Given circle E with diameter CD and radius EA. AB is tangent to E at A. If
AD = 12 and EA = 13, solve for AC. Round your answer to the nearest tenth if
necessary.

To show that (x)^0 for all x in the interval of convergence, we need to select the correct answer option among (a), (b), and (c), which provide explanations for why (x)^0 holds true.

The correct answer is (a) "(x)^0 because of explanation here and 0 for all x." However, the explanation is missing from the given options, so we cannot determine the specific reasoning behind it. In general, any non-zero number raised to the power of 0 is equal to 1. Therefore, (x)^0 is equal to 1 for all x, regardless of the specific function or expression. This is a fundamental property of exponentiation and holds true for any valid value of x within the interval of convergence.

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The solution of x in the equation 3^(x -4) = 6 is x = 5.63

The equation is given as

3^(x -4) = 6

Apply the law of indices on the expression 3^(x -4) to rewrite it

So, we have

3^x/3^4 = 6

The above equation becomes

3^x = 6 * 3^4

Evaluate the product

So, we have

3^x = 486

Take the logarithm of bot sides

xlog(3) = log(486)

Divide both sides by log(3)

x = log(486)/log(3)

Evaluate

x = 5.63

Hence, the solution of x in the equation 3^(x -4) = 6 is x = 5.63

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zw in polar form is zw = 24√2(cos(75°) + i*sin(75°)).

z/w in polar form is z/w = (4√2/3)(cos(-15°) + i*sin(-15°)).

1/z in polar form is 1/z = (1/8)(cos(-30°) + i*sin(-30°)).

Now that we have z and w in polar form, we can find the polar forms for the products and reciprocal of these complex numbers.

Product (zw): To multiply two complex numbers in polar form, we multiply their magnitudes and add their arguments. Applying this to z and w, we have: zw = 8(cos(30°) + isin(30°)) * 3√2(cos(45°) + isin(45°))

Multiplying the magnitudes: |zw| = 8 * 3√2 = 24√2

Adding the arguments: θzw = 30° + 45° = 75 degrees

Therefore, zw in polar form is zw = 24√2(cos(75°) + i*sin(75°)).

Division (z/w): To divide two complex numbers in polar form, we divide their magnitudes and subtract their arguments. Applying this to z and w, we have: z/w = 8(cos(30°) + isin(30°)) / 3√2(cos(45°) + isin(45°))

Dividing the magnitudes: |z/w| = 8 / (3√2) = 8 / 3√2 = 8 / (3 * √(2)) = (8 / 3) * (1 / √(2)) = (8 / 3) * (√(2) / 2) = (4√2) / 3

Subtracting the arguments: θz/w = 30° - 45° = -15 degrees

Thus, z/w in polar form is z/w = (4√2/3)(cos(-15°) + i*sin(-15°)).

Reciprocal (1/z): To find the reciprocal of a complex number in polar form, we take the reciprocal of its magnitude and negate its argument. Applying this to z, we have: 1/z = 1 / [8(cos(30°) + i*sin(30°))]

Taking the reciprocal of the magnitude: |1/z| = 1 / 8 = 1/8

Negating the argument: θ1/z = -30°

Hence the 1/z in polar form is 1/z = (1/8)(cos(-30°) + i*sin(-30°)).

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Answer:

∠FDE or ∠GDA

Step-by-step explanation:

The adjacent angle refers to the angle which lies right next to an angle, and the sum of the angles is 180, meaning they are supplementary.

Here, in this diagram, there are 2 adjacent angles for ∠FDG :

The missing length in the triangle is 56 cm.

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .

Let us form a proportional equation to find the value of missing length

p/21 = 24/9

Apply cross multiplication

9p=21×24

9p=504

Divide both sides by 9

p=56

Hence, the missing length in the triangle is 56 cm.

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Answer:

270 minutes or 4.5 hours

Step-by-step explanation:

You need to find the unit rate in order to solve this problem with the given information. In order to find the unit rate (in minutes) let's find each minute. Do 3600/180=20. You use 180 because that's the amount of minutes in 3 hours. Then, you take 5400 and divide it by 20 to get 270. Convert back to hours and rounded you get 4.5 hours.

the denominators need to be the same so if we multiply the first fraction by 6 and the second by 5, our new equation is

24/30 - 5/30

24-5=19

19/30 is your answer

Answer & Step-by-step explanation:

\(\frac{4}{5}-\frac{1}{6}\)

When you need to subtract fractions, the denominators (bottom) need to be the same. For this, you have to multiply both fractions until the bottom numbers are the same:

Find the lowest common multiple of the denominators:

\(5,10,15,20,25,30\\6,12,18,24,30\)

The LCM of 5 and 6 is 30. Now you have to multiply the top and bottom of the fractions until you get a denominator of 30*:

\(\frac{4(6)}{5(6)}=\frac{24}{30}\\\\\frac{1(5)}{6(5)}=\frac{5}{30}\)

So,

\(\frac{24}{30} -\frac{5}{30}\)

When you subtract fractions, you only change the numerators (top). The denominator will stay the same:

\(\frac{24}{30} -\frac{5}{30}=\frac{19}{30}\)

Since the fraction can't be further simplified,  \(\frac{4}{5}-\frac{1}{6}=\frac{19}{30}\)

:Done

*When you are finding the same denominators, you need to multiply a single fraction's numerator and denominator by the same number. The two different fractions don't need to be multiplied by the same number:

\(\frac{x(a)}{y(a)}-\frac{w(b)}{z(b)}\)

It would take 5040 cubic inches of water to completely fill the aquarium.

We know that the formula for the volume of cuboid :

V = length × width × height

Let us assume that l represents the length of the aquarium, w represent the width and h represents the height.

Here, l = 20 inches

w = 14 inches

and h = 18 inches

Using the formula for the volume of cuboid, the volume of aquarium would be,

V = l × w × h

V = 20 × 14 × 18

V = 5040 cu.in.

Therefore, it would take 5040 cu.in. of water.

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The triple integral can be evaluated numerically using the cylindrical coordinates \($(r,\theta,z)$\) with the limits of integration given by the parabolic cylinder and the planes.

The triple integral we need to evaluate is:

\(\begin{equation}\iiint_{S} f(x,y,z) \,dV\end{equation}\)

where S is bounded by the parabolic cylinder \($z=2y^2$\) and the planes x=0, y=0, z=0, and x=2. To evaluate this integral, we will use the cylindrical coordinates \($(r,\theta,z)$\). The Jacobian of the transformation is r, and the volume element is \($r \, dr \, d\theta \, dz$\). The integral then becomes:

\(\begin{equation}\int_0^{2\pi} \int_0^2 \int_0^{2r^2} f(r,\theta,z) r \, dr \, d\theta \, dz\end{equation}\)

The limits of integration for r come from the planes x=0 and x=2, so r goes from 0 to \($\sqrt{2}$\), and for z come from the parabolic cylinder \($z=2r^2$\), so z goes from 0 to \($2r^2$\).

Finally, the integral becomes:

\(\begin{equation}\int_0^{2\pi} \int_0^{\sqrt{2}} \int_0^{2r^2} f(r,\theta,z) r \, dr \, d\theta \, dz\end{equation}\)

which can be evaluated numerically.

The triple integral can be evaluated numerically using the cylindrical coordinates \($(r,\theta,z)$\) with the limits of integration given by the parabolic cylinder and the planes.

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complete question

Evaluate the triple integral where is bounded by the parabolic cylinder \($z=2y^2$\) and the planes x=0, y=0, z=0, and x=2.

Answer:

The correct option is;

C. 7 - (3z + 8) < 2(z -5)

Step-by-step explanation:

The verbal statement on the left hand side of the less than relationship, can be presented as follows;

7 - (8 + 3z)

Similarly, the verbal statement on the right hand side of the less than relationship, can be presented as follows;

2 × (z -5)

The combined statement can therefore, be presented as follows;

7 - (8 + 3z) < 2 × (z -5), which is the same as 7 - (3·z + 8) < 2(z -5) since we have;

(8 + 3z) is equivalent to (3z + 8), the order of arrangement of the terms within the parenthesis will not alter the total value of the terms within the parenthesis, since the signs remain unchanged

The correct option is therefore;

7 - (3z + 8) < 2(z -5).

A residual is the difference between "the measured and predicted values of the quantity of interest".

In regression analysis, a residual would be the difference between an observable and anticipated value.

The formula is;

Residual = Observed value – Predicted value

Some key features regarding the residuals are-

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Answer:

It's the red option.

Answer:

21x + 12

Step-by-step explanation:

In math, it is

21x + 2(6).

so we have

21x + 2(6) = 21x + 12.

Looking at figure A, we have a prism with a triangular base that looks like a right triangle.

Since the prism has a right triangular base, the base shape is a right triangle (shape 5).

Looking at figure B, we have a prism with a pentagonal base.

Since the prism has a pentagonal base, the base shape is a pentagon (shape 1).

Looking at figure C, we have a prism with a triangular base that looks like an equilateral triangle.

Since the prism has an equilateral triangle base, the base shape is an equilateral triangle.(shape 4).

Looking at figure D, we have a prism with a triangular base that looks like an equilateral triangle.

Since the prism has an equilateral triangle base, the base shape is an equilateral triangle.(shape 4).

Answer:

x intercepts: (1,0), (-3,0)

the roots are 1 and -3

Step-by-step explanation:

Using the Quadratic Formula:

x=−b±sqrt(b2−4ac)/2a

Substitute:

x= -8±sqrt(8^2-4(4)(-12))/2(4)

x=-8±sqrt((64- -192))/8

x=-8±sqrt(256)/8

Solve two equations (±)

x=-8±16/8

x=8/8  and x=-24/8

x=1 and x=-3

Answer:

x = -3

x = 1

Step-by-step explanation:

Hello!

We can solve the quadratic by Factoring the Equation and using the Zero Product Property.

We want to find two numbers that multiply out to -3, but add up to 2. The numbers that work are -1 and 3. We can expand 2x to -x and 3x and factor by grouping.

Set each factor to 0 and solve for x in both.

Therefore, the x-interecpts are -3 and 1.

Answer:

False

Step-by-step explanation:

This statement is false.

The set of whole numbers include the set of Natural numbers "N" = {1, 2, 3, 4, 5, 6, ...}, the set of the negatives of the natural numbers: {-1, -2, -3, -4,...}, and the zero: {0}

We see then that the set of Natural numbers is a subset of the set of whole numbers Z = {... -4,-3,-2,-1, 0,1, 2, 3, 4, 5, ...}

Answer:

false

brainliest to me!

Step-by-step explanation:

0 is a whole number but not a natural number so its false!

Answer:

a) -6

b) 9

c) 27

Step-by-step explanation:

\(2( - 3) = - 6 \\ { - 3}^{2} = - 9 \\ 3 {( - 3)}^{2} = 27\)

\(\textbf{a)}\\\\2a=2(-3) = -6\\\\\textbf{b)}\\\\a^2 = (-3)^2 = 9\\\\\textbf{c)}\\\\3a^2 = 3(-3)^2 = 3 \cdot 9 = 27\)

Answer:

-\(\frac{1}{4}\)

Step-by-step explanation:

The easiest way to find the slope from this equation is to change it into slope-intercept form. To find slope-intercept form solve for y.

First, subtract 4x from both sides

Then, divide both sides by 16

Finally, simplify the equation

Slope-intercept form is written as y=mx+b. In the equation above m is -1/4, so that is the slope.

Answer:

4*x+16*y-(12)=0

4x + 16y - 12 = 4 • (x + 4y - 3)

y=mx+b

In this formula :

y tells us how far up the line goes

x tells us how far along

m is the Slope or Gradient i.e. how steep the line is

b is the Y-intercept i.e. where the line crosses the Y axis

The X and Y intercepts and the Slope are called the line properties. We shall now graph the line x+4y-3 = 0 and calculate its properties.

Notice that when x = 0 the value of y is 3/4 so this line "cuts" the y axis at y= 0.75000

y-intercept = 3/4 = 0.75000

When y = 0 the value of x is 3/1 Our line therefore "cuts" the x axis at x= 3.00000

x-intercept = 3/1 = 3.00000

Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is 0.750 and for x=2.000, the value of y is 0.250. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of 0.250 - 0.750 = -0.500 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

Slope = -0.500/2.000 = -0.250

Answer: 181 square inches

Step-by-step explanation:

Here's a more detailed explanation: To determine if a graph is a function, you can use the vertical line test. The vertical line test states that if you can draw a vertical line that intersects the graph in more than one place, then the graph is not a function.

Determining whether a graph represents a function is an important concept in mathematics, especially in algebra and calculus. A function is a set of ordered pairs where each input is associated with exactly one output.

So, if you take a ruler or a straight edge and place it vertically on the graph, and it intersects the graph in two or more points, then the graph is not a function. This is because if two points in the graph have the same x-value, they must have different y-values, since functions can only have one output for each input.

On the other hand, if you place a vertical line anywhere on the graph and it intersects the graph in only one point, then the graph is a function.

It's also important to remember that a function must also pass the horizontal line test, which means that no horizontal line can intersect the graph in more than one place.

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Answer:

(2,6)

Step-by-step explanation:

x+2y = 14

y = x+4

Substitute x+4 into the first equation for y

x+2(x+4) = 14

Distribute

x+2x+8 = 14

3x+8 = 14

Subtract 8 from each side

3x+8-8 = 14-8

3x = 6

Divide by 3

3x/3 = 6/3

x = 2

Now solve for y

y = x+4

y =2+4

y =6

(2,6)

Answer:

D. (2, 6)

Step-by-step explanation:

Put y as x+4 in the first equation and solve for x.

x + 2(x + 4) = 14

x + 2x + 8 = 14

3x = 14 - 8

3x = 6

x = 2

Put x as 2 in the second equation and solve for y.

y = 2 + 4

y = 6

Triangle ABC and Triangle DEF are congruent, as stated, of 7:3 with scale factor of isocellus triangle.

Find scale factor?

According to the scale factor, the ratio obtained by dividing the equivalent side lengths of like figures.

Triangle ABC and Triangle DEF are congruent, as stated.

Similar figures have equivalent angles and sides that are equal.

To determine the scale factor,

You must ascertain the ratio between the triangle's corresponding sides.

In order to obtain the sides of the other triangle, multiply each side of the first triangle by the same number.

What we're looking for is the scale factor, which is represented by the number.

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Answer:

9 books

Step-by-step explanation:

78=b(6)+c(4)

78=9(6)+6(4)

78=54+24

78=78-True

As per linear equation, Cindy bought 9 books online.

"A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation.

The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant. The standard form of a linear equation in two variables is of the form Ax + By = C. Here, x and y are variables, A and B are coefficients and C is a constant."

Given, Cindy was buying books ($6 each) and candles ($4 each).

She bought 15 items and spent $78.

Let, she bought 'x' books.

Therefore, she bought (15 - x) candles.

Now, the cost of the total 15 items is

= $[6x + 4(15 - x)]

= $[6x + 60 - 4x]

= $[2x + 60]

Therefore, 2x + 60 = 78

⇒ 2x = 78 - 60

⇒ 2x = 18

⇒ x = 9

Therefore, Cindy bought 9 books.

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3/4 is the total.

See attached image for explanation.

Please consider marking "Brainliest".

Thanks <3

Answer:

186

Step-by-step explanation:

First, Convert 0.3% into as decimal ( 0.003 )

then, Multiply 0.003 and 62,000 and your answer is 186

Do these steps for every question like this and I guarantee you will get it right.

maybe this is a answer!!!

Simple Interest = (Principal * Rate * Time) / 100

Principal = Sum borrowed

Rate = 12% p.a.

Time = 2 years

Simple Interest = Rs.1920

we get:

1920 = (Principal * 12 * 2) / 100

Simplifying this equation, we get:

1920 * 100 = Principal * 12 * 2

192000 = Principal * 24

Principal = 192000 / 24

Principal = 8000

Therefore, Mrs. Joshi borrowed Rs.8000 from the bank.

Answer:

Direct variation

Step-by-step explanation:

Direct variation:y=kx

Inverse variation: y=k*1/x