differential equation, (11y² - xy)dx + x²dy = 0, is [tex]y = \frac{x}{11 ln (x) + C}[/tex].

The provided question is incomplete. The complete question is:

"Use the method for solving homogenous equations to solve the following differential equation.

(11y² - xy)dx + x²dy = 0".

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The general form of the equation for the given circle centered at O(0, 0) is x^2 + y^2 = 41

The given parameters are

Center = (0, 0)

Point = (4, 5)

Rewrite the given parameters are

(a, b)= (0, 0)

(x, y) = (4, 5)

The general form of the equation for the given circle is represented as:

(x - a)^2 + (y - b)^2 = r^2

Substitute the known values in the above equation to calculate the radius r

(4 - 0)^2 + (5 - 0)^2 = r^2

Evaluate the difference

4^2 + 5^2 = r^2

Evaluate the exponent

16 + 25 = r^2

Evaluate the sum

41= r^2

Rewrite as

r^2 = 41

Substitute r^2 = 41 in (x - a)^2 + (y - b)^2 = r^2

(x - a)^2 + (y - b)^2 = 41

Substitute (a, b)= (0, 0) in (x - a)^2 + (y - b)^2 = 41

(x - 0)^2 + (y - 0)^2 = 41

Evaluate the difference

x^2 + y^2 = 41

Hence, the general form of the equation for the given circle centered at O(0, 0) is x^2 + y^2 = 41

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[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Here we go ~

[tex]\qquad \sf  \dashrightarrow \: (1.6 \times 10 {}^{5} ) \sdot(2 .3 \times {10}^{1} )[/tex]

[tex]\qquad \sf  \dashrightarrow \: (1.6 \times 2.3) \sdot(10 {}^{5} \times 10 {}^{1} )[/tex]

[tex]\qquad \sf  \dashrightarrow \: 3.68 \times 10 {}^{6} [/tex]

A state license plate consists of three letters followed by three digits. If repetition is allowed, the number of different ways in which license plates are possible is 17,576,000.

An arrangement of items in a specific order is referred to as a permutation. When the order of the arrangements counts, it is a mathematical technique that establishes the total number of alternative arrangements in a collection.

Calculation for the permutation -

Three letters are followed by three digits on a state license plate.

26 letters from a to z and 10 numbers from 0 to 9 make up the alphabet.

The potential of arrangements is due to the license plate's composition of three letters and three numerals.

Total ways = 26×26×26×10×10×10

                  = 17,576,000

Therefore, the number of different ways in which license plates are possible is 17,576,000.

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Answer:

[tex]T_{2} = \frac{P_{2} V_{2} T_{1}} {P_{1} V_{1}}[/tex]

Step-by-step explanation:

The Combined Gas Law expression is:

P₁V₁ / T₁ = P₂V₂ / T₂

To solve for T₂, you need to.....

[tex]\frac{P_{1} V_{1} }{T_{1} } = \frac{P_{2} V_{2} }{T_{2} }[/tex]                                  <------ Original expression

[tex]\frac{T_{2} P_{1} V_{1} }{T_{1} } = {P_{2} V_{2} }[/tex]                               <----- Multiply both sides by T₂

[tex]{T_{2} P_{1} V_{1} } = {P_{2} V_{2} T_{1}}[/tex]                          <----- Multiply both sides by T₁

[tex]T_{2} = \frac{P_{2} V_{2} T_{1}} {P_{1} V_{1}}[/tex]                                  <----- Divide both sides by P₁V₁

The number of cuboids of dimension 2 cm x 3 cm x 4 cm, required to make a cube is 9.

Dimensions of the cuboid Deeksha made are given as 2 cm x 3 cm x 4 cm.

Thus, the volume of this cuboid = 2*3*4 cm³ = 24 cm³.

Using the formula for the volume of cuboid as the product of the three sides.

Deeksha wants to make a cube combining some number of these cuboids.

Assuming the side length of the cube to a, the volume of the cube = a³.

Assuming the number of cuboids required to make 1 cube to be n, we can write that a³ = n*(24 cm³).

To make this relation true, we need the right-hand side to be a perfect cube.

Prime factorizing the volume of the cuboid, we get 24 cm³ = 2³ * 3 cm³.

To make it a perfect cube, we need to multiply 3², by it.

Thus, n = 3² = 9.

Thus, the number of cuboids of dimension 2 cm x 3 cm x 4 cm, required to make a cube is 9.

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The provided question is incorrect. The correct question is:

"Deeksha made cuboid of size 2 cm x 3 cm x 4 cm. how many such

cuboids will be required to make a cube?"

Answer:

100.5 inches

Step-by-step explanation:

If each course has 3/8 inch of concrete below it  (including the bottom one)

  8 in * 12   + 3/8 in * 12 = 100 1/2 inches

Answer:

If you divide it out and it comes out a whole number unless the original set of numbers is a fraction