A 2-column table has 4 rows. The first column is labeled x with entries 1, 2, 3, 4. The second column is labeled y with entries 4.5, 6.75, 10.125, 15.1875.
What is the multiplicative rate of change of the exponential function represented in the table?

1.5
2.25
3.0
4.5
A 2-column table has 4 rows. The first column is labeled x with entries 1, 2, 3, 4. The second column is labeled y with entries 4.5, 6.75, 10.125, 15.1875.
What is the multiplicative rate of change of the exponential function represented in the table?

1.5
2.25
3.0
4.5

Step-by-step explanation:

As it is given that, a cylinder has a height of 15 yards and the volume of the cylinder is 15,260.4 cubic yards and we are here to find the radius of the cylinder.

\( \: \)

We know that,

\({ \longrightarrow\qquad{\frak {\pmb{ \pi {r}^{2}h = Volume_{(cylinder) } }}}} \\ \\\)

Where,

\( \: \)

Now, we will substitute the given values in the formula :

\( \: \)

\({ \longrightarrow\qquad{\sf {\pmb{ 3.14 \times {r}^{2} \times 15 = 15260.4 }}}} \\ \\\)

\({ \longrightarrow\qquad{\sf {\pmb{ {r}^{2} \times 47.1 = 15260.4 }}}} \\ \\\)

\({ \longrightarrow\qquad{\sf {\pmb{ {r}^{2} = \dfrac{15260.4}{47.1} }}}} \\ \\\)

\({ \longrightarrow\qquad{\sf {\pmb{ {r}^{2} \ = 324 }}}} \\ \\\)

\({ \longrightarrow\qquad{\sf {\pmb{ r = \sqrt{324} }}}} \\ \\\)

\({ \longrightarrow\qquad{ \underline{ \boxed{\pmb {\frak{ r = 18 } }}}}} \: \: \: \bigstar\\ \\\)

\( \: \)

Therefore,

Answer:

Step-by-step explanation:

Given:

To Find:

Solution:

Here we are given height and volume of the cylinder. To find the radius of the cylinder We will substitute the value of height and volume in give formula:

Volume of cylinder = πr²h

➝ 15,260.4 = 22/7 × (r)² × 15

➝ 15,260.4 = (r)² × 330/7

➝ 15,260.4 = (r)² × 47.1

➝ 15,260.4/47.1 = (r)²

➝ 324 = (r)²

➝ √324 = r

➝ 18 = r

Hence,

From the graph provided, the coordinates of the two points are;

The distance between two points is;

Then, we substitute the values into the formula, we have;

The distance d, between the points is;

Answer:

Step-by-step explanation:

The graph is widest when the coefficient of \(x^2\) has the smallest absolute value.

The graph is narrowest when the coefficient of \(x^2\) has the largest absolute value.

By comparing the graphs of the functions, function 1: y = 0.25x2 is the widest and function 4: y = -16x2 is the narrowest.

The graph is widest when the coefficient of \(x^{2}\) has the smallest absolute value.

The graph is narrowest when the coefficient of \(x^{2}\) has the largest absolute value.

The answer lies in the coefficient for the \(x^{2}\) term. When the absolute value of the coefficient gets bigger, the graph gets narrower (positive and negative simply show the direction the parabola is pointing, with positive opening up and negative opening down).

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Answer:

4,978 because after 3 digits you have to put a coma

Answer:

4,978

Step-by-step explanation:

Answer:

Step-by-step explanation:

X=-x^2+x-5

The percentage of $898.01 billion that is spent on $161.4 billion​ is equal to 17.97%.

In Mathematics, a percentage simply refers to any number that is expressed as a fraction of hundred (100). This ultimately implies that, a percentage indicates the hundredth parts of any given number.

In order to determine the percentage, we would use the following mathematical expression:

Percentage = 161.4/898.01 × 100

Percentage = 0.1797 × 100  

Percentage = 17.97%

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The distance between base of ladder and the building should be

4.4 meter.

The Pythagoras theorem states that if a triangle is right-angled (90 degrees), then the square of the hypotenuse is equal to the sum of the squares of the other two sides.

AC² = AB² + BC²

Given,

Height of the window from the ground AB = 9 meter

Length of the ladder AC = 10 meter

Distance between base of ladder and building BC = ?

By Pythagorean theorem,

In the right ΔABC

AC² = AB² + BC²

10² = 9² + BC²

BC² = 10² - 9²

BC² = 100 - 81

BC² = 19

BC = √19

BC = 4.359 meter

BC = 4.4 meter

Hence, base of ladder should be 4.4 meter away from the building.

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Answer:

100

Step-by-step explanation:

perfect square  (a - b)^2 = a^2 - 2ab + b^2

In this case

20x = 2 * x * 10

and

10^2 = 100

so

(x - 10)^2 = x^2 - 20x + 100

Therefore, the missing constant term is 100

.

Answer:

3

Step-by-step explanation:

Given,

v = 54

l = 6

w = 3

To find : Value of h = ?

Formula : -

v = lwh

h = v/lw

h = 54/( 6 × 3 )

= 54/18

h = 3

Hence, the value of h is 3.

Distributive Property of real numbers states the following statement

a( b + c ) = ab + bc

The distributive property is a property of multiplication used in addition and subtraction. This property states that two or more terms in addition or subtraction with a number are equal to the addition or subtraction of the product of each of the terms with that number.

For example:

1. 5 x ( 3 + 8 ) = 5x3 + 8x5

2. 10 x ( 9 - 8 ) = 10x9 - 10x8

The associative property is a math rule that says that the way in which factors are grouped in a multiplication problem does not change the product.

For example:

1. 5 x ( 4 x 2 ) = ( 5 x 4 ) x 2 = ( 5 x 2 ) x 4 = 40

firstly we are grouping 4 and 2 together and multiplying them first then multiply it by 5.

secondly we are grouping 5 and 4 together and multiplying them first then multiply it by 2.

thirdly we are  grouping 5 and 2 together and multiplying them first then multiply it by 4.

The basic difference between Distributive Property and Associative Property.

Hence, Distributive Property of real numbers states the following statement: a( b + c ) = ab + bc

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Answer:

no angle c is not supplementary

Step-by-step explanation:

Angle A and angle B are supplementary

A+B=180°   Equation 1

The measure of angle B is equal to four times the complement of angle A

The complement of angle A=90°-A

B=4(90°-A)  

B=360°-4A

Substitute the value of B in equation 1

A+360°-4A=180°

-3A=-180°

A=60°

The measure of angle A=60°

B=360°-4A=360°-4(60°)=120°

The measure of angle B=120°

Answer:

angle A + angle B = 180°

angle A + angle C = 180°

subtracting angle A and 180• from both sides we get,

angle B = angle C

The inequality for the given statement is y > -8x+9.

inequality, In mathematics, a statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.

Given that,

The statement is "The value of y is greater than the sum of negative eight times the value of x and 9".

According the given statement

First taking the sum of negative eight times the value of x and 9.

-8x+9

Then,

y is greater than -8x+9.

y > -8x+9

Hence, The inequality for the given statement is y > -8x+9.

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If the line represented by y = 4x + 2 is dilated by a scale factor of 4 centered at the origin, the new equation of the image line is y = 16x + 8, and the statement about the image that is true is that the slope is the same as the original line, but the y-intercept is four times greater.

If the line represented by y = (1/4)x + 2 is dilated by a scale factor of 4 centered at the origin, the image of the line will have a steeper slope, but the y-intercept will remain the same. The new equation for the dilated line would be y = (4 * 1/4)x + 2, simplifying to y = x + 2.

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The divergence of the vector field f(x, y) = ln(x² + y²) * [7, 19, 2] / r³ is given by (56x + 40y)/(r³(x² + y²)).

To calculate the divergence of a vector field, we need to find the dot product of the gradient operator (∇) with the given vector field.

Let's calculate the divergence of the vector field f(x, y) = ln(x² + y²) * [7, 19, 2] / r³, where r = √(x² + y²) is the magnitude of the position vector.

Step-by-step solution:

Find the gradient of the scalar function ln(x² + y²):

∇(ln(x² + y²)) = (∂/∂x, ∂/∂y)(ln(x² + y²))

= (1/(x² + y²))(2x, 2y)

= (2x/(x² + y²), 2y/(x² + y²))

Multiply the gradient by the given vector field:

(∇(ln(x² + y²)) * [7, 19, 2]) = (2x/(x² + y²), 2y/(x² + y²)) * [7, 19, 2]

= (14x/(x² + y²) + 38y/(x² + y²), 38x/(x² + y²) + 2y/(x² + y²), 4x/(x² + y²) + 4y/(x² + y²))

Divide the result by r³:

(1/r³) * (14x/(x² + y²) + 38y/(x² + y²), 38x/(x² + y²) + 2y/(x² + y²), 4x/(x² + y²) + 4y/(x² + y²))

= (14x/(r³(x² + y²)) + 38y/(r³(x² + y²)), 38x/(r³(x² + y²)) + 2y/(r³(x² + y²)), 4x/(r³(x² + y²)) + 4y/(r³(x² + y²)))

The divergence of the given vector field f is therefore given by:

div(f) = 14x/(r³(x² + y²)) + 38y/(r³(x² + y²)) + 38x/(r³(x² + y²)) + 2y/(r³(x² + y²)) + 4x/(r³(x² + y²)) + 4y/(r³(x² + y²))

Simplifying the expression:

div(f) = (56x + 40y)/(r³(x² + y²))

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Answer:

i dont know

Step-by-step explanation:

bye

The Pythagorean theory can be used to plot irrational numbers on a number line and this is explained below.

To plot an irrational number, say √2, on a number line using Pythagorean theory, we first draw a right triangle with one leg measuring 1 and the hypotenuse measuring √2 (the irrational number we want to plot). Using Pythagorean theory, we can calculate the length of the other leg to be √(√2² - 1²) = √(2 - 1) = √1 = 1.

Next, we place the right triangle on the number line with the shorter leg starting at 0 and the hypotenuse ending at √2. We can then mark off a point at 1 along the number line, corresponding to the length of the other leg of the triangle.

By repeating this process, we can plot other irrational numbers on the number line using Pythagorean theory.

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By the polynomial remainder theorem, because x = 2i is a zero of f(x), we have no remainder upon dividing f(x) by x - 2i.

Computing the quotient yields

\(\dfrac{x^4+x^2+a}{x-2i} = x^3+2ix^2-3x-6i+\dfrac{12+a}{x-2i}\)

Then if the remainder term is 0, follows that a = -12.

If 2i is a solution to f(x) = \(x^4\) + x² + a, then substituting 2i into the function yields f(2i) = 12 + a and to make this true since 2i is a solution, a must be -12.

We have,

Function:

f(x) = \(x^4 + x^2 + a\)

Calculate f(x) at x = 2i :

\((2i)^4 = 2^4 \times i^4\)

= 16 * (i²)²

= 16 * (-1)²

= 16 * 1

= 16

Calculate (2i)²:

(2i)² = 2^2 * i² = 4 * (-1) = -4

Now we can substitute these values into the function f(x) = \(x^4\) + x² + a:

f(2i) = \(2i^4\) + (2i)² + a

= 16 - 4 + a

= 12 + a

Since you mentioned that 2i is a solution to the function f(x), it means that f(2i) should equal 0:

f(2i) = 0

12 + a = 0

Solving for 'a':

a = -12

Thus,

The value of 'a' that satisfies the condition f(2i) = 0 is -12.

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Micah received 1/2 of Savi's share and Juan got the balance.

"A method to find a single unit value from a multiple unit value and to find a multiple unit value from a single unit value."

We always count the unit or amount value first and then calculate the more or less amount value.

For this reason, this procedure is called a unified procedure.

Many set values ​​are found by multiplying the set value by the number of sets.

A set value is obtained by dividing many set values ​​by the number of sets.

According to our question-

total amount = $280=x

savi= 4*juan= 11

micah= 1/2 savi= 1/2*280/100= 1.4

juan got balance= 267.6

Hence, Micah received 1/2 of Savi's share and Juan got the balance.

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can send full pictures to me

The standard form of 3x² - 9x + 2 is 3x² - 9x + 2.

A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. In other terms, a "polynomial function of degree 2" is a quadratic function.

Given:

A quadratic function,

3x² - 9x + 2.

The standard form of the quadratic function is

ax² + bx + c.

The standard form of 3x² - 9x + 2 is 3x² - 9x + 2.

Therefore, 3x² - 9x + 2.

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Answer:

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Answer:

they got -21 when they were supposted to get +21

and they also got +6x when they were supposted to get -6x

Step-by-step explanation:

that's because -3 and 2x are multiplied together and when you are multiplying negative and positive number you need to get negative result.

when you are multiplying negative with negative number, you will get positive number.

The fraction of the brownies left is 1/12.

We need to find out what fraction of the brownies is left.

Let " r " denote the fraction that is left.

Then we have r + 1/4 + 2/6 + 1/3 = 1

⇒ r + 1/4 + 1/3 + 1/3 = 1 (Writing the fraction 2/6 in the simplest form)

⇒ r + 1/4 + 2/3 = 1

⇒ r + (3 + 8)/12 = 1 (taking LCM of 4, 3 and adding the fractions 1/4 and 2/3)

⇒ r + 11/12 = 1

⇒ r = 1 - 11/12

⇒ r = (12 - 11)/12

⇒ r  = 1/12.

Therefore, the fraction of the brownies left is 1/12.

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Disclaimer:

The fractions provided in the question are not clear.

Assuming the following to answer the given question.

Molly ate 1/4 of the brownies,

Milo ate 2/6 of the brownies, and

Morgan ate 1/3 of the brownies.

An equation that can  can be used to find the number of sales Luke made this week is; 191 + 16.55x = ¹/₃(573 + 49.65x)

We are told to represent the number of sales as x.

Now, Luke works at a store and earns a fixed amount of $191 plus $16.55 per sale. This is represented as; 191 + 16.55x

Noah works at a different store and earns a fixed amount of $573 plus $49.65 per sale. This is represented as; 573 + 49.65x

We are told that they both made the same number of sales but Luke earned a third of what Noah earned. Thus;

191 + 16.55x = ¹/₃(573 + 49.65x)

An equation that can  can be used to find the number of sales Luke made this week is;

191 + 16.55x = ¹/₃(573 + 49.65x)

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Answer:

7 bows

Step-by-step explanation:

I will assume that the numbers are \(1\frac{1}{4}\) and \(8\frac{3}{4}\). To find the answer, we can do:

\(8\frac{3}{4} / 1\frac{1}{4}\\ = \frac{35}{4} / \frac{5}{4} \\= \frac{35}{4} * \frac{4}{5}\\= \frac{35}{5}\)

= 7 bows