a. How much is 50% of 10 liters of milk?

Answer:

Recursive:

[tex]f(1)=35, f(n)=f(n-1)+10[/tex]

Explicit:

[tex]f(n)=35+10(n-1)[/tex]

And the 20th term is 225.

Step-by-step explanation:

We have the sequence:

35, 45, 55, 65.

Notice that each subsequent term is 10 more than the previous term.

Therefore, our common difference is (+)10.

Recursive Rule:

The standard format for the recursive rule is:

[tex]f(n)=a, f(n)=f(n-1)+d[/tex]

Where a is the initial term and d is the common difference.

From our sequence, we know that a the initial term is 35.

And as determined, our common difference d is 10.

Substitute. Hence, our recursive rule is:

[tex]f(1)=35, f(n)=f(n-1)+10[/tex]

Explicit Rule:

The standard format for the explicit rule is:

[tex]f(n)=a+d(n-1)[/tex]

Where a is the initial term and d is the common difference. So, let’s substitute 35 for a and 10 for d. Hence, our explicit formula is:

[tex]f(n)=35+10(n-1)[/tex]

Now, let’s find the 20th term. We will utilize the explicit rule since the recursive rule can get tedious. Substitute 20 for n because we would like to 20th term. Thus:

[tex]f(20)=35+10(20-1)[/tex]

Evaluate:

[tex]\begin{aligned} f(20)&=35+10(19) \\ f(20)&=35+190 \\ f(20)&=225 \end{aligned}[/tex]

Hence, the 20th term is 225.

Answer:

1 2/5 = 1 1/2

7/9 = 1

4/9 = 1/2

3 5/7 = 4

Step-by-step explanation:

1. we must round 1 2/5

based on the answer choices we can determine that 1 1/2 is the most rational answer. This is because it is not only the only answer with the whole number, 1 but also 2/5 would round to 1/2.

2. We must round 7/9

This would round up to 1. This is because it is closest to the whole number, not 0 and not 1/2.

7 * 2 = 14

9 * 2 = 18

14/18 is only 4/18 away from being 1. This means that it would round up to 1.

3. we must round 4/9

This rounds to 1/2. If you multiply both side by 2:

4 * 2 = 8

9 * 2 = 18

8/18 for that to be 1/2 it would need 1/18. Thus this rounds up to 1/2.

4. We must round 3 5/7

5/7 would round up to a whole number.

3 + 1 = 4

Thus 3 5/7 = 4 when rounded to the nearest whole number.

Answer:

B.

Step-by-step explanation:

The percent change is approximately 55 %

Answer:

600 people

Step-by-step explanation:

30x12=600.

Answer:

0.166666 in fraction form is 83333/500000.

Step-by-step explanation:

Answer:

Step-by-step explanation:

20x+85=

20(6)+85=

120+85= $205

Answer:

The false choices are A, C, and E

Step-by-step explanation:

Let's make an example:

p=1

q=2

s=sqrt(3)

t=sqrt(6)

Since pq=1*2=2, the answer is rational and A is false.

Since pt=1*sqrt(6)=sqrt(6), the answer is irrational and B is true.

Since p/q=1/2=0.5, the answer is rational and C is false.

Since st=sqrt(3)*sqrt(6)=sqrt(18), the answer is irrational and D is true.

Since s/t=sqrt(3)/sqrt(6)=sqrt(1/2), the answer is irrational and E is false.

The false statements are:

The product pq is irrational.

The quotient pq is irrational.

The quotient st is rational.

A rational number is a number can be expressed as a fraction of two whole numbers. While, an irrational number is a number that cannot be expressed as the fraction of two whole numbers.

Examples of rational numbers are: 6, 2,3

Examples of irrational numbers are: √2, √3

Let p and q be represented with 2 and 6 respectively.

The product of 2 and 3 = 2 x 6 = . The number is a rational number

Let p and t be represented with 2 and √2 respectively.

The product of 2 and √2 = 2 x√2 = 2√2. The product is irrational

The quotient of pq = 6 /2 = 3.

The quotient is rational.

Let s and t be represented with √2, √3. The product is √2 x √3 = √6. The product is irrational.

The quotient of s and t = √2 /√3.

The number is irrational.

To learn more about rational numbers, please check: https://brainly.com/question/15815501?referrer=searchResults

Answer:

Line 1 = Negative

Line 2 = Zero

Line 3 = Positive

Line 4 = Undefined

Step-by-step explanation:

Line 1's gradient is negative since it's sloping down.

Line 2's gradient stays at 0 since it does not go upwards or downwards.

Line 3's gradient is positive since it's tilting upwards.

Line 4's gradient is undefined since the line shoots up on the same point on the x-axis so the gradient cannot be determined by a single rational number.

Answer:

a) (-2,2), (-1,-1), (1,-1), (3,7)

b) x=1.4

Answer:

a) (-2, 2), (-1, -1), (1, -1), (3, 7)

b) x = 1.4

Step-by-step explanation:

a) Plug in your x & solve for y.

[tex]y = (-2)^2 - 2\\y = 2\\y = (-1)^2 - 2\\y = -1\\y = (1)^2 - 2\\y = -1\\y = (3)^2 -2\\y = 7[/tex]

b) Same thing as a, but just plug in 0 for y & solve for x

[tex]0 = x^2 -2\\2 = x^2\\\sqrt(2) = x\\1.4 = x[/tex]

Answer:

G

Step-by-step explanation:

The expression that expresses her purchasing restrictions is:

13c + 10d = 150.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Given, Cheyenne is deciding between the ways she has to buy music. Albums on CD cost $13 but downloads of an album only cost $10. If she can spend up to $150 on music purchases.

Let "c" be the CDs she bought

and "d" be the albums she downloads

Price of total CD = 13c

price of total download = 10d

Thus, an equation that satisfies the situation:

13c + 10d = 150

therefore, Her purchasing limitations are expressed in the following way:

13c + 10d = 150.

Learn more about expression here:

https://brainly.com/question/14083225

#SPJ3

Answer:

168x12 and u get ur answer

Step-by-step explanation:

just do 168x12

if it sells 168 tickets and each is $12, then:

12 x 168 = 2,016

total cost = $2,016

Answer:

[tex]m=\frac{-1}{3}[/tex]

General Formulas and Concepts:

Pre-Algebra

Algebra I

Step-by-step explanation:

Step 1: Define

Point (-7, -4)

Point (2, -7)

Step 2: Find slope m

Answer:

Down there! Idk if it was what your looking for but this is what I got..

Step-by-step explanation:

(-∞,∞)

Step-by-step explanation:

PART A:

given

This is true for all values of x.

So,x∈-∞,+∞

PART B:

When ,left hand side=

right hand side=

so,left hand side =right hand side

When ,left hand side=

right hand side=

so,left hand side =right hand side

When ,left hand side=

right hand side=

so,left hand side =right hand side

Answer:

5+4-12=4-7   9-12=4-7   -3= -3

5+0-12=0-7   5-12=0-7   -7= -7

5+5-12=5-7   10-12=5-7  -2= -2

Step-by-step explanation:

Answer:

I honestly think its neither

Example 1: Find the equation of the line passing through the points (–1, –2) and (2, 7).

Step 1: Find the slope of the line.

To find the slope of the line passing through these two points we need to use the slope

formula:

Step-by-step explanation:

use this on your problem

Answer:

it equals 89/90

Step-by-step explanation:

the gcf of 89, 90 is 1, so the fraction can not be simplified. The answer is 89/90.

Answer:

I'm not sure but I think it's LDTC

Step-by-step explanation:

9514 1404 393

Answer:

  x = -1/2

Step-by-step explanation:

Anything raised to the power of 0 is 1.

  (1/2)^(2x+1) = 1 = (1/2)^0

Equating exponents gives ...

  2x +1 = 0

  2x = -1 . . . . subtract 1

  x = -1/2 . . . divide by 2

Answer:

Accounting for its formula,

The statue is roughly 12ft. tall

Step-by-step explanation:

17 i think I hope its right

Answer:

X = 12

Measure of exterior angle = 80

Step-by-step explanation:

Angles P and Q are equal to the right side of R ( solve for x )

Answer

2,1

Step-by-step explanation:

all the others or on one side besides that one with is on the line

The ordered pair which is not in the solution set of 2x – y > 3 is that which is a solution of the graph of 2x – y = 3 and is; (2, 1)

According to the question;

Evidently, among the choices of coordinates; only (2, 1) is a solution of the equation 2x – y = 3.

By testing;

As such, since (2,1) is a solution of the equation 2x – y = 3, it can't also be a solution of 2x – y > 3.

Read more:

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Answer:

The answer is 75/50

Step-by-step explanation:

Answer:

75/W = 150/100

75/W = 3/2

W x 75/W = W x 3/2

75 = 3W/2

2 x 75 = 2 x 3W/2

150 = 3W

so the answer should be 50 = W

Answer:

x = 80

Step-by-step explanation:

x + 30 = 110 (opposite sides are congruent/equal)

x = 110 - 30 (subtract the 30 from both sides to get X by itself)

x = 80 (simplify)

Answer:

c.  $120.75

Step-by-step explanation:

The correct answer between all the choices given is the third choice or letter C. I am hoping that this answer has satisfied your query and it will be able to help you in your endeavor, and if you would like, feel free to ask another question.

Answer:

Simplifying

6(2x + -1) = 4 + 7x

Reorder the terms:

6(-1 + 2x) = 4 + 7x

(-1 * 6 + 2x * 6) = 4 + 7x

(-6 + 12x) = 4 + 7x

Solving

-6 + 12x = 4 + 7x

Solving for variable 'x'.

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

Add '-7x' to each side of the equation.

-6 + 12x + -7x = 4 + 7x + -7x

Combine like terms: 12x + -7x = 5x

-6 + 5x = 4 + 7x + -7x

Combine like terms: 7x + -7x = 0

-6 + 5x = 4 + 0

-6 + 5x = 4

Add '6' to each side of the equation.

-6 + 6 + 5x = 4 + 6

Combine like terms: -6 + 6 = 0

0 + 5x = 4 + 6

5x = 4 + 6

Combine like terms: 4 + 6 = 10

5x = 10

Divide each side by '5'.

x = 2

Simplifying

x = 2

Step-by-step explanation:

Answer:

A) D) g(x) = 2x - 8

2) B) y = 3/4x - 1 and y = -4/3x + 9

Step-by-step explanation:

1)

In the table, we have the points

(5, 2)

(7, 6)

(9, 10)

(10, 12)

This seems to be a linear relationship, so let's try that:

A linear relationship can be written as:

y = a*x + b

where a is the slope and b is the y-axis intercept.

For a line that passes through the points (x1, y1) and (x2, y2), the slope can be written as:

a = (y2 - y1)/(x2 - x1)

If we use the first two points, we get the slope:

a = (6 - 2)/(7 - 5) = 4/2 = 2

if we use the first and last point, we get the slope:

a = (12 - 2)/(10 - 5) = 10/5 = 2

Then we can conclude that this is a linear relationship with a slope equal to 2.

y = 2*x + b

To find the value of b, we can just replace any of the points of the data table in the equation, for example, i will use the point (5, 2).

this means that x = 5, and  y = 2.

2 = 2*5 + b

2 = 10 + b

2 - 10 = b

-8 = b

Then the equation is:

y = 2*x - 8

the correct option is: D) g(x) = 2x - 8

2) Here we have two lines, notice that we can with just looking at the image, know the y-intercept of each line.

The one with a positive slope (grows to the right) has a y-intercept = - 1.

The one with a negative slope (grows to the left) has a y-intercept =  9.

The two options that match this condition are:

B) y = 3/4x - 1 and y = -4/3x + 9

C) y = 3/4x - 1 and y = -3/4x + 9

Where the only difference is the slope of the black line.

so et's check which slope matches that line.

In the graph we can see that it passes through the points:

(0, 9) and the point (6, 1)

Then the slope is:

a = (1 - 9)/(6 - 0) = -8/6 = -4/3

Then the correct option is where the negative slope is -4/3, that one is

B) y = 3/4x - 1 and y = -4/3x + 9

Answer:

1/7x or 1/7

Step-by-step explanation:

the equation for slope is

y2-y1 over x2 minus x1, so basically it means that you find the second x which in this case is 12 and subtract the first x which is 5. 12-5 is 7

You also do -7 minus -6 for the y2-y1 stuff so it is -7 plus 6 cuz the double - signs cancel out to positive.

-7 + 6 is 1

1 over 7 is 1/7