Let R be the region in the first quadrant bounded by the x-axis, the graph of x=y2+2, and the line x=4. What is a the interval for the area of R?

There is no inverse of the parabola function

An open curve or conic section known as a parabola is created when a right circular cone and a plane perpendicular to one of the cone's elements cross. It is a quadratic equation-defined symmetric U-shaped curve. A function's inverse is the graph of the function projected over the line y=x.

There is no inverse function for the parabola because it is not a one-to-one function. A one-to-one function is one in which every element in its domain corresponds to precisely one element in its range. It's not a one-to-one function in a parabola because as the x value increases, the y value might take a variety of values and vice versa. It can't be inverted because of this.

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The water level will increase by 0.00167 inches, so the correct option is A.

We know that Lisa spilled a volume of 1 quart of water on its pool, and the dimensions of the pool are:

12ft = 12*(12 inches) = 144 inches

20ft = 20*(12 inches) = 240 inches.

And we know that:

1 quart = 57.75 in³

Then if the level change is H, then then we can write the equation for the volumes:

1 quart = volume of increase in the pool

1 quart = (144 in)*(240 in)*H

57.75 in³ =  (144 in)*(240 in)*H

H = (57.75 in³)/( (144 in)*(240 in))

H = 0.00167 in

So the correct option is A.

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The number of laps that Noriko needs to run is given as follows:

6 laps.

The number of laps that Noriko needs to run is obtained applying the proportions in the context of this problem.

The length of one lap is given as follows:

1/6 miles.

Hence the number of laps that Noriko needs to run for a total of one mile is obtained dividing one mile by the length of a single lap, as follows:

1/(1/6) = 6 x 1 = 6 laps.

Each lap around the school's track is of 1/6 mi.

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Answer:

Step-by-step explanation:

as the there is a box one time had :

300-----> 6150g

2150----> 5150g ( 5.15 kg converted to grams which is time 1000)

divide each number on its weight you will find the difference is 20.5  g which is the weight

6150/300= 20

5150/250= 20

When we put the following numbers in ascending order, the order becomes 790×10^-3 < 0.0079 × 10^3 < 79 < 7.9 × 10^2.

In ascending order, we need to arrange any given set of data in such a way that the smallest number comes first, and then comes the next bigger number, and then the next bigger, and so on. The largest number in that given data set comes at the end. We have to arrange the following in such a manner as well.

Since we can deduce that 790×10^-3 is the smallest of the lot, it comes first. The next bigger number is 0.0079 × 10^3 and so, it comes right after that. Just after this is the number 79 and then, the largest number of this data set is 7.9 × 10^2 and so, it is at the last. Hence, the order is as such -

= 790×10^-3 < 0.0079 × 10^3 < 79 < 7.9 × 10^2.

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The fraction of the watermelons that is ripe is 2 / 5.

The percentage of the watermelons that is ripe is 40%.

The water melons that is not rip is more likely to be picked at random because it is more in number

12 of the 30 watermelons were ripe. The fractions of the watermelon that are ripe can be calculated as follows:

fraction of watermelon that are ripe = 12 / 30

fraction of watermelon that are ripe = 6 / 15

fraction of watermelon that are ripe = 2 / 5

Hence, the percentage of the water melon that are ripe can be calculated as follows:

percentage of water melon that is ripe = 2 / 5 × 100

percentage of water melon that is ripe = 200 / 5

percentage of water melon that is ripe = 40%

If one of the watermelons is picked at random. It is more likely the watermelon that is not ripe  is picked. This is because the unripe watermelon has a higher probability of been picked because it is high in number.

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Answer: D

Step-by-step explanation: ? question

They spend $52 in total for the movie ticket and popcorn.

The substitution method is a simple way to solve a system of linear equations algebraically and find the solutions of the variables.

Given that,

Tickets (t) = $8

Popcorn & Soda (s)= $5

Friends = 4

Since all friends bought the same thing the equation will be set as

4(t +s) = m OR 4t +4s = m

Using substitution, you plug each variable

t = 8 and s = 5

4((8) + (5)) = m

4(8+5) = m => 4(13) =m => 52=m

OR

4(8) + 4(5) = m => 32 + 20 = m =>

52 =m

Thus, They spend $52 in total for the movie ticket and popcorn.

Complete question: Four friends went to the movies each ticket cost $8 and each person bought popcorn and a soda for $5 how much did they spend in all? let m stand for the amount of money spent

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The parabola's conventional form is y^2=4ax, which results in a parabola with an axis parallel to the x-axis, a vertex at the origin, a focus at (a,0), and a directrix at (x=a).

Since a=2 in your example, y^2=4ax is the result. The y-axis serves as the parabola's axis. The directrix equation is y = -a, which is equivalent to y = -12. There is a parabola's vertex at (0,0).

You must be aware that a parabola's equation in a vertex form is y=a(xh)^2+k, where a stands for the equation's slope, in order to determine the focus of a parabola. We can deduce from the formula that the parabola's focus lies at (h, k+1/4a).

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The number is one more than 39 is 40

Numbers are mathematical objects used for counting, measuring, and labeling. The original example is the natural numbers 1, 2, 3, 4, etc. Numbers can be linguistically represented by numerals. More generally, individual numbers can be represented by symbols called digits. For example, "5" is the number representing the number five. Since only a relatively small number of symbols can be remembered, basic numbers are usually organized into number systems, which are systematic ways of representing each number.

It is a mathematical term used to compare two quantities and to establish a relationship between two quantities in which one term is greater than the other. The terms greater than, less than, and equal are used to compare two numbers, amounts, or amounts. Each term has a separate letter. B. "greater than" is represented by ">".

According to the Question:

To better understand this question,

It can be expressed as 1 more than 39, 1 more than 39, 39 plus 1.

Thus,

1 more than 39 is the same as 39 plus 1. So the answer for 1 greater than 39 is calculated as:

Therefore,

1 + 39 = 40.

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The length of the longer base of the trapezoid is TP = 13 units

The Trapezoid is a 4 sided polygon. Two sides of the shape are parallel to each other and they are termed as the bases of the trapezoid. The non-parallel sides are known as the legs or lateral sides of a trapezoid.

There are three types of trapezoids , and those are given below:

a) Isosceles Trapezoid

b) Scalene Trapezoid

c) Right Trapezoid

The area of the Trapezoid is given by

Area of Trapezoid = ( ( a + b ) h ) / 2

where , a = shorter base of trapezium

b = longer base of trapezium

h = height of trapezium

Given data ,

Let the area of the trapezoid be A = 100 units²

Now , the length of the longer base b = 32 units

The length of the shorter base a = 8 units

Let the height of the trapezium be = h

Area of Trapezoid = ( ( a + b ) h ) / 2

Substituting the values in the equation , we get

100 = ( 32 + 8 ) x h / 2

200 = 40h

Divide by 40 on both sides of the equation , we get

h = 5 units

Now , the height be PE , where E lies 12 units from T

Now , from the Pythagoras equation , we get

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

Substituting the values in the equation , we get

TP² = PE² + TE² , where PE is the height of the triangle

TP² = 5² + 12²

TP² = 169

Taking square roots on both sides of the equation , we get

TP = 13 units

Hence , the length of the trapezium is 13 units

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Step-by-step explanation:

domain : the interval or set of all valid x-values.

range : the interval or set of all valid y-values (function result values).

A is correct

theoretically all real numbers are valid as x. but for this application of the function only non-negative integer values make sense (e.g. half a cycle does not make any sense).

C is correct

via A we are allowing all real numbers to be valid input values, so, we have to allow also all real numbers to be valid output (function result) values.

D is correct

the y-intercept means the y-value, when the function curve intersects the y-axis.

this is only possible, when x = 0.

5⁰ = 1

as any x⁰ = 1

F is correct

the bigger x, the bigger 5^x.

and the smaller x, the closer y, the function result, gets to 0. particularly, when we allow negative input values (as we said in A).

To evaluate 1/2yz when y = 3/5 and z = -17/8, we first substitute the given values for y and z into the expression:

1/2(3/5)(-17/8)

Next, we can simplify this by multiplying the fractions:

1/2 * 3/5 * -17/8 = (-3/10) * (-17/8)

To multiply the fractions we multiply the numerators and denominators separately:

(-3/10) * (-17/8) = (-3 * -17)/(10 * 8)

Then we can simplify the numerator by combining like terms:

(-3 * -17)/(10 * 8) = 51/40

So the final result of the expression is 51/40.

Answer:

_51/80

Step-by-step explanation:

1/2*3/5*_17/8

1/2×3/5×(_17/8)

3/10×(_17/8)

_51/80

The inequality expression and solution to a system of inequalities graphically is xx + yy <= 18

We can represent the system of inequalities as follows:

xx + yy <= 18 (representing the maximum number of pieces of furniture that can be shipped)

A possible solution could be:

xx = 8 (number of tables sold)

yy = 10 (number of chairs sold)

100yy + 450xx >= 3200 (representing the minimum amount of money that must be made from the sale of chairs and tables)

xx >= 8 (representing the minimum number of tables that must be sold)

To graphically represent this system of inequalities, we can begin by graphing the first inequality in a coordinate plane. The inequality xx + yy <= 18 can be represented by a line with the equation y = -x + 18.

Next, we can graph the second inequality. The inequality 100yy + 450xx >= 3200 can be represented by a line with the equation y = -(4.5/5)x + 80.

Finally, we can graph the third inequality, which is a horizontal line at y = 8.

Now we can graph these three inequalities, one line for each inequality, and see where they intersect. The point where all three lines intersect is one possible solution for the system of inequalities.

A possible solution could be:

xx = 8 (number of tables sold)

yy = 10 (number of chairs sold)

However, this solution is within the constraints of the problem and satisfies all three inequalities.

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The segment addition postulate holds true in this example.

The segment addition postulate states that if two line segments have the same end points, then the two segments are congruent. This postulate can be expressed using the following formula: AB + BC = AC. This formula states that the sum of the lengths of two segments with the same endpoints (AB and BC) is equal to the length of the third segment (AC). To illustrate this rule, imagine a line segment AB with a length of 5 units. If we add another line segment BC to the same line segment, with a length of 3 units, then the combined length of the two segments (AB + BC) would be 8 units, which is also the length of the third segment (AC). Therefore, the segment addition postulate holds true in this example.

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Complete question:

Is the Segment Addition Postulate true?

The exponential equation that describes the monster's growth, in meters, is given as follows:

y = 0.02(5)^x.

The height of the monster after 3.7 days is given as follows:

19.3 meters.

An exponential function is defined as follows:

y = ab^x.

For which the parameters are given as follows:

Considering the initial height of the monster and the fact that the height is multiplied by five each day, the function is given as follows:

y = 0.02(5)^x.

Hence the height after 3.7 days is given as follows:

y = 0.05(5)^3.7

y = 19.3 meters.

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The lateral surface area of a cylinder is 1110.8 cm².

Consider a very thin cross section of a cylinder whose thickness is [dh] {differential or very small value}. The volume of this cross section would be -

dV = πr² dh

For complete cylinder -

∫dV = πr² ∫dh

[V - 0] =  πr² [h - 0]

V =  πr²h

Given are the dimensions of a cylinder are shown in the diagram.

We can write the lateral surface area as -

LSA = 2πrh

LSA = 2 x 3.14 x 8.8 x 20.1

LSA = 1110.8  square centimeters.

Therefore, the lateral surface area of a cylinder is 1110.8 cm².

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The lengths a and b be value of a = 24 sinθ, and b = 24 cosθ.

sinθ = opposite / hypotenuse

cosθ = adjacent / hypotenuse

tanθ = opposite / adjacent

The side that touches the angle but is not the hypotenuse is referred to as the adjacent side, while the side that is immediately across from the angle is referred to as the opposite side and does not touch the angle. The triangle's longest side is always the hypotenuse.

This information allows us to identify an as the opposing side and b as the neighboring side. Now all you have to do is utilize your angle to get the value of these lengths using SOHCAHTOA.

Since an is the opposite side, we shall utilize sine for it. Keep in mind that your hypotenuse is 24; therefore, we can enter in the data we have and solve for the missing lengths:

sinθ = opposite / hypotenuse

       = a / 24

    a = 24sinθ

For b, because it is the adjacent side, we will use cosine.

cosθ = adjacent / hypotenuse

        = b / 24

     b = 24cosθ

Therefore, the value of a = 24sinθ, and b = 24cosθ.

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A function's range is the set of values which that function can take. This represents the collection of values that the function returns after we enter an x value.

The domain of a procedure is the set of values that can be plugged into it. This set contains the x values in a function like f. (x).

A function's range is indeed a set of integers that it can generate.

In certain terms, this is the set of y-values obtained by plugging all possible x-values into the function. The domain is the set of all potential x-values.

A function in mathematics is a defined interaction between this and an autonomous variable (x) and a completely reliant variable (y).

A function's range refers to all of the potential values for y. The method used to calculate a function's range is y = f. (x).

The distinction between the lowest and highest numbers is called the range. When there are extraordinarily high or low values, the range can be deceiving.

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Answer:

[tex]\textsf{1)} \quad 4.1875[/tex]

[tex]\textsf{2)} \quad \dfrac{1}{2}x^{4}-x^{3}+x^{2}-3x+\text{C}[/tex]

Step-by-step explanation:

Fundamental Theorem of Calculus

If differentiating takes you from one function to another, then integrating the second function will take you back to the first with a constant of integration:

[tex]\displaystyle \int \text{f}(x)\:\text{d}x=\text{F}(x)+\text{C} \iff \text{f}(x)=\dfrac{\text{d}}{\text{d}x}(\text{F}(x))[/tex]

The area between a curve and the x-axis can be found using definite integration.  The definite integral of f(x) with respect to x between the limits x = a and x = b:

[tex]\displaystyle \int^b_a \text{f}(x)\; \text{d}x=\left[\text{g}(x)\right]^b_a=\text{g}(b)-\text{g}(a)[/tex]

where a is the lower limit and b is the upper limit.

[tex]\boxed{\begin{minipage}{4 cm}\underline{Integrating $x^n$}\\\\$\displaystyle \int x^n\:\text{d}x=\dfrac{x^{n+1}}{n+1}\left(+\text{C}\right)$\end{minipage}}[/tex]

Given function:

[tex]\text{f}(x)=\dfrac{1}{4}x^3+\dfrac{1}{6}x+1[/tex]

From inspection of the given graph:

Therefore:

[tex]\begin{aligned}\displaystyle\int^2_{-1}\left(\dfrac{1}{4}x^3+\dfrac{1}{6}x+1\right)\;\text{d}x&=\left[\dfrac{1}{4\cdot4}x^{3+1}+\dfrac{1}{6\cdot 2}x^{1+1}+x\right]^2_{-1}\\\\&=\left[\dfrac{1}{16}x^4+\dfrac{1}{12}x^2+x\right]^2_{-1}\\\\&=\left(\dfrac{1}{16}(2)^{4}+\dfrac{1}{12}(2)^2+(2) \right)-\left(\dfrac{1}{16}(-1)^4+\dfrac{1}{12}(-1)^2+(-1)\right)\\\\&=\left(1+\dfrac{1}{3}+2\right)-\left(\dfrac{1}{16}+\dfrac{1}{12}-1\right)\\\\&=\dfrac{10}{3}+\dfrac{41}{48}\\\\&=\dfrac{67}{16}\\\\&=4.1875\end{aligned}[/tex]

[tex]\begin{aligned}\displaystyle \displaystyle \int (x^2+1)(2x-3)\; \text{d}x&=\displaystyle \int \left(2x^3-3x^2+2x-3\right)\; \text{d}x\\\\&=\dfrac{2}{4}x^{3+1}-\dfrac{3}{3}x^{2+1}+\dfrac{2}{2}x^{1+1}-3x+\text{C}\\\\&=\dfrac{1}{2}x^{4}-x^{3}+x^{2}-3x+\text{C}\end{aligned}[/tex]

The quadratic equation has a negative value that is a maximum if vertex constant is negative but vertex y-coordinate is negative, while it has a positive value that is a minimum if vertex constant is positive by vertex y-coordinate is positive.

Graphically speaking, quadratic functions are parabolae and their absolute extremes are called vertices. There are three ways to describe quadratic functions:

Standard form

y = a · x² + b · x + c

Factor form

y = a · (x - r₁) · (x - r₂)

Vertex form

y - k = C · (x - h)²

Where:

Vertex form offers us a quick possibility to answer this question, from its understanding we get the following conclusions:

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Yes. 64 is a real number. Real numbers can be expressed as infinite decimal expansion.

Real numbers includes integers, natural numbers. Real numbers can be of positive and can be of negative numbers. Real numbers can be both a rational number or a irrational numbers. These two are the main groups of real numbers. Rational numbers are written as the ratio of two integers. Irrational numbers are not written as the ratio of two integers. Irrational numbers are the type of real numbers. 64 is a real number as well as a perfect square of a number. It is a perfect square of the 8. This explains the properties of Real numbers.

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The cost of lower and upper level seats are $28 and $18 each, respectively.

Let x be the cost of the lower level seats

We know that the upper level seats are $10 cheaper, so their cost can be expressed as the algebraic expression x - 10.

We also know that the total number of seats is 8000, and 3000 of them are upper level seats, and a sellout has a total revenue of $194 000.

So we can set up the following algebraic equation:

(8000 - 3000)x + 3000(x - 10) = 194 000

Simplify the equation and solve for the value of x.

5000x + 3000x - 30 000 = 194 000

8000x = 224 000

x = 28

So, the cost of the lower section seats is $28 and the cost of the upper level seats is $18.

The problem seems incomplete, it must have been

"In a small hockey arena with 8000 seats there are 3000 upper level seats which are $10 cheaper than the remaining lower section seats. For a sellout to a Memorial Cup game the total revenue was $194 000. Find the cost of each type of ticket."

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Answer: i am really sorry but no whts

The area of the composite figure is 124 square miles.

Composite figures are the result of uniting two or more geometric figures, in this case, we need to determine the area of a composite figure that results from the union of two right triangles and two rectangles, whose area formulas are described below:

Rectangle

A = w · l

Right triangle

A = 0.5 · w · l

Where:

Now we proceed to calculate the area of the composite figure:

A = 0.5 · (6 mi) · (18 mi) + 0.5 · (8 mi) · (3 mi) + (6 mi) · (5 mi) + (4 mi) · (7 mi)

A = 124 mi²

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The product of 4 and 0 is zero.

We know that a product is an operation where two or more numbers are multiplied together to get a single result.

In case of small numbers a multiplication is considered repeated addition, and we can solve simple multiplication problems by adding repeatedly.

Generally, the types of multiplication method : addition method, long multiplication, grid method, drawing lines and by splitting two digit numbers into Tens and Ones

We know that if we multiply any non-zero real number by zero then the result / product is always 0.

This property of multiplication is called as the Zero property of multiplication.

So, the product of 4 and 0 is always zero.

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Answer: Add 4 to both sides

Hope this helps :)

Step-by-step explanation:

20=6x-4

+4      +4

24=6x

/6   /6

4=x

The expression 1.3H represents the relationship between the number of health points restored by Eiko's healing spell with and without the magic ring.

H represents the number of health points restored by the spell without the ring. The expression 0.3H represents the additional 30% increase in the power of the spell due to the magic ring, as the ring increases the spell's power by 30%.

Adding the two, H + 0.3H, gives us the total number of health points restored by the spell with the magic ring, which is equal to 1.3 times the number of health points restored by the spell without the ring.

So, when Eiko is wearing the magic ring, her healing spell restores 1.3 times as many health points as without the ring, represented by the expression 1.3H.

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The angle between lines 2x 3y =- Z is 90°

We will simplify the given equation of lines in the standard form of x/a=y/b=z/c

where a, b and c are the direction ratios of the line.

We will calculate the angle between these lines using the formula:

[tex]cos\alpha =\frac{a_{1}a_2 +b_1b_2+c_1c_2}{\sqrt{a_1^2+b_1^2+c_1^2}\sqrt{a_2^2+b_2^2+c_2^2} }[/tex]

we are given two lines as 2x = 3y = – z and 6x = -y = -4z

We can write them in standard form xa=yb=zc

as:

For 2x = 3y = – z ⇒x/1/2=y/1/3=z/−1/4

Comparing this equation with the standard equation, we get the direction ratios of this line:

a₁= 1/2

b₁=1/3

c₁ = -1

For 6x = -y = -4z ⇒x/1/6=y−1=z/−1/4

Comparing this equation with the standard equation, we get the direction ratios of this line:

a₂= 1/6, b₂= -1, c₂= −1/4

Now, putting these values of a₁, a₂, b₁, b₂, c₁, and c₂

in the equation of cosα, we get

[tex]cos\alpha =\frac{a_{1}a_2 +b_1b_2+c_1c_2}{\sqrt{a_1^2+b_1^2+c_1^2}\sqrt{a_2^2+b_2^2+c_2^2} }[/tex]

[tex]cos\alpha =\frac{\frac{1}{2} *\frac{1}{6} +\frac{1}{3} *(-1)+(-1)\frac{(-1)}{4} }{\sqrt{(\frac{1}{2})^2 +(\frac{1}{3})^2 +(-1)^2}\sqrt{(\frac{1}{6} )^2+(-1)^2+(\frac{-1}{4})^2 } }[/tex]

[tex]cos\alpha =\frac{\frac{1}{12} -\frac{1}{3} +\frac{1}{4} }{{\sqrt{(\frac{1}{2})^2 +(\frac{1}{3})^2 +(-1)^2}\sqrt{(\frac{1}{6} )^2+(-1)^2+(\frac{-1}{4})^2 } } }[/tex]

[tex]cos\alpha =\frac{\frac{1}{12} -\frac{1}{12} }{{\sqrt{(\frac{1}{2})^2 +(\frac{1}{3})^2 +(-1)^2}\sqrt{(\frac{1}{6} )^2+(-1)^2+(\frac{-1}{4})^2 } } }[/tex]

cosα=0°

cos⁻¹(cosα)=cos⁻¹(0)

α=90°

Therefore, the angle between the lines 2x = 3y = – z and 6x = -y = -4z is 90°

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