x - 3y = 9, complete the ordered pair (12, ).

Answer:

  f(x) = (x -6)² +14

Step-by-step explanation:

Completing the square involves writing part of the function as a perfect square trinomial.

The square of a binomial results in a perfect square trinomial:

  (x -h)² = x² -2hx +h²

The constant term (h²) in this trinomial is the square of half the coefficient of the linear term: h² = ((-2h)/2)².

One way to "complete the square" is to add and subtract the constant necessary to make a perfect square trinomial from the variable terms.

Here, we recognize the coefficient of the linear term is -12, so the necessary constant is (-12/2)² = 36. Adding and subtracting this, we have ...

  f(x) = x² -12x +36 +50 -36

Rearranging into the desired form, this is ...

  f(x) = (x -6)² +14

__

Additional comment

Another way to achieve the same effect is to split the given constant into two parts, one of which is the constant necessary to complete the square.

  f(x) = x² -12x +(36 +14)

  f(x) = (x² -12x +36) +14

  f(x) = (x -6)² +14

The approximate measure of angle G is 41.4°. The correct option is C. 41.4°

From the question, we are to determine the measure of angle G

From the law of cosines, we can write that

[tex]cos\ G =\frac{e^{2}+f^{2}-g^{2} }{2ef}[/tex]

In the diagram,

e = 12

f = 10

g = 8

Putting the values into the equation

[tex]cos\ G =\frac{12^{2}+10^{2}-8^{2} }{2\times 12 \times 10}[/tex]

[tex]cos\ G =\frac{144+100-64 }{240}[/tex]

[tex]cos\ G =\frac{180}{240}[/tex]

cosG = 0.75

G = cos⁻¹(0.75)

G = 41.4°

Hence, the approximate measure of angle G is 41.4°. The correct option is C. 41.4°

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Answer:

Step-by-step explanation:

The function with the greatest rate of change over the interval [0, 2] is: D. a

If both faucets are used together, it time taken by them to fill the tub is 4.8 minutes.

Time and work share a fundamental idea in common with other arithmetic topics, namely the idea of proportionality.

When the amount of work is constant, efficiency is inversely proportional to the length of time required.

Important Time and Work Formula:

Calculation for the time taken by both faucet to fill the tub.

The unit should be tub per minute.

Then, do the reciprocal of the result to have minute per tub.

The hot water faucet can fill the tub in 12 minutes.

The cold water faucet can fill the tub in 8 minutes.

The filling rate for both faucets filling the tub at the same time is the sum of their rates.

Let 't' be the time taken by both faucets.

Then,

[tex]\frac{1}{12} +\frac{1}{8} =\frac{1}{t}[/tex]

[tex]\frac{8+12}{8*12} =\frac{1}{t}[/tex]

[tex]\frac{1}{t} =\frac{20}{96}[/tex]

[tex]\frac{t}{1} =\frac{96}{20}[/tex]

t = 4.8

Therefore, the time taken by both faucets to fill the tub is 4.8 minutes.

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the number of possible call letters of a radio station (8 letters long) if the first letter must be a W or a K and no letter is repeated is 4, 845, 456, 0000 call letter

From the given information, we need to find the number which is

First letter have only two possibility.

But we know that there are a total of 26 letters in alphabet.

First letter must be W or K. So remaining 25 letters.

The Remaining 7 letters can be any alphabet (25 letters)

We also know that np letters are repeated.

So, the  second letters have 25 possibility and the third letter have 24 possibility and so one;

Thus, we have

= 2 × 25 × 24 × 23 × 22 × 21 × 20 × 19

Multiply through

= 4, 845, 456, 0000 call letter

Thus, the number of possible call letters of a radio station (8 letters long) if the first letter must be a W or a K and no letter is repeated is 4, 845, 456, 0000 call letter

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Answer:

[tex]\huge\boxed{\sf C, \ D \ and \ E}[/tex]

Step-by-step explanation:

Given expression:

Distribute 2 to both terms.

We can also split 8f into 4f and 4f.

If we take 4 common

= 4(f + f + g)

[tex]\rule[225]{225}{2}[/tex]

Answer: Heya! ~

Step-by-step explanation:

Given: Expression 2(4f + 2g)

We have to choose an equivalent expression to the given expression  2(4f + 2g)

Consider the given expression 2(4f + 2g)  

Apply Distributive property, a( b + c) =ab + ac

We have,

a = 2, b = 4f and c = 2g

2(4f + 2g) = 8f + 4g

Now, take 4 common from each term, we have,

8f + 4f = 4 (2f + g)

Now, We have,

a = 2, b = 4f and c = 2g

2(4f + 2g) = 8f + 4g

Now, take 4 common from each term, we have,

8f + 4f = 4 (2f + g)

Now, an equivalent expression to the given expression  2(4f + 2g) is  8f + 4g and 4 (2f + g)

- Keira

Answer:

[tex]x=\frac{83}{36}[/tex]

Step-by-step explanation:

1) Convert [tex]2\frac{1}{4}[/tex] to  improper fraction. Use this rule: [tex]a\frac{b}{c} =\frac{ac+b}{c}[/tex].

[tex]x-\frac{2\times4+1}{4} = \frac{1}{18}[/tex]

2) Simplify [tex]2\times4[/tex] to 8.

[tex]x-\frac{8+1}{4} =\frac{1}{18}[/tex]

3) Simplify [tex]8+1[/tex] to 9.

[tex]x-\frac{9}{4} =\frac{1}{18}[/tex]

4) Add [tex]\frac{9}{4}[/tex] to both sides.

[tex]x=\frac{1}{18} +\frac{9}{4}[/tex]

5) Simplify [tex]\frac{1}{18} +\frac{9}{4}[/tex] to [tex]\frac{83}{36}[/tex].

[tex]x=\frac{83}{36}[/tex]

Decimal Form: 2.305556

Answer:

83/36

Step-by-step explanation:

x - 2 1/4 = 1/18

x = 1/18 + 9/4

L.C.M= 36,

x = 1x2/18x2 + 9x9/4x9

x = 2/36 + 81/36

x = 83/36

Decimal form = 2.305556

Some of the metrics that I would look at to determine whether or not a new feature will be successful are as follows:

It should be noted that metrics are the measures of quantitative assessment used for comparing, and tracking performance or production.

Metrics are heavily relied on in the financial analysis of companies to make decisions.

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The function that could represent the price tag's height relative to the table top is  h(t) = 4sin (22) +4

The question is incomplete because the options are not given and hence the correct option is shown below

Which function could represent the price tag's height relative to the table top, h(t), after it has been rolling for e seconds?

A n(t) = 2008(832) +2

B. h(t) =-2005(522) +2

C h(t) = –2sin(572) +2

D. h(t) = 4sin (22) +4

Given diameter is 4 inches and the time given is  5 seconds and

the number of rotations given is 4

We need to find the function that could represent the price tag's height relative to the table top .

Diameter = 4

So, Radius will be D/2 = 4/2

Radius=2

time given is  5 seconds and

the number of rotations given is 4

So ,   5/4 = 2π/w

Therefore ,

W = 8π / 5

Therefore

h(t) = h(t) = 4sin (22) +4

Hence The function that could represent the price tag's height relative to the table top is  h(t) = 4sin (22) +4

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The required probability is 0.171.

What is probability?

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.

We can find required Probability as shown:

From 10 coins we choose 7 he guessed correct with probability of each 1/2. For three remaining coins he failed to predict the outcomes of the flip with the probability of 1/2 for each. Similarly for 8,9 or 10 successive trials. Let X denote number of successive trials

[tex]P(X\geq 7)= \tbinom{10}{7}.\frac{1}{2^{10}}+\tbinom{10}{8}.\frac{1}{2^{10}} +\tbinom{10}{9}.\frac{1}{2^{10}}+\tbinom{10}{10}.\frac{1}{2^{10}}[/tex]

[tex]=120.\frac{1}{2^{10}} +45.\frac{1}{2^{10}} +10.\frac{1}{2^{10}} +.\frac{1}{2^{10}}[/tex]

[tex]=\frac{120+45+10+1}{2^{10}}[/tex]

[tex]=\frac{176}{1024}[/tex]

=0.171

Hence, the required probability is 0.171.

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Given question is incomplete. This is complete question:

A man claims to have extrasensory perception. As a test, a fair coin is flipped 10 times and the man is asked to predict the outcome in advance. He gets 7 out of 10 correct. What is the probability that he would have done at least this well if he had no ESP?

Answer:

The sum of all 2 digit multiples of 6 is 810

Step-by-step explanation:

12+18+24+30+36+42+48+54+60+66+72+78+84+90+96 = 810

Answer:

810

Step-by-step explanation:

2 digit multiples of 6 are 12,18,24...90,96

You can just add them on your calculator.

The smallest possible value of N is 23.

According to the statement

we have given that the sequence {1,2,3.....n}

and the sum is 241. we have to find the smallest value of n.

So, for this purpose we use summation formula of an arithmetic sequence

Sn = n /2 ( a1 +an )

Put the values in it then.

Note that the sum of the first 21 integers  is   21 * 22 /2  =  231...this isn't large enough as compare to given value.

And the sum of the first  22 integers  =   22 * 23 / 2  =   253

So    253 - 241  =  12 = omitted sum.....  

but  the sum of two consecutive integers must be odd

And......the sum of the first 23 integers is  23 * 24 / 2  = 276

So.......276 - 241   =  35    = omitted sum

So....the   consecutive integers omitted must be  17  and 18

So....... the smallest value of n  is   23

So, The smallest possible value of N is 23.

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The transformations applied to F(x) is a vertical shift of 2 and a phase shift of π/2.

When a function is transformed, the graph's curve either "moves to the left/right/up/down," "expands or compresses," or "reflects."

Function transformations are highly useful for graphing functions without having to start from scratch because they allow you to move, extend, compress, or reflect the curve.

The graph of the parent function is either "moved," "resized," or "reflected" by a function transformation. The three primary categories of function transformations are as follows:Translation,Dilation and Reflection.

The given function F(x)=cos x is transformed to G(x)=2-sin x, by applying a vertical shift of 2 units upwards and a phase shift of π/2.

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When calculating correlation and regression both sets of data must be Statistical.

According to the statement

we have to find the type of data when we calculate the correlation and regression both sets.

so, The difference between these two statistical measurements is that correlation measures the degree of a relationship between two variables (x and y), whereas regression is how one variable affects another.

And when we calculate both then data sets must be a statistical data. because correlation summarizing direct relationship between two variables  and regression predict or explain numeric response. So, without statistical data this is not possible to calculate correlation and regression both sets.

so, When calculating correlation and regression both sets of data must be Statistical.

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Answer:

4ab2(7a2b2 5a - 4b)

Step-by-step explanation:

28a3b4 20a2b2 − 16ab3

The GCF of 28, 20 and 16 is 4.

GCF of the variables is ab2

So the answer is

4ab2(7a2b2 5a - 4b)

Answer:

4ab2(7a2b2 5a - 4b)

Step-by-step explanation:

Answer:

The gradient is -[tex]\frac{2}{3}[/tex] and the intercept is 2.

Step-by-step explanation:

First, transform the given equation into the slope-intercept form, y = mx + b. The variable m represents slope (gradient) and the variable b represents the intercept.

2x + 3y = 6

3y = -2x + 6

y = -[tex]\frac{2}{3}[/tex]x + 2

The gradient is -[tex]\frac{2}{3}[/tex] and the intercept is 2.

Answer:

[tex]\sf gradient =\dfrac{-2}{3}\\\\ y -intercept = 2[/tex]

Step-by-step explanation:

      [tex]\sf \boxed{\bf y = mx +b}[/tex]

Here m is the slope or gradient and b is the y-intercept.

Write the given equation in slope-intercept form.

  2x + 3y = 6

          3y = -2x + 6

            [tex]\sf y =\dfrac{-2}{3}x +\dfrac{6}{3}\\\\ y = \dfrac{-2}{3}x + 2[/tex]

[tex]\sf gradient =\dfrac{-2}{3}\\\\ y -intercept = 2[/tex]

The y-intercept of the function f(x) is (0, 10/3)

The function is given as:

[tex]f\left(x\right)=\frac{30}{1+2^{3-x}}[/tex]

As x approaches infinity, we have:

[tex]\lim_{x \to \infty} \frac{30}{1+2^{3-x}}[/tex]

This gives

[tex]\lim_{x \to \infty} \frac{30}{1+2^{3-\infty}}[/tex]

[tex]\lim_{x \to \infty} \frac{30}{1+2^{-\infty}}[/tex]

Evaluate

[tex]\lim_{x \to \infty} \frac{30}{1}[/tex]

[tex]\lim_{x \to \infty} 30[/tex]

As x approaches negative infinity, we have:

[tex]\lim_{x \to -\infty} \frac{30}{1+2^{3+x}}[/tex]

This gives

[tex]\lim_{x \to -\infty} \frac{30}{\infty}[/tex]

Evaluate

[tex]\lim_{x \to -\infty} 0[/tex]

Hence, the limits of the function are [tex]\lim_{x \to \infty} 30[/tex] and [tex]\lim_{x \to -\infty} 0[/tex]

Remove the denominator

f(x) = 30

Also, set the numerator to 0

f(x) = 0

Hence, the horizontal asymptotes are y = 30 and y = 0

Set x = 0

[tex]f\left(0\right)=\frac{30}{1+2^{3-0}}[/tex]

Evaluate

[tex]f\left(0\right)=\frac{30}{9}[/tex]

Divide

[tex]f\left(0\right)=\frac{10}3[/tex]

Hence, the y-intercept is (0, 10/3)

The numerator of f(x) is 30.

In (b), we have

The horizontal asymptotes are y = 30 and y = 0

This means that the horizontal asymptotes and the numerator are the same

See attachment for the graph of f(x)

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The solution of the system would be (3,6).

Lets solve the problem,

Other equation: y = 1/3x+5

Slope-Intercept Form: y = mx + b

Slope Formula:

y2-y1/x2-x1 = m

Have to find equation now:

m = (6 - 5)/(3 - 0)

m = 1/3

y = 1/3x + b

5 = 1/3(0) + b

b=5

y = 1/3x + 5

Lets put the substituition method here,

1/3x + 5 = -1/3x + 7

2/3x + 5 = 7

2/3x = 2

x = 3

y = 1/3(3) + 5

y = 1 + 5

y = 6

Therefore the coordinates are (3,6)

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The the next step in the proof is D. Statement: ∠7 ≅ ∠6 and ∠8 ≅ ∠5 Reason: Vertical Angles Theorem.

It should be noted that vertical angles are the angles that are opposite each other when the two line cross.

In this case, 7 ≅ ∠6 and ∠8 ≅ ∠5 Reason: Vertical Angles Theorem.

In conclusion, the correct option is D.

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Answer:

See below.

Step-by-step explanation:

a. If h is the number of hours of labour required to print the cards, construct an equation for the cost of the cards, C.

C = $250 + ($40/hr)*h

b. You have budgeted $1000 for the printing job. How many hours of labour can you afford? Give your answer to the nearest minute.

$1000 = $250 + ($40/hr)*h

($40/hr)*h = $750

h = 18.75 hours

(18.75 hours)(60 min/hr) = 1125 minutes

c. The company estimates that it can print 1000 cards per hour of labour. How many cards will you get printed with your current budget?

(18.75 hr)*(1000 cards/hr) = 18,750 cards

d. An alternative to printing is photocopying. The company charges 15 cents per side for the first 10 000 cards and then 10 cents per side for the remaining cards. Which is the cheaper option for 18 750 single-sided cards and by how much?

Photocopy Cost for the first 1000 single-sided cards is:

(1000 cards)*($0.15) = $150

Photocopy Cost for the final 17,750 single-sided cards is:

(17,750)*($0.10) = $1,775

Totoal photocopy cost for 18,750 single-sided cards is $1,925.  [1775+150]

The cheapest option for 18,750 cards is printing:  $1,000

Printing is (1,925 - 1000) $925 cheaper than photocopying.

It should be noted that mathematical transformations involve changing an image in some prescribed manner.

Your information is incomplete. An overview will be given. A transformation is a general term for the specific ways to manipulate the shape and/or position of a point, a line, or geometric figure.

It should be noted that the original shape of the object is called the pre-Image and the final shape and position of the object is the image under the transformation.

There are four main types of transformations: translation, rotation, reflection and dilation. Also, in geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other

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Answer:

1. a translation and reflection

2. only rigid transfotmations

3. are congruent

Step-by-step explanation:

right on edmentum

Answer:

slope = 2

Step-by-step explanation:

calculate the slope m using the slope formula

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

with (x₁, y₁ ) = (- 1, 0) and (x₂, y₂ ) = (0,2) ← 2 points on the line

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

The difference between the two given fractions is  [tex]\frac{x^{2} +4x-1}{x^{2} +2x}[/tex].

Fraction if a part of whole. It is represented in the form of numerator and denominator.

Given that,

[tex]\frac{x+5}{x+2} -\frac{x+1}{x^{2} +2x}[/tex]

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

Take the LCM of the denominators is [tex]x(x+2)[/tex].

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

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

=   [tex]\frac{x^{2}+4x-1}{x^{2} +2x}[/tex]

Thus, the difference between the two given fractions is  [tex]\frac{x^{2}+4x-1}{x^{2} +2x}[/tex] .

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The given question is not in correct form.

The 95 percent confidence interval for the mean is (266.76,426.24).

A confidence interval is how much uncertainty there is with any particular statistic. Confidence intervals are often used with a margin of error. It tells you how confident you can be that the results from a poll or survey reflect what you would expect to find if it were possible to survey the entire population. Confidence intervals are intrinsically connected to confidence levels.

The formula of Confidence Interval =  Mean ±   [tex]t\frac{Standard Deviation}{\sqrt{number of observations} }[/tex]

where t is a constant

Given:

Mean = 346.5

Standard Deviation = 170.378

t-critical value for 95% Confidence interval with degrees of freedom(df)=n-1= 19 is 2.093

∴ Substituting values in formula we get

E = [tex]2.093 X170.378/\sqrt{20}[/tex] = 2.0931.96 x 38.0976=79.74

95% Confidence interval : (346.5-79.74,346.5+79.74)

95% Confidence interval : (266.76,426.24)

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The size of the angle subtended at the center of the circle is θ = 80.5397°

In circles, a sector is said to be a part of a circle made of the arc of the circle together with its two radii. This means that it is a portion of the circle formed by a portion of the circumference (arc) and radii of the circle at both endpoints of the arc.

The formula for Area of a sector is given as;

A = θ/360 x πr²

where;

θ is the central angle of the sector

r is radius

Given data ,

The area of a sector of a circle of radius 8cm is 45cm²

On simplifying , we get

A = θ/360 x πr²

45 = θ/360 ( 22/7 ) ( 8 )²

45 = ( θ/360 ) ( 201.1428 )

Divide by 201.1428 on both sides , we get

( θ/360 ) = 0.22372159

Multiply by 360 on both sides , we get

θ = 80.5397

Hence , the angle is θ = 80.5397°

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Answer:

Step-by-step explanation:

First prime factorize 135,

135 = 5×3×3×3

Now prime factorize 128,

128=2×2×2×2×2×2×2 = 2^7

the highest prime factor of 135 is 5,

Let 5 be x

the highest power of the lowest prime factor of 128 which is the power 2 is 7

Let 7 be y

According to the question x^y = 5^7

Length of each side is 176 feet ² .

each side of house = 22 feet long

Perimeter of octagon = 8 × sides

Length of each side of house = 8 × 22 ⇒ 176 feet²

Therefore, length of each side is 176 feet ² .

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Step-by-step explanation:

Using translation concepts, the inequality that represents the graph is given as follows:

f(x) > sqrt(1 - x)

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.

The parent square root function is given by:

y = sqrt(x)

It increases to right starting at x = 0, and in this problem it increases to left starting at x = 1, meaning that it was reflected over the y-axis and shifted right one unit, hence the function is:

sqrt(1 - x)

The part graphed is the values above the function, that is, the values that are greater, as the line is only dashed, hence the inequality is:

f(x) > sqrt(1 - x)

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