what type of transformation is defined by the rule (x,y)→(x + 4, y)?
reflection
a translation
dilation

Answer:

if you are asking for decimal its, 0.625.

otherwise 5/8 is also equal to 10/16, 15/24, etc

Step-by-step explanation:

Answer:

y=7/5x+26/5 and y=-5/7x+66/7

Step-by-step explanation:

if it's parallel, it needs to have the same slope, so the equation is y=7/5x+26/5. the perpendicular line is y=-5/7x+66/7.

Answer:

Step-by-step explanation:

if the speed is 6 bracelets per hour then the table will go like this

2   12

5  30

7  42

11  66

16 and 2/3  hours is 100 bracelets

It is proven that the other nth roots of z can be found by multiplying the initial one by the nth roots of unity.

A complex number satisfying the equation \(z^{n-1} = 0\) is known as the nth root of unity. There are about n nth roots of a unit, according to the fundamental theorem of algebra. We know that,\(1=e^{2\pi i}\). Then, the nth root is written as \(\omega=e^{2\pi i/n}\).

The integer of powers of this root between 0 and n-1 provides the other nth roots. Then, the roots are \(1, \omega, \omega^2 ,\cdots \cdots, \omega^{(n-1)}\). Now, factorize the equation \(z^{(n-1)} = 0\) we get the required identity as, \(z^{(n-1)} = (z- 1)(z^{(n-1)}+ z^{(n-2)} + \cdots \cdots+ z + 1) = 0\).  

This indicates that the equation \(1+\omega+ \omega^2+\cdots \cdots+ \omega^{(n-1)}\) is true for all nth roots of unity other than 1.

Roots of unity also have the great quality of being periodic, which results from the fact that n = 1. It is equal to a power of that power mod n if the power is bigger than n.

When ω is a third root of unity, \(\omega^5 + \omega^4 + 1 = \omega^2 + \omega + 1 = 0\).

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Answer:

We will use a Pythagorean identity and alegbra to prove this.

sin^2 + cos^2 = 1, dividing by cos^2 gives

tan^2 + 1 = sec^2.

Now, breaking down the fraction into parts and simplifying gives:

(1-sin^4)/cos^4 = 1/cos^4 - sin^4/cos^4 = sec^4 - tan^4

Now use difference of squares factoring from alegbra.

= (sec^2 + tan^2)*(sec^2 - tan^2)

By rewriting our Pythagorean identity to

sec^2 - tan^2 = 1 and tan^2 = sec^2 - 1,

we can finish the problem.

= (sec^2 + tan^2) * 1 = sec^2 + tan^2

= sec^2 + (sec^2 - 1) = 2*sec^2 - 1.

Step-by-step explanation: D. 20

If initial sample of 458 grams of a radioactive substance decays according to the function \(A(t)=458e^{-0.038t}\) then the half-life of the substance is 0.

Half-life is the time required for a quantity (of substance) to reduce to half of its initial value.

Given,

An initial sample of 458 grams of a radioactive substance decays according to the function

\(A(t)=458e^{-0.038t}\)

We need to find the half life

\(458=458e^{-0.038t}\)

Divide both sides by 458

\(1=e^{-0.038t}\)

Take log on both sides

\(log1=-0.038t\)

0=-0.038t

t=0

Hence, the half-life of the substance is 0.

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The compound interest rate of the investment is 1.10%

The given parameters about the compound interest are

Principal, P = $11,000

Amount, A = $20,000

Time, t = 9

Number of times, n = 12 i.e. monthly interest

To calculate the amount, we have:

A = P(1 + R/n)^nt

Substitute the known values in the above equation, so, we have the following representation

20000 = 11000 * (1 + r/12)^(12 * 9)

This gives

1.82 = (1 + r/12)^108

Take the 108th root of both sides

1 + r/2 = 1.0055

Subtract 1 from both sides

r/2 = 0.0055

Multiply by 2

r = 0.011

Express as percentage

r = 1.10%

Hence, the value of the interest rate is 1.10%

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Answer:

6.66%

Step-by-step explanation:

Compounded Monthly:

�

=

�

(

1

+

�

�

)

�

�

A=P(1+

n

r

​

)

nt

Compound interest formula

�

=

20000

�

=

11000

�

=

9

�

=

12

A=20000P=11000t=9n=12

Given values

20000

=

20000=

11000

(

1

+

�

12

)

12

(

9

)

11000(1+

12

r

​

)

12(9)

Plug in values

20000

=

20000=

11000

(

1

+

�

12

)

108

11000(1+

12

r

​

)

108

Multiply

20000

11000

=

11000

20000

​

=

11000

(

1

+

�

12

)

108

11000

11000

11000(1+

12

r

​

)

108

​

Divide by 11000

1.8181818

=

1.8181818=

(

1

+

�

12

)

108

(1+

12

r

​

)

108

(

1.8181818

)

1

/

108

=

(1.8181818)

1/108

=

[

(

1

+

�

12

)

108

]

1

/

108

[(1+

12

r

​

)

108

]

1/108

Raise both sides to 1/108 power

1.0055509

=

1.0055509=

1

+

�

12

1+

12

r

​

−

1

−1=

−

1

−1

Subtract 1

0.0055509

=

0.0055509=

�

12

12

r

​

12

(

0.0055509

)

=

12(0.0055509)=

(

�

12

)

12

(

12

r

​

)12

Multiply by 12

0.0666108

=

0.0666108=

�

r

6.66108

%

=

6.66108%=

�

r

Convert to percent (multiply by 100)

�

≈

r≈

6.66

%

6.66%

Round to the nearest hundredth of a percent

Answer:

0.41

Step-by-step explanation:

0.25 0.375 0.5 0.625

Answer:

Since r = 1/2, and the fifth term = 1

1 = A×[(1/2)^(5-1)]

1 = A×[(1/2)^4]

1 = A× (1/16)

Step-by-step explanation:

Answer:

7/12

Step-by-step explanation:

1/4 x 3/3 = 3/12

1/3 x 4/4 = 4/12

3/12 + 4/12 = 7/12

Hope this helped! ;) Have a good day! :)

The 95% confidence interval for the effectiveness of the blood-pressure drug is given as follows:

\(22.6 < \mu < 24.4\)

The mean, the standard deviation and the sample size for this problem, which are the three parameters, are given as follows:

\(\overline{x} = 23.5, \sigma = 12.2, n = 775\)

Looking at the z-table, the critical value for a 95% confidence interval is given as follows:

z = 1.96.

The lower bound of the interval is then given as follows:

\(23.5 - 1.96 \times \frac{12.2}{\sqrt{775}} = 22.6\)

The upper bound of the interval is then given as follows:

\(23.5 + 1.96 \times \frac{12.2}{\sqrt{775}} = 24.4\)

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Answer: \(y=\frac{ln(x)}{ln(10)}\)

Step-by-step explanation:

To find the inverse of the function, you first replace the y with x and x with y. Then you solve for y.

\(y=10^x\)                                [replace y with x and x with y]

\(x=10^y\)                                [find natural log of both sides to get y alone]

\(ln(x)=ln(10)^y\)                    [divide ln(10) on both sides]

\(\frac{ln(x)}{ln(10)} =y\)                              

Now that we have found y after switching y with x and x with y, we know that the inverse is \(y=\frac{ln(x)}{ln(10)}\).

The area of the circle with the given radius is 201.088 square units.

The area of a circle is the space occupied by the circle in a two-dimensional plane. Alternatively, the space occupied within the boundary/circumference of a circle is called the area of the circle. The formula for the area of a circle is A = πr², where r is the radius of the circle.

Given that, the radius of a circle is 8 units.

Here, area of a circle

= 3.142×8²

= 3.142×64

= 201.088 square units

Therefore, the area of the circle is 201.088 square units.

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the discount on the dog food is $0.27, and the discounted price is $1.08.

What is the percentage?

A percentage that represents a tenth of a quantity. One percent, denoted by the symbol 1%, is equal to one-hundredth of something; hence, 100 percent denotes the full thing, and 200 percent designates twice the amount specified. A portion per hundred is what the percentage denotes. The percentage refers to one in a hundred. The % sign is used to denote it.

If the original price of the dog food is $1.35 and it is on sale for 20% off, the discount would be:

Discount = 20% of $1.35

Discount = 0.20 x $1.35

Discount = $0.27

Therefore, the discounted price of the dog food would be:

Discounted price = Original price - Discount

Discounted price = $1.35 - $0.27

Discounted price = $1.08

So the discount on the dog food is $0.27, and the discounted price is $1.08.

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Answer:

\((x-6)^2=-1\)

Step-by-step explanation:

Given equation:

\(-6x^2+64x-222=-8x\)

When completing the square, first move the terms in x to the left and the constant to the right of the equation:

\(\implies -6x^2+64x-222=-8x\)

\(\implies -6x^2+64x-222+222=-8x+222\)

\(\implies -6x^2+64x=-8x+222\)

\(\implies -6x^2+64x+8x=-8x+222+8x\)

\(\implies -6x^2+72x=222\)

Factor out the leading coefficient -6 from the left side, then divide both sides by -6:

\(\implies -6(x^2-12x)=222\)

\(\implies \dfrac{-6(x^2-12x)}{-6}=\dfrac{222}{-6}\)

\(\implies x^2-12x=-37\)

Add the square of half the coefficient of the term in x to both sides, forming a perfect square trinomial on the left side:

\(\implies x^2-12x+\left(\dfrac{-12}{2}\right)^2=-37+\left(\dfrac{-12}{2}\right)^2\)

\(\implies x^2-12x+\left(-6\right)^2=-37+\left(-6\right)^2\)

\(\implies x^2-12x+36=-37+36\)

\(\implies x^2-12x+36=-1\)

Factor the perfect square trinomial on the left side:

\(\implies (x-6)^2=-1\)

To solve:

\(\implies \sqrt{(x-6)^2}=\sqrt{-1}\)

\(\implies x-6=\pm i\)

\(\implies x-6+6=\pm i+6\)

\(\implies x=6 \pm i\)

Therefore, the solutions are:

\(x=6+i, \quad x=6-i\)

Answer:

6/x

Step-by-step explanation:

Let f(x) = z

f(x) = 6x

z = 6x

6z = x

6/x = z

With the help of probability we can say that, DUM={GG,BB,GB,BG).

Probability is the concept that describes the likelihood of an event occurring.

In real life, we frequently have to make predictions about how things will turn out.

We may be aware of the result of an occurrence or not.

When this occurs, we state that there is a possibility that the event will occur.

In general, probability has many excellent applications in games, commerce, and this newly growing area of artificial intelligence

The chance of an event can be calculated using the probability formula by only dividing the favourable number of possibilities by the total number of potential outcomes.

hence, DUM={GG,BB,GB,BG)

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The division is solved this way:

It means that the final answer is:

Step-by-step explanation:

The coordinates are (-2,-2)

I won't be able to answer bcause I don't see any question.....

Answer: 15cm

Step-by-step explanation: If the length of the model on the top is 6 cm, then the length of the model on the bottom must be 15 cm

Answer:

Step-by-step explanation:

To find the limit of (n!)^(1/n) as n approaches infinity, we can use the Stirling's approximation for n!, which is:

n! ≈ (n/e)^n √(2πn)

where e is the mathematical constant e ≈ 2.71828, and π is the mathematical constant pi ≈ 3.14159.

Using this approximation, we can rewrite (n!)^(1/n) as:

(n!)^(1/n) = [(n/e)^n √(2πn)]^(1/n) = (n/e)^(n/n) [√(2πn)]^(1/n)

Taking the limit as n approaches infinity, we have:

lim (n!)^(1/n) = lim (n/e)^(n/n) [√(2πn)]^(1/n)

Using the fact that lim a^(1/n) = 1 as n approaches infinity for any constant a > 0, we can simplify the second term as:

lim [√(2πn)]^(1/n) = 1

For the first term, we can rewrite (n/e)^(n/n) as [1/(e^(1/n))]^n and use the fact that lim a^n = 1 as n approaches infinity for any constant 0 < a < 1. Thus, we have:

lim (n/e)^(n/n) = lim [1/(e^(1/n))]^n = 1

Therefore, combining the two terms, we have:

lim (n!)^(1/n) = lim (n/e)^(n/n) [√(2πn)]^(1/n) = 1 x 1 = 1

Hence, the limit of (n!)^(1/n) as n approaches infinity is 1.

Answer:1

Step-by-step explanation:

Answer:

=$114.750

Length of new board cast tower=4.5 Inches

Cost of construction(per inch)=$25.50

To find cost=?

                 =25.50x4.5

                 =$114.750

                      ...................................................................................

The required cost of the construction of a 4.5-inch tower is $114.75.

Given that,
A ratio station collects donations for a new board cast tower. The cost of construction is $25.50 per inch, how much it cost to fund 4.5 inches of the construction is to be determined.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,
The cost of construction is $25.50 per inch.
The cost of 4.5 inches of construction = 25.50 × 4.5 = $114.75.

Thus, the required cost of the construction of a 4.5-inch tower is $114.75.

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The correct option for the function in this problem is:

D- An exponential function is appropriate to model this scenario because, at the end of each year after purchase, the value of the equipment was 0.9 times its value 1 year before.

A decaying exponential function is modeled by:

\(A(t) = A(0)(1 - r)^t\)

In which:

For this problem, during each 1 -year period after the equipment was purchased, the value of the equipment at the end of the period was 10% less than its value at the beginning of the period, hence r = 0.1 and the equation is:

\(A(t) = A(0)(1 - 0.1)^t\)

\(A(t) = A(0)(0.9)^t\)

Which means that option D is correct.

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When P and Q are combined, they will be completely contained in the plane if P and Q are already inside the plane. PQ would therefore be totally in the aircraft.

A plane may contain a number of points. A plane is carrying P and Q. A two-dimensional figure that never ends, the plane. It implies that there is no end. It has a level surface. If we draw a line to join the two points P and Q, the line will also be in the same plane. since the plane never comes to an end.

Collinear points are a group of points that all lie on the same line.The right response to this question is that a segment is a finite portion of a line connecting two locations, including its two ends.Coplanar points are groups of at least four points that all lie on the same plane. Keep in mind that given any two points, they are always coplanar, as are given any three points.

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Step-by-step explanation:

sin Φ  = 5/6 = .8333

Arcsin ( sin Φ) =  arcsin (.8333)

Φ = 56.4 degrees

Answer:

Answer down below

Step-by-step explanation:

h (3x-4)

= \(\frac{1}{3x-4+2}\)

= \(\frac{1}{3x-2}\)

Answer: Part A: 1/26 or 0.38

Part B: 1/59 or 0.017

Step-by-step explanation: