5
What is the slope of the line that contains the points -3,-
2
O
O
11
11
12
11
11
12
and (3, -8)?

Answer:

[tex]\sqrt{60}[/tex]

Step-by-step explanation:

Use the Pythagorean theorem a^2 + b^2 = c^2

In this case you are given a and c, so set the equation up like

2^2 + b^2 = 8^2

b^2 = 8^2 - 2^2

b =[tex]\sqrt{8^{2} -2^{2} }[/tex]

b =[tex]\sqrt{60}[/tex]

The missing statements that completes the proof that proves that quadrilateral ACDB is a parallelogram is explained below.

A quadrilateral that has the following properties is a parallelogram, in reference to the quadrilateral ACDB in the image given:

Given that ΔCFD ≅ ΔBGA, the proof that quadrilateral ACDB is a parallelogram is given below:

Since we know that ΔCFD ≅ ΔBGA, therefore, CD ≅ BA because corresponding parts of congruent triangles are: congruent.

Since we also know that m∠DCA + m∠CAB = 180°, then we also know that both angles are: supplementary.

Transversal A.F cut the two lines, CD and BA, then the interior angles on the same side of the transversal are: supplementary, thus, we it implies we know that lines CD and BA would be: parallel.

Since one pair of sides (CD and BA) are both parallel and congruent, then we know that quadrilateral ACDB is a parallelogram.

Learn more about parallelogram on:

https://brainly.com/question/20526916

#SPJ1

The simplified expression is the one in option B.

Remember that:

[tex]sec(x) = 1/cos(x)\\\\cos(x) = cos(-x)[/tex]

With these two, we can rewrite the numerator as:

[tex]sec(x)*sin(-x) + tan(-x)\\\\\frac{1}{cos(x)}*sin(-x) + tan(x)\\\\\frac{1}{cos(-x)}*sin(-x) + tan(-x)\\\\2*tan(-x)[/tex]

Replacing that in the given expression, we have:

[tex]\frac{2*tan(-x)}{1 + sec(-x)} = \frac{2*tan(-x)}{1 + 1/cos(-x)}[/tex]

Now, if we multiply and divide by cos(-x), we get:

[tex]\frac{2*tan(-x)}{1 + 1/cos(-x)} = \frac{2*tan(-x)}{1 + 1/cos(-x)}*\frac{cos(-x)}{cos(-x)} \\\\= \frac{2*sin(-x)}{1 + cos(-x)}[/tex]

Now remember that:

[tex]cos(x) = cos(-x)\\sin(-x) = -sin(x)[/tex]

With these two properties:

[tex]\frac{2*sin(-x)}{1 + cos(-x)} = \frac{-2*sin(x)}{1 + cos(x)}[/tex]

Then the correct option is B.

If you want to learn more about trigonometric identities:

https://brainly.com/question/7331447

#SPJ1

Max can select 3 toppings from 10 available toppings for his pizza in 120 ways.

A combination is a mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter. In combinations, you can select the items in any order. Combinations can be confused with permutations.

Thus number of ways in which Max can select 3 toppings from 10 available toppings for his pizza is 10C3

=[tex]\frac{10!}{7!3!}[/tex]

= [tex]\frac{8.9.10}{3!}[/tex]

= 120

Thus Max can select 3 toppings from 10 available toppings for his pizza in 120 ways.

Learn more about Permutations and combinations here :

https://brainly.com/question/13387529

#SPJ4

The length of AB is 25 units

The given parameters are

AC = 15 cm

BC = 20 cm

The triangle is right -angled at C.

So, we have:

AB^2 = AC^2 + BC^2

This gives

AB^2 = 15^2 + 20^2

Evaluate

AB^2 = 625

Take the square roots

AB = 25

Hence, the length of AB is 25 units

Read more about right triangles at:

https://brainly.com/question/6322314

#SPJ1

Answer:

C

Step-by-step explanation:

The solution to a system equations is the point(s) of intersection of the 2 graphs.

Assuming that each square grid represents 1 unit, the coordinates of the point intersection is (-2, 2). This is because drawing a vertical line straight down from the point of intersection, we notice that the x-coordinate of the solution is 2 square units on the left of the origin. Drawing a horizontal line from the point of intersection to the y-axis gives us the y-coordinate of y= 2. Thus, the solution is (-2, 2) and the answer is C.

This method of finding the solution is also known as graphical method, where the graphs of the 2 equations are drawn, and the solution is where the lines cuts through each other.

Alternative methods of solving equations include substitution and elimination methods.

*Origin is the point (0, 0) on the graph, and it is the point in which the two axes intersect.

Additional:

For an example of solving by substitution, do check out the following!

Answer:

68 increased by 43% is 97.24.

Step-by-step explanation:

Multiply 68 by 1.43.

68×1.43=97.24

The answer is 97.24.

Hope this helps!

Answer:

97.24 Absolute change, And the actual difference is 97.24 - 68 = 29.24.

Step-by-step explanation:

Answer:

0.35 km per minute, 7 km in 20 minutes

Step-by-step explanation:

1 hr = 60 minutes

21 km per 60 minutes = 21/60 = 0.35 km per minute

In 20 minutes: 0.35*20 = 7 km

Answer:

I guess the first one is correct........

The z-score of Kimmie is -0.625

The formula for calculating the z-score is expressed as;

z = x-η/s

where

η is the mean

s is the standard deviation

x is the Kimmie score

Substitute the given parameter

z = 85.9-88.4/4.0

z = -2.5/4.0

z = -0.625

Hence the z-score of Kimmie is -0.625

Learn more on z-score here: https://brainly.com/question/25638875

#SPJ1

The dive of the Peregrine falcon took 7.5 seconds

How to solve such time related questions?

The key concept for solving such questions is the relationship between speed, distance and time.

The relationship between them is Distance = Speed X Time

Assuming the top speed of  a Peregrine falcon is 240mph.

Distance travelled by the Peregrine falcon = 0.5 miles

By using the formula we get

0.5 = 240 x time

time = [tex]\frac{1}{480}[/tex] hours

time = [tex]\frac{3600}{480}[/tex] seconds = 7.5 seconds

∴ The dive of the Peregrine falcon took 7.5 seconds

Learn more about time related questions here :

https://brainly.com/question/24556634

#SPJ4

A binomial probability density function should be used to represent the probability

The given parameters are:

The proportion that plays sport indicates that

68% of the students do not play sport

So, we have two events, which are

When there are two possible events, then the binomial probability density function should be used

Read more about binomial probability density at:

https://brainly.com/question/15246027

#SPJ1

A statistical question you can ask at least 20 different people can be: "How many pets do you have?"

An hypothetical data for the number of pets 20 sixth graders have has been given and the box plot that displays the data set is in the image below.

A statistical question can be defined as a question that can be answered by collecting a variety of numerical answers that vary. Examples of statistical questions include:

A statistical question you can ask at least 20 different people can be: "How many pets do you have?"

Below is the hypothetical questions that can be assumed you'd get from two people:

0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 4, 5, 5

Description of the people you asked can be: 20 sixth graders in your school.

How you gathered your data can be: Asking them to fill a questionnaire or by interview.

The numerical data from least to the greatest, hypothetically would be:

0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 4, 5, 5

The five-number summary for the hypothetical data would be:

Minimum: 0 (least data point)

Quartile Q1: 1 (middle of the first half of the data distribution)

Median: 1.5 (center of the data)

Quartile Q3: 2.75 (middle of the second half of the data distribution)

Maximum: 5 (greatest data value).

Using the five-number summary generated, the box plot that displays the data set is shown in the image attached below.

Learn more about statistical question on:

https://brainly.com/question/12150562

#SPJ1

Answer:

f(-x) = -4x^3 + 9x, f(x) is an odd function

Step-by-step explanation:

We are given that f(x) = 4x^3 - 9x. In order to solve this problem, we first need to understand what an odd function is and what an even function is. When we have an odd function, f(-x) = -f(x). Meaning, that if we plug -x in for x, we should get -f(x). On the other hand, with an even function, f(-x) = f(x). Even if you change the sign, when you simplify, you will get back the same function. In either case, we have to first find f(-x) to figure this problem out:

[tex]f(-x)=4(-x)^3-9(-x)\\f(-x)=-4x^3+9x[/tex]

We can see from our answer for f(-x) that it is equal to -f(x). We can verify this below:

[tex]-f(x)=-(4x^3-9x)\\-f(x)=-4x^3+9x[/tex]

Since f(-x) = -f(x), our function f(x) is an odd function

The conversion of the vectors into coordinate notation rule are as follows;

It follows from the task content that the vectors given in the task content can be converted to coordinate notation form by mapping x and y to their respective transformation units. It therefore follows that the coordinate notation form of the vectors are;

Read more on coordinate notation;

https://brainly.com/question/24974842

#SPJ1

Using it's concept, the probability of D is 4/7.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

Researching this problem on the internet, A, B and C all have a probability of 1/7. The sum of all probabilities is of 1 = 100%, hence:

[tex]3 \times \frac{1}{7} + P(D) = 1[/tex]

[tex]P(D) = 1 - \frac{3}{7}[/tex]

[tex]P(D) = \frac{4}{7}[/tex]

More can be learned about probabilities at https://brainly.com/question/24372153

#SPJ1

Two lines in a plane can intersect,overlap or be parallel.When two lines intersect they have a common point which lies on both line.This is called solution of the two simultaneous equation which when graphed represent straight lines. Adding the two equations uses  Elimination method to solve for x and y. The x and y value obtained is the common point lying on both the lines.

2x - 3y = 1

+ 2x + 3y = 2  

4x =3 Or x=3/4

Substituting x value in any of the two-equation we can find the corresponding y value .

2x-3y=1

2(3/4) - 3y =1

Solving for y

y= 1/6

The point of intersection of the two lines is ( 3/4, 1/6)

Learn more about simultaneous equation here:https://brainly.com/question/16863577

#SPJ4

Answer:

salad, lamb, cookie

salad, pizza, brownie

garlic bread, lamb, cookie.

garlic bread, pizza, brownie

Answer:

x = 55°

Step-by-step explanation:

That square box indicates a right angle.

A right angle is 90°.

We know that angle x and the 35° angle are making up this 90° angle together.

So, the equation to show what this ship looks like is the following:

[tex]x+35=90[/tex]

This is a simple equation, that if we solve, we get:

[tex]x=55[/tex]

So, x is 55°.

Considering the angle of the ray, it is found that the value of x is of x = 55º.

The ray has an angle of 180º. It is composed by:

Hence:

x + 35 + 90 = 180

x = 180 - 125

x = 55º.

More can be learned about angles and rays at https://brainly.com/question/25770607

#SPJ1

7×50×5 = 1750 minutes

1750minutes/60minutes = 29.161 hours

1. The force necessary to gain a velocity of 60 m/s within 5 mins is 40 N

2. The velocity gained by the object at the end of the second minute is 30 m/s

F = m(v –u) / t

F = 200(60 – 0) / 300

F = 40 N

F = m(v –u) / t

Cross multiply

m(v –u) = Ft

Divide both sides by m

v - u = Ft / m

v - 0 = (150 × 120) / 600

v = 30 m/s

Learn more about momentum:

https://brainly.com/question/250648

#SPJ1

Answer:

55

Step-by-step explanation:

Draw a line through the center (horizontally).

Then draw a vertical line through the vertex of the right angle.

You'll get 2 triangles

I'll let you figure this out, it pretty easy

Remember a straight angle add up to 180 degrees, a triangle adds up to 180 degrees.

To start calculating the volume of the cone, we obtain the following data:

To calculate the volume of a cone, we apply the following formula:

[tex]\boldsymbol{\sf{V=\dfrac{\pi r^{2}h }{3} }}[/tex], where

We solve, substituting our data in the formula:

taking the square root

Multiplying

Dividing

Therefore the volume of the cone is 144 cm³.

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

[tex]\huge\textbf{What is the formula for finding the}\\\\\huge\textbf{the volume of a cone?}[/tex]

[tex]\large\boxed{\mathsf{\dfrac{\pi \times r^2\times h}{3} = volume}}[/tex]

[tex]\bullet\large\textsf{ Whereas, \boxed{r} is your \underline{radius}, \boxed{h} is your \underline{height}, \& \boxed{\pi} is your pi.}[/tex]

[tex]\bullet\large\textsf{The pi }\boxed{(\pi)}\large\textsf{ is approximately equal to 3.14.}[/tex]

[tex]\huge\textbf{What are the labels in your equation?}[/tex]

[tex]\star\ \large\boxed{{Radius}}\rightarrow \textsf{\underline{4\ centimeters}}}}}[/tex]

[tex]\star\ \large\boxed{{Height}}\rightarrow \textsf{\underline{9\ centimeters}}}}}[/tex]

[tex]\star\ \large\boxed{{\pi}}\rightarrow \textsf{\underline{3}}}}}[/tex]

[tex]\huge\textbf{What does should the equation look}\\\\\huge\textbf{like?}[/tex]

[tex]\large\boxed{\mathsf{\dfrac{3 \times 4^2 \times9}{3}}}[/tex]

[tex]\huge\textbf{What are the steps to solve for the}\\\\\huge\textbf{question to get the result?}[/tex]

[tex]\large\boxed{\mathsf{\dfrac{3 \times 4^2 \times9}{3}}}[/tex]

[tex]\large\boxed{\mathsf{= \dfrac{3\times4\times4\times9}{3}}}[/tex]

[tex]\large\boxed{= \mathsf{\dfrac{3\times16\times9}{3}}}[/tex]

[tex]\large\boxed{\mathsf{= \dfrac{48\times9}{9}}}[/tex]

[tex]\large\boxed{\mathsf{= \dfrac{432}{3}}}[/tex]

[tex]\large\boxed{\mathsf{= \dfrac{432 \div 3}{3\div3}}}[/tex]

[tex]\large\boxed{= \mathsf{\dfrac{144}{1}}}[/tex]

[tex]\large\boxed{\mathsf{= 144\div1}}[/tex]

[tex]\large\boxed{= \textsf{144}}[/tex]

[tex]\huge\textbf{What is the result to this question?}[/tex]

[tex]\huge\boxed{\frak{144\ cm^3}}\huge\checkmark[/tex]

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

Answer:

  A. {-4, -3, 7, 8}

Step-by-step explanation:

The ordered pairs representing a function are always written ...

  (input, output)

The set of inputs for the given function is the list of first-numbers of the ordered pairs. Those numbers are -3, -4, 8, 7. When we express them as a set, we like to have the elements of the set in increasing order:

  inputs = {-4, -3, 7, 8} . . . . . . matches the first choice

Answer:

16 slices

Step-by-step explanation:

24* 2/3 = 16

Answer:

I am pretty sure that it is 625.

Answer:

Step-by-step explanation:

please make sure you indicate  whether to factorize , simplify, fatorize by grouping , evaluate, or finding the derivative

The surface area of the figure given is of: 61.3 yd².

The combined surface area of a figure is the area of each figure.

This figure is composed by:

The area of the circle is given as follows:

[tex]A = \pi r^2 = \pi \times 3^2 = 9\pi[/tex]

For the triangle, we need to find it's height, which is the leg of a right triangle, in which one of the sides is 3 and the hypotenuse is 11.4, hence:

h² + 3² = 11.4²

[tex]h = \sqrt{11.4^2 - 3^2}[/tex]

h = 11 yd.

Hence the area of the triangle is:

A = 0.5 x 6 x 11 = 33 yd²

The surface area of the figure is:

9pi + 33 yd² = 61.3 yd².

More can be learned about the surface area of at https://brainly.com/question/21208177

#SPJ1

The angle formed at J and the angle of elevation at L are alternate angles, such that the angle of elevation is 53°

The given parameters are;

Triangle ∆JKL is a right triangle

The slope of the line LJ = Positive

The angle formed by the horizontal line at J = 53°

Required;

The angle of elevation from point L to point J

Solution;

The angle of elevation at L is formed by an horizontal line drawn at L.

The two horizontal lines are parallel, and the angle of elevation at L is the alternate angle to the angle formed by the horizontal line at J.

Given that alternate angles formed between parallel lines having a common transversal are equal, we have;

Learn more about angles formed by parallel lines that have a common transversal here:

https://brainly.com/question/24607467

#SPJ1

Answer:

C. 53 degrees

Step-by-step explanation:

hype'shfiofaudhskjkwdah

Answer:

other side is 12

Step-by-step explanation:

Givens

Perimeter = 64 feet

L = 20

Formula

P = 2L + 2w               Substitute Givens

64 = 2*20 + 2w         Combine

64 = 40 + 2w             Subtract 40 from both sides

64-40 = 40-40+2w    Combine

24 = 2w                      Divide both sides by 2

24/2=2w/2              

12 = w