A school is arranging a field trip to the zoo. The school spends 515.84 dollars on passes for 30 students and 2 teachers. The school also spends 282.90 dollars on lunch for just the students. How much money was spent on a pass and lunch for each student?

Step-by-step explanation:

This is a polynomial so we can use rational roots Theorem to solve the equation.

The rational roots simply states that the roots of a polynomial, in the form of

[tex]p{x}^{n} + ax {}^{n - 1} + bx {}^{n - 2} .....r {}^{0} [/tex]

The possible roots of the polynomial are the factors of

p/r.

We say r^0 to represent the constant and p to represent the leading coeffceint.

So the rational roots states the possible roots of a polynomial is

the factors of leading coeffceint/ the factors of the constant.

In this case, the polynomial leading coeffecient is 3 and its constant is 6 so we do the factors of 3 divided by the factors of 6.

The factors of 3, are plus or minus 1 and 3. divided by factors of 6 which are plus or minus 1,2,3,6. So our possible roots are

positive or negative (1,1/2, 1/3,1/6, 3, 3/2).

Now, we see which of the following roots will that the polynomial, P will equal zero.

It seems that -1 can work so by definition, (x+1) is the a factor of the polynomial. So now we use synetheic or long division to cancel out that factor.

So our factored version of the polynomial is

[tex](x + 1)(3x {}^{3} - 14 {x}^{2} + 13x + 6)[/tex]

Now can we continue and factor the right side of the factors.

3 also works so x-3 is a factor as well so

[tex](3 {x}^{2} - 5x - 2)(x + 1)(x - 3)[/tex]

Now factor the quadratic using factoring by grouping

[tex]3 {x}^{2} - 5x - 2 = 3 {x}^{2} - 6x + x - 2 = 3x(x - 2) + 1(x - 2) [/tex]

So our factor are

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

So in conclusion our factors are

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

And our x values are -1/3, 2, -1, and 3.

Answer:

I = 8000×1×15

--------------

100

I = 120000

----------

100

I = Rs 1200

Answer:

the mmic is back still swords rund eep

Step-by-step explanation:

Answer:

[tex](x+2)(3x^3-5x-10)[/tex]

Step-by-step explanation:

If you don't know how to divide polynomials then I can help with that too or you can just search it up

Answer: Would you like all of them?

Step-by-step explanation:

Answer:

Reducing the angle to where the force is more in line with the direction of motion.

Step-by-step explanation:

Work is commonly defined as force * distance. Since the 75N force is not acting directly in line with the direction of motion (15 degrees offset), we are not utilizing the full 75 N in moving the object. By reducing the angle of offset, we allow more of the force to be used in moving the object and therefore increase the amount of work being done.

Answer:

Decreasing the angle to 10

Step-by-step explanation:

Answer:

10) SAS

12) SAS

13) SSS

11) ASA

14) ASA

Answer:

10. none

11. AAS

12. SAS

13. SSS

14. SAS

15. ASA

Step-by-step explanation:

I'm not going into detail of each question... I have a 101 in geometry right now though and I've already done triangles, so just trust me on this one.

Answer:

27 in²

Step-by-step explanation:

The area (A) is calculated as

A = πr² ( r is the radius ) , then

A = π × 3² = 3 × 9 = 27 in²

The common ratio for the given geometric sequence, written as a fraction is [tex]\frac{5}{8}[/tex]

Given the following geometric sequence:

To determine the common ratio for the given geometric sequence:

The common ratio of a geometric sequence refers to the ratio or constant factor between two (2) consecutive numbers in the sequence.

Mathematically, the common ratio of a geometric sequence is given by the formula:

[tex]C=\frac{T_{n+1}}{T_n}[/tex]

Substituting the given parameters into the formula, we have;

[tex]C = \frac{300}{480} \\\\C=\frac{30}{48} \\\\C=\frac{5}{8}[/tex]

Read more: https://brainly.com/question/13162487

The length of the sides of the square labelled x is b. 6.0 m.

Recall:

Given that the grass area is 64 sq. meters, to find the length of the sides labelled x, first find the area tat has sides labelled x.

Area = Total area of the garden - 64 sq. m

Area = (10 × 10) - 64

Area = 36 sq. m.

Area of square = s²

Lex x = s

x² = 36

x = 6 m

Therefore, the length of the sides of the square labelled x is b. 6.0 m.

Learn more about area of a square on:

https://brainly.com/question/16758129

Step-by-step explanation:

Answer:

6.6 ft.

Step-by-step explanation:

Right triangle: Use this formula a² + b² = c² .  Given c = 12, a = 10 find b

(10)² + b² = (12)²

100 + b² = 144

        b² = 144 - 100

        b² = 44

        [tex]b = \sqrt{44}[/tex]

        b = 6.6

Answer:

33 2/3

Step-by-step explanation:

First you would change 0.2 to a fraction. This would be 1/5. You would then have to make these two have a common denominator. 6 1/3 would also become an improper fraction for visual sake.. The lowest common denominator they share is 15. I've drawn the process in the image above.

So now we have 95/15 and 3/15. From here, we would divide 95 by 3.

95 ÷ 3 = 31 10/15

This would give us 31 and 10/15 servings of pasta in the bowl. If we're talking about full servings, 31 would be the correct number, but if we're talking exact, then it is 31 2/3.

Step-by-step explanation:

y=5(-1)+3

y=-5+3

y=—2

y=5(0)+3

y=3

y=5(1)+3

y=5+3

y=8

y=5(2)+3

y=10+3

y=13

Answer:

If today is Saturday, then after 70 days, we will be on a Saturday again.

Step-by-step explanation:

Basically, 70 days = 10 weeks

Which means: 1 week = 7 days

We also know that if we are on a Saturday, then after a week, we will be on a Saturday again. Therefore, if we are on a Saturday, after 10 weeks or 70 days, we will be on a Saturday again.

Hoped this helped.

Answer:

Y = 56X + 20.50

Step-by-step explanation:

y=mx+c

Assuming that the y intercept is an additional numeral constantly given in a linear function. and the slope represented by the main wage of the job while concluding that it's the slope since it implies rate of change.

hope it's correct

Answer:

3:7

Step-by-step explanation:

She has 3 tennis and 7 soccer

Answer:

m∠URV = 124°

Step-by-step explanation:

hope this helps

Answer:

what is the work to figure out the anwser?

Step-by-step explanation:

Solve from right to left

[tex]\\ \sf\Rrightarrow 0.02349[/tex]

[tex]\\ \sf\Rrightarrow 0.0235\times 10^{-1}[/tex]

[tex]\\ \sf\Rrightarrow 2.35\times 10^{-3}[/tex]

Option C is correct

Using reference angles, it is found that the correct option is:

Angle [tex]\frac{5\pi}{6}[/tex] is on the second quadrant, [tex]\frac{\pi}{2} < \frac{5\pi}{6} < \pi[/tex].

[tex]\pi - \frac{5\pi}{6} = \frac{6\pi}{6} - \frac{5\pi}{6} = \frac{\pi}{6}[/tex]

Angle [tex]\frac{5\pi}{3}[/tex] is on the fourth quadrant, [tex]\frac{3\pi}{2} < \frac{5\pi}{3} < 2\pi[/tex].

[tex]2\pi - \frac{5\pi}{3} = \frac{6\pi}{3} - \frac{5\pi}{3} = \frac{\pi}{3}[/tex]

They have different reference angles, hence:

For more on angles, you can check https://brainly.com/question/24787111

Answer:

A

Step-by-step explanation:

A

[tex](3)\\\\17^{\tfrac 43} = \left(17^{\tfrac13\right)^4 = \left(\sqrt[3]{17}\right)^4 =\left(\sqrt[3]{17}\right)^3 \left(\sqrt[3]{17}\right) = 17\sqrt[3]{17}[/tex]

[tex](4)\\\\\text{First term, a= 4,}\\\\\text{Common difference,}~ d =13-4 = 9\\\\\text{nth term} = a+(n-1)d = 4 +(n-1)9 = 4+9n-9 = 9n-5\\\\\text{ 5000th term} = 9(5000) -5 =44995[/tex]

Answer:

the rise is 6 and the run is 4

Answer:

The rise is 6 and the run is 4

Answer:

x = 40

Step-by-step explanation:

measure of the angles = 1/2( outside arc - inside arc)

       x/2 = 1/2[x + 70 - (x + 30)]

       x/2 = 1/2 ( x + 70 - x - 30)

       x/2 = 1/2 (40)

       2(x/2) = 2(1/2)(40)

            x = 40

Answer:

x = 14

y = 6

Step-by-step explanation:

*Property*

In a parallelogram:

Opposite sides are equal.

Since, the given figure is a parallelogram we can apply this property and equate:

1) 2y + 1 = 13

subtracting 1 from both sides:

=> 2y + 1 - 1 = 13 - 1

=> 2y = 12

dividing both sides by 2:

=> 2y/ 2 = 12/ 2

On the LHS, 2 gets canceled because it's available in the numerator as well as the denominator

On the RHS, 2 gets canceled when 12 is factorised to 6 × 2:

2) x = y + 8

We've got the value of y from equation 1).

Substituting it here:

=> x = 6 + 8

Answer:

Hence, we got the values of x and y as:

[tex]\mathsf{x = 14 }\\ \mathsf{ y = 6}[/tex]

Answer:

72

Step-by-step explanation:

50% means ½ of the usual days,

if 50% = 24 days

then the usual day is 48 days

so, 48+24= 72