Find the Area of this Figure

Answer:

Condition of vectors collinearity 1. Two vectors a and b are collinear if there exists a number n such that

a = n · b

Condition of vectors collinearity 2. Two vectors are collinear if relations of their coordinates are equal.

N.B. Condition 2 is not valid if one of the components of the vector is zero.

Condition of vectors collinearity 3. Two vectors are collinear if their cross product is equal to the zero vector.

N.B. Condition 3 applies only to three-dimensional (spatial) problems.

The proof of the condition of collinearity 3

Let there are two collinear vectors a = {ax; ay; az} and b = {nax; nay; naz}. We find their cross product

a × b = i j k = i (aybz - azby) - j (axbz - azbx) + k (axby - aybx) =

ax ay az

bx by bz

= i (aynaz - aznay) - j (axnaz - aznax) + k (axnay - aynax) = 0i + 0j + 0k = 0

Examples of tasks

Examples of plane tasks

Example 1. Which of the vectors a = {1; 2}, b = {4; 8}, c = {5; 9} are collinear?

Solution: Since the vectors does not contain a components equal to zero, then use the condition of collinearity 2, which in the case of the plane problem for vectors a and b will view:

ax = ay .

bx by

Means:

Vectors a and b are collinear because 1 = 2 .

4 8

Vectors a and с are not collinear because 1 ≠ 2 .

5 9

Vectors с and b are not collinear because 5 ≠ 9 .

4 8

Step-by-step explanation:

Answer:

b) 180

Explanation:

\(180 / 2 = 90\\180 / 3 = 60\\180 / 4 = 45\\180 / 5 = 36\\180 / 6 = 30\)

Hope you have a nice day and a nice Thanksgiving!

A brainiliest would also be nice. thx.

Answer:

2 3/4

Step-by-step explanation:

So area is just base X height

3 X 11/12

2 3/4

Answer:

Step-by-step explanation:

bghgytythghgf66ef

Based on the information given, we know that the two triangles have two pairs of congruent angles. This is sufficient to prove that the two triangles are congruent using the AAS (Angle-Angle-Side) postulate. Therefore, the method I would use to prove the two triangles congruent is **AAS**.

The value of c is 1/17.

It is a branch of mathematics that deals with the occurrence of a random event.

Here it is given that the function f(x) can serve as a probability distribution of the discrete random variable X when f(x) = c(x² + 4), for x = 0, 1 ,2

We have to find the value of c

Since f(x) represents the probability distribution x = 0, 1 ,2

So we have f(0)+f(1)+f(2)=1

c(0²+4)+c(1²+4)+c(2²+4)=1

4c+5c+8c=1

17c=1

Divide both sides by 17

c=1/17

Hence, the value of c is 1/17.

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Determine the value c so that each of the following function can serve as a probability distribution of the discrete random variable X when f(x)=c(x2+4), for x=0, 1,2?

a.

1/3

b.

1/17

c.

1/2

d.

1/13

Given :

\((\dfrac{X}{10}\times 0.24 )- \dfrac{15.5}{7.5} = 9\\\\\)

To Find :

The value of x.

Solution :

\((\dfrac{X}{10}\times 0.24 )- \dfrac{15.5}{7.5} = 9\\\\(\dfrac{X}{10}\times 0.24 ) = 9 + \dfrac{15.5}{7.5}\\\\(\dfrac{X}{10}\times 0.24 ) = \dfrac{(9\times 7.5 )+ 15.5}{7.5}\\\\(\dfrac{X}{10}\times 0.24 ) = \dfrac{83}{7.5}\\\\X = \dfrac{83\times 10}{7.5\times 0.24}\\\\X = 461.11\)

Therefore, the value of X is 461.11 .

Therefore, the volume is changing at a rate of 54 cm3/s when each edge is 3 cm and at a rate of 1014 cm3/s when each edge is 13 cm.

The volume of a cube is given by the formula V = e3, where V is the volume and e is the length of each edge. Therefore, the rate of change of the volume with respect to the edge length is given by the derivative of the volume with respect to the edge length:

dV/de = 3e2

Since the edges are expanding at a rate of 2 cm/s, we can use the chain rule to find the rate of change of the volume with respect to time:

dV/dt = dV/de × de/dt = 3e2 × 2 = 6e2

(a) When each edge is 3 cm, the rate of change of the volume is:

dV/dt = 6(3)2 = 6(9) = 54 cm3/s

(b) When each edge is 13 cm, the rate of change of the volume is:

dV/dt = 6(13)2 = 6(169) = 1014 cm3/s

Therefore, the volume is changing at a rate of 54 cm3/s when each edge is 3 cm and at a rate of 1014 cm3/s when each edge is 13 cm.

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Answer:

68

Step-by-step explanation:

1 foot = 12 inches

Multiply 5 by 12 inches

5 feet = 60 inches

Add the extra 8 inches

60 + 8 = 68 inches

George is 68 inches tall.

Answer:

Step-by-step explanation:

George is 5 feet and 1 foot equals 12 inches, so do 12x5 + the actual 8 inches

12x5=60

60+8=68 inches total

Answer:

The shorter side 6th ft and the longer sides are 11ft

Step-by-step explanation:

The options are not given, but we could solve and arrive at an answer

say the shorter side is x

and the longer side is x+5

we know that the area of a rectangle is given as

x*(x+5)=66

open the bracket

x^2+5x=66

x^2+5x-66=0

Find two factors of  -66  whose sum equals the coefficient of the middle term, which is   5 .

the factors are 11 and -6

splitting the middle term using the two factors  11  and  -6

x2 +11x - 6x - 66=0

x(x+11)-6(x+11)=0

(x-6)=0

x=6

(x+11)=0

x=-11

The shorter side is 6 ft and the longer side is 11 ft

Gender is categorical nominal, end-of-the-year stock classification is categorical and ordinal, and distance is quantitative and ratio.

Quantitative variables are measured with numbers. Some examples include:

Weight measured in kilos

The distance measured in meters or kilometers

Time measured in seconds or hours

On the other hand, a categorical variable is defined by features, categories, or concepts rather than numbers. Here is an example:

Breeds of dogs: Poodles, Boston Terriers, German shepherds, etc.

Moreover, variables can be classified as:

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Answer:

414π

Step-by-step explanation:

Volume of a cylinder = area of circle/ cross-section x height

Area of cross-section = πr² = 6²π = 36π

36π x 11.5 = 414π

Answer:

1300.61936 cm

Step-by-step explanation:

:))

The other number is 456.

Given that the product of two numbers is 155952, one number is 342, we need to find the other number.

So, let the other number be x,

Therefore, x × 342 = 155952

x = 155952 / 342

x = 456

Hence the other number is 456.

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Answer:

7/11 or

7

--

11

Step-by-step explanation:

Hope this helps :)

The smallest number of students so that the random selection of that number of people will guarantee that at least 14 people can be found among the selection who were born in the same month is 25.

What are selections?

A selection principle in mathematics is a rule that states it is possible to obtain mathematically important objects by choosing elements from predetermined sequences of sets. The theory of selection principles investigates these ideas and how they relate to other mathematical characteristics.

Suppose we start with 12 people whose birth months are all different.

If there we add to make 13 people then we can say that at least 2 were born in the same month as there are 12 months in a year.

If we add another student then he could have the same month date as the other 2 but he is more likely to have another birth month.

So we could go on adding 1 student 6 times and get 7 pairs of students with the same birth month.

This is very unlikely but possible.

Which eventually leads us to the smallest number of students is 25 students.

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Answer:

Step-by-step explanation:

70 ÷ 15 = 4.66

4.66 × 39 = 181.974

(A) The range and IQR for boxplot 1 is 10 and 6 respectively.

(B) The range and IQR for boxplot 2 is 12 and 7 respectively.

The interquartile range defines the difference between the third and the first quartile.

The formula for the interquartile range is given below.

Interquartile range = Upper Quartile – Lower Quartile = Q­3 – Q­1

The range is the difference between the lowest and highest values.

The formula for the interquartile range is given below.

Range = Maximum – Minimum

(A) For boxplot 1, we need to find the range and IQR from the given data set.

So, let 34 be the maximum and 24 be the minimum.

\(\text{Range}=\sf 34-24\)

\(\text{Range}=\sf10\)

Therefore, the range is 10.

Now time to find the IQR.

So, let 33 be Q3 and 27 be Q1.

\(\text{IQR}=\sf 33-27\)

\(\text{IQR}=\sf 6\)

Therefore, the IQR is 6.

(B) Now for boxplot 2, we will do the same thing as from part A.

Let's find the range.

So, let 24 be the maximum and 12 be the minimum.

\(\text{Range}=\sf 24-12\)

\(\text{Range}=\sf12\)

Hence, the range is 12.

Now for the IQR.

So, let 22 be Q3 and 15 be Q1.

\(\text{IQR}=\sf 22-15\)

\(\text{IQR}=\sf 7\)

Hence, the IQR is 7.

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Answer:

hi amki nai patajjdkfkejd

Answer:

Radius: 2.1Inches

Step-by-step explanation:

Circumference

Circumference is the linear distance around the circle edge.

Radius

The radius of a circle is any of the line segments from its center to its perimeter. The radius is half the diameter or r = d

2

.

Diameter

The diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints lie on the circle. The diameter is twice the radius or d = 2·r.

The Greek letter π

π represents the number Pi which is defined as the ratio of the circumference of a circle to its diameter or π = C

d

. For simplicity, you can use Pi = 3.14 or Pi = 3.1415. Pi is an irrational number. The first 100 digits of Pi are: 3.1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 5923078164 0628620899 8628034825 3421170679

Answer:

42

Step-by-step explanation:

in a parallelogram, opposite sides have equal lengths.

FM=HJ=42

The ball is in the air for approximately 2.8 + √7 seconds, which rounds to 5.2 seconds when rounded to one decimal place.To write the equation in vertex form, we need to complete the square.

The given equation is h = -4.9t² + 27.44t + 0.584. We can rewrite it as:

h = -4.9(t² - 5.6t) + 0.584

Now, we want to complete the square inside the parentheses. To do this, we need to add and subtract the square of half the coefficient of t. In this case, the coefficient is -5.6, so we have:

h = -4.9(t² - 5.6t + (5.6/2)² - (5.6/2)²) + 0.584

Simplifying, we get:

h = -4.9((t - 2.8)² - 2.8²) + 0.584

Expanding further:

h = -4.9(t - 2.8)² + 4.9(2.8)² + 0.584

Thus, the equation in vertex form is: h = -4.9(t - 2.8)² + 34.328

b) The ball's height when it was hit can be found by evaluating the equation at t = 0:

h = -4.9(0 - 2.8)² + 34.328

h = -4.9(-2.8)² + 4.328

h = -4.9(7.84) + 34.328

h ≈ 0.784 meters

To find the time at which the ball reaches its maximum height, we can use the fact that the maximum height occurs at the vertex of the parabolic equation. The vertex of a parabola in the form h = a(t - h₀)² + k is given by (h₀, k). Comparing this to our equation, we can see that the vertex occurs at t = 2.8 and h = 34.328. Therefore, the ball reaches its maximum height at 2.8 seconds, and the maximum height is 34.328 meters.

The total time the ball is in the air can be determined by finding the time it takes for the ball to reach the ground. When the ball hits the ground, its height is 0. To find this time, we can set the equation equal to 0 and solve for t:

0 = -4.9(t - 2.8)² + 34.328

4.9(t - 2.8)² = 34.328

(t - 2.8)² ≈ 7

t - 2.8 ≈ ±√7

t ≈ 2.8 ± √7

Since time cannot be negative in this context, we can ignore the negative value.

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Answer:

31 and 24

Step-by-step explanation:

Ok so let's just say that are two unknowns are "x" and "y". We can derive the following equation: \(x-y=7\), which also means that x > y so x is going to be representing the larger number.

Now using the the fact that the product is 74, we get the following equation: \(xy=744\)

We can solve for "y" in the second equation, by dividing by "x" on both sides, and then substitute that into the x-y=7 equation

Original Equation:

\(xy=744\)

Divide both sides by "x"

\(y=\frac{744}{x}\)

Original Equation:

\(x-y=7\)

Substitute the 744/x as "y"

\(x-\frac{744}{x}=7\)

Multiply both sides by x

\(x^2-744=7x\)

Subtract 7x from both sides

\(x^2-7x-744=0\)

Now we can just use the quadratic formula: \(x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\) to solve for x

In this case, a=1, b=-7, c=-744

\(x=\frac{-(-7)\pm\sqrt{(-7)^2-4(1)(-744)}}{2(1)}\)

Simplify the discriminant (stuff under radical), the -(-7), and the 2(1)

\(x=\frac{7\pm\sqrt{3,025}}{2}\)

Simplify the radical:

\(x=\frac{7\pm55}{2}\)

In the question it states "two positive numbers", so we know that the negative square root, will give us (7-55)/2 and that isn't positive. So we only take the positive square root solution (7+55)/2

\(x=\frac{7+55}{2}\)

Simplify

\(x=\frac{62}{2}\implies x=31\)

Now we can use either of the initial equations to solve for "y", but the easiest one is x-y=7

\(31-y=7\)

Add y to both sides

\(31=7+y\)

Subtract 7 from both sides

\(24=y\)

We can make sure this also has a product of 744, by using the second equation:

\((31)(24)=744\)

Simplify

\(744=744\)

So these are the two numbers.

The value of positive numbers is 31 and 24.

Given that,

The difference between two numbers = 7

The product of two numbers = 744

Let us assume that,

Two positive numbers are x and y,

Hence, we get;

x - y = 7   .... (i)

And, xy = 744   ..  (ii)

From equation (i);

x = y + 7

Substitute the above value in (ii);

(y + 7) y = 744

y² + 7y = 744

y² + 7y - 744 = 0

y² + 31y - 24y - 744 = 0

y (y + 31) - 24 (y + 31) = 0

(y - 24) (y + 31) = 0

This gives,

y = - 31

This is not possible because the numbers are positive.

Hence, y = 24

From (i);

x - y = 7

x - 24 = 7

x = 7 + 24

x = 31

Therefore, the numbers are 31 and 24.

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The value of line RS is 23

From the diagram shown, we have that line PS, line PQ, line QR and line RS form a square.

Note that the sides of a square are equal to each other.

The relationship is represented as;

Line PS = Line PQ = Line QR = Line RS

We have that;

Substitute the expressions

6x - 5 = 9x - 4

Now, collect like terms

6x - 9x = - 4 - 5

Subtract the like terms

-3x = -9

Make 'x' the subject of formula

-3x/-3 = -9/-3

x = 3

Then, RS = 9x - 4 = 9(3) - 4 = 27 - 2 = 23

Hence, the value is 23

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Answer:

1. 100 - 12y = 16

2. b * (15 + 37) = 156

3. 27 + 12z = 87

4. 135/(5c) = 3

5. w^2 * (12/4) = 300

6. 12d / (25-19) = 4

7. 5x + 13 = 68

Step-by-step explanation:

1.

The product of y and 12 is "12y", so the difference of 100 and this product is "100 - 12y". The value of y is 7, so we have:

100 - 12*7 = 100 - 84 = 16

2.

The sum of 15 and 37 is "15 + 37", and b times this sum is "b * (15 + 37)"

b is equal to 3, so we have:

3 * (15 + 37) = 3 * 52 = 156

3.

The product of z and 12 is "12z", so 27 added to this product is "27 + 12z". The value of z is 5, so we have:

27 + 12*5 = 27 + 60 = 87

4.

The product of c and 5 is "5c", so 135 divided by this product is "135/(5c)". The value of c is 9, so we have:

135/(5*9) = 135 / 45 = 3

5.

The quotient of 12 and 4 is "12/4", so w to the second power times this quotient is "w^2 * (12/4)"

The value of w is 10, so we have:

10^2 * (12/4) = 100 * 3 = 300

6.

The difference of 25 and 19 is "25 - 19", so 12 times d divided by this difference is "12 * d / (25-19)"

The value of d is 2, so we have:

12 * 2 / (25-19) = 24 / 6 = 4

7.

The product of x and 5 is "5x", so this product added to 13 is "5x + 13"

The value of x is 11, so we have:

5*11 + 13 = 55 + 13 = 68

In a case whereby In 1950, a U.S. population model was y = 151. (1.013)^t-1950 million people, where t is the year, the model predict the U.S. population would be 288 million in the year 2000.

Population models are mechanical theories that link alterations in population structure and density to responses at the individual level (life history features in eco-evolutionary theory or vital rates in demographic theory).

The model was given as y=151x(1.013)^t-1950

where the future time t = 2000

Then we can substitute the given year 2000 as the value of 't'

then we will have y=[151x(1.013)^(2000-1950)] = 288 million

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