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The order in which the figure is written is very important because this indicates which sides correspond and which angles correspond.

If quad( DXHW ) is similar to quad( LSCT ),

then side( DX ) is similar to side( LS ), side( XH ) is similar to side( SC ), side( HW ) is similar to side( CT ), and

        side( WD ) is similar to side( TL )

and angle( D ) is congruent to angle( L ), angle( X ) is congruent to angle( S ), angle( H ) is congruent to angle( C ),

       angle( W ) is congruent to angle( T )

The perimeter of the new photograph will be 2.25 times larger than the perimeter of the original photograph.

The area of the new photograph will be 2.25 x 2.25, or 5.0625, times larger than the area of the original photograph.

No one has answered any of my questions from the past week... Did I do something wrong?

What ARE you talking about.. They have ALL been answered.

Here is the last question that you posted:

You have been asking heaps of these questions. 

Haven't you worked it out yet ??!

ABCD is the big one, so if you are dilating to the little one then factor will be between 0 and 1

it must be 12.6/42 = 0.3

Now try and work out why and then try answering them for yourself!

Where do you want the centre of the dilation to be?

In order to determine which pairs of figures are indeed similar, you must compare the ratios of one side to another.

A) \(\frac{18}{27}=\frac{10}{15}\)

Simplifying both the fractions into simplest terms, \(\frac{2}{3}=\frac{2}{3}\), which indeed proves both figures to be similar.

B) Do the same thing with the rectangles.

\(\frac{7}{10}=\frac{14}{18}\)

Doing the exact process, \(\frac{7}{10}\neq\frac{7}{9}\), so these figures here are not congruent.

C) All equilateral triangles are similar.

D) Yet again, check the similarity by comparing the ratio.

\(\frac{18}{24}=\frac{24}{32}\)

Simplifying in simplest terms, \(\frac{3}{4}=\frac{3}{4}\), so this pair of figures are similar. 

A, C, and D are all pairs of figures that are similar.

1) Triangle Sum Theorem

To find \(m\angle 3\), one must understand that the sum of the measures of all the interior angles of a triangle equals 180, which is what the triangle sum theorem states.

2) Corresponding

\(\angle 3\) and \(\angle 4\) are both corresponding angles because both angles maintain the relative positions at the intersection of two lines. 

3) Linear Pair Postulate

4) Subtraction Property of Equality

The final step requires elementary subtraction to figure out the measure of the remaining angle. 

1) Definition of a rectangle

A rectangle is a quadrilateral with 4 right angles. That is all. 

2) \(\overline{JM}\cong \overline{KL}\)

These are the only pair of segments listed that are opposite.

3) \(\overline{ML}\cong\overline{ML}\)

4) Side-Angle-Side Triangle Congruence Theorem

For this particular proof, you are utilizing one side, an included angle, and another side to prove the triangles congruent. 

To find the midpoint of a segment, find the average of the x-coordinates and y-coordinates.

I don't know what the approximate formula is, but my approach would be as follows:

.

F=1 x 2^-(36/14)

F=0.1682 x 100

F=16.82% - fraction of the original drug that remains in bloodstream after 36 hours.

F=1 x 2^-(72/14)

F=0.0283 x 100

F=2.83% - fraction of the original drug that remains in bloodstream after 72 hours.

Your answer is in radians.  The question asks for the result in degrees.  Just multiply your result by 180/pi.

C  =  42° + A           and we know what  A  is,

A  =  46° 

Do you know how to find  C  now?

total number of points  =  ( 2 * number correct ) - ( 0.5 * number incorrect )

a.     score   =   ( 2 * 30 ) - ( 0.5 * 5 )   =   60 - 2.5   =   57.5

b.     No, you must know the number correct and the number incorrect to determine the score.

c.     We want to set the score equal to  80  and solve for the number incorrect.

        Also...let's say  c = number correct  and  w = number incorrect

80  =  2c - 0.5w            We want to solve this equation for  w  .  Subtract  2c  from both sides.

-2c + 80  =  -0.5w         Multiply both sides by  -2 .

4c - 160  =  w

w  =  4c - 160

d.  To graph it, we can say  y = w   and  x = c  .

y  =  4x - 160            To find the x-intercept, plug in  0  for  y  and solve for  x .

0  =  4x - 160

40  =  x                     The x-intercept is  40 .

When there are  0  incorrect, there must be 40 correct to get  80  total points.

y  =  4x - 160            To find the y-intercept, plug in  0  for  x  and solve for  y .

y  =  4(0) - 160

y  =  -160                  The y-intercept is  -160 .

When there are  0  correct, there must be  -160  incorrect to get  80  total points.

Realistically...that is impossible to do!!!

e.     Using the points we just found:     (40, 0)  and  (0, -160)

slope   =   [-160 - 0] / [0 - 40]   =   160/40   =   4

For every  4  additional wrong answers, there must be  1  additional right answer.

f.     w  =  4c - 16                          If  c = 43 ,  then

       w   =   4(43) - 160   =   12

The student must answer  12  questions wrong to get  80  points on the test.

But  43 + 12  =  55 , and there are only  50  questions on the test.

The student cannot get 12 wrong and 43 correct because there aren't enough questions. It's impossible for the student to get exactly  80  points on the test if he gets  43  correct.

The most he can get correct is  42 , which means he must get  8  wrong....remember....this is in order to get exactly 80 points on the test...no more, no less!

The triangle sum theorem states that the sum of measure of all the interior angles in a triangle equals 180; in this case, the fact that both lines are parallel has little significance to this particular problem.

There is a theorem called the Exterior Angle Theorem, which states that the measure of the exterior angle of a triangle equals the sum of the measure of the two nonadjacent angles (also known as remote interior angles).

Knowing this information above, we can set up an equation and solve for x:

Yes, you are right that the isosceles triangle theorem would end this problem in one step.

What’s the measure of angle C

Standard form of a quadratic is in the form \(ax^2+bx+c\), and vertex form is in the form of \(a(x-h)^2+k\).

a) The method of factoring requires a quadratic to be in standard form in order to use its procedure, so standard form is desired.

b) Vertex form is friendlier when it comes to graphing. One can quickly identify the vertex (hence its name vertex form), graph the points to the right, and then reflect about the axis of symmetry. Computationally speaking, it seems to be easier to indentify coordinates with vertex form. 

c) As aforementioned, vertex form allows one to identify the vertex simply by looking at the equation because \((h,k)\) is the vertex. In standard form, one would have to calculate \(\left(-\frac{b}{2a},f\left(-\frac{b}{2a}\right)\right)\), which requires more work.

d) In order to solve a quadratic using its corresponding formula, the formula requires the function be written in standard form. 

2. A transversal cutting parallel lines forms congruent corresponding angles 

3. Definition of congruent

4. A line standing on a line forms a linear pair

5. Linear Pair Theorem

6. Definition of Supplementary

7. Substitution of (3)  into (6)

8. Definition of Suppllementary

2. A line standing on a line forms a linear pair

3. Linear Pair Theorem

4. Definition of Supplementary

5 ,6 look good

7 Subtraction Property  of Equality

10 - x = 5

Add x to both sides

10 = 5 + x

Subtract 5 from both sides

5 = x

There you go! :) Hope this helps

The problem tells us that

A  =  B

and

C  =  42° + A

And we know that the sum of the angles in any triangle is  180° , so

A + B + C  =  180°         Since  A = B , we can substitute  A  in for  B .

A + A + C  =  180°         Since  C = 42° + A , we can substitute  42° + A  in for  C .

A + A + 42° + A  =  180°        Combine the  3  A's  together.

3A + 42°  =  180°                   Subtract  42°  from both sides of the equation.

3A  =  138°                             Divide both sides by  3 .

A  =  46°

And  B = A  so  B = 46°

These angles will be vertical, and thus, equal...so...

[ 3x + 34 ]  =  [ 7x + 10]    subtract 3x, 10 from both sides

24  =  4x      divide both sides by 

6  = x

So.....using   7x + 10.....the angles will measure   7(6) + 10  =  52°