Calculate the average speed of a cyclist that travels 30km in 3 hours

A polynomial function's sum is the result of adding all of its terms together. Simply add the coefficients of each phrase together, followed by the exponents of each term, to obtain the sum.

Take the polynomial function, for instance:

f(x) = 2x² + 4x + 3

The function's sum is  2x² + 4x + 3 = 9

Determine the highest exponent before attempting to get the sum of a polynomial with many terms. Next, sum up each term's coefficients that has that exponent. Add the exponents of each phrase to the total of the coefficients after the coefficients have been added. The polynomial function's sum is the final total.

Take the polynomial function, for instance:

f(x) = 2x³ + 4x² + 3x + 5

The function's sum is 2x³ + 4x² + 3x + 5 = 14

In conclusion, you put the coefficients of each term together to determine the total of a polynomial function, and then you add the exponents of each term to the sum of the coefficients. The polynomial function's sum is the final total.

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If the respective sides are proportional and the corresponding angles are congruent, two triangles are said to be similar.

Triangles with the same form but different sizes are referred to as comparable triangles. Examples of related objects are all equilateral triangles and squares with any side length. In other words, two similar triangles have similar sides that are proportionately equal and similar angles that are congruent.

If two triangles have an equal number of corresponding sides and corresponding angles, they can be compared. Similar figures are objects that have the same shape but various sizes, like two or more figures.

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Step-by-step explanation:

First you show that the triangles are congruent.

Then you show that the segments are congruent by CPCTC (Corresponding parts of congruent triangles are congruent.)

Given:

Segment KM is congruent to segment JM

<L is congruent to <H

We now have 1 pair of sides and 1 pair of angles that are congruent.

Angles KML and JMH are vertical angles, so they are congruent.

Now we have 2 pairs of congruent angles and 1 pair of not included congruent sides.

By AAS, triangle KML is congruent to triangle JMH.

By CPCTC, segment KL is congruent to segment HJ.

The number of miles that the crew has left to lay after 19 days is given as follows:

54 miles.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which the parameters are given as follows:

The parameters for this problem are given as follows:

m = -6, b = 168.

Hence the function is:

y = -6x + 168.

The amount of miles left after 19 days is obtained as follows:

y = -6(19) + 168

y = 54 miles.

The text of the problem is:

"A railroad crew can lay 6 miles of track each day. They need to lay  168 miles of track. "

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Answer:

D' is (16,20)

Step-by-step explanation:

A translation is the movement of the graphed line, either vertically or horizontally. The two given points are A and D:

A (2,11)

D (10,9)

When the line is translated, point A becomes A' (8,22).

Pint A is moved to the right by 6, and up by 11. Lets do the same for point D to make it D'

D' = (10+6, 9+11)

D' = (16,20)

See the attached graph.

A table gives the pairs input-output generated by the function.

We can define a general function as:

y = f(x)

where x is the input that we "feed" into the function, and the function gives y as the outcome.

A pair of input, output is written in a general form as (x, y).

If you have enough of these points, you can make a table:

inputs    outputs

x₁               y₁

x₂               y₂

x₃              y₃

...

That means that:

f(x₁) = y₁

f(x₂) = y₂

etc...

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Answer:

A) [tex]\displaystyle -2\frac{1}{4}[/tex]

Step-by-step explanation:

[tex]\displaystyle \frac{9}{10}\div\biggr(-\frac{2}{5}\biggr)=\frac{9}{10}*\biggr(-\frac{5}{2}\biggr)=\frac{9(-5)}{10(2)}=\frac{-45}{20}=\frac{-9}{4}=-2\frac{1}{4}[/tex]

Answer:36/(x+3)^2*(x-3)^2

Step-by-step explanation:

Answer:

f(-2) = -6

Step-by-step explanation:

f(x)=2x^2+7x        f(-2)

We put -2 in for x and solve

f(-2) = 2(-2)^2 + 7(-2)

f(-2) = 2(4) - 14

f(-2) = 8 - 14

f(-2) = -6

27m^3-64 = (3m)^3 - (4)^3

= (3m-4)((3m)^2 + (3m)(4) + (4)^2)

= (3m-4)(9m^2 + 12m + 16)

The factored form of 27m^3-64 is (3m-4)(9m^2 + 12m + 16)

Answer:

(3m−4)(9m2+12m+16)

Step-by-step explanation:

this is difference of cubes (3m)^3 - (4)^3

now, apply difference of cubes formula

a^3−b^3 = (a−b)(a2+ab+b2)

where a=3m and b=4

(3m−4) ( (3)^2×(m)^2 + 4×3m + (4)^2)

(simplify)

(3m−4)(9m2+12m+16)

Since we are going to check the similarity of the triangles and we have given two sides and angle we have to check the Side-Angle-Side option of the similarity. We have equal angles.

Since we are going to check the similarity of the triangles and we have given two sides and angle we have to check the Side-Angle-Side option of the similarity. We have equal angles. Then, we have to check the proportionality of the sides. If these triangles are equal, then VT/QR=UT/RS. If we calculate it, 28/7=44/11=4. This last number is the similarity ratio and since we have proportionality, ΔQRS ~ ΔVTU.

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The value of a  is 4 , b is 2 and c = -3 after factorising 8t² - 14t + 3

The process of breaking or decomposing an entity (such as a number, a matrix, or a polynomial) into a product of another entity, or factors, whose multiplication results in the original number, matrix, etc., is known as factorisation or factoring.

Factorization is the process of dividing a whole into components that, when multiplied together, equal the original number.

Factoring polynomials involves utilizing prime factorization to break the given polynomial down into a product of two or more polynomials. Polynomials can be readily simplified by factoring them.

The subsequent stages aid in the polynomial factoring process. The steps to factorizing a polynomial are listed below.

The function is 8t² - 14t + 3

so factorising :

8t² - 14t + 3 = 8t² - 12 t - 2t + 3 = 4t(2t - 3) - (2t - 3)

= (4t - 1)(2t -3)

The value of a  is 4 , b is 2 and c = -3

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Answer:

The point is in the second quadrant.

Substitute 6 for r.

The value of y is approximately 5.196.

Step-by-step explanation:

To convert polar coordinates (r,θ) to rectangular coordinates (x,y), we use the following formulas:

x = r * cos(θ)

y = r * sin(θ)

The point is in the second quadrant.

-This statement is true because the polar angle (120°) is in the range of 90° < θ < 180° which correspond to the second quadrant in the cartesian plane.

Start by adding 180° to θ.

This statement is False, because when converting from polar coordinates to rectangular coordinates we don't need to add 180° to the angle, we use the given angle as it is.

Substitute 6 for r.

This statement is true. In this case, the given polar coordinates are (6, 120°), so we substitute 6 for r in the formulas.

The value of x is 3.

This statement is False, to calculate x we use the formula x = r * cos(θ), so in this case x = 6 * cos(120°) = -3, which is not equal to 3.

The value of y is approximately 5.196.

This statement is true, to calculate y we use the formula y = r * sin(θ), so in this case y = 6 * sin(120°) = 6 * 0.866 = 5.196, which is approximately equal to 5.196

Answer:

The point is in the second quadrant

Step-by-step explanation:

The values of x and y in the equations are 3 and 5. Thus, Ryan walked 3 small dogs.

Let L be a giant dog and s be a tiny dog. What we do know is this:

s + L = 9 (9 dogs walked) (9 dogs walked)

(Money received from walking dogs is $51; 5s + 8L = 51)

To address a problem, we can employ substitution or elimination. I'll substitute in this situation (remove L from both sides):

s = 9 - L

5(9 - L) + 8L = 51

Distribute

45 - 5L + 8L = 51

45 + 3L = 51

Subtract 45:

3L = 6

Divide by 3:

L = 2

s = 9 - 2

s = 7

check:

5 * 7 + 8 * 2 = 51

35 + 16 = 51

51 = 51

The values of x and y in the equations are 3 and 5. Thus, Ryan walked 3 small dogs.

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The number that should be added to the expression x²+4x to change it into a perfect square trinomial is 4.

The general form of a perfect square trinomial is (x + y)^2, where x and y are the roots of the trinomial. To check if a trinomial is a perfect square, we can try to factor it into the square of a binomial. We can also complete the square method, which involves adding and subtracting the square of half of the x-coefficient of the linear term and then grouping the resulting terms.

It is important to note that for a trinomial to be a perfect square trinomial, the constant term must be a square of an integer and the linear term must be an even number.

Perfect square trinomials are used in solving quadratic equations and understanding their solutions, they also have applications in algebra, geometry, and trigonometry. Factoring them is a fundamental skill in algebra and is used in solving different types of mathematical problems.

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Complete Question: –

What will make the expression x²+4x a perfect square trinomial?

For x^2 * 5x to end in 5, x must be an odd number.

The last digit of a number is determined by its units digit. For example, the last digit of 123 is 3, the last digit of 789 is 9, and so on.

When you multiply two numbers, the last digit of the product is determined by the last digit of each factor. For example, the last digit of 3 * 4 is 2, the last digit of 6 * 7 is 2, and so on.

In this case, x^2 * 5x is a product of two numbers, x^2 and 5x. To find the units digit of x^2, we can square the units digit of x. The units digit of 5x is the units digit of x.

So, since we want x^2 * 5x to end in 5 , the last digit of x^2 * 5x has to be 5. The last digit of x^2 is the square of the last digit of x, and the last digit of 5x is 5 if x is odd and 0 if x is even.

--The question is not readable, answering to the question below--

"For what value of (x^2) * 5x ends in 5?"

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Answer: 14.31

Step-by-step explanation:

Using Law of Sines, we know that

[tex]\frac{16}{sin(72)} =\frac{PR}{sin(90)}[/tex]

Thus, [tex]PR=16.8233955878[/tex]

Then, using [tex]\frac{\alpha }{sin(\alpha)} =2R[/tex],

we know that [tex]\frac{16.8233955878}{sin(s)} =\frac{16.8233955878}{sin(36)} =28.621670112 = 2R[/tex]

Therefore, [tex]R = 14.310735056[/tex]

The multiplication rule example is calculating the probability that both the balls drawn are red from an urn containing 30 red and 10 blue balls. Two balls are pulled from a bag one after the other without replacement.

As per the multiplication rule, the probability of events A and B happening is equal to the product of the probability of B happening and the conditional probability that event A happens if event B occurs.

If A and B are dependent events, then the probability of both events happening simultaneously is given by:

P(A ∩ B) = P(B).P(A|B)

If A and B are two independent events in an experiment, then the probability of both events happening simultaneously is given by:

P(A ∩ B) = P(A).P(B)

Let's solve our given example

Let A and B represent the events that the first and the second balls are pulled, which are red balls. Now, we have to calculate P(A∩B) or P(AB).

P(A) = P(red balls in first draw) = 30/40

Now, only 10 balls of blue colour and 29 balls of red colour are left in the bag. The probability of pulling a red ball in the second draw is also an example of conditional probability, where the drawing of the second ball depends on the drawing of the first ball.

Hence Conditional probability of B on A will be,

P(B|A) = 29/39

By multiplication rule of probability,

P(A∩B) = P(A) × P(B|A)

P(A ∩ B) = 30/40 × 29/39 = 29/52

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Answer:

a₄ = 67

Step-by-step explanation:

the recursive rule allows a term to be found from the previous term

using the recursive rule

[tex]a_{n}[/tex] = - 3[tex]a_{n-1}[/tex] - 2 , then

a₁ = - 3

a₂ = - 3a₁ - 2 = - 3(- 3) - 2 = 9 - 2 = 7

a₃ = - 3a₂ - 2 = - 3(7) - 2 = - 21 - 2 = - 23

a₄ = - 3a₃ - 2 = - 3(- 23) - 2 = 69 - 2 = 67

The future value is $7,689,500.

The worth of a current asset at a future date based on an estimated rate of growth is known as future value (FV). Investors and financial planners care about future value because it helps them predict how much an investment made now will be worth in the future.

The future value formula assumes a constant rate of growth and a single up-front payment left untouched for the duration of the investment.

Given that,

P = 3500

R = 12%

T = 3 years

Future value (FV) = [tex]I*(1+R)^{T}[/tex]

where:

I=Investment amount

R=Interest rate

T=Number of years

Substituting the values in the formula given:

FV = 3500*(1+12)³= 3500*2197 = 7689500

Thus, the future value is $7689500

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There are 11 trees that are more than 6m tall but not more than 12m tall.

What is the Range?

In mathematics, a range is the set of all output values, or results, of a function. In statistics, a range is a measure of dispersion, which is used to describe the distribution of a set of data.

The table provided gives the frequency of trees at different height ranges. The range for the trees more than 6m tall but not more than 12m tall is 6<h<=9, and the frequency for this range is 11. This means that there are 11 trees in the park that are taller than 6 meters but not taller than 12 meters.

Hence, There are 11 trees that are more than 6m tall but not more than 12m tall.

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The Nature Of roots of quadratic equation "x² + 5x - 14 = 0 " is , that the roots are real and distinct .

In order to find the Nature of Roots of a quadratic equation , we use the Discriminant ,

Suppose the quadratic is given by : ax² + bx + c = 0 ,

then it's discriminant(D) will be written as :  D = b² - 4ac,

The equation is given as : x² + 5x - 14 = 0 ;

On comparing it with the general equation , we get that ;

⇒ a = 1 , b = 5 and c = -14 .

On substituting the values ,

we get ,  D = 5² - 4(1)(-14) ;

⇒  D = 25 + 56 ;

⇒ D = 81 .

We see that the Discriminant (D) is greater than 0 , the roots will be Real and Distinct .

Therefore , the nature of roots is that they are Real and Distinct .

The given question is incomplete , the complete question is

What is the nature of roots of quadratic equation x² + 5x - 14 = 0 ?

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The numbers are 2 and 4.

Difference in math is the result of one of the important mathematical operations, which is obtained by subtracting two numbers. It tells us by how much a number differs from the other.

Addition is a way of combining things and counting them together as one large group. Addition in math is a process of combining two or more numbers.

Here we have,

The difference in two numbers is 2.

2 and 4 are two numbers away from each other.

The sum of the same two numbers is 6.

2+4=6

Hence, In least to greatest order they would be written 2, 4.

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Rachel that swam 2 2⁄3rd mile then another 4 and one-half mile, did 5/12 miles more than Jason

Is a number that expresses the portion of some number over a total. The number that expresses the portion is known as the numerator and the number that expresses the total is known as the denominator.

To solve this problem we must perform the corresponding algebraic operations with mixed fraction.

Data of the problem:

A mixed operation is solved as follows:

For the denominator: the same denominator is placed.

For the numerator:

We transform the mixed fractions into improper fractions and we have:

3 1/2

= [(3*2) + 1)] /2

= [6+ 1] /2

7/2

3 1/4

= [(3*4) + 1)] /4

= [12+ 1] /4

13/4

2 2/3

= [(3*2) + 2)] /3

= [6+ 2] /3

8/3

4 1/2

= [(4*2) + 1)] /2

= [8+ 1] /2

9/2

Calculating how many miles Rachel did more than Jason we have:

Rachel miles more = Rachel - Jason

Rachel miles more = (8/3 + 9/2) - (7/2 + 13/4)

Rachel miles more = [(16 + 27)/6] - [(14 + 13)/4]

Rachel miles more = 43/6 - 27/4

Rachel miles more = (172 - 162)/24

Rachel miles more = 10/24

Simplifying we have:

Rachel miles more = 5/12

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For the equation -6x + 3y = -7 , the x-intercept and y-intercept is obtained as (1.167,0) and (0,-2.333) respectively.

What is an equation?

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").

The given equation is -

-6x + 3y = -7

To find the x-intercept, substitute the value of y = 0.

-6x + 3(0) = -7

-6x + 0 = -7

-6x = -7

Use the arithmetic operation of division -

x = -7/-6

x = 1.167

To find the y-intercept, substitute the value of x = 0.

-6(0) + 3y = -7

0 + 3y = -7

3y = -7

Use the arithmetic operation of division -

y = -7/3

y = -2.333

So, the x-intercept is obtained as x = 1.167 and y-intercept is obtained as  y = -2.333.

A graph can also be plotted to find the intercepts.

Therefore, the intercepts are x = 1.167 and y = -2.333.

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The number 48.050 has five significant figures.

What do you mean by an Significant figures?

Significant figures are the number of digits that add to the correctness of a value, frequently a measurement. The first non-zero digit is where we start counting significant figures. Determine how many significant digits there are given a range of numbers.

Significant figures, also known as significant digits, are the digits in a measurement or a number that carry meaning contributing to its precision. In this case, the number 48.050 has four non-zero digits (4,8,0,5) and one zero (0) between two non-zero digits, which are significant figures.

The trailing zero after the decimal point does not affect the significant figures, it is simply a placeholder to indicate the number is less than one and has a magnitude of 0.050.

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Answer:

G to the power of 5

Step-by-step explanation:

Since there are 5 Gs, the exponent would be 5

Answer: [tex]G^5[/tex]

Step-by-step explanation: G times G times G times G times G is G times itself 5 times, which can be rewritten as [tex]G^5[/tex]

Pedro is initially 700 ft higher than Naomi  

Pedro decended at a greater speed and it was 800 ft/ hr

Pedro reaches the bootom faster than Naomi.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides. We have LHS = RHS (left hand side = right hand side) in every mathematical equation. To determine the value of an unknown variable that represents an unknown quantity, equations can be solved. The statement is not an equation if there is no "equal to" sign in it.

Equations can be divided into three categories based on their degree. The three categories of mathematical equations are as follows:

Linear Equations

Quadratic Equations

Cubic Equations

Pedro's Elevation in feet equation

E = 4200 - 800h

So, initial elevation at h = 0 is

E = 4200 ft for Pedro

Now Naomi's Initial Elevation is 3500 ft.      

So, Pedro is 4200 - 3500 = 700 ft higher than Naomi                                            

at h = 1hr

Pedro's Elevation = 4200 - 800*1 = 3400 ft

and Naomi's Elevation = 2900 ft

Speed of desending of Pedro is = total distance/ total time

= (4200 - 3400)/1 = 800 ft/hr

Speed of desending of Naomi is = total distance/ total time

(3500 - 2900)/1 = 600 ft/hr

For Elevation = 0 for Pedro

0 = 4200 - 800h

h = 4200/800 = 5.25 hr

Naomi's elevation when time is 5.5 is 200 ft  

So, Pedro reaches the bootom faster than Naomi.

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Using trigonometric function the value of x is 51.3°.

What is trigonometric function?

The functions of an angle in a triangle are known as trigonometric functions, commonly referred to as circular functions. In other words, these trig functions provide the relationship between a triangle's angles and sides. There are five fundamental trigonometric functions: sine, cosine, tangent, cotangent, secant, and cosecant.

Here Let us take the given right triangle as ABC.

∠A = x , ∠B = 90° and AB = 25 , AC= 40

Now using Cosine ratio then

Cos  A = [tex]\frac{adjacent}{hypotenuse}[/tex]

=> cos x = [tex]\frac{25}{40}[/tex]

=> cos x = [tex]\frac{5}{8}[/tex]

=> x = [tex]cos^{-1}\frac{5}{8}[/tex]

=> x = 51.3°

Hence the value of x is 51.3°.

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The new points after a rotation of 180 degrees are

M' = (-3,1)

N' = (-8,4)

0' = (-6,6)

P' = (-7,1)

Quadrilateral MNOP has vertices M(3,-1), N(8,-4),O(6. -6), and P(1,-7).

Given a point (x, y) and we rotate by 180 degrees, the new point will be (-x, -y).

Given the coordinate points  M(3,-1), N(8,-4), O(6. -6), and P(1,-7), if these coordinates are rotated 180 degrees, the corresponding coordinate of the pre-image will be at M'(-3,1), N' (-8,4),0'(-6,6) and P'(-7,1).

So, the resulting coordinates will be M'(-3,1), N' (-8,4),0'(-6,6), and P'(-7,1).

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