the 2nd and 5th terms of a gp are 1/18 and 4/243 respectively. Find

Answer: Martin used (x + h)² instead of (x - h)²

Step-by-step explanation:

The vertex form of a quadratic equation is: y = a(x - h)² + k    where

f(x) = x²

g(x) = (x + 3)²

                ↓      

              h= -3

           Shifted LEFT 3 units

Martin is not correct. The graph should be translated left 3 units from parent graph.

Given :

The function \(g(x)=(x+3)^2\)

Martin says the graph should be translated right 3 units from the parent graph

we know that ,

\(f(x)-> f(x-a)\) , the graph will be translated 'a' units right

\(f(x)-> f(x+a)\), the graph will be translated 'a' units left

From the given function g(x), 3 is added with x.

so, the graph of g(x) is translated 3 units left.

Martin is not correct. The graph should be translated left 3 units from parent graph.

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I dont know Im sorry

Step-by-step explanation:

I just want points in not that smart

Answer:

1. Andre wants to buy a bike that has a price tag of $125. What was the wholesale cost of this bike?    $ 96.15

2. If the bike is discounted by 20%, how much will Andre pay (before tax)?  

                         $ 100

                                        I hope this helped <33 !

Answer:

a₄₃ = 181

Step-by-step explanation:

there is a common difference between consecutive terms, that is

17 - 13 = 21 - 17 = 4

this indicates the sequence is arithmetic with nth term

\(a_{n}\) = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

here a₁ = 13 and d = 4 , then

a₄₃ = 13 + (42 × 4) = 13 + 168 = 181

The batch 3,5,7,9,11 represents items in set A which are the sums that are odd. For instance, rolling a 2 and a 3 leads to 2+3 = 5 which is an odd number sum.

The batch 4,8,12 represents the sums that are divisible by 4, ie they are multiples of 4. For instance: 2+6 = 8 is a multiple of 4.

The notation A U B means "A union B". Set union has us combine the two sets together to form one single set as indicated above. We toss out any duplicate entries. In this case, there are no duplicates because sets A and B have nothing in common. This means sets A and B are disjoint or mutually exclusive. If an item is in set A, then it cannot be in set B, and vice versa.

Optionally you can sort the items from smallest to largest getting A U B = {3,4,5,7,8,9,11,12}, but I chose to list 3,5,7,9,11 first to show that those items all belonged originally to set A, and kept 4,8,12 separate as well.

Answer:

The equations have one solution at (5, -5).

Step-by-step explanation:

We are given a system of equations:

\(\displaystyle{\left \{ {{-2x+5y=-35} \atop {7x+2y=25}} \right.}\)

This system of equations can be solved in three different ways:

Graphing the Equations

We need to solve each equation and place it in slope-intercept form first. Slope-intercept form is \(\text{y = mx + b}\).

Equation 1 is \(-2x+5y = -35\). We need to isolate y.

\(\displaystyle{-2x + 5y = -35}\\\\5y = 2x - 35\\\\\frac{5y}{5} = \frac{2x - 35}{5}\\\\y = \frac{2}{5}x - 7\)

Equation 1 is now \(y=\frac{2}{5}x-7\).

Equation 2 also needs y to be isolated.

\(\displaystyle{7x+2y=25}\\\\2y=-7x+25\\\\\frac{2y}{2}=\frac{-7x+25}{2}\\\\y = -\frac{7}{2}x + \frac{25}{2}\)

Equation 2 is now \(y=-\frac{7}{2}x+\frac{25}{2}\).

Now, we can graph both of these using a data table and plotting points on the graph. If the two lines intersect at a point, this is a solution for the system of equations.

The table below has unsolved y-values - we need to insert the value of x and solve for y and input these values in the table.

\(\begin{array}{|c|c|} \cline{1-2} \textbf{x} & \textbf{y} \\ \cline{1-2} 0 & a \\ \cline{1-2} 1 & b \\ \cline{1-2} 2 & c \\ \cline{1-2} 3 & d \\ \cline{1-2} 4 & e \\ \cline{1-2} 5 & f \\ \cline{1-2} \end{array}\)

\(\bullet \ \text{For x = 0,}\)

\(\displaystyle{y = \frac{2}{5}(0) - 7}\\\\y = 0 - 7\\\\y = -7\)

\(\bullet \ \text{For x = 1,}\)

\(\displaystyle{y=\frac{2}{5}(1)-7}\\\\y=\frac{2}{5}-7\\\\y = -\frac{33}{5}\)

\(\bullet \ \text{For x = 2,}\)

\(\displaystyle{y=\frac{2}{5}(2)-7}\\\\y = \frac{4}{5}-7\\\\y = -\frac{31}{5}\)

\(\bullet \ \text{For x = 3,}\)

\(\displaystyle{y=\frac{2}{5}(3)-7}\\\\y= \frac{6}{5}-7\\\\y=-\frac{29}{5}\)

\(\bullet \ \text{For x = 4,}\)

\(\displaystyle{y=\frac{2}{5}(4)-7}\\\\y = \frac{8}{5}-7\\\\y=-\frac{27}{5}\)

\(\bullet \ \text{For x = 5,}\)

\(\displaystyle{y=\frac{2}{5}(5)-7}\\\\y=2-7\\\\y=-5\)

Now, we can place these values in our table.

\(\begin{array}{|c|c|} \cline{1-2} \textbf{x} & \textbf{y} \\ \cline{1-2} 0 & -7 \\ \cline{1-2} 1 & -33/5 \\ \cline{1-2} 2 & -31/5 \\ \cline{1-2} 3 & -29/5 \\ \cline{1-2} 4 & -27/5 \\ \cline{1-2} 5 & -5 \\ \cline{1-2} \end{array}\)

As we can see in our table, the rate of decrease is \(-\frac{2}{5}\). In case we need to determine more values, we can easily either replace x with a new value in the equation or just subtract \(-\frac{2}{5}\) from the previous value.

For Equation 2, we need to use the same process. Equation 2 has been resolved to be \(y=-\frac{7}{2}x+\frac{25}{2}\). Therefore, we just use the same process as before to solve for the values.

\(\bullet \ \text{For x = 0,}\)

\(\displaystyle{y=-\frac{7}{2}(0)+\frac{25}{2}}\\\\y = 0 + \frac{25}{2}\\\\y = \frac{25}{2}\)

\(\bullet \ \text{For x = 1,}\)

\(\displaystyle{y=-\frac{7}{2}(1)+\frac{25}{2}}\\\\y = -\frac{7}{2} + \frac{25}{2}\\\\y = 9\)

\(\bullet \ \text{For x = 2,}\)

\(\displaystyle{y=-\frac{7}{2}(2)+\frac{25}{2}}\\\\y = -7+\frac{25}{2}\\\\y = \frac{11}{2}\)

\(\bullet \ \text{For x = 3,}\)

\(\displaystyle{y=-\frac{7}{2}(3)+\frac{25}{2}}\\\\y = -\frac{21}{2}+\frac{25}{2}\\\\y = 2\)

\(\bullet \ \text{For x = 4,}\)

\(\displaystyle{y=-\frac{7}{2}(4)+\frac{25}{2}}\\\\y=-14+\frac{25}{2}\\\\y = -\frac{3}{2}\)

\(\bullet \ \text{For x = 5,}\)

\(\displaystyle{y=-\frac{7}{2}(5)+\frac{25}{2}}\\\\y = -\frac{35}{2}+\frac{25}{2}\\\\y = -5\)

And now, we place these values into the table.

\(\begin{array}{|c|c|} \cline{1-2} \textbf{x} & \textbf{y} \\ \cline{1-2} 0 & 25/2 \\ \cline{1-2} 1 & 9 \\ \cline{1-2} 2 & 11/2 \\ \cline{1-2} 3 & 2 \\ \cline{1-2} 4 & -3/2 \\ \cline{1-2} 5 & -5 \\ \cline{1-2} \end{array}\)

When we compare our two tables, we can see that we have one similarity - the points are the same at x = 5.

Equation 1                  Equation 2

\(\begin{array}{|c|c|} \cline{1-2} \textbf{x} & \textbf{y} \\ \cline{1-2} 0 & -7 \\ \cline{1-2} 1 & -33/5 \\ \cline{1-2} 2 & -31/5 \\ \cline{1-2} 3 & -29/5 \\ \cline{1-2} 4 & -27/5 \\ \cline{1-2} 5 & -5 \\ \cline{1-2} \end{array}\)                 \(\begin{array}{|c|c|} \cline{1-2} \textbf{x} & \textbf{y} \\ \cline{1-2} 0 & 25/2 \\ \cline{1-2} 1 & 9 \\ \cline{1-2} 2 & 11/2 \\ \cline{1-2} 3 & 2 \\ \cline{1-2} 4 & -3/2 \\ \cline{1-2} 5 & -5 \\ \cline{1-2} \end{array}\)

Therefore, using this data, we have one solution at (5, -5).

1. The quadratic function for the Area in terms of x: A(x) = 24x.

2. The cross-sectional area is maximized when the depth of the gutter is 0.

3. The maximum cross-sectional area is square inches 0.

To determine the depth of the gutter that maximizes its cross-sectional area and allows the greatest amount of water to flow, we need to follow a step-by-step process.

1. Write a quadratic function for the area in terms of x:

The cross-sectional area of the gutter can be represented as a rectangle with a width of 24 inches and a depth of x. Therefore, the area, A(x), is given by A(x) = 24x.

2. The cross-sectional area is maximized when the depth of the gutter is:

To find the value of x that maximizes the area, we need to find the vertex of the quadratic function. The vertex of a quadratic function in form f(x) = ax² + bx + c is given by x = -b/(2a). In our case, a = 0 (since there is no x² term), b = 24, and c = 0. Thus, the depth of the gutter that maximizes the area is x = -24/(2 * 0) = 0.

3. The maximum cross-sectional area is square inches:

Substituting the value of x = 0 into the quadratic function A(x) = 24x, we get A(0) = 24 * 0 = 0. Therefore, the maximum cross-sectional area is 0 square inches.

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Answer:  if with 3.14 v= 37512.5333

if with pi v= 37531.56

Step-by-step explanation:

the formula is 1/3hπr^2

r= 2d so radius is 32

plus numbers in (square it multiple times pi or 3.14 then multiply times height and divide by 3)

Answer:

Step-by-step explanation:

256 ft². Step-by-step explanation: SA=2(lw+lh+wh) where l is length and w is width and h is height. Plug in the given information.

The domain and range of the function is input value and output values respectively.

In math function is defined as  a correspondence from one value x of the first set A to another value y of the second set B.

Here we have to state the domain and range of the function.

AS per the definition of the function, we have identified that the domain of a function is the set of values that we are allowed to plug into our function. Which refers that this set is the x values in a function such as f(x).

And the term range of a function is defined as the set of values that the function assumes and which includes the set is the values that the function shoots out after we plug an x value in.

Complete Question:

State the domain and range of the function for the function f. And enter your answers using interval notation. if it is not a function, enter it in all blanks.

Domain: ____

Range: _____

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Given data:

The given age of Tom is T=P+26.

The expression for the product of their ages is TxP=560.

Substitute (P+26) for T in the second expression.

Thus, the age of Paul is 14 years.

The amount Siya will spend on tiles is given by the expression (1.1 x T / 6) x R234, where T represents the required number of tiles. To calculate the amount Siya will spend on tiles, we need to determine the number of boxes of tiles he needs to purchase and then multiply it by the price per box.

First, we need to determine the number of tiles required. Let's assume the required number of tiles is represented by the variable "T."

Since the builder recommends buying 10% more tiles in case of breakages, Siya needs to purchase 110 percentage of the required number of tiles. This can be calculated as:

110% of T = 1.1 x T

Next, we need to convert the number of tiles into the number of boxes required. We know that one box contains 6 tiles, so the number of boxes Siya needs to purchase is:

Number of boxes = (1.1 x T) / 6

Finally, we can calculate the total cost by multiplying the number of boxes by the price per box:

Total cost = (1.1 x T / 6) x R234

Please note that without knowing the specific number of tiles required (T), we cannot provide an exact amount Siya will spend.

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Answer:

1.0515509 Days

Step-by-step explanation:

Answer: 6p^3+29p^2+22p-21

Answer: y = 12.6

Step-by-step explanation:

Since x = 2 and y = 6.3 * x, y = 6.3 * 2.

6.3 * 2 is equal to 12.6, so y is 12.6.

Answer:

y = 12.6

Step-by-step explanation:

y = 6.3x                     x = 2

Solve for y.

y = 6.3(2)

y = 12.6

So, the answer is 12.6

The amount of cake has been eaten is, 3/4.

What is parts of number?

A decimal fraction can be used to represent decimal numbers. It consists of a whole number and a decimal. In the decimal number 3.25, for instance, 3 is the whole number portion, and 25 is the decimal portion.

Given:

Todrick eats one fourth of lemon cake.

Roberta eats one third of the same cake.

Latasha comes home from work and eats one sixth of the same cake.

Let x be the amount of cake has been eaten.

So from the given information,

\(\frac{1}{4}+\frac{1}{3}+\frac{1}{6} = x\\ \frac{3 + 4 + 2}{12} = x\\ \frac{9}{12} = x \\x = \frac{3}{4}\)

Hence, the amount of cake has been eaten is, 3/4.

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Answer:

2, 4, 6, 8

Step-by-step explanation:

even numbers are numbers that can be equally split in half.

Example:

Answer:

65

Step-by-step explanation:

100, 50, 80, 40, 70, 35, 65.

|____|__|___|___|__|__|

÷2. +30. ÷2. +30 ÷2. +30

A pattern is a recurring arrangement of numbers, forms, colors, and so on. The next number in the given pattern will be 65.

In mathematics, a pattern is a recurring arrangement of numbers, forms, colors, and so on. The Pattern may be applied to any form of event or object. A pattern is defined as a group of integers that are connected to each other in a specified way.

If the given pattern is observed closely then it can be observed that the second number is decreased by half the previous one, while the next number is formed by adding 30, therefore,

Hence, the next number in the given pattern will be 65.

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Answer:

5x  +  150

Step-by-step explanation:

5(x+30) =

5 * x  + 5 * 30 =

5x  + 150

Answer: 7

Step-by-step explanation:

Since there are 42 tubes and each tray can hold 6 tubes, it will be 42/6 which is 7.

Answer:

  C ≈ 22.1°

Step-by-step explanation:

The law of cosines formula is given. Solving it for C, we find ...

  C = arccos((a^2 +b^2 -c^2)/(2ab))

where a and b are the sides adjacent to the angle.

Then we have ...

  C = arccos((14^2 +19^2 -8^2)/(2·14·19)) = arccos(493/532)

  C ≈ 22.1°

__

If you have a fair number of these to do, a spreadsheet is a useful tool. There are also triangle solver apps on the web or your local smart platform that will do this, too.

Answer:

Step-by-step explanation:

360 = x - 17 + 2x - 67 + 3x

360 = 6x - 84

360 + 84 = 6x

444 = 6x

x = 444 : 6

x = 74°

-------------------

check

2 * 74 - 67 + 74 - 17 + 3 * 74 = 360°

the answer is good

Answer:

360°

Step-by-step explanation:

The sum of the exterior angles of any n-gon is 360°

The value of s in the point (s,-3) after using slope formula is -4.

What is slope?

Slope is a term used to define how steep a line is. The rise of a line over the run of a line, or the change in the vertical direction (y) over the change in the horizontal direction, is the definition of slope (x). The slope is the angle at which one is moving forward or backward when skiing down a hill or climbing a mountain. Depending on what it is, the slope may occasionally be fairly flat or extremely steep. The slope of an object indicates how steep it is. Slope knowledge is crucial for daily decision-making. 

Using slope formula,

=> slope m = \(\frac{y_2-y_1}{x_2-x_1}\)

Now the given point  is ,

\((x_1,y_1)=(s,-3) \\(x_2,y_2)=(-8,-4)\)

=> slope m= 1/4

=> \(\frac{1}{4}= \frac{-4+3}{-8-s}\)

=> \(\frac{1}{4} = \frac{-1}{-8-s}\)

=> -8-s=-4

=>-s=-4+8

=> -s=4

=> s =-4.

Hence the value of s is -4.

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The arrow in the ruler pointing to 1 inch.

The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.

The number of parts into which the whole has been divided is shown by the denominator. It is positioned in the fraction's lower portion, below the fractional bar.

How many sections of the fraction are displayed or chosen is shown in the numerator. It is positioned above the fractional bar in the upper portion of the fraction.

We have ten division between two number in a scale.

Now, the point here at 9 division or 0.9 inch.

1/2 inch = 0.5 inch

1 1/2 inch= 1.5 inch

So, the arrow shows nearly the measurement of 1 inch.

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84.13% of the printing jobs will be acceptable.

The new standard deviation required to achieve a minimum of 95% of jobs acceptable is 0.121.

The darkness of the print is measured quantitatively using an index. If the index is greater than or equal to 2.0 then the darkness is acceptable. Anything less than 2.0 means the print is too light and not acceptable. The machines print at an average darkness of 2.2 with a standard deviation of 0.20.

The mean of the darkness of the print is µ = 2.2 and the standard deviation is σ = 0.20.Therefore, the z-score can be calculated as; `z = (x - µ) / σ`.The index required for acceptable prints is 2.0. Thus, the percentage of prints that are acceptable can be calculated as follows;P(X ≥ 2.0) = P((X - µ)/σ ≥ (2.0 - 2.2) / 0.20)P(Z ≥ -1) = 1 - P(Z < -1)Using the standard normal table, P(Z < -1) = 0.1587P(Z ≥ -1) = 1 - 0.1587= 0.8413.

To find the new standard deviation, we can use the z-score formula.z = (x - µ) / σz = (2.0 - 2.2) / σz = -1Therefore, P(X ≥ 2.0) = 0.95P(Z ≥ -1) = 0.95P(Z < -1) = 0.05Using the standard normal table, the z-score value of -1.645 corresponds to a cumulative probability of 0.05. Hence,z = (2.0 - 2.2) / σ = -1.645σ = (2.0 - 2.2) / -1.645= 0.121.

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Solution:

Given:

The table of the poll results;

The formula for calculating probability is given by;

a) The P(Democrat) is;

Therefore, the probability that it is a democrat is 0.3625

b) The P(worse) is;

Therefore, the probability that it is worse is 0.4593

c) The P(worse|Democrat)- This is a conditional probability.

We use the conditional probability formula to solve this.

Conditional probability is given by;

Hence,

Therefore, the probability of worse given democrat is 0.5805

d) The P(Democrat|worse) is;

Therefore, the probability of democrat given worse is 0.4582

e) The P(Democrat and worse) is;

Therefore, the probability of democrat and worse is 0.2105

Answer:

4/5

Step-by-step explanation:

There are so many points on the graph whose coordinates are impossible to estimate. Look for two "nice" points--points with integer coordinates. The line passes through (-2, 0) and (3, 4).

Slope = rise / run. It's the ratio of vertical change to horizontal change as you move from one point on the line to another.

Moving from (-2, 0) to (3, 4), the vertical change is 4 - 0 = 4.

The horizontal change is 3 - (-2) = 5.

The slope is 4/5

Answer:

8

Step-by-step explanation:

125 + 85=210.

210 * 8 = 1680.

Therefore, the answer is 8.