Are these triangles congruent?

Answer:

See below

Step-by-step explanation:

We want to prove that

[tex]\sin(x)\tan(x) = \dfrac{1}{\cos(x)} - \cos(x), \forall x \in\mathbb{R}[/tex]

Taking the RHS, note

[tex]\dfrac{1}{\cos(x)} - \cos(x) = \dfrac{1}{\cos(x)} - \dfrac{\cos(x) \cos(x)}{\cos(x)} = \dfrac{1-\cos^2(x)}{\cos(x)}[/tex]

Remember that

[tex]\sin^2(x) + \cos^2(x) =1 \implies 1- \cos^2(x) =\sin^2(x)[/tex]

Therefore,

[tex]\dfrac{1-\cos^2(x)}{\cos(x)} = \dfrac{\sin^2(x)}{\cos(x)} = \dfrac{\sin(x)\sin(x)}{\cos(x)}[/tex]

Once

[tex]\dfrac{\sin(x)}{\cos(x)} = \tan(x)[/tex]

Then,

[tex]\dfrac{\sin(x)\sin(x)}{\cos(x)} = \sin(x)\tan(x)[/tex]

Hence, it is proved

Answer:

C.) <-11, -10>

Step-by-step explanation:

Let's define how to work with vectors.

For two vectors:

V = <a, b>

W = <c, d>

The product of a scalar k and a vector is given by:

k*V = k*<a, b> = <k*a, k*b>

And the sum (or difference) of two vectors is given by:

V ± W  = <a, b> ± <c, d> = <a ± c, b ± d>

Now that we know this, we can solve the problem.

Here we have the vectors:

u = <2, 1>

v = <5, 4>

then:

2u - 3*v = 2*<2, 1> - 3*<5, 4>

             = <2*2, 2*1> - <3*5, 3*4>

             = <4, 2> - <15, 12>

             = <4 - 15, 2 - 12>

             = < -11, -10>

Then the correct option is C.

Given:

The given statements are:

[tex]p:2x=16[/tex]

[tex]q:3x-4=20[/tex]

To find:

The converse of [tex]p\to q[/tex].

Solution:

The statement [tex]p\to q[/tex] means if p, then q and the converse of this statement is [tex]q\to p[/tex].

[tex]q\to p[/tex] means if q , then p.

We have, [tex]p:2x=16[/tex] and [tex]q:3x-4=20[/tex].

So, the converse of given statement is:

[tex]q\to p:[/tex] If [tex]3x-4=20[/tex], then [tex]2x=16[/tex].

Therefore, the correct option is D.

Answer: Therefore, the correct option is D.

Step-by-step explanation:

Given:

p: 2x = 16

q: 3x – 4 = 20

RE

Which is the converse of p - q?

ООО

If 2x + 16, then 3x - 47 20.

If 3x - 420, then 2x + 16.

If 2x = 16, then 3x – 4 = 20.

If 3x - 4 = 20, then 2x = 16

To find:

The converse of .

Solution:

The statement  means if p, then q and the converse of this statement is .

means if q , then p.

We have,  and .

So, the converse of given statement is:

If , then .

Therefore, the correct option is D.

Answer:

x+53+69=180

x+122=180

x=180-122

x=58

Solution :

a).

Given :

R = 0.636, [tex]$S_x = 99$[/tex], [tex]$S_y=113, M_x=108, M_y=129$[/tex]

Here R = correlation between the two variables

        [tex]$S_x , S_y$[/tex] =  sample standard deviations of the distance and travel time between the two train stops, respectively.

      [tex]$M_x, M_y$[/tex] = means of the distance and travel between two train stops respectively.

The slope of the regression line is given by :

Regression line, [tex]b_1[/tex]  [tex]$=R \times \left(\frac{S_y}{S_x}\right)$[/tex]

                            [tex]$=0.636 \times \left(\frac{113}{99}\right)$[/tex]

                            = 0.726

Therefore, the slope of the regression line [tex]b_1[/tex] is 0.726

The equation of the regression line is given by :

[tex]$\overline {y} = b_0+b_1 \overline x$[/tex]

The regression line also has to pass through the two means. That is, it has to pass through points (108, 129). Substituting these values in the equation of the regression line, we can get the value of the line y-intercept.

The y-intercept of the regression line [tex]$b_0$[/tex] is given by :

[tex]$b_0=M_y-(b_1 \times M_x)$[/tex]

  = 129 - (0.726 x 108)

  = 50.592

Therefore, the equation of the line is :

Travel time = 20.592 + 0.726 x distance

b).[tex]\text{ The slope of the line predicts that it will require 0.726 minutes}[/tex] for each additional mile travelled.

The intercept of the line, [tex]$b_0$[/tex] = 0.529 can be seen as the time when the distance travelled is zero. It does not make much sense in this context because  it seems we have travelled zero  distance in 50.529 minutes, but we could interpret it as that the wait time after which we start travelling and calculating the distance travelled and the additional time required per mile. Or we could view the intercept value as the time it takes to walk to the train station before we board the train. So this is a fixed quantity that will be added to travel time. It all depends on the interpretation.

c). [tex]$R^2=0.404$[/tex]

This means that the model accounts for around 40.4% variation in the travel time.

Answer:

B. y + z = x

Step-by-step explanation:

x is an exterior angle of the triangle.

y and z are the opposite angles opposite the exterior angle.

The exterior angle theorem of a triangle states that the measure of an exterior angle equals the measure of the sum of the two angles opposite the exterior angle.

Thus:

y + z = x

Answer:

[tex]radius=6.68cm[/tex]

Step-by-step explanation:

Formula to find radius:

[tex]r=\frac{C}{2\pi }[/tex]

[tex]r=42/2\pi[/tex]

[tex]r=42/2(3.14)[/tex]

[tex]r=6.68cm[/tex]

hope this helps......

9514 1404 393

Answer:

  4² = 16

Step-by-step explanation:

The applicable rule of exponents is ...

  1/a^-b = a^b

So, ...

 [tex]\dfrac{1}{4^{-2}}=\boxed{4^2 = 16}[/tex]

_____

Additional comment

If you were to evaluate this using the Order of Operations, you would evaluate the exponent first:

  1/4^-2 = 1/(1/16)

Then, you would do the division.

 1/(1/16) = 16

__

We sometimes find it convenient to manipulate exponential terms to the form with the smallest positive exponents before we begin the evaluation.

Answer:

The equation of the line is [tex]y + 3 = m(x + 4)[/tex], in which m is found as such [tex]am = -1[/tex], considering a the slope of the given line.

Step-by-step explanation:

Equation of a line:

The equation of a line, in point-slope form, is given by:

[tex]y - y_0 = m(x - x_0)[/tex]

In which m is the slope and the point is [tex](x_0,y_0)[/tex]

Perpendicular lines:

If two lines are perpendicular, the multiplication of their slopes is -1.

Passes through the point (-4,-3)

This means that [tex]x_0 = -4, y_0 = -3[/tex]

So

[tex]y - y_0 = m(x - x_0)[/tex]

[tex]y - (-3) = m(x - (-4))[/tex]

[tex]y + 3 = m(x + 4)[/tex]

The equation of the line is [tex]y + 3 = m(x + 4)[/tex], in which m is found as such [tex]am = -1[/tex], considering a the slope of the given line.

Step-by-step explanation:

{x:x is an integer where x>-3 and x<3}

Answer:

n = 975

Step-by-step explanation:

[tex]a_1 = 5 = 5 \times 1\\a_2 = 10 = 5 \times 2\\\\Therefore, \ a_n = 5 \times n\\[/tex]

[tex]Given \ a_n = 4875\\\\So, a_n = 5 \times n \\\\=> 4875 = 5 \times n\\\\=>\frac{4875}{5} = n\\\\=> 975 = n[/tex]

Answer:

(a) There is a significant relationship between y and [tex]x_1, x_2, x_3, x_4[/tex]

(b) [tex]SSE_{(x_1 ,x_2 ,x_3 ,x_4) }= 45[/tex]

(c) [tex]SSE_{(x_2,x_3)} = 100[/tex]

(d) [tex]x_1[/tex] and [tex]x_4[/tex] are significant

Step-by-step explanation:

Given

[tex]y = 17.6+3.8x_1 - 2.3x_2 +7.6x_3 +2.7x_4[/tex] --- estimated regression equation

[tex]n = 30[/tex]

[tex]p = 4[/tex] --- independent variables i.e. x1 to x4

[tex]SSR = 1760[/tex]

[tex]SST = 1805[/tex]

[tex]\alpha = 0.05[/tex]

Solving (a): Test of significance

We have:

[tex]H_o :[/tex] There is no significant relationship between y and [tex]x_1, x_2, x_3, x_4[/tex]

[tex]H_a :[/tex] There is a significant relationship between y and [tex]x_1, x_2, x_3, x_4[/tex]

First, we calculate the t-score using:

[tex]t = \frac{SSR}{p} \div \frac{SST - SSR}{n - p - 1}[/tex]

[tex]t = \frac{1760}{4} \div \frac{1805- 1760}{30 - 4 - 1}[/tex]

[tex]t = 440 \div \frac{45}{25}[/tex]

[tex]t = 440 \div 1.8[/tex]

[tex]t = 244.44[/tex]

Next, we calculate the p value from the t score

Where:

[tex]df = n - p - 1[/tex]

[tex]df = 30 -4 - 1=25[/tex]

The p value when [tex]t = 244.44[/tex] and [tex]df = 25[/tex] is:

[tex]p =0[/tex]

So:

[tex]p < \alpha[/tex] i.e. [tex]0 < 0.05[/tex]

Solving (b): [tex]SSE(x_1 ,x_2 ,x_3 ,x_4)[/tex]

To calculate SSE, we use:

[tex]SSE = SST - SSR[/tex]

Given that:

[tex]SSR = 1760[/tex] ----------- [tex](x_1 ,x_2 ,x_3 ,x_4)[/tex]

[tex]SST = 1805[/tex]

So:

[tex]SSE_{(x_1 ,x_2 ,x_3 ,x_4)} = 1805 - 1760[/tex]

[tex]SSE_{(x_1 ,x_2 ,x_3 ,x_4) }= 45[/tex]

Solving (c): [tex]SSE(x_2 ,x_3)[/tex]

To calculate SSE, we use:

[tex]SSE = SST - SSR[/tex]

Given that:

[tex]SSR = 1705[/tex] ----------- [tex](x_2 ,x_3)[/tex]

[tex]SST = 1805[/tex]

So:

[tex]SSE_{(x_2,x_3)} = 1805 - 1705[/tex]

[tex]SSE_{(x_2,x_3)} = 100[/tex]

Solving (d): F test of significance

The null and alternate hypothesis are:

We have:

[tex]H_o :[/tex] [tex]x_1[/tex] and [tex]x_4[/tex] are not significant

[tex]H_a :[/tex] [tex]x_1[/tex] and [tex]x_4[/tex] are significant

For this model:

[tex]y =11.1 -3.6x_2+8.1x_3[/tex]

[tex]SSE_{(x_2,x_3)} = 100[/tex]

[tex]SST = 1805[/tex]

[tex]SSR_{(x_2 ,x_3)} = 1705[/tex]

[tex]SSE_{(x_1 ,x_2 ,x_3 ,x_4) }= 45[/tex]

[tex]p_{(x_2,x_3)} = 2[/tex]

[tex]\alpha = 0.05[/tex]

Calculate the t-score

[tex]t = \frac{SSE_{(x_2,x_3)}-SSE_{(x_1,x_2,x_3,x_4)}}{p_{(x_2,x_3)}} \div \frac{SSE_{(x_1,x_2,x_3,x_4)}}{n - p - 1}[/tex]

[tex]t = \frac{100-45}{2} \div \frac{45}{30 - 4 - 1}[/tex]

[tex]t = \frac{55}{2} \div \frac{45}{25}[/tex]

[tex]t = 27.5 \div 1.8[/tex]

[tex]t = 15.28[/tex]

Next, we calculate the p value from the t score

Where:

[tex]df = n - p - 1[/tex]

[tex]df = 30 -4 - 1=25[/tex]

The p value when [tex]t = 15.28[/tex] and [tex]df = 25[/tex] is:

[tex]p =0[/tex]

So:

[tex]p < \alpha[/tex] i.e. [tex]0 < 0.05[/tex]

Hence, we reject the null hypothesis

Now,

1 million = 10 lakhs

4 millions = 10 * 4

= 40 lakhs

There are 40 lakhs in 4 millions.

I hope it's help you...

Mark me as brainliest...

Answer: There are 40 lakhs in 4 million.

Step-by-step explanation:

A lakh is 1,00,000. We can divide 4 million by 1,00,000 to get our answer.

[tex]\frac{4,000,000}{1,00,000}[/tex]

The 5 zeros on the 4 million and on 1,00.000 cancel each other out giving us

[tex]\frac{40}{1} \\40[/tex]

Answer:

Tuesday's z-score was of -1.325.

The percentile rank of sales for this day was the 9.25th percentile.

Step-by-step explanation:

Z-score:

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

A department store, on average, has daily sales of $21,000. The standard deviation of sales is $3600.

This means that [tex]\mu = 21000, \sigma = 3600[/tex]

On Tuesday, the store sold $16,230 worth of goods. Find Tuesday's z score.

This is Z when X = 16230. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{16230 - 21000}{3600}[/tex]

[tex]Z = -1.325[/tex]

Tuesday's z-score was of -1.325.

What is the percentile rank of sales for this day

This is the p-value of Z = -1.325.

Looking at the z-table, this is of 0.0925, and thus:

The percentile rank of sales for this day was the 9.25th percentile.

Answer:

A. Whole numbers less than or equal to 100

Step-by-step explanation:

The domain is the set of x numbers that can be plugged in to a certain equation.

Since the capacity of this movie theater is 100, x can be between 0 and 100, inclusive.

Answer choice A makes sense because whole numbers are definitionally positive integers and this choice caps out at 100.

Answer:

Tan A = 8/15

Sin A = 8/17

Cos A = 15/17

I start feeling tired now

Answer:

[tex]\textbf{Hello!}[/tex]

[tex]\Longrightarrow2^2+2z=0[/tex]

[tex]\Longrightarrow x_{1,\:2}=\frac{-2\pm \sqrt{2^2-4\cdot \:1\cdot \:0}}{2\cdot \:1}[/tex]

[tex]\Longrightarrow \sqrt{2^2-4\cdot \:1\cdot \:0}[/tex]

[tex]\Longrightarrow =\sqrt{2^2-0}[/tex]

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

[tex]\Longrightarrow=2[/tex]

[tex]\Longrightarrow x_{1,\:2}=\frac{-2\pm \:2}{2\cdot \:1}[/tex]

[tex]\Longrightarrow x_1=\frac{-2+2}{2\cdot \:1},\:x_2=\frac{-2-2}{2\cdot \:1}[/tex]

[tex]\Longrightarrow\frac{-2+2}{2\cdot \:1}[/tex]

[tex]\Longrightarrow =\frac{0}{2\cdot \:1}[/tex]

[tex]\Longrightarrow =\frac{0}{2}[/tex]

[tex]=0[/tex]

[tex]\Longrightarrow\frac{-2-2}{2\cdot \:1}[/tex]

[tex]\Longrightarrow =\frac{-4}{2\cdot \:1}[/tex]

[tex]\Longrightarrow =\frac{-4}{2}[/tex]

[tex]\Longrightarrow =-\frac{4}{2}[/tex]

[tex]=-2[/tex]

[tex]x=0,\:x=-2\Longleftarrow[/tex]

[tex]\underline{HOPE ~IT~HELPS}[/tex]

D. 63

2a+5b+3c

2(12)+5(6)+3(3)

24+30+9=63

Hope this helps! :)

Answer:

1000

Step-by-step explanation:

Volume = 10 * 10 * 10 = 1000

Answer:

[tex]Volume = 1000[/tex]

Step-by-step explanation:

Formula to find volume of cube:

[tex]Volume=a^{3}[/tex]

[tex]Volume = 10^{3}[/tex]

[tex]Volume = 10*10*10[/tex]

[tex]Volume = 1,000[/tex]

hope this helps.....

Answer:

576

Step-by-step explanation:

5 square root 2 is 25

25 minus 1 is 24

24 square root 2 is 576

Answer:

25

Step-by-step explanation:

[tex](5\sqrt{(2-1)} ^{2}[/tex]

[tex](5\sqrt{1}) ^{2}[/tex]

Answer:

4.2025 [tex]\pi m^{2}[/tex]

Step-by-step explanation:

Answer:

The other side is 7.48 yards.

Step-by-step explanation:

Given that,

Hypotenuse = 15 yards

One leg = 13 yards

We need to find the length of the other leg. We can use the Pythagoras theorem to find it such that,

[tex]H^2=b^2+h^2[/tex]

Where

h is other leg

Put all the values,

[tex]h=\sqrt{H^2-b^2} \\\\h=\sqrt{(15)^2-(13)^2} \\\\h=7.48\ yd[/tex]

So, the other side is 7.48 yards.

Answer:

m = 6

n = 2√3

Step-by-step explanation:

Reference angle = 30°

Hypotenuse = 4√3

Opposite = n

Adjacent = m

✔️To find m, apply CAH:

Cos θ = Adj/Hypo

Substitute

Cos 30° = m/4√3

4√3 × Cos 30° = m

4√3 × √3/2 = m (cos 30 = √3/2)

(4*3)/2 = m

6 = m

m = 6

✔️To find n, apply SOH:

Sin θ = Opp/Hypo

Substitute

Sin 30° = n/4√3

4√3 × Sin 30° = n

4√3 × ½ = n (Sin 30 = ½)

2√3 = n

n = 2√3

Answer:

(A.)

21% selected health care as the sector most likely to lead the market in the next 12 months.

47% of managers classified themselves as bullish or very bullish on the stock market.

(B.)

The average return expected on equities over the next 12 months for equities was 11.2% for the population of investment managers.

(C.)

The length of time it will take for technology and telecom stocks to resume sustainable growth is estimated to be about 2.5 years by investment managers.

Step-by-step explanation:

Descriptive statistics gives a quantitative evaluation of particular scenario or information.

Here, the percentage of people who selected health care to lead the market in the next 12 months and the the percentage of managers who classified themselves as bullish or very bullish are examples of descriptive statistics.

The inference Given in the problem is about all investment managers, which is the population mean.

And the lengtb of time it will take for technology and telecom stocks to resume sustainable growth is estimated to be about 2.5 years by investment managers.

Answer: Choice D

[tex]x_n = f(x_{n-1})[/tex]

This basically says "the nth term is found by computing math, aka evaluating some function, based on the (n-1)th term".

As an example, we could have a function that simply squares the input

Let's say we started at 5. It squares to 25 which in turns squares to 625, and so on. Each new term is based on the old term. Namely, we squared the old n-1 term to get the new nth term.

Given:

Lines DE and AB intersect at point C.

To find:

The value of x.

Solution:

In the given figure it is clear that the angles  and  are lie on a straight line AB.

              [Linear pair]

Subtract 5 from both sides.

Divide both sides by 7.

Therefore, the correct option is B.

The area of the irregular polygon is 121.5 units squared.

The irregular polygon can be divided into a rectangle and a pentagon.

Therefore, the area is the sum of the area of the pentagon and the rectangle.

Therefore,

area of the rectangle = 6 × 10 = 60 units²

area of the pentagon = 1/ 2 × perimeter × apothem

area of the pentagon = 1  /  2 × 30 × 4.1

area of the pentagon = 123 / 2

area of the pentagon = 61.5 units²

Therefore,

area of the irregular polygon = 61.5 + 60  = 121.5 units²

learn more on irregular polygon here: https://brainly.com/question/12879526

#SPJ1

Answer:

[tex]40 - 8 = 32 \\ \frac{32}{40} \times 100 \\ = 80\%[/tex]