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2 years ago

Find an equation for the graph

Mathematics

1 answer:

Elanso [62]2 years ago

6 0

Answer:

y=6^x+0.612 - 4

Step-by-step explanation:

x = -4 ---> horizontal asymptote

m = 6 ---> use points (0, -1) and (1, 5)

Parent function of the graph: $y=b^x$

Our equation: $y=6^x$

Add alterations:

Reflections = N/A
Vertical & horizontal shifts = down 4
Vertical & horizontal stretches = left approx 0.612

Final equation: y=6^x+0.612 - 4

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Applying Properties of Exponents In Exercise,use the properties of exponents to simplify the expression.

Mkey [24]

Answer:

$1.~e^{-2} \\2.~e^{\frac{7}{2}}\\3.~e^8\\4.~e^{\frac{-11}{2}}$

Step-by-step explanation:

We have to simplify the given exponential exponents.

Exponential Properties:

$e^0 =1\\e^a.e^b = e^{a+b}\\\\\displaystyle\frac{e^a}{e^b} = e^{a-b}\\\\(e^a)^b = e^{ab}\\\\e^{-a} = \frac{1}{e^a}$

Simplification takes place in the following manner:

$(e^{-3})^\frac{2}{3}\\(e^a)^b = e^{ab}\\=e^{-3\times \frac{2}{3}}\\=e^{-2}$

$(e^4)(e^{\frac{-1}{2}})\\e^a.e^b = e^{a+b}\\=e^{(4+\frac{-1}{2})} \\= e^{\frac{7}{2}}$

$(e^{-2})^{-4}\\(e^a)^b = e^{ab}\\= e^{-2\times -4}\\=e^8$

$(e^{-4})(e^{\frac{-3}{2}})\\e^a.e^b = e^{a+b}\\=e^{(-4+\frac{-3}{2})} \\= e^{\frac{-11}{2}}$

4 0

3 years ago

If 27y is a multiple of 9 where y is a digit . What is the minimum value of Y.

stiv31 [10]

<h3>Answer: 0</h3>

Explanation:

The single digits are {0,1,2,3,4,5,6,7,8,9}

So naturally 0 is the first thing to test.

The number 270 is a multiple of 9 because 9*30 = 270. The digits of 270 add to 2+7+0 = 9 showing that it's a multiple of 9. Refer to the "divisibility by 9 rule".

The next possible value of y will be 9 units higher than y = 0, so we go for y = 9. Meaning that 279 is also a multiple of 9 (because 2+7+9 = 18 is a multiple of 9).

4 0

2 years ago

Find formula of s in terms of a, b, cos(x)

Alecsey [184]

Answer:

$\displaystyle s = \frac{2ab\cos x}{a+b}$

Step-by-step explanation:

We want to find a formula for s in terms of a, b, and cos(x).

Let the point where s intersects AB be D.

Notice that s bisects ∠C. Then by the Angle Bisector Theorem:

$\displaystyle \frac{a}{BD} = \frac{b}{AD}$

We can find BD using the Law of Cosines:

$\displaystyle BD^2 = a^2 + s^2 - 2as \cos x$

Likewise:

$\displaystyle AD^2 = b^2+ s^2 - 2bs \cos x$

From the first equation, cross-multiply:

$bBD = a AD$

And square both sides:

$b^2 BD^2 =a^2 AD^2$

Substitute:

$\displaystyle b^2 \left(a^2 + s^2 - 2as \cos x\right) = a^2 \left(b^2 + s^2 - 2bs \cos x\right)$

Distribute:

$a^2b^2 + b^2s^2 - 2ab^2 s\cos x = a^2b^2 + a^2s^2 - 2a^2 bs\cos x$

Simplify:

$b^2 s^2 - 2ab^2 s \cos x = a^2 s^2 - 2a^2 b s \cos x$

Divide both sides by s (s ≠ 0):

$b^2 s -2ab^2 \cos x = a^2 s - 2a^2 b \cos x$

Isolate s:

$b^2 s - a^2s = -2a^2 b \cos x + 2ab^2 \cos x$

Factor:

$\displaystyle s (b^2 - a^2) = 2ab^2 \cos x - 2a^2 b \cos x$

Therefore:

$\displaystyle s = \frac{2ab^2 \cos x - 2a^2 b \cos x}{b^2- a^2}$

Factor:

$\displaystyle s = \frac{2ab\cos x(b - a)}{(b-a)(b+a)}$

Simplify. Therefore:

$\displaystyle s = \frac{2ab\cos x}{a+b}$

5 0

3 years ago

If A and B are two independent events with P(A)=2÷3 and P(B) =1÷5, find P(AUB).

iren [92.7K]

Answer:

$for \: independent \: events : \\ P(AUB) = P(A) + P(B) \\ P(AUB) = \frac{2}{3} + \frac{1}{5} \\ = \frac{13}{15}$

Step-by-step explanation:

P(AUB) is P(A) + P(B) because P(AnB) is zero.

$P(AUB) = P(A) + P(B) - P(A{ \huge{n} }B) \\ P(AUB) = P(A) + P(B) + 0$

3 0

3 years ago

13. What does a correlation coefficient of r = - 0.97 generally imply about the graph of a data set? *

White raven [17]

The answer is B. The closer the r value is to 1 or -1, the better the fit is. If the r value is negative, the slope is negative. If the r value is positive, the slope is positive.

8 0

3 years ago