Which diagram suggests a correct construction of a line that is parallel to given line l and passes through given point q?

The volume of the solid under the hyperbolic paraboloid [tex]z = 4 + x^2-y^2[/tex] and above the square r = [−1, 1] × [0, 2] is [tex]20\text{ cubic units}[/tex]

The question is asking us to find the volume bounded by the following surfaces

To do this, we have to evaluate the triple integral

[tex]\displaystyle \int\limit_0^2\,dx \int\limit_{-1}^1\,dy\int\limit_0^{4+x^2-y^2}\,dz[/tex]

First, we integrate with respect to [tex]z[/tex]

[tex]\displaystyle \int\limit_0^2\,dx \int\limit_{-1}^1\,dy\int\limit_0^{4+x^2-y^2}\,dz\\\\=\displaystyle \int\limit_0^2\,dx \int\limit_{-1}^1\,dy(4+x^2-y^2)[/tex]

Next, we integrate with respect to [tex]y[/tex]

[tex]\displaystyle \int\limit_0^2\,dx \int\limit_{-1}^1\,dy(4+x^2-y^2)\\\\=\displaystyle \int\limit_0^2\,dx \left[4y+x^2y-\dfrac{y^3}{3} \right]_{-1}^1\\\\=\displaystyle \int\limit_0^2\,dx \left[ \left(4(1)+x^2(1)-\dfrac{(1)^3}{3} \right)- \left(4(-1)+x^2(-1)-\dfrac{(-1)^3}{3} \right)\right]\\\\=\displaystyle \int\limit_0^2\,dx \left(\dfrac{22}{3}+2x^2 \right)\\\\[/tex]

Finally, we integrate with respect to [tex]x[/tex]

[tex]\displaystyle \int\limit_0^2\,dx \left(\dfrac{22}{3}+2x^2 \right)\\\\=\left[\dfrac{22}{3}x+\dfrac{2x^3}{3}\right]_0^2\\\\=\left(\dfrac{22}{3}(2)+\dfrac{2(2)^3}{3}\right) - \left(\dfrac{22}{3}(0)+\dfrac{2(0)^3}{3}\right)\\\\=20 \text{ cubic units}[/tex]

The volume of the solid is [tex]20\text{ cubic units}[/tex]

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Answer:

  True

Step-by-step explanation:

In simplest terms, if the triangle is ΔABC with ∠B≅∠C, then you can show ΔABC ≅ ΔACB using the ASA congruence theorem. (BC≅CB by the symmetric property). Then AB ≅ AC by CPCTC (corresponding parts of congruent triangles are congruent).

To remove the area of 20'x22' from the total space of 2240 square feet, multiply the dimensions to get the area to deduct, which is 440 square feet. Then subtract this from the total area to find the remaining space, which is 1800 square feet.

To deduct an area of 20 feet by 22 feet from a total space of 2240 square feet, you first need to calculate the area of the space you are removing. To find the area of a rectangle, you multiply its length by its width.

Area to deduct = Length × Width = 20' × 22' = 440 square feet.

Next, subtract the area to deduct from the total space:

Remaining space = Total space - Area to deduct = 2240 sq ft - 440 sq ft = 1800 square feet.

Therefore, you are left with 1800 square feet of space after deducting the area of 20'x22' from the original total space of 2240 square feet.

Answer:

(y-6)

Step-by-step explanation:

[tex]y^2 - 10y + 24[/tex]

We need to find out two factors whose product is 24 and sum is -10

-6  times -4 = 24

-6  +    -4 = -10

So two factors are -6  and -4

We write the factors inside the parenthesis

(y-6) (y-4)

Factor (y-4) is already given

So another factor is (y-6)

Final Answer:

y - 6

Explanation:

To find another factor of the quadratic expression (y^2 – 10y + 24) given that (y – 4) is one factor, we need to perform factorization. Let's find the factors of the constant term, 24, which when added together give us the coefficient of the middle term, which is –10.
The factors of 24 are: 1, 2, 3, 4, 6, 8, 12, and 24.
We are looking for two factors of 24 that add up to –10, and since one of the given factors is (y – 4), we are specifically looking for factors that would give us ((y - 4)) when multiplied by a binomial of the form (y - n), where (n) represents the other factor.
Now, notice that the factors 6 and 4 add up to 10, and when multiplying two binomial factors, we actually find such that when expanded they give us the original quadratic expression. In this case, (6 times 4 = 24), and (-6 + (-4) = -10), which are our constant and coefficient of \(y\), respectively.
Therefore, we can write the quadratic expression as the product of two binomial expressions: ((y - 6)(y - 4))
Since we are already given that \(y - 4\) is a factor, the other factor must be (y - 6).

Answer:

Option: B is the correct answer.

  B. The function has more than one x-intercept.

Step-by-step explanation:

We are given a table of  values as follows:

            x                    y

           -3                    4

            0                    -3

             1                     2

             5                    0

             11                    7  

As we know that a function is a continuous function this means that the graph first decreases from 4 to -3 ( since at x=-3 we have y=4 and at x=0 we have y= -3) and then it increases from -3 to 7 ( since at x=0 we have y= -3 and at x=11 we have y=7)

Hence, the function will intersect the x-axis two times between x= -3 and x=11.

           Hence, the function has more than one x-intercept.

Answer: The function had more than in intercept,

Step-by-step explanation:

If the gross income is $34,100,113.67 was deducted from each paycheck for his 401(k) plan.

It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.

The usage of percentages is widespread and diverse. For instance, numerous data in the media, bank interest rates, retail discounts, and inflation rates are all reported as percentages. For comprehending the financial elements of daily life, percentages are crucial.

It is given that last year, a janitorial supervisor had a gross income of $34,100 of which he contributed 8% to his 401(k) plan.

As a result,

=8% of 34,100

=0.08(34,100)

=2728

Given that there are 12 months in a year and he is paid every two months, or twice a month, for a total of 24 payments,

=2728/24

= 113.666

Thus, if the gross income is $34,100,113.67 was deducted from each paycheck for his 401(k) plan.

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The conversion of 68 kilometers into meters gives 68000 meters, not 0.068 meters. The error arises due to dividing instead of multiplying the kilometers by 1000 (because 1 km equals 1000m).

When you are converting from kilometers to meters, you need to understand that 1 kilometer is equal to 1000 meters. Therefore, to convert 68 kilometers to meters, you should multiply 68 by 1000, not dividing it. You calculate 68km * 1000 = 68000m. So, 68 kilometers is equal to 68,000 meters, not 0.068 meters. The response 0.068 meters is incorrect because it is vastly smaller than the actual conversion result.

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The probability that a student graduates given that the student plays one or more sports = probability that students play one or more sports and who graduate/probability that students play one or more sports

  = 0.67 / 0.72

  = 0.9306 (Answer)

Answer:

The height of the original triangle is [tex]5\ inches[/tex]

Step-by-step explanation:

we know that

The scale factor is equal to divide the length of the corresponding side of the reduced triangle by the length of the corresponding side of the original triangle

Let

z-----> the scale factor

x----->  the length of the corresponding side of the reduced triangle

y-----> the length of the corresponding side of the original triangle

so

[tex]z=\frac{x}{y}[/tex]

in this problem we have

[tex]z=0.4[/tex]

[tex]x=2\ in[/tex] -----> the height of the reduced triangle

substitute and solve for y

[tex]0.4=\frac{2}{y}[/tex]

[tex]y=2/0.4=5\ in[/tex]

Answer:

x = 8.4

Explanation:

Mathematics uses numbers, variables, and operations, particularly in algebraic expressions. An example of this is the equation 5x + 2 = 12, where '5' and '2' are numbers, 'x' is variable, and '+' and '=' are operation symbols.

The subject that uses numbers, variables, and operations is Mathematics. This combination is commonly seen in algebraic expressions. For example, in the equation 5x + 2 = 12, '5' and '2' are numbers, 'x' is a variable, and '+' and '=' are operation symbols. The numbers are used as constants or coefficients, the variable represents an unknown value, and the operations symbols dictate how these elements should interact. Through algebra, we can solve this equation and find the value of the variable 'x'.

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In Mathematics, particularly Algebra, numbers, variables and operation symbols are frequently used. This language is evident in forms like scientific and exponential notation, which are methods to represent large quantities using powers of ten.

The system of using numbers, variables, and operation symbols is commonly seen in Mathematics. In particular, this is prominent in Algebra, where numbers are often represented by variables, and operations like multiplication, division, addition, or subtraction involve these variables. One form of this language includes scientific notation. Scientific notation is a mathematical expression used to represent very large numbers using powers of ten. For instance, 500,000,000 can be written as 5 × 10^8 in scientific notation. Another way to express large quantities is through exponential notation, where the number is represented as a product of two numbers, one of which is a power of ten. Learning and practicing how to use these forms becomes essential for further scientific studies.

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In the function sin⁻¹(9x + 1), the 'outside' function is sin⁻¹(x). This is because it is the function performing an operation on the 'inside' function, which is 9x + 1.

For the function sin−1(9x + 1), the 'inside' function is indeed 9x + 1. The 'outside' function is sin⁻¹(x), also known as the inverse sine or arcsine function. In composite functions, the 'inside' function is the function that is being acted on, while the 'outside' function is the function carrying out the action on the inside function. So here, the action of sine inverse or arcsine is being performed on the 'inside' function 9x + 1.

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Answer:

Markup percent = 117.50%

Step-by-step explanation:

Markup percent = (sales price - unit cost)/unit cos  *100

Given: Unit cost = $16.55, sales price = $35.99

Now plug in these given values in the above formula, we get

Markup percent = (35.99 - 16.55)/16.55 *100

= (19.44/16.55)*100

= 117.50%

Hope this will helpful.

Thank you.