f(x) = x2. What is g(x)?

Answer:

Ok, our function is:

f(x) = 3*(x - 1)^2 + 2.

First, domain:

We should assume that the domain is all the set of real numbers, and then we see if for some value we have a problem.

In this case we do not see any problem (we can not have a zero in the denominator, and there is no function that has problems with some values of x)

Then the domain is the set of all real numers.

Vertex:

Let's expand our function:

f(x) = 3*x^2 - 3*2*x + 1 + 2

f(x) = 3*x^2 -6*x + 2

The vertex of a quadratic function:

a*x^2 + b*x + c is at:

x = -b/2a

here we have:

a = 3 and b = -6

x = 6/2*3 = 6/6 = 1.

And the value of y at that point is:

f(1) = 3*(1 - 1)^2 + 2 = 2

Then the vertex is at: (1, 2)

Range:

The range is the set of all the possible values of y.

Ok, we can see that the leading coefficient is positive, this means that the arms of our quadratic function will go up.

Then the minimal value of our quadratic function is the value at the vertex, y = 2.

This means that the range can be written as:

R = y ≥ 2

So the range is the set of all real numbers that are larger or equal than 2.

Answer:

x = 33

Step 1:

First, let's add the values together from both parentheses.

2x + x = 3x

1 + (-10) = -9

Now we are left with:

3x - 9 = 90.

Step 2:

Add 9 on the left side to cancel out the 9. Add it to the right side.

3x = 99

Finally, divide both sides by 3 to get our answer.

3x / 3 = x

99 / 3 = 33

x = 33

━━━━━━━☆☆━━━━━━━

▹ Answer

x = 3

▹ Step-by-Step Explanation

[tex]\frac{9}{150} \\\\150/3 = 50\\9/3 = 3\\\\x = 3[/tex]

Hope this helps!

CloutAnswers ❁

━━━━━━━☆☆━━━━━━━

Answer:

4%

Step-by-step explanation:

There are ₁₃C₃ ways to choose 3 diamonds from 13.

There are ₃₉C₁ ways to choose 1 non-diamond from 39.

There are ₅₂C₄ ways to choose 4 cards from 52.

Therefore, the probability is:

₁₃C₃ ₃₉C₁ / ₅₂C₄

= 286 × 39 / 270,725

≈ 0.04

The approximate probability that exactly three of the cards are diamonds is 4%.

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

We are given that standard deck of 52 playing cards contains 13 cards in each of four suits: hearts, diamonds, clubs, and spades.

Since we can see that there are ₁₃C₃ ways to choose 3 diamonds from 13.

₃₉C₁ ways to choose 1 non-diamond from 39.

₅₂C₄ ways to choose 4 cards from 52.

Therefore, the probability is:

₁₃C₃ ₃₉C₁ / ₅₂C₄

= 286 × 39 / 270,725

≈ 0.04

Therefore, the answer could be 4 percent.

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Answer:

y=3/4x-2

Step-by-step explanation:

two points from graph (0-2) and (8,4)

find slope m: y2-y1/x2-x1

m=4+2/8-0

m=6/8=3/4

x=0 then y=b=-2

y=3/4x-2

Answer:

y = 6x -27

Step-by-step explanation:

y-3=6(x-5)

Distribute

y-3 = 6x-30

Add 3 to each side

y-3+3 = 6x-30+3

y = 6x -27

This is in slope intercept form  y=mx+b where m is the slope and b is the y intercept

Hey there! I'm happy to help!

Slope intercept form is y=mx+b. So, the first thing we want to do is isolate y on side of the equation.

y-3=6(x-5)

We use distributive property to undo parentheses.

y=3=6x-30

We add 3 to both sides.

y=6x-27

Now, this in slope intercept form.

Have a wonderful day! :D

Answer:

The third one

Step-by-step explanation:

Translation is when it moves

Answer:

w>10

length = 40

Step-by-step explanation:

Let

Width=w

Length=4w

Perimeter is less than 100 inches

Perimeter of a rectangle= 2( Length + width)

100 < 2(4w+w)

100 < 8w+2w

100 < 10w

w > 10

Length =4w

=4 × 10

=40 inches

Answer:

5/2l <100

Step-by-step explanation:

PLATO

Answer:

Z=101

Step-by-step explanation:

A=2

B=3

C=5

D=7

E=11

F=13

From the above illustration, it can be deduced that A to Z represent prime numbers in ascending order.

Prime numbers are natural numbers that are greater than 1 and are only divisible by 1 and itself.

Therefore,

G=17

H=19

I=23

J=29

K=31

L=37

M=41

N=43

O=47

P=53

Q=59

R=61

S=67

T=71

U=73

V=79

W=83

X=89

Y=97

Z=101

Answer:

-1 is the answer

Step-by-step explanation:

I can't do the explanation of this question

Answer:

-1

Step-by-step explanation:-19 + 18 is basically how it is they end up canceling each other out except for the -1 which is the answer.

Answer:

Step-by-step explanation:

P = 2•(¹/₂•24•16) + 2•(20•20) + 24•20 = 384 + 800 + 480 = 1664 yd²

Answer:

0.88175960442

Step-by-step explanation:

The square root of 0.7775 is 0.88175960442

The value of standard deviation will be;

⇒ 0.8803

What is mean by square root of a number?

A square root of a number is a value that multiplied by itself gives the same number.

Given that;

The value of Variance = 0.7775

Now,

Since, The standard deviation is the square root of the variance.

Hence, We can formulate;

The value of standard deviation = √0.7775

                                                 = 0.8803

Thus, The value of standard deviation will be;

⇒ 0.8803

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Answer:

h=6.003 cm

Step-by-step explanation:

[tex] \frac{1}{3} \pi {r}^{2} h \: \: is \: the \: volume \: of \: cone[/tex]

1/3×22/7×7×7×h=308

h=308/51.3

Answer:

h = 6 cm

Step-by-step explanation:

r = 7 cm

Volume of cone = 308 cm³

[tex]\frac{1}{3}\pi r^{2}h=308\\\\\\\frac{1}{3}*\frac{22}{7}*7*7*h=308\\\\\\h=\frac{308*3*7}{22*7*7}\\\\\\h=2*3[/tex]

h = 6 cm

Answer:

The shaded area is 18 ft^2

Step-by-step explanation:

First find the area of the total trapezoid

A = bh

A = 1/2 ( b1+b2) *h

   = 1/2 ( 6+12) *6

   = 1/2 ( 18)*6

   =54

Now find the area of the triangle

A = 1/2 bh

   = 1/2 ( 12) * 6

   = 36

Subtract the triangle from the trapezoid

54-36

18

The shaded area is 18 ft^2

Answer:

D. 18 sq.ft

Step-by-step explanation:

Lets make it simple and short.

Area of a triangle is 1/2 b h

b = 6

h = 6

Area = 1/2 * 6 * 6

Area = 18 sq.ft

Answer:

5/14 = 0.36

7/10 = 0.7

5/6 = 0.83

11/15 = 0.73

19/21 = 0.9

(round to the tenth)

so the answer is;

5/14, 7/10, 11/15, 5/6, 19/21

Step-by-step explanation:

Hope it helps!

Answer:

[tex]1035[/tex]

Step-by-step explanation:

(63756×60)/(70×5280)

=1035

Answer:

375 mm cubed

Step-by-step explanation:

The volume would stay the same because the same number of the same pennies are being used.

If the question was asking for the surface area, then the answer would be different.

Hope that helped!!! k

Answer: 375 mm cubed

Answer:

approximately 12.04 units

Step-by-step explanation:

We'll use the Pythagorean Theorem to solve this problem.

There are two points here.  The horizontal distance between them is 8 units and the vertical distance is 9.

According to the Pythagorean Theorem (or the Distance Formula), the distance between the two points is

d = √(8^2 + 9^2) = √(64 + 81) = √145 units, or approximately 12.04 units.

Answer:

6450g

Step-by-step explanation:

1kg = 1000g

6.45kg = 6450

The watermelon weighs 6450 grams.

Given that a watermelon weighs 6.45 kilograms.

We need to convert its unit into grams.

To convert kilograms to grams, you need to multiply the weight in kilograms by 1000, as there are 1000 grams in 1 kilogram.

The watermelon weighs 6.45 kilograms, you can use the following formula to convert it to grams:

Weight in grams = Weight in kilograms × 1000

Let's do the math:

Weight in grams = 6.45 kilograms × 1000 = 6450 grams

So, the watermelon weighs 6450 grams.

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Answer:

[tex]\boxed{3^5}[/tex]

Step-by-step explanation:

Hey there!

Look at the image below↓

By looking at the image we can tell the PR expression is [tex]3^5[/tex].

Hope this helps :)

Answer:

Below in bold.

Step-by-step explanation:

Dividing  by primes:

3 ) 243

3 )  81

3 )  27

3)     9

        3.

So the prime factors of 243 are 3 * 3 * 3 * 3 * 3  or  3^5.

Answer:

Step-by-step explanation:

The expression 4 raised to 4 can be written in mathematical term as [tex]4^4[/tex] and this means the value of 4 in four places as shown;

[tex]4^4\\\\= 4 * 4* 4* 4\\\\= (4 * 4)* (4* 4)\\\\= 16*16\\\\= 256\\\\[/tex]

Hence the expression 4 raised to 4 is equivalent to 256

Answer:

1/7 is left

Step-by-step explanation:

What is left to read after the first week

1 - 3/7

7/7 - 3/7

4/7

He read 3/4 of this the second week

4/7 * 3/4

3/7 was read

4/7 - 3/7 is what is left

1/7 is left

Answer:

The correct answer is

Step-by-step explanation:

1/7 of the book is left to read.

Hope this helps....

Have a nice day!!!!

Answer:

Cylinder has a formula

π×r²×h

so of it is open

π×r²×h - π×r²

Answer:

pls give brainiest

Step-by-step explanation:

A=2πr×h(r+h)

Answer: negative correlation

Step-by-step explanation: If you look at the points in this graph here, I would say that those points are very close to a perfect line.

Notice that the slope of the line is negative.

This means it will be a negative correlation.

So the line is a very good estimate of the points.

Answer:

x = 1/2

Step-by-step explanation:

Let's represent this in a mathematical way,

(x+1)^2 - x^2 = 2

Ok now we expand,

x^2 + 2x + 1 -x^2 = 2

rearrange,

x^2 - x^2 + 2x + 1 = 2

subtract,

2x + 1 = 2

subtract 1 from both sides,

2x + 1 - 1 = 2 - 1

2x = 1

Now divide 2 from both sides and get your answer,

x = 1/2

Answer:

[tex](x + 1) { }^{2} - x {}^{2} = 2[/tex]

[tex]x {}^{2} + 2x + 1 - x {}^{2} = 2[/tex]

[tex]2x + 1 = 2[/tex]

[tex]x = 1 \div 2[/tex]

Answer:

(5*7)-f

Step-by-step explanation:

Algebraic expression for the given statement is [tex]5 \cdot 7 -f[/tex]

Algebraic expression is the combination of terms that consists of numbers  and variables connected by arithmetic operators.

Given statement is 5 times the quantity 7 minus a number f in an algebraic expression.

We need to write it in an algebraic expression

5 times a quantity. for product we use multiplication sign

For addition we use + sign and for difference we use minus sign .

5 times the quantity 7 means 5 multiplied by 7

[tex]5 \cdot 7[/tex]

5 times the quantity 7 minus a number f  

subtract f from the expression we got

[tex]5 \cdot 7 -f[/tex]

Algebraic expression for the given statement is [tex]5 \cdot 7 -f[/tex]

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Answer:

Approximately [tex]58.28\; \rm m \cdot s^{-1}[/tex].

Step-by-step explanation:

The velocity of an object is the rate at which its position changes. In other words, the velocity of an object is equal to the first derivative of its position, with respect to time.

Note that the arrow here is launched upwards. (Assume that the effect of wind on Mars is negligible.) There would be motion in the horizontal direction. The horizontal position of this arrow will stays the same. On the other hand, the vertical position of this arrow is the same as its height: [tex]y = 62\, t - 1.86\, t^2[/tex].

Apply the power rule to find the first derivative of this [tex]y[/tex] with respect to time [tex]t[/tex].

By the power rule:

Therefore:

[tex]\begin{aligned}\frac{dy}{d t} &= \frac{d}{d t}\left[62 \, t - 1.86\, t^2\right] \\ &= 62\,\left(\frac{d}{d t}\left[t\right]\right) - 1.86\, \left(\frac{d}{d t}\left[t^2\right]\right) \\ &= 62 \times 1 - 1.86\times\left(2\, t) = 62 - 3.72\, t\end{aligned}[/tex].

In other words, the (vertical) velocity of this arrow at time [tex]t[/tex] would be [tex](62 - 3.72\, t)[/tex] meters per second.

Evaluate this expression for [tex]t = 1[/tex] to find the (vertical) velocity of this arrow at that moment: [tex]62 - 3.72 \times 1 =58.28[/tex].

Answer:

58.28 m/s

Step-by-step explanation:

y = 62t - 1.86t²

Speed, S = dy/dt = 62 - 2(1.86)t

S = 62 - 3.72t

When t = 1

S = 62 - 3.72 = 58.28 m/s

Answer:

Hope it helps U can still ask me if u have confusions

Answer:

  60+16√30 cm² ≈ 147.64 cm²

Step-by-step explanation:

You can figure the height of the object from ...

  V = Bh

  120 cm^3 = (30 cm^2)h

  4 cm = h . . . . . divide by 30 cm^2

However, this is insufficient to tell you the surface area.

__

If you assume that the base is square, then its side length is

  A = s^2

  s = √A = √(30 cm^2) = (√30) cm

The lateral surface area can then be found from the perimeter of the base and the height

  LA = Ph = (4√30 cm)(4 cm) = 16√30 cm^2

The total surface area will be the sum of this lateral area and the area of the two bases:

 total area = 16√30 cm^2 +2·30 cm^2

 total area = (60 +16√30) cm^2 ≈ 147.64 cm^2

__

For any other shape, the total area will be larger. It can be arbitrarily large, unless limits are put on the dimensions of the object.

Answer:

13. [tex]\frac{\sqrt[5]{x^4} }{x}[/tex].

14. [tex]v = \pm3\sqrt{5}[/tex]

15. 2.

Step-by-step explanation:

13. [tex]x^{1/5} * x^{-2/5}[/tex]

= [tex]x^{1/5 + (-2/5)}[/tex]

= [tex]x^{1/5 - 2/5}[/tex]

= [tex]x^{-1/5}[/tex]

= [tex]\frac{1}{x^{1/5}}[/tex]

= [tex]\frac{x^{4/5}}{x^{1/5 + 4/5}}[/tex]

= [tex]\frac{x^{4/5}}{x}[/tex]

= [tex]\frac{\sqrt[5]{x^4} }{x}[/tex].

14. [tex]v^2 - 45 = 0[/tex]

[tex]v^2 = 45[/tex]

[tex]\sqrt{v^2} = \pm\sqrt{45}[/tex]

[tex]\sqrt{v^2} = \pm\sqrt{3^2 * 5}[/tex]

[tex]v = \pm3\sqrt{5}[/tex].

15. [tex]\sqrt[3]{2} * \sqrt[3]{4}[/tex]

= [tex]\sqrt[3]{2 * 4}[/tex]

= [tex]\sqrt[3]{2 * 2 * 2}[/tex]

= [tex]\sqrt[3]{2 ^3}[/tex]

= 2.

Hope this helps!