Dani had $200 in her savings account. When she turned 18, the bank began charging her a $5.00/month fee. Write a function in terms of a for the balance of her savings account if she doesn't notice the monthly fee.

Complete the following. Use standard slope-intercept form.

The standard form of the equation Y=(x-2)² + 4 is written as y=x²-4x+6.

A standard form serves as a gauge for how widely scattered the data is in comparison to the mean.

The data are grouped around the mean when the standard deviation is low.

A parabola with the point at its vertex represents this equation (2,4). On a coordinate plane, the equation can be graphed, revealing a parabola that extends upwards and has a minimum value of 4 at the point (2,4).

The factored version of the equation

Y=(x-2)² + 4 is y =  (x-2) (x-2) + 4

This representation of the equation demonstrates that it is the result of two binomials. When the common element is eliminated, the equation can be made simpler (x-2).

The equation is now more easily expressed as

y = (x-2) (x-2) + 4 = (x-2)² + 4.

Expanded form of the equation

Y=(x-2)² + 4 is expressed as y = x² - 4x + 6.

This representation of the equation demonstrates that it is the outcome of expanding (x-2)².

You may use this equation to determine the vertex of the parabola, which is (2,4). The vertex is the location where the parabola's value is at its lowest.

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The function g in vertex form is g (x) = –5x^2 – 3.

In this case, the parent function is:

f (x) = x^2

First, after the reflection across the x-axis, we will get:

f (x) = –f (x)

And, the function will be:

g (x) = –x^2

Then, vertically stretched by a factor of 5, we will get:

g (x) = –5x^2

Last, translated 3 units down, we will get:

g (x) = –5x^2 – 3

Thus, the vertex form of the function g will be:

g (x) = –5x^2 – 3

In mathematics, a translation is a transformation which occurs when a figure is moved from one location to another location without changing its size or shape.

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The procedure of solving linear equations in two variables by substitution includes selecting one eqn and solving it for one variable, substituting the result in another equation, solving the new eqn, and finally substituting the value into any of the eqns and solving for another variable.

An equation is a linear equation in two variables if it is written in the form of ax + by + c=0, where a, b & c are real numbers and the coefficients of x and y, i.e a and b (≠ 0).

To solve systems using substitution, follow these steps:

Step 1. Select one equation and solve it for one of its variables.

Step 2. In the other equation, substitute the value get from step 1.

Step 3. Solve the new equation.

Step 4. Substitute the value found into any equation involving both variables and solve for the other variable.

Step 5. Check the solution in both original equations.

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Answer:

-36

Step-by-step explanation:

3*-12=-36

Answer: -36

Step-by-step explanation:

It is possible to construct a triangle whose sides are 4.5 cm 3.5 cm and 6.4 cm because the sum of two sides are greater than the third sides.

In the given question, we have to check that it is possible to construct a triangle whose sides are 4.5 cm 3.5 cm and 6.4 cm.

To check whether the given sides can make a triangle or not, we have to check that the sum of two sides always greater than the third side.

To check this we firstly add the 4.5 and 3.5

4.5 + 3.5 > 6.4

8 > 6.4

Now we add 4.5 and 6.4

4.5 + 6.4 > 3.5

10.9 > 3.5

Now we add 3.5 and 6.4

3.5 + 6.4 > 4.5

9.9 > 4.5

It is possible to construct a triangle whose sides are 4.5 cm 3.5 cm and 6.4 cm because the sum of two sides are greater than the third sides.

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The length 4.5 cm 3.5 cm 6.4 cm can be the dimensions of a triangle according to rule.

Considering the dimensions of triangle, the one side of the triangle should be less than the sum of other two sides. Based on the rule, let us say that 4.5, 3.5 and 6.4 cm is side a, b and c.

Keep the values to compare the sides

Side a + side b > side c

4.3 + 3.5 > 6.4

Add the digits

7.8 > 6.4

Side b + side c > side a

3.5 + 6.4 > 4.5

Add the digits

9.9 > 4.5

side c + side a > side b

6.4 + 4.5 > 3.5

Add the digits

10.9 > 3.5

All the sides follow the rule. Therefore, the mentioned lengths are possible for a triangle.

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The expression " [tex]\frac{2}{3}[/tex] to the exponent of 3" is represented as , [tex](\frac{2}{3} )^{3}[/tex] , and the value of  [tex]\frac{2}{3}[/tex] to the exponent of 3 is [tex]\frac{8}{27}[/tex] .

What are Exponents ?

The Exponents are defined as the representation of a number that is multiplied by several to itself .

For Example : 8 multiplied by two times to itself , can be represented in exponential form as  8² .

We have to find the value of  " [tex]\frac{2}{3}[/tex] to the exponent of 3" ;

the given exponential expression can be solved further as :

⇒ [tex](\frac{2}{3} )^{3} = \frac{2}{3} \times \frac{2}{3} \times \frac{2}{3}[/tex]

On simplifying ,

we get ;

⇒ [tex]\frac{2\times 2 \times 2}{3 \times 3\times 3}[/tex]

⇒ [tex]\frac{8}{27}[/tex] .

Therefore , the value of  " [tex]\frac{2}{3}[/tex] to the exponent of 3" is [tex]\frac{8}{27}[/tex] .

The given question is incomplete , the complete question is

What is [tex]\frac{2}{3}[/tex] to the exponent of 3 ?

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Due to the corresponding angle property, which requires that the sum of neighboring opposite angles be 180, the angles are 90 and 79.8.

In Euclidean geometry, an angle is a shape that is made up of two rays, known as the angle's sides, that meet at a point in the middle known as the angle's vertex. Two rays may combine to form an angle in the plane where they are positioned. When two planes collide, an angle is also created. They are referred to as dihedral angles. An angle in plane geometry is the possible configuration of two rays or lines that share a termination. The origin of the English term "angle" is the Latin word "angulus," which meaning "horn." The vertex is the point where the two rays, also known as the sides of the angle, converge.

given

Due to the property of matching angles,

the angles are 90 and 21x + 8

90 + 21x + 18 = 180

= 108 + 21x = 180

= 21x = 72

x = 3.42

Due to the corresponding angle property, which requires that the sum of neighboring opposite angles be 180, the angles are 90 and 79.8.

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The next term in the geometric sequence will be 512.

A series of non-zero integers where every term after the first is obtained by increasing the one before it by a constant, non-zero value known as the scale factor.

Let a₁ be the first term and r be the common ratio.

Then the nth term of the geometric sequence is given as,

aₙ = a₁ · (r)ⁿ⁻¹

The sequence is given below.

2, 8, 32, 128

The first term is 2 and the common ratio is calculated as,

r = 8 / 2

r = 4

Then the next term in the sequence will be given as,

a₅ = 2 · (4)⁵⁻¹

a₅ = 2 · (4)⁴

a₅ = 2 · 256

a₅ = 512

The next term in the geometric sequence will be 512.

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The next term of the sequence is 512.

A geometric sequence is a sequence of numbers that follows a pattern were the next term is found by multiplying by a constant called the common ratio, r.

Given:

Sequence :2,8, 32, 128,...

As, the sequence is a geometric progression which can be expressed as

[tex]Tn = ar^{n-1[/tex]

Here, a is the first term = 2

n is the number of terms = 5 (next term is the 5th term)

r is the common ratio = 8/2 = 32/8 = 4

So, [tex]Tn = ar^{n-1[/tex]

[tex]T_5[/tex] = 2[tex](4)^{5-1[/tex]

[tex]T_5[/tex] = 2 x [tex]4^4[/tex]

[tex]T_5[/tex]= 2 x 256

[tex]T_5[/tex]= 512

Hence, the next term is 512

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fractions are a way of expressing the part of a whole.

3 3/4 = 15/4

22 1/2 = 90/4

90/4 ÷ 15/4 = 6

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The exponential form of 72 can be written as [tex]2^{3}[/tex] . [tex]3^{2}[/tex] . It can be written using the prime factorization of the number.

The exponential form is an easier way of writing repeated multiplication involving base and exponents. To write the exponential form we have to write the prime factorization of that number. Prime factorization of the number is that number written as a product of prime numbers or as a product of powers of prime numbers. A basic exponential function from its definition is of the form f(x) = b x, where 'b' is a constant and 'x' is a variable. generally it refers to the positive valued function of a real variable. We can find the prime factorization of a number using factor trees, which are tools used to repeatedly break a number into products until all of the factors are prime numbers.

72 = 2 × 2 × 2 × 3 × 3 =  [tex]2^{3}[/tex] . [tex]3^{2}[/tex]

Therefore, the exponential form of 72 can be expressed as [tex]2^{3}[/tex] . [tex]3^{2}[/tex] .

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An examination of two or more independent variables using simple linear regression will provide a straight line. Sometimes a curved line is generated by a multiple regression incorporating a number of related variables.

What does analysis of linear regression entail?

When predicting a variable's value based on the value of another variable, linear regression analysis is utilized. The dependent variable is the one you want to be able to forecast.

                 The independent variable is the one that you are utilizing to forecast the value of the other variable.

Why do we use linear regression analysis?

It is crucial to comprehend linear regression since it offers a method for calculating and forecasting future events. Finding predictions and evaluating them can aid many firms and people by enabling them to operate more efficiently and produce thorough research materials.

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An inequality is a relationship that compares two numbers or other mathematical expressions in an unfair manner. When comparing the sizes of two numbers on the number line, it is most frequently used. The graph of each equation or inequality is given the attachment.

The graph, visual depiction of statistical information or a functional relationship between variables. Graphs serve a predictive purpose because they can highlight broad trends in the quantitative behaviour of data. However, they can be inaccurate and occasionally deceptive as mere approximations.

Most graphs have two axes: a horizontal axis for a set of independent variables and a vertical axis for a set of dependent variables. A broken-line graph is the most typical type of graph, with time usually acting as the independent variable.

16. 2y – 4x < 8

=  2y < 4x + 8

= y < 2x + 4

17. -4y > -x + 12

= y > x/4 + -3

18. | x + 3 |= y

y = | x + 3 |

19.  |2x – 6| + 2 = y

y = |2x – 6| + 2

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The value of the evaluated iterated integral is 6.667.

As per the given data the iterated integral is [tex]$\int_2^3 \int_0^2 x y^2 d x d y$[/tex]

Here we have to evaluate the given iterated integral to find the value of [tex]$\int_2^3 \int_0^2 x y^2 d x d y$[/tex] .

The definite integral of a real-valued function f(x) with respect to a real variable x on an interval (a, b) is expressed as

[tex]$\int_a^b f(x) d x=\mathrm{F}(\mathrm{b})-\mathrm{F}(\mathrm{a})$[/tex]

Here,

[tex]$\int=$[/tex] Integration symbol

a - Lower limit

b - Upper limit

f(x) - Integrand

dx - Integrating agent

Thus, [tex]$\int a b f(x) d x$[/tex] is read as the definite integral of f(x) with respect to dx from a to b.

Indefinite integrals are implemented when the boundaries of the integrand are not specified.

[tex]& \int_2^3 \int_0^2 x y^2 d x d y \\[/tex]

Integrate the given iterated integral.

We get:

[tex]& \int_2^3 x d x \int_0^2 y^2 d y \\[/tex]

[tex]& =\int_2^3 x d x\left(\left.\frac{y^3}{3} \right|_0 ^2\right) \\[/tex]

Substitute the limits in y.

[tex]& =\int_2^3 \frac{8}{3} x d x \\[/tex]

[tex]& =\left.\frac{8}{3\times2} x^2\right|_2 ^3 \\[/tex]

[tex]& =\left.\frac{4}{3} x^2\right|_2 ^3 \\[/tex]

Substitute the limits in x.

[tex]& =\frac{4}{3} \times 9-\frac{4}{3} \times 4 \\[/tex]

[tex]& =\frac{20}{3}[/tex]

= 6.667.

Therefore answer is 6.667.

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The type of water-based ecosystem that can be found in all regions of North Carolina are Ocean Pond

A tiny body of quiet, pure water is called a pond. It varies from a river or stream since there is no flowing water in it, and it differs from a lake because it is only a tiny area and only 1.8 meters deep.

About 71 percent of the surface of the Earth is covered by the ocean, a vast body of saltwater. Oceanographers and nations throughout the world have historically classified the planet's ocean into four separate regions: the Pacific, Atlantic, Indian, and Arctic seas.

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The correct statement is three fourths raised to the fourteenth power.

The Power rule for exponents: (am)n = am*n. To raise a number with an exponent to a power, multiply the exponent times the power. Negative exponent rule: x–n = 1/xn. Invert the base to change a negative exponent into a positive.

The important laws of exponents are :

Given:

(((3/4)^4 * (3/4)^3)^2

Now,

((3/4)^ ( 4+3))^2

=((3/4)^7)^2

=(3/4) ^(7*2)

=(3/4)^14

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The option are:

nine sixteenths raised to the twenty fourth power

nine sixteenths raised to the fourteenth power

three fourths raised to the twenty fourth power

three fourths raised to the fourteenth power

A relationship that compares two numbers or other mathematical expressions in an unequal way is known as an inequality. It is most frequently used to compare the sizes of two numbers on the number line.

Inequality is the absence of an equality link between two expressions or values. So inequality emerges from an imbalance.

a) inequality represents the solution to the given inequality

such as

3b > 48

3b /3 > 48/3

b>16

b) inequality represents the solution to the given inequality

such as

M/7 > -56

7 * M/7 > 7 * -56

m>-392

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Step-by-step explanation:

calculating backwards :

12:39 pm minus 1 hour 13 minutes = 11:26 am

the cake needs to get into the oven latest at that time.

caucuses further backwards :

11:26 am minus 26 minutes = 11:00 am

Evan has to start latest at 11:00 am to have the cake ready at 12:39 pm.

Answer:

perpendicular slope to line k is 4

Step-by-step explanation:

calculate the slope of line k using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (4, 3 ) and (x₂, y₂ ) = (8, 2 )

m = [tex]\frac{2-3}{8-4}[/tex] = [tex]\frac{-1}{4}[/tex] = - [tex]\frac{1}{4}[/tex]

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-\frac{1}{4} }[/tex] = 4

the slope of a line perpendicular to line k is 4

Answer:

(40÷4)+(8÷4)

(24÷4)+(24÷4)

Step-by-step explanation:

1 box holds —> 4 cup cakes

x boxes holds —> 48 cup cakes

cross multiply

48 × 1 = 4 × x

48 = 4x

[tex] \frac{ \\ 48}{4} = \frac{4x}{4} [/tex]

x = 12

since the number of boxes needed to hold 48 cup cakes are 12 we need to look for an expression that is equivalent with our figure.

lets try

(24 ÷ 4) + (20 ÷ 4)

= 6 + 5

= 11 (Not correct)

(40 ÷ 4) + ( 8 ÷ 4)

= 10 + 2

= 12 ( correct)

(40 × 4) + ( 8 × 4)

= 160 + 32

= 192(Not correct)

(24 ÷ 4) + (24 ÷ 4)

= 6 + 6

= 12(correct)

48 × 4

= 192(Not correct)

i hope i helped

To find the formula of an exponential function from a table, you need to identify two points that fall on the exponential curve, and then use them to find the function's base.

The first step is to identify two points that fall on the exponential curve. Look for two pairs of x and y values that are not too far apart. For example, (1, 2) and (2, 4) are good choices.

Next, you use these two points to find the base of the function, which is the number b in the equation y = b^x. To do this, you take the ratio of the y-values and the logarithm of that ratio with base b. The logarithm of the ratio is equal to the difference of the x-values.

For example, if you have (1, 2) and (2, 4) you can find the base by taking log2(4/2)=log2(2)=1, which means that the base of the function is 2.

Now you have the base you can write the formula of the exponential function as y = 2^x.

It is important to note that you can use the same process with other bases, such as base 10 or base e, depending on the problem and the logarithm function you have available.

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On solving the quadratic function x²+6x+8, the solutions x = -4 and x = -2 are obtained.

What is a quadratic function?

A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. It is also known as the polynomial of degree 2 since the greatest degree term in a quadratic function is of second degree.

The given quadratic function is - x²+6x+8

To solve the function first multiply - 8 ×  x² = 8x²

Take the LCM of  8x².

8x² = 2 × 2x × 2x

Now, we need to form such two numbers that if added or subtracted gives 6x and when multiplied gives 8x².

8x² = 4x × 2x

6x = 4x + 2x

Factorize the equation using the numbers obtained -

= x²+6x+8

= x²+ 4x + 2x + 8

= x(x + 4) +2(x + 4)

= (x + 4)(x + 2)

This gives the value as x = -4 and x = -2.

Therefore, the solution points are x = -4 and x = -2.

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Answer:

x = - 0.9

Step-by-step explanation:

- 5.4 = 4x - 1.8 ( add 1.8 to both sides )

- 3.6 = 4x ( isolate x by dividing both sides by 4 )

[tex]\frac{-3.6}{4}[/tex] = x , that is

x = - 0.9

Answer:       0.9                                                                                                                                                                                                                                         Step-by-step explanation:

The answer to each of the absolute functions is given below.

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is are the absolute function equations.

|5 + m| < 13

5 + m < 13     and       5 + m < - 13

[a] - and

4|y + 6| ≥ 3

|y + 6| ≥ 3/4

y + 6 ≥ 3/4   or   y + 6 ≥  -3/4

[b] - or

|g - 3| = - 2

we can write -

g - 3 = - 2

g = 1

and

g - 3 = - (-2)

g - 3 = 2

g = 5

Therefore, the answer to each part is given above.

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There are number of factors of 36 are 9 and number of array Courtney can make with the photo is 9.

factor, in mathematics, a number or algebraic expression that divides another number or expression evenly—i.e., with no remainder. For example, 3 and 6 are factors of 12 because 12 ÷ 3 = 4 exactly and 12 ÷ 6 = 2 exactly. The other factors of 12 are 1, 2, 4, and 12.

In math, an array refers to a set of numbers or objects that will follow a specific pattern.

the arrays can Courtney make with the 36 photos are,

1 by 36,

36 by 1,

2 by 18,

18by 2,

3 by 12,

12 by 3,

4 by 9,

9 by 4,

6 by 6.

the factors of 36 are,

1, 2, 3, 4, 6, 9, 12, 18, 36

∴ 9 ( factors ) = 9 ( arrays )

Therefore, there are number of factors of 36 are 9 and number of array Courtney can make with the photo is 9.

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Answer:

56.8x+39.2 Welcome :D

Step-by-step explanation:

Answer:

[tex]56.8x+39.2[/tex]

Step-by-step explanation:

First, you must distribute the 2's to the expressions:

2(4.4x+7.6) = 2(4.4x) + 2(7.6) which is equal to 8.8x + 15.2 and;

2(24x+12) = 2(24x) + 2(12) = 48x + 24

Now add both: 8.8x + 48x + 24 + 15.2 ; combine like terms.

56.8x + 39.2 is what you get from doing that.

This cannot be simplified any further, and therefore is your answer:

56.8x + 39.2

To determine if the set of ordered pairs satisfies an exponential function, x -coordinates must have a constant increment.

We know that generally exponential function is written in the form function can be written in the form y = ab^x ,

where a and b are real numbers such that, a ≠ 0 , b > 0 , and b ≠ 1

a is called the initial value of function

and b is the constant ratio

We know that as x increases by a constant value, the value of y increases by a common ratio. This is characteristic of all exponential functions.

To determine whether the set of ordered pairs satisfies an exponential function, the condition that 'The x -coordinates must have a constant increment' must be satisfied.

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If the salesperson has the given the assets and liabilities. The value of the liquid assets is: D. $613,570.

Liquid assets can be defined as those assets that can be turn into cash with a short period of time.

Now let find the liquid asset using this formula

Liquid assets = Retirement Portfolio + Investment

Where:

Retirement Portfolio = $473,906

Investments = $139,664

Let plug in the formula

Liquid assets = $473,906 + $139,664

Liquid assets = $613,570

Therefore we can conclude that the correct option is D.

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The amount invested in each mutual fund is $400 and $1200 respectively

Simultaneous equations are two or more algebraic equations that share variables e.g. x and y . They are called simultaneous equations because the equations are solved at the same time. For example, below are some simultaneous equations: 2x + 4y = 10 and 8x − 4y = 2

Let represent the amount the first fund get by x and the amount the second fund get by y.

Therefore x+y = 1600 equation 1

and 9/100 × x + 4/100 × y = 84

9x/100 + 4x/100 = 84

multiply through by 100

9x + 4x = 8400 equation 2

using elimination method

9x+ 9y = 14400 equation 3

9x + 4y = 8400 equation 4

subtract equation 4 from 3

5y = 6000

divide both sides by 5

y = 6000/5

y = $1200

substitute 1200 for y in equation 1

1200+x = 1600

x = 1600-1200

x = 400

Therefore the first fund will get $400 and the second fund will get $1200

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Answer:

5:9

Step-by-step explanation:

just divide both sides by 5 and then you get the ratio 5:9

Answer: 5/9 g

Step-by-step explanation: