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3 years ago

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? y<0 y>0 y<4 y>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

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3 years ago

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4a-b Evaluate the expression when a=5 and b=-7

stepladder [879]

Answer:

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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3 years ago

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3 years ago

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

Westkost [7]

Given:

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.

Value of x:

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.

Measure of arc XYZ:

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°

Measure of arc XZ:

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