Prime factor 4x^2-81=0

Answer:

Step-by-step explanation:

Notice that the yellow area is a compound area. Its height is 10 inches.

We can divide this area in three figures, one rectangle and two squares, where the square sides are 2 inches long.

So, the area of the squares is

[tex]A_{squares}=(2in)^{2} +(2in)^{2}=4in^{2} +4in^{2} =8in^{2}[/tex]

On the other hand, the rectangle has a height of 10 inches, and its base is 2 inches long. So its area is

[tex]A_{rectangle}=(10in)(2in)=20in^{2}[/tex]

Therefore, the yellow area is

[tex]A_{yellow}=A_{squares} +A_{rectangle}=8in^{2} +20in^{2} =28in^{2}[/tex]

So, the answer is 28 square inches.

The domain of this function is  { - 4, - 1, 0, 3 } and range of the function is

{ - 4 }.

Suppose we have an ordered pair (x, y) then the domain of the function is the set of values of x and the range is the set of values of y for which x  is defined.

The domain of the function f(x) is the set of x values that are

{ - 4, - 1, 0, 3 }

and the range of the function f(x) is { - 4 }.

As for every input, the output of the function remains the same so it is a constant function.

learn more about the domain and range here :

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Answer:

D.

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The evaluation of[tex]\( \oint_C \mathbf{F} \cdot d\mathbf{r} \)[/tex]  using Stokes' Theorem is [tex]\( \pi e - \pi \).[/tex]

To evaluate[tex]\( \oint_C \mathbf{F} \cdot d\mathbf{r} \)[/tex]  using Stokes' Theorem, we first need to find the curl of the vector field [tex]\( \mathbf{F}(x, y, z) = yz\mathbf{i} + 9xz\mathbf{j} + e^xy\mathbf{k} \)[/tex] . The curl is given by[tex]\( \nabla \times \mathbf{F} \)[/tex] , which, for this vector field, is [tex]\( (e^x - 9z)\mathbf{k} \).[/tex]

Now, we compute the surface integral over the surface ( S) bounded by the circle  C . The given circle is[tex]\( x^2 + y^2 = 1 \)[/tex] with ( z = 3 ). The surface is the disk in the plane (z = 3) with radius ( r = 1 ). The surface integral is then [tex]\( \iint_S \nabla \times \mathbf{F} \cdot d\mathbf{S} = \iint_S (e^x - 9z) \, dS \)[/tex] , where  dS is the area element. The projection of  S  onto the xy-plane is the circle  C , so [tex]( dS = dA = \pi \).[/tex]

The final step is to evaluate[tex]\( \iint_S (e^x - 9z) \, dS \)[/tex] over the disk. Since  z = 3 over the entire surface, the integral simplifies to [tex]\( \iint_S (e^x - 9 \cdot 3) \, dS = \pi e - \pi \).[/tex]  Therefore, the final answer is[tex]\( \pi e - \pi \)[/tex] after applying Stokes' Theorem to evaluate the circulation of [tex]\( \mathbf{F} \)[/tex] around the circle C .

The logarithmic equation log2(8) = 3 convert to exponential form as 2^3 = 8.

Converting the logarithmic equation log2(8) = 3 to exponential form involves recognizing the base and the exponent.Logarithms state that if logb(A) = C, then the equivalent exponential form would be bC = A. In this case, since 2 is the base and 3 is the exponent to which 2 must be raised to get 8, we can write 2^3 = 8.

To further clarify, logarithms are simply a way to represent exponents, and they are widely utilized in mathematics to simplify the multiplication and division of exponents. A logarithm with a base of 10 is known as the common logarithm and is often written without a base as log(A). In contrast, when another base is used, it is indicated as logb(A). The relationship between logarithms and exponents is leveraged in various scientific and engineering fields to represent and calculate large numbers conveniently.

Answer: Option B 3-4i is the correct option

Explanation:

we have formula for discriminant [tex]D=b^{2}-4ac[/tex]

after that we find the required variable that is to be find according to the quadratic equation given suppose we have to find x

then we have formula [tex]x=\frac{-b\pm\sqrt{D}} {2a}[/tex]

Here we have [tex]\pm[/tex] of roots if we have one root 3+41 other would be of opposite sign and hence,definitely be 3-4i.

Therefore Option B 3-4i is the correct option.

Answer:

Find out the what is the percent of increase .

To prove

As given

A store increases the price of a sweater from $20 to $22.

Increase in the price = Increase price - Initial price  

                                  = $22 - $20

                                  = $2

Formula

[tex]Percentage = \frac{increase\ in\ price\times 100}{Initial\ price}[/tex]

Here initial price = $20

increase in price = $2

put in the formula

[tex]Percentage = \frac{2\times 100}{20}[/tex]

[tex]Percentage = \frac{200}{20}[/tex]

Percentage = 10%

Therefore the increase in the price is 10% .

Option (e) is correct.

Final answer:

The percent of increase when a store raises the sweater's price from $20 to $22 is calculated as 10%, using the formula of difference over original price times 100, Option E is correct.

Explanation:

The question asks for the percent of increase when a store increases the price of a sweater from $20 to $22. To find the percentage increase, we take the increase in price ($2), divide it by the original price ($20), and then multiply by 100 to convert to a percentage. Thus, the calculation is (($22 - $20) / $20) * 100 = (2 / 20) * 100 = 0.10 * 100 = 10%.

Answer:

Option B is correct.

Step-by-step explanation:

Given Geometric series : 3 , 1 , [tex]\frac{1}{3}\:,\:\frac{1}{9}\:,\:\frac{1}{27}[/tex]

To find: Sum of the series.

First term of the geometric series, a = 3

Common ration of the Geometric series, r = [tex]\frac{second\:term}{first\:term}=\frac{1}{3}[/tex]

Sum of the finite Geometric series , [tex]S_n=\frac{a(1-r^n)}{1-r}[/tex]

Sum of the given 5 term term of given series , [tex]S_5=\frac{3(1-(\frac{1}{3})^5)}{1-\frac{1}{3}}=\frac{3(\frac{3^5-1}{3^5})}{\frac{3-1}{3}}[/tex]

=  [tex]\frac{\frac{3^5-1}{3^3}}{2}=\frac{243-1}{2\times3^3}=\frac{121}{27}[/tex]

Therefore, Option B is correct.

To divide 198 by 9 using the partial quotients method, you estimate how many times 9 fits into 198, subtract, and sum up the partial results to get the final answer of 22.

To solve 198 ÷ 9 using the partial quotients method, follow these steps:

Estimate how many times 9 can go into 198. We start with a rough estimate that 9 can go into 198 around 20 times.

Calculate 9 x 20 = 180. Subtract this from 198, yielding 198 - 180 = 18.

Next, determine how many times 9 can fit into the remaining 18. This is 2 times since 9 x 2 = 18.

Subtract 18 from 18, resulting in a remainder of 0.

Add the partial quotients: 20 + 2 = 22.

So, 198 ÷ 9 = 22 using the partial quotients method.