f(x) = 3 x + 1 and g (x) = 2x - 3. find g (f(x))

The converse statement is "If a person is 13 years old or older, then the person is a teenager. The converse is valid" . Option D

The converse of a conditional statement is defined as a statement that is formed when the hypothesis and conclusion of a sentence are both reversed or interchanged.

If the conditional statement is expressed as a → b

The converse statement is referred to as b → a

It is important to note that the original statement must be a conditional statement for a converse statement to derived from it.

Given the conditional statement:

"If a person is a teenager, then the person is 13 years old or older."

The converse statement would be written as;

If a person is 13 years old or older, then the person is a teenager.

We can see that the converse statement is valid because anyone that is 13 or older is a teenager

Hence, the converse statement is valid. Option D

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The nth term of the arithmetic sequence when the numbers given are 7, 4, 1, -2 is 6 - 3n.

It should be noted that an arithmetic sequence has a common difference. In this case, the values that are given include 7, 4, 1, -2.

First term = 7

The common difference between the numbers include:

= Second term - First term

= 4 - 7

= -3

The nth term will be:

= a + (n - 1)d

where a = 7

d = -3

= a + (n - 1)d

= 7 + (n - 1) -3

= 7 -3n - 1

= 6 - 3n

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Answer:

(0,2)

Step-by-step explanation:

x  = [tex]\frac{2-2}{2}[/tex] = [tex]\frac{0}{2}[/tex] = 0  We are finding the average of the x values (2 and -2)

y = [tex]\frac{-5+9}{2}[/tex] = [tex]\frac{4}{2}[/tex] = 2  we are finding the average of the y values (-5 and 9)

The relation between x and y such that the point (x, y) is equidistant from point(2, -5) and(-2, 9) = 2x + 7y = -14

Points (2, -5) and (-2, 9).

let (x, y) be A

Let (2, -5) = (-2, 9) = B

Ax = Bx (length)

Squaring on both sides

Ax² = Bx²

By distance formula

(x - 2)² + (y +5)² = (x + 2)² + (y - 9)²

x² - 4x + 4 + y² +10y + 25 = x² + 4x + 4 + y² - 18y + 81

8x + 28y = -56

by multiplying both sides by 4

2x + 7y = -14

This is the relationship between the points (x, y) which is equidistant to A and B.

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a trough has ends shaped like isosceles triangles, with width 2 m and height 5 m, and the trough is 10 m long. then the height of the water change when the water is 4 m deep is 1/8 m/min

The depth of the water is 4/5 of the depth of the trough, so the width of the surface will be 4/5 of the width of the trough:

 4/5 × 2 m = 8/5 m

Then the surface area of the water is ...

 Area = LW = (10 m)(8/5 m) = 16 m²

The rate of change of height multiplied by the area gives the rate of change of volume:

 2 m³/min = (16 m²)(h')

 h' = (2 m³/min)/(16m²) = 1/8 m/min

Hence , the height of the water change when the water is 4 m deep is 1/8 m/min

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Equation is y= 56x that models the relationship between x ,the number of hours Mark reads, and y, the number of pages of the book he reads.

The term rate of change (ROC) describes the rate at which something changes over time. Thus, it is not the amount of individual changes themselves but rather the acceleration or deceleration of changes (i.e., the rate). Rate of change is a tool used in finance to comprehend price returns and spot trend momentum.

Given Data

The hours are indicated by = x

The calculation for the number of pages is =y

Read 42 pages every [tex]\frac{3}{4}[/tex] hour

You can model the equation as follows:

y = mx +b

Rate of change = [tex]\frac{change in y}{change in x}[/tex]

Rate of change = 42 ÷[tex]\frac{3}{4}[/tex]

Rate of change = 42 ×[tex]\frac{4}{3}[/tex]

Rate of change = 56

Equation y= 56x

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Answer:

p = 11

Step-by-step explanation:

This Question tests on the concept of Angle Properties.

Given from the diagram above, we can form up a equation:

4p + 7 + 90 + 3p + 6 = 180 (Sum of Angles in a Triangle)

Now we can solve for p from the equation.

[tex]4p + 7 + 90 + 3p + 6 = 180 \\ 7p + 103 = 180 \\ 7p = 180 - 103 \\ 7p = 77 \\ p = \frac{77}{7} = 11[/tex]

(a) AB, BC, CD, and DA are, respectively, and long.

(b) AB, BC, CD, and DA have slopes of 0, 0, and 2, respectively.

(c) AC and BD have lengths of 8 and 72, respectively.

(d) AC and BD have slopes of 1 and 1, respectively.

A quadrilateral is a polygon having four sides, four angles, and four vertices.

There is a quadrilateral called ABCD.

The quadrilateral's vertices are A(3,5), B(7,7), C(5,3), and D. (1,1).

The side AB measures [(3-7)2 + (5-7)2] = 20.

The side BC measures [(7-5)2 + (7-3)2]. =√20 .

The side CD measures [(5-1)2 + (3-1)2] in length. = √20.

The side DA measures [(1-3)2 + (1-5)2] = 20 in length.

The diagonal AC measures [(3-5)2 + (5-3)2] = 8 in length.

The diagonal BD is [(7-1)2 + (7-1)2] in length. =√72 .

The slope of side AB is equal to 1/2 (7-5)/(7-3)

The slope of the side BC is equal to zero (7-3)/(7-3)

The side CD has a slope of (3-1)/(5-1) = 1/2.

DA's side has a slope of (5-1)/(3-1) = 2.

The sides AD and BC are parallel to one another and have the same length.

Equal in length and parallel to one another are sides AB and CD.

Each side is parallel to the side next to it.

As a result, we draw the conclusion that ABCD is a quadrilateral.

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Answer:

216 miles

Step-by-step explanation:

so the base fee is 18.99, subtract the total (219.87) by 18.99.

219.87-18.99=200.88

200.88 divided by 0.93 (charge for each mile driven)

200.88/0.93=216

thats a lot of miles.

The solution of given inequalities are x > -3 and x ≤ 5.

When resolving an inequality, you can do one of the following: add the same amount to each side; deduct the same amount from each side; multiply or divide each side by the same positive amount. You must flip the inequality sign if you multiply or divide each side by a negative number.

Given inequalities are 2x - 5 > -11 and -10x - 6 ≥ 44.

To solve the first inequality,

2x - 5 > -11

Adding 5 on both sides,

2x - 5 + 5 > -11 + 5

2x > -6

Divide both sides by 2,

x > -3

To solve the second inequality,

-10x - 6 ≥ 44

Adding 6 on both sides,

-10x - 6 + 6 ≥ 44 + 6

-10x ≥ 50

Divide both sides by -10, and change the inequality sign

x ≤ 5

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Answer:

(5, 4)

Step-by-step explanation:

What is Orthocenter?

A point where the altitudes of the triangle meet is known as the point of concurrency or simply the orthocenter of the triangle

The expression 8 ( 3x - 7 ) when expanded gives 24xx - 56.

The cornerstone of mathematics is the theory of operations; we use it to compute and remember fundamental truths. The subsequent three characteristics are applied to addition and multiplication: Commutative Property, Associative Property, and Distributive Property.

The distributive property of binary operations in mathematics generalizes the distributive law, which states that in elementary algebra, equality is always true.

Consider the expression 8( 3x - 7 ),

Let's say y is equal to 8( 3x - 7 ).

By using the distributive property:

y = 8 × 3x - 8 × 7

y = 24x - 56

Therefore,

8( 3x - 7 ) = 24x - 56

Therefore, when the expression 8( 3x - 7 ) is expanded we obtain the expression 24x - 56.

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So basically 130+90=220 and 6+8=14. And 220+14=234.

Since the isotope has only a very little amount in nature, it does not largely affect the  atomic mass of lithium.

The term isotope has to do with the atoms of the same element that do have the same atomic number but different mass numbers. The implication of this is that isotopes have the same number of protons but do not have the same number of neutrons.

Note that the average atomic mass of an atom is the weighted average of the atomic masses of all the isotopes of the compound. The isotopes that contribute greatly towards the atomic mass are those that have a larger percentage abundance.

Given that the new lithium isotope, 8Li identified  is a trace isotope, meaning that it exists in a very tiny quantity, it does not any noticeable effect on the  atomic mass of lithium.

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Step-by-step explanation:

1) 5.45 ÷ 65

2) 109/20 x 1/65=

3) 109/1300 or 0.08384615

Answer:

see explanation

Step-by-step explanation:

the volume (V) of the container is

V = 10 × 4 × 5 = 200 m³

change the dimensions of the box to m , to be same as container

l = 50 cm = 0.5 m , b = 40 cm = 0.4 m , h = 20 cm = 0.2 m

then

volume of box = 0.5 × 0.4 × 0.2 = 0.04 m³

Number of boxes that can be stored in container is

200 ÷ 0.04 = 5000

thus no more than 5000 boxes can be placed in the container

Using proportions, it is found that Elizabeth should order 42 mugs and 18 t-shirts.

A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using the unit rates, then operations such as multiplication or division are used to find the equivalent amounts.

In the context of this problem, we have to consider that:

Hence the number of mugs that she has to order is found as follows:

256/6 = 42 (rounded down, as the remainder means that the last guest to receive a mug is the 252th guest).

The number of t-shirts that she has to order is given as follows:

256/14 = 18 (also rounded down, following the same logic as the number of mugs).

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Equation represents a line which is parallel to the line

y = 1/2x +3 with (2,5)

Since you are looking for an equation that is parallel to a line, the slope is the same: m = 1/2

Use Point-Slope equation [y-y1 = m(x-x1)]

with the given point (2,5): y-

5=1/2(x-2)

Distribute the 1/2: y-5=1/2x-1

Move the 5 to the other side to put it in y=mx+b form: y=1/2x-1+5

Answer:

y=1/2x+4

A parallel equation can be located in what way?

In the absence of an intersection, two lines are said to be parallel. Each line has the same slope. In the event that m1=m2, f(x)=m1x+b1 and g(x)=m2x+b2 are parallel. If m 1 = m 2, then f (x) = m 1 x + b1 and g (x) = m 2 x + b2 are parallel.

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There are different 2,808,000 passwords possible which are the correct answer would be option (B)

A permutation is defined as a mathematical process that determines the number of different arrangements in a set of objects when the order of the sequential arrangements.

Sue picks a new password for her email that consists of 3 letters, 2 digits, and a special character (! or #) which is given in the question.

As per the given condition,

For the first letter, we have 26 options.

For the second letter, we have 25 options, because one letter is already used.

For the third letter, we have 24 options, because 2 letters are already used.

For the first digit, we have 10 options.

For the second digit, we have 9 options, because one is already used.

For the first special character (! or #), we have 2 options.

Then the total number of combinations is:

Combinations = 26×25×24×10×9×2 = 2,808,000

So if we can not repeat digits or letters, we can make 2,808,000 different passwords.

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Answer:

Step-by-step explanation:

9 divided by 1557

(Tell me if you mean 1557 divided by 9 lol the wording is strange :] )

See screenshot!

julia wants to purchase a pair of headphones that are on sale for $42.79. the sales tax rate in her county is 6%. then Julia have to pay $2.57 as sales tax on purchase of headphones.

Given,

The cost of headphones which Julia wants to purchase on sale = $ 42.79

The sales tax in Julia's country = 6%

We have to calculate the amount of sales tax Julia will pay on the purchase:

That is,

Sales Tax Value = Percentage of sales tax × Price of headphones

Sales Tax Value = (6 / 100) × 42.79

Sales Tax Value = 0.06 × 42.79

Sales Tax Value = 2.5674

Sales Tax Value ≈ 2.57

Therefore, Julia have to pay $2.57 as sales tax on purchase of headphones.

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The probability of selecting two lemon filled donuts in a row is 7/92.

Probability is used to determine the odds that a random event would happen. The odds that the random event happens has a probability value that lies between 0 and 1. If it is certain that the event would happen, the probability value would be 1. If it is certain that the event would not happen, the probability value is 0.

The donuts are picked without replacement because the donut are eaten as they are picked.

Probability = (number of lemon filled donuts / total number of donuts) x [(number of lemon filled donuts / total number of donuts) - 1]

(7/24) x (6/23) = 7/92

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Considering the definition of a line, x-intercept and y-intercept, the  x-intercept and y-intercept are (3, 0) and (0,6) respectively.

A linear equation o line can be expressed in the form y = mx + b

where

The point [y-intercept] is where the line crosses the y-axis, and occurs when x = 0.

The point [x-intercept] is that value of x for which the expression is equal to 0 and the line crosses the x-axis.

In this case, the line is 10x +5y=30. Expressed in the form y = mx + b, you get:

5y= 30 - 10x

y= (-10x + 30)÷5

y= -10/5x + 30/5

y= -2x +6

where:

The point [y-intercept] is represented by the value of the y-intercept b. So the point [y-intercept] is (0,6).

Being the point [intersection x] that value of x for which the expression is equal to 0 or y is equal to 0, in this case it is calculated as:

0= -2x + 6

-6= -2x

(-6)÷ (-2)= x

3=x

Finally, the point [x-intercept] is (3,0).

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The statement that is best supported by the graph is; Jillian's car holds more gasoline, but Nikki's car gets better gas mileage.

The total amount of gasoline each car tank can hold is shown on the left of each graph on the y-axis.

Jillian's car holds 22 gallons.

Nikki's car holds 20 gallons.

Jillian's car holds more gasoline.

Now we need to see which car gets better gas mileage. Getting better gas mileage means you can go farther with each gallon of gas.

With Jillian's car, after using 22 gallons of gas, you have gone 350 miles, and the gas tank is empty.

350 miles with 22 gallons is 350/22 = 15.9 miles per gallon.

With Nikki's car, you start with only 20 gallons. By the time you drive 350 miles, you still have some gas left. Not only did you start with less gas, 20 gal vs. 22 gal, but after driving the same distance, 350 miles, there is still some gas left in the tank, 6 gallons.

That means Nikki's car used 20 - 6 = 14 gallons to drive 350 miles. 350/14 = 25 miles per gallon.

The more miles per gallon you get, the better the mileage. Thus;

25 miles per gallon is better mileage than 15.9 miles per gallon.

Nikki's car has a smaller gas tank, but it gets better mileage.

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The value of x is 18 and the value of ∠A (interior angle) is 73°.

According to the given figure,

We have:

∠A = 6x-35°

∠B = 3x+53°

The two parallel lines have been cut by another line.

(Note that when a line divides two parallel lines then the sum of the interior angles on the same side is 180° and the alternate interior angles are equal to each other.)

So, we will have the following expression:

∠A + ∠B = 180°

(6x-35+3x+53)° = 180°

9x+18 = 180

9x = 180-18

9x = 162

x = 162/9

x = 18

Now, putting the value of x in ∠A,

∠A = 6x-35°

∠A = (6*18-35)°

∠A = (108-35)°

∠A = 73°

Hence, the value of x is 18 and the measurement of ∠A is 73°.

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The decomposition of 240 - 135 = 105 will be 15(16 - 9) = 15(7) = 105

It should be noted that decomposition simply means breaking down of the numbers that are given or illustrated.

It should be noted that the numbers 240 - 135 = 105 all have a common factor of 15. This will be broken down as:

240 - 135 = 105

15(16 - 9)

= 15(7)

= 105

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Answer:

Similarity: Both are odd numbers

differences:  3 > 1  

Similarity: Both are Consecutive natural numbers

differences: 3 is an odd number and 4 is an even number

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Answer:

[tex]-9k-7[/tex]

Step-by-step explanation:

Replace n with -9k.

Answer:4/3-2

Step-by-step explanation: