Determine whether the triangles are similar. If so, what are the similarity statement and the postulate or theorem used? (image attached)thank you ! :)

ANSWER

EXPLANATION

Two lines are perpendicular if they have opposite reciprocal slopes. So, to find the line, first, we have to find the slope of the line tangent to the graph of y = 1/x at x = 2. To do so, we have to find the derivative of the function and evaluate it at x = 2. That is the slope of the tangent line at that point.

The derivative of the function is,

So, the slope of the tangent line at x = 2 is,

Therefore, the slope of the perpendicular line is the opposite reciprocal,

So we have that the perpendicular line we are looking for is,

We have to find the y-intercept, b. We know that this perpendicular line intersects the graph at the tangency point, so with that point, we will find b.

The x-coordinate of the tangency point is x = 2, and the y-coordinate is,

Substitute (x, y) with (2, 1/2) in the equation of the line to find b,

Subtract 8 from both sides,

Hence, the equation of the line perpendicular to the tangent of the graph at x = 2 passing through the tangency point is,

Solution:

Given:

Marcus have 44 CDs, Sherry have 34 CDs and Kristen have 22 CDs.

Let us assume that Kristen has x numbers of CD's.

According to the provided situation,

Marcus have twice the number of CDs as Kristen.

Number of CDs of Marcus = 2x

The number of CDs of Sherry is 12 more than the CDs of Kristen

Number of CDs of of Sherry = 12 + x

Total number of CDs combined are 100.

So, we can write,

x + 2x + (12 + x) = 100

4x + 12 = 100

Any equation with the highest degree of variable as one, just like the above equation is called Linear Equation.

Further solving the Equation,

4x + 12 = 100

4x = 88

x = 22

The number of CDs that Kristen has is 22.

The number of CDs that Marcus have is 2(22).

The number of CDs Marcus gas is 44.

The number of CDs Sherry has is (12 + x) which is equal to 34.

The number of CDs Kristen, Marcus and Sherry have is 22, 44 and 34 respectively.

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There is a 0.0530 percent probability that the randomly chosen study participant will be shorter than 68 inches.

The standard deviation of a random variable, sample, statistical population, data set, or probability distribution is the square root of its variance.  Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.

We have been given that

μ = 68.3

σ = 4.0

Find the probability that a study participant has a height that is less than 68 inches.

We are supposed to find P(x<68)

x = 68

z = (x - μ) / σ

z = (68 - 68.3) / 4

z = -0.3 / 4

z = -0.075

Use z table :

So, P(z<-0.0725)=0.0530

So, The probability that the study participant selected at random is less than 68 inches tall is 0.0530

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STEP-BY-STEP EXPLANATION:

What to do? Convert percentage to fraction

Given parameter

0.0032%

Yes, the probability approaches each time will result in getting a sample that is representative of the population of that group class.

If you are going on and properly conducting the specific research on a specific population, you will totally want to make sure that your taken sample of that population is absolutely representative.

If in any case your sample is a kind of representative of your total population, you will be able to confidently take up and generalize the results of your study to that of the population.

In order to be a representative sample, the sample of the group must represent the total population as a whole.

For instance, if the researcher’s population of absolute interest has 60% of people of total ages 18-25 and 40% of the total people ages from about 26-40, then the representative sample must also absolutely reflect this ratio.

The best way of ensuring a representative sample is to have a complete list (i.e., sampling frame) of all the elements in the present population and know that each and every element (e.g., people or present households) on the list that has a nonzero chance (but then it is not necessarily required to be an equal chance) of being included in the entire sample.

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Consider that the volume of a rectangular prism is given by the following formula:

V = l·h·w

l: length = 4 cm

w: width = 5.1 cm

h: height = 9 cm

replace the previous values of the parameters into the formula for V:

V = (4 cm)(5.1 cm)(9 cm)

V = 183.6 cm³

Hence, the volume of the rectangular prism is 183.6 cm³

The theorem that would be used to justify that triangles ABC and CDA are congruent is: SAS.

If we can show that the two sides and one included angle in one triangle is congruent to the two corresponding sides and an included angle in another triangle, then we can state that the two triangles are congruent to each other by the SAS congruence theorem.

Triangles ABC and CDA have the following:

Side AD is congruent to side BC [one pair of congruent sides]

Side AC is congruent to side CA based on the reflexive property [one pair of congruent sides]

Angle 1 is congruent to angle 2 [one pair of included congruent angle]

Therefore, the above information satisfies the SAS congruence theorem. Therefore, they are congruent triangles based on the SAS. The theorem that justifies why they are congruent is therefore SAS.

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Area of Sector.

The area of a sector is given by the formula below:

Substituting these values into the formula above, we get

Thus, the correct answer is 46.5 square meters.

1) [tex]\overline{AB} \cong \overline{CD}[/tex] (given)

2) [tex]\angle BAC \cong \angle ACD[/tex] (given)

3) [tex]\overline{AC} \cong \overline{AC}[/tex] (reflexive property)

[tex]\triangle ABC \cong \triangle CDA[/tex] (SAS)

We have the following points:

A(-11, -3) and B(-2,5)

The distance between AB is:

C(7,1) and D(x, 9)

the value of x is -2

we have the equation

A=bh

solve for h

that means -----> isolate the variable h

so

step 1

Divide both sides by b

A/b=bh/b

simplify

A/b=h

rewrite

Answer: 1/2

Step-by-step explanation:

1) Find the equation of sin of angle K

Sine is opposite/hypotenuse.

Opposite of K = 5.

the hypotenuse of K = 10

You then get 5/10

2) Simplify the fraction

5/10 = 1/2

a. Sin (θ) = √35 / 6

b. Tan (θ) = Tan θ = √35

c. Sec (θ) = 6

d. Csc (90° -θ) = 6

Note that according to trigonometric identities:

cos θ = Adjacent / Hypotenuse

From the question:

cos θ = 1/6

Comparing this with the given trigonometric identity:

Adjacent, A = 1

Hypotenuse, H = 6

Let us look for the opposite, O

Using the pythagora's theorem

H² = A² + O²

6² = 1² + O²

36 = 1 + O²

36 - 1 = O²

O² = 35

O = √35

Therefore, Opposite = √35

a) Sin θ = Opposite / Hypotenuse

Sin θ = √35 / 6

b) Tan θ = Opposite / Adjacent

Tan θ = √35 / 1

Tan θ = √35

c) Sec θ = 1 / cos θ

Sec θ = 1 ÷ 1/6

Sec θ = 1 x 6

Sec θ = 6

d) Csc ( 90 - θ) = Sec θ

Since Sec θ = 6

Csc ( 90 - θ) = 6

Answer:

It would be, Yes, No, Yes, Yes.

Hope this helps!

y = f(x+2) -1 is the equation which describes the graphed function.

Translation is the act of moving a shape or a figure from one location to another. A figure can move in translation up, down, right, left, or anywhere else in the coordinate system. Only the object's position changes during translation; its size stays the same. In mathematics, a translation is the up, down, left, or right movement of a shape. Because the translated shapes appear to be exactly the same size as the original ones, they are consistent with one another. Just one or more directions have been altered.

Given,

When F crosses the x-axis when it is negative.

-1 indicates a 1 unit down translation.

So, the equation will be y = f(x+2) -1.

y = f(x+2) -1 is the equation which describes the graphed function.

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Expression of the given interval (-4,-1) in inequality notation is -4< x <-1.

As given,

Given interval:

( -4 , -1 )

Let us consider x variable belongs to given interval x ∈ ( -4 , -1 ).

Therefore, the expression of the given interval (-4,-1) in inequality notation is -4 < x < -1.

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Answer:

24

Step-by-step explanation:

We will use the proportional concept to solve it.

So, 6/13 = x/52

x = 6*4

x = 24

So, height of tree is 24 feet

Looking at the figure, we can tell that the top is a triangle and the base is a trapezium. To find the area of the figure, we would find the sum of the triangle and the trapezium.

Recall, the formula for finding the area of a triangle is expressed as

Area = 1/2 x base x height

Looking at the triangle,

base = 9 + 9 = 18

height = 3

Thus, Area = 1/2 x 18 x 3 = 27

Again, the formula for finding the area of a trapezium is expressed as

Area = 1/2(a + b)h

where

h is the height of the trapezium

a and b are the lengths of the parallel sides

Looking at the trapezium,

a = 9 + 9 = 18

b = 13.4 + 13.4 = 26.8

h = 12

Area = 1/2(18 + 26.8)12

Area = 268.8

rounding to the nearest whole number,

Area = 269 squared ft

Answer: a. (-10, 0) u(12, infinity)

b. (negative infinity, -10) u(0, 12)

All of this is assuming that the ends of both functions are continuing in the direction it's going shown in the graph.

Step-by-step explanation:

f(x) and g(x) basically means the y value. So when f(x) is greater than g(x), it's saying the y value for the f(x) line is greater than the y value for g(x). This happens when x = -10 till x = 0 and x = 12 till forever going right.

Side note: (-10, 0) is a way to write the domain, with the first number meaning the start and the second number meaning the end.

We have the sequence:

We rewrite the sequence as:

From the previous equations, we see that the general term is given by:

Replacing n = 19, we get:

Answer

Population means μ as a tri-linear inequality is given as 58.852< m<61.548 with a confidence interval of 99.5%.

What is a confidence interval?

Mean, x= 60.2

sample size, n= 867

standard deviation=21.9

population mean m as a tri-linear inequality is given by,

The t value for a 99.5% Confidence interval because the sigma is unknown.

From Inverse t Distribution Calculator, the Confidence interval is 0.995 and the degree of freedom is 867-1=866

One-sided t-Score: 1.8125

We can now determine the standard error E:

E=1.8125(21.9/√867)=1.348

We can now create the confidence interval by:

x - E < m< x + E

60.2-1.348< m <60.2+1.348

58.852< m<61.548

Population means μ as a tri-linear inequality is given as 58.852< m<61.548 with a confidence interval of 99.5%.

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Note that the data is in ascendinhg order.

We shall find the position of the pth percentile as follows;

We now have;

In the 34th and 35th position we have;

ANSWER:

The new coordinates are (-1, 7), (-3, 3) and (-8, 5)

To get the new coordinates after the translation, we will first find the initial coordinates of the three vertices

The three vertices: (3, 3), (1, -1) and (-4, 1)

A translation of 4 units to the left:

A translation of 4 units up:

Plotting the points:

The cost of 12.49 is fixed, while the extra cost for toppings is 1.5 per topping.

If we have a total of t topping, the cost of the toppings will by 1.50t, adding the fixed cost, we will have the total cost, which should be equal to d. so we have the equation:

Now, we can manipulate the equation to check which ones are equivalent to it.

As we can see, the first one is missing the 1.50, so it is not equivalent.

The second have the 1.50, it is just inverted:

So, it is equivalent.

The third had the t and d switched, so it is not equivalent.

The fourth get the 1.50t to the other side, but don't change the sign accordingly, so it is not equivalent.

The fifth solved for t let's do that:

So, it is equivalent.

The sixth don;t distribute the denominator correctly, so it is not equivalent.

So, the alternatives that are equivalent are:

The second and fifth.

The domain of the functions F(x)=|x|, g(x)=x+9, f o g is x ∈ R the functions exist for all real numbers.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

The function f(x):

f(x) = |x|

The domain of the function is:

x ∈ R

g(x) = x + 9

The domain of the function:

x ∈ R

f o g = f(g(x)) = |x + 9|

The domain of the function f o g is x ∈ R

Thus, the domain of the functions F(x)=|x|, g(x)=x+9, f o g is x ∈ R the functions exist for all real numbers.

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the sum of the internal angles of the 4-sided polygon is 360, therefore

then

answer: a. y = 116° and z = 61°

Data:

• Distance ( ,D ,)= 144 miles

• Time ( ,t ,) = 4 hours

• Speed of Ahmed (,A,): unknown

• Speed of Blake (,B,): unknown

• Formula of speed:

Procedure:

• As Blake travels 8 mph faster than Ahmed

Since they are traveling towards each other, we can add up their speeds as follows:

Using the distance formula, we can find the speed:

To know the speed of Blake:

Answer:

• Blake = 292 mph

• Ahmed = 284 mph

Answer: X=5

Step-by-step explanation: If x is 5 more than y, and y is 3 less than z. Well we already know z=3 so z=3 - 3 less than Y=0. Making Y=0, and if x is five more than Y, 5+0=5. Making x=5