Given f(x)=x+2 and g(x)=4-x^2 find the following (g o f)(x)

Answer:

Acute scalene triangle.

More Information:

Sides: a = 10   b = 11   c = 12

Area: T = 51.521

Perimeter: p = 33

Semiperimeter: s = 16.5

Angle ∠ A = α = 51.318° = 51°19'4″ = 0.896 rad

Angle ∠ B = β = 59.17° = 59°10'10″ = 1.033 rad

Angle ∠ C = γ = 69.513° = 69°30'46″ = 1.213 rad

Height: ha = 10.304

Height: hb = 9.367

Height: hc = 8.587

Median: ma = 10.368

Median: mb = 9.579

Median: mc = 8.631

Inradius: r = 3.122

Circumradius: R = 6.405

Vertex coordinates: A[12; 0] B[0; 0] C[5.125; 8.587]

Centroid: CG[5.708; 2.862]

Coordinates of the circumscribed circle: U[6; 2.242]

Coordinates of the inscribed circle: I[5.5; 3.122]

Exterior (or external, outer) angles of the triangle:

∠ A' = α' = 128.682° = 128°40'56″ = 0.896 rad

∠ B' = β' = 120.83° = 120°49'50″ = 1.033 rad

∠ C' = γ' = 110.487° = 110°29'14″ = 1.213 rad

How to Solve:

The calculation of the triangle has two phases. The first phase calculates all three sides of the triangle from the input parameters. The first phase is different for the different triangles query entered. The second phase calculates other triangle characteristics, such as angles, area, perimeter, heights, the center of gravity, circle radii, etc. Some input data also results in two to three correct triangle solutions (e.g., if the specified triangle area and two sides - typically resulting in both acute and obtuse) triangle).

1. Input data entered: sides a, b, and c.

a=10

b=11

c=12

We know the lengths of all three sides of the triangle, so the triangle is uniquely specified. Next, we calculate another of its characteristics - the same procedure for calculating the triangle from the known three sides SSS.

a=10

b=11

c=12

2. The triangle perimeter is the sum of the lengths of its three sides

3. Semiperimeter of the triangle

The semiperimeter of the triangle is half its perimeter. The semiperimeter frequently appears in formulas for triangles to be given a separate name. By the triangle inequality, the longest side length of a triangle is less than the semiperimeter.

4. The triangle area using Heron's formula

Heron's formula gives the area of a triangle when the length of all three sides is known. There is no need to calculate angles or other distances in the triangle first. Heron's formula works equally well in all cases and types of triangles.

5. Calculate the heights of the triangle from its area.

There are many ways to find the height of the triangle. The easiest way is from the area and base length. The triangle area is half of the product of the base's length and height. Every side of the triangle can be a base; there are three bases and three heights (altitudes). Triangle height is the perpendicular line segment from a vertex to a line containing the base.

6. Calculation of the inner angles of the triangle using a Law of Cosines

The Law of Cosines is useful for finding a triangle's angles when we know all three sides. The cosine rule, also known as the Law of Cosines, relates all three sides of a triangle with an angle of a triangle. The Law of Cosines extrapolates the Pythagorean theorem for any triangle. Pythagorean theorem works only in a right triangle. Pythagorean theorem is a special case of the Law of Cosines and can be derived from it because the cosine of 90° is 0. It is best to find the angle opposite the longest side first. With the Law of Cosines, there is also no problem with obtuse angles as with the Law of Sines because the cosine function is negative for obtuse angles, zero for right, and positive for acute angles. We also use inverse cosine called arccosine to determine the angle from the cosine value.

7. Inradius

An incircle of a triangle is a tangent circle to each side. An incircle center is called an incenter and has a radius named inradius. All triangles have an incenter, and it always lies inside the triangle. The incenter is the intersection of the three-angle bisectors. The product of the inradius and semiperimeter (half the perimeter) of a triangle is its area.

8. Circumradius

The circumcircle of a triangle is a circle that passes through all of the triangle's vertices, and the circumradius of a triangle is the radius of the triangle's circumcircle. The circumcenter (center of the circumcircle) is the point where the perpendicular bisectors of a triangle intersect.

9. Calculation of medians

A median of a triangle is a line segment joining a vertex to the opposite side's midpoint. Every triangle has three medians, and they all intersect each other at the triangle's centroid. The centroid divides each median into parts in the ratio of 2:1, with the centroid being twice as close to the midpoint of a side as it is to the opposite vertex. We use Apollonius's theorem to calculate the length of a median from the lengths of its side.

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Solution:

LCM of 9 and 19 is the smallest number among all common multiples of 9 and 19.

The first few multiples of 9 and 19 are (9, 18, 27, 36, 45, 54, . . . ) and (19, 38, 57, 76, 95, . . . ) respectively.

There are 3 commonly used methods to find LCM of 9 and 19 - by listing multiples, by division method, and by prime factorization.

To calculate the LCM of 9 and 19 by the division method, we will divide the numbers(9, 19) by their prime factors (preferably common). The product of these divisors gives the LCM of 9 and 19.

In this case, we get:

Then, the LCM would be:

so that, the correct answer is:

Answer: C) 60

Step-by-step explanation: If you keep adding 12 the only number that I get on the list is 60.

Answer:

the angle between west and Northwest is 90°

has being supplementry angles

hope it helps

Answer:

45°

Step-by-step explanation:

the angle between north and west is 90°

northwest is situated centrally between north and west at an angle of 45°

Answer:

y = (-1/4)x - 10

Step-by-step explanation:

y = 4x - 1

y = -1/4x - 1

(4, -11),

(x₁, y₁)  

y - y₁ = m(x - x₁)

y - (-11) = (-1/4)(x - 4)

y + 11 = (-1/4)x + 1

   -11                 -11

-------------------------------

y = (-1/4)x - 10

I hope this helps!

The slope of the given lines are:

Graph 1 = 1/3

Graph 2 = -1/3

Graph 3 = 3

Graph 4 = -3

To find the slope (m) of a given line on a coordinate plane, choose any two points on the line, (x1, y1) and (x2, y2), then find the slope by plugging in the values of the coordinates into the formula below:

Slope of a line (m) = change in y / change in x = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex].

Find the slope of Graph 1:

Using two points on the line, (0, 0) and (3, 1):

Slope of graph 1 (m) = (1 - 0)/(3 - 0)

Slope of graph 1 (m) = 1/3

Find the slope of Graph 2:

Using two points on the line, (0, 0) and (-3, 1):

Slope of graph 2 (m) = (1 - 0)/(-3 - 0) = 1/-3

Slope of graph 2 (m) = -1/3

Find the slope of Graph 3:

Using two points on the line, (0, 0) and (1, 3):

Slope of graph 3 (m) = (3 - 0)/(1 - 0) = 3/1

Slope of graph 3 (m) = 3

Find the slope of Graph 4:

Using two points on the line, (0, 0) and (-1, 3):

Slope of graph 4 (m) = (3 - 0)/(-1 - 0) = 3/-1

Slope of graph 4 (m) = -3

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Answer:

a) 199

f(-6)= 5(-6)^2 - 3 (-6) + 1 =199

b) 37

f(3)= 5(3)^2 - 3 (3) + 1 =37

The equation without fraction is 51 - 8x = 0

So, the equation is:

Rewrite in a more simplified form:

first, take the LCM, we get -

Now, take LHS denominator 3 to RHS:

Now, take 4 from RHS to LHS:

At last, decrease 9 by 60:

Therefore, the equation without fraction is 51 - 8x = 0

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Answer:

[tex]y=\frac{2}{3}x +\frac{4}{3}[/tex]

Step-by-step explanation:

[tex]-2x+3y=-6\\3y=2x-6\\y=\frac{2}{3}x-2\\ \\\\Then\\y-0=\frac{2}{3}(x-(-2)\\ y-0=\frac{2}{3}x+\frac{4}{3} \\Therefore, the answer is y=\frac{2}{3}x+\frac{4}{3}[/tex]

we can made a visula representation of the problem so:

So we can made an equation like:

and we can solve for x so:

Answer: X=6

Step-by-step explanation: you can set AB plus BC to AC because they both are equal to the full line so..

2X-2+3=3X-5

First off add like terms so..

-2+3= 1 and then add 5 to the negative 5 and 1 which now leaves you with

2X+6=3X

Now you see more like terms ( 2X,3X)

Now subtract 2X from 3x which will leave you with

6=1X

Now to separate X and get you answer you see it’s 1X and 1X = X prior to defined answer, therefore you will be with X=6. Have a great day

Answer:

(x - 3) (5x + 1)(x + 1).

Step-by-step explanation:

5x^3 - 9x^2 - 17x - 3

As the first coefficient is 5 and the last -3, so product is -15, we could try if (x-3) is a factor:

By the Factor Theorem, if x-3 is a factor then f(3) = 0.

f(3) = 5(3)^3 - 9(3)^2 - 17(3) - 3

= 135 - 81 - 51 - 3 = 0

So, x - 3 is a factor.

Now divide:

x - 3)5x^3 - 9x^2 - 17x - 3(5x^2 + 6x + 1 <------- Quotient

       5x^3 - 15x^2

                    6x^2 - 17x

                    6x^2 - 18x

                                    x - 3

                                    x - 3

                                     .......

Factoring 5x^2 + 6x + 1:

= (5x + 1)(x + 1)

So, the answer is:

(x - 3) (5x + 1)(x + 1).

The operations which must be part of the inverse function g(x) are:

An inverse function can be defined as a type of function that is obtained by reversing or undoing a mathematical operation in a given function (f(x)).

In Mathematics, a given function (f(x)) and its inverse function has the following property f⁻¹(f(x)) = x.

Generally speaking, the inverse of multiplication is division while addition is the inverse of subtraction. In this context, we can reasonably and logically deduce that a "division by 2," followed by an "addition of 3" to the function f(x) are the operations that must be part of the inverse function g(x).

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From the given question

There are given that the :

After two weeks, the total miles is 276 and after 3 weeks, the total miles are 413

Now,

The total miles did they ride in the third week is:

Hence, the total miles in the third week is 137.

Answer:

(1; 8)

Step-by-step explanation:

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

y = (10 + 6) = 8

By solving |4n+2|=34 solve for N we get 8 .

What is N factor?

The factorial of a non-negative integer n, denoted by n!, is the  product of all positive of  integers less than or equal to n. The factorial of n also  equals to the product of n with the next smaller factorial: For example, These are  value of 0! is 1, according to the  convention for an empty of product.

Sol-|4n+2|=34
Split into two equations
4n+2 = 34 or 4n+2=-34
4n+2 =34
Rearrange variable to the left side of the equation
4n =34-2
Calculate the sum or difference
4n=32
Devide both side of the equation by the coefficient of variable
n=32/4
Cross out the common factor
n=8
When n=8
LHS = |4×8+2|=34
RHS =34
LHS =RHS
Thus 8 is valid.

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By using proportions, it is discovered that each favor costs $5.

Using the rule of three and proportions, this problem can be resolved.

The party's price is increased by $40 with the addition of 8 favors.

A proportion is an equation that sets two ratios at the same value.

Using the rule of three and proportions, this problem can be resolved.

The party's price is increased by $40 with the addition of 8 favors.

The threes rule states:

$40 for 8 favors

$1 for 1 favor

Cross-multiplication application

8x=40

x= 40/8

x = 5

There is a $5 fee for each favor.

A proportion is an equation that sets two ratios at the same value. For instance, you could express the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls) There are 1 in 4 boys and 3 in 4 girls. 0.25 are male (by dividing 1 by 4).

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Compound interest exists as the interest you gain on interest. The balance in the account after 2 years is $42266.

Compound interest simply refers to the fact that an investment, loan, or bank account's interest accrues exponentially over time as opposed to linearly over time. The word "compound" is crucial here.

'Compound interest' simply indicates earning interest on your savings, and also, eventually, on the interest that those savings earn.

The appropriate formula is

A = P(1 +r/n[tex])^{(nt)[/tex]

where P = 19,000, r = 0.4, n = 365, t = 2.

substitute the values in the above equation, we get

A = 19,000(1 +0.4/365[tex])^{(365 \times2)[/tex]

simplifying the above equation, we get

A = 42266.7592

The balance in the account after 2 years is $42266.

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Answer:

Given:

Model : Ship = 3 : 400

The surface area of the model = 7200 cm²

To Find:

The surface area of the actual ship in m²

Let's start with the map scale given:

Model : Ship = 3 : 400

We start by adding in a unit. Usually, we choose the units associated with the model:

Model : Ship = 3 cm : 400 cm

Now, according to tot the question, we know that the actual ship is in m:

Model : Ship = 3 cm : 400 ÷ 100 m

Model : Ship = 3 cm : 4 m

The question asked for surface area, so the units have to be in squares:

Model : Ship = (3 cm)² : (4 m)

Model : Ship = 9 cm² : 16 m²

Now, that we have the units set correctly according to the question requirement, we will find 1 branch of the model:

Model : Ship = 9 cm² : 16 m²

Model : Ship = 9÷9 cm² : 16÷9 m²

Model : Ship = 1 cm² : 16/9 m²

Finally, we can find the required units by multiplying both sides with the required units:

Model : Ship = 1 cm² : 16/9 m²

Model : Ship = 1 x 7200 cm² : 16/9 x 7200 m²

Model : Ship = 7200 cm² : 12800 m²

Answer: The surface area of the ship is 12800 m²

(by the way, this was copied from the same website)

hope this helps :)

Write the inequality for the statement and solve for v

It means that v is less than or equal to -4. The solution set for this inequality is:

By solving inequality, we can conclude that the artist will not make a profit if he sells 15 necklaces.

So, is the artist in profit if he sells 15 necklaces:

Inequality is 12n ≥ 170 +3.50n: (let n = 15)

Therefore, by solving inequality, we can conclude that the artist will not make a profit if he sells 15 necklaces.

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The correct question is given below:
A jewelry artist is selling necklaces at an art fair. It costs $170 to rent a booth at the fair. The cost of materials for each necklace is $3.50. The artist is selling the necklaces at $12 each. The inequality 12n> 170 +3.50n represents the situation in which the artist makes a profit. Will the artist make a profit if he sells 15 necklaces? Show how you know.

Given the following question:

First expression:

Second expression:

Step 1

Find the equation of both lines using

Where,

Hence,

For the second line we will have

Step 2

Hence expressed the graphed solution as a piecewise function

The number of miles that is covered is  1458 miles.

The term gas mileage refers to the distance that have been covered by the car using a given volume of gas. It is common that the unit that is used to measure the volume of the gas is the US gallon.

We have been told that;

420 miles could be covered by the use of 20 gallons

1 mile can be covered by the use of 1 mile  * 20 gallons/ 420 miles

= 0.048 gallons

If 1 mile requires  0.048 gallons

x miles requires 70 gallons

x = 1 mile  * 70 gallons/0.048 gallons

x = 1458 miles

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SOLUTION.

AC and BD will intersect at the mid-point between points A and C.

So let's find the mid-point between points A and C

Point A(-2, 4) and point C(-6, 0)

This becomes

Therefore, the correct answer is option C.

Answer: Extrapolation ,from the above can be defined as using a linear regression equation and any x- value to predict any y-value.

Step-by-step explanation:

Extrapolation regression makes use of estimated regression equation to predict a new value y for specific X values not in the range of the sampled data used to estimate our regression equation

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Answer:

AC= 3.2

Step-by-step explanation:

two trianglesare similar

so AC : BC = DF : EF

AC : 4 = 3:2.4

4×3.2 = AC×4

12.8=4×AC >>>> (÷4) both sides

3.2= AC

The simplified expression of 7 * 2 * 7 * 5 is 490

The expression is given as

7*2*7*5

Rewrite the expression properly

This is done as follows

7 * 2 * 7 * 5

The factors of the expression have different basis

i.e. Basis = 7 , 2 and 5

This means that we cannot apply the law of indices

Solving further, we have the following equation:

7 * 2 * 7 * 5 = 7 * 2 * 7 * 5

Rearrange the factors

So, we have

7 * 2 * 7 * 5 = 7 * 7 * 2 * 5

Evaluate the products of 7 and 7 in the above equation

So, we have

7 * 2 * 7 * 5 = 49 * 10

Finally, we have

7 * 2 * 7 * 5 = 490

Hence, the simplified expression of the expression given as 7 * 2 * 7 * 5 is 490

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The simplified expression of the given 7 x 2 x 7 x 5 will be; 490

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

The expression is given as;

7 x 2 x 7 x 5

Rewrite the expression properly as follows;

7 x 2 x 7 x 5

The factors of the expression have different basis that is;

Basis = 7 , 2 and 5

Thus we can't apply the law of indices

Solving further, we have the equation;

7 x 5 x 7 x 2 = 7 x 2 x 7 x 5

Rearrange the factors;

7 x 2 x 7 x 5 = 7 x 7 x 2 x 5

7 x 2 x 7 x 5 = 49 x 10

Finally, we have the following

7 x 2 x 7 x 5 = 490

Hence, the simplified expression of the given 7 x 2 x 7 x 5 will be; 490

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Given

V(5, -2)

T(10, -3)

Procedure

For V:

The equation of the horizontal straight line corresponds to y = -2.

The equation of the vertical straight line corresponds to x = 5

For T:

The equation of the horizontal straight line corresponds to y = -3.

The equation of the vertical straight line corresponds to x = 10

The percent tip when Jayden's dinner bill is $29 is 18%.

According to the question,

We have the following information:

Bill of Jayden's dinner = $29

After adding the tip, Jayden paid $34.22.

Now, we will find the percent tip.

First, we will find the amount added to the bill.

$(34.22-29)

$5.22

Now, let's take the percent tip to be x%.

x% of 29 = 5.22

29x/100 = 5.22

29x = 522

x = 522/29 (29 was in multiplication on the left hand side. So, it is in the division on the right hand side.)

x = 18%

Hence, the percent tip on Jayden's dinner is 18%.

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An inequality to determine the number of levels you can play in 60 minutes is 5 + 7l ≤60

What is a linear equation?

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

Here, it is given that :

Time for setting up the game = 5 minutes

Time to play each level = 7 minutes

Let  l represent the number of levels played.

So, Time to play l levels = 7l

So, b = 5+7l

Now we are required to  Write an inequality to determine the number of levels you can play in 60 minutes.

So, the inequality becomes :

5 + 7l ≤60

Hence an inequality to determine the number of levels you can play in 60 minutes is 5 + 7l ≤60

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