Suppose y varies directly with x, and y = 14 when x = 2. What direct variation equation relates x and y? What is the value of y when x = 6? Explain. Show your work

A. The equation y = 2x relates x and y. When x = 6, y =2(6) or 12.
B. The equation y = 14x relates x and y. When x = 6, y =14(6) or 84.
C. The equation y = 7x relates x and y. When x = 6, y =7(6) or 42.

We can determine the height of a triangle when we know the base and area of the triangle using the area formula of triangle in base and height, that is

A = 1/2 × b × h

A triangle is a three sided polygon. The height of the triangle is the perpendicular distance of the not-included vertex to the considered base.

The formula to determine area of a triangle of base b and height h is

A = 1/2 × b × h

Therefore to determine the height of a triangle when base and area is given, we substitute the given values in appropriate units in the formula.

h = 2×A/ b

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The roots of a quadratic equation are the values of x that make the equation equal to 0.

The general form of a quadratic equation is [tex]ax^2[/tex] + bx + c = 0, where a, b, and c are constants.

To find the roots of the equation [tex]ax^2[/tex] - 16 = 0, we can use the quadratic formula:

x = (-b +/- sqrt(b^2 - 4ac))/(2a)

In this case, a = 1, b = 0, and c = -16. Plugging these values into the quadratic formula, we get:

x = (-0 +/- sqrt(0^2 - 41(-16)))/(2*1)

x = (-0 +/- sqrt(256))/(2)

x = (-0 +/- 16)/(2)

The roots of the equation are x = 8 and x = -8.

The complete question is:-

What are the roots of the quadratic equation x2 − 16 =0?

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Answer:

$1772.10

Step-by-step explanation:

10% = 0.1

Take 1611 times 0.1 = $161.10

So, the 10% cheaper is $161.10

We add both numbers to find the price of last year's season ticket!

1611 + 161.10 = $1772.10

So, the price of last year season's ticket is $1772.10

Let's check to see if it is correct!

$1772.10 - $161.10 = $1611

So, my answer is correct!

Answer:

$1,790

Step-by-step explanation:

x -.1x = 1611  Combine like terms

.9x = 1611  Divide both sides by .9

x = 1790

Check:

1790 - .1(1790) = 1611

1790 - 179 = 1611

1611 = 1611

Answer:

C, D

Step-by-step explanation:

Compare each choice with

x² + 5x - 8 = 0

A.

x² + 7x - 9 = 2x + 1

x² + 5x - 10 = 0

No

B.

x² + 4x - 5 = x - 3

x² + 3x - 2 = 0
No

C.

x² + 10x - 2 = 5x + 6

x² + 5x - 8 = 0

Yes

D.

12x + 4 = 7x + 12 - x²

x² + 5x - 8 = 0

Yes

Answer: C, D

Answer:

The next two terms in the Fibonacci sequence would be 23 and 37.

Step-by-step explanation:

The Fibonacci sequence is a series of numbers in which each number is the sum of the two preceding ones, usually starting with 0 and 1. So the next term in the sequence is found by adding the two previous terms, like this:

1 + 4 = 5

4 + 5 = 9

5 + 9 = 14

9 + 14 = 23

14 + 23 = 37

ME adds up the variances and divides the result by n. In this context, an error is defined as an uncertainty in a measurement or the difference between the measured value and the true/correct value.

In mathematics and statistics, the mean is the average of a set of variables. The simple arithmetic mean (add the numbers and divide the total by the number of observations), geometric mean, and harmonic mean are all ways for calculating the mean. The mean (average) of a data set is computed by adding all of the numbers in the set and dividing by the number of values in the set. When arranging data from smallest to greatest, the median is the value in the middle. The mode is the most commonly occurring number in a data set.

Here,

Subtract each measurement from another.

Find the absolute value of each difference from Step 1.

Add up all of the values from Step 2.

Divide Step 3 by the number of measurements.

Mean Error (ME) is calculated by adding the variances and dividing the result by n. An error in this sense is an uncertainty in a measurement, or the discrepancy between the measured value and the true/correct value.

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The equation Y=-2x is a linear equation, which can be plotted on a graph as a straight line.

The equation can be written in slope-intercept form as y=mx+b, where m is the slope and b is the y-intercept. In this case, the slope is m=-2 and the y-intercept is b=0. Therefore, the equation can be written as y=-2x+0.

The slope of the line is negative, meaning that as x increases, y decreases. The y-intercept is zero, which means that the line passes through the origin (0,0).

For example, if x = 2, then y = -2(2) + 0 = -4. Therefore, the point (2, -4) is on the line. Similarly, if x = 4, then y = -2(4) + 0 = -8, so the point (4, -8) is also on the line.

The graph of the equation y=-2x would thus be a line starting at the origin (0,0) with a negative slope. As x increases, y decreases, and the line never crosses the y-axis.

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To find the total balance in an account that earns a simple interest rate of 8% per year, we can use the formula A = P(1 + rt), where A is the total balance, P is the initial principal (or amount invested), r is the annual interest rate, and t is the number of years. In this case, the annual interest rate is 8%, so we can substitute 0.08 for r in the formula. Since Kadeem wants to find his total balance in one step, we can set t equal to 1 year. So, to find Kadeem's total balance in one year in one step, he needs to multiply his current balance by 1 + 0.08 = 1.08. Therefore, Kadeem should multiply his current balance by 1.08 to find his total balance in a year in one step.

Answer:

this it's no a math problem

Answer:

[tex]c=2.50x[/tex]

Step-by-step explanation:

The cost per pound of chicken is [tex]50/20=\$2.50[/tex].

So, the equation is [tex]c=2.50x[/tex].

To find the median of a set of numbers, you need to arrange the numbers in order from smallest to largest, and then find the middle number. In this case, the numbers are already in order: 2, 3, 4, 4, 6, 9.

There are 6 numbers in the set, so the median is the middle number, which is 4.

the median value, which is arrived at by sorting all the data points and selecting the central one (or if there are two middle numbers, taking the mean of those two numbers). Example: When the numbers are sorted, the number 4 is in the middle (1, 4, 7), making it the median of the numbers 4, 1 and 7.

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Answer:

Base: 135 Pound

Torso: 135 Pound

Step-by-step explanation:

The snowman Weighed is 472 pounds

The head was 202 Pound

We have to find the total weight of the base and torso

472 - 202 = 270 pound

So, 270 pounds is the total weight of the base and torse

We know the base and torso weigh the same amount

So take 270 divided by 2 = 135 Pound

So, the Base weight is 135 Pound

      the Torso weight is 135 Pound

Answer:

101 pounds

Step-by-step explanation:

if the torso and base weighs the same as the head

then each by itself should weigh 101 pounds

I hope this helps

and i hope i understood the question

Answer:

144 seconds

Step-by-step explanation:

4.5 seconds = 5 pages

x second = 160 pages

cross multiply

you get: 5x= 160 ×4.5

which equals 720 divide it by 5 you get 144

Yes, the number 16 is a square.

It is the square of the number 4, since 4 x 4 = 16.

A square root is a factor in mathematics that, when multiplied by itself, equals the initial number. For instance, 3 and -3 are both square roots of 9.

The square of a number's root is the value under the root. For instance, (3 + 2) = 3. Any even number's square unit will only include even numbers.

Each and every nonnegative real number x has a distinct nonnegative square root, known as the primary square root, which is represented by the symbol x, also known as the radical sign or radix. As an illustration, we write 9=3 to denote that 3 is the number 9's fundamental square root. The word (or integer) whose square root is being examined is known as the radicand. The word or number that appears beneath the radical symbol, in this case, 9, is referred to as the radicand. The principal square root can alternatively be expressed in exponent notation for nonnegative x as x1/2.

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SSS means side side side, SAS means side angle side and AAA means angle angle angle.

There are some postulates which can be used to prove that the two given triangles are similar. If two triangles are similar then we can find as a result that their respective sides and angles are also equal.

If three sides are given then we will use the SSS postulate

If two sides and one angle is given then we will use the SAS postulate

If three angles are given then we will use the AAA postulate.

Therefore SSS, SAS, and AAA are postulated that are used to prove two triangles are similar.

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In the given group of answer choices x-intercept, the only point that has a y-coordinate of 0 is (0, -1).

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Answer: 17 gallons of gas to travel 748 miles

Step-by-step explanation:

First, we have to find how many miles he can travel with 1 gallon of gas

Take 308 divided by 7 = 44 miles of travel per gallon of gas

Then take 748 divided by 44 = 17 gallons

So, it takes 17 gallons of gas to travel 748 miles

Answer:

Isaac needs 17 gallons of gas to travel 748 miles.

Step-by-step explanation:

This problem is giving you the ratio of gallons to miles.

⭐A ratio is a fraction that compares two different units

⭐ In this problem, the units are gallons and miles

In order to find how many gallons Isaac needs to travel 748 miles, we need to create a proportion.

⭐ A proportion is when you make two ratios equal to each other to solve for one unit

First, let's identify the ratios in this situation. Let x = the number of gallons needed to travel 748 miles.

Ratio 1: 7 gallons/ 308 miles

Ratio 2: x gallons/748 miles

Now, set these two ratios equal to each other. Remember to keep the same units as either the numerator or denominator.

[tex]\frac{7}{308} = \frac{x}{748}[/tex]

Next, cross multiply to solve for x.

[tex]7(748) = 308x\\5,236 = 308x\\x = 17[/tex]

∴ Isaac needs 17 gallons of gas to travel 748 miles!

If the four-digit personal identification number (PIN) cannot start with a 0 and must be an odd number, then 0 four-digit pins are conceivable.

There are 10 possible digits (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) that can be used in a four-digit PIN. However, we are told that the PIN cannot begin with a 0, so there are only 9 possible digits that can be used for the first digit.

For the second, third, and fourth digits, any of the 10 digits can be used. Therefore, there are 9 x 10 x 10 x 10 = 9,000 four-digit PINs that can be created using any of the 10 digits.

We are also told that the PIN must be an odd number. This means that the last digit of the PIN must be odd. There are 5 odd digits (1, 3, 5, 7, and 9), so there are 5 possible digits that can be used for the last digit.

For the first three digits, any of the 9 digits that can be used for the first digit can be used. Therefore, there are 9 x 10 x 10 = 900 four-digit PINs that can be created using only odd digits.

However, we have double-counted the PINs that begin with 0. Since these PINs are not allowed, we need to subtract them from the total number of possible PINs. There are 9 x 10 x 10 = 900 four-digit PINs that begin with 0, so we need to subtract these from the total number of possible PINs.

The final number of possible four-digit PINs that cannot begin with 0 and must be odd is 900 - 900 = 0. Therefore, there are 0 four-digit PINs that meet these criteria.

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The domain of the function [tex]f(x)=\frac{1}{x}[/tex]  is all real numbers except 0.

The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's domain is the collection of values it can take as input.

For example, let us take a function [tex]f(x)=\frac{1}{x}[/tex].

For this function, the domain is all the values x can take.

Here x cannot take 0 because 1/0 is not defined.

So, the domain of the function is all real values except 0 which can also be written as:

Domain= R-{0}

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How many pattern block trapezoids would create 2 hexagons?

The inverse of function y = x² is ±√x .

Given equation,

y = x²

We have to find the inverse.

By interchanging x and y variables,

y² = x

Solve this equation for y now. This is the inverse of this function.

Take the square root of both sides.

y = ±√x

Then the inverse of the function given is :

f⁻¹(x) = ±√x

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Answer:

in both questions the answer is option d.

The missing number in the pair of equivalent expressions is 9.

To solve this problem, you can use the model provided to represent the expressions 15 + 9 and 5 + 3.

For the expression 15 + 9, you can place 15 in the first row of five squares and 9 in the second row of five squares, like this:

[15] [9]

For the expression 5 + 3, you can place 5 in the first row of three squares and 3 in the second row of three squares, like this:

[5] [3]

Then, you can use the model to find the missing number in the pair of equivalent expressions. Since the two expressions are equivalent, the missing number should be in the same position as the number 3 in the second row of the model.

If you look at the first expression, you can see that the missing number is in the same position as the number 9. Therefore, the missing number in the pair of equivalent expressions is 9.

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The value of p when x = 21 is p = 32/3 .

Given :

we know that ,

A relationship between two variables, x, and y, represent an inverse variation if it can be expressed in the form  p * x = k or p = k / x

we know that

For p = 14, x = 16

Find the value of k

k = p * x

substitute the values

k = 14 * 16

= 224

so

The equation is equal to

p = 224 / x

if x = 21

substitute the value of x in the equation

p = 224 / 21

Divide by 7 both numerator and denominator

p = 32 / 3

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For a normal distribution, a negative value of z indicates D. the z is to the left of the mean.

A continuous probability distribution known as the "normal distribution" has values that are symmetrically distributed mostly around the mean.

The standard deviation determines the width of the curve in a normal distribution, which depicts a symmetrical plot of data around its mean value. It is represented graphically by the "bell curve.

Z is the number of standard deviations from the mean given by the formula:

z = ( X - μ ) ÷ ( σ )

where

x is the raw score,

μ is the population mean, and

σ is the population standard deviation

A negative value means that the number of standard deviations of an observation is to the left of the mean.

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We can identify an expression to see the numbers, variables and mathematical operator between them.

An expression consists of at least two terms along with a sign. Terms can be a constant and variables or constant and variables accompanied by a number. In each case, there is one symbols in between. As example, 2+3z is a expression where 2 is a number called constant which is separated from variables z by a addition sign +, 3 is called coefficient of z.

Mathematical expression is made up of combination of terms. We can find an expression with two or more numerical terms which are called numerical expression. Besides there are fractional expression with or without variables. We can identify an algebraic expression to observe that it has numbers, variables and operator. We can distinguish an equation from an expression by an equal sign. Whenever, an equal sign is present among the mathematical terms then the expression is called equation.

As example. the above expression is written as 2+3z=0

it is an equation, and we can determine the unknown value z.

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Since a rectangle is rolled along length then circumference of circle is equal to length of rectangle and breadth equals to height.

=) 2*pi*r = 42cm

=) 2*22/7 * r = 42cm

=) r = 42*7 / 2*22

=) r = 147/22 cm

Since Volume of cylinder = pi* r^2*h

= 22/7 * 147/22 * 147/22 * 16 cm^3

= 2245.09 cm^3.

Answer:

30 shirts

Step-by-step explanation:

What we know:

30 seconds = 3 shirts

1 minute 30 seconds = 9 shirts

30 seconds per each 3 shirts

shirts:      3, 6, 9, 12, 15, 18, 21, 24, 27, 30

minutes: .5, 1, 1.5, 2, 2.5, 3, 3.5, 4, 4.5, 5

Answer:

30 shirts

Step-by-step explanation:

Here, 25 and 25 are both middle numbers we can average them to get the median, which is 25.

The median of the data is given by the middle number which is obtained after arranging all the data in a certain order.

For example, we have numbers 1,2,3,4 and 5 which is a data of five data points.

Now, here if we see that two numbers are to the left of 3 and two numbers are to the right of 3, therefore the median of this data is 3.

In higher standards, the formulae of median are given by -

Divide the number of observations by two.  

Now here arise two cases -

1. If there are an odd number of observations, round that number up, and the value in that position is the median.

2. If the number of observations is even, take the average of the values found above and below that position.

So, in a similar manner the median here is given by 25.

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First make the graph of the functions, then  if the two graphs are symmetric with respect to the line y = x (mirror images over y = x ), then they are inverse functions.

Symmetric

A figure or shape that can be divided into two equal parts by a line is called symmetric figures.

Inverse Functions

The inverse function of a function f  is a function that undoes the operation of f. The inverse of f exists if and only if f is bijective, and if it exists, is denoted by F^-1.

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