A side of the triangle below has been extended to form an exterior angle of 135°. Find the value of xx.

The angles that are formed by the parallel lines and the transversal are:

1. Vertical Angles

2. Same-side Exterior Angles

3. Corresponding Angles

4. Alternate Interior Angles

5. Alternate Exterior Angles

6. Same-side Interior Angles

7. Adjacent Angles

The following are special angle pairs that are formed when a transversal intercepts two parallel lines:

1. Vertical Angles: These are nonadjacent angles that share the same vertex and are directly opposite each other. An example of such angle pair is angle 6 and angle 7.

2. Same-side Exterior Angles: These are exterior angles that lie on the same side of a transversal but on sperate parallel lines. Example include angle 2 and angle 8.

3. Corresponding Angles: These angles are located on each parallels lines that are cut across by a transversal and lie relatively in the same corner to each other. An example is, angle 1 and angle 5.

4. Alternate Interior Angles: an example of such pair of interior angles that lie on opposite side of a transversal is, angle 3 and angle 6.

5. Alternate Exterior Angles: An example of a pair of alternate exterior angle is angle 2 and 7.

6. Same-side Interior Angles: These pair of angles are interior angles on the same side of a transversal. Example of such pair of angles is, angle 4 and angle 6.

7. Adjacent Angles: These are angles that share a common side and a vertex, an example is: angle 1 and angle 2.

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Answer:

6.5ft

Step-by-step explanation:

[tex]A=s^{2} \\42.25=s^{2} \\\sqrt[2]{42.25}=\sqrt[2]{s} \\6.5=s[/tex]

Answer:

6.5ft

Step-by-step explanation:

Let f(x) be a function; thus, the reflection across the y-axis of f(x) is given by f(-x).

Therefore, in our case,

Simplifying,

Thus, the answer is g(x)=x^3-8x^2+9x+11, the first option (top to bottom).

Let us divide 6 by 1/4

6/1 ÷ (1/4)

6/1*4/1 (Turning the second fraction upside down and multiplying it by the first fraction)

24 (Multiplying)

The answer is 24.

Answer:

Step-by-step explanation:

Since there are four 1/4 in 1 then you have to multiple 6*4= 24!

Albert floating in hot air balloon and Isabelle standing at ground are 29 meters far apart from each other.

What is hot air balloon?

A hot air balloon is a lighter in weigh than air. It is an object made up of an envelope-like bag that holds heated air. A wicker basket, gondola, or capsule suspended below transports people and a heat source, typically an open flame produced by burning liquid propane. A capsule also carries passengers in some long-distance or high-altitude balloons.

Lets understand with the help of a right angle triangle, The point from where the hot air balloon taken off be point A, and the point where Isabelle is standing is point B, and the point where the balloon is point C.

The AB= distance between Isabelle and the point from where hot air  balloon taken off = base of the imagined triangle,

AC = height at which hot air balloon is floating = perpendicular of the imagined triangle

BC = distance between Isabelle and hot air balloon = Hypotenuse of the imagined triangle

Applying Pythagoras theorem,

(BC)² = (AC)² + (AB)²

(BC)² = (20)² + (21)²

BC = 29

Hence Albert and Isabelle are 29 meters far apart.

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On comparing the given expressions we get-

[tex]9^{-2} < (\frac{1}{9}) ^{-1}[/tex]

[tex](\frac{1}{9}) ^{-1} < (\frac{1}{9}) ^{-2}[/tex]

[tex]9^{-1} > 9^{-2}[/tex]

Here, we are given 3 pairs of expression. Let us evaluate them one by one.

[tex]9^{-2}[/tex] _ [tex](\frac{1}{9}) ^{-1}[/tex]

The negative exponent means that the base is the reciprocal raised to a positive power. Thus, [tex]9^{-2}[/tex] can be written as- [tex](\frac{1}{9}) ^{2}[/tex] = 1/81

similarly, [tex](\frac{1}{9}) ^{-1}[/tex] can be written as- [tex](9}) ^{1}[/tex] = 9

Thus, the expression becomes-

1/81 _ 9

clearly we can see that 1/81 < 9

Now, we have [tex](\frac{1}{9}) ^{-1}[/tex] _ [tex](\frac{1}{9}) ^{-2}[/tex]

As shown above, the expression can be simplified as-

[tex](9) ^{1}[/tex] _ [tex](9) ^{2}[/tex]

9 _ 81

clearly we can see that 9 < 81

Next, we have- [tex]9^{-1}[/tex] _ [tex]9^{-2}[/tex]

we can write this as-

1/9 _ 1/81

Clearly, 1/9 > 1/81

Hence, we have solved the given inequalities.

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25(8+ x)=14

25*8+ 25x =14

200+ 25x= 14

25x=14-200

25x = -186

x = -186/25

x= -7.44

Answer:

Domain: A, [tex)(-\infty, \infty)[/tex]

Range: [tex][4, \infty)[/tex]

Step-by-step explanation:

The domain is the set of x-values and the range is the set of y-values.

The length of the diameter of the circle is found as the 2×(√5).

,

For the given question;

The equation of the circle is given as;

(x-4)^2+(y-2)^2=5

Comparing the equation of the circle with the standard form.

Radius r² = 5

Then, r = √5

Now, the diameter is the twice of the radius.

Diameter = 2×radius

Diameter = 2×(√5)

Thus, the length of the diameter of the circle is found as the 2×(√5).

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Using the normal distribution, it is found that:

a) The variable used in this problem is: The time (in hours) a 4-year old spends unsupervised per day.

b) The distribution is: X ~ N(3, 1.8).

c) The probability is P(X < 1) = 0.1335, and is given by the bottom left graph.

d) The percentage of children who spend over 10 hours a day unsupervised is of 0.01%.

e) 90% of the children spend at least 0.7 hours unsupervised.

The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is given by the following rule:

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

The variable used in this problem is:

The time (in hours) a 4-year old spends unsupervised per day, as the distribution involves only 4-year old children, and the mean and the standard deviation are measured in hours.

The mean and the standard deviation of the distribution are given, respectively, by:

[tex]\mu = 3, \sigma = 1.8[/tex].

Hence the distribution can be described approximately as follows:

X ~ N(3, 1.8).

The probability that a person spends less than 1 hour a day unsupervised is the p-value of Z when X = 1, hence:

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

Z = (1 - 3)/1.8

Z = -1.11

Z = -1.11 has a p-value of 0.1335.

The bottom left graph shows this probability, as the number in hours cannot be less than 0(there is no negative number of hours).

The proportion of children who spends over 10 hours a day unsupervised is one subtracted by the p-value of Z when X = 10, hence:

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

Z = (10 - 3)/1.8

Z = 3.89

Z = 3.89 has a p-value of 0.9999

1 - 0.9999 = 0.0001, hence the percentage is of 0.01%.

For item e, the measure is the 10th percentile, which is X when Z = -1.28, hence:

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

-1.28 = (X - 3)/1.8

X - 3 = -1.28 x 1.8

X = 0.7 hours.

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Given:

There are given that the slope and the point:

Explanation:

To find the equation, first, we need to see the formula for slope-intercept form:

So,

From the slope-intercept formula;

Where,

Now,

We need to find the value of b by using given information:

So,

Put all the given values into the given slope-intercept form:

Then,

Put the value of b and m into the slope-intercept form;

So,

Final answer:

Hence, the equation of a line is shown below;

The probabilities that have been calculated here are:

The probability that he is a smoker = 0.08 + 0.16

= 0.24

The given probability that has been calculated is 0.24.

The probability that he does not have lung disease = 0.16 + 0.73

= 0.89

The probability that he has lung disease given that he is a smoker

= 0.08 / 0.08 + 0.16

= 0.08 / 0.24

= 0.333

The probability here is calculated to be 0.333

The probability that he has lung cancer given that he does not smoke

= 0.03 / 0.03 + 0.73

= 0.03 / 0.76

= 0.0395

The given probability here is 0.0395

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The equation of a line in 2 point form is

So, inputting the points, we have

So, the equation of our line is y = x + 4

Given the following expression:

You need to follow the steps shown below in order to solve the exercise:

1. Since you know the value of "x", you must substitute it into the given equation:

2. Now you must solve the multiplication:

3. Finally, you need to solve the addition in order to find the value of the expression. Therefore, you get that the result is the following:

The answer is:

A (0,2) B (5,4)

C(1,8) D( 3,3)

Apply the slope formula:

For AB

For CD

So both slopes are negative reciprocals of each other.

They are perpendicular lines.

For a polynomial to be in standard form, the terms are arranged from the highest exponent to the lowest exponent.

Thus, from the polynomials given, the polynomial in standard form is:

This is because the term with the highest exponent is the first term, the next exponent is 3, followed by the term with an exponent of 2, then the last term is the term with the least exponent.

ANSWER:

The equation of a line is given by

where m is the slope of the line and (x1,y1) is a point where the line passes through.

In our case we have a point but we don't have the slope yet, so we have to find it. To do this we have to remember that two lines are parallel if and only if their slopes are equal, that is

We know that the line we are looking for is parallel to the line

we notice that this line in written in the slope-intercept form

then its slope is 13.

Since the line is parallel to the one we are looking for, our slope is also 13.

Using the point (9,12) and the slope the equation of the line is

now we have to write in the slope-intercept form

Therefore the line is

Answer:

8 points for solving 6 questions?? Nah thats worth 25 points

Step-by-step explanation:

335 children should be in the park, if the ratio of children to adults at an amusement park is typically 5 to 3 and 201 adults are in the park.

A ratio is the comparison of two similar quantities or the proportion of one similar quantity to another. With the same meaning, ratios can be expressed in three different ways using words or symbols. In other words, ratios can be expressed by sandwiching a fraction bar, the word "to," or the ratio symbol ":" between the two values being compared.

The ratio of ninth-graders to tenth-graders can take on any of the three forms listed below, using the previous example of comparing the two groups of students in Ms. Jones' class:

10 /20

10 to 20

10 : 20

Given ratio of children to adults is 5:3

5 + 3 = 8

5/8 are children and 3/8 are adults

Let the total no. of people be x

3/8 = 201/x

x = 201 × 8/3

  = 536

Now. no. of children is

5/8 × 536

= 335

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Answer:

[tex]3x^2\left(3+x\right)[/tex]

Step-by-step explanation:

Look for common factor: [tex]3x^{2}[/tex] since we take the least exponent

and between numbers (3,9) the common factor is 3.

Thefore, we need to divide [tex]3x^2[/tex] by the equation.

[tex]3x^2(3+x)[/tex].

[tex]9x^2+3x^3[/tex]

[tex]\frac{9x^2}{3x^2} +\frac{3x^3}{3x^2} \\ \\3x^2(3+x)[/tex]

[tex]9x^2+3x^3=3x^2(3+x)[/tex].

Answer: 500,000

Step-by-step explanation: To round the numbers their nearest hundred thousand, first we have to make the first five digits into the lower  number that ends with zero  

Example: 52437 is rounded to the nearest hundred thousand is  52000

Sorry if you don't understand I'm just bad at explaining :) T^T

Part 1

Relative maxima are where the function changes from increasing to decreasing.

Part 2

None, see above.

Part 3

Relative minima are where the function changes from decreasing to increasing.

Part 4

None, see above.

Explanation:

The formula is given below as

By substituting the values, we will have

Hence,

The final answer to the nearest hundredth is

We will first sketch the problem

Let x be the vertical distance above the ground

Using the trigonometric ratio;

cross-multiply

The value of x is 9.

Given:

The length of the tangent lines are given as, 5x and 7x-18.

The objective is to find the value of x.

The two tangents of a circle drawn from a point outside a circle will always be equal.

Then, the value of x can be solved by,

Hence, the value of x is 9.

Answer:

5,12,13

Step-by-step explanation:

first you write out a^2 or a squares + b^2=C ^2 You plug in for a and b the smaller numbers then for c you put the biggest number. Now square everything. And you should get 25 for a. 144 for b. 169 for c. Now add a and b which is25+144 and that equals 169. So 5,12,13 is your answer.

Answer: it is yes

Step-by-step explanation:

When the crate folow top botom nuberto

We need to find the point given the domain and range of the relation:

For domain and range, the result includes the number. Hence, the end values are given by the points.

For point C:

(-6,4)

Because point c is on quadrant two, where x is negative and y is positive.

Also, it takes the higher y value.

For point D:

(6,3)

Because point D is on quadrant 1, where x is positive and y is also positive.