3. Given that (5,12, 13) is a Pythagorean triple, which of the following isn't a Pythagorcan
triple?
(1) (10, 24, 26)
(3) (50,120,130)
(2) (10, 17, 18)
(4) (15, 36, 39)

Given:

The parent function is [tex]f(x)=x^2[/tex]

We need to determine the function g(x) created from the function f(x) by moving the graph left 9 units, vertically stretching it by a factor of 4, and shifting the graph up 5 units.

Shift left 9 units:

The rule to shift the graph c units to the left is given by

[tex]y=f(x+c)[/tex]

where c is the positive real number.

Hence, to shift the graph 9 units to the left is given by

[tex]f(x)=(x+9)^2[/tex]

Vertical stretch by a factor of 4:

The rule to stretch the graph vertically by a factor of c is given by

[tex]y=cf(x)[/tex]

where [tex]c>1[/tex]

Hence, to stretch the graph vertically by a factor of 4, we have;

[tex]f(x)=4(x+9)^2[/tex]

Shifting 5 units up:

The rule to shift the graph c units upward is given by

[tex]y=f(x)+c[/tex]

where c is the positive real number.

Hence, to shift the graph 5 units upward is given by

[tex]f(x)=4(x+9)^2+5[/tex]

Therefore, the function [tex]g(x)=4(x+9)^2+5[/tex] is created from the graph [tex]f(x)=x^2[/tex] by moving the graph left 9 units, vertically stretching it by a factor of 4 and shifting up 5 units.

Hence, the graph g(x) is [tex]g(x)=4(x+9)^2+5[/tex]

The function g(x) created from f(x) = x^2 by moving the graph left 9 units, vertically stretching it by a factor of 4, and shifting the graph up 5 units is g(x) = 4*(x+9)^2 + 5.

To generate the function g(x) from f(x) = x^2, you will perform several transformations on it:

So, after performing these transformations to f(x) = x^2, you get the function g(x) = 4*(x+9)^2 + 5.

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Answer:

34.54 inches.

Step-by-step explanation:

The formula for the circumference of the circle is given as [tex]C=\pi d[/tex], where [tex]\pi[/tex] is rounded to 3.14 and d is the diameter of the circle, 11 inches. Simply plug these values into the equation for the circumference to get your answer:

[tex]C=\pi d\\C=(3.14)*(11)[/tex]

C = 34.54 inches

Answer:

34.54 inches

Step-by-step explanation:

C=πd

d=11

C = 11 * 3.14

C = 34.54 inches

"more" means added to, or addition. So 8 more than 'x' is:

x + 8

Answer:

2 x minus 3 y = 12

Negative 4 (2 x minus 3 y) = negative 4 (12)

Step-by-step explanation:

y = two-thirds x minus 4

y = (⅔)x - 4

Multiply the entire equation by 3

3y = 2x - 12

2x - 3y = 12

Multiply both sides by -4

-4(2x - 3y) = -4(12)

Answer:

b

Step-by-step explanation:

The calculation of the circumference of a circle with a radius of 32 inches, using 3.14 for PI, gives a result of 201.0 inches.

The subject of this question involves calculating the circumference of a circle. The formula used to find the circumference of a circle is 2πr, where r is the radius of the circle. Here, π is approximated to 3.14 as given in the question, and the radius r is given as 32 inches.

Substituting the given values into the formula, we get circumference = 2 * 3.14 * 32 = 200.96 inches. Thus, the circumference of the circle to the nearest tenth is "201.0 inches."

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Answer:

24

Step-by-step explanation:

The difference in the number of their marbles is 28 Buah.

The ratio of Faiz's marbles to Bayu's marbles is given as 4:11. If the total number of marbles they have is 60, you can find the number of marbles each of them has.

Let x be the common multiplier for both parts of the ratio. Then, Faiz has  4x marbles, and Bayu has 11x marbles.

The total number of marbles is the sum of their marbles:

4x + 11x = 60

Combine like terms:

15x = 60

Divide by 15 to find x :

x = 4

Now, substitute x back into the expressions for Faiz and Bayu's marbles:

- Faiz's marbles: [tex]\( 4x = 4 \times 4 = 16 \)[/tex]

- Bayu's marbles: [tex]\( 11x = 11 \times 4 = 44 \)[/tex]

The difference in the number of their marbles is [tex]\( 44 - 16 = 28 \)[/tex].

So, the correct answer is: C. 28 Buah

Complete question:

Perbandingan kelereng Faiz dan Bayu 4:11. Their total color is 60. The best color of them is ...

16 pieces

24 pieces

28 pieces

44 pieces

Answer:

The exponential form is 49 to the power of one-half equals 7 ⇒ 4th answer

Step-by-step explanation:

The exponential equation of  [tex]log_{b}(m)=n[/tex]  is [tex]b^{n}=m[/tex] , where b is the base, n is the exponent of b and m is the value of [tex]b^{n}[/tex]

Ex: If  [tex]log_{3}(81)=4[/tex] , that means b = 3 , n = 4 and m = 81, then its exponential form is [tex]3^{4}=81[/tex]

Now let us solve the question

∵ The equation is  [tex]log_{49}(7)=\frac{1}{2}[/tex]

∴ The base is 49

∴ The exponent is [tex]\frac{1}{2}[/tex]

∴ The answer is 7

- Substitute them in the form of the exponential form

∴ The exponential form is [tex](49)^{\frac{1}{2}}=7[/tex]

The exponential form is 49 to the power of one-half equals 7

The given equation is log49(7) = 1/2. To convert it to exponential form, we can write it as 49^(1/2) = 7.

The given equation is:

log49(7) = 1/2

To convert this equation to exponential form, we need to remember that logarithms and exponentials are inverse functions. Therefore, we can write the equation as:

491/2 = 7

Hence, the exponential form of the given equation is 49 raised to the power of 1/2 equals 7.

Answer: False

Step-by-step explanation:

Answer:

the third answer is right

Step-by-step explanation:

its a rhombus because the 4 sides are of equal length and the opposite sides are parallel but there are no right angles.

Answer:

a = 15.59   c= 31.18

27 tan 30 = a

c cos 30 = 27

c = 27/cos30

c = 31.18

Answer:

Nitrogen 7  = 1     ---- Most Basic

Nitrogen 1 =  2    

Nitrogen 3 =  3    ------ Least Basic

Step-by-step explanation:

The basicity of amino acids is as a result f the unshared pair of electrons in the Nitrogen atoms.

Part of the rule of basicity of organic compounds(amino acids) posits that:

The more  unstable an electron pair is, the more basic it is.

From the diagram attached below;

Nitrogen 7 posses and unstable electron due to the lone pair of electron in the NH₃⁺ which renders it most basic .

Nitrogen 1 and 3 are in ring form thereby they are less basic But nitrogen 1 is  more basic compared to nitrogen 3 because lone pair on Nitrogen 1 is not involved in resonance unlike Nitrogen 3 that is  resonance stabilized (i.e alternating by a resonance effect).

Another phenomenon to deduce the basicity of Histidine is the effect of hybridization.

Basicity of Organic Compounds increases with decreasing s character.

Therefore, the trend of basicity is as follows: sp³ > sp² > sp

Because in sp; the lone pairs are most stable, hence least basic

And in sp³; the lone pairs are least stable; hence most basic.

Therefore; From the diagram attached below:

Nitrogen 7  = 1     ---- Most Basic

Nitrogen 1 =  2    

Nitrogen 3 =  3    ------ Least Basic

Answer:

Median and Interquartile range (IQR)

Step-by-step explanation:

I did it :)

Answer:

[tex]n > -4[/tex]

Step-by-step explanation:

Step 1:  Convert into an expression

Twice a number minus 4 is less than three times the number

   [tex]2n - 4 < 3n[/tex]

Step 2:  Solve for the number

[tex]2n - 4 - 2n < 3n - 2n[/tex]

[tex]-4 < n[/tex]

Answer:  [tex]n > -4[/tex]

Answer:

30 minutes

Step-by-step explanation:

Just look at the minutes only. Since you need 4 o'clock to 4:30, its only 30 minutes.

Answer:

30 minutes

Step-by-step explanation:

All you have to do is subtract 4:30 and 4:00 and get 30 minutes.

Answer:

d > - 7

Step-by-step explanation:

John is to have more then -7 dollars in his account by the end of this month.

Now,  the variable d is the number of dollars in John's bank account at the end of the month.

Therefore, the inequality in terms of d that is true only if John meets his monthly goal will be

d > - 7 (Answer)

Answer:

cot θ = 24/7

Step-by-step explanation:

This will be difficult to explain without a diagram, but let's proceed.

Since sec θ = 25/24 (secant θ is equal to hypotenuse/adjacent) the hypotenuse of the triangle is 25 and the side adjacent to θ will be equal to 24. To find the opposite side-length you can use the Pythagorean theorem.

25^2 = 24^2 + a^2    (You can use either a or b as the variable)

625 = 576 + a^2    (Subtract 576 from each side)

a^2 = 49

a = 7    (The sqrt of 49 is 7    |    This is the side-length of the opposite side relative to θ)

Since cotangent is always adjacent/opposite:

cot θ = 24/7

Answer:

a) 7.54189*10^-8

b) 0.99999999

c) E ( X ) = 0.39 , s ( X ) = 0.604

Step-by-step explanation:

Solution:-

- We will assume the proportion of people with A- blood group is independent and remains constant for a fairly small sample of n = 6 Americans selected at random.

- We will denote a random variable X = The number of americans out of 6 that have blood group type A-.

- The random variable is assumed to follow binomial distribution.

- The probability of success is the proportion of people in U.S that have blood group type A-, p = 0.065:

                        X ~ Bin ( 6 , 0.065 )

Where, r represents the number of americans out of selected 6 have blood group A-. The pmf of a binomial variate is given as:

                       P ( X = r ) = nCr * ( p ) ^r * ( 1 - p ) ^ ( n - r )

a) Find the probability that all 6 are type A-

- We will pmf given above and set r = 6. And evaluate the resulting probability:

                     P ( X = 6 ) = 6C6 * ( p )^6 * ( 1  - p ) ^ ( 0 )

                                      = p^6

                                      = ( 0.065 )^6  

                                      = 7.54189*10^-8

b) Find the probability that at most 4 of them are type A-

- We will pmf given above and evaluate the following expression:

                     P ( X ≤ 4 ) = 1 - P ( X = 5 ) - P ( X = 6 )

                     P ( X ≤ 4 ) = 1 - 6C5 * ( p )^5 * ( 1  - p ) ^ ( 1 ) - p^6

                                      = 1 - 6*(0.065)^5 ( 0.935 ) - 0.065^6

                                      = 1 - 6.50923*10^-8 - 7.54189*10^-8        

                                      = 0.99999999          

c) Find the mean and standard deviation.

- The mean E ( X ) of the defined random variable distributed binomially is given by:

                     E ( X ) = n*p = 6*0.065 = 0.39 people

- The mean s( X ) of the defined random variable distributed binomially is given by:

                    s ( X ) = √n*p*q = √(6*0.065*0.935) = 0.604

Answer: 9 miles

Step-by-step explanation: 6 divided by 2 is 3 and 3 times 3 is 9.

Answer:

18

Step-by-step explanation:

3/4 divided by 1/4 equals 3

3 times 6 equals 18

Answer:

Zero

Step-by-step explanation:

There is no solution to this.

Answer:

$67

Step-by-step explanation:

There are 23 thousand clicks, so as it pays per thousand you need to divide $1 540 by 23, which results in 66.9.... reacurring which when rounded is (a) for $67.

Let's evaluate explicitly [tex]f(x+k)[/tex]:

[tex]f(x)=2x+4\iff f(x+k)=2(x+k)+4=2x+2k+4[/tex]

If this must equal [tex]2x+22[/tex], we have

[tex]2x+2k+4=2x+22 \iff 2k+4=22 \iff 2k=18 \iff k=9[/tex]

Answer:

For what values of does the equation (2 + 1)^2 + 2 = 10 − 6 have two real and equal roots?

Step-by-step explanation:

For what values of does the equation (2 + 1)^2 + 2 = 10 − 6 have two real and equal roots?

Answer:

I agree with Jose that the sum of the probability that a randomly selected pen will not be black and the probability that the pen will not be red is 1.

Step-by-step explanation:

If we sum the probability of not black and probability of not red, we will get 1.

The probability of not black means probability of red i.e 50/450

The probability of not red means probability of black i.e 400/450.

When we add the probability, we get 1.

50/450 + 400/450 = 450/450 = 1

Invariably, the statement is same as finding probability of black and probability of red; just that the value are interchanged.

Answer:

  47 seconds

Step-by-step explanation:

It takes 37 seconds to scan 37 items at the rate of 1 second per item. It takes an additional 10 seconds to process the payment. Then the total time is ...

  37 +10 = 47 . . . seconds

Answer:

32.55 cm  

Step-by-step explanation:

         Let x = the length of wire that becomes a circle.

Then 74 - x = the length of wire that becomes a square

Circumference of circle + perimeter of square = 74

1. Expression for the side of the square

P = 4s = 74 - x

s = ¼(74 - x)

2. Expression for the radius of the circle

C = 2πr = x

r = x/(2π)

3. Expression for the total area

[tex]\begin{array}{rcl}\text{Total area} & = &\text{area of circle+ area of square}\\A & = & \pi r^{2} + s^{2}\\& = &\pi \left(\dfrac{x}{2 \pi}\right)^{2} + \left (\dfrac{1}{4}(74 - x)\right)^{2}\\\\ & = & \dfrac{x^{2}}{4 \pi} + \dfrac{1}{16}(5476 - 148x + x^{2})\\\\ & = & 0.07958x^{2} + 342.25 - 9.25x + 0.0625x^{2}\\A & = & 0.1421x^{2} -9.25x + 342.25 \\ \end{array}[/tex]

This is the equation of a parabola.

In standard form,

ƒ(x) = 0.1421x² -9.25x + 342.24

a = 0.1421; b = -9.25; c = 342.24  

The parabola opens upwards, because a > 0. Therefore, the vertex is a minimum.

The vertex of a parabola occurs at

x = -b/(2a) = 9.25/(2 × 0.1421) = 9.25/(0.2842) = 32.55

The circumference of the circle is 32.55 cm.

The graph below shows that the area of the circle is a minimum when x = 32.55 cm

Answer: the population of the culture 6 days after inoculation is 2313.

Step-by-step explanation:

The growth rate is exponential. We would apply the formula for exponential growth which is expressed as

y = b(1 + r)^ t

Where

y represents the population after t days.

t represents the number of days.

b represents the initial population.

r represents rate of growth.

From the information given,

b = 1000

r = 15% = 15/100 = 0.15

t = 6 days

Therefore

y = 1000(1 + 0.15)^6

y = 1000(1.15)^6

y = 2313

Answer:

She forgot to find the y intercept add it in the equation

y = .5x-6

Step-by-step explanation:

First we need to find the slope

m = (y2-y1)/(x2-x1)

   = (-5 - -7.5)/ (2 - -3)

   =(-5 +7.5)/( 2+3)

   = 2.5/5

   = 1/2

Substitute into the slope intercept form of the equation

y= mx+b

y= .5x +b

We need to determine b by substituting a point into the equation

-5 = .5(2) +b

-5 = 1+b

Subtract 1 from each side

-5-1 = 1-1+b

-6 = b

y = .5x-6

Answer:

She forgot the y-intercept

y = 0.5x - 6

Step-by-step explanation:

y = 0.5x + c

-5 = 0.5(2) + c

c = -6

Correct equation:

y = 0.5x - 6

Answer:

26 °, 51 °, 103 °

Step-by-step explanation:

-A triangle is a 3-sided regular polygon.

-The sum of it's interior angles add up to 180°.

-Only the 26 °, 51 °, 103 ° set add exactly up to 180° and therefore satisfies the triangle's interior angles condition.

Answer:

The answer A trust me

Step-by-step explanation:

Answer:

b 25

Step-by-step explanation:

Answer:

A)-5 if its without parenthasis around 5+ 3

Step-by-step explanation

2 minus 3 is -1 and -1 times 5 is -5