If a car with an average speed of 50 miles per hour travels for 30 minutes, how far will it have gone?

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.

fisher has x cars

 sawyer has 3 times as many so he has 3x cars

Answer is B

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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Answer: [tex]\angle WXY=125^{\circ}[/tex]

Explanation: Since, a kite has one pair of congruent angles and its main diagonal bisects its opposite angles.

Therefore, According to the given figure,

[tex]\angle WXY=\angle WZY[/tex]

And, WY is the main diagonal which bisects angles ZWX and XYZ.

So, [tex]\angle ZWX =2\times \angle ZWY= 2\times 43^{\circ}=86^{\circ}[/tex]

And, [tex]\angle XYZ =2\times \angle XYW= 2\times 12^{\circ}=24^{\circ}[/tex]

Since, Sum of all angles of a quadrilateral is equal to [tex]360^{\circ}[/tex]

Therefore, [tex]\angle WXY+\angle WZY+\angle XYZ+\angle ZWX=360^{\circ}[/tex]

⇒[tex]2\times \angle WXY+ 86^{\circ}+24^{\circ}=360^{\circ}[/tex]

⇒[tex]2\times \angle WXY=360^{\circ}-110^{\circ}=250{\circ}[/tex]

⇒ [tex]\angle WXY=125^{\circ}[/tex]

Answers:

  A. If two angles are linear pairs, the angles are supplementary. The two angles are linear pairs. Therefore, the angles are supplementary.  

 B. If an object is a square, it is a parallelogram. The object is a square. The object is a parallelogram.

 C. If it is snowing, the play will be cancelled. It is snowing. Therefore, the play is cancelled.

  These are right.

Answer:

Law of detachment:

Statement 1: If a, then b

Statement 2: a

Conclusion: b

(A)

1. If two angles are linear pairs, then the angles are supplementary.

2. The two angles are linear pairs.

Let a be the statement " two angles are linear pairs"

let b be the statement "the angles are supplementary"

then, 1 and 2 can be written as;

1. if a , then b

2. a

So, by the law of detachment we can deduce that b is true.

i.e, The angles are supplementary.

(B)

1. If an object is a square, then it is a parallelogram.

2. The object is a square.

Let a be the statement " an object is a square"

let b be the statement "The object is a square"

then, 1 and 2 can be written as;

1. if a , then b

2. a

So, by the law of detachment we can deduce that b is true.

i.e, The object is a parallelogram.

(C)

1. If  it is snowing, then the play will be cancelled.

2. It is snowing.

Let a be the statement "it is snowing"

let b be the statement "the play will be cancelled"

then, 1 and 2 can be written as;

1. if a , then b

2. a

So, by the law of detachment we can deduce that b is true.

i.e, The play is cancelled.

Only option A, B and C  are examples of the Law of Detachment.

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 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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Answer:

Step-by-step explanation:

Given is the polynomials as

1) [tex]f(x) = x^3+2x^2-x-2[/tex]

The graph of this function has x intercepts as

-2, -1 and 0

Since f(x) =0 has solutions equivalent to x intercepts we see that the roots are

-2,-1 and 0

2) Given is a polynomial as

[tex]f(x) = 2x^3+5x^2-8x-20 =0[/tex]

Using rational roots theorem we find that

the roots possible are ±1.±2,±4,±5,±10,±20,±1/2,±5/2

Using remainder theorem we see that

f(2) =f(-2)=0

By using division, we find that the other factor is 2x+5

Hence roots are 2,-2, -2.5

Answer:

option b

Step-by-step explanation:

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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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]