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Two parallel lines AB and CD are intersected by a transversal line EF that intersects AB at a point I and CD at a point K. Another transversal line GH is drawn right to GH and intersects AB at a point J and CD at point L.

In the figure, and ∠EIA ≅ ∠GJB. Complete the following statements to prove that ∠IKL ≅ ∠DLH.

∠EIA ≅ ∠IKC and ∠GJB ≅ ∠JLD because they are corresponding angles of parallel lines cut by a transversal.

So, if ∠EIA ≅ ∠GJB, then ∠IKC ≅ ∠JLD by the ________

A. Subtraction of Property
B. Substitution Property of Congruency
C. Addition Property of Congruency
D. Transitive Property of Congruency

∠IKL and ∠IKC and ∠DLH and ∠JLD are pairs of supplementary angles by the ____

A. Vertical Angles Theorem
B. Congruent Supplements Theorem
C. Linear Pair Theorem
.

m∠IKL + m∠IKC = 180° (1)
∠IKC ≅ ∠JLD, so m∠IKC = m∠JLD (2)
Applying the _____

A. Subtraction Property of Equality
B. Substitution Property of Congruency
C. Addition Property of Congruency
D. Transitive Property of Congruency

to equations (1) and (2), we get m∠IKL + m∠JLD = 180°.

Therefore, ∠IKL and ∠JLD are supplementary angles.

We've already shown that ∠DLH and ∠JLD are supplementary angles. Therefore, ∠IKL ≅ ∠DLH by the ____

A. Vertical Angeles Theorem
B. Definition of Supplementary Angles
C. Congruent Supplements Theorem
D. Linear Pair Theorem
.

Answer:

(2,11)

Step-by-step explanation:

What is substitution method?

The substitution method is where you plug in an expression that defines a variable into the other equation so you are left with one variable in which you can solve for.

In order to use the substitution method, one of the variables must be defined by an expression (e.g. x = 8y + 2 , the x is defined by the expression 8y + 2. )

Rearranging terms to define x or y

We have the two equations 2x + y = 15 and 7x - 2y = -8

The equation we would rearrange would likely be 2x + y = 15 as the y is by itself meaning we could easily change a few things to define it.

2x + y = 15

==> subtract 2x from both sides

2x - 2x + y = 15 - 2x

==> simplify

y = 15 - 2x

Plugging ( or substituting ) y's defined expression into the other equation.

Now that we have rearranged the equation to where "y" is being defined we can plug in the expression defined by y into the other equation and then solve for x.

2nd equation : 7x - 2y = -8

==> plug in y = 15 - 2x

7x - 2(15-2x) = -8

==> distribute the 2

7x - 30 + 4x = -8

==> combine like terms

11x - 30 = -8

==> add 30 to both sides

11x = 22

==> divide both sides by 11

x = 2

Substituing the value of x into one of the equations and then solving for y.

Now that we have calculated the value of x we can calculate the value of y by plugging in the value of x into one of the equations and solving for y.

2x + y = 15

==> plug in x = 2

2(2) + y = 15

==> multiply 2 and 2

4 + y = 15

==> subtract 4 from both sides

y = 11

The solution is (2,11)

Checking our work:

To check our work we can plug in the value of x and y into both equations. If both are true then the solution is correct but if one or both are false then the solution is incorrect.

First equation; 2x + y = 15

==> plug in x = 2 and y = 11

2(2) + 11 = 15

==> multiply 2 and 2

4 + 11 = 15

==> add 4 and 11

15 = 15

Second equation; 7x - 2y = -8

==> plug in x = 2 and y = 11

7(2) - 2(11) = -8

==> multiply 7 by 2 and 11 by -2

14 - 22 = -8

==> subtract 22 from 14

-8 = -8

Both are correct therefore (2,11) is the correct solution

Answer:

[tex]a=2\\\\ b = 20\\\\ c = 47[/tex]

Step by step explanation:

[tex]a(x) = 2(x+5)^2 -3\\\\~~~~~~~=2(x^2 +2 \cdot 5 \cdot x +5^2) -3\\\\~~~~~~~=2(x^2 +10x+25) -3\\\\~~~~~~~=2x^2 +20x +50 -3 \\\\~~~~~~~=2x^2 +20x +47\\\\\text{By comparing}~ 2x^2 +20x +47~ \text{with the standard form}~ ax^2 +bx+c,\\\\a=2,~ b = 20,~ c = 47[/tex]

Answer:

A or 57 7/9ft3

Step-by-step explanation:

13/3x10/3x4/1 = 520/9=57 7/9

Answer:

C. 73

Step-by-step explanation:

angles A and C will be the same because their sides are the same length!

so to solve this, let's set up an equation

now let's solve!

angle A = 73

let me know if you have any questions :)

Answer:

C!

Step-by-step explanation:

8x+72.8=5x+84.5

8x-5x = 84.5-72.8

3x = 11.7

x = 3.9

x = {3.9}

Answer:

B. AC > AB

Step-by-step explanation:

AC is the longest line and AB is shorter than AC

The average speed, in km/minute, of the train is 2.79 km/minute

From the question, we are to calculate the average speed in km/minute

From the given information,

Distance travelled = 503 km

Time taken = 3 hours = 3 × 60 minutes = 180 minutes

Using the average speed formula,

Average speed = Distance / Time

∴ Average speed of the train = 503 / 180

Average speed of the train = 2.79 km/minute

Hence, the average speed, in km/minute, of the train is 2.79 km/minute

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Answer:90 degree

Step-by-step explanation:

Answer:

x = 90°

Step-by-step explanation:

According to the Angle Sum Property of Triangles, the sum of the internal angles is 180°.

Answer: c or a

Step-by-step explanation:

Answer:

3.6%

Step-by-step explanation:

Because the two events are independent, their probabilities are multiplied, so the probability of a student being born in March and having a blood type of O+ is 9% * 40% = 0.09 * 0.40 = 0.036 = 3.6%

The price per share of the stock of the high-tech firm that was purchased by Jake is  $50.

Percentage is a measure of frequency that calculates the fraction of an amount out of hundred.

What is the price per share of the stock purchased by Jake = current value / ( 1 + percentage increase)

61 / 1.22 = $50

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The equation that describes the which gives the area of the pen, A, as a function of x, the length of fence parallel to the barn is A = 130x - x²

The pen is rectangular. Therefore,

area of a rectangle = lw

where

Therefore,

perimeter = 2w + l

perimeter = 2w + x

130 = 2w + x

130 - x = 2w

w = 65 - 1/ 2 x

A = xw

A = x(65 - 1/ 2 x)

A = 65x - 1 / 2 x²

Therefore, the function that represents A, the area of the pen is as follows:

A = 130x - x²

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The attached graph represents the graph of the function f(x) = |x - 3| + 2

The equation of the function is given as:

f(x) = |x - 3| + 2

The above equation is an absolute value function, and it has the following parameter:

Vertex = (3,2)

Next, we plot the graph of the function (see attachment)

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Answer:

A its becuase im rewlly smart

The domain and range of the given function are equal to (0, 3.85) and (0, 18.75) respectively.

In this exercise, you're given the following function h(t) = -4.87t² + 18.75t. Next, we would equate the function to zero (0) to determine its domain as follows:

0= -4.87t² + 18.75t.

4.87t(-t + 3.85) = 0

t = 0 or t = 3.85.

Therefore, the domain is 0 ≤ t ≤ 3.85 or (0, 3.85).

h(t) = -4.87t² + 18.75t

h(t) = -4.87(t² - 3.85t + 3.85 - 3.85)

h(t) = -4.87(t - 1.925)² + 18.05

Therefore, the range is 0 ≤ h ≤ 18.05 or (0, 18.75).

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Answer:

A on EDGE 2022

Step-by-step explanation:

Answer:

3a

Step-by-step explanation:

Answer:

In the end, the answer is: 30,000

Step-by-step explanation:

Answer:

D) None of the choices are correct.

Explanation:

Given triangles AHL and NKG

Sides which are congruent:

So, AHL ≅ NKG. There are no such options.

Based on the transformations that occurred, the preimage is most likely the topmost right image.

The transformations list shows that the first transformation was the reflection across the horizontal line drawn.

When a reflection is done, the shape looks like the inverse of itself. The only shape that looks like an inverse and is therefore a reflection is the bottom right shape which means the preimage must be the top right image.

Remaining part of question:

Which is the preimage?

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Answer:

Two angles forming a linear pair are always supplementary. Linear pair of angles are formed when two lines intersect each other at a single point, and the sum of angles of a linear pair is always equal to 180°.

Step-by-step explanation:

Two angles forming a linear pair are always supplementary. Linear pair of angles are formed when two lines intersect each other at a single point, and the sum of angles of a linear pair is always equal to 180°.

Question :

Answer :

They are formed when two lines intersect each other at one point and the sum of angles is 180⁰ .

Step-by-step explanation:

please Mark me brainlist!!

Answer:

line BC

Step-by-step explanation:

Line BC is the only line that doesn’t touch line AG

Answer:

(p + q) + r

is the correct answer

Answer:

x=28

Step-by-step explanation:

cos60°=14/x

0.5=14/x

x=14/0.5

x=28

Answer:

A. 28

Step-by-step explanation:

The value of x is equal to 18

Hope this helps and please feel free to comment, ask questions, give feedback, and correct me if I am wrong!

Have a great day!

:)

Answer: once tom eats 6 candys he will have the same number as sue

Step-by-step explanation:

Answer:

After 6 minutes they will both have 0 candies.

Answer: 1/10

Step-by-step explanation:

(1 x 4)/(8x5)

4/40

1/10

Answer:

4

Step-by-step explanation:

Given :

f(x) = x² - 6x + 8

=============================================================

Solving :

Splitting the middle term :

⇒ f(x) = x² - 6x + 8

⇒ f(x) = x² - 2x - 4x + 8

⇒ f(x) = x (x - 2) - 4 (x - 2)

⇒ f(x) = (x - 4)(x - 2)

============================================================

Solutions :

⇒ x - 4 = 0 ⇒ x = 4

⇒ x - 2 = 0 ⇒ x = 2

Answer:

B

Step-by-step explanation:

if

x=3

y=2

-2xy²

3

2³=8

-2×3×8

= -48

[tex]\\ \rm\Rrightarrow g(x)=6(\dfrac{3}{2})^x[/tex]

[tex]\\ \rm\Rrightarrow g(-1)=6(\dfrac{3}{2})^{-1}=6(\dfrac{2}{3})=2(2)=4[/tex]

[tex]\\ \rm\Rrightarrow g(0)=6[/tex]

[tex]\\ \rm\Rrightarrow g(1)=6(\dfrac{3}{2})=3(3)=9[/tex]

[tex]\\ \rm\Rrightarrow g(2)=6\times\dfrac{9}{4}=13.2[/tex]

Attached the graph

Answer:

Given function:

[tex]g(x)=6\left(\dfrac{3}{2}\right)^x[/tex]

To find each of the points, substitute the given values of x into the function:

[tex]x=-1 \implies g(-1)=6\left(\dfrac{3}{2}\right)^{-1}=4[/tex]

[tex]x=0 \implies g(0)=6\left(\dfrac{3}{2}\right)^{0}=6[/tex]

[tex]x=1 \implies g(1)=6\left(\dfrac{3}{2}\right)^{1}=9[/tex]

[tex]x=2 \implies g(2)=6\left(\dfrac{3}{2}\right)^{2}=13.5[/tex]

Therefore:

[tex]\large \begin{array}{| c | c | c | c | c |}\cline{1-5} x & -1 & 0 & 1 & 2 \\\cline{1-5} g(x) & 4 & 6 & 9 & 13.5 \\\cline{1-5} \end{array}[/tex]

As the function is exponential, there is a horizontal asymptote at [tex]y=0[/tex].

Therefore, as [tex]x[/tex] approaches -∞ the curve approaches [tex]y=0[/tex] but never crosses it.

So the end behaviors of the graph are:

Plot the points on the graph and draw a curve through them.

Answer:

Step-by-step explanation:

A:  The expression 4x = 2x - 2 reduces to x = -1.  This is true for all values of y, since y is not a factor in this expression.

The two other equations intersect at point (-1, -4).  See the attached graph (Solutions2)

y = 4x

y = 2x−2

============

Mathematically, we can substitute the value of y from the first equation into the second:

y = 2x−2

(4x) = 2x−2

2x = -2

x = -1

The intersection of this two lines is (-1,-4).  Since x=-1, this is also the solution to 4x=2x-2, as per the above.

B:  See attached Result Table

C:  See GraphEquation2