sanjay can travel 342 miles in 6 hours. at this rate, how far can he travel in 5 hours?

The answer is c.

If you have a root (a), it can also be written as (x-a).

(x+6),(x-1),(x-4)

Multiply all of them together to get the equation

(x+6)(x-1)(x-4)=

(x2-x+6x-6)(x-4)=

(x2+5x-6)(x-4)=

(x3+5x2-6x-4x2-20x+24)=

x3+x2-26x+24

To find a polynomial with given roots −6, 1, and 4, we create factors (x + 6), (x - 1), and (x - 4). Multiplying these factors, we get the polynomial x3 - 5x2 - 21x + 24.

Finding the Polynomial with Given Roots

To find a polynomial with roots of −6, 1, and 4, we need to create factors that each set to zero at these roots. A polynomial is a product of its factors, and a root is a solution to the equation where the polynomial is equal to zero. The factors corresponding to the roots −6, 1, and 4 are (x + 6), (x - 1), and (x - 4) respectively. Multiplying these factors gives us the polynomial:

(x + 6)(x - 1)(x - 4) = x3 - (1 + 4)x2 + (4 - 1 - 24)x + (6 x 1 x 4)

Let's expand and simplify:

x3 - 5x2 - 21x + 24

Therefore, the polynomial with roots of
−6, 1, and 4 is x3 - 5x2 - 21x + 24.

The difference in quotients arises because dividing by smaller numbers results in larger quotients. For example, 80,000 divided by 2,000 equals 40, while dividing by 200 equals 400, and by 20 equals 4,000.

To understand this, let's calculate each quotient step-by-step:

The differences in results are due to the different divisors. As you divide by smaller numbers, the quotient increases because each division breaks the total into more parts.

Division and multiplication are closely related; dividing by a number is the same as multiplying by its reciprocal.

Summary

The fundamental concept here is that dividing by a larger number results in a smaller quotient, whereas dividing by a smaller number results in a larger quotient. This difference is evident when comparing the quotients of 80,000 divided by 2,000 (40), 200 (400), and 20 (4,000).

To find the number of student and adult tickets sold at a baseball game, we can set up a system of equations using the given information. Solving the system of equations will give us the values of the variables. In this case, 150 student tickets and 250 adult tickets were sold.

Let's assume that the number of student tickets sold is 'x' and the number of adult tickets sold is 'y'.

According to the information given, the total attendance was 400 people, so we can write the equation: x + y = 400.

The total ticket sales were $1050, so we can write another equation: 2x + 3y = 1050.

Now we have a system of equations that we can solve to find the values of x and y.

Using substitution or elimination method, we find that x = 150 and y = 250.

Therefore, 150 student tickets and 250 adult tickets were sold.

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the distance between the R and the T is

4 units

The amount of the original bill at johnny rockets was $32.50.

An equation is an expression used to show the relationship between two or more numbers and variables.

Let a represent the total bill.

You and four friends split the bill equally. each person share was $6.50. Hence:

a / 5 = 6.50

a = 32.5

The amount of the original bill at johnny rockets was $32.50.

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Answer:

[tex]\$60[/tex]

Step-by-step explanation:

Let

x------> the cost of the barrel of oil before the increase

we know that

[tex]100\%+20\%=120\%[/tex]

[tex]120\%=\frac{120}{100} =1.2[/tex]

so

[tex]1.2x=72[/tex]

Solve for x

[tex]x=72/1.2=\$60[/tex]

To estimate the height of a mountain using angles of elevation from two points, set up a system of trigonometric equations based on right triangles and solve for the height using algebra.

To estimate the height of a mountain given two angles of elevation at different points, we use trigonometric concepts. At the first point, the angle of elevation is 32°, and at a point 1000 feet closer, the angle is 35°. To solve this, we can set up two right triangles that share the same height (the mountain) but have different base lengths. Denote the height of the mountain as h, the distance from the first observation point to the base of the mountain as d, and use the trigonometric tangent function:

Tan(32°) = h / d

Tan(35°) = h / (d - 1000)

This creates a system of two equations with two variables. We solve for h by manipulating the equations to isolate h and substituting into one of the equations. We can use trigonometric tables or a calculator to find the values for Tan(32°) and Tan(35°), and then solve for the distance d, which subsequently allows us to find the height h by simple algebraic rearrangement.

The perimeter of a rectangle is an application of the Distributive property is shown below.

The dividing Property it is necessary to multiply each of the two integers by the factor before performing the addition operation when a factor is multiplied by the sum or addition of two words.

This property can be stated symbolically as: A ( B+ C) = AB + AC.

Given:

As, we know the perimeter of a rectangle is twice the sum of its length and width.

let length of rectangle be 'l' unit and width of rectangle is 'w' unit.

So, the Perimeter of rectangle =2L+2W

                                                   =  2(L+W)

Here, 2 is distributed over length of width in parenthesis.

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[tex]4\dfrac{1}{3}\div\left(-\dfrac{5}{6}\right)\qquad(*)\\\\\text{Convert the mixed number to the improper fraction:}\\\\4\dfrac{1}{3}=\dfrac{4\cdot3+1}{3}=\dfrac{12+1}{3}=\dfrac{13}{3}\\\\(*)=\dfrac{13}{3}\div\left(-\dfrac{5}{6}\right)\\\\\text{By dividing by a fraction, we multiply by its reciprocal.}\\\\=\dfrac{13}{3}\cdot\left(-\dfrac{6}{5}\right)\qquad\text{simplify}\\\\=\dfrac{13}{3\!\!\!\!\diagup_1}\cdot\left(-\dfrac{6\!\!\!\!\diagup^2}{5}\right)=-\dfrac{13\cdot2}{1\cdot5}=-\dfrac{26}{5}=-\dfrac{25+1}{5}=-5\dfrac{1}{5}[/tex]

Answer:

the answer is 13/3  ÷ ( - 5/6 )  my luv :)

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hope i helped ! < 33

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                                         the crown under my answer :)

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Step-by-step explanation:

Answer:

How many distinct triangles can be formed for which m∠E = 64°, g = 9, and e = 10?

⇒ 1 triangle(s)

How many distinct triangles can be formed for which m∠J = 129°, k = 8, and j = 3?

⇒ 0 triangle(s)

Answer:

The first one is 1. The second one is 0.

Step-by-step explanation:

I just did it and got it right.

To determine if a pair of numbers is relatively prime, we need to find their greatest common divisor (GCD). If the GCD is 1, then the numbers are relatively prime. The pair 14 and 81 is relatively prime.

For two numbers to be relatively prime, their greatest common divisor (GCD) must be 1.

We can find the GCD by finding the prime factors of each number and determining if they have any common factors.

Let's take a look at each pair of numbers:

Therefore, the pair of numbers that is relatively prime is 14 and 81.