Which function has a minimum and is transformed to the right and down from the parent function, f(x) = x²?
O g(x)=-9(x + 1)²-7
Og(x) = 4(x-3)² +1
O g(x)=-3(x-4)²-6
Og(x)= 8(x-3)²-5

Answer:

[tex](-7[/tex]±[tex]\sqrt{17}) /2[/tex]

Step-by-step explanation:

First, convert this into a quadratic, [tex]x^{2}+7x+8=0[/tex]. We can use the quadratic formula for this, [tex](-7[/tex]±[tex]\sqrt{7^{2}-4(1)(8)})[/tex][tex]/2(1)[/tex]. This becomes [tex](-7[/tex]±[tex]\sqrt{49-32})/2[/tex]. This is [tex](-7[/tex]±[tex]\sqrt{17}) /2[/tex]. This is your answer

Answer:

1

Step-by-step explanation:

Points on a coordinate plane are written as (x,y) coordinates. The vertical axis is the y axis. If your point is "one unit up" its y-value is 1. (The horizontal axis is the x-axis. The x-value is 6.)

Answer:

1540

Step-by-step explanation:

This is an arithmetic progression.

a = first term = 10

Common difference = d = second term - first term

                                         = 12 - 10

                                     d  = 2

Last term = l = 78

First we have to find how many terms are there in the sequence using the formula:  l = a + (n-1)*d

                   78 = 10 + (n -1) * 2

               78 -10 = (n -1)*2

                     68 = (n -1) *2

               68 ÷2 =  n -1

                      34 = n - 1

                 34 + 1 = n

                         n = 35

There are 35 terms.

  [tex]\sf \boxed{\test{\bf Sum = $\dfrac{n}{2}(a +l)$}}[/tex][tex]\sf \boxed{\text{\bf Sum =$\dfrac{n}{2}(a+l) $}}[/tex]

            [tex]\sf =\dfrac{35}{2}(10+78)\\\\ =\dfrac{35}{2}*88\\\\ = 35 * 44\\\\= 1540[/tex]

Step-by-step explanation:

This is an arithmetic progression.

a = first term = 10

Common difference = d = second term - first term

= 12 - 10

d = 2

Last term = l = 78

First we have to find how many terms are there in the sequence using the formula: l = a + (n-1)*d

78 = 10 + (n -1) * 2

78 -10 = (n -1)*2

68 = (n -1) *2

68 ÷2 = n -1

34 = n - 1

34 + 1 = n

n = 35

There are 35 terms.

\sf \boxed{\test{\bf Sum = $\dfrac{n}{2}(a +l)$}} \sf \boxed{\text{\bf Sum =$\dfrac{n}{2}(a+l) $}}

Sum =

2

n

(a+l)

\begin{gathered}\sf =\dfrac{35}{2}(10+78)\\\\ =\dfrac{35}{2}*88\\\\ = 35 * 44\\\\= 1540\end{gathered}

=

2

35

(10+78)

=

2

35

∗88

=35∗44

=1540

Patrick has an absolute advantage in playing quarterback.

Given a table containing touchdowns and field goals by Partrik and Field goals as under:

Person                       Touchdowns                         Field goals

Patrik                              39                                            13

Jimmy                             25                                            5

We are required to find a person who has an absolute advantage in playing quarterback.

Absolute advantage is the ability of an individual, company to produce greater advantage of good or service than the individual.

Total of touchdowns and field goals by Patrik=39+13=52

Total of touchdowns and field goals by Jimmy=25+5=30

We can see that total of touchdowns and field goals by Patrik is greater than total of touchdowns and field goals by Jimmy. So Patrik has an absolute advantage playing quarterback.

Hence Patrick has an absolute advantage in playing quarterback.

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Question is incomplete as it should include the following table:

Person                       Touchdowns                         Field goals

Patrik                              39                                            13

Jimmy                             25                                            5

Total Saving of Ethan is = $4600

Saving after donating 20% = $4600-$920

                                              =$3680

What is Percentage ?

As a fraction of 100, a percentage is a number or ratio. Although the abbreviations "pct.", and occasionally "pc" are also used, the percent sign ("percent") is frequently used to indicate it. A % has no dimensions and no associated unit of measurement.

How to calculate percentage?

Calculating a percentage involves dividing an item by its sum and multiplying the result by 100. The formula for percentage calculation is (value/total value)100%

Solution :

Let the Saving be 100%

Donated salary 20% = $920

finding 80% of the saving

Formula for percentage:

                                        [tex]\frac{value}{total value} *100[/tex]

                                        =[tex]\frac{20}{100} *920[/tex]

                                        = [tex]5*920[/tex]

                                        = [tex]4600[/tex]

Then the Total saving =$4600

The Total saving after donating 20% = $3680

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The value of sample proportion is found to be 0.253.

The sample proportion [tex]\hat{p}[/tex] indicates the percentage of people in a sample who exhibit a particular quality or attribute.

Divide the number of individuals (or items) who possess the desired attribute by the overall sample size to obtain the sample proportion.

Now, according to the question;

The 90% confidence interval for a proportion is found to be (0.22,0.28).

The confidence interval for the sample is given as-

Confidence interval = Sample proportion ± Margin of Error

Let [tex]\hat{p}[/tex] be the sample proportion.

The level of significance = 1 - 0.90

                                         = 0.10 (10%)

From z-value table, at a significance level of 5% (two-sided), z has a critical value of 1.645.

90% confidence interval = [tex]\hat{p} \pm 1.645 \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}[/tex]

Thus,                       0.22 = [tex]\hat{p} - 1.645 \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}[/tex], and

                               0.28 = [tex]\hat{p} + 1.645 \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}[/tex]

Covert both equation in the form of [tex]\hat{p}[/tex] and equating to each other.

[tex]\begin{aligned}&0.22+1.645 \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}=0.28-1.645 \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}\\&1.645 \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}+1.645 \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}=0.28-0.22\\&2 \times 1.645 \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}=0.06\\&\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}=\frac{0.06}{2 \times 1.645}\\&\sqrt{\frac{\hat{\nu}(1-\hat{p})}{n}}=0.02\end{aligned}[/tex]

Take square root,

[tex]\begin{gathered}\frac{\hat{p}(1-\bar{p})}{n}=0.0004 \\n=\frac{\hat{p}(1-\bar{p})}{0.0004}\end{gathered}[/tex]

Substituting the value of 'n' in the receptive equation to get the value of [tex]\begin{aligned}0.22 &=\hat{p}-1.645 \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}} \\0.22 &=\hat{p}-1.645 \times \sqrt{\frac{\hat{p}(1-\hat{p})}{p(1-\hat{p})}} \times 0.0004 \\0.22 &=\hat{p}-1.645 \times \sqrt{0.0004} \\0.22 &=\hat{p}-(1.645 \times 0.02) \\0.22 &=\hat{p}-0.033 \\\hat{p}=& 0.22+0.033=0.253\\\end{aligned}[/tex]

Therefore, the value of sample proportion is 0.253.

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Answer:

B

Step-by-step explanation:

[tex]\frac{x}{x-3}[/tex] × [tex]\frac{2x}{x+5}[/tex] ( no factors cancel on numerator / denominator )

= [tex]\frac{x(2x)}{(x-3)(x+5)}[/tex]

= [tex]\frac{2x^2}{x^2+2x-15}[/tex]

The number of ways we can select 3 cracked and 2 good is 1200 ways.

Given there are 5 eggs in which 3 eggs are cracked and 2 eggs which are good.

We have to find the number of ways we can select 3 cracked and 2 good eggs from 5 eggs.

Number of ways can be found through permutations.

The factorial of n  equals the product of n with the smaller factorial..

Permutations is the technique of calculating  various ways in which objects from a set may be selected, generally without replacement, to form subsets.

n[tex]P_{r}[/tex]=n!/(n-r)!

So the number of ways will be 5[tex]P_{3}[/tex]*5[tex]P_{2}[/tex]

([tex]5P_{3}[/tex] for cracked eggs and [tex]5C_{2}[/tex] for good eggs)

=5!/(5-3)!*51/(5-2)!

=5*4*3*2!/2!*5*4*3!/3!

=5*4*3*5*4

=1200

Hence there are 1200 ways through which 3 cracked and 2 good eggs can be selected from 5 eggs.

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Answer:

Khan Academy.

Step-by-step explanation:

You can go on khan academy and search up "area and graphs." The videos should immediately pop up. there are also lessons if you don't want to risk getting your problem wrong. If you are still confused and do not understand please just comment and I will respond.

Answer:jio

Step-by-step explanation:

The missing number for the subtraction of matrices is 4.

The subtraction of two matrices of the same size is really direct. You just need to subtract the elements that are in the same position, then:

[tex]A = \left[\begin{array}{ccc}a_{11}&a_{12}\\a_{21}&a_{22}\end{array}\right] \\\\B = \left[\begin{array}{ccc}b_{11}&b_{12}\\b_{21}&b_{22}\end{array}\right]\\\\A - B = \left[\begin{array}{ccc}a_{11} - b_{11}&a_{12}-b_{12}\\a_{21} - b_{21}&a_{22}-b_{22}\end{array}\right][/tex]

Then the missing therm will just be equal to the difference between the last two elements of each matrix:

-2 - (-6) = -2 + 6 = 4

The missing number is 4.

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Hence, the customary units of capacity in Sava's are 1 Fluid ounce, 1 Cup, 1 Pint, 1 Quart and 1 Gallon.

According to the question,

The customary units of capacity in Sava's are 1 fluid ounce, 1 Cup, 1 Pint, 1 Quart and 1 Gallon.

Customary units and its equivalent  

1 Fluid ounce = 2 Tablespoons

1 Cup = 8 fluid ounces

1 Pint = 2 cups

1 Quart = 2 pints

1 Gallon = 4 quarts

Hence, the customary units of capacity in Sava's are 1 Fluid ounce, 1 Cup, 1 Pint, 1 Quart and 1 Gallon.

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1111 is the greatest common divisor of all numbers.

Lets simplify the problem,

1234  +  4321   =   5555

2345  +  5432   =   7777

3456  +  6543   =   9999

4567  +  7654   =   12221

5678  +  8765   =   14443

6789  +  9876   =   16665

After it , we get:

5555 _=_ 101 * 11  * 5

7777 = 101 * 11 * 7

9999 = 101 * 11 * 3 * 3

12221 = 101 * 11 * 11

14443 = 101 * 11 * 13

16665 = 101 * 11 * 3 * 5

abcd(5555, 7777, 9999, 12221, 14443, 16665)  =  101 * 11  =  1111

Hence we get 1111 is the greatest common divisor.

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Maximum value = 880/3.

Maximizing the objective function in the LP model means that the value occurs in an acceptable set of decisions. Linear programming refers to selecting the best alternative from the available alternatives that can represent the objective and constraint functions as linear mathematical functions.

As mentioned above, the equation is an example of a constraint. You can use this to think about what it means to solve equations and inequalities. For example, solving 3x + 4 = 10 yields x = 2. This is an easy way to express the same constraints.

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The exponential form of ⁵√13³ is [tex]13^{3/5}[/tex].

Hence, option D) is the correct answer.

This question is incomplete, the complete question is:

Which of the following is equivalent to 5 sqrt 13³ ?.

A) 13^2.

B)13^15.

C)13^(5/3).

D)13^(3/5)

Given the expression; 5 sqrt 13³

This can be represented as; ⁵√13³

To convert from radical form to exponential form, we use apply the radical rule;

[tex]\sqrt[n]{a^m} = a^{m/n}[/tex]

Hence,

[tex]\sqrt[5]{13^3} = 13^{3/5}[/tex]

The exponential form of ⁵√13³ is [tex]13^{3/5}[/tex].

Hence, option D) is the correct answer.

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The variation given in the first question is not a direct variation and there is no constant of variation.

y = k × x

when

y = -40 and x = -0.5

y = k × x

-40 = k × -0.5

-40 = -0.5k

k = -40/-0.5

k = 80

When y = 8 and x = 2.5

y = k × x

8 = k × 2.5

8 = 2.5k

k = 8 / 2.5

k = 3.2

When y = 4 and x = -3

y = k × x

4 = k × -3

4 = -3k

k = -4/3

when y = 8 and x = -6

y = k × x

8 = k × -6

8 = -6k

k = 8/-6

k = -4/3

This is a direct variation and the constant of proportionality is -4/3

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Answer:

C

Step-by-step explanation:

Exponential functions have 2 things in common

-They increase infinitely once they approach a certain point

-They don't decrease anymore once they approach a certain point

The correct statements are –6x + 15 < 10 – 5x and a number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right.

Inequality are expressions not separated by an equal sign. Given the inequality expression:

–3(2x – 5) < 5(2 – x)

Expand

-6x +15 < 10 - 5x

Collect the like terms

-6x+5x < 10 - 15

-x <-5

x > 5

Hence the correct statements are –6x + 15 < 10 – 5x and a number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right.

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Step-by-step explanation:

x=8-y

2x-y=7

2(8-y)-y=7

16-2y-y=7

-3y=-9

y=3

x=8-y

x=8-3=5

Answer:

Hello

Step-by-step explanation:

Méthode par combinaisons linéaires:

[tex]\left\{ \begin{array}{ccc|c|c}x+y&=&8&1&-2\\2x-y&=&7&1&1\\\end {array} \right.\\\\\\\left\{ \begin{array}{ccc}3x&=&15\\-3y&=&-9\\\end {array} \right.\\\\\\\boxed{\left\{ \begin{array}{ccc}x&=&5\\y&=&3\\\end {array} \right. }\\[/tex]

Proof:

5+3=8 and 2*5-3=7

Answer:

C.

Step-by-step explanation:

For any of the given functions, all of the first input values (x-values) in the relation are considered the domain values. On the other hand, the output values (y-values) are called the range values of the given equation.

The mapped relation is the domain (1, 2, 3). Since this is domain values (x-values), the correct answer will be the mapped with 1, 2, and 3 on the left side.

The correct answer is C.

Hope this helps!

Answer:

1.

a.) 24in

b.)75.36in

c.)452.16in

Step-by-step explanation:

1a. The radius is half of the diameter, so all you have to do is add 12 + 12 which is 24.

1b. the circumfrence of a circle is C (Circumfrence)=[tex]2\pi r[/tex] so replace radius for 12 and then do 3.14(pi) x 2 which will get you 6.28 times 6.28 by 12 and you will get 75.36.

1c. Area=[tex]\pi r^{2}[/tex] so first do the radius by the second power, or [tex]r * r[/tex], susitute r for 12 and you will get 144, times 144 by pi and you will get 452.16in

Sorry I could not answer every question but hope this helps!

Answer:

Step-by-step explanation:

43.55 + 18.62 = 62.17

Answer:

Min: 32

Lower Quartile: 36

Median: 42

Upper Quartile: 47

Max: 53

Interquartile: 11

Step-by-step explanation:

The min. is just the lowest number.  The lower quartile is the number in the middle of the numbers below 42, the median is the number in the very middle, the upper quartile is the middle number above 41 and the interquartile is the upper quartile minus the lower quartile.  

x² ( 4x - 3)

Apply the multiplicative law of distribution.

Multiply the monomial

Multiply the monomial

Therefore, the correct option is "C".

The causes of variation that can be identified and eliminated are called; Assignable Causes.

There are two primary causes of variation in the quality of a product or process. These two primary causes are called;

Now, Common causes of variation are defined as random causes that we cannot identify. However, Assignable causes of variation are those that can be identified and eliminated.

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Using Pythagoras theorem, the top of the ladder moving down when the foot of the ladder is 3 feet from the wall is of -0.518 feet/sec.                      

Let distance from the wall to the foot of the ladder is 'x' feet and the height of the top of the ladder is 'y' feet.

Pythagoras theorem, [tex]x^{2} + y^{2} = (12)^{2}[/tex]       --->(1)

Given,[tex]\frac{dx}{dt}= 2feet/second[/tex]   at x=3

Put x=3 in Pythagoras theorem equation (1)

[tex](3)^{2} + y^{2} = 144[/tex]

         [tex]y^{2} = 144 - 9[/tex]

        [tex]y^{2}[/tex]  =  135

        y = 11.61

Derive equation (1) w.r.t to 't'

[tex]2x\frac{dx}{dt} + 2y\frac{dy}{dt} = 0[/tex]                ---->(2)

substitute the value of 'x', 'dx/dt' and 'y' in equation (2), we get the fast of the top of the ladder moving down when the foot of the ladder is 3 feet from the wall

[tex]2(3)(2) + 2 (11.61)\frac{dy}{dt} = 0[/tex]

12 + 23.22 [tex]\frac{dy}{dt}[/tex]  = 0

                  [tex]\frac{dy}{dt}= \frac{-12}{23.22}[/tex]

                  [tex]\frac{dy}{dt} = -0.518[/tex]

Hence,  using Pythagoras theorem the top of the ladder moving down when the foot of the ladder is 3 feet from the wall is of -0.518 feet/sec.  

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Answer:

Step-by-step explanation:

x times 8 +12

8x+x=9x-12

Answer = 9x-12