i need help with math

We need to find the n term formula:

The given sequence represents an arithmetic sequence and it follows the next form:

Where a represents the first term, in this case, a= -31

n is the term of the sequence

And d is the constant:

Let's find the constant

a1 to a2 =

-32 to -132, then, -32 needs -100 units bo equal to -132.

Now, -132 need -100 units to be equal to -232.

-232 needs -100 units to be equal to -332

Therefore, the constant d is equal to -100, d=-100

Replacing these values:

Then:

With this n formula, we can replace n=40, then, we will find a40:

Therefore:

Answer:

(x, y) = (4,-7)

Explanation:

To solve the system we need to graph the line that each equation represents, then the solution will be the point where the lines cross.

So, to graph the line for the first equation 2x + y = 1, we need to identify two points in the line.

Then, if x = 0, y is equal to:

2x + y = 1

2(0) + y = 1

y = 1

And if x = 1, y is equal to:

2(1) + y = 1

2 + y = 1

2 + y - 2 = 1 - 2

y = -1

So, for the first equation, we have the points (0, 1) and (1, -1)

In the same way, for the second equation x - 2y = 18, we get:

If x = 0, y is equal to:

0 - 2y = 18

-2y = 18

y = 18/(-2)

y = -9

If x = 2, y is equal to:

2 - 2y = 18

2 - 2y - 2 = 18 - 2

-2y = 16

y = 16/(-2)

y = -8

So, for the second equation, we have the points (0, -9) and (2, -8)

Therefore, the graph of both lines is:

So, the solution of the system is the point (x, y) = (4, -7)

If we refer the level 0 to the sea level.

Then, 10 feet belox the sea level is -10 and 10 above is 10 feet (positive).

Then, the bottom of the canyon is at level y=-70 4/5 (referred to the sea level) and the nest is y=652 feet.

Then, the distance is D=y2-y1=652-(-70)=652+70=772 feet.

The distance between canyon bottom and nest is 772 feet.

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For the condition  p: x < 0 and  q: y < 0;  p ∨ q represent quadrants 2, 3, and 4 is correct because in these quadrants x, y, or both are negative coordinates.

We are told that p: x<0 and q: y<0.

As a result, pVq = quadrants 2, 3, and 4, because both x and y are negative within those quadrants.

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Given the set G = ( z l z is an integer and -3 < z <_ 0) , we are to write out all the elements in the set.

First you must take note of the inequality signs.

First aspect of the inequality-3 < z means that z is a value greater than -3 exclusive -3. The values are -2, and -1

The second part of the inequality z <_ 0 means that z is less than or equal to 0, this means that 0 is inclusive because of the equal to sign.

Hence the set of element G will be -2, -1 and 0. In set notataion, it is represented as:

G = {-2, -1, 0}

Note that -3 is not part of the element G

The steps to use the excel formulas are:

Some steps to use the excel formulas are:

Therefore, the steps to use the excel formulas are:

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Given

Answer

The graph of the parabola is given as

The vertex of is (-3,-5). The parabola opens right. The focus is 3 units away from vertex. The directrix is 6 units away from focus. Focus is at (0,-5). The equation of the directix is x = - 6

Hello there. To solve this question, we'll need to set up a system of equations with 3 equations and 3 variables.

In each equation, we'll have the amounts for protein, carbohydrates and vitamin A.

Talking about protein:

Each serving of salmon steak has 30 grams of protein, baked eggs contains 20 grams of protein and acorn squash contains 4 grams of protein.

Say the servings of salmon steak, baked eggs and acorn squash are the variables x, y and z, respectively. We multiply x, y and z by the respective values for the protein of each serving and add them up. It should be equal to the amount of protein the dietitian was thinking of.

30x + 20y + 4z = 113

Talking about carbohydrates:

The same thing will apply to carbs, we multiply the variables by how many carbs we can get for eachserving. A serving of salmon steak gives you 10 grams of carbs, baked eggs gives you 3 grams of carbs and acorn squash gives you 15 grams.

10x + 3y + 15z = 54

Talking about vitamin A:

Repeat the same process, this time using the values for the vitamin A you get form each serving.

x + 20y + 37z = 135.5

Then we have the following system of equations:

Solving this system of equations, you can use the method of your choice.

After you solved it, you find the values:

1.5 serving of salmon steak, 3 servings of baked eggs and 2 servings of acorn squash.

Absolute value simply means the number must be made positive. Since 9/5 is positive already the absolute value remains 9/5

According to the information given, the randome sample that was asked about their opinion was 700 men, however the results of the survey were given as "4 out of 5 drivers"

This information is misleading because the results should have been thrown for men and not for drivers since the sample does not give any information saying that all 700 men are drivers.

The correct answer is: A

Answer:

Explanation:

The slope is defined as the rise/ run. If a line passes through any two points (x0, y0) and (x1, y1) then the slope m is given by

Now, in our case (x0, y0) = ( -19, 6) and (x1, y1) = (15, 16); therefore, the slope is

Simplifying the above gives

which is our answer!

EXPLANATION:

Given;

We are told that Joey's drawer contains the following;

Black dress socks = 3

Black ankle socks = 3

Brown dress socks = 6

Brown ankle socks = 4

Required;

If a sock is chosen at random, find the probability that it is brown or is a dress sock.

Step-by-step solution;

The drawer contains a total of 16 socks.

Also, there is a total of 9 dress socks and 10 brown socks.

The probability of choosing a brown or dress sock will be determined by the following formula;

We can now substitute the values given for this experiment as follows;

ANSWER:

The probability that Joey would select a sock at random that is brown or is a dress sock is

Option D is the correct answer.

For the show there are two types of tickets:

Advance tickets, that cost $25

Same-day tickets, that cost $40

We know that for one function there were 60 tickets sold for a total amount of $205.

Let "a" represent the number of advanced tickets sold and "s" represent the number of same-day tickets sold.

The total number of tickets sold for the function can be expressed as the sum of the number of advance tickets (a) sold and the number of same-day tickets sold (s)

If each advance ticket costs $25 and there were "a" advance tickets sold, the total earnings for advance tickets can be expressed as 25a

And if each same-day ticket costs $40 and there were "s" same-day tickets sold, the earnings for selling same-day tickets can be expressed as 40s

The total earnings for the performance can be expressed as the sum of the earnings for selling advance tickets and the earnings for selling same-day tickets:

Both equations established form an equation system and we can use them to determine the number of advance and same-day tickets sold:

-First, write the first equation for one of the variables, I will write it for "a"

-Second, replace the expression obtained for "a" into the second equation:

From this expression, we can calculate the value of "s", first, you have to distribute the multiplication on the parentheses term, which means that you have to multiply both terms by 25:

Next, simplify the like terms

Pass "1500" to the other side by applying the inverse operation to both sides of it, which means that you have to subtract 1500 to both sides of the equal sign:

And finally divide both sides by 15 to reach the value of s

With the value of s calculated, you can replace it into the expression obtained for a and calculate its value:

So with the information given, the number of advanced and same-day tickets sold are:

a=146.33

s=-86.33

PART A

For our beautiful sun, we'll have that:

This way,

PART B

We'll have the equation:

Solving for b,

Now we'll use the following property:

This way,

The averge rate of change on the interval -1≤x≤5 for the given function f(x)= -3|x+2|-1 is -3.

In the given question we have to find the averge rate of change on the interval -1≤x≤5 for the given function.

Thegiven function is f(x)= -3|x+2|-1

The interval [a,b]=[-1,5]

As we know that the average rate of change of function f(x) on [a,b] is given by

R = {f(b)-f(a)}/(b-a)

As we know that a= -1 and b=5.

R = {f(5)-f(-1)}/(5-(-1))...........................(1)

Firstly we finding the f(-1) and f(5)

Now put x= -1 in the given function.

f(-1)= -3|-1+2|-1

f(-1)= -3|1|-1

f(-1)= -3-1

f(-1)= -4

As we know that b= 5.

Now put x= 5 in the given function.

f(5)= -3|5+2|-1

f(5)= -3|7|-1

f(5)= -3*7-1

f(5)= -21-1

f(5)= -22

Now putting the value in equation 1.

R = (-22-(-4))/(5+1)

R = (-22+4)/6

R = -18/6

R = -3

Hence, the averge rate of change on the interval -1≤x≤5 for the given function f(x)= -3|x+2|-1 is -3.

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Answer:

Explanation:

the Here the equation of amount of salt in the barrel at time t is given by

a

At time t=7 minute the amount of salt will be

The amount of salt after 7 min will be 7.20lb.

b

At time t=14minute the amount of salt will be

Amount of salt will be 11.93 lb

d

From the graph, for large t the value Q(t) the amount of salt approaches to 21 lb.

4 gallons of water weigh 33.4 pounds how much do 7.5 gallons of water weigh

Applying proportion

33.4/4=x/7.5

solve for x

x=(33.4/4)*7.5

First we find the speed in mi/h.

We know that 20 h 45 min is equal to 20.75 hours, then the speed is

Now we convert the speed to ft/min:

Therefore you would have to drive at a speed of 6161.27 ft/min

So,

Let "t" be the number of minutes she will run today.

Given that she will run more than 11 laps today, then we can set up the inequality:

This is because 11 laps take 44 minutes to run, and if she will run more than 44 minutes, so t>44.

Given:

To calculate the length of an arc, the formula is;

Therefore, the radius of the circle 32 units.

The equation is that represent exponential decay is:

The rate in the equation of an exponential decay is negative, this would make it reduce expentially, rather than grow.

The best equation that demonstrate this is:

Where the rate is 0.35

By using Quadratic formula, the solutions are

[tex]x = \frac{7 + \sqrt{13}}{6}[/tex] or [tex]x = \frac{7 - \sqrt{13}}{6}[/tex]

Fourth option is correct.

What is Quadratic equation?

At first it is important to know about equation

Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.

A two degree equation is known as Quadratic equation.

If [tex]ax^2+bx + c = 0 (a\neq 0)[/tex] be a quadratic equation,

[tex]x = \frac{-b \pm \sqrt{b^2 -4ac}}{2a}[/tex]

This is the quadratic formula

Here,

The given quadratic equation is

[tex]3x^2 = 7x - 3\\3x^2 - 7x + 3 = 0\\[/tex]

a = 3, b = -7, c = 3

x =

[tex]\frac{-(-7)\pm\sqrt{(-7)^2 - 4\times 3 \times 3}}{2\times 3}\\\frac{7 \pm \sqrt{49 - 36}}{6}\\\frac{7 \pm \sqrt{13}}{6}[/tex]

[tex]x = \frac{7 + \sqrt{13}}{6}[/tex] or [tex]x = \frac{7 - \sqrt{13}}{6}[/tex].

Fourth option is correct.

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ANSWER:

The solution is:

STEP-BY-STEP EXPLANATION:

We must convert the matrix into a system of linear equations.

Each vertical represents the letters x, y and z, the first the x, the second y and the third the z. The fourth value is the value of the independent term that would be equal to the other expression, just like this:

We operate and the system will finally be like this

let's solve the system and we have:

We have to calculate the water remaining in A after B is complete.

This will be equal to the volume of A minus the volume of B.

The volume of each cylinder is equal to the area of the base times the height, so we can calculate this difference as:

Answer: the remaining volume is approximately 141.4 cubic feet.

1/3 = 0.333333333333

Then

3.33333333 is a whole number

= 3 + 1/3

ANSWER:

669.87 cubic feet

STEP-BY-STEP EXPLANATION:

The volume of the cone is given as follows:

We know the value of the radius and height, we replace and calculate the volume:

Therefore, the volume of the cone is 669.87 cubic feet.

The transformation for a points using a dilation factor k follows the rule:

Applying this to the points given

The equation of the parabola in vertex form is

where the point (h,k) is the coordinate of the vertex. From our picture, we can note that (h,k)=(-6,-4).

By substituting these values into our first equation, we have

which gives

Now, we can find the constant a by substituting one of the other given point. If we choose point (0,-2) into this last equation, we get

which gives

then, by moving -4 to the left hand side, we have

and finally, a is equal to

hence, the equation of the parabola in vertex form is

Now, lets convert this equation into a standrd form. This can be done by expanding the quadratic term and collecting similar term. That is, by expanding the quadratic terms, we obtain

now, by distributing 1/18, we have

which is equivalent to

and finally, the parabola equation in standard form is