What are the missing parts that correctly complete the proof?

The products of two numbers involves multiplying them.

The two numbers are -5 and 6

Let the numbers be x and y.

So, we have:

[tex]\mathbf{x \times y = -30}[/tex]

[tex]\mathbf{x + y = 1}[/tex]

Make x the subject in [tex]\mathbf{x + y = 1}[/tex]

[tex]\mathbf{x = 1 - y}[/tex]

Substitute [tex]\mathbf{x = 1 - y}[/tex] in [tex]\mathbf{x \times y = -30}[/tex]

[tex]\mathbf{(1 - y)y = -30}[/tex]

Expand

[tex]\mathbf{y - y^2 = -30}[/tex]

So, we have:

[tex]\mathbf{y^2 -y - 30 = 0}[/tex]

Expand

[tex]\mathbf{y^2 -6y + 5y - 30 = 0}[/tex]

Factorize

[tex]\mathbf{y(y -6) + 5(y - 6) = 0}[/tex]

Factor out y - 6

[tex]\mathbf{(y + 5) (y - 6) = 0}[/tex]

Solve for y

[tex]\mathbf{y = -5\ and\ 6}[/tex]

Hence, the two numbers are -5 and 6

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The measure of angle <0 in the right triangle is approximately 30 degrees.

To find the measure of angle <0 in the right triangle, we can use trigonometry. The side opposite to angle <0 is given as 5 inches. The hypotenuse is given as 10 inches. We can use the sine ratio to find the angle:

sin(<0) = opposite/hypotenuse

substituting the given values:

sin(<0) = 5/10 = 0.5

Now, to find the measure of angle <0, we can use the inverse sine function:

<0 = arcsin(0.5)

Using a calculator, we find that the measure of angle <0 is approximately 30 degrees.

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To have an inverse function, a function f must be onto the function,

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

Inverse function of function is defined as the, that modified and derived  function from parent function that has domain[range of parent function] and range [domain of parebt function].

here,
To have an inverse function, a function f must be onto function, because it is neccessary that the function gives one distinct image for the distinct pre-image.

Thus, To have an inverse function, a function f must be onto function,

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To have an inverse function, a function must be bijective, meaning it is both one-to-one (injective) and onto (surjective). An example is shown with the function f(x) = x^2 which is not injective, hence doesn't have an inverse function.

In mathematics, to have an inverse function, the original function, represented as f, must be both injective (one-to-one) and surjective (onto). This dual property is called being bijective. This means every element of the function's domain maps to one distinct element in the function's range (injective) and that every element in the range has a pre-image in the domain (surjective).

For example, consider the function f(x) = x^2. This function is not injective, as both f(-2) and f(2) give the same output, hence it does not have a true inverse function across all real numbers.

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The Answer is C 5/6

250/300 reduced and simplified is 5/6

Answer:

The probability that the student is right-handed given that the student is a girl is:

[tex]\dfrac{5}{6}[/tex]

Step-by-step explanation:

From the tree diagram we have to find the probability that the students is right handed given that the student is a girl.

Let A denote the event that the student is a girl.

and B denote the event that the student is right handed.

We are asked to find the probability:

P(B|A)

We know that P(B|A) is calculated as:

[tex]P(B|A)=\dfrac{P(A\bigcap B)}{P(A)}[/tex]

There are a total of 500 students.

Out of which 300 are girls.

( i.e. [tex]P(A)=\dfrac{300}{500}=\dfrac{3}{5}[/tex]    )

and out of 300 girls 250 are right handed.

( i.e. [tex]P(A\bigcap B)=\dfrac{250}{500}=\dfrac{1}{2}[/tex]  )

Hence,

[tex]P(B|A)=\dfrac{\dfrac{1}{2}}{\dfrac{3}{5}}\\\\\\P(B|A)=\dfrac{5}{6}[/tex]

Hence,The probability that the student is right-handed given that the student is a girl is:

[tex]\dfrac{5}{6}[/tex]

The measure of the complementary angle will be 61°.

The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360 °.

Complementary angle - Two angles are said to be complementary angles if their sum is 90 degrees.

An angle measures 29°.

Let 'x' be the complementary angle. Then the measure of the complementary angle is given as,

x + 29° = 90°

Simplify the equation, then we have

x + 29° = 90°

x = 61°

The measure of the complementary angle will be 61°.

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When two parallel lines are cut by a transversal vertical lines are not always congruent.

A line that goes through two lines in the same plane at two different points is called a transversal. When determining whether two or more other lines in the Euclidean plane are parallel, transversals play a role. Different kinds of pairs of angles are created when two lines intersect a transversal: alternate angles, corresponding angles, consecutive exterior angles, and consecutive interior angles. If the two lines are parallel, Euclid's parallel postulate states that consecutive interior angles are supplementary, that corresponding angles are equal, and that alternate angles are equal.

Given  to find the pairs of angles are not always congruent when two parallel lines are cut by a transversal,

when parallel lines are cut by a transversal some pair of angles are congruent like alternative exterior angle, corresponding angles and  

Consecutive interior angles all the pairs are congruent and equal.

but When a transversal line cuts through two parallel lines, vertical lines are not always congruent.

Therefore vertical lines are not always congruent.

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Answer:

option b

Step-by-step explanation:

Answer:

The triangles are similar by AA

Step-by-step explanation:

12/40 =0.3

28 *0.3 = 8.4

it will cast a 8.4 foot long shadow

Answer:

The shadow cast by a 28-foot tree is 8.4 foot.

Step-by-step explanation:

The rule of three is a way of solving problems of proportionality between three known values and one unknown, establishing a relationship of proportionality between all of them. In the case of direct proportionality, when one magnitude increases, the other increases (  or if one magnitude decreases, the other will also decrease)

This is an example of application of this rule:

40 foot tree ⇒ 12 foot shadow

28 foot tree ⇒ x foot shadow

Then, to solve and calculate the value of x, which is the value of the shadow cast by the 28-foot tree, perform the count:

x=[tex]\frac{28*12}{40}[/tex]

x=[tex]\frac{336}{40}[/tex]

x=8.4

This means that the shadow cast by a 28-foot tree is 8.4 foot.

The false statement among the given options is B) 21,730 > 22,341. The greater than, less than symbols should be accurately used to compare two numbers. The other given statements are true.

The false statement in the given options is B) 21,730 > 22,341. This statement is saying that 21,730 is greater than 22,341, which is false. In mathematics, '<' symbol represents 'less than' and '>' represents 'greater than'. So, the statement B) is false because 21,730 is not greater than 22,341, but less.
Comparing the following two statements A) 21,730 < 22,341 and C) 22,341 > 21,730, we can see they are actually the same statement, restated in a different manner. Both statements are saying that 21,730 is less than 22,341 which is true.
The statement D) 22,341 < 24,687 is also true because 22,341 is less than 24,687.

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Answer:

C

Step-by-step explanation:

I did it and got it right!