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The triangles are similar due to SAS congruence postulate rule.

Similar Triangles are defined as two triangles with the same shape, equal pair of corresponding angles, and the same ratio of the corresponding sides. The triangles that like one another but may not be exactly the same size are said to be similar triangles. When two objects have the same shape but different sizes, they can be said to be similar. This indicates that identical shapes superimpose one another when enlarged. The term "Similarity" refers to this characteristic of like shapes.

Given triangles are similar due to SAS congruence postulate rule.

SAS or Side-Angle-Side Similarity Criterion,

According to the SAS similarity theorem, If any two of the first triangle's sides are exactly proportional to those of the second triangle, and if the angle created by these two sides of each individual triangle is equal, then the two triangles must be similar triangles.

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Answer:

(0, -10a)

Step-by-step explanation:

From the picture attached,

Coordinates of a point have been given as (-10a, 0)

x-coordinate → distance of the point from the origin on x-axis

y-coordinate → distance of the point from the origin on y-axis

Therefore, distance of the given point on x-axis = -10a [(-) sign denotes the negative side of the x-axis]

Distance of the other point with unknown coordinates (x, y) (on y-axis) from the origin = y

And y = 10a

Therefore, coordinates of the unknown point will be (0, -10a).

[Here (-) sign denotes the negative side of the y-axis]

The table that represents a function in the options given is: Table A. (see image attached below).

Recall:

In the tables given, only the first table has exactly one y-value assigned or related to every x-value given.

Therefore, the table that represents a function in the options given is: Table A. (see image attached below).

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Answer:

Graph A

Step-by-step explanation:

Answer:

Step-by-step explanation:

Since the base of the pyramid PABCD is a rectangle, the shape in question is a rectangular based pyramid. Volume of a rectangular based pyramid is expressed as V = 1/3 * Base Area * Height of the pyramid.

Given a rectangle ABCD with AB = 8 and BC = 4, the area of the rectangle will be equivalent to the base area of the pyramid.

Base Area = Length * Breadth

Base Area = AB * BC

Base Area = 8*4 = 32

If [tex]\overline{PA}\perp \overline{AD}\ and \ \overline{PA}\perp \overline{AB}[/tex], and PB = 17, then the height of the pyramid is PB = 17.

Volume of the pyramid = 1/3 * 32 * 17

Volume of the pyramid = 1/3 * 544

Volume of the rectangular based pyramid = 181.33

Answer:

$11.25

Step-by-step explanation:

Total money given to the taxi driver=36+25% of 36=45

Each person will pay (45/4)=11.25

Answer:

5+39 this is the answer 5+39

Answer:

Student t-distribution.

Step-by-step explanation:

In this scenario, a test is being conducted to test the difference between two population "means" using data that are gathered from a matched pairs experiment. If the paired differences are normal, then the distribution used for testing is the student t-distribution.

In Statistics and probability, a student t-distribution can be defined as the probability distribution which can be used to estimate population parameters when the population variance is not known (unknown) and the sample population is relatively small. The student t-distribution is a statistical distribution which was published in 1908 by William Sealy Gosset.

A student t-distribution has a similar curve with the normal distribution curve, except that it is fatter and a little bit shorter.

Answer:

299.88 mi. !!!!!

you just multiple all of them together to get the area!!!

Answer:

55

Step-by-step explanation:

The first crayon is chosen out of 11,so there are 11 choices

11

The second crayon is chosen out of 10 crayons left so there are 10 choices

10

11*10 = 110

But we do not care about the order, so we divide by 2 since there are 2 places

110/2 =55

Answer:

55

Step-by-step explanation:

Equation is a = n * (n-1)

11 * 10 = 110

Order doesn't matter, and two colors, so divide by 2.

110/2 = 55

Answer:

16×14 = -9×(-8) = -13×7

Falso

Step-by-step explanation:

Answer:

1. step 4

2.idk

3. step 2

4.-5n = 1 --------->  n= -1/5

n + 15 = -10 -------> -25

n/5 = -1/5 ------> n = -1

n - 13 = -12 ------> n = 1

5. cant see the drop down menu or possible answers

but if an answer is the addition one thing

then the second one is the subtraction thing

Step-by-step explanation:

Answer:

The standard error of the sample mean is [tex]\sigma_{\= x } = 0.40[/tex]

Step-by-step explanation:

From the question we are told that

     The population mean is  [tex]\mu = 5.30 \ hours[/tex]

     The population standard deviation is [tex]\sigma = 3.20 \ hours[/tex]

      The sample size is  [tex]n = 64[/tex]

Generally the standard error of the sample mean is mathematically represented as

               [tex]\sigma_{\= x } = \frac{\sigma}{\sqrt{n} }[/tex]

substituting values

                [tex]\sigma_{\= x } = \frac{3.20}{\sqrt{64} }[/tex]

                [tex]\sigma_{\= x } = 0.40[/tex]

Answer:

[tex]\boxed{\frac{1}{2} }[/tex]

Step-by-step explanation:

Hey there!

Well given,

[tex]\frac{2}{5} * 1 \frac{3}{12}[/tex]

We need to make 1 3/12 improper,

1*12 = 12

12 + 3 = 15

[tex]\frac{2}{5} * \frac{15}{12}[/tex]

2*15 = 30

5*12 = 60

[tex]\frac{30}{60}[/tex]

Simplified

[tex]\frac{1}{2}[/tex]

Hope this helps :)

Answer:

a. an independent-samples design.

Step-by-step explanation:

Independent sample design is the one in which samples are selected randomly. It is the observation which is not dependent on any other value. The statistical analysis is based on the assumption that the samples are independent. The study in this scenario is not dependent on any other variable and is based on independent sample design.

Answer:

Step-by-step explanation:

L =  4 ft

W  = 3 ft

H = 7 ft

volume = LWH/3 = 28 ft³

Answer:

84 pounds

Step-by-step explanation:

If 1/3 of a book is equal to 28 pounds then 28*3 will give you your answer

Answer:

  60°

Step-by-step explanation:

You have the rotation matrix ...

  [tex]\left[\begin{array}{cc}\cos{\theta}&-\sin{\theta}\\\sin{\theta}&\cos{\theta}\end{array}\right]=\left[\begin{array}{cc}\dfrac{1}{2}&-\dfrac{\sqrt{3}}{2}\\\dfrac{\sqrt{3}}{2}&\dfrac{1}{2}\end{array}\right][/tex]

This tells you the angle of rotation is ...

  [tex]\tan{\theta}=\dfrac{\sin{\theta}}{\cos{\theta}}=\dfrac{\left(\dfrac{\sqrt{3}}{2}\right)}{\left(\dfrac{1}{2}\right)}=\sqrt{3}\\\\\theta=\arctan{\sqrt{3}}=60^{\circ}[/tex]

The angle of rotation is 60°.

Answer:

B----- 60

Step-by-step explanation:

Answer:

Three

Step-by-step explanation:

Assuming the grade score from 70 to 100 is A; for grade score from 60 to 69 is B and grade score from 50 to 59 is C. Well it is certain there are three peaks in the distribution of scores

9514 1404 393

Answer:

  sin(tan^-1(x)) = x/√(x² +1)

Step-by-step explanation:

We know that for an angle in a right triangle...

  Tan = Opposite/Adjacent

and

  Sin = Opposite/Hypotenuse

so we can let Opposite = x and Adjacent = 1. The Pythagorean theorem tells us that ...

  Hypotenuse² = Opposite² + Adjacent² = x² +1

Then the sine of the angle is ...

  sin(tan^-1(x)) = x/√(x² +1)

Answer:

[tex](\frac{4}{3},-\frac{10}{3})[/tex]

Step-by-step explanation:

If the extreme ends of a line segment AC are A[tex](x_1,y_1)[/tex] and C[tex](x_2,y_2)[/tex].

If a point B(x, y) divides the segment in the ratio of m : n

Then the coordinates of the point B are,

x = [tex]\frac{mx_2+nx_1}{m+n}[/tex]

y = [tex]\frac{my_2+ny_1}{m+n}[/tex]

If the ends of AC are A(-2, 5) and C(2, -5) and a point B divides it in the ratio of m : n = 5 : 1

Therefore, coordinates of this point will be,

x = [tex]\frac{5\times (2)+1(-2)}{5+1}[/tex]

  = [tex]\frac{10-2}{5+1}[/tex]

  = [tex]\frac{8}{6}[/tex]

  = [tex]\frac{4}{3}[/tex]

y = [tex]\frac{5\times (-5)+1(5)}{5+1}[/tex]

  = [tex]\frac{-25+5}{6}[/tex]

  = [tex]-\frac{20}{6}[/tex]

  = [tex]-\frac{10}{3}[/tex]

Therefore, coordinates of the point B are [tex](\frac{4}{3},-\frac{10}{3})[/tex].

Answer:

-1

Step-by-step explanation:

Twice a number of 4 equals 8

4×2=8

less than 9 of the quotient (answer) of twice a number of 4, is -1

8-9= -1

The required expression for Nine less than the quotient of twice a number and four gives the equation, y =2x/4 - 9.

An expression Nine less than the quotient of twice a number and four. is to be determined.

The process in mathematics to operate and interpret the function to make the function simple or more understandableis called simplify and the process is called simplification.

The quotient is the result when one value gets divided by some other value.

Using simple arithmetic,
Let the number be x,
A number y is equal to nine less than the quotient of twice of x and four. So,
y = quotient of 2x and four - 9
y = 2x/4 - 9

Thus, the required expression for Nine less than the quotient of twice a number and four gives the equation, y =2x/4 - 9.

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Answer:

equal value and function

Step-by-step explanation:

Answer:

a) Means: 24 and 2; Extremes: 4 and 12

b) Means: 6 and 16; Extremes: 24 and 4

c) Means: 8 and 8; Extremes: 4 and 16

d) Means: 50 and 3; Extremes: 6 and 25

Step-by-step explanation:

The Means and Extremes in a proportion are defined based on the writing the proportion in one lie using colons the indicate the fraction, like in:

a : b = c : d The extremes values here are those that you see at the extreme left and extreme right of that expression. That is: a, and d.

The Means are the values that appear in the middle of the one line expression, that is: b and c.

Recall as well that the proportion can also be written with fractions:

a : b = c : d  is the same as:   a / b = c / d

so convert the expression to a one line with colons when the question comes in fraction form, and that way you can answer.

Answer:

the area of a section of a circle is [tex]\frac{1}{360}[/tex]* Θ * (area of the circle)

the theta/360 tells us the amount of circle currently in question

so , the answer will be 1/3 pi r^2        [A]

Answer:

The  upper limit is    

                   [tex]k = 52.94[/tex]

Step-by-step explanation:

From the question we  told that

     The  sample size is [tex]n = 16[/tex]

      The sample mean is  [tex]\= x = 50[/tex]

      The sample variance is  [tex]\sigma ^2 = 36[/tex]

For  a  95% confidence interval the confidence level is  95%

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

             [tex]\alpha = 100 - 95[/tex]

              [tex]\alpha = 5 \%[/tex]

              [tex]\alpha = 0.05[/tex]

Next we obtain the critical value of  [tex]\frac{\alpha }{2}[/tex] from the normal distribution table(reference- math dot armstrong dot edu), the value is  

              [tex]Z_{\frac{ \alpha }{2} } = 1.96[/tex]

Generally the margin of error is mathematically represented as

             [tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma}{\sqrt{n} }[/tex]

 Here  [tex]\sigma[/tex] is the standard deviation which is mathematically evaluated as

                  [tex]\sigma = \sqrt{\sigma^2}[/tex]

substituting values

                  [tex]\sigma = \sqrt{36}[/tex]

=>                [tex]\sigma = 6[/tex]

So

                    [tex]E = 1.96 * \frac{6}{\sqrt{16} }[/tex]

                     [tex]E = 2.94[/tex]

The 95% confidence interval is mathematically represented as

                 [tex]\= x - E < \mu < \= x + E[/tex]

substituting values

                [tex]50 -2.94 < \mu <50 +2.94[/tex]

                [tex]47.06 < \mu <52.94[/tex]

The  upper limit is    

                   [tex]k = 52.94[/tex]

Answer:

1. Make a list of activities and the number of students:

Watching TV: 32

Talking on the phone: 41

Video games: 24

Reading: 15

2. Then combine the data in a bar graph as shown in the picture

Step-by-step explanation:

Given,

the bigger triangle (∆GFH), <HGF = 90° and <GFH = 60° and GF = 4

In the 30-60-90 triangle, FH = 4×2 = 8

or you can find it like this,

cos60 = 4/FH

FH = 4/cos60 = 8

Now, I is the midpoint of FH, so, FI = 8/2 = 4

now for ∆FGI,

<GFI = 60°, GF = 4, FI = 4, it's a equilateral triangle, so we can say GI = 4

Now we need to find the height of ∆FGI, for that,

area of ∆FGI = (√3/4)×4² = 4√3 = 6.92820323..

So height (GJ) = 2×area/side = 2×4√3/4 = 2√3 = 3.46410162.. [height of ∆GFI (Because altitude is perpendicular distance from a point) = GJ, given]

now, in ∆GJI, GJ = 2√3, GI = 4 and <GJI = 90° (since itsy altitude, the angle will be a right angle, i.e. 90°)

So, JI = √{4²-(2√3)²} = 2

Area = 2×2√3/2 = 2√3 = 3.46410162.. = 3.46 (rounded to the nearest hundredth)

Answer:

2.7 in²

Step-by-step explanation:

Given that ∆BAC ~ is similar to ∆EDF, the ratio of the area of ∆BAC to the area of ∆EDF = the square of the ratio of their corresponding sides.

Thus, let x be the area of ∆EDF

[tex] \frac{6}{x} = (\frac{3}{2})^2 [/tex]

[tex] \frac{6}{x} = \frac{9}{4} [/tex]

Cross multiply

[tex] x*9 = 4*6 [/tex]

[tex] 9x = 24 [/tex]

[tex] \frac{9x}{9} = \frac{24}{9} [/tex]

[tex] x = 2.67 [/tex]

Area of ∆EDF = 2.7 in²