Find the slope of a line perpendicular to the line whose equation is 10x-12y=-2410x−12y=−24. Fully simplify your answer

The multiple of 2 means any number that is completely divisible by 2.

A multiple in mathematics is basically that number which is formed by multiplying a particular number and it is completely divisible by that number.

If we talk about the number 2, then the multiple of 2 will mean that any number that is formed by multiplying 2 into it.

For example, 6 is a number which can be written as 2 x 3.

Here, 3 is multiplying two times and it becomes 6, so, it is a multiple of 2. Also, if any number is appearing in the table of 2 then it is a multiple of 2.

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To calculate the deposit, we need to add up the amounts of the two checks and the cash: $90.50 + $90.50 + $45.00 + $150.00 = $376.00. Therefore, the deposit is $376.00.

The problem asks us to calculate the deposit amount for two checks of $90.50 each, and cash of $45.00 and $150.00. To solve the problem, we simply add up the amounts of the checks and cash to find the total deposit amount. Adding $90.50 and $90.50 gives us $181.00, and adding this to the cash amounts of $45.00 and $150.00 gives us a total of $376.00. Therefore, the deposit amount is $376.00. This is the total amount of money that will be added to the account when the checks and cash are deposited.

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We know that the given expression 6x - x - 4 is (2) this is not equivalent to 7x − 4.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement.

It's possible to multiply, divide, add, or subtract with this mathematical operation.

An expression in mathematics is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division, etc.)

So, the given expressions are:

7x - 4 and 6x - 4 - x

Now,

7x - 4 and 6x - x - 4

7x - 4 and 5x- 4

Then, we can easily say that the given expressions are not equivalent.

Therefore, we know that the given expression 6x - x - 4 is (2) this is not equivalent to 7x − 4.

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Complete questions:
Explain how you can tell if the expressions 7x – 4 and 6x – 4 – x are equivalent. Sample Response: 6x − x = 5x.

1. The new expression is now 5x − 4.

2. This is not equivalent to 7x − 4.

Answer:

when they both are separated they form a right angled triangle 90°

The solution to the system of linear equation by substitution method is as follows :  x = 1 and y = -3

6x − 9 = y

y = −3x

let's substitute the value of y in the first equation as follows;

6x - 9 = -3x

add -3x to both sides of the equation

6x + 3x - 9 = -3x + 3x

9x - 9 = 0

add 9 to both sides of the equation

9x - 9 + 9 = 0 + 9

9x = 9

divide both sides by 9

x = 9 / 9

x = 1

let's find y by substituting the value of x in the second equation

y = -3x

y = -3(1)

y = -3

Therefore, x = 1 and y = -3

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The fraction of the height of Cleopatra's clock that is the height of Ptolemy's clock is 2/5

A fraction is a mathematical concept that represents a part of a whole or a ratio between two quantities. It is typically written in the form of a numerator over a denominator, separated by a horizontal line, such as 1/2, 3/4, or 7/8.

Given that the volume of cylinder = πr^2h

Let's denote the height and radius of Cleopatra's water clock as h_c and r_c, respectively, and the height and radius of Ptolemy's water clock as h_p and r_p, respectively.

Since both clocks drain uniformly, we can use the formula for the volume of a cylinder to relate the height and radius of each clock to the time it takes to drain:

Volume of Cleopatra's clock = [tex]\pi r^2_ch_c[/tex]

Volume of Ptolemy's clock = [tex]\pi r^2_ph_p[/tex]

Since Cleopatra's clock drains in 4 hours, the rate of draining is (Volume of Cleopatra's clock) / (4 hours), and similarly for Ptolemy's clock.

We are given that after 2 hours of draining, both clocks have the same water height.

Therefore, we can set the two rates of draining equal to each other and solve for the ratio of heights:

(Volume of Cleopatra's clock) / (4 hours) = (Volume of Ptolemy's clock) / (5 hours)

hc/hp = [tex](r_p/r_c)^2 * (5/4)[/tex]

After two hours of draining, the water height in both clocks is the same, so we can set the volume of water in each clock equal to each other:

[tex]r^2_ch_c/2 = r^2_ph_p[/tex]

Now, we can solve for the ratio of water heights after each clock has been draining for three hours:

Water height in Cleopatra's clock after 3 hours = [tex]h_c - (3/4)h_c = (1/4)h_c[/tex]

Water height in Ptolemy's clock after 3 hours = [tex]h_p - (3/5)h_p = (2/5)h_p[/tex]

hp= 1/10

Therefore, the fraction of the height of Cleopatra's clock that is the height of Ptolemy's clock is:

hp/hc = 1/10/(1/4) = 2/5

And the fraction of the water height of Ptolemy's clock that is equal to the water height of Cleopatra's clock after each has been draining for three hours is:

hc/(2/5)hp = (1/4)/(2/5)(1/10)

= 5/4.

Hence,

The fraction of the height of Cleopatra's clock that is the height of Ptolemy's clock is: 2/5

The fraction of the water height of Ptolemy's clock that is equal to the water height of Cleopatra's clock after each has been drained for three hours is: 5/4.

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2) The probability that in a cricket match, a batswoman did not hit a boundary, when she hits it 6 times out of 30 balls played, is 80%.

3) The probability of a family having:

i) 2 girls = 31.67%

ii) 1 girl = 54.27%

iii) No girl = 14.06%

iv) The sum of the probabilities = 1 or 100%

The probability refers to the likelihood that an expected event or outcome occurs when there are many possible outcomes.

We compute probability as the quotient of the the expected success and the total number of successes.

Probability lies between zero and one and is usually expressed as a decimal, fraction, or percentage.

The number of boundary hits = 6

The total number of balls the batswoman played = 30

The probability that the batswoman did not hit a boundary = 1 - 6/30

= 0.8 or 80%.

The chance that the batswoman hit a boundary = 6/30 = 0.2 or 20%.

The total number of families with 2 children = 1,500

The number of families with 2 girls = 475

The number of families with 1 girl = 814

The number of families with 0 girl = 211

The probability of a family having:

i) 2 girls = 475/1,500 = 0.3167 or 31.67%

ii) 1 girl = 814/1,500 = 0.5427 or 54.27%

iii) No girl = 211/1,500 = 0.1406 = 14.06%

iv) The sum of the probabilities = 1 or 100%

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The total cost for 10 hours of work would be 25 + 50(10) = 525.

Cost is the monitorial associated with the purchase of production of food or service if can include the prices of material of which is over it and other expenses that are related to the production of the code of service cost is a major fraction of when deciding whether to purchase a product something as it is and indicator of the value of the product of sound service.

The marginal cost of producing 5 items can be calculated using the equation C(x)=1300+4x/10. The marginal cost is the cost associated with producing one additional item. To calculate the marginal cost, we can plug in x=5 into the equation.

The equation in slope-intercept form for cost, c, after h hours of service is c = 25 + 50h.

The total cost for 8 hours of work would be 25 + 50(8) = 425.

The total cost for 10 hours of work would be 25 + 50(10) = 525.

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To convert 1 teaspoon to 1 ml multiply the volume by the conversion ratio of  4.928922.

Add the volume to the conversion ratio to convert a teaspoon measurement to a millilitre measurement.

You may convert between teaspoons and milliliters using the following straightforward formula:

tablespoons in milliliters = 4.928922

One-third of a tablespoon's volume is represented by a teaspoon. [1] Although a teaspoon is roughly equivalent to 4.9 millilitres, on nutrition labels, a teaspoon is actually equal to 5 millilitres. 

The teaspoon is a common volume measurement in the US. Teaspoons can be written as tsp, although they can also be spelled as t, ts, or tspn.

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The area of the segment is 28.92 unit square

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

Angle, θ = 50 degrees

Radius, r = 15 units

Using the above as a guide, we have the following:

Area of a segment =  (½) × r² × [(π/180)(θ – sin(θ)]

Substitute the known values in the above equation, so, we have the following representation

Area of a segment =  (½) × 15² × [(π/180)(15 – sin(15 degrees)]

Evaluate

Area of a segment =  28.92

Hence, the area is 28.92

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There is no general rule that says a system of linear equations cannot have exact solutions that are integers greater than 1. The existence of such solutions depends on the specific coefficients and constraints of the system

It is not true that a system of linear equations cannot have exact solutions that are integers greater than 1. In fact, there are many systems of linear equations that have such solutions.

However, there are certain types of systems of linear equations that do not have integer solutions, or may not have any solutions at all. For example, if the coefficients of the variables in the equations are irrational numbers, then it is possible that the system has no integer solutions.

Furthermore, some systems of linear equations may have solutions that are not integers, but are instead fractions or irrational numbers. This is because the solutions to a system of linear equations are determined by the intersection points of the lines or planes that represent the equations, and these intersection points may not always fall on integer coordinates.

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The minimum number of x intercepts is 1.

( Table attached)

What is the x-intercept?

The intersection of a function or equation's graph with the x axis is known as the x intercept. This can be compared to a point having a value of 0.

For any given curve, the x-intercept is a coordinate that is plotted on the x-axis. To put it another way, the x-intercept is the value of the x coordinate at the point where the graph crosses the x-axis, or we can say that it is the value of the x coordinate at a point where the value of the y coordinate equals zero.

The minimum number of x intercepts is 1.

With a positive leading coefficient an odd degree polynomial will start negative and end positive. With a negative leading coefficient an odd degree polynomial will start positive and end negative.

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Answer:

31.08 billion

Step-by-step explanation:

If the shoe sales for a certain company were 25.9 billion, and the sales are projected to increase by 20%, we can calculate the projected amount by adding the increase to the original sales:

Projected sales = Original sales + (Increase percentage × Original sales)

Plugging in the values we have:

Projected sales = 25.9 billion + (0.20 × 25.9 billion)

Projected sales = 25.9 billion + 5.18 billion

Projected sales = 31.08 billion

Therefore, the projected amount of shoe sales for the company is 31.08 billion.

To show that a statement is false, we need to find a counterexample where the statement does not hold true. Here are the counterexamples for each statement:

The sum of any three odd numbers is even.

Counterexample: 1 + 3 + 5 = 9, which is an odd number. Therefore, the statement is false.

When an even number is added to the product of two odd numbers, the result will be even.

Counterexample: 1 {square} 3 + 2 = 5, which is an odd number. Therefore, the statement is false.

When an odd number is squared and divided by 2, the result will be a whole number.

Counterexample: Let's take an odd number, say 3. If we square it, we get 3{square}2 = 9. If we divide 9 by 2, we get 4.5, which is not a whole number. Therefore, the statement is false.

In each of these cases, we have found a counterexample that shows that the statement is false. It is important to remember that just because a statement holds true for some examples, it does not necessarily mean it holds true for all examples. Finding counterexamples is an important tool in mathematical reasoning and can help us to refine and improve our understanding of mathematical concepts.

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The time 10 pm can be expressed in military time as 2200 hours .

In military time, the hours of the day are expressed in a 24-hour format,

The time starts from 0000 (midnight) hours and goes up to 2359 (11:59 PM) hours.

To convert a time from the standard 12-hour clock to military time, we add 12 hours to any time in the afternoon or evening .

In this case , to convert 10 PM to military time, we add 12 hours to the time ;

⇒ 10 PM + 12 hours = 22:00 hours or 2200 hours ;

Therefore, 10 PM in military time is 2200 hours.

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In regression analysis, the variable being explained or predicted is called option (b) dependent variable.

The dependent variables are defined the variable the depends up on other variables. The independent variable(s) are the variables that are believed to have an influence on the dependent variable and are used to explain or predict the variation in the dependent variable.

The regression variable(s) refer to the variables that are included in the regression model as predictors, whether they are independent or dependent. The residual variable refers to the difference between the observed values of the dependent variable and the predicted values from the regression model.

Therefore, the correct option is (b) dependent variable

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Step-by-step explanation:

1 ft = 12 in

so,

36 in = 36/12 = 3 ft

24 in = 24/12 = 2 ft

therefore, the area of the rectangle is

3×2 = 6 ft²

The  single natural logarithm for the expression 4 + ln 2 - ln 4 is ln(2). So, correct option is A.

To express 4 + ln 2 - ln 4 as a single natural logarithm, we can use the properties of logarithms to combine the terms.

First, we can use the rule that ln(a) - ln(b) = ln(a/b) to simplify ln 2 - ln 4:

ln 2 - ln 4 = ln(2/4) = ln(1/2)

Now, we can rewrite the expression as:

4 + ln(1/2)

We can use another logarithmic property, ln(a) + ln(b) = ln(ab), to write this as:

4 + ln(2^(-1))

Simplifying further:

4 - ln(2)

Therefore, 4 + ln 2 - ln 4 can be expressed as a single natural logarithm of:

ln(2^2 / 2) = ln(2)

So, the answer is (a) ln 2.

In general, when simplifying expressions involving logarithms, it's helpful to remember the logarithmic properties and rules, such as the product, quotient, and power rules, as well as the fact that ln(e) = 1. By applying these rules systematically, we can simplify complex expressions into simpler forms that are easier to work with.

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Answer:

Step-by-step explanation:

40 desks

Thus, only 6.25 grammes of the initial 200 grammes of Co-60 will be present after 26.3 years.

Any time energy is moved, radiation is created. A substance does not need to be radioactive in order to emit radioactivity. Radiation is not always released by element compounds. Alpha particles, light, and heat are all instances of radiation.

To solve this problem, we can use the exponential decay formula:

N = N0 * (1/2)^(t/T)

where:

N is the amount of Co-60 remaining after a time t

N0 is the initial amount of Co-60

t is the time elapsed since the initial measurement

T is the half-life of Co-60

We are given N0 = 200 g, T = 5.26 years, and t = 26.3 years. We can plug in these values to get:

N = 200 * (1/2)^(26.3/5.26)

Simplifying the exponent, we get:

N = 200 * (1/2)⁵

Evaluating the exponent, we get:

N = 200 * 1/32

N = 6.25

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The correct question is:

the half-life of colbalt-60 (used in radiation therapy) is 5.26 years (actual data). How much a of 200 g sample of colbalt-60 will remain after 26.3 years?

The number 1.07  × 10⁸ in standard form is 107,000,000.

To write 1.07 × 10⁸ in standard form, we need to move the decimal point to the left or right such that there is only one non-zero digit to the left of the decimal point.

In this case, we have 1.07 × 10⁸, which means we have a value of 1.07 times 10 raised to the power of 8. To convert this to standard form, we need to move the decimal point 8 places to the right since 10 is being raised to the power of 8.

1.07 × 10⁸ = 107,000,000

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The slope of the line passing through the points (3,4) and (-4,-5) is 9/7.

The slope of a line passing through two points can be found using the slope formula, which calculates the change in the y-coordinate divided by the change in the x-coordinate between the two points. To find the slope of the line passing through (3,4) and (-4,-5), we plug the coordinates into the slope formula and simplify. The slope formula gives the rate at which the line rises or falls relative to its horizontal movement. A positive slope means that the line is rising from left to right, while a negative slope means that the line is falling from left to right. In this case, the slope is positive, indicating that the line rises from left to right.

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if £1=1. 62USD then, £650 is equivalent to $1053 in US dollars and £450 is equivalent to $729 in US dollars.

To convert British pounds to US dollars, we can multiply the pound amount by the exchange rate of pounds to dollars.

£650 in USD:

£1 = $1.62, so we can write:

650 x 1.62/1 = 1053

Therefore, £650 is equivalent to $1053 in US dollars.

£450 in USD:

Using the same method, we can calculate the value of £450 in US dollars as follows:

450 x 1.62/1 = $729

Therefore, £450 is equivalent to $729 in US dollars.

The conversion of British pounds to US dollars is a common currency exchange process, as both currencies are widely used in international trade and finance. The exchange rate between the two currencies represents the value of one currency in terms of the other. In this case, the exchange rate of £1 to $1.62 means that one British pound is worth 1.62 US dollars. To convert a certain amount of British pounds to US dollars, we simply multiply the pound amount by the exchange rate. The resulting dollar amount reflects the value of the pounds in the equivalent US dollars. Exchange rates can fluctuate frequently due to various economic and political factors, affecting the value of currencies and international transactions.

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Answer:

0.80*c = 20

Step-by-step explanation:

"80% of c is 20" can be written as:

  0.80*c = 20

80% of c is 0.80*c

"is" can be written as "="

Put these two together to obtain:

  0.80*c = 20

Jane bought 4 pounds of jolly ranchers.

To calculate how many pounds of jolly ranchers Jane bought, we need to divide the total worth of jolly ranchers by the price per pound.
Determine the price per pound of jolly ranchers. This information is not provided in the question, so we will need to assume a price. Let's say that the price per pound of jolly ranchers is $2.50.
Divide the total worth of jolly ranchers by the price per pound.
$9.75 ÷ $2.50 = 3.9
Round the answer to the nearest whole number, if necessary. In this case, 3.9 rounds up to 4.

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When the number"52" is divided by the number "2" , we get the answer as  26 .

The Division is defined as a mathematical operation , which is used to find the quotient of two quantities. It involves dividing a given number (the dividend) by another number (the divisor) to find the result (the quotient) .

We have to divide , the number 52 by 2 ,

It is represented as : 52/2 ;

Let the answer after performing division be = "x" ;

which means ; x = 52/2 ;

⇒ x = 26 ;

Therefore , On dividing 52 by 2 , the answer is 26 .

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To divide 52 by 2, we can use the long division method. The quotient is 26.

To divide 52 by 2, you can use long division method. Write 52 as the dividend and 2 as the divisor. Divide 5 (the first digit of the dividend) by 2 (the divisor), which gives you 2 as the quotient. Multiply the quotient (2) by the divisor (2), which equals 4. Subtract 4 from 5 to get 1. Bring down the next digit, which is 2. Repeat the process by dividing 12 by 2, which gives you 6 as the quotient. Multiply the quotient by the divisor to get 12, and subtract from the remaining digit 2, which gives you 0. Therefore, 52 divided by 2 equals 26.

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Answer:

The correct answer is B. 200 and 100. When y is inversely proportional to x, it means that the ratio of x to y remains constant. In this case, when x = 20, y = 400, which means that the ratio of x to y is 20/400. Since the ratio is constant, we can use that ratio to find the values of y when x = 40 and x = 80. When x = 40, y = (20/400) x 40 = 200 and when x = 80, y = (20/400) x 80 = 100.

The figure represents the four angles of a quadrilateral.

Angel is a geometric figure that can be described as the amount of rotation between two straight line or planes and angles is measured in degree with the full circle being 360°.

The angles are labeled t, q, r and s. The measure of angle t and q is 93 degrees, while the measure of angle r and s is 87 degrees. This means that the quadrilateral is a parallelogram since opposite angles of a parallelogram are equal. The measure of each of the remaining angles is 180 degrees minus the measure of the known angles, which means that angle t and q are 87 degrees and angle r and s are 93 degrees. The sum of the angles of a parallelogram is 360 degrees, which further confirms that the figure is a parallelogram.

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As a result, if the two angles' measurements are (3y+11) and (11y+15) and they are congruent, then y must equal -1/2.

An angle is a geometric figure formed by two rays that have a common endpoint, called the vertex. The rays are also known as the sides or legs of the angle. Angles are typically measured in degrees, with a full circle measuring 360 degrees. Angles can also be measured in radians, which are another unit of angular measurement used in mathematics and physics. One radian is equal to the angle subtended by an arc of a circle that has a length equal to the radius of the circle. The size of an angle is determined by the amount of rotation that occurs between the two rays. This is typically measured relative to the positive x-axis, with counterclockwise rotations being considered positive and clockwise rotations being considered negative. Angles are used in a wide range of mathematical and scientific applications, including geometry, trigonometry, physics, engineering, and architecture. They are also used in many everyday situations, such as measuring the size of an opening or the angle of incidence of sunlight on a surface.

Here,

If the two angles are congruent, then they must have the same measure.

So we can set the expressions for the measures of the two angles equal to each other and solve for y:

3y + 11 = 11y + 15

Subtracting 3y from both sides:

11 = 8y + 15

Subtracting 15 from both sides:

-4 = 8y

Dividing both sides by 8:

y = -1/2

Therefore, if the measure of the two angles is (3y+11) and (11y+15) and they are congruent, then y must equal -1/2.

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Answer:

Option 3: about 14 inches

Step-by-step explanation:

The notebook paper is in the form of a rectangle of length

[tex]l = 11[/tex] inches and width [tex]w = 8.5[/tex]  inches

The diagonal of such a rectangle is given by the Pythagorean formula
[tex]d = \sqrt{l^{2} + w^{2}}[/tex]

Substituting the values of [tex]l[/tex] and [tex]w[/tex]:

[tex]d = \sqrt{11^{2} + 8.5^{2}}\\\\d = \sqrt{121 + 72.25}\\\\d = \sqrt{193.25}\\\\d= 13.9014\;inches[/tex]

This corresponds to Option 3: about 14 inches