Solve:
5x-2y = 6
5x-2y = -4

Please show your work or explain what method you used to solve it (substitution, graphing, or elimination)

The common ratio for infinite geometric series with first term -3/2 and sums twice the common ratio is -1/2.

First keep in mind the common ratio must -1 < r < 1 for geometric series converges.

Common ratio can be calculated using standard formula for infinite geometric series converges which is Sum = a/(1-r) with a as first term and r as common ratio. So,

Since sum is twice the common ratio, so the equation is

2r = a/(1-r)

we can substitute (1-r). So,

2r(1-r) = a

2r-2r^2 = -3/2

we can multiple all by two. So,

4r-4r^2 = -3

0 = 4r^2-4r-3

0 = (2r-3)(2r+1)

So the result is either r = 3/2 or r = -1/2. as previously mentioned above, r result only in -1 < r < 1. So, the result of r = 3/2 is rejected.

Thus, the common ratio is -1/2.

You question is incomplete, but most probably your full question was

An infinite geometric series has first term -3/2 and sums to twice the common ratio. Find the sum of all possible values for the common ratio.

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Answer:

Each side is 5 units long

Step-by-step explanation:

Since the opposite angles are equal then x + 2 = 3x - 4

So solve for x: so  4+2 = 3x - x

6 = 2x

3 = x

So one side is x + 2 = 3 + 2 = 5

The other side is 3x - 4 = 3(3) - 4 = 9-4 = 5

Answer:

10×7 inches?

Step-by-step explanation:

mona lisa = 30inches × 21inches

notebook is 11 × 9

(30/21) ÷ 3= 10/7

So 10 × 7.

The slope of the line when graphing x1 on the horizontal axis and x2 on the vertical axis is -3/4.

To determine the slope of the line when graphing x1 on the horizontal axis and x2 on the vertical axis, we need to rearrange the given equation in the slope-intercept form, y = mx + b, where m is the slope.

6x1 + 8x2 = 240

First, let's isolate x2: 8x2 = -6x1 + 240

Dividing both sides by 8: x2 = (-6/8)x1 + 30

Now we have the equation in the form y = mx + b, where x1 is represented as the independent variable on the horizontal axis (x) and x2 as the dependent variable on the vertical axis (y).

Comparing the equation to y = mx + b, we can see that the coefficient of x1, which is -6/8 or -3/4, represents the slope of the line.

Therefore, the slope of the line when graphing x1 on the horizontal axis and x2 on the vertical axis is -3/4.

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Answer:

4•(2+5)^2 -5^2 = 171

Step-by-step explanation:

Do BIDMAS
(brackets, indices, division, multipy, add, sub)

so brackets
4*7^2-5^2
then do the indices
4*49-25
then the multiply
196-25
= 171
Hope this helps

Answer: Brackets => 4 x (7)^2 - 5^2
               Indices/Orders => 4 x 49 - 25

               Multiplication => 196 - 25

               Subtraction => 171

No, X or y-axis scale does not have to always start at zero. In a line chart, it's OK to start the axis at a number other than zero

A line that is used to take or mark measurements is known as an axis in mathematics. Two crucial axes of the coordinate plane are the x and y axes. A horizontal number line is the x-axis, while a vertical number line is the y-axis. The coordinate plane is created by the perpendicular intersection of these two axes.

Given,

No, X or y-axis scale does not have to always start at zero.

A line chart encodes data using location (x, y coordinates), whereas a bar chart represents data using length. In a line chart, it's OK to start the axis at a number other than zero despite many claims that they are always misleading since this minute difference influences how a reader utilizes the chart.

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The number of written in standard form is 9.45 × 10⁵

From the question, we are to write the given number in standard form

The given number is

Nine hundred forty-nine thousand

That is,

945000

To write a number in standard form, we will write the number as a decimal number between 1.0 and 10.0, multiplied by a power of 10.

The number, 945000, written in standard form is

9.45 × 10⁵

Hence, the number of written in standard form is 9.45 × 10⁵

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Answer:

The answer is 9/x-1

Step-by-step explanation:

Because both terms have the same denominator, then we can subtract the numerators upon the same denominator:

⇒ x+1/x-1 - x-8/x-1 = ((x + 1) - (x - 8))/(x - 1)

                             = (x + 1 - x + 8)/(x - 1)     [expand the brackets and simplify]

                             = 9/(x - 1)

A population has a mean μ=135 and a standard deviation Ï=28.

The mean of the sampling distribution of sample means is equal to the population mean, that is 135.

The standard deviation of the sampling distribution of sample means can be calculated by using the formula

SE = Ï /\(\sqrt{n}\)

Where Ï is the population standard deviation and n is the sample size.

By putting the given values we get

SE = 28 / \(\sqrt{57}\) = 3.7

Hence, the mean of the sampling distribution of sample means is 135, and the standard deviation is 3.7.

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This might help a bit, i hope

Answer:

\( A = \dfrac{512 \pi}{3}~ft^2 \)

Step-by-step explanation:

area of sector, A:

\(A = \dfrac{n}{360^\circ}\pi r^2\)

n = measure of the central angle of the sector in degrees

r = radius of circle

Here we have n = 240°, and r = 16 ft.

\(A = \dfrac{240^\circ}{360^\circ}\pi \times (16~ft)^2\)

\( A = \dfrac{2}{3}\pi \times 256~ft^2 \)

\( A = \dfrac{512 \pi}{3}~ft^2 \)

The car travels 30 miles in 45 minutes with the speed 40 miles/hour with the constant speed.

Velocity is the rate and direction of an object's movement, whereas speed is the time rate at which an object is moving along a path. In other words, velocity is a vector, whereas speed is a scalar value. The distance traveled by a moving object in a specific amount of time is its speed. How quickly something is moving is determined by its speed. The distance traveled by an object in a given amount of time divided by the time gives the object's average speed.

Here,

45 minutes/60 minutes= .75 hours (this gives you the amount of time in hours)

time x speed = distance

.75 hours time x 40 mph speed = 30 miles distance

With a constant speed of 40 miles per hour, the car covers 30 miles in 45 minutes.

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There are 15 different books and 3 each can be arranged on a shelf i.e., there are 15/3 i.e., 5 shelves to arrange the book in the the display case.

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Answer:

77 "

Step-by-step explanation:

'mean' is the average of all of the heights

( 84 + 84  + 77 + 63 + 70 + 70  + x) / 7 = 75

  x = 77

Answer:

I AM sure u will find answers in googl

let me go check

Step-by-step explanation:

1. 2

2. The X axis

3. 1 up and 5 left (-5, 1)

The arithmetic mean, also known as the average, is a measure of central tendency that represents the typical value of a set of data. All the data points must be added together, then divided by the number of data points. This is option (d).

To calculate the arithmetic mean, we sum up all the data points and then divide the sum by the number of data points.

Option (a) is incorrect because multiplying the data points together does not result in the arithmetic mean. Multiplication is used in other calculations, such as finding the product or calculating the geometric mean.

Option (b) is incorrect because excluding outliers is not necessary when calculating the arithmetic mean. The arithmetic mean takes into account all the data points, including outliers, providing a balanced representation of the data set.

Option (c) is incorrect because the arithmetic mean is not determined by the most frequently occurring data point. The most frequent data point is associated with the mode, which is a different measure of central tendency.

Therefore, option (d) is the correct method for calculating the arithmetic mean, as it involves adding all the data points together and then dividing by the number of data points.

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The value of the relative frequency distribution of the first interval, having a frequency of 14, and the total frequency given is 40, is 0.35.

In a Relative Frequency Distribution, we list how often a data value appears and scale it using the total frequency.

The sum of Relative Frequencies adds to 1.

In the question, we are informed that the first interval has a frequency of 14.

This implies that the data appears 14 times in the first interval.

Also, we are told that the total frequency is 40.

Thus, the relative frequency can be calculated as the ratio of the frequency of the interval to the total frequency.

Therefore, Relative frequency = 14/40 = 0.35.

Thus, the value of the relative frequency distribution of the first interval, having a frequency of 14, and the total frequency given is 40, is 0.35.

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The equation of circle can be written as (x-4)^2+ (y+2)^2 = 6^2. The center of the circle is (4,-2) and radius is 6.

What is a circle?

A circle is locus of points which have same distance from a point known as center. Circle is a 2 dimensional figure.

We are given a equation

x^2+y^2-8x+4y-16 = 0

Using completing square method

x^2-8x+ 16+y^2+4y+4-36=0

(x-4)^2 + (y+2)^2 = 6^2

Comparing with standard equation

The center of circle is (4,-2) and and radius of the circle is 6.

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Using Newton's method, the approximation x2 for the equation 6√x = 2x^2 - 5x, with a starting value of x0 = 2, rounded to the nearest thousandth, is x2 ≈ 1.352.

Newton's method is an iterative numerical method used to approximate the roots of a function. In this case, we want to find the solution to the equation 6√x = 2x^2 - 5x.

To use Newton's method, we start with an initial guess or starting value,

which is x0 = 2 in this case. We then iterate using the formula:

x_(n+1) = x_n - f(x_n)/f'(x_n)

where x_(n+1) is the next approximation, x_n is the current approximation, f(x) is the function we want to find the root of, and f'(x) is the derivative of the function.

First, we need to rewrite the equation as a function f(x) = 6√x - 2x^2 + 5x = 0.

Taking the derivative of f(x) with respect to x, we get f'(x) = 3/x^(5/6) - 4x + 5.

Now, we can start the iterations:

Substitute x0 = 2 into f(x) and f'(x) to calculate f(2) and f'(2).

Use the formula x_(n+1) = x_n - f(x_n)/f'(x_n) to calculate x1.

Repeat the process by substituting x1 into f(x) and f'(x) to calculate f(x1) and f'(x1), and then use the formula to calculate x2.

After two iterations, we obtain the approximation x2 ≈ 1.352 when rounded to the nearest thousandth.

Note: The process can be repeated to obtain even more accurate approximations by using x2 as the new starting value and applying the formula again.

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The timber is long enough to be used as one of the crossbars if DE is attached at the midpoints of legs BA and BC.

It is defined as the conversion from one quantity unit to another quantity unit followed by the process of division, and multiplication by a conversion factor.

It is given that:

Carpentry In each support for the garden swing, the crossbar DE is attached at the midpoints of legs BA and BC.

The length of AC = 4 1/2 = 9/2 = 4.5 feet

As we know,

1 feet = 12 inches

4.5 feet = 12x4.5 = 54 inches

The scale factor = 1/2

Carpenter has 30 inches

The length of DE = 30/2 = 15 inches

Thus, the timber is long enough to be used as one of the crossbars if DE is attached at the midpoints of legs BA and BC.

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The final grade is 98.05% , which is calculated by multiply assignment grade by its weight and then add it to the remaining percentage of the final.

To calculate your final grade considering the weightage of the first assignment, you need to multiply your assignment grade by its weight and then add it to the remaining percentage of the final.

Given:

- Assignment 1 grade: 87%

- Assignment 1 weight: 15%

- Remaining percentage of the final: 100% - 15% = 85%

To calculate the contribution of Assignment 1 towards your final grade, you multiply your assignment grade by its weight:

Contribution = Assignment 1 grade * Assignment 1 weight

Contribution = 87% * 15% = 0.87 * 0.15 = 0.1305

The remaining percentage of the final is 85%.

To calculate your final grade, you add the contribution of Assignment 1 to the remaining percentage:

Final grade = Contribution + Remaining percentage

Final grade = 0.1305 + 85% = 0.1305 + 0.85 = 0.9805

To express the final grade as a percentage, you can multiply it by 100:

Final grade = 0.9805 * 100 = 98.05%

Therefore, your final grade, taking into account the weightage of Assignment 1, is 98.05%.

When calculating your final grade with weighted assignments, you multiply each assignment's grade by its weight and then sum them up to determine the overall contribution towards the final grade. In this case, since Assignment 1 is worth 15% of the final grade, you multiply your grade (87%) by its weight (15%) to find its contribution (0.1305).

The remaining percentage of the final is calculated by subtracting the weight of Assignment 1 from 100%. In this case, it is 85%. You add the contribution of Assignment 1 (0.1305) to the remaining percentage (85%) to find the final grade (0.9805 or 98.05%). So, your final grade, taking into account the weightage of Assignment 1, is 98.05%.

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The area of a shape is the amount of space it occupies.

The dimension of the paper is given as: 12-inch by 8-inch

So, its area is:

\(Area = 12 * 8\)

\(Area = 96\)

Hence, the area of the paper is 96 square inches

The dimensions of the 4 right triangles are: Two 2 inches by 9 inches, and two 3 inches by 6 inches

So, the combined area is:

\(Area = 0.5(2 * 2 * 9 + 2 * 3 * 6)\)

\(Area = 36\)

Hence, the combined area of the triangle cutouts is 36 square inches

The area of the parallelogram is the difference between the areas of the paper and the four right triangles.

So, we have:

\(Area = 96 - 36\)

\(Area = 60\)

Hence, the area of the parallelogram is 60 square inches

The base is given as 9.22

So, we have:

\(Area = Base * Altitude\)

This gives

\(60 = 9.22* Altitude\)

Divide both sides by 9.22

\(Altitude = 6.51\)

Hence, the altitude of the parallelogram is 6.51 inches

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Answer:    The area of the paper is 96 square inches

   The combined area of the triangle cutouts is 36 square inches

   The area of the parallelogram is 60 square inches

   The altitude of the parallelogram is 6.51 inches

Step-by-step explanation:

There are 10 possible outcomes in the sample space.

To determine the number of outcomes in the sample space, we need to consider the number of possible sequences of paint jars the painter can try before finally obtaining the purple color.

Since the painter does not repeat any of the jars, we can count the outcomes by considering the possible positions of the purple jar within the sequence.

In the first attempt, there are 4 different jars she can choose from.

If the purple jar is not chosen in the first attempt, there are 3 remaining jars she can choose from in the second attempt.

If the purple jar is not chosen in the second attempt, there are 2 remaining jars she can choose from in the third attempt.

If the purple jar is not chosen in the third attempt, there is only 1 remaining jar she can choose from in the fourth attempt.

Since the purple jar must be chosen at some point, it will be one of the four attempts. Therefore, the total number of outcomes in the sample space is the sum of the outcomes at each step:

4 + 3 + 2 + 1 = 10

So, there are 10 possible outcomes in the sample space.

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60,20,,30 is the answer

Therefore, the solution to this equation problem is Suan, Hong, and Juan messages are 22 ,68 and 17.

In an equation, two mathematical expressions are said to be equal if their values are the same. The equivalence of two or more variables is demonstrated by a mathematical formula. It is identified by the equal ('=') sign. The formula is, for example, 8+2=12-2. The left and right sides of the equation are equivalent in the example above. A assertion that "this equals that" is what constitutes an equation.

Here,

Let x represent the number of text messages that Susan sent during the weekend.

Let y represent the number of text messages that Hong sent during the weekend.

Let z represent the number of text messages that Juan sent during the weekend.

Susan, Hong, and Juan sent a total of 107 text messages over their cell phones during the weekend. This means that

107=  x + y + z

Juan received four times as many mails from Hong.

Thus,

y = 4z

Juan sent 5 fewer messages than Susan. This means that

x = z + 5

Substituting y = 4z and x = z + 5 into equation 1, it becomes

z + 5 + 4z + z = 107

z + 4z + z = 107 - 5

6z= 102

z = 102/6 = 17

x = z + 5 = 17 + 5 = 22

y = 4z = 17×4 = 68

Therefore, the solution to this equation problem is Suan, Hong, and Juan messages are 22 ,68 and 17

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Answer:

4.24

Step-by-step explanation:

3.64 + 3/5

3.64 + 0.6 <--- 3/5 = 0.6 as a decimal

= 4.24 <--- Final answer

Answer:

6x + 20 + 4x + 80 - 2x=180

6x + 4x - 2x= 180 - 80 - 20

8x = 80

x = 10

The value of x in the triangle is 10, the value of each angle are; 80, 40 , 60 respectively

The total angle can be added as

note that the total angle in the triangle is 180

\(6x + 20 + 4x + 80 - 2x=180\)

\(6x + 4x - 2x= 180 - 80 - 20\)

\(8x = 80x = 10\)

Then we can know the angles as ;

\(6x + 20=(6*10) +20 =80\\4x = 4*10 = 40\\80 - 2x = 80 - (2*10) = 60\)

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