The following flowchart proof with missing statements and reasons proves that if a line intersects two sides of a triangle and divides these sides proportionally, the line is parallel to the third side:

Answer:

Step-by-step explanation:

[tex]1+tan^2\theta=sec^2\theta\\tan^2\theta=sec^2\theta -1 \\tan^2\theta=(sec\theta-1)(sec\theta+1)\\\implies \frac{1}{sec\theta-1} =\frac{sec\theta+1}{tan^2\theta} \\\\and \quad \frac{1}{sec\theta+1} =\frac{sec\theta-1}{tan^2\theta} \\\\ \frac{1}{sec\theta-1} + \frac{1}{sec\theta+1} = \frac{sec\theta+1}{tan^2\theta} + \frac{sec\theta-1}{tan^2\theta}\\\\=\dfrac{2sec\theta}{tan^2\theta}\\\\=\dfrac{2cos^2\theta}{cos\theta.sin^2\theta}\\\\\\=2cos\theta.cosec^2\theta[/tex]

[tex]\angle PYZ=116^{\circ}[/tex] (angles on a line add to 180 degrees)

[tex]\angle ZYQ=58^{\circ}[/tex] (angle bisector)

[tex]\angle XYQ=122^{\circ}[/tex] (angle addition postulate)

[tex]\angle QYP=58^{\circ}[/tex] (angle bisector)

Reflex [tex]\angle QYP=302^{\circ}[/tex] (an angle and its reflex angle add to 360 degrees)

[tex]\frac{1820728291}{14285714286}[/tex]

Answer:

X=3

Step-by-step explanation:

First you can distribute the 4 to 2x-1 making is 8x-4

8x-4+2x+2=28

Now add like terms

8x+2x-4+2=28, 10x-2=28

Add 2 to both sides

10x=30

Divide both sides by 10

x=3

Answer:

  z = 110°

Step-by-step explanation:

Angles z and the one marked 70° form an linear pair, hence are supplementary.

  z = 180° -70° = 110°

The angle made by two chords is half the sum of the arcs intercepted by those chords. Here, that means ...

  70° = 1/2(60° +x)   ⇒   x = 140° -60° = 80°

The arc w completes the circle of 360°, so we have ...

  w +x +79° +60° = 360°   ⇒   w = 360° -219° = 141°

Finally, z is the average of w and 79°:

  z = (w +79°)/2 = (141° +79°)/2 = 110° . . . as above

The tangent or tanθ in a right-angle triangle is the ratio of its perpendicular to its base. The height of the mountain is 3110.5767 feet.

The tangent or tanθ in a right-angle triangle is the ratio of its perpendicular to its base. it is given as,

[tex]\rm Tangent(\theta) = \dfrac{Perpendicular}{Base}[/tex]

where,

θ is the angle,

Perpendicular is the side of the triangle opposite to the angle θ,

The base is the adjacent smaller side of the angle θ.

The height of the mountain from the first point,

[tex]\tan(29^o) = \dfrac{H}{x+1000}\\\\H = (1000+x) \times \tan(29^o)[/tex]

The height of the mountain from the second point,

[tex]\tan(34^o) = \dfrac{H}{x}\\\\H = x \times \tan(34^o)[/tex]

Equating the height,

H = H

(1000+x) × tan(29°) = x tan( 34°)

x = 4611.5767 feet

Now, the height of the mountain is,

H = x tan(34°)

H = 3110.54776 feet

Hence, the height of the mountain is 3110.5767 feet.

Learn more about Tangent (Tanθ):

https://brainly.com/question/10623976

#SPJ1

Pn(Z>zp)=1−p%

Given a variable X following a normal distribution with mean μ and standard deviation σ, the area below the curve that corresponds to all values that are less than a that is, X<a

is the probability P(X<a). This probability is usually calculated by converting the variable X to a standard normal variable Z (forming z scores) defined by:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

The variable Z follows the standard normal distribution with a mean of 0 and a standard deviation of 1.

The standard normal probabilities are typically found by using the standard normal tables or other computational means such as calculators or software.

Pn(Z>zp)=1−p%

Here Pn is the probability for the standard normal variable.

Learn more about mean here https://brainly.com/question/18060320

#SPJ4

Answer:

Y intercept: (0,2) Slope: 1/3

Step-by-step explanation:

X is horizontal. Y is vertical the slope touches at (0,2).

The slope goes up by one and right by three cause it connects to the line

for the second one all you would have to do is increase the slope first number like 4/3

Answer:

a. What is the measure of ∠CAT?   Answer:  70°

b. What is the measure of ∠BAR?  Answer:  50°

c. What is the measure of ∠RAT?  Answer:   110°

d. What is the measure of ∠CAB? Answer:   130°

e. What is the measure of ∠BAT? Answer:    60°

Step-by-step explanation:

I just looked at the degrees of the protractor.

Hope this helps!

If not, I am sorry.

The missing segment in the image below is 78 units.

An equation is an expression that shows the relationship between two or more variables and numbers.

The ratio or two corresponding sides of similar shapes are in the same proportion.

Let x represent the missing side, hence:

(x + 26)/26 = 48/12

x =78

The missing segment in the image below is 78 units.

Find out more on equation at: https://brainly.com/question/13763238

#SPJ1

The missing term in the expression ___( 2a-1)  is 6b.

An expression is an algebraic statement that consists of variables, constants, and mathematical operators.

The expression 12ab-6b is equivalent to

6b( 2a-1)

(By taking the common factors out of the given expression.)

Therefore, the missing term in the expression is 6b.

To know more about Expression

https://brainly.com/question/14083225

#SPJ1

Based on the data, table that shows a proportional relationship is the first table.

Data is said to be proportional if it increases or decreases at a constant rate.

The first table has proportional data because the height increases by 5 centimeters everyweek, which shows a constant rate.

Note: This question is incomplete; below I attach the missing section:

Learn more about proportional in https://brainly.com/question/7096655?

#SPJ1

Answer:

159.3

Step-by-step explanation:

456 - 121.3 = 334.7

333.7 - 175.4 = 159.3

Hope this helped

Answer:

152

Step-by-step explanation:

You actually don't need to find the thirds number. Just by taking 456 and dividing it by three, you will get your answer and the average of the three numbers.

Answer:

was there a list to choose from

Step-by-step explanation:

19, 26, 33, 40, 47

The statement about the system of of equations that are true are as follows:

The system of equation can be solved as follows;

2x - 7y = - 13

2x + 11y = 1

18y = 14

y = 14 / 18

y = 7 / 9

2x  = 1 - 11(7 / 9)

2x = 1 - 77 / 9

2x = 9 - 77 / 9

2x = -68 / 9

cross multiply

18x = -68

x = -68 / 18

x = -34 / 9

Hence, the statement about the system of of equations that are true are as follows:

learn more on system of equations here:https://brainly.com/question/21620502

#SPJ1

Let [tex]a,b,c[/tex] be the randomly selected lengths. Without loss of generality, suppose [tex]a

[tex]P(A + B \ge C) = P(A + B - C \ge 0)[/tex]

where [tex]A,B,C[/tex] are independent random variables with the same uniform distribution on [0, 1].

By their mutual independence, we have

[tex]P(A=a,B=b,C=c) = P(A=a) \times P(B=b) \times P(C=c)[/tex]

so that the joint density function is

[tex]P(A=a,B=b,C=c) = \begin{cases}1 & \text{if }(a,b,c)\in[0,1]^3 \\ 0 & \text{otherwise}\end{cases}[/tex]

where [tex][0,1]^3=[0,1]\times[0,1]\times[0,1][/tex] is the cube with vertices at (0, 0, 0) and (1, 1, 1).

Consider the plane

[tex]a + b - c = 0[/tex]

with [tex](a,b,c)\in\Bbb R^3[/tex]. This plane passes through (0, 0, 0), (1, 0, 1), and (0, 1, 1), and thus splits up the cube into one tetrahedral region above the plane and the rest of the cube under it. (see attached plot)

The point (0, 0, 1) (the vertex of the cube above the plane) does not belong the region [tex]a+b-c\ge0[/tex], since [tex]0+0-1=-1<0[/tex]. So the probability we want is the volume of the bottom "half" of the cube. We could integrate the joint density over this set, but integrating over the complement is simpler since it's a tetrahedron.

Then we have

[tex]\displaystyle P(A+B-C\ge0) = 1 - P(A+B-C < 0) \\\\ ~~~~~~~~ = 1 - \int_0^1\int_0^{1-a}\int_{a+b}^1 P(A=a,B=b,C=c) \, dc\,db\,da \\\\ ~~~~~~~~ = 1 - \int_0^1 \int_0^{1-a} (1 - a - b) \, db \, da \\\\ ~~~~~~~~ = 1 - \int_0^1 \frac{(1-a)^2}2\,da \\\\ ~~~~~~~~ = 1 - \frac16 = \boxed{\frac56}[/tex]

Using the rule of dilation, 5/4, the length of C'A' is: A. 10 units.

Dilation is a form of transformation that creates a new image that is similar to the original one.

The images formed are similar images shown in the diagram given, therefore, using the rule of dilation, Dy = 5/4, we would have:

CA × 5/4 = C'A'

Plug in the given value

8 × 5/4 = C'A'

10 = C'A'

C'A' = 10 units

Learn more about dilation on:

https://brainly.com/question/3457976

#SPJ1

Trigonometric substitution may useful when integrating the integrals root of a sum or difference of two squares.

In arithmetic, trigonometric substitution is the substitution of trigonometric features for other expressions. In calculus, trigonometric substitution is a way of comparing integrals.

Moreover, one can also use trigonometric identities to simplify sure integrals containing radical expressions.

You can use trig substitution even when you do not have square roots. particularly, if you have an integrand that looks like an expression in the square roots proven inside the above table, then you can use trig substitution.

Learn more about Trigonometric substitution here: https://brainly.com/question/17199316

#SPJ4

Answer:

33x - 13 = 13x + 7

Step-by-step explanation:

If "G" is the midpoint of line FH, then both segments (lines FG and GH) must be the same length. Therefore, to find "x", you can set both segments equal to each other. After doing this, you can simplify and isolate to find "x".

FG = 33x - 13

GH = 13x + 7

FG = GH

33x - 13 = 13x + 7

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Assuming that your equation should}\\\huge\textbf{look like that: }[/tex]

[tex]\mathbf{33x - 13 = 13x + 7}[/tex]

[tex]\huge\textbf{If so:}[/tex]

[tex]\mathbf{33x - 13 = 13x + 7}[/tex]

[tex]\huge\textbf{SUBTRACT 13x to BOTH SIDES}[/tex]

[tex]\mathbf{33x - 13 - 13x = 13x + 7 - 13x}[/tex]

[tex]\huge\textbf{SIMPLIFY IT!}[/tex]

[tex]\mathbf{20x - 13 = 7}[/tex]

[tex]\huge\textbf{ADD 13 to BOTH SIDES}[/tex]

[tex]\mathbf{20x - 13 + 12 = 7 + 13}[/tex]

[tex]\huge\textbf{SIMPLIFY IT!}[/tex]

[tex]\mathbf{20x = 20}[/tex]

[tex]\huge\textbf{DIVIDE 20 to BOTH SIDES}[/tex]

[tex]\mathbf{\dfrac{20x}{20} = \dfrac{20}{20}}[/tex]

[tex]\huge\textbf{SIMPLIFY IT!}[/tex]

[tex]\mathbf{x = \dfrac{20}{{20}}}[/tex]

[tex]\mathbf{x = 1}[/tex]

[tex]\huge\text{Answer: \boxed{\mathsf{33x - 13 = 13x + 7}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

Step-by-step explanation:

1. R= {(2, 2), (3, 5), (4, 10), (4, 17)}

2. Domain = {1, 2, 3, 4}

3.  Range = {2, 3, 4, 5, 10, 17}

The domain of a function is the set of values that we are allowed to plug into our function.

The range of a function is the set of values that the function assumes.

Given:

R = { ( 1 + x , 1 + x^2 ) ∶ x≤ 4, ∈ }

1) R= {(2, 2), (3, 5), (4, 10), (4, 17)}

2) Domain = {1, 2, 3, 4}

3) Range = {2, 3, 4, 5, 10, 17}

Learn more about this concept here:

https://brainly.com/question/13005066

#SPJ1

Yes, the bathroom have enough water and shampoo for 35 long haired and 40 short haired members.

Inequality can be define as the relation of equation contains the symbol of ( ≤, ≥, <, >) instead of equal sign in an equation.

For 35 long haired and 40 short haired member.
Put this values in the given equation.

For water 70L+60S < 5600
  70 x 35 + 60 x 40
2450+2400
4850 <5600
inequality holds

For shampoo 0.02L+0.01S ≤ 1.50
0.02 x 35 + 0.01 x 40
0.7 + 0.4
1.1 < 1.50
inequality holds

Thus, the bathroom have enough water and shampoo for 35 long haired and 40 short haired members.

Learn more about inequality here:

brainly.com/question/14098842

#SPJ1

If the sample size is n=40 ,mean of 20 and a standard deviation then the sampling distribution is normally distributed.

Given sample size is 40, sample mean is 20, sample standard deviation is 5.

We have to find whether the distribution is normally distributed or not.

Normal distribution is an arrangement of a data set in which most values cluster in the middle of the range and the rest taper off simultaneously towards either extreme. It may be one tailed or two tailed also.

Yes the given distribution whose sample size is 40, sample mean of 20 and sample standard deviation of 5 is normally distributed as the sample size is greater than 30.

Signs of normal distribution are:

Hence the sampling distribution is normally distributed.

Learn more about normal distribution at https://brainly.com/question/4079902

#SPJ4

ye answer's here  

Answer:

30°

Step-by-step explanation:

x + 90 = 2 × 60 ( angle at center = 2 × angle at circumference.)

x +90 = 120

x = 120-90

x = 30°

Answer:

t ≥ 192

Step-by-step explanation:

To isolate t in the inequality 6.50t ≥1248, divide by 6.50 on both sides. There you are left with t ≥ 192 which means the cheerleading team must sell 192 t-shirts or more to make their profit goal. Graph this using a closed circle at 192 moving upwards. (You didn't include a picture of the given graphs in your problem)

Answer:

{(-3, -2), (-4, 3), (-1, 0), (3, -7)}

Step-by-step explanation:

When you find the inverse of a function you swap the x and the y. So let's look at a couple examples and see what happens to the x and y values

Radical:

[tex]y=\sqrt{x}[/tex]

So let's just look at perfect squares so it's a bit easier to understand

(0, 0)

(4, 2)

(9, 3)

Now let's find the inverse:

[tex]x=\sqrt{y}[/tex]

Now to make this concept a bit easier to understand let's leave it in this form. Well the first notable thing, is that any operations applied to y will now apple to x, and any operations applied to x will apply to y (in this case the square root).

So if I input 9 as the y, the x will be 3

If I input 4 as y, the x will become 2

Some points are

(0, 0)

(2, 4)

(9, 3)

You'll notice the x and y values are swapped, well it's simply because you swap the x and y's place. this is also why the domain and range are swapped

So given the points {(-2, -3),  (3, -4), (0, -1), (-7, 3)} you simply swap the x and y to get:            {(-3, -2), (-4, 3), (-1, 0), (3, -7)}

Answer:

D

Step-by-step explanation:

Answer:

848.23 mm²

Step-by-step explanation:

LA = πdh

LA = 3.14159 × 18 mm × 15 mm

LA = 848.23 mm²

Answer:

your slow

Step-by-step explanation:

Step-by-step explanation:

good study habits will help! study before you plan on sleeping and designate times to do your work