PLAESE HELP ME FAST THIS IS WORTH 20 POINTS

The length of the other diagonal, DF is 44 cm.

Pythagorean theorem states that for a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

We can apply this theorem only in a right triangle.

Example:

The hypotenuse side of a triangle with the two sides as 4 cm and 3 cm.

Hypotenuse side = √(4² + 3²) = √(16 + 9) = √25 = 5 cm

We have,

Since the kite has two pairs of congruent adjacent sides, we know that the diagonals of the kite are perpendicular bisectors of each other.

Therefore, we can use the Pythagorean theorem to find the length of the other diagonal DF.

Let x be the length of the other diagonal, DF.

We know that one diagonal EG has a length of 24 cm, so we can use the Pythagorean theorem to find the length of the perpendicular bisector of EG, which is half of DF.

By the Pythagorean theorem, we have:

[tex](20/2)^2 + (x/2)^2 = 24^2\\100 + (x/2)^2 = 576\\(x/2)^2 = 476\\x/2 = \sqrt(476)\\x = 2 \times 21.86\\x = 43.72\\x = 44[/tex]

Therefore,

The length of the other diagonal DF is 44 cm

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The width that gives the maximum area of the rectangular pen is 12 feet, and the maximum area is 144 square feet.

To maximize the area of a rectangle with a fixed perimeter, you want to make the rectangle as close to a square as possible. This maximizes the area because it distributes the available fencing evenly among the sides, optimizing the area enclosed. The given function, A = 24x - x^2, represents the area of a rectangle with width 'x' and length 'L' where L = (48-2x) / 2.

Maximization or minimization of a function occurs at its turning point. For a quadratic function like ours, the maximum or minimum happens at the vertex. The x-coordinate of the vertex is given by -b/2a. So, in our function A = -x^2 + 24x (which is the same as 24x - x^2), a = -1, b = 24.

Substitution gives: x = -(24) / 2*(-1) = 12 feet. Therefore, the width that gives you the maximum area is 12 feet.

Substitute x = 12 into the function to find the maximum area: A = 24*12 - 12^2 = 288 - 144 = 144 square feet.

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To find two real numbers whose sum is 2 and product is -48, we form a quadratic equation x^2 - 2x - 48 = 0. Using the quadratic formula, we get two pairs of numbers (8, -6) and (-6, 8) that satisfy the given conditions.

To find two real numbers that satisfy the given conditions, namely their sum being 2 and their product being –48, we can set up a system of equations or use a . Let's denote the two numbers as x and y. We know:

We can express y in terms of x from the first equation: y = 2 - x. Substituting this into the second equation gives us:

x(2 - x) = -48

This simplifies to a quadratic equation:

x^2 - 2x - 48 = 0

Using the, x = (-b ± √(b^2 - 4ac)) / (2a), with a = 1, b = -2, and c = -48, we find the two possible values for x, which in turn gives us the corresponding values for y:

x = (2 ± √(4 + 192)) / 2

x = (2 ± √196) / 2

x = (2 ± 14) / 2

Therefore, the two solutions are x = 8 or x = -6. Since we were looking for two numbers, using x + y = 2, the corresponding y values are y = -6 and y = 8, respectively. Hence, the two pairs of numbers that satisfy the conditions are (8, -6) and (-6, 8).

divide 143.00 by 11.00

143/11 = 13

Answer is 2. 13.0 hours

Answer:

Step-by-step explanation:

Byron earns $11.00 per hour.

Lets say he works for x hours

for x hour Byron earn =11x

It is given that

Byron have to work to earn= $143.00

so

11x= 143

x=143/11

x=13

so He must work for 13.0 hours .

Answer:

Step-by-step explanation:

but what ab this one:  Find the length of the hypotenuse of a right triangle with legs of 5 ft and 12 ft.

A right triangle in which one angle is the right angle and the two sides are perpendicular to each other. Hence, the length of the hypotenuse is [tex]20ft[/tex].

What s the right triangle?

A right triangle or right-angled triangle, or more formally an orthogonal triangle, formerly called a rectangle triangle, is a triangle in which one angle is a right angle, i.e., in which two sides are perpendicular.

Here, the lengths of the triangle are [tex]12ft[/tex] and [tex]16ft[/tex] .

As we know,

[tex]H^{2}=P^{2}+B^{2}[/tex]      ..........[tex](1)[/tex]

Now, substituting the values in the equation [tex](1)[/tex], we get

[tex]H^{2}=(12)^{2}+(16)^{2}\\H^{2}=144+256\\H^{2}=400\\H=\sqrt(400)\\H=20ft[/tex]

Hence, the length of the hypotenuse is [tex]20ft[/tex].

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The matrix represents the system of linear equations: -3x + 5y = 15 and 2x + 3y = -10.

The matrix represents the system of linear equations. Each row corresponds to an equation and each column to a coefficient of the unknowns. So, the given matrix:

-3  5  |  15
2  3  | -10

Represents the system of linear equations:

-3x + 5y = 15

2x + 3y = -10

Where x and y are the unknown variables that we are trying to solve for.

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Answer:

a. They are same side interior angles. Angle A measures 55°.

They are same side interior angles. Angle A measures 55° which is correct option(A).

Interior angles is defined as those that lie inside a shape, or those that are located in the region enclosed by two parallel lines that cross each other at a horizontal angle.

Alternate Interior Angles is defined as these angles are created when a transversal intersects two parallel lines. The opposing sides of the transversal produce this non-adjacent pair of angles.

Vertical angles is defined as when two lines meet each other at a point. They are always equal to each other, In other words, four angles are created anytime two lines cross or intersect.

Corresponding angles is defined as any pair of angles that are both on the same side of the transversal and of one of the two lines that it intersects.

Given angle measure as 125°

Therefore, they are same side interior angles. Angle A measures 55°.

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Answer: Hello mate!

A linear equation has the form y = ax + b

where x is the variable, a is the slope and b is the x-intercept.

We want to find the pararel line to y = -2x + 10

A paralel line of this, will be another line with the same slope ( -2 in this case) and a different x-intercept; then our line has the shape of:

y = -2x + b

and we know that this line pases through the point (6,8), and with this info we could find the value of b:

8 = -2*6 + b

b = 8 + 12 = 20

then y = -2x + 20 is the pararel line that passes through the point (6.8)

Then the correct answer is the option a:

a) y - 8 = -2(x - 6) = -2x + 12

y = -2x + 12 + 8 = -2x + 20

Answer:

b. Rock Samples

Explanation:

Rock samples are obtained by drilling with special drills into the substance.

So, holes drilled several kilometers into Earth's crust provide direct evidence about Earth's interior in the form of a rock samples.

The measure of the angle is 30 degrees

A supplementary angle can be defined as an angle that sum up t0 180 degrees.

The two angles must add up to 180 degrees, that is, angles on a straight line.

The properties of supplementary angles are;

From the information given, we have that;

The angle measures 150 degrees less of supplementary angles

Then,

180 - 150

30 degrees

Hence, the value is 30 degrees

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The two supplementary angles in question measure 15° and 165° respectively, with one angle being 150° less than the other.

We are given that one angle measures 150° less than its supplementary angle. By definition, supplementary angles add up to 180°. Let's call the angle in question 'A', and its supplementary angle 'B'.

We thus have the following relationship:

A = B - 150°

and

A + B = 180°

Substituting the first equation into the second, we get:

(B - 150°) + B = 180°

This simplifies to:

2B - 150° = 180°

2B = 330°

B = 165°

Now that we know the measurement of B, we can find A:

A = 165° - 150°

A = 15°

So, the two angles are 15° and 165° respectively.