How can you change a rational number to a decimal? Can you give an exsample?

Answer:

(a) (f o g)(x) =  x^2 - 15x + 54

(b) (g o f)(x) = x^2 + 3x - 9

(c) (f o f)(x) = x^4 + 6x^3 + 12x^2 + 9x

(d) (g o g)(x) = x - 18

Step-by-step explanation:

f(x) = x^2 + 3x

g(x) = x - 9

(a)

(f o g)(x) = f(g(x)) = (g(x))^2 + 3(g(x)) = (x - 9)^2 + 3(x - 9)

(f o g)(x) = x^2 - 18x + 81 + 3x - 27

(f o g)(x) = x^2 - 15x + 54

(b)

(g o f)(x) = g(f(x)) = f(x) - 9 = x^2 + 3x - 9

(c)

(f o f)(x) = f(f(x)) = (x^2 + 3x)^2 + 3(x^2 + 3x)

(f o f)(x) = x^4 + 6x^3 + 9x^2 + 3x^2 + 9x

(f o f)(x) = x^4 + 6x^3 + 12x^2 + 9x

(d)

(g o g)(x) = g(g(x)) = x - 9 - 9 = x - 18

Answer:

[tex]-5\sqrt{7}[/tex]

Step-by-step explanation:

2√28 - 3√63

4√7 - 9√7

- 5√7

Answer:

- 5√7

Step-by-step explanation:

Answer:

(a) Triangles are similar if corresponding angles are congruent and the ratios of the lengths of corresponding sides are equal.

(b) x = 24

(c) y = 17; z = 51

Step-by-step explanation:

(a) Triangles are similar if corresponding angles are congruent and the ratios of the lengths of corresponding sides are equal.

(b)

15/45 = 8/x

1/3 = 8/x

x = 3 * 8

x = 24

(c)

a^2 + b^2 = c^2

x^2 + 45^2 = z^2

24^2 + 45^2 = z^2

576 + 2025 = z^2

z^2 = 2601

z = 51

15/45 = y/z

1/3 = y/51

3y = 51

y = 17

Answer:

600 numbers

Step-by-step explanation:

For six-digit numbers, we need to use all digits 8,0,1,3,7,5 each once.

However, 0 cannot be used as the first digit, because it would make a 5-digit number.

Therefore

there are 5 choices for the first digit (exclude 0)

there are 5 choices for the first digit (include 0)

there are 4 choices for the first digit

there are 3 choices for the first digit

there are 2 choices for the first digit

there are 1 choices for the first digit

for a total of 5*5*4*3*2*1 = 600 numbers

Answer:

68 square cm

Step-by-step explanation:

Interior square WXYZ is making four right triangles of equal bases (8 cm) and heights (2 cm) inside the square ABCD. Therefore,

Area of shaded Square = Area of square ABCD - 4 times area of one right triangle.

[tex] = {10}^{2} - 4 \times \frac{1}{2} \times 8 \times 2 \\ = 100 - 32 \\ = 68 \: {cm}^{2} [/tex]

Answer:

The correct option is;

B. Range

Step-by-step explanation:

In descriptive statistics which analyses the quantitative summary of the statistical data, the range is the region or area or the statistical interval where the data is obtained from and as such the range (in descriptive statistics) gives a guide to the dispersion of the statistical information.

The range is best suited for the representation of the dispersion when the size of the data set is small.

Answer:

Every choice is not equivalent to 4✖️38.

Step-by-step explanation:

4✖️38=152

A. 54✖️4=216

B. 12✖️18=216

C. 72✖️3=216

D. 12✖️72=864

Every choice is not equivalent to 4✖️38.

Answer:

50%

Step-by-step explanation:

its 50% it will land on head and 50% it will land on tails since there is only two sides on a coin

Answer:

1/2 or .5

p(1/2)

Step-by-step explanation:

its simple, there are 2 sides to a coin, so there are 2 possible outcomes. and the question asks what is the probability of the coin landing on one or in other wrds, its asking what is te probilitity of one of the two heads to be up. SO the probility is 1/2

Answer:

[tex]\Large \boxed{\mathrm{100\pi \ cm^2 }}[/tex]

Step-by-step explanation:

[tex]\displaystyle area \ of \ circle \ = \ \pi (\frac{diameter}{2} )^2[/tex]

[tex]\displaystyle A \ = \ \pi ( \frac{20}{2} )^2[/tex]

[tex]\displaystyle A \ = \ \pi ( 10 )^2[/tex]

[tex]\displaystyle A \ = \ 100\pi[/tex]

Answer: Vertically shifting it by 3

The transformation of a function is horizontally shrink by a factor of 3 .

Let’s go ahead and look at how f(x) = x2 will be affected by a scale factor of 1/2 and 1/3.

How do you horizontally shrink  by a factor of 3 ?

Learn more about Transformation on :

brainly.com/question/10644134

#SPJ2

Answer:

20 meters

Step-by-step explanation:

The track is circular so it means that after Patrick raced the entire track he is back at the starting point. In other words, every 440 meters he is back to the beginning.

So we would have that, if he races round the track twice, he would run 440(2) = 880 meters and he would be back at the starting point.

The problem asks us how far is he from the starting point at the 900 meter mark. If at 880 meters he is at the starting point, then at 900 meters he would be [tex]900-880=20[/tex] meters from the starting point.

Hello, please consider the following.

[tex]x^2 + 10x + 25 = 8\\\\\text{\bf We can notice that } x^2+10x+25=(x+5)^2 \text{ so}\\\\x^2 + 10x + 25 = (x+5)^2=8\\\\\text{\bf We take the root.}\\\\x+5=\pm\sqrt{8}\\\\\text{\bf We subtract 5}\\\\\boxed{x=-5-\sqrt{8}} \ \ or \ \ x=-5+\sqrt{8}[/tex]

In the box, you can find the smallest solution.

Thank you.

Answer:

X = 14,700

Step-by-step explanation:

you can use a calculator to get the x.

X=3816371/(27×63)

Answer:

B The graft of h is the graft of g vertically shifted up 3 units

Answer:

z=-3

Step-by-step explanation:

1:open the brackets.

2:take 21 to the other side to be subtracted by 42

3:you get a -z but you can take it to the other side to get a +z but -21 divide to get the answer

42=-7(z-3)

-7(z-3)=42

-7z+21=42

-7z=42-21

-7z=21

therefore,

z=21\-7

that is, -21\7=-3

Answer:

[tex]\huge \boxed{\mathrm{-1}}[/tex]

Step-by-step explanation:

[tex](5xe^2 - 3x) - (5xe^2 - 3x+1)[/tex]

Distribute negative sign.

[tex]5xe^2 - 3x- 5xe^2 +3x-1[/tex]

Combine like terms.

[tex]0xe^2 +0x-1[/tex]

[tex]0-1=-1[/tex]

Answer:

m∠C = 102°

Step-by-step explanation:

This is is a cyclic quadrilateral

• The sum of opposite angles in a cyclic quadrilateral is equal to 180°

m∠D + m∠B = 180°

m∠B = 180° - m∠D

m∠B = 180° - 80°

m∠B = 100°

If you look at the above diagram properly, you will notice there are are angles outside the circle. We refer to this an exterior or external angles in a cyclic quadrilateral

• Note that m∠B is Opposite the exterior angle m∠CDA

Hence,

m∠CDA = 2 × m∠B

m∠CDA = 2 × 100°

m∠CDA = 200°

• m∠CDA = m∠CD + m∠DA

m∠DA = m∠CDA - m∠CD

m∠DA = 200° - 116°

m∠DA = 84°

• Another external angle we need to find is m∠DAB

m∠DAB = m∠DA + m∠AB

We know that m∠DA = 84°, therefore,

m∠DAB = 84° + 120°

m∠DAB = 204°

• The final step is to solve for m∠C

m∠DAB is Opposite m∠C

Hence

m∠C = 1/2 × m∠DAB

m∠C = 1/2 × 204

m∠C = 102°

Answer:

m<PQT= 94°

Step-by-step explanation:

If line QS bisect <PQR

m<PQS = m < SQR

7x-6= 4x+15

7x-4x= 15+6

3x= 21

X= 21/3

X= 7

m<PQS= 7x-6

m<PQS= 7(7)-6

m<PQS= 49-6

m<PQS= 43°

m<PQS= m<SQR

<mSQR=43°

m<PQR= m<PQS + m < SQR

m<PQR=43+43

m<PQR= 86°

BUT

m<PQR= m<TQW

m<PQT= m<RQW

m<PQR+m<TQW +m<PQT+ m<RQW

= 360°

Let m<TQW= x

86+86+x+x= 360

2x+172= 360

2x= 188

X= 94°

m<PQT= 94°

Question 1:

Price per milliliter

Small $4.50 / 250ml

Medium $9.95 / 500 ml

Large $16.95 / 1000 ml

Question 2:

$9.95 / 500 ml > $4.50 / 250ml > $16.95 / 1000 ml

Question 3 - 4:

$4.50 / 250ml = ($4.50 * 6) / (250ml * 6 ) = $27 / 1500ml = 0.018

$9.95 / 500 ml = ($9.95 * 3) / (500 ml * 3) = $29.85 / 1500ml = 0.019

$16.95 / 1000 ml = ($16.95 * 3) / (1000 ml * 3) = $50.85 / 1500ml = 0.0339

( Use the first one for question 3 and the second for question 4)

$4.50 / 250ml would be the cheapest way to get 1500ml.

$9.95 / 500ml would be the most expensive way to get 1500ml.

I hope this helps you! Tell me if I'm wrong!

Hello, because of the geometric sequence we can say that:

[tex]\alpha = \dfrac{b}{a}=\dfrac{c}{b}\\\\\dfrac{c}{a}=\dfrac{c*b}{a*b}=\dfrac{c}{b}\dfrac{b}{a}=\alpha^2\\\\\text{So the equation becomes.}\\\\ax^2+bx+c=0<=>x^2+\dfrac{b}{a}x+\dfrac{c}{a}=0\\\\<=>x^2+\alpha x+ \alpha^2=0\\\\\Delta=b^2-4ac = \alpha^2-4\alpha^2=-3\alpha^2 < 0[/tex]

So there is no real root, so the function does not cut the x axis.

Thank you

For the given quadratic function, the x-axis is not cut by the function because there is no true root.

To determine values for various parameters, quadratic functions are employed in a variety of scientific and engineering disciplines. A parabola is used to graphically illustrate them. The orientation of the curve is defined by the highest degree factor.

As per provided data in question,

α = b/a = c/b

c/a = (c × b)/(a × b) = (c/b) (b/a) = α²

For the equation,

ax² + bx + c = 0

x² + b/a(x) + c/a = 0

⇒ x² + ax + α² =0

Δ = b² - 4 ac = α² - 4α²

Δ = -3α² < 0, which means that no real root is there.

To know more about quadratic functions:

https://brainly.com/question/27958964

#SPJ2

Answer:

r = 1

Step-by-step explanation:

2πr = x

πr² = y

x = 2y

2πr = 2πr²

r = 1

1) 3 is the Coefficient.

2) 10 is the constant.

3) 10.8 is the ans.

Answer:

(3.5,4)

x coordinate =

[tex] \frac{5 + 2}{2} [/tex]

= 3.5

y coordinate =

[tex] \frac{ - 1 + 9}{2} [/tex]

= 4

midpoint = (3.5,4)

Answer:

(  3.5,4)

Step-by-step explanation:

To find the midpoint

Add the x coordinates together and divide by 2

(5+2)/2 = 7/2 = 3.5

Add the y coordinates together and divide by 2

(9+-1)/2 = 8/2 = 4

( 3.5,4)

Given that

To Find

Formula

Solution

→ Volume = πr²h

Using π as 3.14

→ 3.14 × 10 × 10 × 20 = Volume

→ 314 × 20 = Volume

→ 6280 inches² is the holding capacity of the container.

Answer:

6280

Step-by-step explanation:

this is correct on khan academy

Answer:

D) 84cm

Step-by-step explanation:

Square area = √(441cm²) = 21 cm

perimeter = 4*21 = 84 cm

C, because we multiply the exponents to get the answer.

Answer:

C

Step-by-step explanation:

Using the rule of exponents

[tex](a^{m}b^{n}) ^{p}[/tex] = [tex]a^{mp}[/tex] × [tex]a^{np}[/tex]

Thus

[tex](7^{2}5^{6})^4[/tex]

= [tex]7^{2.4}[/tex] × [tex]5^{6.4}[/tex]

= [tex]7^{8}[/tex] × [tex]5^{24}[/tex] → C

verifying, by putting [tex] \theta=60^{\circ}[/tex]

LHS≠RHS

hence the question is FALSE

Answer:

A

Step-by-step explanation:

First, we are already given the sides adjacent and opposite to ∠x. Therefore, we can use the tangent function. Recall that:

[tex]\tan(x)=opp/adj[/tex]

The opposite side is 20 while the adjacent side is 14.

Plug in the numbers. Use a calculator:

[tex]\tan(x)=20/14=10/7\\x=\tan^{-1}(10/7)\\x\approx55.0080\textdegree\approx55\textdegree[/tex]

Edits: Improved Answer. Removed Wrong Answer.

Answer:

55

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

tan theta = opp/ adj

tan x = 20/14

Taking the inverse tan of each side

tan ^-1 tan x = tan ^ -1 (20/14)

x =55.0079798

To the nearest degree

x = 55

Answer:

Step-by-step explanation:

i) The union of the two sets is the list of elements that are in either. Duplicates are listed only once.

  U = {1, 2, 3, 4, 5, 10, 11, 12}

  A' = U - A = {10, 11, 12}

  A'∪B' = {10, 11, 12}∪{1, 2, 4} = {1, 2, 4, 10, 11, 12}

__

ii) A has 5 elements, so has 2^5 = 32 subsets, including the empty set and the whole set.

Answer:

Step-by-step explanation:

The question above means that how many numbers can divide 2003 with a remainder of 23

That means all the numbers are less than 2003

The number of numbers that have this property are only

Hope this helps you