Find the length of the short leg on the following right triangle.

It has been proven that the trigonometric Identity (1 - secA + tanA)/(1 + secA + TanA) is equal to; (secA + tanA - 1)/(secA + tanA + 1)

We want to prove that;

(1 - secA + tanA)/(1 + secA + TanA) = (secA + tanA - 1)/(secA + tanA + 1)

We know from trigonometric identities that;

(secA)² – (tanA)² = 1   ----(1)

Also, from algebra we know that;

a² - b² = (a + b)(a - b)

The numerator of LHS of the original given Identity is:

1 - sec A - tan A

Using equation 1, we can say that;

(secA)² – (tanA)² - (sec A + tan A)

⇒ (sec A + tan A)(sec A - tan A) - (sec A - tan A)

This can be factorized to get;

(sec A - tan A)(sec A + tan A - 1)

Similarly, the denominator can be expressed as;

(sec A - tan A)(sec A + tan A + 1)

Thus, combining the numerator and denominator together gives us:

[(sec A - tan A)(sec A + tan A - 1)]/[(sec A - tan A)(sec A + tan A + 1)]

⇒ (secA + tanA - 1)/(secA + tanA + 1)

That expression is equal to the Right hand side and as such the Trigonometric Identity is proved.

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(a) The relation is a function because each value of x maps onto only one value of y.

(b) Domain is [tex](-\infty, 3][/tex], range is [tex][-1, \infty)[/tex].

Answer: The average change in elevation is 27 feet per second.

Step-by-step explanation:

 A submarine dives = 378 feet

          Time taken in the total diving = 14 seconds.

So, according to the question, the average change in the elevation  can be calculated by

                            ⇒ Feet per second = feet/ second

                             ⇒ the average change = 378/14

                            ⇒ elevation = 27 feet per second.

Change in elevation is basically the distance covered in one second.

The construction is the construction of the Perpendicular bisector.

The steps for the construction of perpendicular bisectors are as follows:

Open the compass more than half of the distance between A and B, and scribe arcs of the same radius centered at A and B.

Call the two points where these two arcs meet X and Y. Draw the line between X and Y.

So, the point where this line meets the line segment; M is called the mid point and the line XY is the perpendicular bisector of the line AB.

The figure is a construction of perpendicular bisector.

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Answer:

P = $900

Step-by-step explanation:

Simple Interest Formula: [tex]A = P(1+rt)[/tex]

Where A is the final amount,

P = Principal

r = Interest Rate in Percent or [tex]\frac{r}{100}[/tex] per annum

t = time in years

From the information given in the question,

A = $918

r = 2% per annum or [tex]\frac{2}{100}[/tex]

t = 1 year

Lets substitute these values to find P, the principal.

[tex]P(1+(\frac{2}{100} )(1))=918\\P(1+0.02)=918\\1.02P=918\\P = \frac{918}{1.02} \\=$900[/tex]

Therefore, P = $900

Answer:

$64,208.33

Step-by-step explanation:

100% - 33% = 67%

Since she pays 33% in taxes, she will only get 67% of the $23 million.

1 year = 12 months

20 years = 20 × 12 months = 240 months

There are 240 months in 20 years.

monthly amount = 67% of $23 million / 240

monthly amount = 0.67 × $23,000,000 / 240

monthly amount = $64,208.33

Answer:

9/28 and 32.1%

Step-by-step explanation:

So the sample space consists of all products for (5 * 1, 5 * 2, 5 * 3.... and the same thing for 6, 7, and 8)

This gives you the sample space: {5, 10, 15, 20, 25, 30, 6, 12, 18, 24, 30, 36, 7, 14, 21, 28, 35, 42, 8, 16, 24, 32, 40, 48}.

The size of the sample space is 4 * 6, since for each number (5, 6, 7, 8), there are 6 products (the dice have six numbers). This means the sample space has 24 combinations, you can also verify this by manually counting the sample space.

Now filtering the sample space so you only get a product that is 28 or higher you get: {30, 30, 36, 28, 35, 42, 32, 40, 48} which has 9 possible combinations that have a product greater than or equal to 28. Divide this by the entire sample space and you get a probability of: 9/28, which in decimal form is approximately: [tex]0.3214[/tex]. Multiplying this by 100 gives you: [tex]32.1[/tex]%

The ratio of the side lengths of the triangle will be 3:10 or 3/10.

From the information given, the first triangle has sides 6 and 9 while the large triangle has sides 20 and 30.

Based on this, the ratio will be:

= 6/20 = 9/20

= 3/10 = 3/10

Therefore, the ratio is 3:10.

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Rate is the distance between the cars increasing two hours later is 52 miles/hr

Let x(t) be distance of first car from starting point at time t

Let y(t) be distance of second car from starting point at time t

Let s(t) be distance between the two cars at time t. We need to evaluate ds/dt at time t = 2.

We know x2(t) + y2(t) = s2(t). Therefore 2x * dx/dt + 2y * dy/dt = 2s * ds/dt. The 2s cancel.

At t=2 hours, x = 96 miles. and y = 40 miles.

We will need the distance between the cars at t=2:

s(2) = √x(2)2 + y(2)2 = √96 2 + 40 2 = √10816 = 104.

Now fill in x * dx/dt + y * dy/dt = s * ds/dt at time t = 3 and solve for ds/dt:

96 * 48 + 40 * 20 = 104 * ds/dt

ds/dt = 5408/104 = 52 miles/hr

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In this example, the sampling interval is 10.

A researcher gets a list of all 500 members of the National Association of Social Work in Yourtown that she wants to include in her study. She only has the funding and time to survey 50 members. She takes her list of members, randomly selects a starting point, and then selects every tenth name from the list to be included in her sample.

In this example, the sampling interval is 10.

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Answer:

If AD=AE the the bisector CD. will be the coefficient of AE

The smallest positive integer that has a square root that is greater than 10 is 101

Let the integer be represented by n

The square root is greater than 10.

So, we have:

[tex]\sqrt n > 10[/tex]

Square both sides

n > 100

The above means that the integer is greater than 100.

The smallest integer greater than 100 is 101

Hence, the smallest positive integer that has a square root that is greater than 10 is 101

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2.46

A Type I error is rejecting the null when it is true.

If the critical value is 2.45, and you have a test statistic of 2.46, you have the least chance among the other choices of rejecting the null and it happens to be true.

We got another hypothesis here and our alternative that is less than five. So that's how we're gonna write it.

We're gonna be looking at a left tail test since it's less than the mean, Our means, always going to be in the middle here. And what we're trying to calculate is the probability that this is true.

The level of significance which is selected in

Step 1 (e.g., α =0.05) dictates the critical value.

For example, in an upper-tailed Z test, if α =0.05 then the critical value is Z=1.645.

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The relative frequencies for all pets are given-

The relative frequency for dog is 0.4.

The relative frequency for cat is 0.35.

The relative frequency for bird is 0.15.

The relative frequency for fish is 0.1

The ratio of the total number of events occurring in a scenario to the number of times an event occurs is known as relative frequency.

Relative Frequency = Subgroup frequency/ Total frequency.

Relative Frequency = f/ n.

where, f = total frequency

n = subgroup frequency

Calculation for the relative frequencies of the pet types:

(1) Relative frequency for dog:

Total frequency is 20.

The frequency for dog is 8.

Relative frequency for dog =  frequency for dog/total frequency

                                             = 8/20

                                             = 0.4

Relative frequency for dog = 0.4.

(2) Relative frequency for cat:

Total frequency is 20.

The frequency for cat is 7.

Relative frequency for cat =  frequency for cat/total frequency

                                             = 7/20

                                             = 0.35

Relative frequency for cat = 0.35.

(3) Relative frequency for bird:

Total frequency is 20.

The frequency for bird is 3.

Relative frequency for bird =  frequency for bird/total frequency

                                             = 3/20

Relative frequency for bird = 0.15.

(4) Relative frequency for fish:

Total frequency is 20.

The frequency for fish is 2.

Relative frequency for fish =  frequency for fish/total frequency

                                             = 2/20

Relative frequency for fish = 0.1.

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Answer:

The value of [tex]$(f \circ g)(x)$[/tex] is [tex]$4+4 x$[/tex] and [tex]$(g \circ f)(x)$[/tex] is [tex]$4 x-16$[/tex].

Step-by-step explanation:

It is given in the question functions f(x) as 4-x and g(x)=-4x.

It is required to find [tex]$(f \circ g)(x)$[/tex] and [tex]$(g \circ f)(x)$[/tex].

To find [tex]$(f \circ g)(x)$[/tex], substitute g(x)=-4x for x in f(x) and simplify the expression.

To find [tex]$(g \circ f)(x)$[/tex], substitute f(x)=4-x for x in g(x) and simplify the expression.

Step 1 of 2

Substitute g(x)=-4x for x in f(x) and simplify the expression.

[tex]$$\begin{aligned}&(f \circ g)(x)=f(g(x)) \\&(f \circ g)(x)=4-g(x) \\&(f \circ g)(x)=4-(-4 x) \\&(f \circ g)(x)=4+4 x\end{aligned}$$[/tex]

Step 2 of 2

Substitute f(x)=4-x for x in g(x) and simplify the expression.

[tex]$$\begin{aligned}&(g \circ f)(x)=g(f(x)) \\&(g \circ f)(x)=-4 f(x) \\&(g \circ f)(x)=-4(4-x) \\&(g \circ f)(x)=4 x-16\end{aligned}$$[/tex]

The slope of the line that represents the relationship is 0.7692

The formula for calculating the slope of a line is expressed as;

Slope = y2-y1/x2-x1

Using the coordinate points (1.3, 1) and (2.6, 2)

Substitute

Slope = 2-1/2.6-1.3

Slope = 1/1.3

Slope = 0.7692

Hence the slope of the line that represents the relationship is 0.7692

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Answer:

42

Step-by-step explanation:

    Two tangents from a point outside the circle to some point to a circle are of equal lengths.

CB = 3+ 5 = 8

CD = 3+ 4 = 7

DA = 4 + 9 = 13

AB = 9+ 5 = 14

Perimeter = 8 + 7 + 13 + 14

                = 42

Answer: (35,35,110) and (40,60,80)

Step-by-step explanation:

If given all 3 side lengths, it can only describe one triangle. Angles alone are not enough to guarantee how a triangle looks.

side lengths of 6 ft, 8 ft, and 10 ft - no because all sides are defined

angle measurements of 35°, 35°, and 110° - yes because three angles can describe more than one triangle

angle measurements of 30°, 40°, and 50° - no because the sum of the angles is 120 degrees. Triangles have a combined total of 180 degrees

angle measurements of 40°, 60°, and 80° - yes because 3 angles

side lengths of 4 cm, 6 cm, and 9 cm 6 - no because all sides are defined

Brainliest please :D

Answer:

10

Step-by-step explanation:

In a 45-45-90 right triangle, the hypotenuse is sqrt(2) times the length of the leg.

The rule that describes a reflection across the line y = x is given as (x, y) ⇒ (y, x)

Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, translation, rotation and dilation.

Translation is the movement of a point either up, down, left or right on the coordinate plane.

The rule that describes a reflection across the line y = x is given as (x, y) ⇒ (y, x)

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Answer:

The Answer is B.

Step-by-step explanation:

If you were to look at the slope, 3x. You would look to see if the graphs have a slope of 3x. You go three up and one right.

The inequality are –6x + 15 < 10 – 5x and a number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right.

Inequality are expressions not separated by an equal sign. Given the inequality expression below;

–3(2x – 5) < 5(2 – x)

Expand

-6x  + 15 < 10 - 5x

Collect the like terms

-6x + 5x < 10 - 15

-x < -5

x > 5

Hence the correct representations of the inequality are –6x + 15 < 10 – 5x and a number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right.

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Point A: ( -1, 4 )

Point B: ( 1 ,0 )

To get from Point B to Point A, we must rise 4 and run -2 So using rise over run we have m = -2

Explanation:

After observing:

And

[tex]\sf slope \ (m) : \dfrac{y_2 - y_1}{x_2- x_1} = \dfrac{rise}{run} \ \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points[/tex]

[tex]\rightarrow \sf slope \ (m) = \dfrac{rise}{run} = \dfrac{4-0}{-1-1} = \dfrac{4}{-2} = -2[/tex]

Answer:

b. The graph of g(x) is a translation 10 units right and 8 units up from the graph of f(x).

Step-by-step explanation:

See attached image.

Both distributions are bell-shaped and symmetric but where the peak falls on the number line is determined by the mean.

The given statement is false.

A bell curve is a graph depicting the ordinary distribution, which has a shape harking back to a bell. The top of the curve suggests the mean, mode, and median of the records accrued.

The everyday distribution is a bell-fashioned and symmetrical distribution this is used to calculate the opportunity. in the everyday distribution, the mathematics means, mode, and median are usually the same, and the normal distribution is likewise called the Gaussian distribution.

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