Find the value of x in 4^x+64^x= 272

The derivative of the natural log function y = e^(-1/x^2) is

The given function is

y = e^(-1/x^2)

The given function is rearranged as

y = e^(-1/x^2) = e^u such that u = (-1/x^2)

Applying chain rule

y = e^u

y' with respect to u = e^u

u = (-1/x^2) = -x^(-2)

u' with respect to x = 2x^(-3)

(y' with respect to u) *  (u' with respect to x)

= e^u * 2x^(-3)

plugging in the value of u

=  e^(-1/x^2) * 2x^(-3)

= 2x^(-3)e^(-1/x^2)

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Answer:

d = -5

Step-by-step explanation:

[tex]\frac{4}{5}d + 3 = -2 -\frac{1}{5}d\\ \\ \frac{4}{5}d + \frac{1}{5} d = -3 -2\\\\\frac{4+1}{5}d = -5\\\\ \frac{5}{5} d = -5\\\\d = -5[/tex]

Check:

[tex](\frac{4}{5} )(-5) + 3 = (-2) - (\frac{1}{5})(-5)\\\\(\frac{-20}{5} ) + 3 = -2 - (\frac{-5}{5} ) \\\\-4 + 3 = -2 + 1\ = -1[/tex]

y + 2 = 5/2 (x - 6) ; 5x-2y=34 ; y=5/2x-17 is the equations of the line that goes through the point (6,-2) and is perpendicular to the line y+2=-2/5(x-10), Hence the correct options are B, C and F.

The standard forms of the equation of a line are:

Slope-intercept form:

y = mx + c

Where m indicates the slope of the line and c is the y-intercept

Intercept form:

x/a + y/b = 1

General form of the equation of the straight line, i.e. Ax+By+C = 0

x/(-C/A) + y/(-C/B) = 1

where a = -C/A and b = – C/B

Normal form:

The equation of the line whose length of the normal from the origin is p and the angle made by the normal with the positive x-axis is given by α is given by:

x cos α+y sin α = p

Given,

Point = (6,-2) = (x2,y2)

Equation of line = y+2=-2/5(x-10)

General equation of the line = y - y1 = m ( x-x1 )

After comparing we get,

Slope of the given line = -2/5

As we know both the lines are perpendicular to each other so, product of their slopes must be equal to -1.

m1 × m2 = -1

-2/5 × m2 = -1

We get m2 = 5/2

So the equation of the line having slope  5/2 and passing through  (6,-2) is:

y - y2 = m2 ( x-x2 )

y -(-2) = 5/2 (x - 6)

y + 2 = 5/2 (x - 6)

Hence, we get equation of the line as y + 2 = 5/2 (x - 6) .

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Answer: 19.2, 1.7, 15.93, 0.0512

Step-by-step explanation:

We can multiply these straight across but the trick with decimals is that your answer needs to have the same decimal place distance as what you are multiplying. In the first question, we go one decimal place. In the second, we go two decimal places. In the fourth, we go four decimal places.

Answer: x = 0, 8, -5

Step-by-step explanation:

We are trying to solve what value we substitute x into to get the value of 0. We have x outside of (x² - 3x - 40), and we can set that equal to 0. That will be one value of x because we are still left with (x² - 3x - 40). To solve this, we can factor it out into (x-8)(x+5). Set each equal to 0, (x-8) = 0 which leaves us with x = 8, and (x+5) =0, which leaves us with x = -5.

Answer:

30 divided by 0.08 will get you 375

Step-by-step explanation:

Diving the polynomial expression f(m) = 8m^3 + 5m^2 - 32m - 20 and g(m)  = 8m + 5, as (f/g)(m) using long division gives m^2 - 4

Long division refers to a way of dividing large numbers including polynomials

performing the long division  (f/g)(m) gives

divisor               8m + 5

dividend            8m^3 + 5m^2 - 32m - 20                      

quotient            m^2

multiplication (quotient and divisor) = 8m^3 + 5m^2

subtraction (dividend - result of multiplication) =  - 32m - 20                       new dividend =  - 32m - 20

divisor               8m + 5

dividend           - 32m - 20                    

quotient            -4

multiplication (quotient and divisor) = - 32m - 20    

subtraction (dividend - result of multiplication) =  0               

new dividend = 0

The quotient is then added as

m^2 - 4

The second option is the correct option

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The experimental probability of choosing a blue golf ball based on Lorena's trials is 0.75.

Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true

In this case, Lorena chooses a golf ball from the bucket at random 4 times and 3 times, he picked blue balls.

The probability of picking a blue ball will be:

= Number of times a blue ball was picked / Total number of trials

= 3/4

= 0.75

The probability is 0.75.

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Answer:

60%

Step-by-step explanation:

i actually hope this helps!

answer the answer is 200

Step-by-step explanation:

490-290

Answer:

b=(cd-ax)/y

Step-by-step explanation:

b=(cd-ax)/y

In given word problem ,

a) 2040  more kilojoules of energy would you use in an hour of jogging than an hour of swimming .

b)  45 minutes 2 seconds of walking would you have to do to burn up the 1,130 kilojoules in a candy bar.

What is word problem ?

   Our extensive collection of math word problems ranges from addition, subtraction, multiplication, and division to more specialised operations. Mathematical questions that are written as one or more sentences and ask students to use their mathematical understanding to solve problems from "real-life" situations are known as word problems. As a result, for kids to understand the word problem, they need to be familiar with the terminology that goes along with the mathematical symbols that they are already used to.

Here the given ,

=> 1 minute walking = 25 kilojoules

=> 1 minute jogging = 84 kilojoules

=> 1 minute swimming = 50 kilojoules.

a) 1 hour = 60 minutes.

1 hour jogging = 60*84 = 5040 kilojoules.

1 hour swimming = 60*50 = 3000

Then , => 5040-3000=2040 kilojoules.

Therefore 2040  more kilojoules of energy would you use in an hour of jogging than an hour of swimming .

b) x minute of walking = 1130 kilojoules.

=> 25*x=1130

=> x = 1130/25 = 45minutes 2 seconds.

Therefore 45 minutes 2 seconds of walking would you have to

do to burn up the 1,130 kilojoules in a candy bar.

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The required sum of the first twenty terms of the series ∑n=1log 5r are in AP will be 32.37.

There are four basic properties of logarithms:

logₐ(xy) = logₐx + logₐy.

logₐ(x/y) = logₐx - logₐy.

logₐ(xⁿ) = n logₐx.

logₐx = logₓa / logₓb.

We have been given that the terms of the series ∑n=1log 5r are in AP.

As per the given question,

∑n(log(5r)) = log(5·1)+log(5·2)+log(5·3)+...+log(5·n)

n = 20

∑log(5r) = log(5·1)+log(5·2)+log(5·3)+...+log(5·20)

Using the property of logarithmic logₐ(xy) = logₐx + logₐy,

∑log(5r) = (log(5)+log(1)) + (log(5)+ log(2))+(10g(5)+Log(3))+ ...(10g(5)+Log(20))

∑log(5r) = (log(5)+log(5)+log(5)+...+log(5)

∑log(5r) = 20·1og(5)+((log(1)+log(2)+log(3)+...+log(20)

Using property of logarithmic logₐ(xy) = logₐx + logₐy,

∑log(Sr)=20·1og(5)+log(1×2×3×...20)

∑log(5r) = 20-log(5)+log(201)

∑log(5r) = 32.365524703598

Rounded to the nearest hundredth decimal,

∑log(5r) = 32.37

Thus, the required sum of the first twenty terms of the series ∑n=1log 5r in AP will be 32.37.

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Answer:

D

Step-by-step explanation:

supplementary angles sum to 180° , that is

∠ 1 + ∠ 2 = 180°

67° + ∠ 2 = 180° ( subtract 67° from both sides )

∠ 2 = 113°

Omar deposited d dollars into a savings account y years ago. ... following expressions could be used to determine the zeros of the function f (x) when f (x).

Step-by-step explanation:

The image point of the point (-3, -2) after the transformation r x-axis R 270° is; (3, -2).

It follows from the task content that the image point of the pair of coordinates given is to be determined.

Given point is; (-3, -2).

Hence, after a reflection over the x-axis; we have; (-3, 2).

Also, after a rotation of 270°, it follows that we have; (x, y) ==> (-x, -y).

Therefore, the image point is; (-(-3), -(2)).

The image point is therefore; (3, -2).

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Answer:

70

Step-by-step explanation:

If lines l and m are parallel, then using the corresponding angles theorem, the angle that forms a linear pair with angle [tex]x[/tex] is [tex]110^{\circ}[/tex].

This means that [tex]x=70[/tex].

Probability = number of desired event occurrences/number of events in sample space = 9/36 = 1/4

Probability is the branch of mathematics that deals with numerical descriptions of how likely an event is to occur or how likely it is that a claim is true. The probability of an event is a number between 0 and 1, with 0 signifying impossibility and 1 expressing certainty.

A compound event is made up of two separate events.

Here is a table of probable sums of two die rolls. Die 1 and Die 2 values are listed along the side and top. The figures are roughly near the middle. The sum of Die 1 = 2 and Die 2 = 2 is 4, for example.

          Die 2

Die1    1   2   3   4   5   6

1         2   3   4   5   6   7

2         3   4   5   6   7   8

3         4   5   6   7   8   9

4         5   6   7   8   9   10

5         6   7   8   9   10 11

6         7   8   9   10 11  12

Rolling two dice yields 6 * 6 = 36 possible outcomes, or 36 possible sums. There are 36 occurrences in the sample space.

Looking at the table, a 3 or a 9 happens as the sum 9 times, resulting in 9 of the 36 potential occurrences having a sum of 3 or 9.

Probability = number of desired event occurrences/number of events in sample space = 9/36 = 1/4

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The measure of ∠QTS = 58°

Given; A triangle QPR

PQ = PR

this means that ∠ Q = ∠ R

and QR = QT this means ∠ R = ∠ T

And ST ║ QR

and QT is the transversal

From the above mentioned information we can conclude that

∠QTS = ∠TQR -------------- 1

Thus since ∠ Q = ∠ R  

by using angle sum property of triangle we can conclude that

∠ Q + ∠ R = 116  [ exterior angle sum property ]

2 ∠ Q = 116

∠ Q = 58°

this means ∠ TQR = 58°

And from 1 we know that this angle is equal to angle QTS

Thus ∠QTS = ∠TQR = 58°

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Answer:

  XY is tangent to circle Z

Step-by-step explanation:

You want to know if segment XY, measuring 3.6 units, is tangent to circle Z at point X. Segment YZ has length 1.8 units outside the circle, which has radius 2.7 units.

If the triangle XYZ is a right triangle, then we have ...

  XY² +XZ² = YZ²

  3.6² +2.7² = (1.8 +2.7)²

  12.96 +7.29 = 20.25 . . . . . true

Segment XY is a tangent.

If segment YZ is extended across the circle, the lengths of the segments from Y to the circle intersection points are 1.8 and (1.8 +2·2.7) = 7.2. The relation between the secant and the "tangent" will be ...

  3.6² = (1.8)(7.2) . . . . . true

This means XY is a tangent.

Answer:

2nd

Step-by-step explanation:

The coordinates of F' when reflected in the line y=x is F'(1,-7)

Given:

When point F is reflected in the line y = x, the image is located at F"(-7, 1).

The x-coordinate and y-coordinate are reversed when a point is reflected over the line y = x. The x-coordinate and the y-coordinate switch places and become negated if you reflect over the line y = -x (the signs are changed). The point is on the line y = x. (y, x).

so the point  F"(-7, 1) after reflection changes to:

F'(1,-7)

Hence we get the value of F' as (1,-7).

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The equation in slope intercept form is y= (-3/4)x + 95.

An equation can be represented by a linear function. The standard form for the linear equation is:

y= mx+b , for example, y=x+4.

Where: m= the slope.

It can be calculated for Δy/Δx.b= the constant term that represents the y-intercept. For the given example: m=1 and b=4.

It is important to inform that the standard form for the linear equation can be called slope-intercept form.

For writing a linear equation, you need two points. From the given graph, it is possible to extract some points, such as: (20,80), (60,50). Then, you should replace the known points in the slope-intercept form (y=mx+b).

For the point (20,80),  you can write  80=m*20+b. And for the point (60,50), you can write 50=m*60+b.

Thus, you have:80=20m+b   (1)50= 60m +b (2)For solving the previous system, you have to multiply the equation 1 by -1.

Thus,-80=-20m-b   (1)50= 60m +b (2)

After that, sum equations 1 and 2.-80+50 = -20m+60m-30=40mm=-30/40m=-3/4

Now, you have y= (-3/4)* x+b.

For finding coefficient b, you should use one of the given points. For example:

(20,80).

y= (-3/4)*x+b for (20,80)80

= -3/4*(20) +b 80

= - 60/4+bb=80 + 60/4b=(320+60)/4b=380/4b

=95

Therefore, the equation in slope intercept form is y= (-3/4)*x + 95.

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Answer:

Step-by-step explanation:

Solve as below

a) a² + ab with a = 6.6, b = 3.4;

b) x² - xu at x = 0.5, y = 2.5;

c) -5a² - 5ah at a = 4, h = -3;

Answer:

Step-by-step explanation:

a) a² + ab = ?

→ (6.6)² + (6.6 × 3.4)

→ 43.56 + 22.44

→ 66

So, the answer is 66.

b) x² - xu = ?

→ (0.5)² - (0.5 × 2.5)

→ 0.25 - 1.25

→ -1

So, the answer is -1.

c) -5a² - 5ah = ?

→ -5(4)² - 5(4 × -3)

→ (-5 × 16) - (5 × -12)

→ -80 + 60

→ -20

So, the answer is -20.

Answer:

y=x-7

Step-by-step explanation:

we know the y intercept is -7 since when x was 0 g(x) is -7

We write it in slope intercept form which is y=mx+b

m- slope

b- y- intercept

To find slope we do y2-y1/x2-x1

-5+7/2-0

2/2

1

1 is the slope so we just keep it X on the equation and the equation will be

y=x-7

Hopes this helps please mark brainliest

Answer:

36,288

Step-by-step explanation:

The completion of the MACRS annual cost recovery on a straight-line basis is as follows:

Method Purchased  Cost      Recovery     Recovery          Cost

                                                  Class             Year           Recovery

MACRS July 20      $ 5,000           7                 6            A = $833.33

MACRS  Nov. 5      $ 11,000        20                 13           B = $846.15

Ordinarily, the MACRS (modified accelerated cost recovery system) depreciation method is the tax-allowed method that ensures that larger deductions for depreciation expense or cost recovery are made in the beginning years and lower deductions for later years.

However, the same deductions are made each year when the straight-line method is used.

The depreciation expense using the MACRS straight-line method is computed by dividing the asset's cost by the recovery year.

Method Purchased  Cost      Recovery     Recovery          Cost

                                                  Class             Year           Recovery

MACRS July 20      $ 5,000           7                 6            A = $833.33 ($5,000/6)

MACRS  Nov. 5      $ 11,000        20                 13           B = $846.15 ($11,000/13)

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The situation can be represented using the equation 3g + 7 = 40

From the question, we have the following parameters that can be used in our computation:

Length of three sides = g

Length of the fourth side = 7

Perimeter = 40

The perimeter of a quadrilateral is the sum of the sides of the shape

This means that

P = sum of the 4 sides

So, we have

P = g + g + g + 7

Evaluate

P = 3g + 7

Rewrite as

3g + 7 = 40

Hence. the equation that represents the situation is 3g + 7 = 40

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Answer: 85

Step-by-step explanation:

The dimensions of the rectangle is 83 feet x 46 feet

What is the Perimeter of a Rectangle?

The perimeter P of a rectangle is given by the formula, P=2 ( L + W) , where L is the length and W is the width of the rectangle.

Perimeter P = 2 ( Length + Width )

Given data ,

The perimeter P of the rectangle = 258 feet

Let the length of the rectangle be = L

Let the width of the rectangle be = W

And , The width is 37 feet less than the length. ,

So , W = L - 37

Perimeter P = 2 ( Length + Width )

Substituting the values of L and W in the equation , we get

Perimeter P = 2 ( L + L - 37 )

2 ( L + L - 37 ) = 258

( L + L - 37 ) = 129

2L - 37 = 129

Adding 37 on both sides , we get

2L = 166

Divide by 2 on both sides , we get

Length L of the rectangle = 83 feet

Substituting the value of L in equation ,we get

W = L - 37

Width W of the rectangle = 46 feet

Therefore , Length = 83 feet and Width = 46 feet

Hence , the dimensions of the rectangle is 83 feet x 46 feet

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