Line a has the equation "-6x+2y=4." Line b has the equation y=-6x +1. Which line is steeper? Are the lines parallel,perpendicular, or neither

We have found that: AB = (BD/2) * (XZ/AY) and we can solve for BD:

BD = 2 * AB * AY / XZ

What is triangle?

A triangle is a three-sided polygon with three angles. It is a fundamental geometric shape and is often used in geometry and trigonometry.

Since BD is a median of triangle ABC, it divides side AC into two equal parts. Let's label the midpoint of AC as M. Similarly, YW is a median of triangle XYZ and it divides side XZ into two equal parts, with the midpoint labeled as N.

Since AABC~AXYZ, we know that the corresponding sides are proportional. Thus,

AB/AX = AC/AY = BC/BZ

Since AB = BC (given that B is a vertex of both triangles), we have:

AB/AX = AC/AY

We can rewrite this equation as:

AB/AC = AX/AY ----(1)

Since BD is a median of triangle ABC, we have:

BD = 1/2 AC ----(2)

Similarly, since YW is a median of triangle XYZ, we have:

YW = 1/2 XZ ----(3)

From equation (1), we have:

AB/AC = AX/AY

Multiplying both sides by AC, we get:

AB = AX * (AC/AY)

Now, using equation (2), we can substitute AC/2 for BD:

AB = AX * BD/AY

Finally, using equation (3), we can substitute XZ/2 for YW:

AB = (BD/2) * (XZ/AY)

Therefore, we have found that:

AB = (BD/2) * (XZ/AY)

Hence, we can solve for BD:

BD = 2 * AB * AY / XZ

Note that we need to know the actual values of AB, AY, and XZ to find BD.

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Answer:

502

Step-by-step explanation:

4 times 125.50 equals 502

Applying the centroid ratio theorem, we have:

x = 37

DG = 22

AG = 44

AD = 66.

According to the centroid ratio theorem, we have:

AG = 2/3(AD)

AG = x + 7

DG = x - 15

AD = x + 7 + x - 15 = 2x - 8

Plug in the values into the equation

x + 7 = 2/3(2x - 8)

3(x + 7) = 2(2x - 8)

3x + 21 = 4x - 16

3x - 4x = -21 - 16

-x = -37

x = 37

DG = x - 15 = 37 - 15 = 22

AG = x + 7 = 37 + 7 = 44

AD = 22 + 44 = 66

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Answer:

The value of x is 37

The length of segment DG is 22 units

The length of segment AG is 44 units

The length of segment AD is 66 units

The method is: Find the increase and find the ratio of the increase and the old price.

The percentage increase is 20%

A percentage is defined as the ratio that can be expressed as a fraction of 100.

The method below shows how you would calculate the % increase.

First step: Find the increase:

increase = 480 - 400 = $80

Second step: Find the ratio of the increase and the old price and multiply by 100 to express in percentage:

80/400 * 100 = 20%

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Answer:

.

Step-by-step explanation:

Answer:

1) $11472.98

2) $2970.63

Step-by-step explanation:

Using the secant-secant theorem, the possible values of x are x = 6 and x = -10. -10 cannot be a value of x because length cannot be negative.

From the question, we are to determine the value of x in the given diagram.

The Secant-secant theorem states that

"Given two secant segments which share an endpoint outside of the circle, the product of one secant segment and its external segment is equal to the product of the other segment and its external segment"

Thus,

We can write that

5 × (5 + 7) = x × (x + 4)

Simplifying

5 × 12 = x² + 4x

60 = x² + 4x

x² + 4x - 60 = 0

Solve the quadratic equation

x² + 4x - 60 = 0

x² + 10x - 6x - 60 = 0

x(x + 10) - 6(x + 10) = 0

(x - 6)(x + 10) = 0

x - 6 = 0 or x + 10 = 0

x = 6 or x = -10

Since x cannot be negative,

x = 6

Hence, the value of x is 6

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Question: Which of the following are equivalent expressions-240 - (+370).

Solution:

Notice that

-240 -(+370) = -240 - 370 ( that is because - times + is)

then, we have:

240 -(+370) = -240 - 370 = -610.

Answer:

Option 2: (1,0) is the correct answer

Step-by-step explanation:

Given inequality is:

y>-5x+3

In order to find which point is solution to the given inequality we'll put the point one by one in the inequality. If the point satisfies the inequality, then the point is the solution of the inequality.

Putting (0,3) in inequality

\(3 > -5(0)+3\\3>0+3\\3>3\)

Putting (1,0) in inequality

\(0>-5(1)+3\\0>-5+3\\0>-2\)

Putting (-3,1) in inequality

\(1 > -5(-3)+1\\1> 15+1\\1>16\)

Putting (-1,-2) in inequality

\(-2>-5(-1)+3\\-2>5+3\\-2>8\)

The inequality is true for (1,0)

Hence,

Option 2: (1,0) is the correct answer

9514 1404 393

Answer:

  17

Step-by-step explanation:

The number of handshakes among n people is n(n -1)/2. Then ...

  n(n -1)/2 = 136

  n(n -1) = 272 = 17×16*

  n = 17

There were 17 people at the party.

_____

* This factoring can be facilitated by recognition that √272 ≈ 16.5, the number midway between the consecutive factors.

Answer:

Step-by-step explanation:

Answer:

√38

Step-by-step explanation:

√38

step 1: Check which squared numbers can be multiplied by another number to get 38.

Start with these numbers: 4, 9, 16, and 25

Step 2: Testing out the numbers

√25 × __ = 25 can't be divided by 38

√16 × ___ = 16 can't be divided by 38

√9 × ____ = 9 can't be divided by 38

√4 × ____= 4 can't be divided by 38

Step 3: Answer

After trying the square root numbers that could possibly work with √38 none work; which means √38 can't be simplified. So the answer is √38

I hope this helps!

Answer:

The way to represent this it is

\( 12.33 - \frac{0.27}{\sqrt{n} } < \mu < 12.33 + \frac{0.27}{\sqrt{n} } \)

Step-by-step explanation:

From the question we are told that

The sample mean is

The standard deviation is

Given that the confidence level is 95% then the level of significance is mathematically represented as

\(\alpha = (100-95)\)

\(\alpha = 0.05\)

The critical value for \(\frac{\alpha }{2}\) is obtained from the normal distribution table that value is

\(Z_{\frac{\alpha }{2} } = 1.96\)

Now the margin of error is mathematically represented as

\(E = Z_{\frac{\alpha }{2} } * \frac{s}{\sqrt{n} }\)

\(E = \frac{0.27}{\sqrt{n} }\)

Now the error range to show a 95% confidence is mathematically represented as

\(\= x - E < \mu < \= x + E\)

           \( 12.33  -   \frac{0.27}{\sqrt{n} } <  \mu < 12.33  +   \frac{0.27}{\sqrt{n} } \)

Here notice that the significant figure is keep to three to match the significant figure of the given values

Answer:

69

Step-by-step explanation:

According to the Angle Addition Postulate, the measure of m∠ABD = 202°.

According to the Angle Addition Postulate, an angle's measure is equal to the sum of the measures of any two adjacent angles. The Angle Addition Postulate can be used to determine the measurement of a missing angle or to determine the angle produced by two or more other angles.

Given:

The angle measures:

m∠ABC=37°,

and m∠⁡C⁣B⁣D= 165⁢°.

So, according to the angle addition postulate;

m∠ABD = m∠ABC + m∠CBD

Substituting the values,

m∠ABD = 37° + 165⁢°

m∠ABD = 202°

Therefore, the angle measure of m∠ABD = 202°.

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Answer:

$7/lb

Step-by-step explanation:

$70 / 10 lb = $7/lb

Answer:

$7 per pound of letuce

Step-by-step explanation:

We know

10 pounds = $70

1 pounds = ?

We cross multiply and get:

$7 per pound of letuce

So, the answer is $7 per pound of letuce

There must exist a vertex u in T such that the distance between u and v is at most (n-1)/2.

To prove the existence of a vertex u in tree T such that the distance between u and v is at most (n-1)/2, we can employ a contradiction argument. Assume that such a vertex u does not exist.

Since the number of vertices in T is odd, there must be at least one path from v to another vertex w such that the distance between v and w is greater than (n-1)/2.

Denote this path as P. Let x be the vertex on path P that is closest to v.

By assumption, the distance from x to v is greater than (n-1)/2. However, the remaining vertices on path P, excluding x, must have distances at least (n+1)/2 from v.

Therefore, the total number of vertices in T would be at least n + (n+1)/2 > n, which is a contradiction.

Hence, there must exist a vertex u in T such that the distance between u and v is at most (n-1)/2.

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A) A year is 12 months. Multiply monthly pay by 12 for yearly amount:

4500 x 12 = $54,000 per year.

B) the monthly rate of 4,500 per month pays more by: 54,000 - 53,210 = $790 per year

Answer:

21

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

The regression which comprises of both entity & time effect can be expressed as;

\(Y_{it} = B_1X_{it} + \alpha_i + \lambda_i + \mu_{it}\)

Where;

take charge of the state-explicit qualities that don't change over the long run

 controls the variables that differ after some time yet not across substances,

\(u_{it}\) controls state-specific qualities which shift after some time.

Thus, from the options given above:  

The first option lacks or does not involve the time effect as we are only looking for a particular year.

The second option comprises only 2 years of data which implies that we have a time effect involved. In addition to that, there exist a few variables in executing measurements that join fixed effects. In this case, we can utilize regression with time and fixed effect.

(c) The information here is quarterly over an extended period of time. Hence, it would prefer a period arrangement information than a fixed and time impact information. Thus, this is incorrect.

(d) Since no time variable is associated, we reject the option.

Answer:

what do you mean?

Step-by-step explanation:

The notation "m^2" is a shorthand way of saying "square meters".

Chances are you'll simply type in the number and leave out the units, as that's already taken care of.

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

Work Shown:

area = base*height

area = 8*3

area = 24 square meters

---------

Explanation:

We simply multiply the base 8 and height 3 and that's our answer. It's not a trick question even if it might seem like it.

The side that's 7 meters long is never used. The base and height are always perpendicular to one another, which means that they form a right angle (aka 90 degree angle).

The area formula of a parallelogram and rectangle are the same. We can think of a non-rectangular parallelogram as a slanted rectangle in a sense. Imagine you had stacks of blocks to form a rectangle. Now imagine nudging that stack slightly to one side. The blocks themselves don't change, so the area of one wall doesn't change. All that's changed is the shape.

Step-by-step explanation:

4x +8=-12 is the answer

Answer:

R=50

x=65

x-15=50+2x=180

Answer:  The answer is:  " m∡R = 20° " .

__________________________

Step-by-step explanation:

__________________________

Note that ∡R and ∡Q are "supplementary angles".

In these particular case:

  " m∠R + m∠Q = 180 " ;

We are given (in the picture):

_____________________________

" m∠R = (x - 15) " :

and " m∠Q = 2x " ;

_____________________________

So we plug in these values:

_____________________________

→ m∠R + m∠Q = 180  ;

  → (x - 15) + 2x = 180 ;

  → x - 15 + 2x = 180 ;

  → combine the "like terms" on the "left-hand side of the equation" :

   x + 2x = 1x + 2x = 3x ;

  Rewrite as:  3x - 15 = 180 ;

Now add "15" to each side of the equation:

       3x - 15 + 15 = 180 + 15 ;

 to get:

       3x = 195 ;

Now, divide each side of the equation by "3" ; to isolate "x" on the left-hand side of the equation; and to solve for " x" ;

       3x / 3 = 195/3 ;

    to get:  x = 65 ;

Now, we are to solve for:  m∡R ; which is:  " (x - 15) " ;

 So we substitute "65" ; for "x" ;

→  m∡R = x - 15 = 65 - 15 = 50 ;

The answer is:  " m∡R = 50.°

__________________________________

Note:  Alternate method:

Above; when we have:

 "3x - 15 = 180 " ;

we can divide each side of the equation by "3";

 to get:

   1x - 5 = 60 ;

 → x - 5 = 60 ;

Add "5" to each side of the equation:

     x - 5 + 5 = 60 ;

 → x = 60 ;

and then continue acordingly.

__________________________

Best wishes!

Answer:

Step-by-step explanation:

x + x - 2 = 10

2x - 2 = 10

2x = 12

x = 6

y = 6 -2

y = 4

(6,4)

The fish tank has a total volume of 288 inch³. As a result, Jessica's new fish tank has a capacity of 288 inch³ for water.

The volume of a rectangular prism can be calculated using the formula:

V = l x b x h..........(i)

where,

V ⇒ Volume

l  ⇒ length

b ⇒ width

h ⇒ height

From the question, we are given the values,

l = 8 inches

b = 4 inches

h = 9 inches

Putting these values in equation (i), we get,

V = 8 x 4 x 9

⇒ V = 288 in³

Therefore, the fish tank has a total volume of 288 inch³. As a result, Jessica's new fish tank has a capacity of 288 inch³ for water.

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Answer:

Step-by-step explanation:

Let the length is x, then the width is 1/4x.

Find the perimeter of rectangle:

The graph of the function is y = arcsec(x).

Answer:

Step-by-step explanation:

The initial vale is when x = 0

-  That is 75,

The growth factor is 2%.

These are a legitimate probability distribution:

To have a legitimate probability distribution, the probabilities for all possible values of X must satisfy two conditions:

Each probability value must be between 0 and 1, inclusive.

The sum of all probability values must equal 1.

Check if the given probabilities satisfy these conditions:

P(X=-3) = 0.14 (valid)

P(X=1) = 0.1 (valid)

P(X=3) = 0.135 (valid)

P(X=5) = 0.306 (valid)

Now, calculate the remaining probability to check if it satisfies the second condition:

P(X=6) = 1 - (P(X=-3) + P(X=1) + P(X=3) + P(X=5))

P(X=6) = 1 - (0.14 + 0.1 + 0.135 + 0.306)

P(X=6) = 1 - 0.681

P(X=6) = 0.319

Since the calculated probability is valid (between 0 and 1), There is a legitimate probability distribution for the discrete random variable X:

P(X=-3) = 0.14

P(X=1) = 0.1

P(X=3) = 0.135

P(X=5) = 0.306

P(X=6) = 0.319

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