How is the formula for a triangle derived from a parallelogram? Please give a good explanation.

The measure of the other side of the triangle is approximately 7.5 meters.

To find the measure of the other side of the triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.  In this case, we are given the length of one side and the hypotenuse:
Side 1: 4 m
Hypotenuse: 8.5 m

So, in this case, we can write:

8.5^2 = 4^2 + x^2

where x is the length of the other side we are trying to find.

Simplifying the equation, we get:

72.25 = 16 + x^2

Subtracting 16 from both sides, we get:

56.25 = x^2

Taking the square root of both sides, we get:

x = 7.5

Therefore, the measure of the other side of the triangle is 7.5 meters.

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Predicting an individual's annual income is generally easier than predicting the average annual income in a random sample.

This is because individual income is influenced by a combination of personal characteristics, whereas the average income in a random sample is influenced by a wider range of factors, including sample composition and variability.

Predicting an individual's annual income is typically easier due to several reasons. Firstly, individual income is often influenced by personal characteristics such as education, work experience, occupation, and skills, which can be relatively easier to measure and obtain data on. These variables provide important information that can be used to predict an individual's income level.

On the other hand, predicting the average annual income in a random sample is more challenging. The average income in a sample is influenced not only by individual characteristics but also by other factors such as the sample composition and the variability within the sample. The composition of the sample, including factors like age distribution, gender balance, and geographical location, can significantly affect the average income. Additionally, the variability within the sample, including differences in income levels and income distribution, can introduce additional uncertainty and make predictions less accurate.

Overall, while predicting an individual's annual income can be challenging, it is generally easier compared to predicting the average annual income in a random sample. Individual income is influenced by a narrower set of factors, making it more predictable, whereas the average income in a sample is influenced by a wider range of variables, introducing more complexity into the prediction process.

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Answer:

16

Step-by-step explanation:

Always do multiplication first:

6*4 = 24

(-2)(4) = -8

Note: A negative times a positive always equals a negative

After multipying, do addition:

24+ (-8) = 24-8 = 16

Using trigonometric identity, cos(2θ-1) / cos(2θ+1) is equal to [(1 - 2tan^2(θ))cos(1) + 2tan(θ)sin(1)] / [(1 - 2tan^2(θ))cos(1) - 2tan(θ)sin(1)]

We can use the trigonometric identity:

cos(2θ) = 1 - 2sin^2(θ)

to rewrite the expression as follows:

cos(2θ-1) = cos(2θ)cos(1) + sin(2θ)sin(1) = (1 - 2sin^2(θ))cos(1) + 2sin(θ)cos(θ)sin(1)

Similarly,

cos(2θ+1) = cos(2θ)cos(1) - sin(2θ)sin(1) = (1 - 2sin^2(θ))cos(1) -  2sin(θ)cos(θ)sin(1)

Dividing these two expressions, we get:

cos(2θ-1) / cos(2θ+1) = [(1 - 2sin^2(θ))cos(1) + 2sin(θ)cos(θ)sin(1)] / [(1 - 2sin^2(θ))cos(1) - 2sin(θ)cos(θ)sin(1)]

Now, we can use the identity:

tan(θ) = sin(θ) / cos(θ)

to simplify the expression. Specifically, we can express sin(θ) in terms of tan(θ) and cos(θ) as follows:

sin(θ) = tan(θ)cos(θ)

Substituting this into the expression for cos(2θ-1) / cos(2θ+1), we get:

cos(2θ-1) / cos(2θ+1) = [(1 - 2tan^2(θ))cos(1) + 2tan(θ)sin(1)] / [(1 - 2tan^2(θ))cos(1) - 2tan(θ)sin(1)]

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Answer:

V  =  339 in³

Step-by-step explanation:

The formula for the volume of a sphere of radius r is V = (4/3)πr³

Here the diameter is 18 m, so the radius must be 9 m, and the volume of the sphere is

V = (4/3)(3.14)(9 m)², or

V  =  339 in³

Answer:

-16,4 are the two numbers

Answer:

8 bags of chips.

Step-by-step explanation:

First, find the cost per individual unit. It is given that 2 bags of chips cost $6. Find the cost of one bag by dividing 6 with 2:

$6/2 bags = $3/bag

Next, you are solving for the amount of chips you can buy with $24. Divide 24 with the individual cost of $3:

$24/$3 per bag = 8

You can buy 8 bags of chips assuming all things are the same.

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Answer:

Bro, Pick me

Step-by-step explanation:

Seriously, I'll do it

Answer:

I'll do it

Step-by-step explanation:

I'll do it for cheaper than $500

Answer:

i think its 12 i could be wrong so sorry if i am but it might be 12

Step-by-step explanation:

angle Q will be 34° as the triangle is isosceles triangle.

Answer:

It's quite easy

Step-by-step explanation:

people less than 30 years = frequency of people 0 to 15 + 15 to 30 = 8+15 =23

Therefore there are 23 people less than 30 years old.

pls mark me as brainliest pls.

The Even numbers are not divisible by 2 is  equivalent to ~p

P is a statement which is  Even numbers are divisible by 2.

The statement ~p represents the negation of the statement p.

The statement p is "Even numbers are divisible by 2.

The negation of this statement would be Even numbers are not divisible by 2

Hence, the Even numbers are not divisible by 2 is  equivalent to ~p

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Answer:

x = 7

Step-by-step explanation:

Answer:

51%

Step-by-step explanation:

31,408-20,800=10,608÷20,800=0.51×100=51.

You subtract the retail price from the original and you divide the number you get by the original price and then times the number by a hundred.

Answer:

the hardcover is 19.95, and the parback is 6.65. enjoy.

Answer:

where is the diagram???

Step-by-step explanation:

Answer:

C. C and E

Step-by-step explanation:

The solutions for a system of equations is the point of intersection of the two graphs of those equations. Here, there are two points of intersection, that is, two points where the graphs cross. The graphs cross at point C and point E.

C and E are the solutions to this system.

The directional derivative of \(\(f(x, y, z) = 4x^2y + xz^2 + 0y^3z\)\)) in the direction of the origin is approximately -44.041. The closest value to the directional derivative is 44.041000852586912

To find the directional derivative of the function\(\(f(x, y, z) = 4x^2y + xz^2 + 0y^3z\)\) at the point \(\((2, -6, 1)\)\)in the direction of the origin, we need to compute the dot product of the gradient of the function at that point and the unit vector in the direction of the origin.

First, let's find the gradient of \(\(f(x, y, z)\):\)

\(\(\nabla f = \left(\frac{\partial f}{\partial x}, \frac{\partial f}{\partial y}, \frac{\partial f}{\partial z}\right)\)\)

Taking partial derivatives:

\(\(\frac{\partial f}{\partial x} = 8xy\)\\\(\frac{\partial f}{\partial y} = 4x^2 + 0\)\\\(\frac{\partial f}{\partial z} = xz^2\)\)

Evaluating the partial derivatives at the point (2, -6, 1):

\(\(\frac{\partial f}{\partial x}(2, -6, 1) = 8(2)(-6) = -96\)\\\(\frac{\partial f}{\partial y}(2, -6, 1) = 4(2)^2 + 0 = 16\)\\\(\frac{\partial f}{\partial z}(2, -6, 1) = 2(1)^2 = 2\)\)

So the gradient of f(x, y, z) at (2, -6, 1) is \(\(\nabla f(2, -6, 1) = (-96, 16, 2)\).\)

Next, we need to find the unit vector in the direction of the origin, which is the normalized vector \(\(\mathbf{u}\):\)

\(\(\mathbf{u} = \frac{\mathbf{v}}{\|\mathbf{v}\|}\)\)

Where  \(\(\mathbf{v}\)\) is the vector pointing from the origin to the point (2, -6, 1):

\(\(\mathbf{v} = (2, -6, 1)\)\)

Finding the magnitude of  \(\(\mathbf{v}\)\):

\(\(\|\mathbf{v}\| = \sqrt{2^2 + (-6)^2 + 1^2} = \sqrt{41}\)\)

Normalizing \(\(\mathbf{v}\)\):

\(\(\mathbf{u} = \frac{1}{\sqrt{41}}(2, -6, 1)\)\)

Finally, computing the directional derivative by taking the dot product of the gradient and the unit vector:

Directional derivative \(= \(\nabla f(2, -6, 1) \cdot \mathbf{u}\) = \((-96, 16, 2) \cdot \frac{1}{\sqrt{41}}(2, -6, 1)\) = \(-96 \cdot \frac{2}{\sqrt{41}} + 16 \cdot \frac{-6}{\sqrt{41}} + 2 \cdot \frac{1}{\sqrt{41}}\) = \(\frac{-192}{\sqrt{41}} + \frac{-96}{\sqrt{41}} + \frac{2}{\sqrt{41}}\) = \(\frac{-192 - 96 + 2}{\sqrt{41}}\) = \(\frac{-286}{\sqrt{41}}\)\)                      

Approximatingthe numerical value of the directional derivative, we get:

Directional derivative ≈ -44.041

Among the given options, the closest value to the directional derivative is 44.041000852586912, which corresponds to the second option.

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Answer:

3, 3x+5

Step-by-step explanation:

DIFFERENTIATE W.R.T. X

3

EVALUATE

3x+5

'Therefore , the solution of the given problem of function comes out to be  f⁻¹(x) =  1 + x / 5x+2 .

Mathematics is the study of number, their variations, the geographical tissue, architecture, and both both actual and fictitious locations. A equation  is a depiction of the relationship here between number of inputs and the corresponding outputs for each one. A function is just a collection of input that, when put together, provide one variable distinct output with each input. Every function is assigned a city, county, or scope, sometimes known as a realm.

Here,

Given:

=> f(x) = (1 -2x)/(5x-1)

To find f⁻¹(x)

So,

=> y = (1 -2x)/(5x-1)

=>  x =  (1 -2y)/(5y-1)

=> y = 1 + x / 5x+2

=> f⁻¹(x) =  1 + x / 5x+2

Therefore , the solution of the given problem of function comes out to be  f⁻¹(x) =  1 + x / 5x+2 .

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Answer:

the answer is b, theyre congruent

Step-by-step explanation:

also is that flvs?

Answer:

B

Step-by-step explanation:

Answer:

Each person will get 1/24 gallon of milk

Step-by-step explanation:

Answer:

y = 6.7

x = 8

Step-by-step explanation:

3^2 + 6*2 = y

√9 + 36 = y

6.7 = y

10^2 = 6^2 + x

100 = 36 + x

100 (-36) = 36 (-36) +x

√64 = x

8 = x

Answer:

3 seconds

Step-by-step explanation:

We can solve this in either of two ways:  Graphing or taking the first derivative,  I'll use both,

Graphing

Plot the equation.  My DESMOS graph is attached.  One can find the vertex of this curve at 3 seconds.  Bonus:  It reaches a height of 144 units at this point.

Derivative

The first derivative of this function will produce an equation that returns the slope of the line at any point x.

S(t) = 96t - 16t^(2)

S'(t) = 96 - 2*16t

S'(t) = 96 - 32t

The slope of the curve will be 0 when the ball reaches it's maximum height and begins to fall.  Since we want the time it takes to reach a slope of zero, we can set S'(t) to 0 and solve:

S'(t) = 96 - 32t

0 = 96 - 32t

32t = 96

t = 3 seconds

Answer:

£ 90 because

Step-by-step explanation:

4x+x= £ 150

5x =£150

x=£150/5

x=£30

ivan share = 4x=4x£30

=£120

Tanya share =x=£30

difference ,=£120 - £30

=£90

A right triangle is a triangle with one right angle (90 degrees). The hypotenuse of a right triangle is the side opposite the right angle and is usually the longest side of the triangle.

To find the area of the triangle, you will need to use the base and the height of the triangle. In this case, the base of the triangle is 48cm and the height is the length of the side opposite to the right angle.

To find the length of the side opposite to the right angle, you can use the Pythagorean Theorem, which states that the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the lengths of the other two sides. The theorem can be written as:

c^2 = a^2 + b^2

where c is the hypotenuse, and a and b are the other two sides.

So, substituting the values we have:

50^2 = a^2 + 48^2

2500 = a^2 + 2304

a^2 = 2500 - 2304

a^2 = 196

a = 14

Area of the triangle = (1/2) * base * height

= (1/2) * 48 * 14

= 336 cm^2

So, the area of the triangle is 336 cm^2

The area of the triangle is 336 cm²

The area of a triangle can be found using the formula:

Area = (1/2) × base × height

In this case, we know the base is 48cm and the hypotenuse is 50cm. To find the height, we can use the Pythagorean theorem, which states that the square of the length of the hypotenuse (a) is equal to the sum of the squares of the lengths of the other two sides (a and b) in the right triangle.

c² = a² + b²

So in this case, we have:

50² = 48²  + b²

Solving for b, we get:

b =√ 50² - 48²

b = √2500 - 2304

b = √196

b = 14 cm

So the height of the triangle is 14cm.

Now we can use this information to find the area:

area = (1/2) ×48 ×14 = 336 cm²

Hence, we can say the area of the triangle is 336 cm²

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The given limit can be expressed as the definite integral ∫[3π, 5π] cos(x) dx over the interval [3π, 5π].

To express the limit as a definite integral, we can rewrite the sum as a Riemann sum and take the limit as n approaches infinity.

The given sum can be written as:

lim(n → ∞) [Σ(i = 1 to n) cos(xi) Δxi],

where Δxi = (b - a) / n is the width of each subinterval, xi is a sample point in the i-th subinterval, and [a, b] is the interval [3π, 5π].

To express the limit as a definite integral, we can rewrite the sum using the definite integral notation:

lim(n → ∞) [Σ(i = 1 to n) cos(xi) Δxi] = ∫[3π, 5π] cos(x) dx,

where dx represents an infinitesimally small change in x. By taking the limit as n approaches infinity, the sum converges to the definite integral.

Therefore, the given limit can be expressed as the definite integral ∫[3π, 5π] cos(x) dx over the interval [3π, 5π].

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