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3 years ago

Which angle pair is a pair of corresponding angles?

Mathematics

1 answer:

GREYUIT [131]3 years ago

5 0

Answer:

B - <em>∠b and ∠f</em>

Step-by-step explanation:

Corresponding angles are the angles in matching corners of the intersections in the traversal. Since <em>∠b</em> and <em>∠f</em> are in the same position relative to the intersection, they are corresponding.

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Use the method of lagrange multipliers to find

Yanka [14]

Answer:

a) The function is: f(x, y) = x + y.

The constraint is: x*y = 196.

Remember that we must write the constraint as:

g(x, y) = x*y - 196 = 0

Then we have:

L(x, y, λ) = f(x, y) + λ*g(x, y)

L(x, y, λ) = x + y + λ*(x*y - 196)

Now, let's compute the partial derivations, those must be zero.

dL/dx = λ*y + 1

dL/dy = λ*x + 1

dL/dλ = (x*y - 196)

Those must be equal to zero, then we have a system of equations:

λ*y + 1 = 0

λ*x + 1 = 0

(x*y - 196) = 0

Let's solve this, in the first equation we can isolate λ to get:

λ = -1/y

Now we can replace this in the second equation and get;

-x/y + 1 = 0

Now let's isolate x.

x = y

Now we can replace this in the last equation, and we will get:

(x*x - 196) = 0

x^2 = 196

x = √196 = 14

then the minimum will be:

x + y = x + x = 14 + 14 = 28.

b) Now we have:

f(x) = x*y

g(x) = x + y - 196

Let's do the same as before:

L(x, y, λ) = f(x, y) + λ*g(x, y)

L(x, y, λ) = x*y + λ*(x + y - 196)

Now let's do the derivations:

dL/dx = y + λ

dL/dy = x + λ

dL/dλ = x + y - 196

Now we have the system of equations:

y + λ = 0

x + λ = 0

x + y - 196 = 0

To solve it, we can isolate lambda in the first equation to get:

λ = -y

Now we can replace this in the second equation:

x - y = 0

Now we can isolate x:

x = y

now we can replace that in the last equation

y + y - 196 = 0

2*y - 196 = 0

2*y = 196

y = 196/2 = 98

The maximum will be:

x*y = y*y = 98*98 = 9,604

6 0

3 years ago

On Monday, during a one day sale, the price of a suit was decreased by 20%. On Tuesday, the price of the suit was changed back t

nignag [31]

Answer:

25%

Step-by-step explanation:

If we consider the original price of the piece of suit is x.

Given that, on Monday during a one day sale, the price of the suit was decreased by 20%.

Therefore, the new price of the suit on Monday is $x( 1 - \frac{20}{100}) = 0.8x$ .

Now, the price of the suit on Tuesday was changed back to the original price i.e. x.

Therefore, the price is increase by (x - 0.8x) = 0.2x from the price of 0.8x.

So, the percentage change in price of the suit on Tuesday is $\frac{0.2x}{0.8x} \times 100 = 25$ %. (Answer)

8 0

3 years ago

If x = -4, calculate 2x squared - 5

Varvara68 [4.7K]

You just substitute the value of x in the given equation:

f(x) = 2x^2 - 5

f(-4) = 2 (-4)^2 -5 = 27

f(x) : a name given to the equation
f(-4): refer to the equation when the value of the independent variable x has the value between the brackets.

5 0

3 years ago

Which radical expression in the picture is equivalent to t^5/8?

mixas84 [53]

<h3>Answer: Choice B</h3>

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

Explanation:

The rule we use is

$\Large a^{m/n} = \sqrt[n]{a^m} = \left(\sqrt[n]{a}\right)^m$

where 'a' is the base, m stays in the role of the exponent, and n plays the role of the root index (eg: n = 3 is a cube root, n = 4 is a fourth root, and so on).

So for instance,

$\Large 2^{3/4} = \sqrt[4]{2^3} = \left(\sqrt[4]{2}\right)^3$

or in this case,

$\Large t^{5/8} = \sqrt[8]{t^5} = \left(\sqrt[8]{t}\right)^5$

5 0

3 years ago

If the radius of a circle is 75 hundredths of a meter, what is the diameter?

givi [52]

We know that the diameter of a circle is 2 times the radius.

If the radius is 0.75 meters, then the diameter must be 2 x 0.75 meters = 1.5meters

5 0

3 years ago