which shows how to use similar right triangles to find the equation of the line...​

Final answer:

The distance between – 14 and – 5 on a number line is 9 units, calculated by finding the absolute value of the difference between the two numbers.

Explanation:

The distance between two points on a number line is the absolute value of the difference between those two numbers. To find the distance between – 14 and – 5, subtract the smaller number (– 14) from the larger number (– 5) and then take the absolute value:

Distance = |(– 5) – (– 14)|

Distance = |9|

Distance = 9

Therefore, the distance on the number line between – 14 and – 5 is 9 units.

Answer:

[tex]\large\boxed{\left[\begin{array}{ccc}-18&-33\\-42&-27\end{array}\right] }[/tex]

Step-by-step explanation:

[tex]n\cdot\left[\begin{array}{ccc}a&b\\c&d\end{array}\right] =\left[\begin{array}{ccc}(n)(a)&(n)(b)\\(n)(c)&(n)(d)\end{array}\right]\\\\============================\\\\3\cdot\left[\begin{array}{ccc}-6&-11\\-14&-9\end{array}\right] =\left[\begin{array}{ccc}(3)(-6)&(3)(-11)\\(3)(-14)&(3)(-9)\end{array}\right] \\\\=\left[\begin{array}{ccc}-18&-33\\-42&-27\end{array}\right][/tex]

Answer:

the answer is B !

Step-by-step explanation:

Final answer:

The true statement about the greatest integer function is that it is a piecewise function. The common difference of the given sequence is 3.

Explanation:

Let's break down each part of the question to provide a clear and accurate response.

Part 1: Greatest Integer Function

The statement that is true about the greatest integer function is B. The greatest integer function is classified as a piecewise function. The greatest integer function, denoted as [x], returns the greatest integer less than or equal to x. This function is indeed piecewise because it is defined in multiple pieces - for each interval of real numbers between integers, it takes a constant value equal to the lower endpoint of that interval.

Part 2: Common Difference of Sequences

To find the common difference of the sequence – 5, – 2, 1, 4, 7,  …, you subtract any term from the term that follows it. For instance, – 2 - (– 5) = 3. Therefore, the common difference is 3.

Answer:

3/7x

Step-by-step explanation:

21yz

--------------

49xyz

We can break this into pieces

21   1        y          z

--- * ---- * ----- *   ----

49    x      y          z

Now we can simplify. canceling the y terms and the z terms

3*7   1         1          1

------ * ---- * ----- *   ----

7*7    x         1          1

Now we can simplify canceling the 7 terms

3         1        

------ * ----

7         x        

We are left with

3/ 7x

The number he should add on both sides of the equation to complete the square is 36.

The given equation is [tex]x^{2} - 12x = 16[/tex]

Thus, to make it a complete square, both sides of the equation must be a perfect square.

If we add number 36 on both sides of the equation, then the resulting equation is a perfect square.

⇒ [tex]x^{2} - 12x + 36= 16 + 36[/tex]

⇒ [tex](x-6)^{2} = 52[/tex]

∴  [tex](x-6)^{2} = (2\sqrt{13} )^{2}[/tex]

Thus, the given equation is a complete square from both sides.

Therefore, the number he should add on both sides of the equation to complete the square is 36.

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Final answer:

Add 36 to both sides of the equation x²- 12x = 16 to complete the square, transforming it into a perfect square trinomial.

Explanation:

To complete the square for the equation x² - 12x = 16, you need to take half of the coefficient of x, which is -12, and square it. This process transforms the left-hand side into a perfect square trinomial. Therefore, you calculate (12/2)² which equals 36. This is the value that needs to be added to both sides to complete the square. The equation then becomes x² - 12x + 36 = 16 + 36, which simplifies to (x - 6)²= 52

Answer:

Final factor is (x-9)(x+4)

Step-by-step explanation:

Given expression is [tex]x^2- 5x- 36[/tex].

Now we need to factor that expression

[tex]x^2- 5x- 36[/tex]

Find two numbers whose product is -36 and sum is -5.

Two such numbers oare -9 and +4. So we get:

[tex]=x^2- 9x+4x- 36[/tex]

[tex]=x(x-9)+4(x-9)[/tex]

[tex]=(x-9)(x+4)[/tex]

Hence final factor is (x-9)(x+4)

Answer:

(x-9) (x+4)

Step-by-step explanation:

x^2- 5x- 36

What two numbers multiply to -36 and add to -5

-9*4 = -36

-9+4 = -5

(x-9) (x+4)

Answer:

You are most likely a right triangle.

Step-by-step explanation: A polygon with 5 sides is the pentagon. A square has 4 angles, so with this, I can already tell that it is a triangle if it has 3 angles, (one less than a square). Then it says that it has 1 right angle. This would make the triangle a right. I hope this helps.

Final answer:

The polygon described has 'n - 2' sides, 3 angles with one being a right angle, and the other two totaling 90 degrees.

Explanation:

The polygon described in the question has 2 fewer sides than a regular polygon. Let's call the number of sides of the polygon 'n'. So, the polygon has 'n - 2' sides.

The polygon has 1 less angle than a square, which has 4 angles. So, the polygon has 4 - 1 = 3 angles.

The polygon described in the question has 1 right angle. A right angle measures 90 degrees. Since the polygon has 3 angles, and one of them is a right angle, the other two angles must add up to 180 - 90 = 90 degrees.

Putting it all together, the polygon described in the question has 'n - 2' sides, 3 angles with one of them being a right angle, and the other two angles totaling 90 degrees.

Answer:$56 for 4 adults  & 8 students

Step-by-step explanation: so you would do 8*4 then add it to 6*4= 24+32=$56

The expression to represent the cost of 4 adult tickets and 8 student tickets to the museum is 4(6) + 8(4), which totals $56.00.

The question asks for an expression that represents the cost of 4 adult tickets and 8 student tickets to the museum. Given that the price of an adult ticket is $6.00 and the price of a student ticket is $4.00, we can calculate the total cost as follows:
For adult tickets: 4 tickets  imes $6.00 per ticket = $24.00.
For student tickets: 8 tickets  imes $4.00 per ticket = $32.00.
The total cost is the sum of the cost for adult tickets and the cost for student tickets, which can be represented by the expression: 4(6) + 8(4) or $24.00 + $32.00, equaling $56.00 in total.

ANSWER

[tex]x = \frac{ ln(832) }{ ln(4) } [/tex]

EXPLANATION

The given equation is

[tex] {4}^{x - 3} =13.[/tex]

[tex] ln({4}^{x - 3} )= ln(13)[/tex]

We use the power rule of logarithms to get:

[tex](x - 3) ln(4) = ln(13) [/tex]

Expand;

[tex]x ln(4) - 3 ln(4) = ln(13) [/tex]

Solve for x,

[tex]x ln(4)= ln(13) + 3 ln(4) [/tex]

[tex]x ln(4)= ln(13) + ln( {4}^{3} ) [/tex]

[tex]x ln(4)= ln(13) + ln(64) [/tex]

[tex]x ln(4)= ln(13 \times 64) [/tex]

[tex]x ln(4)= ln(832) [/tex]

[tex]x = \frac{ ln(832) }{ ln(4) } [/tex]

Answer:

A. Volley Ball game: 0.20

B. Rugby 7s game: 90%

Step-by-step explanation:

A. Volley Ball game: 12 ≤ x < 21

To calculate the probability, the first step is to evaluate the number of people meeting the requirement and then the number of the total population.

In this case, let's first sum up the total population, meaning the total audience at the Volley Ball game.  If we sum up all attendance numbers for the Volley Ball game (first column), we get 700 + 1,000 + 3,050 + 250 = 5,000 people.

Now, let's find out how many people we have in that attendance being 12 or older but less than 21.  That's the second line of the table, so 1,000.

That means that the probability the Fan Cam gets one of those 12 ≤ x < 21 fans is 1,000 / 5,000, so 1/5, which is equal to 20% or 0.20

B. Rugby 7s game: x > 12

As before, to calculate the probability, the first step is to evaluate the number of people meeting the requirement and then the number of the total population.

The total population is the total attendance of the game, so 500 + 1,000 + 2,500 + 1,000 = 5,000 people in the stadium.

How many of them are NOT less than 12 years of age?  We have to sum up the last 3 rows of the table: 1,000 + 2,500 + 1,000 = 4,500 people 12 or older.

So, what's the possibility one of those 12 or older will be spotted by the Fans Cam?  4500 out of 5,000 = 9/10, or 90%.

Answer:

D

Step-by-step explanation:

This is because when making a triangle, the two shortest sides have to add up to be bigger than the biggest side. For example, A would work because if you did 4+6, it would equal 10 which is bigger than the biggest side. B and C add up to something bigger than 6. However, D is different. If you do 2+4, that equals 6. It has to be bigger than six, not equal

Answer: 20

H(c) = 6.4 + 0.6c

6.4 is the constant.

When the height of the cups is 18.4 the function is:

18.4 = 6.4 + 0.6c

Then, you add 6.4 from both sides

18.4 - 6.4 + 6.4 = 6.4 + 0.6c - 6.4  + 6.4

Simplify

18.4 = 6.4 + 0.6c

Switch sides

6.4 + 0.6c = 18.4

Multiply both sides by 10

6.4 x 10 + 0.6c x 10 = 18.4 x 10

Refine

64 + 6c = 184

Subtract 64 from both sides

64 + 6c - 64 = 184 - 64

Simplify

6c = 120

Divide both sides by 6

6c/6 = 120/6

c = 20

Check the picture below.

make sure your calculator is in Degree mode.

Answer:Cos M = 40/76Cos M = 10/19M = 58

degrees

Step-by-step explanation:

Answer:

x < 3

Step-by-step explanation:

2(4+2x)>5x+5

Distribute

8 +4x > 5x+5

Subtract 4x from each side

8 +4x-4x > 5x-4x+5

8 > x+5

Subtract 5 from each side

8-5 > x+5-5

3 > x

X must be less than 3

Answer:

3. FE

Step-by-step explanation:

ED and DC are both part of the circle, AC is the diameter, FE is the radius

Answer:

D

Step-by-step explanation:

The data CAN NOT change.

D. How many football games the Texans won in the 2014-2015 season would yield data without variability.

The correct option is D.

The measure of variability is a statistical term that refers to the extent to which data points in a dataset are spread out or dispersed from each other. In other words, it measures how much the individual data points deviate from the central tendency of the dataset.

D. How many football games the Texans won in the 2014-2015 season would yield data without variability.

The number of wins is a fixed value that does not vary, and therefore, the data would not have any variability.

In contrast, the other options involve variables that can vary between individuals or households, and therefore would yield data with variability. For example, different friends may have spent different amounts on downloading music, or different households may watch different amounts of TV.

The height of trees can also vary depending on the species, age, and other factors.

Therefore, option D is correct.

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Answer:

[tex]P (2) =\frac{1}{7}[/tex]  Theoretical probability

Step-by-step explanation:

The theoretical probability is defined as:

[tex]P = \frac{number\ of\ desired\ results}{number\ of\ possible\ results}[/tex]

In this case we look for the probability of taking a 2 out of the bag. As there is only one paper with the number 2 in the bag then:

number of desired results = 1

The amount of paper in the bag is equal to 7, so:

number of possible results = 7

Thus:

[tex]P (2) =\frac{1}{7}[/tex]

This is a theoretical probability, since we do not need to perform the experiment to calculate the probability.

To calculate the experimental probability we must perform the following experiment:

Take a paper out of the bag, record the number obtained and then return the paper to the bag.

Now repeat this experiment n times. (Perform n trials)

So:

[tex]P (2) = \frac{number\ of\ times\ you\ obtained\ the\ number\ 2}{number\ of\ trials\ performed}[/tex]

To calculate a theoretical probability you always need to perform an experiment with n trials.

Answer:

c

Step-by-step explanation:

Graph each side of the equation. The solution is the x-value of the point of intersection.

equals =1.25256565

The right answer is about c

I believe is is B: False

Answer: its true

Step-by-step explanation:

x = 3 is a solution for the equation x - 2 = 1. The solution for 7.5 - x = 2.8 is x = 4.7. Both solutions were verified by substituting back into the original equations.

Let's first determine for which equations x = 3 is a solution:

x + 7 = 4

Substitute x = 3: 3 + 7 = 10, which is not equal to 4. Hence, x = 3 is not a solution to this equation.

x - 2 = 1

Substitute x = 3: 3 - 2 = 1, which is correct. Therefore, x = 3 is a solution to this equation.

5 + x = 9

Substitute x = 3: 5 + 3 = 8, which is not equal to 9. Thus, x = 3 is not a solution to this equation.

8 - x = 11

Substitute x = 3: 8 - 3 = 5, which is not equal to 11. Therefore, x = 3 is not a solution to this equation.

The correct option is- b

Now, we solve the equation 7.5 - x = 2.8:

1. Start by isolating x:

7.5 - x = 2.8

2. Subtract 7.5 from both sides of the equation:

-x = 2.8 - 7.5

-x = -4.7

3. Multiply both sides by -1 to solve for x:

x = 4.7

The correct option is- a

Hence, the solution to the equation is x = 4.7.

Therefore x = 3 is a solution for the equation x - 2 = 1. The solution for 7.5 - x = 2.8 is x = 4.7.

The answer is:

The coordinates of the midpoint are:

[tex]x-coordinate=2\\y-coordinate=6[/tex]

We can find the midpoint of the segment with the given endpoints using the following formula.

The midpoint of a segment is given by:

[tex]MidPoint=(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})[/tex]

We are given the points:

[tex](12,4)\\[/tex]

and

[tex](-8,8)\\[/tex]

Where,

[tex]x_{1}=12\\y_{1}=4\\x_{2}=-8\\y_{2}=8[/tex]

So, calculating the midpoint, we have:

[tex]MidPoint=(\frac{12+(-8)}{2},\frac{4+8}{2})[/tex]

[tex]MidPoint=(\frac{4}{2},\frac{12}{2})[/tex]

[tex]MidPoint=(2,6)[/tex]

Hence, we have that the coordinates of the midpoint are:

[tex]x-coordinate=2\\y-coordinate=6[/tex]

Have a nice day!

Answer:

The midpoint is (2, 6)

Step-by-step explanation:

Points to remember

The midpoint of a line segment with end points, (x₁, y₁) and (x₂, y₂)

mid point = [ (x₁ + x₂)/2 , (y₁ + y₂)/2]

To find the midpoint of given line

Here (x₁, y₁)  = (12, 4) and (x₂, y₂) = (-8, 8)

Midpoint = [

 = [(12 +-8)/2 , (4 + 8)/2]

 = (4/2 , 12/2)

 = (2, 6)

Therefore midpoint is (2, 6)

Answer:

see explanation

Step-by-step explanation:

The n th term of a geometric progression is

• [tex]a_{n}[/tex] = a₁ [tex]r^{n-1}[/tex]

where a₁ is the first term and r the common ratio

given a₄ = 24, then

a₁[tex]r^{3}[/tex] = 24 → (1)

Given a₈ = [tex]\frac{8}{27}[/tex], then

a₁[tex]r^{7}[/tex] = [tex]\frac{8}{27}[/tex] → (2)

Divide (2) by (1)

[tex]r^{4}[/tex] = [tex]\frac{\frac{8}{27} }{24}[/tex] = [tex]\frac{1}{81}[/tex]

Hence r = [tex]\sqrt[4]{\frac{1}{81} }[/tex] = [tex]\frac{1}{3}[/tex]

Substitute this value into (1)

a₁ × ([tex]\frac{1}{3}[/tex] )³ = 24

a₁ × [tex]\frac{1}{27}[/tex] = 24, hence

a₁ = 24 × 27 = 648

Answer:

X= -7    

I LOVE LOVE LOVE LOVE EQUATIONS.

Step-by-step explanation:

ALRIGHT!

1. 6*(-x)= -6x

2. 6*(-3)= -18

3. Now right in normal 24= -6x-18

4. Now keep the variables on one side and the numbers on the other and simplify it. And when keeping the variables on one side and the numbers on the other what ever you switch you must change it's expression. So if it's + you make it -  and if it - you make it +. so 6x=-18-24= 6x=-42

5. Now simplify it. as a fraction. 6x = -42 = divide 6 on both sides now X= -7                                                      6       6

Answer:

Journey 1: The travel starts at 30 mph for two hours, after which there is a rest of two hours. The journey then continues slightly faster, at 40 mph for one hour. Then it is time for another rest of one hour. At this point we are 100 miles from home. We return home after two hours of traveling at 50 mph.

Step-by-step explanation:

The slope of the line indicates the speed and can be calculated by dividing the traveled distance by the time it took. This way you can describe all the journeys. Can you do the other two?

Answer:

247 people per square mile

Step-by-step explanation:

Population density is people per area

We need to find the area

We are given the radius

We will assume a circular area since we are given radius

A = pi r^2

A = 3.14 * 5^2

A = 3.14 *25

A = 78.5 miles ^2

19400 people

---------------------

78.5 miles ^2

247.133758 people per square mile

Rounding to the nearest person

247 people per square mile

Answer:

[tex]x=\frac{3}{2}[/tex]

Step-by-step explanation:

When we don't have any base with "log", we assume it to have base 10.

Using the property Log M + Log N = Log(M*N), we can write:

Log (2x-1) + Log 5 = 1

Log ((2x-1)(5)) = 1

We can turn this into exponential form using  [tex]Log_{a} b=x\\a^x=b[/tex]

Thus,

[tex]10^1=(2x-1)(5)\\10=10x-5\\10+5=10x\\15=10x\\x=\frac{15}{10}=\frac{3}{2}[/tex]

Answer:

The two numbers are 15 and 21

Step-by-step explanation:

Lets x = the larger number.

The smaller number is 6 less than the larger number: x - 6

The sum of two numbers is 36

so the equation:

x + x - 6 = 36

2x - 6 = 36

2x = 42

 x = 21

smaller number: 21 - 6 = 15

The two numbers are 15 and 21

First of all, let's convert all the measures to the same unit: 4 feet are 48 inches.

Now, as the wheel turns, there is a proportion between the angle and the distance travelled: for example, when the car moves forward a whole circumference, the angle will be 360°. Conversely, if the wheel turns 180°, then the car will move forward a distance which is half the circumference of the wheel, and so on.

Since the radius is 16 inches, the circumference will be

[tex]C=2\pi r = 32\pi[/tex]

So, we have the following proportion:

[tex]360\div 32\pi = x \div 48[/tex]

that you can read as: "if an angle of 360 corresponds to a distance travelled of [tex]32\pi[/tex], then the unknown angle x corresponds to a distance travelled of 48 inches.

Solving for x, we have

[tex]x = \dfrac{360\cdot 48}{32\pi} = \dfrac{17280}{32\pi} = 171.887338539\ldots \approx 171.9[/tex]

The car wheel with a radius of 16 inches turns through an angle of approximately 171.9° when the car rolls forward 4 feet.

To find the angle through which a car wheel turns when the car rolls forward 4 feet, given that the wheel has a radius of 16 inches, we first convert the distance in feet to inches and then calculate the circumference of the wheel. Finally, we determine the angle using the relationship between the length of arc and the radius.

First, convert the distance from feet to inches:

Next, calculate the circumference of the wheel:

The total distance rolled (48 inches) is less than the circumference of the wheel, so the wheel will not complete a full revolution. To find the angle, we use the formula:

Therefore, the wheel turns through an angle of approximately 171.9° when the car rolls forward 4 feet.

Answer:

Both sides are equal, true for all 'b'

Step-by-step explanation:

Add similar elements: b + 0.17b = 1.17b

1.17b = 1.17b

Multiply both sides by 100

1.17b * 100 = 1.17b * 100

Refine

117b = 177b

Subtract 117b from both sides

117b - 117b = 117b - 117b

Refine

0 = 0

Both sides are equal, true for all 'b'

- Mordancy

Answer:

[tex]275\ mi[/tex]

Step-by-step explanation:

we know that

The distance on the map from Town A and Town C is equal to

3.5 cm+2 cm=5.5 cm

The scale map is equal to

[tex]\frac{2}{100}\frac{cm}{mi}[/tex]

Simplify

[tex]\frac{1}{50}\frac{cm}{mi}[/tex]

That means-----> 1 cm on a map is 50 mi on the actual

so

by proportion

[tex]\frac{1}{50}\frac{cm}{mi} =\frac{5.5}{x}\\ \\x=50*5.5\\ \\x=275\ mi[/tex]