Describe how the graph of y= x2 can be transformed to the graph of the given equation. y = x2 + 3 (5 points)

Answer:  a=4, b=16, c=12

Step-by-step explanation:

Use the intercept form: a(x - p)(x - q)  where p & q are the intercepts.

Given: p = -3, q = -1, and y-intercept (c) = 12

 a[x - (-3)][x - (-1)]

= a(x + 3)(x + 1)

= a(x² + 4x + 3)

= ax² + 4ax + 3a

y-intercept = 12

     3a = 12

       a = 4

   Substitute a = 4

    4x² + 4(4)x + 3(4)

=   4x² + 16x + 12

Answer:

∆y = 95 ft

the vertical distance the shark travels is 95 ft

Step-by-step explanation:

Given;

Initial position y1= 80 ft below the surface of water = -80ft

Final Position y2 = 15 ft above the surface = +15ft

The vertical distance travelled by the shark is;

∆y = y2 - y1 = 15 - (-80) ft

∆y = 15 +80 ft

∆y = 95 ft

the vertical distance the shark travels is 95 ft

Answer:

You first need to convert everything to minutes:

12 noon = 12 x 60 = 720 minutes

9 am = 9 x 60 = 540 minutes

Let x = number of minutes before noon

The time now is 12 noon -x = 720 -x minutes

48 minutes ago it was 720-x-48

720 -x - 48 = 540 + 2x

720-48-540 = 3x

x = 44 minutes

It is 44 minutes before noon, or 11:16 am

Answer:

9:00 am -------------------- 12:00pm ( There are 180 minutes between them)

Go 48 minutes back (132 Minutes between them)

That time is divided by 2

(4x minutes past 9:00 and x minutes left to reach 12:00)

132/3 = 44 minutes are left

Answer:

Length of A=6

Breadth of A=24/6=4

Length of B=6

Breadth of B=12/6=2

Step-by-step explanation:

Total surface area: 36

Ratio is 2:1

So, 2x + 1x = 36

3x=36

x=36/3

x=12

2*12=24

1*12=12

So areas are 24 and 12 respectively

Now, we can say that the sides of the square will be same, 6 cm

6*6=36

so the length of both rectangles will be 6

Hence we can divide each area by 6 and find the breadth.

Length of A=6

Breadth of A=24/6=4

Length of B=6

Breadth of B=12/6=2

Stay safe and stay cool

Hope it helps you.

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Answer: choice B

Step-by-step explanation:

just took the quiz

omm its B. G(x)=(x+8)^2

just took the test

Answer:

[tex]\boxed{20(r + 3t)}[/tex]

Step-by-step explanation:

[tex]20r + 60t[/tex]

Factor out 20 from the expression.

[tex]20(r) + 20(3t)[/tex]

Take 20 as common.

[tex]20(r + 3t)[/tex]

Answer:

Option D is correct.

A voluntary response error was made in this design. This type of sampling only targets those who are passionate about a specific act and call in to vote; it is not a good representation of the population.

Step-by-step explanation:

When humans are given the choice whether to participate in a survey like in this question, most often than not, the survey becomes biased.

This is because only the people or set of people who feel strongly the most about the subject matter of the poll will participate in the survey. This favours the group that disagrees as this group, if given the choice to express their opinion, will most likely be the set of people that will readily express their discontent.

Discontent is more visibly and strongly expressed in humans.

In order to remove this bias, people should have been chosen at random and their responses recorded.

Hope this Helps!!!

Answer:

i.) (-0.25, 0), (1.25, 0)

ii.) (0.5, 2), (1.5, 2)

Step-by-step explanation:

For i, it is asking for the roots of the quadratic, or where the graph crosses the x-axis.

For ii, it is asking for the x-values when y = 2.

Answer:

Step-by-step explanation:

Pls help me with my question roo

The graph of g(x) is g(x) = [tex]3^{x-6}[/tex]

A translation is a rigid transformation because it does not change the size or shape of the original figure. Translations are the simplest transformation in geometry and are often the first step in performing other transformations on a figure or shape.

Given that, graph of g(x) is the result of translating the graph of f(x) = 3ˣ, 6 units to the right.

Translation the graph of the function y = f(x) a units to the right gives the function y = f(x-a)

So, here, f(x) = 3ˣ will be transformed to g(x) = [tex]3^{x-6}[/tex]

Hence, the graph of g(x) is g(x) = [tex]3^{x-6}[/tex]

Learn more about translation, click;

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Answer:

8 is the difference, and 19 and 11 are the numbers. Hope this helped!

Answer: The difference is 8.

Step-by-step explanation:

We will let l represent the larger number s represent the smaller number.

so we know that L + S =30  

Also  2L - 3S = 5  shows the relationship between the numbers.

Now we have two equations.  

L + S =30

2L - 3S = 5  solve using any method.

L + S =30  solve for L  and substitute it into the second equation.

L + S = 30

   -S     -S

L = 30 -S    

2(30-s) - 3s = 5  Distribute

60 - 2s - 3s = 5  combine like terms

60 -5s = 5

-60         -60

-5s = -55

s = 11  

We know the smaller number is 11 so to find the larger number  we will subtract 11 from 30.

30 -11 =  19  

The larger number is 19

so To find the difference we will subtract 11 from 19.

19 -11 = 8

Answer:

P = 5.4641b cm.

Step-by-step explanation:

If the triangle ABC is isosceles and m∠BAC = 120°, we have that:

[tex]mACB = mABC = (180-120)/2 = 30\°[/tex]

Then, in triangle ABH, we have:

[tex]mABH + mBHA + mHAB = 180\°[/tex]

[tex]30\° + 90\° + mHAB = 180\°[/tex]

[tex]mHAB = 60\°[/tex]

If m∠BAC is 120°, we have:

[tex]mHAB + mHAC = 120\°[/tex]

[tex]m∠HAC = 60\°[/tex]

Now we can find the length of AH using the sine relation of angle m∠HAC:

[tex]sin(mHAC) = DH / AH[/tex]

[tex]0.866 = b / AH[/tex]

[tex]AH = b / 0.866 = 1.1547b[/tex]

Now, to find the length of HB and AB, we can use the tangent and cosine relation of the angle m∠HAB:

[tex]tan(mHAB) = HB / AH[/tex]

[tex]1.7321 = HB / 1.1547b[/tex]

[tex]HB = 1.7321 * 1.1547b = 2b[/tex]

[tex]cos(mHAB) = AH / AB[/tex]

[tex]0.5 = 1.1547b / AB[/tex]

[tex]AB = 1.1547b / 0.5 = 2.3094b[/tex]

So the perimeter of triangle ABH is:

[tex]P(ABH) = AB + HB + AH[/tex]

[tex]P(ABH) = 2.3094b + 2b + 1.1547b[/tex]

[tex]P(ABH) = 5.4641b[/tex]

The relation of a and b can be calculated using the tangent relation of the angle m∠HAC:

[tex]tan(mHAC) = DH / AD[/tex]

[tex]1.7321 = b / a[/tex]

[tex]b = 1.7321a[/tex]

Answer:

[tex]Y\approx 84^\circ $(to the nearest angle)[/tex]

Step-by-step explanation:

The lengths of the sides of the scalene triangle are 6, 11, and 12.

We want to use the law of cosines to find the largest angle.

Note that the largest angle is always opposite the largest side.

Therefore:

[tex]1. 12^2 = 11^2 + 6^2-2(11)(6)\cos(Y) \\\\2. 144 = 121 + 36-(132)\cos(Y) \\\\3. 144 = 157 - (132)\cos(Y) \\\\4. -13 = -(132)\cos(Y)\\\\\\5. \cos(Y) = \dfrac{-13}{-132} \\\\6. Y = \arccos \left ( \dfrac{13}{132}\right)\\\\7. Y=84.35^\circ\\\\8. Y\approx 84^\circ $(to the nearest angle)[/tex]

The largest angle is 84 degrees to the nearest angle.

Answer:

The zeroes of a quadratic equation are the points on the graph where it lies on the x-axis.

The vertex is the point where it is the maximum or minimum value of x or y depending on the symmetry.

The symmetry is the line where it cuts the graph through the vertex of the graph dividing it into two equal parts that mirror each other.

The quadratic formula, factoring, and completing the square are the methods used to solve a quadratic equation.

f(x) + 7 shifts the graph 7 units up, f(x +7) shifts the graph 7 units to the left

Step-by-step explanation:

9514 1404 393

Answer:

  33.9 m

Step-by-step explanation:

The relationship between the building height (h), the shadow length (s), and the angle of elevation of the sun (α) is ...

  tan(α) = h/s

  h = s·tan(α) = (18 m)tan(62°) ≈ 33.853 m

The building is about 33.9 meters tall.

Answer:

The first option: -5/4x + 1/6.

Step-by-step explanation:

(3/4x - 2/3) - (-5/6 + 2x)

= (3/4x - 2/3) + 5/6 - 2x

= 3/4x - 2x - 2/3 + 5/6

= 3/4x - 8/4x - 4/6 + 5/6

= -5/4x + 1/6

So, the first option: -5/4x + 1/6.

Hope this helps!

Step-by-step explanation:

D. Graph D the answer is D

Answer:

D. Graph D the answer is D

Step-by-step explanation:

Answer:

Sh. 9000

Step-by-step explanation:

John : Peter = 2 : 1

John/peter = 2/1

John = 2 Peter.... (1)

Amos : John = 4:3

Amos/John = 4/3

Amos = 4/3 John.. (2)

From (1) & (2)

Amos = 4/3 * 2 Peter = 8/3 Peter.... (3)

Since,

Amos + John + Peter = 51000

Therefore,

8/3 Peter + 2peter + Peter = 51000

(8+6+3)/3 *Peter = 51000

17/3 * Peter = 51000

Peter = 51000 * 3/17

Peter = 3000 * 3

Peter = 9000

Hence, amount received by Peter is Sh. 9000.

Answer:

least value of n =4

Step-by-step explanation:

i hope the screenshot of my work broken down step by step helps

Answer:

There are no choices, but [tex]\frac{10}{10.75}[/tex] can be changes in the following ways: multiplying the numerator and the denominator by the same amount, or dividing the numerator and denominator by the same amount.

Hope it helps <3

Answer:

40/43

Step-by-step explanation:

  The fraction

       10

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

   10 3/4

can be simplified by converting 10 3/4 to the improper fraction 43/4:

       10                    10            40

-----------------  =  _______ = ----------

   10 3/4               43/4            43

Next time, please share any answer choices that are given to you.  Thank you.

Answer:

1/8, 2/5 , 1/2, 3/4

Step-by-step explanation:

1/2= 0.5

1/8= 0.1

3/4= 0.8

2/5= 0.4

just arrange them in the order from smallest to largest......

Answer:

⅛ < ⅖ <  ½ < ¾

Step-by-step explanation:

First, rewrite the fractions so that they all have the same denominator.

The new denominator should be the lowest common multiple of the original denominators.

The L.C.M. of 2, 8, 4, and 5 is 40.

When multiplying the denominator to 40, make sure you multiply the numerator with the same value you use to multiply the denominator.

1/2 = 1x20 / 2 x 20 = 20/40

1/8 = 1x5 / 8x5 = 5/40

3/4 = 3x10 / 4x10 = 30/40

2/5 = 2x8 / 5x8 = 16/40

When all the denominators are the same, we can compare the numerator. The greater the numerator, the greater the fraction is.

Between 20, 5, 30, and 16, the smallest is 5, then 16, 20 and greatest is 30.

Since ascending order means listing them out from smallest to greatest, the order should be:

⅛ < ⅖ <  ½ < ¾

Answer:

A

Step-by-step explanation:

Answer:

[tex]-7[/tex]

Step-by-step explanation:

[tex]5(x+9) = 10[/tex]

[tex]5x+45=10[/tex]

[tex]5x = -35[/tex]

[tex]x=-7[/tex]

Hope this helps.

Answer:

-7

Step-by-step explanation:

5(x + 9) = 10

Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.

PEMDAS =

Parenthesis

Exponents (& Roots)

Multiplication

Division

Addition

Subtraction

...and is your order of operation.

First, divide 5 from both sides:

(5(x + 9))/5 = (10)/5

x + 9 = 10/5

x + 9 = 2

Next, isolate the variable x, by subtracting 9 from both sides:

x + 9 (-9) = 2 (-9)

x = 2 - 9

x = -7

x = -7 is your answer.

~

Answer:

0.75

Step-by-step explanation:

Since we use the base 10 decimal system, first convert 3/4 to out of 100:

3/4 = 75/100

We divide 75 by 100 to get 0.75

Answer:

Value of y = 3

Step-by-step explanation:

Given:

y-2<2 ........Eq1

3y+10>16.........Eq2

Find:

Value of y

Computation:

y-2<2

Add 2 both side,

y-2+2<2+2

y < 4

So y = (0,1,2,3)

Put y = 3 in both equation:

y-2<2

3-2<2

1<2

3y+10>16

3(3) + 10 >16

19>16

Both equation get satisfies by y = 3

So, Value of y is 3

Answer:

See attached table

Step-by-step explanation:

Given base b,

the required formulas are:

Area of base = b^2

height: solve for h in 2b^2+4*bh = S =54

where S is the surface of 54

Substitute and solve for h,

h =  (S - 2b^2)/(4b) = (54-2b^2)/(4b) = (27-b^2)/(2b)

The volume is equal to base area times height, or

V = b^2(h)

The completed table is attached.

Answer:45 I think

Step-by-step explanation:

Answer:

[tex]3x - 22 = \frac{x}{4} [/tex]

When twenty two is subtracted from a number multiplied by three the result is the same as the number divided by 4.

Hope this helps you

Answer:

here is the answer

Step-by-step explanation:

statement- the result obtained when 22 is subtracted from 3 times of a number is one-fourth of the number.

situation- rahul sees the price of a toy he wants to buy. after two years he comes to the shop again to buy the product. he notices that the price has become thrice the original. the shopkeeper agrees to reduce an amount of 22 rupees and he pays one fourth of the original price to the shopkeeper and buys the producet. find the original price of the toy.

Answer:

To do that you must divide 4 by 100

Step-by-step explanation:

4 divided by 100 is 0.04

Answer:

4/100

Run two decimal places forward

that's

0.04

Hope this helps you

Answer:

x = 33/5

Step-by-step explanation:

4x+x-15+3-8=13

Combine like terms

5x -20 = 13

Add 20 to each side

5x-20+20 = 13+20

5x =33

Divide by 5

5x/5 = 33/5

x = 33/5