Find the 3rd term of the arithmetic sequence with t 6= 24 and t15=21​

The area of triangle EFG is given as follows:

A = 18.63 square units.

The area of a rectangle of base b and height h is given by half the multiplication of dimensions, according to the formula presented as follows:

A = 0.5bh

The base is given by segment EF as follows:

\(EF = \sqrt{(9 - 4)^2 + (-7 -(-9))^2}\)

EF = 5.4.

The midpoint of EF is given as follows:

M(6.5, -8).

The height is given by the segment MG as follows:

\(MG = \sqrt{(6.5 - 3)^2 + (-2 - (-8))^2}\)

MG = 6.9.

Hence the area is given as follows:

A = 0.5bh

A = 0.5 x 5.4 x 6.9

A = 18.63 square units.

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The y-intercept is the point of (0,y) thus y-intercept of y = 2x + 1 is 1 and it is equal to the given graph of the function.

A graph is a diametrical representation of any function between the dependent and independent variables.

For example y = x² form a parabola now by looking at only the graph we can predict that it has only a positive value irrespective of the interval of x.

As per the given function,

y = 2x + 1

For y-intercept x = 0

y = 2(0) + 1 = 1

Thus, the y-intercept is 1.

In the graph, the line passes the y-axis at y = 1.

Hence "The y-intercept is the point of (0,y) thus y-intercept of y = 2x + 1 is 1 and it is equal to the given graph of the function".

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The given question missing the graph attached below ;

Answer:

Step-by-step explanation:

To find the total number of text messages sent per month by the 23 million people aged 13-17 in the United States, we can multiply the average number of text messages per person (800) by the number of people (23,000,000):

Total number of text messages = 800 text messages/person/month x 23,000,000 people

Total number of text messages = 18,400,000,000 text messages/month

To express this number in scientific notation, we can move the decimal point 10 places to the left, since there are 10 digits to the right of the decimal point:

Total number of text messages = 1.84 x 10^10 text messages/month

Therefore, the total number of text messages sent per month by the 23 million people aged 13-17 in the United States is approximately 1.84 x 10^10 text messages.

Answer:

0.167

Step-by-step explanation:

if you divide 30/180 it will get you a decimal of 0.166666667 but if you were to divide 180 by 30 you will get 6

technecaly your answer would be 0.166666667 but you only take the first number in the decimal which is 0.1 then take six 0.16 then add the 7 0.167

that should end up being your answer if i did the math right

Answer:

Step-by-step explanation:

5/12 * 6/15 =30/180

1/6=1/6

which is true, Right-hand side is equal to left-hand side

By means of algebraic handling, the solution of the linear equation 3 · x + 2 · y = - 6 for y is y = - 3  - (3 / 2) · x.

In this problem we have a linear equation in implicit form, that is, a linear equation where none of the variables is not in function of the rest of variables. Now we proceed to solve the linear equation 3 · x + 2 · y = - 6 for y, where y is in terms of x, by algebraic handling:

3 · x + 2 · y = - 6          Given

2 · y = - 6 - 3 · x           Compatibility with addition / Existence of additive inverse / Modulative property

y = - 3  - (3 / 2) · x        Compatibility with multiplication / Existence of multiplicative inverse / Associative and modulative property / Definition of division / Result

By means of algebraic handling, the solution of the linear equation 3 · x + 2 · y = - 6 for y is y = - 3  - (3 / 2) · x.

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Answer:

\(16203\) days

Step-by-step explanation:

There are 60 seconds per minute, so 3600 sec/hour, and 86400 seconds per day, so the answer is about \(16203\) days.

Answer:

it is a -3/-2

Step-by-step explanation:

Answer:

its step 3  and its c !

Step-by-step explanation:

The step shows where she applied the property that states multiplying two negative numbers will be 11.28. Then the correct step is 4.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

The expression is given below.

⇒ (–1.2) × (–9.4)

Simplify the expression, then we have

⇒ (–1.2) × (–9.4)

⇒ (1.2) × (9.4)

⇒ 11.28

The step shows where she applied the property that states multiplying two negative numbers will be 11.28. Then the correct step is 4.

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The logically equivalent statement to p → q is:

~q → ~p

The conditional statement:

p → q

Assuming p and q are propositions, the conditional statement may be expressed as:

"If p holds true, then q follows suit. "

'

Whenever p is true, q is true as well. This implies that if q is false, then p must also be false.

We can rephrase this statement cleverly using the negative propositions, which include the opposite or contradictory statements.

~p  and ~q

These mean:

Not p and Not q respectively.

Then the statement:

"If q is not true, then p is not true"

Is written as:

~q → ~p

So this is the logically equivalent statement.

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The Complete Question

Given a conditional statement p → q, which statement is logically equivalent?

~p → ~q

~q → ~p

q → p

p → ~q

The correct statements are;

The x-intercept of f(x) and the y-intercept of f–1(x) are reciprocals of each other.

The point of intersection of the two functions indicates that the functions are inverses.

Option C and D

To accurately compare a function and its inverse based on the graphs, we have to know the following;

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Designing an easy do-it-yourself compost bin:

Drawing and Description:

The compost bin can be a simple structure made of wood or wire mesh. It consists of four sides, a bottom, and a removable lid. The sides and bottom are connected securely to form a rectangular shape, while the lid allows for easy access to the contents inside.

The bin can be placed directly on the ground or on a solid surface, depending on personal preference.

Materials Used:

Wood or wire mesh (depending on preference)

Nails or screws to assemble the structure

Size of the Bin:

The size of the bin can vary based on the available space and the amount of compostable materials you generate. A suitable size for a home compost bin could be approximately 3 feet wide, 3 feet deep, and 3 feet tall.

Substances Used to Fill It:

To fill the compost bin, you would need a mix of "green" and "brown" materials. "Green" materials include fruit and vegetable scraps, coffee grounds, tea leaves, grass clippings, and plant trimmings. "Brown" materials consist of dry leaves, shredded newspaper, cardboard, and small twigs.

Household Items That Can Go in It:

You can add a variety of household items to the compost bin, such as fruit and vegetable peels, eggshells, coffee grounds, tea bags, yard waste (leaves, grass clippings, plant trimmings), shredded paper, cardboard, and natural fibers (like cotton or wool scraps).

Time for Compost to Be Ready:

The time it takes for the compost to be ready varies depending on factors like temperature, moisture, and the type of materials used. Generally, it takes about 2 to 6 months for compost to fully decompose and become ready to use.

Using the Compost:

Once the compost has broken down into a dark, crumbly, and earthy material, it is ready to use. You can spread it in your garden beds or pots as a nutrient-rich soil amendment. It improves soil structure, retains moisture, and provides essential nutrients for plants' growth.

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Answer:

Step-by-step explanation:

x-intercept is where the line cuts the x-axis. That is, when y=0.

Substitute y=0 and we get:

       \(0=\frac{1}{3} x-1\)

       \(1=\frac{1}{3} x\)

       \(x=3\)

So x-intercept is the point (3,0).

Answer:

f(6) = 51

Step-by-step explanation:

f(x)= x² + 3x - x/2

In order to find f(6) ,we need to substitute

x by 6 in the expression of f :

f(6) = (6)² + 3(6) - (6)/2

    = 36 + 18 - 3

    = 54 - 3

    = 51

Then

f(6) = 51

Answer:

f(6) = 51

Step-by-step explanation:

Simplify:

  Substitute the value of x

\(\sf f(x) =x^2 + 3x -\dfrac{x}{2}\\\\f(6)=6^2 + 3*6 -\dfrac{6}{2}\\\\\)

        = 36 + 18 - 3

        =  51

Step-by-step explanation:

hope it works

An investment of $6,400 to increase to $14,000 if it is invested at 5% per year compounded continuously is ≈15.6

Define compound interest?

Given that :

P = $ 6,400

Q = $ 14,000

r = 5%

Let P be the initial investment

r be the rate of interest

t be the time

Q be the increase amount

Q = P \(e^{rt} }\)

14,000 = 6,400 (\(e^{0.05t}\))

\(e^{0.05t}\) = \(\frac{14000}{6400}\)

\(e^{0.05t}\)  = 2.187

Taking log on both sides , we get

0.05t = ln (2.187)

0.05t = 0.78

       t = \(\frac{0.78}{0.05}\)

       t ≈ 15.6

An investment of $6,400 to increase to $14,000 if it is invested at 5% per year compounded continuously is ≈ 15.6

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Answer:

\((6x+5)^{2}\)

Step-by-step explanation:

\(36x^{2}+60x+25\)

Just looking at the equation, one can see that the first element (\(36x^{2}\)) and the last element (\(25\)) are both perfect squares. One can see that when one multiplies the number and then doubles the result, the resulting values will be the value in the middle. Therefore, it is clear that is the answer is;

\((6x+5)^2\)

Each function on the left should be matched to all points on the right that would be located on the graph of the function as follows;

f(x) = 2x + 2         ⇒   (0, 2).

f(x) = 2x² - 2        ⇒   (-1, 0).

\(f(x) = 2\sqrt{x+1}\)   ⇒   (0, 2).

In Mathematics and Geometry, a function is a mathematical equation which defines and represents the relationship that exists between two or more variables such as an ordered pair in tables or relations.

Next, we would determine the point or ordered pair that represent a solution on the graph of each of the function as follows;

For the ordered pair (0, 2), we have:

f(x) = 2x + 2

2 = 2(0) + 2

2 = 2 (True).

For the ordered pair (-1, 0), we have:

f(x) = 2x² - 2

0 = 2(-1)² - 2

0 = 2 - 2

0 = 0 (True).

For the ordered pair (0, 2), we have:

\(f(x) = 2\sqrt{x+1}\\\\2= 2\sqrt{0+1}\\\\2 = 2\sqrt{1}\)

2 = 2 (True).

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Hello!

First, let's remember some properties about the rectangle:

• Perimeter,: sum of all four sides.

• Area,: length * width.

Now, let's imagine a rectangle that we don't know the measurements of the sides. We can call them X and Y.

Now, let's write an equation for the perimeter of this rectangle:

P = x +x +y +y

P = 2x +2y

2x + 2y = 52

Now, let's write an equation for the area of the same rectangle:

A = x * y

x * y = 144

At this moment, we have two equations that have the same value for X and Y. So, we can create a system and solve it, look:

If we solve the second equation using the Bhaskara Theorem, we'll obtain two solutions:

y' = 8

y" = 18

We will use the first solution (y=8) as the value of y, and replace it in the equation i:

Now, let's use the second solution (y=18) as the value of y, doing the same way:

So, in this exercise we have two possible solutions for the system, look:

1st: (8,18)

2nd: (18,8)

The correct answer is Graph 1: y = cos(x/4)Graph 2: y = cos(x/2)

Based on the given descriptions of the graphs and the patterns they follow, the correct pairs are:

Graph 1: y = cos(x/4) ⟶ This graph has a period of 8 units and matches the pattern described.Graph 2: y = cos(x/2) ⟶ This graph has a period of 4 units and matches the pattern described.

Graph 3: y = cos(x) ⟶ This graph has a period of 2π (or approximately 6.28 units) and matches the pattern described.

Graph 4: (Not used)

Graph 5: (Not used)

Please note that without visual representation, it's difficult to provide a definitive answer. The pairs are based on the descriptions provided and may vary depending on the actual shapes of the graphs.

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Answer:

C

Step-by-step explanation:

x + y + 10 = 0 ( subtract x + 10 from both sides )

y = - x - 10 → (1)

x² + y - 2 = 0 → (2)

substitute y = - x - 10 into (2)

x² - x - 10 - 2 = 0

x² - x - 12 = 0 ← in standard form

(x - 4)(x + 3) = 0 ← in factored form

equate each factor to zero and solve for x

x + 3 = 0 ⇒ x = - 3

x - 4 = 0 ⇒ x = 4

Chay can use 3 bags of mulch per flower bed.

Chay is buying mulch for the zoo's summer flower beds. She has enough in her budget to purchase 55 bags of mulch. If there are 20 flower beds, how many bags of mulch can be used in each flower bed?The number of bags of mulch that can be used in each flower bed can be found by dividing the total number of bags of mulch by the number of flower beds, as given by the problem.Let X be the number of bags of mulch used in each flower bed. Then, the following equation can be written:Total number of bags of mulch = X × number of flower beds (20)Or, 55 = 20XDividing both sides of the equation by 20, we get: X = 55/20X = 2.75.Therefore, Chay can use 2.75 bags of mulch in each flower bed. However, since we cannot have a fraction of a bag of mulch, she would have to round up to 3 bags of mulch per flower bed to ensure each flower bed has enough mulch.

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9514 1404 393

Answer:

  draw the line using a ruler on which you have identified points 2 7/16 inches apart

Step-by-step explanation:

On your ruler graduated in inches with marks at 1/16-inch intervals, locate the 0 mark and the mark 1/16 inch before the half-inch mark between 2 and 3 inches.

Draw your line along the edge of the ruler between the two marks you have identified: 0 and 2 7/16. The line will be 2 7/16 inches long.

Answer:

the marked price of a mobile is 25% above its cost price when it is sold at a gain of 10%, the profit amount to RS 725 find the marked price of the mobile

Step-by-step explanation:

Hope this helps.......

Answer: the maximum is at (3,4)

Step-by-step explanation:

Answer:

 x = 7

 y = 17

Step-by-step explanation:

Substitution method:

    y = 2x + 3 ---------------(I)

     y = 3x - 4 ----------------(II)

Substitute y = 3x - 4 in equation (I)

        3x - 4 = 2x + 3

 Add 4 to both sides

               3x = 2x + 3 + 4

               3x = 2x + 7

Subtract '2x' from both sides

          3x - 2x = 7

               \(\sf \boxed{\bf x = 7}\)

Substitute x = 7 in any one of the equation, Here I substituting in equation (I)

             y = 2x + 3

            y = 2*7 + 3

               = 14 + 3

            \(\sf \boxed{\bf y = 17}\)

The distance between the points (-1, 5) and (-7, -3) is 10 units.

The distance formula used in finding the distance between two points is expressed as;

D = √( ( x₂ - x₁ )² + ( y₂ - y₁ )² )

Point 1 (-1,5)

Point 2 (-7,-3)​

Plug the given values into the distance formula and simplify.

D = √( ( x₂ - x₁ )² + ( y₂ - y₁ )² )

D = √[(-7 - (-1))² + (-3 - 5)²]

D = √[(-7 + 1)² + (-3 - 5)²]

D = √[-6² + (-8)²]

D = √[36 + 64]

D = √100

D = 10

Therefore, the distance is 10 units.

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Answer:

\(g(x)=-7x+6\)

Step-by-step explanation:

Translations

For a > 0

\(f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}\)

\(f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}\)

\(f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}\)

\(f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}\)

Parent function:

\(f(x)=-7x+7\)

Translation of 2 units left:

\(\implies f(x+2)=-7(x+2)+7\)

Translation of 13 units up:

\(\implies f(x+2)+13=-7(x+2)+7+13\)

Simplifying:

\(\implies g(x)=-7(x+2)+7+13\)

\(\implies g(x)=-7x-14+7+13\)

\(\implies g(x)=-7x+6\)

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