Shanti has just joined a DVD rental club. She pays a monthly membership fee of $4.95, and each DVD rental is $1.95. If Shanti's budget for DVD rentals in a month is $42, how many DVDs can Shanti rent in her first month if she doesn't want to go over her budget? ________ DVDs

Answer:

Let n = the number of nickels that Ari has.

Let p = the number of pennies that Ari has.

The total number of coins she has is 22.

n + p = 22

We have our first equation... But we another one to solve this.

Each penny is going to be $0.01 and a nickel is work $0.05.

And the total is $0.54

Our second equation. 0.05n + 0.01p = 0.54

n + p = 22

0.05n + 0.01p = 0.54

Multiply the top by -0.05

-0.05n - 0.05p = -1.1

0.05n + 0.01p = 0.54

The n terms cancel out.

-0.04p = -0.56

p = 14

Step-by-step explanation:

The graph of g(x) is obtained by the combination of shifting the graph of f(x) to the left 7 units and upward 9 units.

Transformation of a graph: changing the shape and location of a graph.

We already know there are four types of transformation geometry: translation (or shifting), reflection, rotation, and dilation (or stretching).

In general, given the graph of y = f(x) and k > 0, we obtain the graph of:

Furthermore in general, given the graph of y = f(x) and h > 0, we obtain the graph of:

The combination of vertical and horizontal shifts is as follows:

[tex]\boxed{\boxed{ \ y = f(x \pm h) \pm k \ }}[/tex]

The plus or minus sign follows the direction of the shift, i.e., up-down or left-right

Given: [tex]\boxed{ \ f(x) = x^2 \ becomes \ g(x) = (x + 7)^2 + 9 \ }[/tex]

We set h = +7 and k = +9.

In the graph, additionally note the shift of points from (0, 0) to (-7, 9).

Conclusion

The graph of g(x) is drawn by the combination of shifting the graph of f(x) to the left 7 units and upward 9 units.

Keywords: what transformations, change, the graph of f(x), to the graph of g(x), f(x) = x², g(x) = (x + 7)² + 9, translation, shifting, left, upward

The graph of the function [tex]g(x)=(x+7)^{2}+9[/tex] is obtained from the graph of the function [tex]f(x)=x^{2}[/tex] when each point on the curve of [tex]f(x)=x^{2}[/tex] is shifted [tex]7[/tex] units towards the negative direction of [tex]x-[/tex] axis and then shifted [tex]9[/tex] units towards the positive direction of [tex]y-[/tex] axis.

Further explanation:

The functions are given as follows:

[tex]\fbox{\begin\\\ \begin{aligned}f(x)&=x^{2}\\g(x)&=(x+7)^{2}+9\end{aligned}\\\end{minispace}}[/tex]

The objective is to determine the transformation or the way in which the graph of the function [tex]g(x)[/tex] is obtained from the graph of the function [tex]f(x)[/tex].

Concept used:

Shifting of graphs:

Shifting is a rigid translation because it does not change the size and shape of the curve. Shifting is used to move the curve vertically or horizontally without any change in shape and size of the curve.

The function [tex]y=f(x+a)[/tex] and [tex]y=f(x-a)[/tex] is a shift of the curve [tex]y=f(x)[/tex] horizontally towards negative and positive direction of [tex]x-[/tex]axis respectively.

The function [tex]y=f(x)+a[/tex] and [tex]y=f(x)-a[/tex] is a shift of the curve [tex]y=f(x)[/tex] vertically towards positive and negative direction of [tex]y-[/tex]axis respectively.

Step1: Draw the graph of the function [tex]f(x)=x^{2}[/tex].

Figure 1 (attached in the end) represents the graph of the function [tex]f(x)=x^{2}[/tex]. From figure 1 it is observed that the curve of the function [tex]f(x)=x^{2}[/tex] is a parabola with origin as the vertex and mounted upwards.

Step 2: Obtain the graph of the function [tex]g'(x)=(x+7)^{2}[/tex] from the graph of the function [tex]f(x)=x2[/tex].

The function [tex]g'(x)=(x+7)^{2}[/tex] is of the form [tex]y=f(x+a)[/tex].

So, as per the concept of shifting of the graphs the graph of the function [tex]g'(x)=(x+7)^{2}[/tex] is obtained from the graph of the function [tex]f(x)=x^{2}[/tex] when each point on the curve of [tex]f(x)=x^{2}[/tex] is shifted [tex]7[/tex] units towards the negative direction of [tex]x-[/tex]axis.

Figure 2 (attached in the end) represents the graph of the function [tex]g'(x)=(x+7)^{2}[/tex].

In figure 2 the dotted line represents the curve of [tex]f(x)=x^{2}[/tex] and the bold line represents the curve of [tex]g'(x)=(x+7)^{2}[/tex].

Step3: Obtain the graph of the function [tex]g(x)=(x+7)^{2}+9[/tex] from the graph of the function [tex]g'(x)=(x+7)^{2}[/tex].

The function [tex]g(x)=(x+7)^{2}+9[/tex] is of the form [tex]y=f(x)+a[/tex].

So, as per the concept of shifting of graph the graph of the function [tex]g(x)=(x+7)^{2}+9[/tex] is obtained from the graph of the function [tex]g'(x)=(x+7)^{2}[/tex] when each point on the curve of [tex]g'(x)=(x+7)^{2}[/tex] is shifted [tex]9[/tex] units towards upwards or the positive direction of [tex]y-[/tex]axis.

Figure 3 (attached in the end) represents the graph of the function [tex]g(x)=(x+7)^{2}+9[/tex].

In figure 3 the dotted line represents the curve of [tex]g'(x)=(x+7)^{2}[/tex] and the bold line represents the curve of [tex]g(x)=(x+7)^{2}+9[/tex].

From the above explanation it is concluded that the graph of the function [tex]g(x)=(x+7)^{2}+9[/tex] is obtained from the graph of the function [tex]f(x)=x^{2}[/tex] when each point on the curve of [tex]f(x)=x^{2}[/tex] is shifted [tex]7[/tex] units towards the negative direction of [tex]x-[/tex] axis and then shifted [tex]9[/tex] units towards the positive direction of [tex]y-[/tex] axis.

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Answer details:

Grade: High school

Subject: Mathematics

Chapter: Graphing

Keywords: Graph, curve, function, parabola, quadratic, f(x)=x2, g(x)=(x+7)2+9, shifting, translation, scaling, shifting of graph, scaling of graph, horizontal, vertical, coordinate, horizontal shift, vertical shift.

Answer:

In the table, the relation (x, y) is not a function if the missing value of x is

Step-by-step explanation:

In the tab

le, the relation (x, y) is not a function if the missing value of x is

Final answer:

Lines represented by equations in the form x = a constant are vertical lines and are parallel to each other. The correct answer indicating parallel lines is (d) x = 79, y = 47.

Explanation:

To determine which pair of values for x and y indicates that the lines described are parallel, we need to understand that for two lines to be parallel, they must have the same slope. For standard linear equations in the form y = mx + b, where m is the slope, lines with the same m value are parallel. However, when the equation is given in the form x = a constant, as is the case for options (a) and (c), it denotes a vertical line, which does not have a slope in the traditional sense but is parallel to other vertical lines.

Given the information, lines described by equations x = 47 and x = 79 would be parallel since they both represent vertical lines. Therefore, the correct answer is (d) x = 79, y = 47.

To find the probability that the store sells at least 154 gallons of milk on a randomly selected day, we need to standardize the value and use a standard normal distribution table or calculator.

To find the probability that the store sells at least 154 gallons of milk on a randomly selected day, we need to find the area under the Normal distribution curve to the right of 154.

First, we need to standardize the value of 154 using the formula Z = (X - mean) / standard deviation, where X is the value we want to standardize, mean is the mean of the distribution, and standard deviation is the standard deviation of the distribution. Using the given values, we have Z = (154 - 130) / 12 = 2.  

Next, we can use a standard normal distribution table or a calculator to find the cumulative probability associated with a z-score of 2. The probability that a standard normal random variable is greater than 2 is approximately 0.0228.

Therefore, the probability that the store sells at least 154 gallons of milk on a randomly selected day is approximately 0.0228, or option A.

Answer:first u have to multiply 1 .00 by 16 then

The water level in the lake was 12 inches below normal at the beginning of March, decreased by 2 1/4 inches in March, and then increased by 1 5/8 inches in April. By the end of April, the water level was 12 5/8 inches below the normal level.

The student is asking about the changes in water level over the course of two months and wishes to compare the final water level with the normal water level at the end of April. To solve this, we need to perform a series of arithmetic operations with mixed numbers.

The water level was 12 inches below normal at the beginning of March. In March, it decreased by 2 1/4 inches; therefore, we add 2 1/4 inches to the negative deviation (because going further below normal). By the end of March, the water level is 12 + 2 1/4 = 14 1/4 inches below normal.

In April, the water level increased by 1 5/8 inches. We now subtract this value from 14 1/4 inches to find the new level: 14 1/4 - 1 5/8 = 12 5/8 inches below normal. Thus, at the end of April, the lake's water level is still below the normal level.

The water level in the lake ended up being -12 5/8 inches below normal at the end of April. This was calculated by subtracting the March decrease and adding the April increase to the initial level.

The water level in a lake was 12 inches below normal at the beginning of March. After a decrease of 2 1/4 inches in March and an increase of 1 5/8 inches in April, we need to calculate the final water level compared to normal at the end of April.

Step-by-Step Explanation:

Start with the initial level: -12 inches (below normal).

Decrease by March's change: -12 - 2 1/4 = -14 1/4 inches.

Increase by April's change: -14 1/4 + 1 5/8 = -12 5/8 inches.

Therefore, the water level was -12 5/8 inches below normal at the end of April.

Answer: .70 or .7

Step-by-step explanation: To write a percent as a decimal, we simply move the decimal point 2 places to the left so 70% can be written as the decimal .70 or just .7. Both of these answers would work just fine.

Answer: Option B 3-4i is the correct option

Explanation:

we have formula for discriminant [tex]D=b^{2}-4ac[/tex]

after that we find the required variable that is to be find according to the quadratic equation given suppose we have to find x

then we have formula [tex]x=\frac{-b\pm\sqrt{D}} {2a}[/tex]

Here we have [tex]\pm[/tex] of roots if we have one root 3+41 other would be of opposite sign and hence,definitely be 3-4i.

Therefore Option B 3-4i is the correct option.

By definition of fraction of the numbers, The mixed form of the fraction 19/15 is,

⇒ 19/15 = 1 4/15

Division method is used to distributing a group of things or numbers into equal parts. And, Division is just opposite of multiplications.

For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

We have to given that;

The fraction of the number in fraction form is,

⇒ 19/15

Now,

We can simplify the fraction to change into mixed number as;

⇒ 19/15

⇒ 15 ) 19 ( 1

        - 15

         -----

           04

         ---------

Thus, We get;

The fraction is written as;

⇒ 19 / 15

⇒ 1 4/15

Therefore, We get;

By definition of fraction of the numbers, The mixed form of the fraction 19/15 is,

⇒ 19/15 = 1 4/15

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Answer:

(3,0)

Step-by-step explanation:

The retail price of the bracelet is $99. Therefore, option C is the correct answer.

Given that, a jewelry store marks its merchandise up by 80%.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The wholesale price of a bracelet is $55.

Let the retail price of the bracelet be x.

Here, x=55+80% of 55

=55+0.8×55

=55+44

=$99

The retail price of the bracelet is $99. Therefore, option C is the correct answer.

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