Find an equivalent fraction for the decimal number. In your final answer, include all of your work. 0.61 (but 61 is a repetitive decimal)

The value of x that makes the line containing (1,2) and (5,3) perpendicular to the line containing (x,4) and (3,0) is x = 2.

To determine the value of x such that the line containing (1,2) and (5,3) is perpendicular to the line containing (x,4) and (3,0), we need to find the slope of both lines and apply the concept of perpendicular lines.

The slope of a line can be found using the formula:

slope = (change in y) / (change in x)

For the line containing (1,2) and (5,3), the slope is:

slope1 = (3 - 2) / (5 - 1) = 1 / 4

To find the slope of the line containing (x,4) and (3,0), we use the same formula:

slope2 = (0 - 4) / (3 - x) = -4 / (3 - x)

Perpendicular lines have slopes that are negative reciprocals of each other. In other words, if the slope of one line is m, then the slope of a line perpendicular to it is -1/m.

So, we can set up the equation:

-1 / (1/4) = -4 / (3 - x)

Simplifying this equation:

-4 = -4 / (3 - x)

To remove the fraction, we can multiply both sides by (3 - x):

-4(3 - x) = -4

Expanding and simplifying:

-12 + 4x = -4

Adding 12 to both sides:

4x = 8

Dividing both sides by 4:

x = 2

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The graph of the linear equation can be seen in the image below.

Here we have the linear equation:

x - 2y = -2

To graph it, we need to find two points that belong to the line, and then we can graph these and connect them with a line.

If x = 0, we have:

0 - 2y = -2

y = -2/-2 = 1

if x = 1 then:

1 - 2y = -2

1 + 2 = 2y

3 = 2y

3/2 = y

Then we have the points (0, 1) and (1, 3/2), now just graph these points on a coordinate axis and then connect them with a line, we will get:

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Answer:

9

Step-by-step explanation:

5,6,7,8,9

3a. An equation in slope-point for this line is y + 2 = 1/2(x - 0).

3b. The equation in slope-intercept form is y = 1/2(x) - 2.

4a. An equation in slope-point form to represent this function is y - 3875 = -1/695(x - 19375).

4b. The cost of operating a car that has been driven 31250 km is $3892.086.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

Part 3.

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (0 + 2)/(4 - 0)

Slope (m) = 1/2

At data point (0, -2) and a slope of 1/2, a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y + 2 = 1/2(x - 0)

y = 1/2(x) - 2

Part 4a.

Based on the information provided about Jay's business, we would determine the slope of the line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (3900 - 3875)/(2000 - 19375)

Slope (m) = 25/-17375

Slope (m) = -1/695

At data point (19375, 3875) and a slope of -1/695, a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 3875 = -1/695(x - 19375)

Part 4b.

For the cost when x = 31250 km, we have:

y - 3875 = -1/695(31250 - 19375)

y = 17.086 + 3875

y = $3892.086.

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The area of the figure we need to use Rectangle, Triangle and Circle formulas:

Identify the shape: Depending on the figure you have, it could be a rectangle, triangle, circle, or a more complex shape. If it's a composite figure, break it down into simpler shapes.
Use the appropriate formula: Each shape has a specific formula to calculate the area.
- Rectangle: Area = length × width
- Triangle: Area = (base × height) / 2
- Circle: Area = π × (radius²)
Measure the necessary dimensions: Measure the required dimensions (length, width, base, height, or radius) using appropriate units (e.g., meters, centimeters, inches).
Plug the values into the formula: Insert the measured dimensions into the corresponding formula.
Perform calculations: Carry out the necessary mathematical operations to get the area.
Include units: Express the area with the appropriate square units (e.g., square meters, square centimeters, square inches).
(For composite figures) Add or subtract areas: If the figure is composed of multiple shapes, add or subtract their areas accordingly to get the total area of the figure.

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Answer:

75

Step-by-step explanation:

f(4) means to use 4 in place of x.

f(x) = 3(5)^(x-2)

fill in 4 for

f(4) = 3(5)^(4-2)

do the 4-2 subtraction first

f(4) = 3(5)^2

do the 5 to the 2nd power next.

f(4) = 3(25)

last, multiply.

f(4) = 75

This is just following the typical order of operations.

When \(x\) approaches infinity, the function's graph moves closer to the x-axis and horizontal equilibrium point at \(y = 3\). For \(x -2\), which is denoted by such an open ring at \((-2, 3)\) on the graph, the function is undefined.

A graphs is a pictorial display or diagram that displays facts or numbers in an organized way in math. The relationships between multiple things are frequently represented by the points on a graph.

The graph is a mathematics structure made up of a collection of points Coordinates and a set of lines connecting some pairs of VERTICES that may or may not be empty. There is a chance that the edges will be directed, or orientated.

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Answer:

  -23

Step-by-step explanation:

You want the slope of the line whose equation is y -6 = -23(x +6).

The point-slope form of the equation of a line is ...

  y -k = m(x -h) . . . . . . . line with slope m through point (h, k).

Matching the given equation to the above pattern, we see ...

  y -6 = -23(x +6) . . . . . . line with slope -23 through point (-6, 6).

The line's slope is -23.

__

Additional comment

While it is not impossible, it would be unusual for a line to have a slope of -23 in a problem like this. Consistent with equation mangling often seen on Brainly, we suspect the equation is actually ...

  y -6 = (-2/3)(x +6)

and the slope is actually -2/3.

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Set up the synthetic division using the coefficients of the numerator and the root in the denominator. Divide using the rules for synthetic division.−8a2+64a−497+4000a+8

Answer:

a=0

b=1

Step-by-step explanation:

Answer:

a=0 b=1

Step-by-step explanation:

edge 2020 :)

The amount remaining after 50 years is approximately 45.5% of the Initial amount, A₀.

The given exponential function represents the amount A(t) (in grams) of cesium-137 remaining after t years:

A(t) = A₀ * (1/2)^(t/30)

We are asked to find the initial amount A₀ and the amount remaining after 50 years.

1. Initial amount:

The initial amount, A₀, is the amount of cesium-137 present at t = 0 years. To find A₀, we substitute t = 0 into the equation:

A(0) = A₀ * (1/2)^(0/30)

A(0) = A₀ * 1

Since anything raised to the power of zero is 1, we have A(0) = A₀ * 1, which simplifies to A(0) = A₀.

Therefore, the initial amount of the sample is A₀.

2. Amount after 50 years:

To find the amount remaining after 50 years, we substitute t = 50 into the equation:

A(50) = A₀ * (1/2)^(50/30)

Now we can calculate the amount using the given formula:

A(50) = A₀ * (1/2)^(5/3)

To round the answer to the nearest gram, we evaluate the expression and round the result to the nearest gram:

A(50) = A₀ * 0.455

A(50) ≈ A₀ * 0.455

Therefore, the amount remaining after 50 years is approximately 45.5% of the initial amount, A₀.

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Answer:

22.8

Step-by-step explanation:

ratios and unit rates

Answer:

Step-by-step explanation:

2, i would eat there sometimes!

Answer:

3. I would eat there rarely.

Step-by-step explanation:

Please give brainliest!!!

EXPLANATION

Given the expression 12(3y+x).

Let's solve it:

Applying the distributive property:

12*3y + 12*x

Multiplying like terms:

36y + 12x

The answer is 36y + 12x

Answer:

In mathematics, an inequality is a statement that compares two values, indicating that they are not equal, and specifies the relationship between them. In other words, an inequality expresses a relative difference between two values or quantities, rather than an exact equality.

There are different types of inequalities, but the most common ones involve comparisons between numerical values or algebraic expressions using inequality symbols, such as:

Greater than: x > y (read as "x is greater than y")

Less than: x < y (read as "x is less than y")

Greater than or equal to: x ≥ y (read as "x is greater than or equal to y")

Less than or equal to: x ≤ y (read as "x is less than or equal to y")

Inequalities can also involve multiple variables and can be used to describe ranges of values or conditions that must be satisfied. For example, x + y > 5 is an inequality that describes a region of the xy-plane where the sum of x and y is greater than 5.

Inequalities are used extensively in many areas of mathematics, including algebra, calculus, and optimization, and also have applications in other fields such as economics, physics, and engineering.

Step-by-step explanation:

Answer:

b. \(\displaystyle Law\:of\:Cosines\)

Step-by-step explanation:

You would use this law under two conditions:

Hence, you have your answer.

* Just make sure to use the inverse function towards the end, or elce you will throw your answer off!

_______________________________________________

Now, you would use the Law of Sines under three conditions:

* I HIGHLY suggest you keep note of all of this significant information. You will need it going into the future.

I am delighted to assist you at any time.

Answer:

Conditions for SINE RULE:

Conditions for COSINE RULE:

Step-by-step explanation:

Side is the number in m/cm.

Angle is the number with degree/in degree. Like this: ° ° °

With all these, it means you should COSINE rule.

Answer:

x=19/10

Step-by-step explanation:

abcdefghijklmnopqrstuvwxyz

The probability that the word formed STATISTICS will be; 1/10! = 1/3628800

The probability of an occurrence is a figure that represents how likely it is that the event will take place. In terms of percentage notation, it is expressed as a number between 0 and 1, or between 0% and 100%. According to the probability formula, the likelihood that an event will occur is equal to the proportion of favourable outcomes to all outcomes.

The total number of tiles in a bag is; 10

WE are given that once a tile is drawn, we will not place the tile back in the bag.

We should find the probability that randomly selected tiles spell the word, STATISTICS, that is a 10 letter word.

Now when we draw the first tile,

1 st tile = 1/10

Now there are only 9 tiles left.

2nd tile probability = 1/9

Now only 8 tiles left then

3rd tile probability = 1/8

Therefore the probability that the word formed is STATISTICS would be

= 1/10 * 1/9 * 1/8 * 1/7 * 1/6 * 1/5 * 1/4 * 1/3 * 1/2

= 1/10! = 1/3628800

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Zack purchased approximately 269.608 shares of the mutual fund.

To determine the number of shares Zack purchased, we need to divide the total amount he invested by the offer price of the mutual fund.

Given:

Investment amount: $5,500

Offer price: $20.40

To calculate the number of shares, we divide the investment amount by the offer price:

Number of shares = Investment amount / Offer price

Number of shares = $5,500 / $20.40

To simplify the calculation, we can divide both the numerator and denominator by 10. This does not change the result, but it makes the division easier:

Number of shares = $550 / $2.04

Now, we can perform the division:

Number of shares ≈ 269.6078

Since we are asked to round to thousandths, we can round the result to three decimal places:

Number of shares ≈ 269.608

Therefore, Zack purchased approximately 269.608 shares of the mutual fund.

It's important to note that in financial calculations, it is common to round the number of shares to the nearest whole number since partial shares are not typically traded. In that case, Zack would have purchased 270 shares. However, since the question asks for the answer rounded to thousandths, we have provided the answer as 269.608 shares.

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Given that the polynomials p(x) = 5x²-x+ 4 and q(x) = 3x² + 7x-1,

a. The polynomial  p(x) + q(x) =  8x² + 6x + 3.

b. The polynomial  2p(x) - q(x) =  7x² - 9x + 9.

c. The polynomial p(x)q(x) = 15x⁴ - 3x³ + 35x² + 27x - 4

A polynomial is a mathematical function in which the power of the unknown is greater than or equal to 2.

1. Given the polynomials p(x) = 5x²-x+ 4 and q(x) = 3x² + 7x-1, we desire to find p(x) + q(x), we proceed as follows.

To find  p(x) + q(x), we add both polynomials. so, we have that

p(x) = 5x²- x + 4 and g(x) = 3x² + 7x - 1.

So,   p(x) + q(x) = 5x²- x + 4 + 3x² + 7x - 1.

Collecting like terms, we have that the equation

p(x) + q(x) = 5x² + 3x² + 7x - x + 4 - 1.

= 8x² + 6x + 3.

So, p(x) + q(x) =  8x² + 6x + 3.

b. To find  2p(x) + q(x), we add both polynomials. so, we have that

p(x) = 5x²- x + 4 and g(x) = 3x² + 7x - 1.

We multiply p(x) by 2 to obtain 2p(x). so,

2p(x) = 2(5x²- x + 4)

= 10x²- 2x + 8

So,   2p(x) + q(x) = 10x²- 2x + 8 - (3x² + 7x - 1)

= 10x²- 2x + 8 - 3x² - 7x + 1)

Collecting like terms, we have that the equation

2p(x) + q(x) = 10x² - 3x² - 7x - 2x + 8 + 1.

= 7x² - 9x + 9.

So, 2p(x) - q(x) =  7x² - 9x + 9.

c. To find  p(x)q(x), we multiply both polynomials. so, we have that p(x) = 5x²- x + 4 and g(x) = 3x² + 7x - 1.

p(x)q(x) = (5x²- x + 4)(3x² + 7x - 1)

= 5x²×3x² + 5x² × 7x + 5x²(-1) - x × 3x² - x × 7x - x × ×(-1) + 4 × 3x² + 4 × 7x  + 4 × (-1)

= 15x⁴ + 35x² - 5x² - 3x³ - 7x² - x + 12x² + 28x - 4

Colecting like terms, we have that

= 15x⁴ - 3x³ + 35x² - 5x²  - 7x² + 12x² - x + 28x - 4

= 15x⁴ - 3x³ + 35x² + 27x - 4

So, p(x)q(x) = 15x⁴ - 3x³ + 35x² + 27x - 4

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Answer:

Therefore, the measure of angles x is 70°.

Step-by-step explanation:

From the given figure ,

115° is the exterior angle

x° and 45° are the two interior opposite angles to 115°

We know that

An exterior angle formed by extending the side of a triangle is equal to the sum of the two interior opposite angles

⇛ x° + 45° = 115°

⇛ x° = 115°-45°

⇛ x° = 70°

Therefore , x = 70°

Answer:

It is C. Linear pairs make a 180 degree turn. Hope this helps!

Step-by-step explanation:

Answer:

C. ∠GQI, ∠IQM

Step-by-step explanation:

linear pairs must add up to 180°

∠GQI and ∠IQM make a straight line which is 180°

Answer:

the 1 st qn that is no2 c is just down right corner am I right

Step-by-step explanation:

plzzz make me ans as the brainliest ans

Answer:

The apple pies sell for a price is 0.64

Answer:

6/10 or 3/5

Step-by-step explanation:

4/5 = 8/10

8/10 - 2/10 = 6/10 or 3/5

⅗ or 6/10

Step-by-step explanation:

4/5=8/10

8/10-2/10=6/10 or ⅗

Answer:

A

Step-by-step explanation:

(6.2).10=120cm²

Đáp án đó chúc bạn học tốt

Answer:

VW = 23

Step-by-step explanation:

Since VU is 31 and part of it (WU) is 8, the remaining (VW) would be 31-8 = 23.

Answer:

23

Step-by-step explanation:

vw= vu-wu

vw=31-8

vw=23

The equation of the line in slope-intercept form is y = 3x + 4.

We can use the combination formula to determine how many different packages can be created from a set of 24 crayons with 36 different colours.

The formula for the mixture is provided by:

n C r equals n!/r! (n-r)!

where r is the number of items we want to choose, n is the total number of items, and! stands for the factorial of a number, which is the sum of all positive integers up to that number.

In this instance, we are trying to determine how many various methods there are to choose 24 crayons from a set of 36 colours, regardless of the sequence in which they are chosen. Consequently, we can apply the following combination formula:

36 C 24 = 36! / (24! * 12!)

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The Total length of two sides based on the information will be 7x²+2x+1

The Length of the third side will be 4 x³-10x²-7.

Total length of two sides= Side 1 + Side 2

= 8x² − 5x − 2+ 7x − x²+ 3

= 8x²-x²-5x+7x-2+3

= 7x²+2x+1

Length of the third side = Perimeter - Total length of two sides

Length of the third side=4x³ − 3x² + 2x − 6-(7x²+2x+1)

= 4x³ − 3x² + 2x − 6-7x²-2x-1

= 4 x³-10x²-7

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