Which logical argument could you use to prove that triangle ABC is congruent to triangle DEF?
A. SSS Postulate
B. HL Theorem
C. SAS Postulate
D. ASA Postulate

Answer: [tex]6\sqrt{6}+4 \times 6\sqrt{6}-4[/tex] yards

Step-by-step explanation:

Let the length of the walkway be x yards. Then,

[tex](18-2x)(26-2x)=200\\\\4x^2 -88x+468=200\\\\4x^2-88x+268=0\\\\x^2 -22x+77=0\\\\x=\frac{22 \pm \sqrt{22^2 -4(77)}}{2}\\\\=11 \pm 3\sqrt{6}[/tex]

However, [tex]x=11+3\sqrt{6} > 18[/tex], which is illogical, so we take [tex]x=11-3\sqrt{6}[/tex].

So,

[tex]18-2x=18-2(11-3\sqrt{6})=6\sqrt{6}-4\\\\26-2x=26-2(11-3\sqrt{6})=4+6\sqrt{6}[/tex]

Answer: The moon

Step-by-step explanation:

The cone is the solid form that represents "If you cut me in half, my end face will remain the same. Two of my faces are the same, one is curved."

The volume of a cone is defined as the amount of space occupied by a cone in a three-dimensional plane.

∵ The volume of the cone (V )= 1/3πhr²

The number of faces of a regular cone is one, which we may partition vertically into two halves.

This means one base face and lateral face

Now, the number of faces in one half equals the number of faces in the original form.

This meets the conditions outlined in the question.

So, the cone is a solid form.

Thus, the cone is the solid form that represents "If you cut me in half, my end face will remain the same. Two of my faces are the same, one is curved."

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Answer:

r=√6a/5m-1

Step-by-step explanation:

m=√6a+r/5r

cross multiply

5mr=√6a+r

5mr-r=√6a

factorise

r(5m-1)=√6a

divide both sides by the coefficient of r

r=√6a/5m-1

hope it helps

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Answer:

hope it helps u

MATHEMATICS IS OUR OWN LANGUAGE,LETS TALK TOGETHER

Both Adam and Rena re both correct regarding the expression.

An expression simply means an illustration that can be used to represent a scenario or situation.

From the information, Adam writes the expression d−0.75d to find the sale price of the game if the original price is d dollars.

Rena correctly writes another expression, 0.25d, that will also find the sale price of the game if the original price is d dollars.

In this case, they are both correct. This can be illustrated as:

= 1 - 0.75d

= 0.25d

Note that the information was answered based on the information given.

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A place where two or more curves, lines, or edges converge is known as a vertex in geometry (plural: vertices or vertexes), and it is frequently identified by letters like,,,. As a result of this definition, vertices are the intersection of two lines that create an angle as well as the corners of polygons and polyhedra.

The solutions are:

P' = (-4,-7)

Q ' = (-8,-7) (-8,-7)

R ' = (-3,3) (-3,3)

All you have to do is flip the provided points P, Q, and R's x and y coordinates.

The common principle is (x,y) —-> (y,x)

Thus, when we reflect across the line y = x, something like P = (-7,-4) becomes P'= (-4,-7). The similar approach is taken with the other points.

How do you locate a triangle's vertices?

Finding the triangle's vertices on the line y = x as an image

The steps below are used to locate a triangle's vertices using its midpoints:

Identify the midpoints' x and y values;

Calculate the midpoint using the following equations: A = (x 1+ x 3 - x 2, y 1 + y 3-y 2); B = (x 1+x 2-x 3, y 1+y 2-y3); C = (x 2+x 3-x 1, y 2 + y 3 -y 1);.

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The rational numbers are √75, 2. √7, √0. 36, √0. 0144, √3/77, -√36/49

A rational number can simply be described as a number that is expressed as the ratio of two even or odd integers.

The denominator of the fraction or ratio must be greater than zero.

Rational numbers are represented mathematically as a quotient, say x/y of two integers such that y ≠ 0, that is, the denominator is not equal r equivalent to zero.

It is formed from dividing on integer(whether odd or even) by another integer.

The numbers; √75, 2. √7, √0. 36, √0. 0144, √3/77, -√36/49 are all rational numbers

Hence, the numbers are √75, 2. √7, √0. 36, √0. 0144, √3/77, -√36/49

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800 miles is going to be the distance that separates the two aircraft. The distance between the two airplanes will be 1,300 kilometers at the very least.

It is important to keep in mind that the two aircraft's combined speed will be equal to the sum of their separate speeds when calculating their overall speed. In addition, the pilots of the two aircraft have one hour to find each other.

According to the information that was provided, the distance that separates the aircraft after they have flown for forty-five minutes is two hundred miles. As a result, the following will constitute the remaining distance:

= 1 hour - 45 minutes = 15 minutes.

When this occurs, the distance between the planes will be as follows:

= 200/15 × 60

= 200 × 4

= 800 miles

As a result, there will be a gap of 1300 kilometers between the two aircraft.

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The equations of the line according to the given points will be:

We know that,

The equation of a line passing through two points is:

( y -y 1) / ( x - x1 ) = ( y2 - y1 ) / ( x2 - x1 )  

(y - 2) / (x - 5) = (-4 - 2) / (3 - 5)

=> (y - 2) / (x - 5) = -6 / -2

=> y - 2 = 3 (x - 5)

=> 3x - 15 - y + 2 = 0

=> 3x - y - 13 = 0

Some more equations of the same line can be calculated just by multiplying the coefficients of x and y so that they remain proportional to the previous equation.

For Example,

Here we can see that the coefficients of x and y and also the constant term are proportional to every equation compared with each other.

These lines are also called coincident lines.

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Answer:29

Step-by-step explanation:

9+4 spots times five days

Answer:  The slope is [tex]\frac{1}{2}[/tex].

Step-by-step explanation:

[tex]Slope = \frac{y_{2}-y_{1} }{x_{2}-x_{1} } =\frac{-1-2}{1-7} =\frac{-3}{-6} =\frac{3}{6}=\frac{1}{2}[/tex]

Answer:

[tex]a_{n}[/tex] = 2n - 6

Step-by-step explanation:

there is a common difference between consecutive terms , that is

- 2 - (- 4) = 0 - (- 2) = 2 - 0 = 2

this indicates the sequence is arithmetic with nth term

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

here a₁ = - 4 and d = 2 , then

[tex]a_{n}[/tex] = - 4 + 2(n - 1) = - 4 + 2n - 2 = 2n - 6

the rule is then 2n - 6

We will have the following:

First, we can see that the probability of picking an even number at first is:

And then, the probability of picking another even card without replacing the previous one will be:

Now, the probability of this happening one after the other will be:

So, the probability will be of 20%.

The equation of his allowance in slope-intercept form is y = 0.5x + 8

He received $18 in allowance the week he did 20 chores.

He received $12 in allowance the week he did 8 chores.

The ordered pairs will be (8,12) and (20,18)

The slope intercept form is

y = mx + b

Where m is the slope

b is the y intercept

m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Substitute the values in the equation

m = (18-12)/(20-8)

m = 6/12

= $0.5 per chores

Now we have to find b,

Substitute the value of any ordered pair in the slope intercept form

12 = 0.5×8+b

12 = 4+b

b = 12-4

b = 8

Hence, the equation of his allowance in slope-intercept form is y = 0.5x + 8

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Answer:

Step-by-step explanation:

Step-by-step explanation:

open the bracket

y - 1 = 3x - 12

add 1 to both sides

y = 3x - 11

I think that should be it

Answer:

AB

Step-by-step explanation:

the angles DCB and ACB are supplementary angles (together 180°).

simply because the sum of all angles around a single point on one side of a line is suggests 180° (it represents a half-circle).

so, the inner angle ACB is

ACB = 180 - 50 = 130°

because the sum of all angles in a triangle is also always 180°, there are only 50° left for the other 2 angles.

so, the inner angle at C is clearly the largest angle in the triangle ABC.

the larger an angle, the longer the opposing side.

the largest angle has the longest opposing side in the triangle.

the opposing side of the inner angle C is AB. and that is therefore the longest side in the triangle ABC.

ANSWER

EXPLANATION

We want to find the probability that the average of all participants in the study was fewer than 10,200 breaths each night.

To do this, first, we have to find the z-score corresponding to the sample mean:

where x = sample mean

μ = population mean

σ = standard deviation

n = sample size

Therefore, the z-score is:

Now, using the standard normal table, we can find P(z < 1.01).

Therefore, the probabilityis:

That is the answer.

Option a is correct using algebric formulas.

(x + y)³ = x³ + y³ +3xy( x + y )

(x + y + z)² = x² + y² + z² + 2( xy + yz + zx )

So breaking it into

(( x + y )³)² = (x³ + y³ +3xy( x + y ))²

(x³ + y³ +3xy( x + y ))² = x^6 + y^6 + 9x²y²(x² + y² + 2xy) + 2( x³y³ + 3xy^4( x + y ) + 3x^4y( x + y) )

x^6 + y^6 + 9x²y²(x² + y² + 2xy) + 2( x³y³ + 3xy^4( x + y ) + 3x^4y( x + y) )

So after rearranging the terms

we get  (x + y)^6 as

x6 + 6x5y + 15x4y2 + 20x³y3 + 15x²y4 + 6xy5+y6

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SOLUTION:

Step 1:

In this question, we are given the following:

Step 2:

From the question,

We have that:

The values of each composite function are:

a) -1

b) -1

c) 2

d) 0

e) 2

f) -4

We have,

These are composite functions.

It is written as:

(f o g) (x) = f (g(x))

Now,

From the table, the values for each function f and g at specific values x are taken.

a.

(f o g)(1)

f(g(1)) = f(0) = -1

b.

(f o g) (-1)

f(g(-1)) = f(0) = -1

c.

(g o f) (-1)

g(f(-1)) = g(-2) = 2

d.

(g o f) (0)

g(f(0)) = g(-1) = 0

e.

(g o g) (-2)

g(g(-2)) = g(2) = 2

f.

(f o f) (-1)

f(f(-1)) = f(-2) = -4

Thus,

The values of each composite function are:

-1, -1, 2, 0, 2, and -4.

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None of the available possibilities is an equivalent expression.

Supplemental methods add up to 180 degrees, just like all other options.

    If two expressions function the same way while having different looks, they are said to be comparable. Two identical algebraic expressions have the same value when the same value(s) for the variable are entered (s).

  No one in the available possibilities satisfies the requirement of a comparable expression.

2x - 15 + 3x + 15 = 180

2x - 10 + 3x = 180

5x - 10  = 180

5x - 10 + 10 = 180 +10

add the numbers

5x = 190

5x /5 = 190 5

x = 38

As a result, none of the possibilities shown are identical expressions.

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The probability that it rained at that game is 0.49.

Probability is the the ratio of a particular event with total number of event. It tells the possibility that an event can occur.

Probability that it rains P(R) = 0.60

probability that it won't rain P(R') = 1-0.60

= 0.4

Red sparrows have a past record of 4 wins and 5 loses when it does not rain, that is

P( winning/R') = 4/9                 (win% = 4/total that is 5+4 which is 9)

P( lose/R') = 5/9                       (lose % = 5/total)

When it rain the past record is 2 wins and 7 loses

P( win/R ) = 2/9

P( lose/R ) = 7/9

P (win) = P(R)*P(win/R) + P(R')*P(win/R')

= 4/9*0.4 + 2/9*0.6

If red sparrows win, then the probability that it rained at game

P (R/win) = P ( R η win) / P (win)

= 0.49

Therefore, we can conclude that the the probability that it rained at that game is 0.49.

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The solution set of real numbers that are 3 units from -2 is :

|x +2| = 3

Here

Function : |x +2| = 3

since ,

|x +2| = 3 => x + 2 = 3 ∨ x + 2 = -3

x = 3 - 2 ∨ x = -3 - 2

x = 1 ∨ x = -5

| - 2 - 1 | = | -3| = 3

| -2 -(-5) | = | -2 + 5 | = 3.

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The coordinates of G is (d+c, b)

This is because the opposite sides of any parallelogram are equal in length, and so the length of side HG is equal to the length of side EF.

a) The length of side HG is equal to the horizontal distance (x2 - x1): xG - 0

The length of side EF is equal to the horizontal distance (x2 - x1): d - (-c) = d +c

Thus:

xG - 0 = d + c

xG = d + c

Therefore the x-coordinate of G is d + c

b) To find the y-coordinate of G, we also apply the idea that sides GF and HE are equal.

The length of side GF is equal to the vertical distance (y2 - y1): yG - 0

The length of side HE is equal to the vertical distance (y2 - y1): b - 0

Thus:

yG - 0 = b -0

yG = b

Therefore the y-coordinate of G is b

Finally, the coordinates of G is (xG, yG) = (d+c, b)

Answer's

Step-by-step explant

Answer:

Explanation:

Given the ordered pair (-2, 4 1/2), where x = -2 and y = 4 1/2 = 9/2 = 4.5. Plotting this point, we'll have;

Note that quadrants are numbered in an anti-clockwise manner with the top right portion of the graph as Quadrant I. Looking at the plotted point, we can see that it lies in Quadrant II.

The coordinates of the image of triangle ABC would be A (-1, -1), B (3, 2), and C (4, -6)  after translation, and if the original coordinates are A(-3,2) B(1,5) C(2,-3).

A point is transformed when it is moved from where it was originally to a new location. Translation, rotation, reflection, and dilation are examples of different transformations.

Let assume A(-3,2) B(1,5) and C (2,-3) are original coordinates

The following translation is being used: (x, y) ⇒ (x + 2, y - 3)

First, take your x-coordinates and add them by two because it is the translation utilized to solve for your x-coordinate.

You would receive the following for yours x's: A (-1, y ) B (3, y) C (4, y)

Next, remove three from each of your y-coordinates because it is the translation being utilized to solve for your y-coordinate.

You would receive the following for your y's: A (x, -1) B (x, 2) C (x, -6)

Finally, you would take each one and put it together, or piece it together.

Hence, the coordinates of the image of triangle ABC after translation would be A (-1, -1), B (3, 2), and C (4, -6).

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Step 1

Write the equation of a line in slope point form

Where;

Step 2

Find the equation to represent the cost of the topsoil.

The equation that represents the cost of the topsoil is

y=30x

Step 3

Find how the cost of the topsoil compares to the cost of the mulch.

28-6x = 2x -84

Add 6x to both sides:

28 = 8x -84

Add 84 to both sides

112 = 8x

Divide both sides by 8

X = 112/8

X = 14

It seems there is some missing info on this question. However, if you are simplifying, then the simplified version of the given expression would be...

[tex]10a^1^9[/tex]

Hope this helps!

Data:

• Monthly budget: $15

• Price of a package of ramen: $1.48

• Price of a music download: $1.15

Procedure:

Answer: 10.1