Given the figure below, find the values of x and z.

Answer:

B. The variable s represents the number of students in each class.

C. The coefficient 14 represents the number of classes in the 9th grade.

Step-by-step explanation:

The total number can be found by multiplying the number of the things with the number of people producing it. For example if 5 boys make 5  colored ropes the total number of ropes will be 5*5= 25.

In this question the combinations rule is used for variuos number of classes which are 14. Now we have to find the number of students which are s (s-1). Suppose s= 6 so the number of students would be 6(6-1) = 6(5) = 30

We will multiply the number of classes 14 with the number of students s(s-1) to get the total number of cards produced.

Answer:

a) half life is 3h 17 minutes

b) function of residue drug after t hours with initial quantity = 500 mg

        f(t) = 500 (0.81^t)

c) drug left in patient's system after 24 hours

   = 0.00 grams (to the hundredth of a gram.

Step-by-step explanation:

Given:

Drug initial active weight, A = 500 mg

Residue active weight, f(t) = A 0.81^t

t = time in hours.

a) half life

Half life is T, such that f(T) = 0.5A =>

0.5A = A(0.81^t)

0.81^t = 0.5

t*log(0.81) = log(0.5)

t = log(0.5) / log(0.81) = -0.6931 / -0.2107 = 3.2894 hours

= 3 h 17.36 minutes

b) Equation of function of residue drug as a function of time t in hours

A=500 mg

f(t) = A(0.81^t)    substitute A = 500 mg

= 500(0.81^t)  mg

c) weight of residue drug after 24 hours to the hundredth of a gram.

t=24 hours

A=500

f(t) = 500(0.81^t)    substitute t=24 hours

= 500(0.81^24)

= 3.181 mg

= 0.003181 g

Answer:

16

Step-by-step explanation:

[tex] {w}^{2} - 8w + { {4}^{2} } \\ = {w}^{2} - 8w + \boxed{ 16} \\= (w-4)^2 [/tex]

Answer:

Step-by-step explanation:

a² + 2ab +b² = (a+ b)²

w² - 8w + _?___

a = w

2ab = -8w

2*w*b = -8w

b = -8w/2w

b = 4

8w = 2 * 4*w

w² - 8w + 4² =w² -8w + 16

power of a quotient

edge 2021

The law used to simplify the expression is quotient of powers.

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Given is an expression, 3¹⁰ / 3⁴, we need to determine the law used to simply the expression,

3¹⁰ / 3⁴

For this case we have an expression formed by a division of powers of the same base in which we must apply a law to simplify said expression.

By the definition we have the property of the power quotient of the same base set:

xᵃ / xᵇ = x⁽ᵃ⁻ᵇ⁾

So, using the same,

3¹⁰ / 3⁴ = 3⁽¹⁰⁻⁴⁾ = 3⁶

Thus, to simplify the expression we must use the property of the power quotient of the same base.

Hence, the law used to simplify the expression is quotient of powers.

Learn more about expression, click;

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We can find roots by setting f(x) = 0 --> x^4 - x^3 - 13x^2 + x + 12 = 0.

Factoring f(x) to make things easier for us gives us (x - 1)(x + 1)(x - 4)(x + 3), which, equal to 0, gives us the ability to set each set of parentheses = 0.

x - 1 = 0 gives us x = 1.

x + 1 = 0 --> x = -1.

x - 4 = 0 --> x = 4.

x + 3 = 0 --> x = -3.

our roots are x = 1, -1, 4, and -3.

Answer:

y = -4

Step-by-step explanation:

x = 3 is a vertical line.

The perpendicular line passes through (0, -4) (x, y)

y = -4

The line is perpendicular, so the line should be also horizontal.

Answer:

y = -4

Step-by-step explanation:

The line x = 3 is a vertical one; any line perpendicular to x = 3 is a horizontal line (which has a zero slope).  

Thus, the desired line is a horizontal one that passes through (0, -4) and is represented by y = -4.

Answer:

The independent variable is the depth below the surface of the lake the dependent is the tempeature of the water

Step-by-step explanation:

Tempeture = depth x

Answer:

Simplifying

41 = 12d + -7

Reorder the terms:

41 = -7 + 12d

Solving

41 = -7 + 12d

Solving for variable 'd'.

Move all terms containing d to the left, all other terms to the right.

Add '-12d' to each side of the equation.

41 + -12d = -7 + 12d + -12d

Combine like terms: 12d + -12d = 0

41 + -12d = -7 + 0

41 + -12d = -7

Add '-41' to each side of the equation.

41 + -41 + -12d = -7 + -41

Combine like terms: 41 + -41 = 0

0 + -12d = -7 + -41

-12d = -7 + -41

Combine like terms: -7 + -41 = -48

-12d = -48

Divide each side by '-12'.

d = 4

Simplifying

d = 4

Answer:

last three questions are statistical question

Answer:

The last three questions

Step-by-step explanation:

Answer:

15 miles

Step-by-step explanation:

Currently, he can run 3.5 * 2 = 7 mph. Adding 1/2 mph to that gives us 7.5 mph, so therefore, in 2 hours he can run 7.5 * 2 = 15 miles.

Answer:

15

Step-by-step explanation:

because its correct just did the thing.

Answer:

y = 3/4x + 17/4

Step-by-step explanation:

Step 1: Find slope m

m = (5 - 2)/(1 + 3)

m = 3/4

y = 3/4x + b

Step 2: Find b

5 = 3/4(1) + b

5 = 3/4 + b

b = 17/4

Step 3: Rewrite equation

y = 3/4x + 17/4

Answer:

y = 3/4x + 17/9

Step-by-step explanation:

Find the slope:

5 - 2/ 1 - (- 3)

3/ 1 + 4

3/4

Find the y-intercept:

2 = 3/4(-3) + b

2 = -9/4 + b

17/4 = b

Put it in an equation:

y = 3/4x + 17/9

Answer:

money invested at 3% is $4000

Step-by-step explanation:

let the money invested in 3% account be x

then money invested in 5% account = 6000 - x

we know interest = p*r*t/100

p is the principle amount invested

here t = 1 year

interest on 3% money

interest= x*3*1/100 = 3x/100

interest on 5% money

interest= (6000-x)*5*1/100

Total interest earned on both the account

3x/100 + 5(6000-x)/100 = (3x + 30,000 - 5x)/100 =( 30000-2x)/100

given that total interest earned = $220

thus

( 30000-2x)/100 = 220

=> 30000-2x = 220*100= 22,000

=> -2x = 22,000- 30,000

=> x = -8000/-2 = 4000

Thus, money invested at 3% = x = $4000

Answer:)

$4000

Step-by-step explanation:

Answer:

-1 10/17

Step-by-step explanation:

Answer:

y = 1 10/17

Step-by-step explanation:

The LCD is 9y.  Multiply all three terms by 9y:

(9y)(12)                   (9y)(4)

----------- + 8(9y) = -----------

     y                           9

This reduces to 108 + 72y = 4y, or 108 = -68y

Dividing both sides by 68, we get y = 1 10/17

Answer:

The answer is option A.

Step-by-step explanation:

Surface area of a sphere is 4πr²

where r is the radius

radius = diameter / 2

radius = 16/2 = 8cm

Surface area of the sphere is

4π (8)²

= 4(64)π

= 256π

= 804.2cm²

Hope this helps you.