is 5 rational or irrational

Answer: the rate of change of the distance between the car and the person at that instant is 4 meters per second

Step-by-step explanation:

According to the Pythagorean theorem, we have:

d^2 = (12^2 + 9^2)

Differentiating both sides with respect to time:

2d * (dd/dt) = 0 + 2(9) * (9''), Simplifying the equation, we get:

2d * (dd/dt) = 2(9) * (9'')

Substituting the given values:

2d * (dd/dt) = 2(9) * (4) [the car is moving at a constant velocity of 4 m/s]

Simplifying further:

2d * (dd/dt) = 72

we divide both sides by 2d:

dd/dt = 72 / (2d)

substitute this value into the equation to find the rate of change of the distance:

dd/dt = 72 / (2 * 9) = 4 m/s

The rate of change of the distance between the car and the person at that instant is -12/5 meters per second.

Given information:

The person is standing 12 meters east of the intersection.

The car is driving away from the intersection to the north at a constant speed of 4 meters per second.

At a certain instant, the car is 9 meters from the intersection.

Using the Pythagorean theorem, determine D(t) in terms of the car's distance from the intersection, which we'll call x(t).

Since the person is 12 meters east of the intersection, the distance D(t) can be expressed as:

[tex]D(t) = \sqrt{(x(t)^2 + 12^2)[/tex]

Differentiating both sides of the equation with respect to time, we get:

[tex]dD/dt = (1/2) * (x(t)^2 + 12^2)^{(-1/2)} * 2x(t) * dx(t)/dt[/tex]

So, dx(t)/dt = -4

Substituting this value into the equation for dD/dt, we have:

[tex]dD/dt = (1/2) * (x(t)^2 + 12^2)^{(-1/2)} * 2x(t) * (-4)[/tex]

[tex]dD/dt = -4x(t) / \sqrt{(x(t)^2 + 144)[/tex]

At the instant when the car is 9 meters from the intersection, substitute x(t) = 9 into the equation:

[tex]dD/dt = -4(9) / \sqrt{(9^2 + 144)[/tex]

          = -36 / √(81 + 144)

          = -36 / √225

          = -36 / 15

          = -12/5

Therefore, the rate of change is -12/5 meters per second.

Learn more about Rate of change here:

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Answer:

The answer is 51

Step-by-step explanation:

f(x) = 5x + 4

g(x) = −2x + 1

To find f(6)+g(-8) first find f(6) and g(-8) and add them

For f(6) we have

f(6) = 5(6) + 4

= 30 + 4

= 34

For g(-8)

g(-8) = - 2(-8) + 1

= 16 + 1

= 17

So we have

f(6)+g(-8) is

34 + 17

= 51

Hope this helps you

I hope this helped! Good luck with the rest of your class :)

Answer:

(-2,-7)

Step-by-step explanation:

Answer:

-2,-7

Step-by-step explanation:

NIJFNC JFVNJNFDVCMK DSN CHSFBNCODJ MKNVF

Step-by-step explanation:

Answer:

The answer would be 35066 :)

Step-by-step explanation:

(y+5554) + y = 64578

Combine like terms

2y = 64578-5554

2y = 59024

y = 29512

x = 29512 + 5554 = 35066

Answer:

15

Step-by-step explanation:

f(5) = (5)^2 - 2(5) = 25 - 10 = 15

=======================================================

Explanation:

This is a piecewise function as it is composed of two pieces.

The equation for f(x) depends on what x is. Specifically whether it is even or odd.

If x is even, then f(x) = x^2-4. If x is odd, then f(x) = 3x-2

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

f(4) means f(x) when x = 4. We have an even number input for x, so we'll go with f(x) = x^2-4

f(x) = x^2 - 4

f(4) = 4^2 - 4

f(4) = 16 - 4

f(4) = 12

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

When x = 5, x is now odd, so use f(x) = 3x-2

f(x) = 3x-2

f(5) = 3(5) - 2

f(5) = 15 - 2

f(5) = 13

Answer:

Option c.

Step-by-step explanation:

From the given table, it is clear that

[tex]P(2)=\dfrac{1}{36}[/tex]

[tex]P(6)=\dfrac{5}{36}[/tex]

[tex]P(7)=\dfrac{6}{36}[/tex]

The increasing rate of probability between a sum of 2 and a sum of 6 is

[tex]r_1=\dfrac{P(6)-P(2)}{6-2}[/tex]

[tex]r_1=\dfrac{\dfrac{5}{36}-\dfrac{1}{36}}{4}=\dfrac{1}{36}[/tex]

The increasing rate of probability between a sum of 6 and a sum of 7 is

[tex]r_2=\dfrac{P(7)-P(6)}{7-1}[/tex]

[tex]r_2=\dfrac{\dfrac{6}{36}-\dfrac{5}{36}}{1}=\dfrac{1}{36}[/tex]

Since [tex]r_1=r_2[/tex], therefore the probability increases at the same rate over both intervals.

Hence, the correct option is c.

Answer:

c)the probability increases at the same rate over both intervals

Step-by-step explanation:

it was right on khan academy

Answer:

36/25

Step-by-step explanation:

((7*3*2)/7*5)^2 * ((7^0)/(5^-3))^3 * 5^-9

(42/35)^2 * (1/5^-9) * 5^-9

36/25 * 5^9 * 5^-9

36/25 * 5^(9-9)

36/25 * 1

Answer:

35/25

Step-by-step explanation:

i hope this helps

Answer:

true

Step-by-step explanation:

Answer:

x = -3 is not a function because, for one thing, its graph does not pass the vertical line test.

Step-by-step explanation:

Answer:

The prime factors of a number are all the prime numbers that, when multiplied together, equal the original number. You can find the prime factorization of a number by using a factor tree and dividing the number into smaller parts.

Step-by-step explanation:

Answer:

A) QRST ∼ GFED

Step-by-step explanation:

We have to compare the ratios of all the sides one by one. Once I divided each side length by the equivalent side length on all four sides of both quadrilateral, make sure they are all equal.

Answer:

A) QRST is similar to GFED

Step-by-step explanation:

quadrilateral GFED is 1.25 times larger than quadrilateral QRST not to be confused with QRST is similar to DEFG because then the sides would not correspond to each other

Answer:

  a rectangle

Step-by-step explanation:

Translation and rotation are rigid transformations. They do not change the shape or size. The figure is still a rectangle after these transformations.

Answer:

The smallest four digit number divisible by 18, 24, and 32 is 1152.

Step-by-step explanation:

The LCM of the 3 numbers are 288

Then, the smallest four-digit number would equal 1152 (288*4)

Take L.C.M. of 18,24,32= 288

Resulting in 1152 :)

Answer:

not quite sure what this is asking for but the average speed is 7800/11

Answer:

d

Step-by-step explanation:

2/5÷ 1/10 = [tex]\frac{2}{5}*\frac{10}{1}[/tex]

               = 2 * 2

               = 4

Answer:

b

Step-by-step explanation:

LCD of (5, 10): 10

2/5=4/10(multiply top and bottom by 2)

(4/10)/(1/10)= 4

Therefore, 1/10 is 1/4th of 2/5

Answer: 3060

Step-by-step explanation:

Formula : (r+1)th term of [tex](a+b)^n[/tex] : [tex]T_{r+1}=\ ^nC_r(a)^{n-r}(b)^r[/tex]

To find: Coefficient of [tex]x^{14}y^4[/tex] in the expansion of [tex](x + y)^{18}[/tex].

Let the term in the expansion of [tex](x + y)^{18}[/tex] be [tex]^{18}C_r x^{18-r}y^r=x^{14}y^4[/tex]

[tex]\Rightarrow\ r=4[/tex]

Now, Coefficient = [tex]^{18}C_r=^{18}C_4=\dfrac{18!}{4!14!}[/tex]     [[tex]^nC_r=\dfrac{n!}{r!(n-r)!}[/tex]]

[tex]=\dfrac{18\times17\times16\times15\times14!}{14!(24)}\\\\=3060[/tex]

Hence, the coefficient of [tex]x^{14}y^4[/tex] in the expansion of [tex](x + y)^{18}[/tex] is 3060 .

Answer:

7z + 4.5y = 2650

z + y = 450

Step-by-step explanation:

The first equation represents the amount of money made from ticket sales for both adult and child tickets.

The second equation represents the amount of customers, both adult and child, that attended the theatre.

Using both equations you cans find the number of adults and children that attended the theatre.

Cheers.

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

Edit: Solving for the variables

There are two easy ways to solve for these values. The first is using an augmented matrix and solving with that method.

7 4.5 | 2650

1 1 | 450

After are augmented matrix is set up, we simply use row operations on the matrix to solve for 1s on the diagonal.

The second method for solving is equation addition or variable substitution to solve for each variable.

7z + 4.5y = 2650

z + y = 450

7(450-y) + 4.5y = 2650

3150 - 7y + 4.5y = 2650

-2.5y = -500

y = 200

Plug back in y into one of the equations to solve for z.

z + 200 = 450

z = 250

So there were 250 adults and 200 children.

Answer:

i think u r correct

Step-by-step explanation:

good job

Answer:

B, C, and E ([tex]x\leq -7,[/tex] The graph has a closed circle, and -7 is part of the solution.)

Step-by-step explanation:

Let's first solve the inequality of [tex]15\geq 22+x[/tex].

[tex]15\geq x+22[/tex]

[tex](15)-22\geq( x+22)-22[/tex]

[tex]-7\geq x[/tex]

[tex]x\leq -7[/tex]

So the final equation comes out to be [tex]x\leq -7[/tex].

This graph has a closed circle as it is a greater than OR equal to.

And -7 is a part of this solution as it is the number x is being compared to.

Let me know if I got anything wrong.

Answer:

5

Step-by-step explanation:

Take the length of the string and divide by the length of a bead

15/3 = 5

We can fit 5 beads

Answer:

5 beads

Step-by-step explanation:

In order to find out how many 3-inch beads could fit onto a 15-inch string, we have to divide the numbers to find out how many beads could fit onto the string.

[tex]\frac{15}{3} =5[/tex]

Maurice can fit 5 beads onto the 15-inch string.

Answer:

[tex]\Large \boxed{(x+4)(x-1)}[/tex]

Step-by-step explanation:

Hello,

[tex]x^2+3x-4\\\\\text{*** The product of the zeroes is -4=-1*4 and their sum is -3=-4+1. ***}\\\\\text{*** So we can factorise. ***}\\\\x^2+3x-4=x^2-x+4x-4=x(x-1)+4(x-1)=\large \boxed{(x+4)(x-1)}[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

The factors of given function are (x + 4) and (x - 1)

To undestand more, check below explanation.

The modeled for algebra tiles is given as,

                 [tex]f(x)=x^{2} +3x-4[/tex]

We have to find the factors of given function.

Factoring means finding expressions that can be multiplied together to give the given equation.

If a quadratic equation can be factored, it is written as a product of linear terms.

            [tex]f(x)=x^{2} +3x-4\\\\f(x)=x^{2} +4x-x-4\\\\f(x)=x(x+4)-1(x+4)\\\\f(x)=(x+4)(x-1)[/tex]

Hence, the factors of given function are (x + 4) and (x - 1)

Learn more about the factors here:

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Answer:

B

Step-by-step explanation:

So, for five cups of water, you need one cup of sugar. 1s=5w.

Now, you divide both sides by five.

1/5s=1/w

Answer:

(x45)

Step-by-step explanation:

(x2) (x4) (x-5)

(x8) (x-5)

(x45)

Answer:

Four books  because there are the most dots over that spot on the bottom number line thingy

Answer:

M=-1, N=7

Step-by-step explanation:

Something went wrong on the 4th line.

From the third line, it should read

2x^2-x+6Mx-3M+4

=x(2x-1+6M) - 3M+4

Equating with the RHS,

2x-1+6M = 2x-7

6M = -7+1 = -6

M = -1

Therefore

N = -3M+4 = -3(-1)+4 = 7

or

M=-1, N=7

Answer:

I think it is 441

Step by step explanation:

To make a rectangle you need to pick any two of the vertical lines, and any two of the horizontal lines. So there would be 91 squares and 441 rectangles.