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Romashka [77]
3 years ago
6

If (a^x a ^y) - a^z = a^m then express m in terms of x, y and z.​

Mathematics
1 answer:
omeli [17]3 years ago
8 0

Answer:

m = x+y-z

Step-by-step explanation:

Given the expression.

(a^x a ^y) ÷ a^z = a^m

We are to express m in terms of x, y and z.

Using the multiplicative law of indices, the expression becomes:

a^{x+y} ÷ a^z = a^m

Applying the division rule in indices

a^{x+y} ÷ a^z = a^{x+y-z}

The equation becomes

a^{x+y-z} = a^m

Cancel out the base and equate the powers as shown:

x+y-z = m

Hence the expression of m in terms of x, y and z is m = x+y-z

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Fed [463]

Here a right angled triangle given. one angle with measure 45^o given. The three sides of the triangle given 4, x, y.

We have to find, the sides which is opposite, adjacent and hypotenuse here.

We know that the side opposite to right angle is always hypotenuse. So, hypotenuyse = y.

The side adjacent to the given angle 45^o is x. So, here adjacent = x.

The opposite side is opposite to the given angle. So, opposite = 4.

Now we will use SOHCAHTOA that is sin(x) =\frac{Opposite}{Hypotenuse} , cos(x) =\frac{Adjacent}{Hypotenuse} , tan(x) =\frac{Opposite}{Adjacent}, where x is the angle given.

To get x, we will use tan. So we will get,

tan(45^o) = \frac{4}{x}

We know the value of tan(45^o) = 1. By substituting the value we will get,

1 =\frac{4}{x}

To find x, we have to move x here to the left side by multiplying it to both sides. We will get,

(1)(x) = (\frac{4}{x}) (x)

x = 4

So we have got the value of x here.

Now to find y, we will use the trigonometric function sine.

sin(45^o) =\frac{4}{y}

we know the value of sin(45^o) =\frac{\sqrt{2}}{2}

By substituting the value we will get,

\frac{\sqrt{2}}{2}  = \frac{4}{y}

By cross multiplying we will get,

(\sqrt{2}) (y) = (4)(2)

\sqrt{2}y = 8

We will get y by dividing both sides by \sqrt{2}, we will get,

\frac{\sqrt{2}y}{\sqrt{2}}   =\frac{8}{\sqrt{2} }

y =\frac{8}{\sqrt{2}  }

Now we will rationalize the denominator by multiplying \sqrt{2} to the top and bottom.

y =\frac{8\sqrt{2}}{(\sqrt{2})(\sqrt{2})}

y =\frac{8\sqrt{2}}{2}

y = 4\sqrt{2}

So we have got the required values of x and y.

8 0
3 years ago
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for solving equations such as this chrome would be the best thing n

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A retailer purchased a camera for rs.1560 and sold it at 5% loss find the loss amount​
zzz [600]

Answer:

Loss is Rs. 78

Step-by-step explanation:

Solution:

Given,

  • Cost Price (CP)= Rs.1560
  • Loss Percent (L%) = 5%

Here,

L%= L/CP ×100%

or,. 5 =L/1560×100

or,. 5×1560/100 =L

or,. L= Rs.78

Therefore, Loss is Rs.78

3 0
2 years ago
1. What is the area of the figure below? (1 point)
maw [93]

Answer: 36in2

Step-by-step explanation:

A= base *height

=12*3

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4 0
3 years ago
According to the University of Nevada Center for Logistics Management, 6% of all mer-
Fudgin [204]

Answer:

a) The point estimate of the proportion of items returned for the population of

sales transactions at the Houston store = 12/80 = 0.15

b) The 95% confidence interval for the proportion of returns at the Houston store = [0.0718 < p < 0.2282].

c) Yes.

We set an hypothesis and construct a test statistics. The test statistics result gives us:

Z calculated  = 2.2545, and this gives us the p-value = 0.0121. We assumed 95% confident interval. Hence, the level of significance (α) = 5%. Conclusively, since the p-value ==> 0.0121 is less than (α) = 5%, the test is significant. Hence, the proportion of returns at the Houston store is significantly different from the returns  for the nation as a whole.

Step-by-step explanation:

a) Point estimate of the proportion = number of returned items/ total items sold = 12/80 = 0.15.

b) By formula of confident interval:

CI(95%) = p ± Z*\sqrt{\frac{p*(1-p)}{n} }  =  0.15 \pm 1.96 *\sqrt{\frac{0.15*(1-0.15)}{80} },

CI(95%) = [0.0718 < p < 0.2282]

c) The hypothesis:

H_{0}: The proportion of returns at the Houston store is not significantly different from the returns  for the nation as a whole.

H_{a}: The proportion of returns at the Houston store is significantly different from the returns  for the nation as a whole.

The test statistics:

Z = \frac{\hat{p} - p_{0}}{\sqrt{\frac{p*(1-p)}{n} }}, where p_{0} is the proportion of nation returns.

Z calculated  = 2.2545, and this gives us the p-value = 0.0121. We assumed 95% confident interval. Hence, the level of significance (α) = 5%. Conclusively, since the p-value ==> 0.0121 is less than (α) = 5%, the test is significant. Hence, the proportion of returns at the Houston store is significantly different from the returns  for the nation as a whole.

6 0
3 years ago
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