Select the reason why these triangles are
similar. If they are not, select "Not similar".
Α. ΑΑ
B. SAS
C. SSS
D. Not similar

Answer:

17) x=8

18) [tex]x=\sqrt{189}[/tex] or [tex]x= 3\sqrt{21}[/tex]

Step-by-step explanation:

So the rule is [tex]a^{2} +b^{2} =c^{2}[/tex], "c" being the hypothenuse, or the long line that is opposite to the right angle.

17) We know that both values of x are equal to each other, which makes everything 10x easier!

                                               [tex]x^{2} +x^{2} =(8\sqrt{2}) ^{2}[/tex]

(by the way we know the x values are our a and b values because they are legs! the way I like to remember the legs is that they are connected to the right angle box, and therefore support the hypothenuse)

simplify (╥︣﹏╥)    

                                                [tex]2x^2=8^2(\sqrt{2} )^{2}[/tex]  

                                                  [tex]2x^2=64(2)[/tex]

                                                   [tex]2x^2=128[/tex]    

                                                  [tex]x^{2}= 128/2[/tex]  

                                                     [tex]x^{2} =64[/tex]

                                                        x=8      

18) Just pretend that the flipped triangle doesn't exist. It's parallel to the other triangle with values on it, and basically servers no purpose other than being parallel to the sister triangle :)

Anyways, since we know the hypothenuse (15) but we don't know one of our leg values (x), we're going to change our equation a bit!

                                                    [tex]c^{2} - b^{2} = a^{2}[/tex]

It doesn't matter if you put the one leg value in a or b, just as long as you stick to that same equation you started with the entire time!

                                                   [tex]15^{2} -6^{2} =x^{2}[/tex]

                                                   [tex]225-36=x^{2}[/tex]  

                                                     [tex]x^{2} =189[/tex]

                                               [tex]x=\sqrt{189}=3\sqrt{21}[/tex]

        The more you do these, the easier they'll get, so don't worry!

Answer:

.60 I think

I hope you get it right

Answer:

the first box is 7, the second would be -10, but since it already has ‘x -‘, just put 10

Step-by-step explanation:

Answer:

1 4/15 balls

Step-by-step explanation:

From the question, we are told that:

Chase caught 2/3 of the balls hit to left field.

Ryan caught 3/5 of the balls hit to right field.

The Lowest common denominator for both fraction is given as 15

Hence, the equivalent fractions for each boy is calculated such that the denominators of both fraction is 15

For Chase:

We Multiply both numerator and Denominator by 5

2 × 5 /3 × 5 = 10/15

2/5 = 10/15

For Ryan

We Multiply both numerator and Denominator by 3

3 × 3 /5 × 3 = 9/15

3/5 = 9/15

The total amount of the balls they both caught is:

10/15 + 9/15

= 19/15 = 1 4/15

Answer : The curved surface area of solid cylinder is [tex]3520cm^2[/tex]

Step-by-step explanation :

As we are given that:

Diameter of solid cylinder = 8 cm

Length or Height o solid cylinder = 140 cm

Formula used to calculate the curved surface area of cylinder is:

Curved surface area of cylinder = [tex]2\pi r\times h[/tex]

where,

r = radius of cylinder

h = height or length of cylinder

Radius of cylinder = [tex]\frac{Diameter}{2}=\frac{8cm}{2}=4cm[/tex]

Now putting all the given values in above formula, we get:

Curved surface area of cylinder = [tex]2\times \frac{22}{7}\times 4cm\times 140cm[/tex]

Curved surface area of cylinder = [tex]3520cm^2[/tex]

Therefore, the curved surface area of solid cylinder is [tex]3520cm^2[/tex]

Given:

Diameter of a solid cylinder = 8cm

Length (height) of cylinder = 140 cm

To find:

The curved surface area of the cylinder.

Solution:

We have,

Diameter = 8cm

Radius = [tex]\dfrac{8}{2}=4\text{ cm}[/tex]

Height = 140 cm

Curved surface area of a cylinder is

[tex]CSA=2\pi rh[/tex]

where, r is radius and h is height.

Putting r=4 and h=140 in the above formula, we get

[tex]CSA=2\times \dfrac{22}{7}\times 4\times 140[/tex]

[tex]CSA=2\times 22\times 4\times 20[/tex]

[tex]CSA=3520[/tex]

Therefore, the curved surface area of the cylinder is 3520 square cm.

Answer:

1. 2m - n + 2

Step-by-step explanation:

12×4m - 12×2n + 12×4. ( because 12 is multipled by whole bracket)

48m - 24n + 48.

2m - n + 2. (by finding common factor 24)

Answer:

The answer is below

Step-by-step explanation:

A linear function is a function in the form y = mx + b, where y and x are variables, b is the y intercept (value of y at x = 0) and m is the slope (rate of change).

Let x represent the year and y represent the amount of rainfall in inches. The linear function can be gotten by selecting any two pair of points from the table in the form (x, y).

Let us use the points (2004, 62.33) and (2007, 60.74). The equation is gotten using:

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)\\\\y-62.33=\frac{60.74-62.33}{2007-2004}(x-2004) \\\\y-62.33=-0.53(x-2004)\\\\y-62.33=-0.53x+1062.12\\\\y=-0.53x+1124.45[/tex]

The graph is plotted using geogebra.

The average rainfall from 2004 to 2013 is 59.945

Given data of rainfall:

2004    62.33

2005    61.8

2006    61.27

2007    60.74

2008    60.21

2009    59.68

2010    59.15

2011     58.62

2012    58.09

2013    57.56

it is the sum of all the observations divided by the total number of observations.

average rainfall A

(62.33+61.8+61.27+60.74+60.21+59.68+59.15+58.62+58.09+57.56)/10

A= 59.945

thus, the average rainfall from 2004 to 2013 is 59.945

to get more about the average visit:

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8/10 = 0.8

Therefore, 0.8 (8/10) is put on the number line shown below.

Answer:

x + 3 with the remainder of -9

Step-by-step explanation:

       ___x__+__3_____

x + 4 | X^2 + 7x + 3

          - (x^2 + 4x)

                       3x + 3

                      -(3x + 12)

                                -9

So the answer is x + 3 with the remainder of -9

The simplified form of the given expression is 0.2x-1.5y.

The given expression is 4.2(2x-0.5y)-2(4.1x-0.3y).

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.

The given expression can be solved as follows

4.2(2x-0.5y)-2(4.1x-0.3y)

= 8.4x-2.1y-8.2x+0.6y

=  8.4x- 8.2x-2.1y+0.6y

= 0.2x-1.5y

Therefore, the simplified form of the given expression is 0.2x-1.5y.

To learn more about an expression visit;

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Given:

[tex]\Delta PQR\cong \Delta XYZ[/tex]

[tex]PQ=3a+4[/tex]

[tex]XY=5a-12[/tex]

To find:

The value of a and PQ.

Solution:

We have,

[tex]\Delta PQR\cong \Delta XYZ[/tex]

[tex]PQ\cong XY[/tex]                            (CPCTC)

So,

[tex]PQ=XY[/tex]

[tex]3a+4=5a-12[/tex]

Isolating variable terms, we get

[tex]3a-5a=-4-12[/tex]

[tex]-2a=-16[/tex]

Divide both sides by -2.

[tex]a=\dfrac{-16}{-2}[/tex]

[tex]a=8[/tex]

Now,

[tex]PQ=3a+4[/tex]

[tex]PQ=3(8)+4[/tex]

[tex]PQ=24+4[/tex]

[tex]PQ=28[/tex]

Therefore, the value of a is 8 and the value of PQ is 28.

Answer:

yeah i think they are all right :)

Step-by-step explanation:

Answer:

2x-9y=-27

Step-by-step explanation:

hope this helps. :)

Answer:

1) AB

2) BC

3) AC

ABC

4) PA and OH

5) SO and CP

6) CA and SH

hope you can get to bed soon!

Answer:

the third one

Step-by-step explanation:

Answer:

25?

Step-by-step explanation:

sorry if im wrong

Answer:

hii

Step-by-step explanation:

Answer:

4 dozen.

Step-by-step explanation:

Total number of eggs required =2*24 = 48

One dozen = 12 so the answer is 4 dozen eggs.

Answer:

negative three

Step-by-step explanation:

i don't get what your asking for.

Answer:

slope: -2

Step-by-step explanation:

Answer:

Sin F = 0.6

Step-by-step explanation:

From triangle ABC, applying Pythagoras theorem to determine the length AB;

[tex]/hyp/^{2}[/tex] = [tex]/adj1/^{2}[/tex] + [tex]/adj2/^{2}[/tex]

[tex]/AC/^{2}[/tex] = [tex]/BC/^{2}[/tex] + [tex]/AB/^{2}[/tex]

[tex]/20/^{2}[/tex] = [tex]/16/^{2}[/tex] + [tex]/AB/^{2}[/tex]

400 = 256 + [tex]/AB/^{2}[/tex]

[tex]/AB/^{2}[/tex] = 400 - 256

           = 144

AB = [tex]\sqrt{144}[/tex]

     = 12

AB = 12, AC = 20, BC = 16

Therefore since ΔABC ≅ ΔDEF, and each side of triangle DEF is [tex]\frac{1}{3}[/tex] the length of the corresponding side of triangle ABC.

Then,

DE = [tex]\frac{1}{3}[/tex]AB =  [tex]\frac{1}{3}[/tex] x 12

     = 4

EF =  [tex]\frac{1}{3}[/tex]BC =  [tex]\frac{1}{3}[/tex] x 16

     = [tex]\frac{16}{3}[/tex]

DF =  [tex]\frac{1}{3}[/tex]AC =  [tex]\frac{1}{3}[/tex] x 20

     = [tex]\frac{20}{3}[/tex]

Then, applying trigonometric function to ΔDEF, we have;

Sin F = [tex]\frac{opposite}{hypotenuse}[/tex]

        = [tex]\frac{DE}{DF}[/tex]

        = 4 ÷ [tex]\frac{20}{3}[/tex]

        = 4 x [tex]\frac{3}{20}[/tex]

        = [tex]\frac{3}{5}[/tex]

Sin F = 0.6

Answer:

f(x) = -x + 2x + 5

is odd since f(x) = -5

f(x) = x + 8x

is neither because f(x) = 0

f(x) = -7x² + 5

is odd since f(x) = √5/7

f(x) = 5x + 3x? – 7x + 1

is odd

Answer:

17/33

Step-by-step explanation:

The repeating decimal [tex]$0.\overline{51}$[/tex] is equal to [tex]$\boxed{\frac{17}{33}}$[/tex].

A fraction is a component of a whole. Mathematically, the number is expressed as a quotient, where the numerator and denominator are divided. In a simple fraction, both are integers. In a complex fraction, a fraction can be found in either the numerator or the denominator. A suitable fraction has a numerator that is smaller than its denominator.

Let [tex]$x = 0.\overline{51}$[/tex]. Multiplying both sides of this equation by 100 gives,

[tex]$100x = 51.\overline{51}\\[/tex]. Subtracting the first equation from the second equation eliminates the repeating decimal,

giving:

[tex]\begin1100x - x &= 51.\overline{51} - 0.\overline{51}\\ \99x &= 51 \\\ \\end[/tex]

x = 51/99

Therefore, the repeating decimal [tex]$0.\overline{51}$[/tex] is equal to [tex]$\boxed{\frac{17}{33}}$[/tex].

Learn more about fractions here:

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