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Answer:

21

Step-by-step explanation:

Answer:

yes it  is a rational number

Step-by-step explanation:

if we convert the mixed fraction into an improper fraction, we will get:

6 1/2  = 13/2

Recall that the definition of an Rational number is that it can be expressed as a division of two integers.

in our case, the numerator is 13 (which is an integer) and the denominator is 2 (which is also an integer)

hence according to our definition it is a rational number

The mixed fraction number 6 1/2 is a terminating number. Then the number is a rational number.

If the value of a numerical expression is terminating then they are the rational number then they are called the rational number and if the value of a numerical expression is non-terminating then they are called an irrational number.

The mixed fraction number is given below.

⇒ 6  1/2

Convert the mixed fraction number into the fraction number. Then we have

⇒ 6  1/2

⇒ 6 + 1/2

⇒ (12 + 1)/2

⇒ 13/2

Convert the fraction number into a decimal number. Then we have

⇒ 13/2

⇒ 6.5

The mixed fraction number 6 1/2 is a terminating number. Then the number is a rational number.

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The equation of the parabola is \($\dfrac{(x - 4)^2}{8(y - 1)} = 1$\)

The equation of a parabola with focus (h, k + p) and directrix y = k - p can be written as:

\($\dfrac{(x - h)^2}{4p(y - k)} = 1$\)

In this case, the focus is (4, 3) and the directrix is y = -1. Comparing this with the general equation of a parabola, we can determine the value of p.

k + p = 3 (since the y-coordinate of the focus is 3)

k - p = -1 (since the equation of the directrix is y = -1)

Adding these two equations, we get:

2k = 2

Dividing by 2, we find:

k = 1

Substituting this value back into one of the equations, we can solve for p:

1 + p = 3

p = 2

So, the value of p for this parabola is 2.

The equation of the parabola can be written as:

\($\dfrac{(x - 4)^2}{8(y - 1)} = 1$\)

This represents a parabola with focus at (4, 3) and directrix y = -1.

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There are 5 one fifths for every 1 whole number:

5/5 = 1

200 x 5 = 1000

There are 1000 one fifths in 200

The volume of the box with surface area 10 is given by the formula V = 2.5x^2 - 0.25x^4, where x is the length of a side of the square base.

To find a formula for the volume of the box with surface area A and square base with side x, we first need to find the height of the box. Since the box has a square base, the area of the base is x^2. The remaining surface area is the sum of the areas of the four sides, each of which is a rectangle with base x and height h. Therefore, the surface area A is given by:

A = x^2 + 4xh

Solving for h, we get:

h = (A - x^2) / 4x

The volume V of the box is given by:

V = x^2 * h

Substituting the expression for h, we get:

V = x^2 * (A - x^2) / 4x

Simplifying, we get:

V = (Ax^2 - x^4) / 4

The domain of V is all non-negative real numbers, since both x^2 and A are non-negative.

To graph V as a function of x, we can use a graphing calculator or plot points using a table of values. The graph will be a parabola opening downwards, with x-intercepts at 0 and sqrt(A) and a maximum at x = sqrt(A) / sqrt(2).

To find the maximum value of V, we can take the derivative of V with respect to x and set it equal to 0:

dV/dx = (2Ax - 4x^3) / 4

Setting this equal to 0 and solving for x, we get:

x = sqrt(A) / sqrt(2)

Plugging this value of x into the formula for V, we get:

V = A^1.5 / (4sqrt(2))

Therefore, the maximum value of V is A^1.5 / (4sqrt(2)).

To find the formula for the volume of a box having surface area 10, we simply replace A with 10 in the formula we derived earlier:

V = (10x^2 - x^4) / 4

Simplifying, we get:

V = 2.5x^2 - 0.25x^4

Therefore, the volume of the box with surface area 10 is given by the formula V = 2.5x^2 - 0.25x^4, where x is the length of a side of the square base. The domain of V is all non-negative real numbers.

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Answer:

55 i think

Step-by-step explanation:

A relation in math is a set of ordered pairs containing two elements, one from each set. The first element is from the domain and the second from the range.

Relations can be expressed as a set of ordered pairs, as a graph, or as a mapping diagram. A function is a special type of relation in which, for every element in the domain, there is one and only one element in the range. This is expressed mathematically by stating that for every x in the domain, there is one and only one y in the range such that y = f(x). To calculate a relation, the domain and range values are paired with each other, and the ordered pairs are written down. For example, if the domain is {2,3,4,5} and the range is {7,8,9,10}, then the relation would be {(2,7),(3,8),(4,9),(5,10)}.

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Answer: 8

Step-by-step explanation: to find 20% multiply 40 by .20

Answer:

the first one is c if you round it up and for the second question that is 4.95

Step-by-step explanation: hope this helps

Answer:

so you will put the point above the zero across from 6

the slope is rise/run

Step-by-step explanation:

Answer: Your answer would be C: f¹(x) = x³ + 11

Answer:

\(f'(x)= \frac{13}{(2x+3)^2}\\\)

Step-by-step explanation:

\(f(x)= \frac{3x-2}{2x+3} \\\)

\(f'(x)=\frac{dy}{dx} = \frac{d}{dx}(\frac{3x-2}{2x+3})\\ f'(x)= \frac{(2x+3)\frac{d}{dx}(3x-2)-(3x-2)\frac{d}{dx}(2x+3) }{(2x+3)^{2} } \\f'(x)= \frac{(2x+3)(3)-(3x-2)(2)}{(2x+3)^{2} } \\\)

\(f'(x)= \frac{6x+9-6x+4}{(2x+3)^{2} }\\ f'(x)= \frac{13}{(2x+3)^2}\\\)

Answer:

The zero product property tells us that if we multiply two quantities together and get zero, then one or both of these is equal to zero.

In symbols this means that if ab = 0 then a = 0, b = 0 or both.

This means that if we have a product equal to zero one of both of the factors (the things we are multiplying together) is equal to zero.

Of the equations given, the only one that has product (a few terms multiplied together) equal to zero is -(x-1)(x+9)=0 so this is the one that can most appropriately be solved by the zero product property.

We can re-write -(x-1)(x+9) = 0 as (-1)(x-1)(x+9) = 0 which means (x-1) or (x+9) or both equal zero. It should be clear that -1 cannot equal zero.

To solve we set x - 1 = 0 and obtain x = 1.

Next we set x + 9 = 0 and obtain x = -9

The solutions to the equation are x = -9 and x = 1.

We are, however, asked for two equations. Though none of the remaining equations has a product set equal to zero, we can re-write the equation  by factoring 3x from each term on the left-hand side. Doing so gives us . Now we have a product equal to zero which means that one or both of the factors on the left-hand side equals zero.

That is, 3x equals 0, or x-2 equals 0 or both do. If 3x = 0 then x = 0. If x-2=0 then x=2. As such the solution to the equation is x = 0, x = 2.

Step-by-step explanation: sorry if its a lot

The value of x in the equation (2+10^x)^0.50=7 is approximately 1.158 (rounded to three decimal places).

To find the value of x, we can start by isolating the term inside the parentheses on the left-hand side of the equation:

(2+10^x)^0.50 = 7

Raising both sides to the power of 2, we get:

2+10^x = 49

Next, we can subtract 2 from both sides:

10^x = 47

To solve for x, we can take the logarithm of both sides using base 10 logarithm:

log10(10^x) = log10(47)

x = log10(47)

Using a calculator, we find that log10(47) is approximately 1.672.

Therefore, the value of x in the equation (2+10^x)^0.50=7 is approximately 1.158 (rounded to three decimal places).

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Answer:

(-1,1)

Step-by-step explanation:

Answer:

(- 1, 1 )

Step-by-step explanation:

2x - 3y = - 5 → (1)

3x + y = - 2 → (2)

multiplying (2) by 3 and adding to (1) will eliminate y

9x + 3y = - 6 → (3)

add (1) and (3) term by term to eliminate y

11x + 0 = - 11

11x = - 11 ( divide both sides by 11 )

x = - 1

substitute x = - 1 into either of the 2 equations and solve for x

substituting into (2)

3(- 1) + y = - 2

- 3 + y = - 2 ( add 3 to both sides )

y = 1

solution is (- 1, 1 )

Answer:

12

Step-by-step explanation:

Answer:

In geometry, postulates are statements that are accepted as true without proof. The three postulates for congruent triangles are ASA, SSS, and SAS. These postulates are used to prove that two triangles are congruent.

ASA Postulate:

ASA stands for "Angle, Side, Angle." This postulate states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

Visual example:

In the above image, ΔABC and ΔDEF have ∠A ≅ ∠D, ∠B ≅ ∠E, and AB ≅ DE. Therefore, we can conclude that ΔABC ≅ ΔDEF by ASA postulate.

SSS Postulate:

SSS stands for "Side, Side, Side." This postulate states that if the three sides of one triangle are congruent to the three sides of another triangle, then the two triangles are congruent.

Visual example:

In the above image, ΔABC and ΔDEF have AB ≅ DE, BC ≅ EF, and AC ≅ DF. Therefore, we can conclude that ΔABC ≅ ΔDEF by SSS postulate.

SAS Postulate:

SAS stands for "Side, Angle, Side." This postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

Visual example:

In the above image, ΔABC and ΔDEF have AB ≅ DE, BC ≅ EF, and ∠B ≅ ∠E. Therefore, we can conclude that ΔABC ≅ ΔDEF by SAS postulate.

Overall, the ASA, SSS, and SAS postulates are important tools in proving the congruence of triangles in geometry. They allow us to make logical deductions about the properties of triangles based on their corresponding angles and sides.

Answer:

They are different because ASA means that the two triangles have two angles and the side between the angles congruent. SAS means that two sides and the angle in between them are congruent

Step-by-step explanation:

and sss If all the three sides of one triangle are equivalent to the corresponding three sides of the second triangle, then the two triangles are said to be congruent by SSS rule.

\(4x+22~ > ~-2(14+3x)\implies 4x+22~ > ~-28-6x\implies 10x+22 > -28 \\\\\\ 10x > -50\implies x > \cfrac{-50}{10}\implies x > -5\)

Check the picture below.

The slope of the line passing through the coordinates 8(0, 0) and (-2 , 1) is -1/2

The formula for calculating the slope of a line is expressed as

slope = y2-y1/x2-x1

Given the coordinate points (0, 0) and (-2 , 1), the slope is expressed as:

Slope = 1-0/-2-0

Slope = 1/-2

Slope = -1/2

Hence the slope of the line passing through the coordinates 8(0, 0) and (-2 , 1) is -1/2

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The slope of the line m is - 1 / 2.

The slope a line can be found as follows:

slope = m = y₂ - y₁ / x₂ - x₁

using (0, 0)(2, -1)

hence,

slope = - 1 - 0 / 2 - 0

slope = - 1 / 2

hence,

slope = - 1 / 2

Therefore, the slope of the line m is - 1 / 2.

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Answer:

\(\sqrt{1}\)

Step-by-step explanation:

Anything to the zeroth power becomes 1, and anything to the negative power can be turned into the root of it. For example, 1 to the -2 power = \(\sqrt{1\\}\)

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To eliminate the xs in the system of equations, we multiply the second equation by -2 and add them

From the question, we have the following parameters that can be used in our computation:

2x + 9y = 18

x + y= 12

To eliminate the xs in the system of equations, we multiply the second equation by -2

So, we have

2x + 9y = 18

-2x + -2y = -24

Next, we add the equations

7y = -6

Hence, the new equation is 7y = -6

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Answer:

angle A measure 50 defree and angle B measure 40 degrees

The numbers are:

First number is:

6

Second number is:

3^2 = 9

4^2 = 16

So, Square Root of 15 is really close to 4, but less.

Third Number is:

4.5

Fourth Number is:

3.2

Fifth Number is:

5^2 = 25

6^2 = 36

So, square root of 27 is close to 5, but greater.

Least to Greatest:

The surface area of the shape is 168 square cm

The surface area of a figure is the area of the faces of the given figure.

For the given figure, the area will be the sum of area of 2 triangles and 3 rectangles.

Area = (6*3) +(10*6)+(6+10) +(10*3)

Surface area = 18 + 120 + 30

Surface area = 168 square cm

Hence the surface area of the shape is 168 square cm

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To evaluate the integral ∫3x cos(8x) dx, we need to find an antiderivative of the given function. The result will be expressed in terms of x and may include a constant of integration, denoted by C.

To evaluate the integral, we can use integration by parts, which is a technique based on the product rule for differentiation. Let's consider the function u = 3x and dv = cos(8x) dx. Taking the derivative of u, we get du = 3 dx, and integrating dv, we obtain v = (1/8) sin(8x).

Using the formula for integration by parts: ∫u dv = uv - ∫v du, we can substitute the values into the formula:

∫3x cos(8x) dx = (3x)(1/8) sin(8x) - ∫(1/8) sin(8x) (3 dx)

Simplifying this expression gives:

(3/8) x sin(8x) - (3/8) ∫sin(8x) dx

Now, integrating ∫sin(8x) dx gives:

(3/8) x sin(8x) + (3/64) cos(8x) + C

Thus, the evaluated integral is:

∫3x cos(8x) dx = (3/8) x sin(8x) + (3/64) cos(8x) + C, where C is the constant of integration.

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The quotient rule states that when dividing two powers

that have the same base, subtract their exponents.

Since each of the powers in this problem has a base of g,

we can simplify the expression by subtracting the exponents.

4 - 2 is 2 so our answer is g².