Charles owed 390$ to his friend. On the first day Charles paid his friend 12$. Each following week the amount Charles paid his friend increased by the same amount. After 10 payments, Charles had paid back the full amount. By how much did each payment increase?

Final answer:

The nth term of the sequence can be found using the formula Tn = a + 4(n - 1), where a is the first term and n is the term position. This is based on the characteristics of an arithmetic sequence.

Explanation:

This pattern indicates that the sequence is an arithmetic sequence, where each term is obtained by adding a constant difference to the preceding term.

To find the nth term of an arithmetic sequence, we use the formula:

Tn = a + (n - 1)d

Where Tn is the nth term, a is the first term, n is the position of the term in the sequence, and d is the common difference between terms. For this sequence, d = 4.

Substituting the known values into the formula gives us:

Tn = a + 4(n - 1)

This expression allows us to calculate the nth term of the sequence given the first term (a) and the position (n) of the term we want to find.

Answer:

The correct answer is 10x² + 3xy + 6x - y² + 3y

Step-by-step explanation:

It is given an expression (2x + y)(5x - y + 3)

To find the product

(2x + y)(5x - y + 3) = 2x * 5x  - 2x*y + 2x*3 + y*5x -y² + 3y

 = 10x² - 2xy + 6x + 5xy - y² + 3y

 = 10x² + 3xy + 6x - y² + 3y

Therefore the correct answer is

10x² + 3xy + 6x - y² + 3y

The product of (2x + y) and (5x – y + 3) is found by using the distributive property of multiplication over addition, which gives us: 10x^2 + 3xy + 6x - y^2 + 3y.

To find the product of (2x + y) and (5x – y + 3), we need to use the distributive property of multiplication over addition. This involves multiplying each term within the first parentheses by each term in the second parentheses.

The steps are as follows:

The result is 10x^2 -2xy + 6x + 5xy - y^2 + 3y. Simplifying further gives us: 10x^2 + 3xy + 6x - y^2 + 3y.

So, the product of (2x + y) and (5x – y + 3) is 10x^2 + 3xy + 6x - y^2 + 3y.

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Answer:

The equation would be:

[tex]x^2+y^2=169[/tex]

In the attachment!!!

Hope this helps!!!

[tex]Sofia[/tex]

  10,000

x 10,000

________

100,000,000

Answer:

100,000,000

Step-by-step explanation:

To determine which inequality is true, compare the absolute values of the given numbers. The correct answer is B, |-8| < |-5|.

To determine which inequality is true, we need to compare the absolute values of the given numbers. Absolute value is the distance of a number from zero on the number line. In this case:

Therefore, the correct answer is B, |-8| < |-5|.

Answer:

9

Step-by-step explanation:

since 2 is the minimum and 31 is the maximum you subtract 31 by 22

To find the range of the given data set, follow these steps:
1. Identify the maximum value in the data set.
2. Identify the minimum value in the data set.
3. Subtract the minimum value from the maximum value.
Let's apply these steps to the provided data set:
Data set: 31, 31, 22, 28, 23
Step 1: Find the maximum value.
Looking at the numbers, the maximum value is 31. (Both occurrences of 31 are considered, but since they are the same, the maximum is still 31.)
Step 2: Find the minimum value.
Looking at the numbers, the minimum value is 22.
Step 3: Calculate the range.
Subtract the minimum value from the maximum value: 31 - 22 = 9.
Hence, the range of the given data set is 9.

Answer: The answer is 785.4

Step-by-step explanation: Equation is 2πrh+2πr²

Plug in your numbers and hit enter!

Hope this helps

For this case we have by definition, that the surface area of a cylinder is given by:

[tex]SA = 2 \pi * r * h + 2 \pi * r ^ 2[/tex]

Where:

A: It's the radio

h: It's the height

According to the given data we have:

[tex]SA = 2 \pi * (5) * 20 + 2 \pi * (5) ^ 2\\SA = 200 \pi + 50 \pi\\SA = 250 \pi\\SA = 785 \ units ^ 2[/tex]

ANswer:

[tex]785 \ units ^ 2[/tex]

The answer is 1/5

Step-by-step explanation:

You have the probability of getting 1/5 correct.

For this case, we have by definition, the calculation of probabilities:

[tex]probability = \frac {number\ of \favorable\ cases} {number\ of\ possible\ cases}[/tex]

We have 5 possible answers, and we have only one favorable case, that is, only one correct option among the 5 possible answers.

So, we have:

[tex]Probability = \frac {1} {5} = 0.2[/tex]

Answer:

0.2

Answer:

15: 15, 30, 45, 60, 75, 90, 105, 120, 135...etc, 20: 20, 40, 60, 80, 100, 120, 140...etc, 45: 45, 90, 135, 180, 225, 270....etc

Common Multiples: Is 180, Because all of them have a multiple of 180.

Step-by-step explanation:

Hope i helped you. :)

Answer:

15:

20:

45:

hope this helps

A.

If you multiply the original equation by 3 you get -45x+3y=54, which is the exact same as A, therefore they have infinite solutions.

Answer:

x= number of tickets bought

y= total

44x+12=y

Answer:

n >10.5

Step-by-step explanation:

Let n be our number

2/3 n+5 >12

Subtract 5 from each side

2/3 n +5-5 >12 -5

2/3 n >7

Multiply each side by 3/2 to isolate n

3/2*2/3n > 7 *3/2

n > 21/2

n >10.5

Answer:12

Step-by-step explanation: 12x2/3=8

8+5=13 GG

Start with

[tex]\dfrac{2a+3b}{a+b}=7[/tex]

Assuming [tex]a\neq -b[/tex], multiply both sides by [tex]a+b[/tex]

[tex]2a+3b = 7a+7b[/tex]

Solve for [tex]a[/tex]

[tex]5a = -4b \iff a = -\dfrac{4b}{5}[/tex]

Substitute this value for [tex]a[/tex] in the desired expression:

[tex]\dfrac{2a}{b} = \dfrac{\frac{-8b}{5}}{b} = -\dfrac{8}{5}[/tex]

You were correct! :)

ANSWER

No, because there is no common ratio

EXPLANATION

The given sequence is

-1, 1, 4, 8

If this sequence is geometric, then there should be a common ratio among the consecutive terms.

[tex] \frac{1}{ - 1} \ne \frac{4}{1} \ne \frac{8}{4} [/tex]

Hence the sequence

-1, 1, 4, 8

is not a geometric sequence.

Answer:

The sequence is not a geometric sequence

Step-by-step explanation:

In a geometric sequence you find the following term multiplying the current by a fixed quantity called the common ratio.

To prove if a sequence is geometric we need to check if the ratio is consistent across the sequence. To check for the ratio we use the formula:

[tex]r=\frac{a_n}{a_{n-1}}[/tex]

were

[tex]r[/tex] is the ratio

[tex]a_n[/tex] is the current term  

[tex]a_{n-1}[/tex] is the previous term

Let's star with 1, so [tex]a_n=1[/tex] and [tex]a_{n-1}=-1[/tex]

[tex]r=\frac{a_n}{a_{n-1}}[/tex]

[tex]r=\frac{1}{-1}[/tex]

[tex]r=-1[/tex].

Now let's check 4 and 1, so [tex]a_n=4[/tex] and [tex]a_{n-1}=1[/tex]

[tex]r=\frac{a_n}{a_{n-1}}[/tex]

[tex]r=\frac{4}{1}[/tex]

[tex]r=4[/tex]

Since the ratios between two pair of numbers are different, we can conclude that the sequence is not geometric.

Answer:

Part a) The width of parking lot is 87m.

Part b) The length of rectangular pool is 94 m

Step-by-step explanation:

a) The area of parking lot Area= 8439 m^2

Length of Parking Lot = Length = 97 m

Width of Parking Lot = Width= ?

Area of rectangle = Length * Width

Putting the values,and finding width,

8439 = 97 * Width

=> Width = 8439/97

=> Width = 87 m

So, The width of parking lot is 87m.

b) Perimeter of rectangular pool = Perimeter= 344 m

Width of rectangular pool = Width = 78 m

Length of rectangular pool = Length = ?

The formula for perimeter is:

Perimeter = 2*(Length + Width)

Putting values in the formula:

344 = 2*(Length + 78)

344/2 = Length + 78

172 = Length + 78

=> Length = 172 - 78

Length = 94 m

So, the length of rectangular pool is 94 m.

To find the percentages of things on a two-way frequency table, calculate the relative frequencies by dividing each frequency value by the total number of observations and multiplying by 100. This will give you the proportion of each category expressed as a percentage.

To find the percentages of things on a two-way frequency table, you need to calculate the relative frequencies. The relative frequency is the fraction or decimal value that represents the proportion of each category. You can obtain the relative frequencies by dividing each frequency value by the total number of observations and then multiplying by 100 to convert it into a percentage.

For example, if you have a frequency of 5 in a certain category out of 100 total observations, the relative frequency would be -

= 5/100

= 0.05 or 5%.

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Finding percentages in a two-way frequency table involves understanding joint, marginal, and conditional distributions. Relative frequencies are calculated row by row, and expected frequencies are calculated based on population size and expected percentages. Marginal and conditional distributions focus on one variable or a subpopulation, respectively.

To find the percentages of things on a two-way frequency table, you first need to understand what the contents of the table represent. The numbers in the body of the table are called joint frequencies. For example, if you have a value of 20 signifying the count of women who prefer football, and the total sample size is 50, then the percentage of relative frequency is (20/50)*100 = 40%.

Expected frequencies are calculated by multiplying the expected percentages by the total population size. For example, with an expected percentage of 0.15 and 600 as the total population, you'd calculate 0.15*600=90 as the expected frequency.

Relative frequencies are calculated by dividing each frequency by the total frequency. For example, if in one row the frequency is .25, and the total cumulative frequency so far is .15, then the cumulative relative frequency for that row would be .15 + .25 = .40. Repeat this process for each row to fill out the rest of the table.

A marginal distribution involves focusing on only one of the variables in the table. The reason why 20 (in the ratio 20/50) is a marginal frequency is because it represents the margin or part of the total population that is women.

A conditional distribution goes a step further by focusing on a particular subset of the population, not just one variable. For example, if we focus only on the subset of women who prefer football, we'd calculate the conditional distributions differently.

To find statistical measures such as the median, you can use the cumulative relative frequencies. In this case, you would look for the value corresponding to the 50th percentile in the cumulative relative frequency column.

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Answer:

A rectangular prism and a cube.

Step-by-step explanation:

A rectangular prism when sliced by a plane can have a square facing up, meaning that a square will be produced. A cube has all square faces and when cut horizontally will produce a square.

Answer:

[tex]\large\boxed{Q1.\ q(x)=\dfrac{1}{2}x+\dfrac{7}{2},\ q(2)=\dfrac{9}{2}}\\\boxed{Q2.\ t(x)=\dfrac{1}{2}x+\dfrac{7}{2},\ t(0)=\dfrac{7}{2}}[/tex]

Step-by-step explanation:

[tex]\text{The slope-intercept form of an equation of a line:}\\\\y=mx+b\\\\m-slope\\b-y-intercept\\\\\text{The formula of a slope:}\\\\m=\dfrac{y_2-y_1}{x_2-x_1}\\\\\text{We have}\\\\q(-1)=3\to(-1,\ 3)\\q(3)=5\to(3,\ 5)[/tex]

[tex]\text{Calculate the slope:}\\\\m=\dfrac{5-3}{3-(-1)}=\dfrac{2}{4}=\dfrac{2:2}{4:2}=\dfrac{1}{2}\\\\\text{We have the equation:}\\\\y=\dfrac{1}{2}x+b\\\\\text{Put the coordinates of the point (-1, 3) to the equation:}\\\\3=\dfrac{1}{2}(-1)+b\\\\3=-\dfrac{1}{2}+b\qquad\text{add}\ \dfrac{1}{2}\ \text{to both sides}\\\\3\dfrac{1}{2}=b\to b=3\dfrac{1}{2}=\dfrac{7}{2}[/tex]

[tex]q(x)=\dfrac{1}{2}x+\dfrac{7}{2}\\\\q(2)-\text{put x = 2 to the equation:}\\\\q(2)=\dfrac{1}{2}(2)+\dfrac{7}{2}=\dfrac{2}{2}+\dfrac{7}{2}=\dfrac{9}{2}[/tex]

[tex]t(-4)=3\to(-4,\ 3)\\t(4)=4\to(4,\ 4)\\\\m=\dfrac{4-3}{4-(-4)}=\dfrac{1}{8}\\\\y=\dfrac{1}{8}x+b\\\\\text{put the coordinates of the point (4,\ 4):}\\\\4=\dfrac{1}{8}(4)+b\\\\4=\dfrac{1}{2}+b\qquad\text{subtract}\ \dfrac{1}{2}\ \text{from both sides}\\\\3\dfrac{1}{2}=b\to b=3\dfrac{1}{2}=\dfrac{7}{2}\\\\t(x)=\dfrac{1}{2}x+\dfrac{7}{2}\\\\t(0)=\dfrac{1}{2}(0)+\dfrac{7}{2}=0+\dfrac{7}{2}=\dfrac{7}{2}[/tex]

Answer:

that the are both have a right angle. And that the are both cones.

Step-by-step explanation:

Answer:

3 : 5

Step-by-step explanation:

The ratio can be determined using the radii or the heights of the 2 cones

radii  6 : 10 = 3 : 5 ← in simplest form

height 9 : 15 = 3 : 5 ← in simplest form

Perimeter =525.66 ft

Area = 10913.27 ft2

See photo

Answer:

[tex]\boxed{4}[/tex]

Step-by-step explanation:

When you reflect a point (x, y) across the x-axis, the x-coordinate remains the same, but the y-coordinate gets the opposite sign.

Thus,  the y-coordinate becomes [tex]\boxed{\textbf{4}}[/tex].

Answer:

Step-by-step explanation:

Parallel lines have the same slope.

The slope-intercept form of an equation of a line:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept

We have the equation of the line m:

[tex]m:\ y=3x+3\to m=3[/tex]

Therefore the equation of a line n parallel to the line m is:

[tex]y=3x+b[/tex]

where b is any real number

Answer y = 3x + b

Step-by-step explanation:

Circumference can be found using [tex]C=2\pi r[/tex] formula. Where [tex]r[/tex] is radius.

Now we just put in the data.

[tex]C=2\pi\times26=52\pi\approx\boxed{163.36}[/tex]

If the radius is 26, firstly we have to calculate the diameter. The diameter is 2 times the radius.

Radius = 26

Diameter = 26 × 2 = 52

Circumference of circle = π × Diameter

= π × 52

= 163.3628 or 163.4 (to 1 dp)

Answer:

x+3

Step-by-step explanation:

1. Use formula for the difference of squares:

[tex]a^2-b^2=(a-b)(a+b)[/tex]

to factor

[tex]x^2-9=(x-3)(x+3).[/tex]

2. Factor [tex]x^2+8x+15:[/tex]

[tex]x^2+8x+15=x^2+3x+5x+15=x(x+3)+5(x+3)=(x+3)(x+5).[/tex]

Now you can see that [tex]x+3[/tex] is the common factor.

Answer:

x + 3

Step-by-step explanation:

x² - 9 ← is a difference of squares and factors as

x² - 9 = (x - 3)(x + 3)

To factor x² + 8x + 15

Consider the factors of the constant term (+ 15) which sum to give the coefficient of the x- term (+ 8)

The factors are + 5 and + 3, since

5 × 3 = 15 and 5 + 3 = 8, thus

x² + 8x + 15 = (x + 5)(x + 3)

Thus the factor (x + 3) is common to both

7/9 is going to be the greatest since it is the only positive number and the. it’s going to be -4/5 and then the least is going to be -1/14.

-1/14 , -4/5 , 7/9

The numbers -1/14, 7/9, -4/5 arranged from least to greatest are -4/5, -1/14, 7/9. This is found by converting fractions to decimals for easier comparison and then arranging them in order.

To go about solving this, we first consider each number's location on the number line. The numbers closer to the left are smaller than those on the right. Given the numbers -1/14, 7/9, and -4/5, we can start by converting each fraction to a decimal for easier comparison.

-1/14 equals approximately -0.0714, 7/9 equals approximately 0.7777, and -4/5 equals -0.8. Therefore, from smallest to largest, these numbers can be arranged as -0.8, -0.0714, 0.7777. Converting these back to fractions gives us the desired result: -4/5, -1/14, 7/9.

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This relation is a function because a function, in fact this is a linear function. We have that:

[tex]\left[\begin{array}{cc}x & y\\2 & 3\\4 & 4\\6 & 5\\8 & 6\end{array}\right][/tex]

As you can see below, all the points have been plotted an this is a linear function. Therefore, with two points we can get the equation, so:

[tex]The \ equation \ of \ the \ line \ with \ slope \ m \\ passing \ through \ the \ point \ (x_{1},y_{1}) \ is:\\ \\ y-y_{1}=m(x-x_{1}) \\ \\ \\ y-3=\frac{4-3}{4-2}(x-2) \\ \\ \\ y-3=\frac{1}{2}(x-2) \\ \\ y=\frac{1}{2}x-1+3 \\ \\ y=\frac{1}{2}x+2 \\ \\ \\ Where: \\ \\ (x_{1},y_{1})=(2,3) \\ \\ (x_{2},y_{2})=(4,4)[/tex]

Finally, the equation is:

[tex]\boxed{y=\frac{1}{2}x+2}[/tex]

Answer:

y=0.5x +2

Step-by-step explanation:

The graph of the function f(x) = cos(2x) + 1 is added as an attachment

Sketching the graph of the function

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

f(x) = cos(2x) + 1

The above function is a cosine function that has been transformed as follows

Next, we plot the graph using a graphing tool by taking not of the above transformations rules

The graph of the function is added as an attachment

Answer:

x=-4

Step-by-step explanation:

Answer:

Use desmos.com/calculator. It is a graphing calculator that can do many things

Step-by-step explanation:

say thanks and vote

Do 3/4 of 2/3

Turn the demoninator into 12 so:

9/12 8/12 so I’m guessing C

Answer:  The correct option is (D) [tex]\dfrac{8}{9}.[/tex]

Step-by-step explanation:  Given that [tex]\dfrac{3}{4}[/tex] of Melissa's friends babysit for extra money and [tex]\dfrac{2}{3}[/tex] of her friends babysit and pet sit.

We are to find the fraction of her friends those who babysits also pet sits.

Total fraction of Melissa's friends is given by

[tex]F=\dfrac{3}{4}.[/tex]

Therefore, the fraction of her friends those who babysits also pet sits is given by

[tex]f=\dfrac{\frac{2}{3}}{\frac{3}{4}}=\dfrac{2}{3}\times\dfrac{4}{3}=\dfrac{8}{9}.[/tex]

Thus, the required fraction is [tex]\dfrac{8}{9}.[/tex]

Option (D) is CORRECT.