What is the probability that a point chosen at random in the rectangle is also in the blue triangle

To use synthetic division to divide a polynomial by a linear expression, follow the steps: arrange the terms, change the sign of the linear expression, bring down the coefficient, multiply and add, write the result, and determine the quotient and remainder.

To use synthetic division to divide a polynomial by a linear expression, follow these steps:

In this case, the quotient is[tex]9x^3 + 4x^2 + 5x + 2[/tex].

Answer:

f(52) = 32,951,280,099

Step-by-step explanation:

In Fibonacci sequence, the sum of the two preceding sequence of the sequence is always equivalent to the next sequence.

For example, this is a Fibonacci sequence 1,2,3,5,8... As you can see that the sum of the two preceding sequence gave the next sequence i.e 1+2 = 3, 2+3 = 5, 3+5 = 8 etc and the chain continues like that.

If we are now given two large numbers of. Fibonacci sequence to bef(50)=12,586,269,025 and f(51)= 20,365,011,074

The next sequence f(52) will be the sum of the preceding sequences f(50) and f(51) that is;

f(52) = f(50) + f(51)

f(52) = 12,586,269,025 + 20,365,011,074

f(52) = 32,951,280,099

The resulting numbers if they are added is 32,951,280,099.

Answer:

c

Step-by-step explanation:

The increase of Omar's mass from 6000kg to 7000kg will raise the mean mass of the elephants because the mean involves all values. However, it won't affect the median mass because the position of the middle value in the set won't change.

The correction of Omar's mass from 6,000 kilograms to 7,000 kilograms will affect both the mean and the median mass of the elephants. However, the effect on each measure of central tendency will be different.

The mean is the average, calculated by adding up all values and then dividing by the number of values. If Omar's weight is increased, the total mass of the elephants will increase, leading to an increase in the mean mass of the elephants.

However, the median, which is the middle value when all values are arranged in ascending order, will not change because it only depends on the arrangement of values, not their actual size. Since Omar's mass is already the largest value, an increase in his mass will not change the position of the middle value.

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Solution :

Give that, a 72° sector in a circle ,

Area of Sector in a circle =

[tex] \pi \times r^{2} \times( \frac{\theta}{360} )\\ \:\: where, r = radius\, of\, the\, circle\ \\ \theta = angle \,in \, degrees [/tex]

Suppose radius of circle is r .

then Volume of sector of circle

[tex] \pi \imes r^{2} \times (\frac{72}{360} )= 16.4\pi\\\\r^{2} = \frac{16.4 \pi}{\pi \times \frac{72}{360} } = \frac{16.4 \times 360}{72} [/tex]

Area of a Circle of radius, r, [tex] A = \pi\times r^{2} [/tex]

Put [tex] r^{2} = \frac{16.4 \times 360}{\times 72} [/tex]

Area of Circle, A = [tex] \pi \times \ \frac{16.4 \times 360}{72} =82 \pi[/tex]

given, [tex] \pi =3.14 [/tex]

[tex] volume =82 \times 3.14 = 257.48 [/tex]

Hence, Area of circle= 257.48

Answer:257.48 yd sq

Step-by-step explanation: took de quiz

Answer:

The correct option is C. The height of the cylinder is 9 cm.

Step-by-step explanation:

The radius of cone is 12 cm and the height of cone is 12 cm.

The volume of cone is

[tex]V=\frac{1}{3}\pi r^2h[/tex]

[tex]V_1=\frac{1}{3}\pi (12)^2(12)[/tex]

[tex]V_1=576\pi[/tex]

The radius of cylinder is 8 cm. The volume of cylinder is

[tex]V=\pi r^2h[/tex]

[tex]V_2=\pi (8)^2h[/tex]

[tex]V_2=64\pi h[/tex]

It is given that the volume of cone and cylinder is same.

[tex]V_1=V_2[/tex]

[tex]576\pi=64\pi h[/tex]

[tex]\frac{576\pi}{64\pi}=h[/tex]

[tex]9=h[/tex]

Therefore the height of the cylinder is 9 cm and option C is correct.

To find the height of the cylinder that has the same volume as a cone, we can compare their volumes. By setting the volumes equal to each other and simplifying the equation, we find that the height of the cylinder is 9 cm.

To find the height of the cylinder, we need to compare the volumes of the cone and the cylinder. The formula for the volume of a cone is V = (1/3)πr^2h, where r is the radius and h is the height. The volume of the cone with radius 12 cm and height 12 cm is (1/3)π(12^2)(12) = 576π cm³. Now, let's calculate the volume of the cylinder using the formula V = πr^2h, with radius 8 cm. We know that the volumes of the cone and the cylinder are equal, so 576π = π(8^2)h. Simplifying this equation, we get 576π = 64πh. Dividing both sides of the equation by 64π, we find h = 9 cm. Therefore, the height of the cylinder is 9 cm.

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Answer:

C. (11,-23)

Step-by-step explanation:

The given equations are

[tex]3a+b=10[/tex].....................equation 1

[tex]-4a-2b=2[/tex]...................equation 2

Multiply first equation by 2

[tex]6a+2b=20[/tex]

Now add this new equation to 2nd equation

[tex]6a-4a +2b-2b = 20+2[/tex]

[tex]2a = 22[/tex]

Divide both sides by 2

[tex]a=11[/tex]

We got a=11 , plug this value in anyone equation

3(11)+b=10[tex][/tex]

[tex]33+b=10[/tex]

Subtract 33 from both sides

[tex]b=-23[/tex]

So solution is (a,b) = ( 11,-23)

Answer:

it is 6 so have a merry christmas

Step-by-step explanation:

Answer:

Hence, A radius is half the diameter.

Step-by-step explanation:

The question is asked as:

A radius is [tex]a_0[/tex] the diameter.

i.e. what is the value of the constant [tex]a_0[/tex] such that the radius and the diameter are related to each other.

We know that:

The Radius is the length of the line through the center that touches a point on the edge of the circle.

The diameter is the length of the line through the center that touches two points on the edge of the circle.

Hence Radius is half the diameter.

so the value of [tex]a_0=\dfrac{1}{2}[/tex]

( Or we can say Diameter is twice the radius of the circle.

[tex]d=2r\\\\r=\dfrac{1}{2}d[/tex]

where d denotes the diameter of the circle and r denotes the radius of the circle ).

Answer:

D. [tex]y=-2x-1[/tex]

Step-by-step explanation:

We have been given a line on coordinate plane. We are asked to find the equation of our given line.

First of all, we will find slope of our given line using points [tex](-2,3)[/tex] and [tex](0,-1)[/tex] in slope formula.

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex], where,

[tex]y_2-y_1[/tex] = Difference between two y-coordinates,

[tex]x_2-x_1[/tex] = Difference between two x-coordinates of same y-coordinates.

Upon substituting our given values in slope formula, we will get:

[tex]m=\frac{-1-3}{0--2}[/tex]

[tex]m=\frac{-4}{0+2}[/tex]

[tex]m=\frac{-4}{2}[/tex]

[tex]m=-2[/tex]

Now, we will use slope-intercept form of equation [tex]y=mx+b[/tex], where,

m = Slope of line,

b = The y-intercept.

Upon looking at our given graph, we can see that y-intercept is [tex]-1[/tex].

Therefore our required equation would be [tex]y=-2x-1[/tex] and option D is the correct choice.

Answer:

50

Step-by-step explanation:

First we have to find the height. Since we know the area we can use it to find the height. The area of a triangle is A=bh1/2 or half of the base times the height. So if we plug in what we know and solve, we can find the height. 336=48 x h x 1/2. The height is 14. Now we can solve for the hypotenuse using the Pythagorean Theorem. a^2 + b^2 = c^2 plug in what we know... 14^2 + 48^2 = c^2 simplify to get 196+2304= c^2 and further 2500= c^2 so find the square root of 2500. You will get 50.

Answer: 12 different combinations were possible.

Step-by-step explanation:

Given: At LaMar’s birthday party, his parents served slices of plain, sausage, or pepperoni pizza.

i.e. The number of types of pizza = 3

They also served cups of milk, orange juice, apple juice, or lemonade.

i.e. The number of  types of drinks = 4

Now, if each guest at the party chose one slice of pizza and one type of drink, then the number of different possible combinations are :

[tex]3\times4=12[/tex]

Hence, there were 12 different combinations .