While filing your income tax, you report annual contributions of $100 to a public radio station, $300 to PBS (television station), $150 to a woman’s shelter, and $450 to other charitable organizations.

Find your monthly expense.

Answer:

Step-by-step explanation:

To show that the expression \(\ln(\sqrt{2} + 1) - \ln\left(\frac{1}{\sqrt{2}}\right)\) is equal to \(-\ln\left(1 - \frac{1}{\sqrt{2}}\right)\), we can simplify both sides of the equation using the properties of logarithms. Here are the steps:

Step 1: Simplify the expression on the left side:

\(\ln(\sqrt{2} + 1) - \ln\left(\frac{1}{\sqrt{2}}\right)\)

Step 2: Apply the logarithmic property \(\ln(a) - \ln(b) = \ln\left(\frac{a}{b}\right)\) to combine the logarithms:

\(\ln\left(\frac{\sqrt{2} + 1}{\frac{1}{\sqrt{2}}}\right)\)

Step 3: Simplify the expression within the logarithm:

\(\ln\left(\frac{(\sqrt{2} + 1)}{\left(\frac{1}{\sqrt{2}}\right)}\right)\)

Step 4: Simplify the denominator by multiplying by the reciprocal:

\(\ln\left(\frac{(\sqrt{2} + 1)}{\left(\frac{1}{\sqrt{2}}\right)} \cdot \sqrt{2}\right)\)

\(\ln\left(\frac{(\sqrt{2} + 1) \cdot \sqrt{2}}{\left(\frac{1}{\sqrt{2}}\right) \cdot \sqrt{2}}\right)\)

\(\ln\left(\frac{(\sqrt{2} + 1) \cdot \sqrt{2}}{1}\right)\)

Step 5: Simplify the numerator:

\(\ln\left(\frac{(\sqrt{2} + 1) \cdot \sqrt{2}}{1}\right)\)

\(\ln\left(\sqrt{2}(\sqrt{2} + 1)\right)\)

\(\ln\left(2 + \sqrt{2}\right)\)

Now, let's simplify the right side of the equation:

Step 1: Simplify the expression on the right side:

\(-\ln\left(1 - \frac{1}{\sqrt{2}}\right)\)

Step 2: Simplify the expression within the logarithm:

\(-\ln\left(\frac{\sqrt{2} - 1}{\sqrt{2}}\right)\)

Step 3: Apply the logarithmic property \(\ln\left(\frac{a}{b}\right) = -\ln\left(\frac{b}{a}\right)\) to switch the numerator and denominator:

\(-\ln\left(\frac{\sqrt{2}}{\sqrt{2} - 1}\right)\)

Step 4: Simplify the expression:

\(-\ln\left(\frac{\sqrt{2}}{\sqrt{2} - 1}\right)\)

\(-\ln\left(\frac{\sqrt{2}(\sqrt{2} + 1)}{1}\right)\)

\(-\ln\left(2 + \sqrt{2}\right)\)

As we can see, the expression \(\ln(\sqrt{2} + 1) - \ln\left(\frac{1}{\sqrt{2}}\right)\) simplifies to \(\ln(2 + \sqrt{2})\), which is equal to \(-\ln\left(1 - \frac{1}{\sqrt{2}}\right)\).

Answer:

Your answer will be $166.26

Step-by-step explanation:

i found this out because i multiplied 51 times 3.26

For the expression \(x^64 + ax^b + 25\) to be a perfect square for all integer values of x, b must be 64, and a must be a perfect square, written as a = \(y^2.\)

To determine the values of a and b such that the expression\(x^64 + ax^b\) + 25 is a perfect square for all integer values of x, we need to analyze the properties of perfect squares.

A perfect square is an expression that can be written as the square of another expression. In this case, we want the given expression to be in the form of\((x^n)^2,\) where n is an even integer.

Let's examine the given expression: \(x^64 + ax^b\) + 25

For it to be a perfect square, the quadratic term \(ax^b\)must have the same exponent as the leading term\(x^6^4.\) This means b must be equal to 64.

So we have:\(x^64 + ax^64 + 25\)

Now, we can rewrite this as:\((x^32)^2 + 2(x^32) (\sqrt{a}) + (\sqrt{25})^2\)

By comparing this with the standard form of a perfect square, (\(x^n +\sqrt{k} )^2\), we can deduce that √a must be equal to x^32 and \(\sqrt{25}\) must be equal to \(\sqrt{k.}\)

Therefore, we have: \(\sqrt{a} = x^3^2\)and\(\sqrt{25} = \sqrt{k}\)

From the second equation, we know that k = 25.

Now, substituting the value of k back into the first equation, we have: \(\sqrt{a} = x^3^2\)

To satisfy this equation for all integer values of x, a must be a perfect square. Therefore, we can express a as a =\(y^2\), where y is an integer.

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Answer:

Put "<" between -0.171100011 _____ -0.171100010

Step-by-step explanation:

-0.171100010 is greater than -0.171100011  because they are negative numbers so -0.171100011 is further than -0.171100010 to 0, therefore -0.171100010 is greater.

Mark brainliest if this helped :)

At the same rate as his 100-meter freestyle swim in the 2012 Olympics, Nathan Adrian could have completed one loop of a 25-meter pool in 11.88 seconds.

The idea of proportionality can be applied. The time it would take Nathan Adrian to complete one lap in a 25-meter pool is known to be 47.52 seconds for the 100-meter freestyle. Since the tempo is constant while the distance varies, we can establish a ratio:

100 meters / 47.52 seconds = 25 meters / x seconds

where x is the unknown time for one lap in the 25-meter pool.

To solve for x, we can cross-multiply:

100 meters * x seconds = 47.52 seconds * 25 meters

100x = 1188

Dividing both sides by 100, we get:

x = 11.88 seconds

Therefore, at the same rate as his 100-meter freestyle swim in the 2012 Olympics, Nathan Adrian could have completed one loop of a 25-meter pool in 11.88 seconds.

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Answer:

1 and 7

Step-by-step explanation:

Given that,

The parallel lines j and k are cut by a transversal l.

We need to find the pair of angles are alternate interior angles.

Angles that are on opposite sides of the transversal and are in between the other two lines are alternate angles.

In this figure, angles 1 and 7 form alternate interior angles. Hence, the correct option is (D).

Answer:3 and 7

Stepby-step explanation:

Answer:

-25

Step-by-step explanation:

\( \dfrac{(20 - 5^2)(16 + 2^2)}{-2^3 + (3 \times 2^2)} = \)

First, do all exponents.

\( = \dfrac{(20 - 25)(16 + 4)}{-8 + (3 \times 4)} \)

Now do each operation in parentheses.

\( = \dfrac{(-5)(20)}{-8 + 12} \)

Multiply in the numerator. Add in the denominator.

\( = \dfrac{-100}{4} \)

Divide the numerator by the denominator.

\( = -25 \)

Answer:

-25

Step-by-step explanation:

PEMDAS

The PEMDAS rule is an acronym representing the order of operations in math:

Given expression:

\(\sf \dfrac{(20-5^2)(16+2^2)}{-2^3+(3 \times 2^2)}\)

As the given expression is a fraction, carry out the operations in the numerator and denominator first before finally dividing them.

Following PEMDAS, carry out the calculations inside the parentheses first, then carry out the rest of the calculations following the order of operations:

Parentheses

Calculate the exponents inside the parentheses:

\(\implies \sf \dfrac{(20-25)(16+4)}{-2^3+(3 \times 4)}\)

Multiply:

\(\implies \sf \dfrac{(20-25)(16+4)}{-2^3+(12)}\)

Add and subtract:

\(\implies \sf \dfrac{(-5)(20)}{-2^3+(12)}\)

Exponents

Calculate the exponent:

\(\implies \sf \dfrac{(-5)(20)}{-8+(12)}\)

Multiply and Divide

Multiply:

\(\implies \sf \dfrac{-100}{-8+(12)}\)

Add and Subtract

Add:

\(\implies \sf \dfrac{-100}{4}\)

Finally, divide the numerator by the denominator:

\(\implies \sf -25\)

Answer:

x = 2, x = -3/2

Step-by-step explanation:

Factors to be (x-2)(2x+3) = 0

x =2, x = -3/2

Answer:

Step-by-step explanation:

2x²-x-6=0

2x²-(4-3)x-6=0

2x²-4x+3x-6=0

2x(x-2)+3(x-2)=0

(x-2)(2x+3)=0

Perimeter of the parallelogram = 210 in.

Area of parallelogram = 2,484 in.²

Perimeter of parallelogram = 2(a + b), where a and b are its sides.

Area of parallelogram = (b)(h), where h is its height and b is the length of one of its bases.

Given:

a = 51 in.

b = 54 in.

h = 46 in.

Perimeter of the parallelogram = 2(54 + 51) = 210 in.

Area of parallelogram = (b)(h) = (54)(46) = 2,484 in.²

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Hey there!

We simply have to do 182/2.8, and you will get the area (65m^2).

We know that the formula for area is length x width, and the formula for volume is length x width x height. In the volume formula, we can see it can also be area x height to get volume. So, we know that area x height = volume, right? And in this equation, we are given volume and height. If          V = ha, with V = volume; h = height; a = area, we can divide "h" on both sides, and we get V/h = a, or volume divided by height is area. To solve for the above equation, we can plug the numbers in the formula: 182/2.8 = a, or 65 = a.

Hope this helps! Have an amazing day, and remember, you've got this!

Answer:

Triangle

Step-by-step explanation:

It has three side unlike the others can't have three sides

Answer:

total is (12-4=5(^19 <6>) THIS IS MY ANWER

At the point of the least cost of fencing the cost function has a zero

derivative.

Reasons:

Shape of the pen = Rectangular

Area of the pen = 24 yd²

Cost of material on one side of the fence = $6 per yard

Cost of material on the remaining three sides = $3 per yard

Required:

The least cost of fencing the pen

Solution:

The least cost is a minimum value of the cost function

Let L represent the length of the fence and let W represent the width of the fence

We have;

The perimeter of the fence = 2·L + 2·W

The area of the pen, A = L × W = 24

One of the length, L, of the fence costs $6 per yard and the other length L,

of the opposite side costs $3 per yard.

The cost of fencing, C  3 × 2·W + 3 × L + 6 × L = 6·W + 9·L

C = 6·W + 9·L

\(\displaystyle W = \mathbf{\frac{24}{L}}\)

Which gives;

\(\displaystyle C = 6 \cdot \frac{24}{L} + 9 \cdot L = \frac{144}{L} + 9 \cdot L = \mathbf{\frac{144 + 9 \cdot L^2}{L}}\)

The shape of the above function is concave upwards.

At the minimum value, we have;

\(\displaystyle \frac{dC_{min}}{dL} = \frac{d}{dL} \left(\frac{144}{L} + 9 \cdot L\right) = 9 - \frac{144}{L^2} = 0\)

Which gives;

\(\displaystyle \frac{144}{L^2} = 9\)

\(\displaystyle \frac{144}{9} = L^2\)

By symmetric property, we have;

\(\displaystyle L^2 = \frac{144}{9}\)

\(\displaystyle L = \sqrt{ \frac{144}{9}} = \frac{12}{3} = 4\)

The length of the fence that gives the least cost, L = 4 yards

\(\displaystyle At \ L = 4, \ W = \frac{24}{4} = 6\)

The width of the fence at least cost, W = 6 yards

Cost, C = 6·W + 9·L

Least cost, \(C_{min}\) = 6 × 6 + 9 × 4 = 72

The least cost of the fencing, \(C_{min}\) = $72.00

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Answer:

The red one?

Step-by-step explanation:

Sorry if my answer is wrong

Answer:

If you have the coordinates of two points, you can use the distance formula to find the length of the line segment between them. The distance formula is:

\(d =\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)

where:

And to find a perimeter add all the sides as the perimeter is the sum of all sides of the shape or object.

Perimeter: Sum of all sides

Area : Length * breadth or base*height for rectangle

Answer:

-12x + 5 > -19

-12x > -24

x < 2

Answer:

0.2

Step-by-step explanation:

Answer:

(x+6)^2+(y-7)^2= 29

Step-by-step explanation:

general exqn-> (x-h)^2+(y-k)^2=(r)^2

here, h= -6 and k=7

r= √ 29

Therefore, exqn of circle=

(x+6)^2+(y-7)^2= 29

Answer:

(x + 6)² + (y - 7)² = 29

Step-by-step explanation:

the equation of a circle in standard form is

(x - h )² + (y - k )² = r²

where (h, k ) are the coordinates of the centre and r is the radius

here (h, k ) = (- 6, 7 ) and r = \(\sqrt{29}\) , then

(x - (- 6) )² + (y - 7)² = (\(\sqrt{29}\) )² , that is

(x + 6 )² + (y - 7 )² = 29

Answer:

A.

Step-by-step explanation:

The vertical line test is a way of finding out if a relation is a function.

Graph the relation.

Then imagine a vertical line moving from left to right over the graph of the relation.

If the vertical line intersects at most one point of the graph in any position you place the vertical line, then the relation is a function.

This function passes the vertical test since it never intersects more than one point on the vertical line at a time.

Answer: A.

Answer:

Step-by-step explanation:

Figure 1 = (-1,1)

Figure 2 = (-2,5)

So the answer should be x + (-1) and y + (4)

Answer:

A. the angular speed is 3771.4 rad/min

b. 5921 rpms

Step-by-step explanation: I just got this same question right on a test.

The length of time that it will take for each of the workout sessions would be: Plan A = 1.5 hours, and Plan B =  0.5 hours.

The length of the sessions can be obtained by first obtaining drawing a system of equations for the two cases. On Wednesday, we can represent the sessions as follows:

2A + 12B = 9 hours

On Thursday, we would have

5A + 3B = 9 hours

2A + 12B = 9  Eqn 1

5A + 3B = 9   Eqn 2

Multiply equation 2 by -4

2A + 12B = 9

-20A - 12B = -36

2A - 20A = 9 -36

-18A = -27

Divide both sides by -18

A = 1.5 hours

For B, substitute A in the first equation

2(1.5) + 12B = 9

3 + 12B = 9

12B = 9 - 3

12B = 6

Divide both sides by 12

B = 0.5

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Complete Question:

Ann the trainer has two solo workout plans that she offers her clients: Plan A and Plan B. Each client does either one or the other (not both). On Wednesday there were 2 clients who did Plan A and 12 who did Plan B. On Thursday there were 5 clients who did Plan A and 3 who did Plan B. Ann trained her Wednesday clients for a total of 9 hours and her Thursday clients for a total of 9 hours. How long does each of the workout plans last?

Answer:

D

Step-by-step explanation:

The linear function that has the same y-intercept as the given graph is the equation y = -2x + 10, corresponding to option 3.

To determine the linear function with the same y-intercept as the graph, we need to find the equation of the line passing through the points (3, 4) and (5, 0).

First, let's find the slope of the line using the formula:

slope (m) = (change in y) / (change in x)

m = (0 - 4) / (5 - 3)

m = -4 / 2

m = -2

Now that we have the slope, we can use the point-slope form of a linear equation to find the equation of the line:

y - y1 = m(x - x1)

Using the point (3, 4) as our reference point, we have:

y - 4 = -2(x - 3)

Expanding the equation:

y - 4 = -2x + 6

Simplifying:

y = -2x + 10

Now, let's check the given options to find the linear function with the same y-intercept:

Option 1: The table with x-values (-3, -1, 1, 3) and y-values (-4, 2, 8, 14)

The y-intercept is not the same as the given line. So, this option is not correct.

Option 2: The table with x-values (-4, -2, 2, 4) and y-values (-26, -18, -2, 6)

The y-intercept is not the same as the given line. So, this option is not correct.

Option 3: The table with x-values (-5, -3, 3, 5) and y-values (-15, -11, 1, 5)

The y-intercept is the same as the given line (10). So, this option is correct.

Option 4: The table with x-values (-6, -4, 4, 6) and y-values (-26, -14, 34, 46)

The y-intercept is not the same as the given line. So, this option is not correct.

Therefore, the linear function that has the same y-intercept as the given graph is the equation y = -2x + 10, corresponding to option 3.

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Answer:

(b) 310 mi, 12.76km/liter

Step-by-step explanation:

We are told that Toronto is 500 km north on Highways. Since 1 km = 0.62 mi, then Toronto is: 500 × 0.62 = 310 miles

Aanya’s car averages 30 mi/gallon.

We are told that 1 mi = 1.61 km

Thus, her average is now;

30 × 1.61 km/gallon = 48.3 km/gallon

We are told that 1 qt = 0.946 liters

But also, 0.25 gallon = 1 qt

Thus;

0.25 gallon = 0.946 litres

Thus, 1 gallon = 0.946/0.25 litres = 3.784 litres

Thus, 48.3 km/gallon to km/litres = 48.3/3.784 = 12.76 km/litres

Answer is 310 miles and 12.76 km/litres

Answer: 95.5

Step-by-step explanation:

If you order the numbers from least to greatest and alternate revoking numbers the number in the middle, or median will be 95.5

Answer:

4,130

Step-by-step explanation:

4780-650=4130 ft