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DanielleElmas [232]
3 years ago
7

Please solve this question fast.

Mathematics
1 answer:
Alexxandr [17]3 years ago
3 0

Answer:

See Explanation

Step-by-step explanation:

{a} =  {6}^{x},  \:  \: b = {6}^{y}  ...(given) \\  {a}^{y}. {b}^{x}  = 36..(1) \\ pluggig \: the \: values \: of \: a \: and \: b \: in \: (1) \\  ({6}^{x}) ^{y} . ({6}^{y}) ^{x} =  {6}^{2}  \\ {6}^{xy}.{6}^{xy} =  {6}^{2}  \\  {6}^{xy + xy}  =  {6}^{2}  \\  {6}^{2xy}  =  {6}^{2}  \\ bases \: are \: equal \: so \: exponentes \: will \: also \: be\\ \: equal \\  \therefore \: 2xy = 2 \\ xy =  \frac{2}{2}  \\ \huge \red { \boxed{ xy = 1}} \\ hence \: proved \\

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What is the range of the function y=e^4x?<br><br> y&lt;0<br> y&gt;0<br> y&lt;4<br> y&gt;4
Oliga [24]

We have been given the function y=e^{4x}

We know that the range is set of y values for which the function is defined. Therefore, we will find the value for x and then observe the restriction is y's values.

y=e^{4x}\\\ln y = \ln (e^{4x})\\\ln y =4x\\x=\frac{1}{4}\ln y

Now, we know that logarithm function is not defined for negative values. Hence, the value for y is always greater than zero.

Therefore, the range of the function is given by y>0

B is the correct option.

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3 years ago
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4a-b<br> Evaluate the expression when a=5 and b=-7
stepladder [879]

Answer:

27

Step-by-step explanation:

So first we need to plug in 5 as the variable a and -7 as the variable b

4(5)-(-7)

Next we multiply the 4 and the 5 together to get 20

4(5) = 20   or    4 x 5 = 20

20-(-7)

Now we subtract negative 7 from 20

20-(-7) = 27

This can also be written as 20 plus 7 as a mathematical rule states: two negatives make a positive. So:

20-(-7) = 20 + 7

Both of these are equivalent in every sense of the word and give us our final answer of 27

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A prism with a triangular base has a volume of 432 cubic feet. The height of the prism is 8
Rashid [163]

Answer:

9 feet

Step-by-step explanation:

Given:

A prism with a triangular base has a volume of 432 cubic feet.

The height of the prism is 8.

The triangle base has a base of 12 feet.

Question asked:

The height of the triangular base of the prism = ?

solution:

Volume of  triangular prism = Area of triangle \times height

432 = Area of triangle \times8

Dividing both side by 8

54 = Area of triangle

54 =  \frac{1}{2} \times base \times height

54 = \frac{1}{2} \times12\times height\\54 = \frac{12}{2} \times height

Multiplying both side by 2

108 = 12 \times height

Dividing both side by 12

9 = height

Thus, height of the triangular base of the prism is 9

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Find the value of x and then the measure of Arc XYZ and Arc XZ. Show work on a piece of paper.
Westkost [7]

<u>Given</u>:

The measure of arc XY is (31x)°

The measure of arc YZ is (35x - 16)°

We need to determine the value of x, measure of arc XYZ and arc XZ.

<u>Value of x:</u>

From the figure, it is obvious that the arcs XY and YZ are congruent.

Thus, we have;

31x=35x-16

Subtracting both sides by 35x, we have;

-4x=-16

   x=4

Thus, the value of x is 4.

<u>Measure of arc XYZ:</u>

The measure of arc XYZ is given by

m \widehat{XYZ}=m \widehat{XY}+m \widehat{YZ}

The measure of arc XY is given by

m \widehat{X Y}=31(4)=124^{\circ}

The measure of arc YZ is given by

m \widehat{Y Z}=35(4)-16=124^{\circ}

Hence, the measure of arc XYZ is given by

m \widehat{XYZ}=124^{\circ}+124^{\circ}=248^{\circ}

Therefore, the measure of arc XYZ is 248°

<u>Measure of arc XZ:</u>

The measure of arc XZ is given by

m \widehat{XZ}=360^{\circ}-m \widehat{XYZ}

Substituting the values, we have;

m \widehat{XZ}=360^{\circ}-248^{\circ}

m \widehat{XZ}=112^{\circ}

Thus, the measure of arc XZ is 112°

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3 years ago
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