Need number 11 please!!!

Need Number 11 Please!!!

Answers

Answer 1

The coordinates of the inverse function f⁻¹(x) will be swapped of the coordinates of the function f(x).

The complete question is attached below.

What is inverse of a function?

Let the function will be  

f: X → Y

Then the inverse function will be

f⁻¹: Y → X

If the coordinates of the function f(x) are given.

Then the coordinates of the inverse function f⁻¹(x) will be swapped of the coordinates of the function f(x).

         f(x)                          f⁻¹(x)

     (33, 40)                   (40, 33)

     (-19, -15)                  (-15, -19)

    (-28, 47)                   (47, -28)

    (-15, -34)                  (-34, -15)

      (50, 0)                     (0, 50)

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Need Number 11 Please!!!

Related Questions

distance between (-5,1) and (0,-4)?

Answers

Answer:

7.07106781187

Express cos A as a fraction in simplest terms.

Answers

Answer:

See below

Step-by-step explanation:

Here is one way

cos^2 + sin^2 = 1

cos^2 = 1 - sin^2  

For angle A      cos^2 = 1 - (10/26)^2

                          cos ^2 = 1 - 100/676

                                       =  576/676

                              cos A = 24/26   = 12/13

Another way would be to use the Pythagorean theorem to find length of AB .... then cos A =   length AB / 26

What percent of 48 listings is 36 listings

Answers

Answer:

75%

Step-by-step explanation:

48x=36

x=36/48

x=3/4

x=0.75=75%

A pool a possible candidate for a student council consists of 14 freshmen and 8 softwares how many different councils consisting of 5 freshmen and 7 sophomores are possible

Answers

The different councils consisting of 5 freshmen and 7 sophomores are possible 9216.

We have given that,

A pool of possible candidates for a student council consists of 14 freshmen and 8 software.

We have to determine the how many different councils consisting of 5 freshmen and 7 sophomores are possible

What is the combination?

[tex]_n C_r=\frac{n !}{r ! (n-r) !}_n C_r = number of combinations\\\n = total number of objects in the set\\\r = number of choosing objects from the set[/tex]

The total number of the council is

[tex]_{10} C_5\times _9 C_7[/tex]

=252(36)

=9216

The different councils consisting of 5 freshmen and 7 sophomores are possible 9216.

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Sum to n terms of each of following series. (a) 1 - 7a + 13a ^ 2 - 19a ^ 3+...​

Answers

Notice that the difference in the absolute values of consecutive coefficients is constant:

|-7| - 1 = 6

13 - |-7| = 6

|-19| - 13 = 6

and so on. This means the coefficients in the given series

[tex]\displaystyle \sum_{i=1}^\infty c_i a^{i-1} = \sum_{i=1}^\infty |c_i| (-a)^{i-1} = 1 - 7a + 13a^2 - 19a^3 + \cdots[/tex]

occur in arithmetic progression; in particular, we have first value [tex]c_1 = 1[/tex] and for [tex]n>1[/tex], [tex]|c_i|=|c_{i-1}|+6[/tex]. Solving this recurrence, we end up with

[tex]|c_i| = |c_1| + 6(i-1) \implies |c_i| = 6i - 5[/tex]

So, the sum to [tex]n[/tex] terms of this series is

[tex]\displaystyle \sum_{i=1}^n (6i-5) (-a)^{i-1} = 6 \underbrace{\sum_{i=1}^n i (-a)^{i-1}}_{S'} - 5 \underbrace{\sum_{i=1}^n (-a)^{i-1}}_S[/tex]

The second sum [tex]S[/tex] is a standard geometric series, which is easy to compute:

[tex]S = 1 - a + a^2 - a^3 + \cdots + (-a)^{n-1}[/tex]

Multiply both sides by [tex]-a[/tex] :

[tex]-aS = -a + a^2 - a^3 + a^4 - \cdots + (-a)^n[/tex]

Subtract this from [tex]S[/tex] to eliminate the intermediate terms to end up with

[tex]S - (-aS) = 1 - (-a)^n \implies (1-(-a)) S = 1 - (-a)^n \implies S = \dfrac{1 - (-a)^n}{1 + a}[/tex]

The first sum [tex]S'[/tex] can be handled with simple algebraic manipulation.

[tex]S' = \displaystyle \sum_{i=1}^n i (-a)^{i-1}[/tex]

[tex]\displaystyle S' = \sum_{i=0}^{n-1} (i+1) (-a)^i[/tex]

[tex]\displaystyle S' = \sum_{i=0}^{n-1} i (-a)^i + \sum_{i=0}^{n-1} (-a)^i[/tex]

[tex]\displaystyle S' = \sum_{i=1}^{n-1} i (-a)^i + \sum_{i=1}^n (-a)^{i-1}[/tex]

[tex]\displaystyle S' = \sum_{i=1}^n i (-a)^i - n (-a)^n + S[/tex]

[tex]\displaystyle S' = -a \sum_{i=1}^n i (-a)^{i-1} - n (-a)^n + S[/tex]

[tex]\displaystyle S' = -a S' - n (-a)^n + \dfrac{1 - (-a)^n}{1 + a}[/tex]

[tex]\displaystyle (1 + a) S' = \dfrac{1 - (-a)^n - n (1 + a) (-a)^n}{1 + a}[/tex]

[tex]\displaystyle S' = \dfrac{1 - (n+1)(-a)^n + n (-a)^{n+1}}{(1+a)^2}[/tex]

Putting everything together, we have

[tex]\displaystyle \sum_{i=1}^n (6i-5) (-a)^{i-1} = 6 S' - 5 S[/tex]

[tex]\displaystyle \sum_{i=1}^n (6i-5) (-a)^{i-1} = 6 \dfrac{1 - (n+1)(-a)^n + n (-a)^{n+1}}{(1+a)^2} - 5 \dfrac{1 - (-a)^n}{1 + a}[/tex]

[tex]\displaystyle \sum_{i=1}^n (6i-5) (-a)^{i-1} =\boxed{\dfrac{1 - 5a - (6n+1) (-a)^n + (6n-5) (-a)^{n+1}}{(1+a)^2}}[/tex]

The length of the base of a triangle is twice its height. If the area of the triangle is 16 square kilometers, find the height.

Answers

Answer:

4

Step-by-step explanation:

Area of a triangle = bh/2

B = 2h

16 = 2h × 2/2

h×2 = 16

2h = 16

* put a square root on both sides then u will get the answer which is

Height of the triangle = 4

Solvex + 5-6 = 7.
OA. x = -8 and x = -18
OB. x = 8 and x = -8
C. x = -8 and x = 18
OD. x = 8 and x = -18

Answers

I got x=8
Because 5-6=-1….. 7- -1= 8…… then it’s just that.I



I don’t understand the answers given tho but that’s my guess

The population of a large city can be calculated using the function P=345,000(1.01). What can you say about the rate of change from year 1 to year 2 compared to the rate of change from year 9 to year 10?

Answers

Rate of change (ROC) refers to how quickly something changes over time.

What is rate of change?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 slowdown of changes (i.e., the pace). Rate of change is a tool used in finance to comprehend price returns and spot trend momentum.Divide the change in y-values by the change in x-values to determine the average rate of change. Identifying changes in quantifiable parameters like average speed or average velocity calls for the knowledge of the average rate of change.The ratio between the change in the values of the y variables and the change in the values of the x variables is known as the rate of change.

Given data :

The rate of change will be the same for all years. The rate of change is 7%. The . basic formula for this equation is: I(1+R)^T, where I = Initial amount, R = Rate of growth, and T = Time. So the R here is 0.07, or 7%. The growth RATE is constant, the growth AMOUNT will increase each year.

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Which of the following points would fall on the line produced by the point-slope form equation y - 2 = 3(x - 5) when graphed?

(4, 5)

(6, 5)

(5, 5)

(1, 4)

Answers

The point is (6, 5).

What is graph?

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

Given :

y - 2 = 3(x - 5)

Those point will satisfy after putting the value of x and y we get LHS= RHS.

take (4, 5)

5-2 = 3(4-5)

3= -3

Hence, not satisfied.

take, (6, 5)

5-2 = 3(6-5)

3= 3

Hence, satisfied.

take, (5, 5)

5-2 = 3(5-5)

3= 0

Hence, not satisfied.

take, (1, 4)

4-2 = 3(1-5)

2= -12

Hence, not satisfied.

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how to evaluate 16/81 1/2

Answers

An expression is defined as a set of numbers, variables, and mathematical operations. The value of (16/81)^(1/2) is 4/9.

What is an Expression?

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.


The value of the given expression (16/81)^(1/2) can be calculated as shown below,

[tex](\dfrac{16}{81})^{\frac12}\\\\=\sqrt{\dfrac{16}{81}}\\\\= \dfrac49[/tex]

Hence, the value of (16/81)^(1/2) is 4/9.

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Answer:

★The square root of 16/81 = 4/9.

(x) = x + 0.14x, then find the value of T(290).
A. 300.45
B. 351.2
C. 325.8
D. 330.6

Answers

Answer:

  D.  330.6

Step-by-step explanation:

To evaluate the function for a specific value of x, put that value where x is in the function definition, and do the arithmetic.

__

T(x) = x +0.14x . . . . . given function definition

T(290) = 290 +0.14×290 = 290 +40.6 . . . . substitute 290 for x

T(290) = 330.6

The value of T(290) will be 330.6.The relation between them is shown as T(x)  is dependent and x is the independent variable. Option D s correct.

What is a function?

A connection between independent variables and the dependent variable is defined by the function.

Functions help to represent graphs and equations. A function is represented by the two variables one is dependent and another one is an independent function.

Given relation;

T(x) = x +0.14x

Substitute the value of x we get;

T(290) = 290 +0.14×290

T(290) = 330.6

Hence, option D s correct.

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The temperature is dropping at a rate of five degrees per hour.
Let d represent the number of degrees the temperature drops.
Let t represent the number of hours that pass.
Which is the dependent variable?
Othe number of hours
Othe number of degrees the temperature drops
O the rate at which the temperature drops
the day of the week

Answers

Answer:

The rate at which the temperature drops.

Step-by-step explanation:

In science, the dependent variable is what you are measuring.
In math, the dependent variable is what you are evaluating.

Same idea, different topic.

Answer:

d=temp drop

t=hours

dependent variable is the temperature drops because the number of hours will tell you how much the temprature drops

this is the equation

total temp drops=t x 5

hope this helps!?

For which value of x is the expression y
=
a. 1
b. -1
C. 5
d. -5
3x-3
x-5
- undefined?

Answers

1

Step-by-step explanation:

when we put 1 in the equation the nominator becomes zero and it becomes undefined

Hii!

___________________________________________________________

[tex]\stackrel\star\rightsquigarrow\circ\boldsymbol{\underbrace{Answer:}}}\circ\leftharpoonup[/tex]

The value of x should be 5! ^^

[tex]\stackrel\star{\rightsquigarrow\circ\boldsymbol{\underbrace{Explanation:}}}\circ\leftharpoonup[/tex]

[tex]\boxed{\\\begin{minipage}{7cm} For\,an\,expression \\ \boldsymbol{to\,be\,und efined,} \\ \,its\,denominator\,should\,be\,zero \end{minipage}}}[/tex]

Remember this! ^^

Now let's consider this:

Which value of x will make the denominator equal to 0?

Is it 1? If we stick 1 in, we will not obtain 0.

[tex]\twoheadrightarrow\sf y=\cfrac{3\cdot1-3}{1-5}[/tex]

[tex]\bullet[/tex] Simplify this

[tex]\twoheadrightarrow\sf y=\cfrac{3-3}{-4}[/tex]

---

We will obtain 0 in the numerator, but not in the denominator; if the numerator is 0, then the fraction, or fractional expression, is 0.

Let's try 5. 5-5 is equal to 0, so this sounds promising! ^^

[tex]\twoheadrightarrow\sf y=\cfrac{3\cdot5-3}{5-5}[/tex]

[tex]\bullet[/tex] Look what we obtain when we simplify

Don't we obtain 15-3/0?

Like I said above, if an expression has 0 as its denominator, it's undefined.

--

Hope that this helped! Best wishes.

[tex]\textsl{Reach far. Aim high. Dream big.}[/tex]

--

solve the equation uding the most direct method: 3x(x+6)=-10?​

Answers

To solve this problem, you will use the distributive property to create an equation that can be rearranged and solved using the quadratic formula.

Distribute

Use the distributive property to distribute 3x into the term (x + 6):

[tex]3x(x+6)=-10[/tex]

[tex]3x^2+18x=-10[/tex]

Rearrange

To create a quadratic equation, add 10 to both sides of the equation:

[tex]3x^2+18x+10=-10+10[/tex]

[tex]3x^2+18x+10=0[/tex]

Use the Quadratic Formula

The quadratic formula is defined as:

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

The model of a quadratic equation is defined as ax² + bx + c = 0. This can be related to our equation.

Therefore:

a = 3b = 18c = 10

Set up the quadratic formula:

[tex]\displaystyle x=\frac{-18 \pm \sqrt{(18)^2 - 4(3)(10)}}{2(3)}[/tex]

Simplify by using BPEMDAS, which is an acronym for the order of operations:

Brackets

Parentheses

Exponents

Multiplication

Division

Addition

Subtraction

Use BPEMDAS:

[tex]\displaystyle x=\frac{-18 \pm \sqrt{324 - 120}}{6}[/tex]

Simplify the radicand:

[tex]\displaystyle x=\frac{-18 \pm \sqrt{204}}{6}[/tex]

Create a factor tree for 204:

204 - 1, 2, 3, 4, 6, 12, 17, 34, 51, 68, 102 and 204.

The largest factor group that creates a perfect square is 4 × 51. Therefore, turn 204 into 4 × 51:

[tex]\sqrt{4\times51}[/tex]

Then, using the Product Property of Square Roots, break this into two radicands:

[tex]\sqrt{4} \times \sqrt{51}[/tex]

Since 4 is a perfect square, it can be evaluated:

[tex]2 \times \sqrt{51}[/tex]

To simplify further for easier reading, remove the multiplication symbol:

[tex]2\sqrt{51}[/tex]

Then, substitute for the quadratic formula:

[tex]\displaystyle x=\frac{-18 \pm 2\sqrt{51}}{6}[/tex]

This gives us a combined root, which we should separate to make things easier on ourselves.

Separate the Roots

Separate the roots at the plus-minus symbol:

[tex]\displaystyle x=\frac{-18 + 2\sqrt{51}}{6}[/tex]

[tex]\displaystyle x=\frac{-18 - 2\sqrt{51}}{6}[/tex]

Then, simplify the numerator of the roots by factoring 2 out:

[tex]\displaystyle x=\frac{2(-9 + \sqrt{51})}{6}[/tex]

[tex]\displaystyle x=\frac{2(-9 - \sqrt{51})}{6}[/tex]

Then, simplify the fraction by reducing 2/6 to 1/3:

[tex]\boxed{\displaystyle x=\frac{-9 + \sqrt{51}}{3}}[/tex]

[tex]\boxed{\displaystyle x=\frac{-9 - \sqrt{51}}{3}}[/tex]

The final answer to this problem is:

[tex]\displaystyle x=\frac{-9 + \sqrt{51}}{3}[/tex]

[tex]\displaystyle x=\frac{-9 - \sqrt{51}}{3}[/tex]

Use the graph of the function to find its domain and range. Write the domain and range in interval notation

Answers

Answer:

Step-by-step explanation:

In how many ways can $9$ friends sit at a circular table if two of them, Anna and Bob, insist on having exactly two people seated between them? (As usual, two seatings are considered the same if one is a rotation of the other.)

Answers

There are 10,080 different ways in which the friends can seat on the circular table.

In how many ways the friends can seat?

There are 9 friends, such that two of them need to be separated by exactly two people.

Because the table is circular, we can consider the first position as the position where Bob is.

Now let's count the number of options for each of the other 8 positions. (counting to the left).

The next two positions have 7 and 6 options respectively (as these can be taken by any of the other 7 friends)

For the next seat, we could seat Anna or one of the remaining 5 friends.

Let's assume we seat Anna there, then for each of the next positions, we will have, respectively, 5, 4, 3, 2, 1 options.

The total number of combinations is given by the product between the numbers of options, so we have:

C = 7*6*5*4*3*2*1

But we also need to consider the case where Anna is on the first position (and Bob on the third), so we just need to add a factor equal to 2.

C = 2*(7*6*5*4*3*2*1) = 10,080

There are 10,080 different ways in which the friends can seat on the circular table.

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If f(n)= n²-n, then f(-4) is
O-20
12
-12
20

Answers

Answer:

20

Step-by-step explanation:

Plug in -4 for n:

(-4)^2 - (-4) = 16 + 4 = 20

Determine the growth defined by the equation y=1.4(3.72)^x.

Answers

Answer:

the type of growth defined by the equation is Exponential growth.

Step-by-step explanation:

Exponential growth :-Exponential growth is a pattern of data that shows greater increases with passing time, creating the curve of an exponential function. It occurs when the instantaneous rate of change of a quantity with respect to time is proportional to the quantity itself

expression for exponential growth -

f(x) = k(1+t)^x

f(x) = exponential growth

k = initial amount

t = rate of growth

x = no  of time interval

therefor,

the equation shown in the question represents exponential growth with increasing time.

hence, Exponential growth is the correct answer.

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Which is true regarding the graphed function f(x)?
• f(O) = 3
• f(5) = - 1
• f(3) = 2
O f(2) = -2

Answers

Answer:

f(5) = -1

Step-by-step explanation:

The points on the graph are (0,4), (1,3),(2,2), (3,1), (4,0), (5,-1).

The answers are in the form:

f(x) = y

That is, the number in the parenthesis is the x and the number by itself on the right is the y. The only one that is a point on the line is f(5) = -1, which is the point (5,-1)

Solve the following word problem.
Money is invested at two rates of interest. One rate is 8 % and the other is 2%. If there is $1300 more invested at 8 % than at 2 %. find the amount invested at
each rate if the total annual interest received is $350. Let x = amount invested at 8% and y = amount invested at 2 %. Then the system that models the problem
[x = y + 1300
is
Solve the system by using the method of addition.
0.08x +0.02y = 350,

Answers

Answer:

at 8%: $3760at 2%: $2460

Step-by-step explanation:

You are given a system of equations and asked to solve it by the method of addition. That method requires you add a multiple of one equation to the other so that one of the variables is eliminated. In some cases, this is easier if multiples of both equations are added together. The resulting single-variable equation is then solved in the usual way.

__

look

The given system of equations is ...

x = y +13000.08x +0.02y = 350

We notice the first equation has the variables on opposite sides of the equal sign, and both their coefficients are 1. The second equation has the variables on the same side of the equal sign, and their coefficients are 0.08 and 0.02.

plan

To eliminate a variable by the "addition method," we need to have the variable on the same side of the equal sign with opposite coefficients. Or, we need to have the variable on opposite sides of the equal sign with the same coefficient.

Both of the x-variables are on the left side, so we need opposite coefficients. We can get that by multiplying the first equation by -0.08, or by multiplying the second equation by -12.5. We judge the first of these choices to be easier.

The y-variables are on opposite sides of the equal sign, so we need equal coefficients. We can get that by multiplying the first equation by 0.02, or the second equation by 50.

solution

We choose to multiply the first equation by 0.02, so we can eliminate the y-variable. Here is the result of doing that, then adding the results

  (0.02)(x) +(0.08x +0.02y) = (0.02)(y +1300) +(350)

  0.10x +0.02y = 0.02y +376 . . . . . eliminate parentheses

  0.10x = 376 . . . . . . . . . subtract 0.02y from both sides. y is eliminated

  x = 3760 . . . . . . . . . divide by 0.10

  y = x -1300 = 2460

__

The amount invested at 8% was $3760; the amount invested at 2% was $2460.

_____

Additional comment

We chose to eliminate y for a couple of reasons. x is the amount at the higher rate. We have found that solving for the higher-rate amount usually works best for preventing errors. The other reason is that multiplying by 0.02 results in smaller numbers, which we consider easier to deal with.

Had we multiplied by -0.08 to eliminate x, we would have ...

  -0.08(x) +(0.08x +0.02y) = -0.08(y +1300) +(350)

  0.02y = -0.08y +246

We judge -0.08(1300) +350 harder to calculate mentally, than 0.02(1300) +350.

  0.10y = 246

  y = 2460; x = 2460+1300 = 3760

Graph the equation.

Y= - 3/2x

Answers

Answer:

Step-by-step explanation:

Help, Help, Brainliest available to the best Answer!



Find the Variance

Answers

Considering the given data-set, it's mean and the formula, the variance is of 870 lbs².

What is the variance of a data-set?

The variance of a data-set is given by the sum of the differences squared between each observation and the mean, divided by the number of values.

The mean is the sum of all observations divided by the number of observations, hence:

M = (145 + 175 + 180 + 205 + 120)/5 = 165.

And the variance, in lbs squared, is given by:

V = [(145-165)² + (175-165)² + (180-165)² + (205-165)² + (120-165)²]/5 = 870.

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The interior angle of a regular polvgon is 9 times the size of its exterior angle
Work out how many sides the polygon has

Answers

Answer:   20 sides

==================================================

Work Shown:

x = exterior angle

9x = interior angle

interior + exterior = 180

9x+x = 180

10x = 180

x = 180/10

x = 18

n = number of sides

n = 360/x

n = 360/18

n = 20

There are 20 sides to the regular polygon.

Side notes:

The formula to determine n only works for regular polygons.A polygon with 20 sides is known as an icosagon.Any pair of adjacent interior and exterior angles are supplementary. They add to 180 degrees.

Follow the steps to find the area of the shaded region.


First use the formula below to find the area of the whole sector.


Sector Area= ( angle of sector/360). R2


Sector Area = ? Cm^2
Round to four decimal places.

14 cm

46°

14 cm

Answers

The area of the sector, to 4 decimal places, is 78.6794 cm².

We have given that,

Sector Area= ( angle of sector/360). R2

We have to determine the Sector Area

What is the Area of a Sector of a Circle?

Area of sector = ∅/360 × πr².

We have given the following:

∅ = 46°

Radius (r) = 14 cm

Area of sector = 46/360 × π(14²)

Area of sector ≈ 78.6794 cm²

The area of the sector is approximately 78.6794 cm².

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Angle RSU is complementary to angle UST. Angle QSR is congruent to angle RSU.

Lines Q, R, U, and T extend from point S from left to right. Angle R S T is a right angle.
Which statement is true about angles UST and QSR?

They are complementary.
They are supplementary.
They are congruent.
They are obtuse.

Answers

Answer:

Statement 1 is correct

Angles UST and QSR are complementary.

Step-by-step explanation:

Complementary angles are those angles whose addition gives result of 90°

Congruent angles are those angles which are equal to each other. We can say that there values are same.

Here angle RSU is complementary to angle UST.

Therefore there addition is equal to 90°

∠RSU + ∠UST =  90° - (i)

Here angle QSR is congruent to angle RSU.

Therefore their values are equal.

It means ∠QSR =∠RSU -(ii)

From equation (i) and (ii) we get

∠QSR + ∠UST =  90°

So angles UST and QSR are complimentary angles.

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Answer:

Step-by-step explanation:

A

CON PROCESOS POR FAVOR

Answers

Answer:

[tex] \dfrac{149}{40} [/tex]

[tex] \dfrac{38}{15} [/tex]

Step-by-step explanation:

[tex] (\dfrac{7}{8} + \dfrac{4}{5}) - (\dfrac{9}{20} + \dfrac{-5}{2}) =  [/tex]

[tex] = (\dfrac{7}{8} \times \dfrac{5}{5} + \dfrac{4}{5} \times \dfrac{8}{8}) - (\dfrac{9}{20} + \dfrac{-5}{2} \times \dfrac{10}{10}) [/tex]

[tex] = (\dfrac{35}{40} + \dfrac{32}{40}) - (\dfrac{9}{20} + \dfrac{-50}{20}) [/tex]

[tex] = \dfrac{67}{40} - (-\dfrac{41}{20}) [/tex]

[tex] = \dfrac{67}{40} + \dfrac{41}{20} \times \dfrac{2}{2} [/tex]

[tex] = \dfrac{67}{40} + \dfrac{82}{40} [/tex]

[tex] = \dfrac{149}{40} [/tex]

[tex] (-\dfrac{6}{4} + \dfrac{3}{2}) + (\dfrac{6}{5} + \dfrac{4}{3}) = [/tex]

[tex] = (-\dfrac{3}{2} + \dfrac{3}{2})+ (\dfrac{6}{5} \times \dfrac{3}{3} + \dfrac{4}{3} \times \dfrac{5}{5}) [/tex]

[tex] = 0 + \dfrac{18}{15} + \dfrac{20}{15} [/tex]

[tex] = \dfrac{38}{15} [/tex]

two sides and an angle are given below. determine whether the given information results in one triangle, two triangles, or no triangle at all. solve any resulting triangle(s). b = 8, c= 7, b = 170°

Answers

Answer:

  A. single triangle. C = 8.74°, A = 1.26°, a = 1.01

Step-by-step explanation:

When two sides and an angle are given, the possibility of two (or zero) triangles exists only when the given angle is opposite the shorter of the two given sides. That is not the case here, so the given measures define one unique triangle.

Law of Sines

The law of sines tells us the sides and angles have the relation ...

  sin(A)/a = sin(B)/b = sin(C)/c

We can use this first to find angle C:

  sin(C) = c/b·sin(B)

  C = arcsin(c/b·sin(B)) = arcsin(7/8·sin(170°)) ≈ 8.7394°

  ∠C ≈ 8.74°

Remaining measures

Now that we know two angles, we can find the third:

  A = 180° -B -C = 180° -170° -8.74° = 1.26°

  ∠A = 1.26°

Using the law of sines again, we can find the measure of side 'a'.

  a = b·sin(A)/sin(B) = 8·sin(1.26°)/sin(170°) ≈ 1.01346

The measure of segment 'a' is about 1.01 units.

__

Additional comment

If 'a', 'b', and angle A are given, there will be zero triangles if b/a·sin(A) > 1. If b/a·sin(A) < 1 and b > a, there will be two (2) triangles. Otherwise, as here, there will be one unique triangle.

if p = (-1,-1) find the image of p under the following rotation. 90 degrees counterclockwise about the origin

Answers

Answer:

( 1, - 1 )

Step-by-step explanation:

5. Identify the sign of the leading coefficient and describe the end behaviour. Using this
information, decide if each function is cubic or quartic.

Answers

The sign of the leading coefficient can be found using the graph of a polynomial function.

What is polynomial?

Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.

[tex]\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n[/tex]

We have given the graph of polynomial functions:

In the first graph:

The leading coefficient is positive.

x → ∞, f(x) → ∞

x → -∞, f(x) → -∞

Degree of a function = 3

In the second graph:

The leading coefficient is negative.

x → ∞, f(x) → -∞

x → -∞, f(x) → -∞

Degree of a function = 4

In the third graph:

The leading coefficient is positive.

x → ∞, f(x) → ∞

x → -∞, f(x) → ∞

Degree of a function = 4

In the fourth graph:

The leading coefficient is negative.

x → ∞, f(x) → -∞

x → -∞, f(x) → ∞

Degree of a function = 3

Thus, the sign of the leading coefficient can be found using the graph of a polynomial function.

Learn more about Polynomial here:

brainly.com/question/17822016

#SPJ1

6(2x²-5) = [?]
x = -3

Answers

Answer:

78

Step-by-step explanation:

plug in -3 as x

6(2(-3)^2-5)

6(2(9)-5)

6(18-5)

6(13)

78

Answer: 78

Step-by-Step Solution:

=> 6(2x² - 5) ; when x = -3

Substitute the value of ‘x’ :-

= 6(2x² - 5)
= 6(2(-3)² - 5)
= 6(2(9) - 5)
= 6(18 - 5)
= 6(13)
= 6 * 13
=> 78
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