Given that 9x–4y = 20. Find y when x= -2

9514 1404 393

Answer:

  a) f(-2.5) = 62.6875; f(-1.5) = -13.0625; (-2.5, -1.5) contains a real root

  b) there are 1 each of positive and negative real roots; 2 complex roots

  c) -2 and 1/3 are the rational real roots

  d) x ∈ {-2, 1/3, -1/3 +i(√2)/3, -1/3 -i(√2)/3}

Step-by-step explanation:

a) f(-2.5) = 62.6875; f(-1.5) = -13.0625. The function changes sign between -1.5 and -2.5, so there is a real root in that interval.

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b) The given coefficients have one sign change, so there is one positive real root. Changing the signs of odd-degree terms makes the signs + - + - -, so there are three sign changes. There are 1 or 3 negative real roots, and possibly 2 complex roots. The constant term is non-zero, so zero is not a root. Here's your table:

  positive real roots: 1

  negative real roots: 1 or 3

  complex roots: 2 or 0

  zero roots: none

The graph is attached. It shows 2 real roots, one positive and one negative, so there are 2 complex roots. (There are 4 roots in total, so if only 2 are real, the other 2 are complex.)

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c) Possible rational roots are of the form ...

  ±{1, 2}/{1, 3, 9}

Listed, they are ...

  ±{1/9, 2/9, 1/3, 2/3, 1, 2}

The actual real roots are -2 and 1/3.

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d) The graph shows the real roots to be -2 and 1/3. The original leading coefficient of 3 is the product of the leading coefficients of the factors. Writing the factor (x -1/3) as (3x -1) lets us reduce the leading coefficient of the quadratic term from 9 to 3. The result of dividing factors (x+2) and (3x-1) from the original function is shown in the attachment. It is a parabola with vertex (-1/3, 2/3), so the factorization is ...

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

The roots of the quadratic term are ...

  3(x +1/3)² = -2/3

  x +1/3 = ±√(-2/9)

  x = (-1 ±i√2)/3

So, the entire list of roots is ...

  x ∈ {-2, 1/3, -1/3 +i(√2)/3, -1/3 -i(√2)/3}

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Additional comment

The roots of a quadratic are easily found by knowing its leading coefficient and its vertex. If factoring known real roots from a higher-degree polynomial results in a quadratic, then the remaining complex roots are easily found. A graphing calculator is a wonderful tool for this process.

Answer:0

Step-by-step explanation:

Annually compounded interest: 4,031.75

Simple interest: 3,900.00

Answer:

1239.3 cm^3

Step-by-step explanation:

The volume of a cone is 1238.7 cm³.

It is a shape of a Christmas tree where there is a base of radius r and a top point called the apex.

The volume of a cone is (1/3)πr²h.

We have,

Height = 17.6 cm

Diameter = 16.4 cm

Radius = 16.4/2 = 8.2 cm

Now,

The volume of a cone = (1/3)πr²h.

V = 1/3 x 3.14 x 8.2 x 8.2 x 17.6

V = 1238.87 cm³

Thus,

The volume of a cone is 1238.7 cm³.

Learn more about cones here:

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Answer:

Step-by-step explanation:

There are 12 months in one year, so there would be 12*y in y years.

Answer:

there 12 months in one 1 year

Step-by-step explanation:

Answer:

-500

Step-by-step explanation:

Answer:

< LK

Step-by-step explanation:

The higher the angle, the bigger the opposite side, so since 123 is bigger than 114, LK is bigger than MN

Answer:

3

Step-by-step explanation:

_+(-4) = -1

_-4 = -1

_ = 3

Answer:

It's the same process, change 4 4/5 to an improper fraction = 24/5 then set up a proportion

4 bananas/(24/5) kg = 3 bananas/x kg take cross products

4x = 3 (24/5) = 72/5  divide by 4 (this is the same as multiplying by 1/4)

x = 72/20, change this to a mixed number = 3 12/20 = 3 3/5 kg

Step-by-step explanation:

Natural numbers are a part of the number system which includes all the positive integers from 1 till infinity and are also used for counting purpose. It does not include zero. In fact, 1,2,3,4,5,6,7,8,9…., are also called counting numbers excluding zero, fractions, decimals and negative numbers.

The whole numbers are the numbers 0, 1, 2, 3, 4, and so on (the natural numbers and zero). Negative numbers are not considered "whole numbers." All natural numbers are whole numbers, but not all whole numbers are natural numbers since zero is a whole number but not a natural number.

Natural numbers are also all numbers 1, 2, 3,4.. and so on. They are the numbers you usually count and they will continue on into infinity. Whole numbers are all natural numbers including 0. 0, 1, 2, 3, 4… Integers include all whole numbers and their negative counterpart, -4, -3, -2, -1, 0,1, 2, 3, 4,…

So in all these words, this means that natural numbers are all the numbers not including 0 and negative and whole numbers are all the numbers including 0 and negative.

Answer:

42/55

Step-by-step explanation:

6/5 times 7/11 = 42/55

Answer: 10%×$650=$585

$585-$450=$135 Mark up.

HOPE THIS HELPS

Answer:

0.205, 21%, 1/4, 0.3, 1/3

Step-by-step explanation:

Hi! How I was taught to do these was convert them all into percentages.

0.3 ---> 30%

1/3 ---> 33.33%

21% ---> 21%

1/4 ---> 25%

0.205 --> 20.5%

Now that we have these, order from least to greatest. Make sure you use the form it gave you in the question!

Answer:

6s-35

Step-by-step explanation:

not sure

Answer:

most likely always. either that or sometimes I hope that answers your question!

Answer:

[tex]m = -\frac{1}{2}[/tex]

[tex]y\ intercept = -1[/tex]

[tex]y = -\frac{1}{2}x -1[/tex]

Step-by-step explanation:

Given

[tex](x_1,y_1) = (-2,0)[/tex]

[tex](x_2,y_2) = (0,-1)[/tex]

Required

Determine the slope and y intercept from graph

To calculate the slope, we have:

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

[tex]m = \frac{-1-0}{0 - (-2)}[/tex]

[tex]m = \frac{-1}{0 +2}[/tex]

[tex]m = -\frac{1}{2}[/tex]

The y intercept is when [tex]x = 0[/tex]

So,

[tex]y\ intercept = -1[/tex]

The equation is then calculated using:

[tex]y = m(x - x_1) + y_1[/tex]

This gives

[tex]y = -\frac{1}{2}(x - (-2)) + 0[/tex]

[tex]y = -\frac{1}{2}(x - (-2))[/tex]

[tex]y = -\frac{1}{2}(x +2)[/tex]

[tex]y = -\frac{1}{2}x -\frac{1}{2}*2[/tex]

[tex]y = -\frac{1}{2}x -1[/tex]

See attachment for graph

Answer:

The graph shown is y = -1/2

x +-1 .

Step-by-step explanation:

did on edge

Answer:

x = -1

Step-by-step explanation:

Answer:

1,2,3,4,6,8,9,12,18,24,36,72.

Step-by-step explanation:

What you are looking for are numbers that multiply by each other to equal 72, like 1 and 72 or 8 and 9. Factor tree may help, search it up :)

so wt's the question of this pic?

Answer:

21+x

Step-by-step explanation:

Because this does not equal anything, we can't solve for x. Instead, we can just simplify the equation. Since there is a + sign to the left of the parentheses, it shows that we do not need to distribute.

13+(x+8)

21+x

Hope this helps!! Have a nice day ^^

Answer:

First off you would distribute the invisible positive 1 to the x and 8

Then you will get 13+x+8

Last add 13 and 8 to get 21

Your final answer is 21+x

Step-by-step explanation:

Answer:

f(-3) = g(-3)

Step-by-step explanation:

f(-3) = -4

g(-3) = -4

Therefore, they intersect at that point.

9514 1404 393

Answer:

  1/9^5

Step-by-step explanation:

  [tex]\dfrac{9^2}{9^7}=\dfrac{9\cdot 9}{9\cdot 9\cdot 9\cdot 9\cdot 9\cdot 9\cdot 9}=\dfrac{1}{9\cdot 9\cdot 9\cdot 9\cdot 9}=\boxed{\dfrac{1}{9^5}}[/tex]

_____

An exponent is an indicator of repeated multiplication. As you can see, factors in the numerator cancel those in the denominator, so the result is the difference of the exponents.

Answer:

139

Step-by-step explanation:

PEMDAS or Order of Operations

Answer:

2.53%

Step-by-step explanation:

all you have to do is 1 / 39.51 = about 0.0253 = 2.53%

Answer:

9x+1

Step-by-step explanation:

2x+1+7x

2x+7x+1

9x+1

Answer:

Step-by-step explanation: Angle A is 45 degrees so it represents 1/8 of a rotation. so it has a measure π/4 rads. Angle B is 90 degrees so it represent 1/4 of a rotation. so it has a measure of π/2 rads. Angle C represents 180 degrees so that represent 1/2 of a rotation so it has a measure of π rads. Angle D is 270 degrees so it represents 3/4 of a rotation . Therefore, Angle D has a measure of  6π/4.

The for angle A 1/8 and π/4, for angle B 1/4 and π/2, for angle C 1/2 and π, and for angle D 3/4 and 6π/4.

The measurement between the two lines is called an "Angle" when the two lines or rays converge at a common location.

From the figure attached:

Angle A represents 1/8 of a full rotation. Therefore, Angle A has a measure of π/4 radians.  

Angle B represents 1/4 of a full rotation. Therefore, Angle B has a measure of π/2 radians.  

Angle C represents 1/2 of a full rotation. Therefore, Angle C has a measure of π radians.  

Angle D represents 3/4 of a full rotation. Therefore, Angle D has a measure of 6π/4 radians.

Thus, the for angle A 1/8 and π/4, for angle B 1/4 and π/2, for angle C 1/2 and π, and for angle D 3/4 and 6π/4.

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Answer:

it is %224 profit on the skates

Step-by-step explanation:

Answer:

500

Step-by-step explanation:

150(100) = 15000 / 30 = 500