Find the perimeter of the triangle whose vertices are the following specified points in the plane.
(-9,-6), (-5, 0) and (10,-7)

Probability of an event = (number of favorable event) / (total number of event).

P(B) = (Event B) / (total number of event).

Probability of getting 1 = 1/6.

Rolling dice is an independent event, it is not dependent on how many times it’s been rolled.

Probability of getting 1 three times in a row = probability of getting 1 first time × probability of getting 1 second time × probability of getting 1 third time.

Probability of getting 1 three times in a row = (1/6) × (1/6) × (1/6) = 1/216.

Hence, the probability of getting 1 three times in a row is 0.463%.

Answer:

45

Step-by-step explanation:

If the expression be x² - 3x - 4 then the factorize term be (x - 4)(x + 1).

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

If the expression, ax³ + bx² - 5x + 2a is exactly divisible by x² - 3x - 4, then it is also divisible by both x - 4 and x + 1

If f(x) = ax³ + bx² - 5x + 2a, then f(4) = f(-1) = 0 by the factor theorem.

Hence, a(4)³ + b(4)² - 5(4) + 2a = 0 and

a(-1)³ + b(-1)² - 5(-1) + 2a = 0

⇒ so, 66a + 16b = 20 and a + b = -5

33a + 8b = 10     ...(1)

a + b = -5           ...(2)

simplifying the above (1) and (2), we get

33a + 8(-5 - a) = 10

i.e. 25a - 40 = 10

so, a = 2 ⇒ b = -7

Therefore, the function be f(x) = 2x³ - 7x² - 5x + 4

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Answer: $1.50 per hour

Step-by-step explanation:

Answer:

Step-by-step explanation:

B

Answer: A

Step-by-step explanation:

First you add up the total prices of both cars

$67,000

Next find 8.875% of that and add to total price of both cars

Answer= $72,946.25

Answer:

2250ml

Step-by-step explanation:

The concentrate-to-water ratio is 2:9. This means 2ml of concentrate requires 9ml of water. We have 500ml of concentrate, which is 250 times more than 2ml, so to find the amount of water, we also multiply 9ml by 250:

2ml concentrate : 9ml water

(Multiply both sides by 250)

500ml concentrate : 2250ml water

Answer:

2787

Step-by-step explanation:

add them all together

Step-by-step explanation:

answer, verified answer

The exact value of cosine is 4/5

From the question, we have the following parameters that can be used in our computation:

(8,-6) be a point on the terminal side of an angle

Using the above as a guide, we have the following:

Cos(angle) = x/(√x² + y²)

In this case

x = 8 and y = -6

substitute the known values in the above equation, so, we have the following representation

Cos(angle) = 8/(√8² + (-6)²)

So, we have

Cos(angle) = 8/10

Simplify

Cos(angle) = 4/5

Hence, the value is 4/5

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Answer:

240 cm, 320 cm, 400 cm

Step-by-step explanation:

The drawing length multiplied by the scale factor gives the real length.

3 cm × 80 = 240 cm

4 cm × 80 = 320 cm

5 cm × 80 = 400 cm

Answer: 240 cm, 320 cm, 400 cm

There was a 305.1% increase in the value from 2000 to 2010.

What is Percent?

To compute a percentage, divide the value by the entire amount and multiply the result by 100.

To calculate the percent increase, we need to determine the difference between the two values and divide it by the original value, then multiply by 100 to express it as a percentage.

For the year 2000:

Percent increase = (22.5 - 5.53) / 5.53 * 100 = 305.05%

And rounded to the nearest tenth of a percent, this would be 305.1%.

So, There was a 305.1% increase in the value from 2000 to 2010.

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Answer:  

Translates to x-(x+6) which simplifies to -6

=====================================================

Explanation:

x = some number

x+6 = the sum of x and 6

x-(x+6) = subtract the previous amount from x

x-x-6 .... distribute the negative through to each term

-6

No matter what number you started with, you'll always end up with -6 as the fully simplified answer. The x variables cancel.

Example:

Pick 10 as the starting number. Subtract off 10+6 = 16 to get 10-16 = -6.

Answer: The shape of the supply curve for tickets to football games at the stadium with 70,000 seats is upward-sloping. This means that as the price of tickets increases, the quantity of tickets supplied also increases.

The reasoning behind this is simple: when the price of tickets is high, there is more incentive for the sellers (e.g. the stadium, ticket resellers, etc.) to sell more tickets. They have the ability to supply more tickets as the demand for tickets at the high price is likely to be higher, thus increasing their profits.

However, it is important to note that the upward slope of the supply curve is not necessarily linear. The supply curve for tickets to football games is likely to be more elastic in the higher price range, meaning that as the price continues to increase, the quantity supplied may increase at a slower rate. This is because at some point, even if the price continues to rise, there will be a limit to how many tickets can actually be sold due to a decrease in demand.

Overall, the upward-sloping shape of the supply curve for tickets to football games at the stadium with 70,000 seats reflects the basic principle of supply and demand: as the price increases, the quantity supplied will also increase, but at some point, the increase in price will lead to a decrease in demand, limiting the quantity supplied.

Step-by-step explanation:

Answer:

C, I did the math

hope this helps

Answer:1 5/12 or written the other way 17/12

Step-by-step explanation:

Answer:

The quotient is 3x^3 + 2x and the remainder is 0.

Step-by-step explanation:

Quotient: 3x³ + 2x

Remainder: -5

Answer:

3x^3 - 3x^2 + x - 1

x + 1 | 3x^4 + 2x^2 - 6x + 1

- (3x^4 + 3x^3)

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

-x^3 - 6x + 1

- (-x^3 - x^2)

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

-5x^2 - 6x + 1

-(-5x^2 - 5x)

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

-x + 1

Therefore, the quotient is 3x^3 - 3x^2 + x - 1, and the remainder is -x + 1.

For every $2 note used, Mrs. Chong used 3/5 of a $5 note. Since she used 15 notes in total, and the number of $2 notes used must be an integer, we can see that she used 10 $2 notes. That means she used 3/5 * 10 = 6 $5 notes.

What is Inequalities?

Inequalities are mathematical statements used to express the comparison between two values. Unlike equalities (e.g., 3 + 4 = 7), which use the "equals" sign (=), inequalities use symbols such as "greater than" (>), "less than" (<), "greater than or equal to" (>=), and "less than or equal to" (<=) to express a relationship between the values.

Let's call the number of $10 notes Mrs. Chong used as "x".

We know the total amount she paid was $64, and the number of notes used was 15, so we can set up an equation:

10x + 5y + 2z = 64

Where "y" is the number of $5 notes used and "z" is the number of $2 notes used. We know that x + y + z = 15 (because this is the total number of notes used).

We can substitute x = 15 - y - z into the first equation:

10(15 - y - z) + 5y + 2z = 64

Expanding the equation:

150 - 10y - 10z + 5y + 2z = 64

Combining like terms:

150 - 5y + 3z = 64

Subtracting 150 from both sides:

-5y + 3z = -86

Dividing both sides by -5:

y - (3/5)z = 17.2

So, for every $2 note used, Mrs. Chong used 3/5 of a $5 note. Since she used 15 notes in total, and the number of $2 notes used must be an integer, we can see that she used 10 $2 notes. That means she used 3/5 * 10 = 6 $5 notes.

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Use the information provided to write the equation of the circle Center (-8, 11) Radius is 2  is equal to (x + 8)² + (y - 11)² = 4.

What is equation of the circle?

To write the equation of a circle, we need to know its center and radius. If we have the center at point (a, b) and the radius is r, the equation of the circle is:

                     (x - a)² + (y - b)² = r²

If you have the specific values of a, b, and r, you can plug them into this equation to get the equation of the circle.

The general equation of a circle with center (h, k) and radius r is:

(x - h)² + (y - k)²= r²

Using the given information, we can substitute the values into the equation:

(x - (-8))² + (y - 11)² = 2²

Simplifying, we get:

(x + 8)² + (y - 11)² = 4

Therefore, the equation of the circle with center (-8, 11) and radius 2 is:

(x + 8)² + (y - 11)² = 4

This equation represents all the points that are 2 units away from the center (-8, 11).

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Answer:

0.0075

Step-by-step explanation:

Answer:

the correct answer is letter A

Answer: [tex]f^{-1} (x) = \sqrt{x} +1[/tex]

Step-by-step explanation:

[tex]y = x^2 - 2x + 1[/tex]

We know straight away the inverse will be a square root function. We also know that this inverse will have a restriction on the domain, (because you can only take the square root of a positive number).

So, to find the inverse, first we'll switch the x and y and solve for y:

[tex]x = y^2 - 2y +1[/tex]

[tex]x = (y-1)^2[/tex], (factor!)

±[tex]\sqrt{x} = y - 1[/tex]

So, the inverse "function" is:

[tex]f^-1(x)[/tex] = ±[tex]\sqrt{x} +1[/tex]

But theres an issue here!

If we tried graphing this, this "function" would not pass the vertical line test, so its not really a function at all!

We need to restrict the domain to only include the values that are above the x axis.

So our final inverse function is:

[tex]f^{-1} (x) = \sqrt{x} +1[/tex]

Answer:

Step-by-step explanation:

(a) Using de Moivre's Theorem, we have that:

z^n = cos(nθ) + i sin(nθ)

1/z^n = cos(-nθ) + i sin(-nθ)

So, we can find z^n + 1/z^n as:

z^n + 1/z^n = (cos(nθ) + i sin(nθ)) + (cos(-nθ) + i sin(-nθ)) = 2 cos(nθ)

And z^n - 1/z^n as:

z^n - 1/z^n = (cos(nθ) + i sin(nθ)) - (cos(-nθ) + i sin(-nθ)) = 2i sin(nθ)

(b) To express the equation 2z^4 - 5z^3 + 7z^2 - 5z + 2 = 0 in terms of cos(θ), we can substitute z with cos(θ) + i sin(θ):

2(cos(4θ) + i sin(4θ)) - 5(cos(3θ) + i sin(3θ)) + 7(cos(2θ) + i sin(2θ)) - 5(cos(θ) + i sin(θ)) + 2 = 0

Expanding the right hand side using the trigonometric identities, we get:

2 cos(4θ) - 5 cos(3θ) + 7 cos(2θ) - 5 cos(θ) + 2 = 0

Note that the real and imaginary parts are separate, so we can simplify this equation to a real equation by equating the real and imaginary parts to 0.

(c) To solve the equation 2 cos(4θ) - 5 cos(3θ) + 7 cos(2θ) - 5 cos(θ) + 2 = 0, we can use numerical methods or analytical methods such as the roots of unity.

Once the roots are found, they can be represented on an Argand diagram by plotting the real and imaginary parts of each root as a point in the complex plane. The magnitude of each point represents the magnitude of the complex number, and the argument (angle) represents the argument of the complex number.

Answer:

Right, Isosceles

Step-by-step explanation:

The little square in the corner means its right angled, so a right triangle. This also means that it cannot be acute or obtuse.

The two hash marks shows two sides are the same. So it is isosceles. This also means it cannot be scalene or equilateral.

Answer:

360 cm^2

Step-by-step explanation:

The length of the rectangle can be found using the formula for perimeter:

Perimeter = 2 * (length + width)

Rearranging the equation, we can solve for the length:

length = (Perimeter - 2 * width) / 2

Plugging in the given values:

length = (78 - 2 * 15) / 2 = (78 - 30) / 2 = 48 / 2 = 24 cm

Next, the area of the rectangle can be found using the formula:

Area = length * width

Plugging in the given values:

Area = 24 * 15 = 360 cm^2

Answer:

im pretty sure it is 4/9

Step-by-step explanation:

From the question, we are to determine the probability of selecting two cards with D and D

From the formula for probability, we have that

P(D) = Number of favorable outcomes to D / Total number of possible outcomes

From the given information,

Number of favorable outcomes to D = 2

Number of possible outcomes = 3

Thus,

P(D) = 2/3

Then,

The probability of selecting two cards that have D and D with replacement is

P(D, D) = P(D) × P(D)

P(D, D) = 2/3 × 2/3

P(D, D) = 4/9

Hence, the probability is 4/9.

The measure of the first angle is 128. 5 degrees

From the information given, we have that;

Let the second angle be x

We have the representation as;

3x - 26 + x = 180

collect the like terms, we get;

3x + x = 180 + 26

Add or subtract the like terms

4x = 206

Make 'x' the subject of formula by dividing by the coefficient of x, we get;

x = 206/4

divide the values

x = 51.5 degrees

Then, the angle is 128 .5 degrees

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Answer:

120°

Step-by-step explanation:

We need to find the missing angle <SRM

The angles inside a triangle always add up to 180°. So this means:

<TSR+<STR+<TRS=180°

65°+55°+<TRS=180°

120°+<TRS=180°

<TRS=180°-120°=60°

All angles along a straight line add up to 180°. This means:

<TRS+<SRM=180°

60°+<SRM=180°

<SRM=180°-60°=120°

Answer:

120° is the answer please mark. brainly