The vertical line test is a method to determine if a relation is a function. It says: If you can draw a vertical line anywhere that intersects the graph of the relation in two or more points, then the relation not a function. Explain how the vertical line test proves that a relation is not a function.​

Given that 1 kilogram of honeydew melon and 2 kilograms of watermelon, which cost her $7 and 3 kilograms of honeydew melon and 3 kilograms of watermelon, spending a total of $15 on the melons

Let x be the cost of a kilogram of honeydew melon and y be the cost of a kilogram of watermelon.

The system of equation is

Multiply equation (1) by 3, we get

Subtracting equation (2) from equation (3), we get

Dividing by 3, we get

Substitute y=2 in equation (1), we get

Subtracting 4 from both sides, w get

The cost of a kilogram of honeydew melon =$ 3.

The cost of a kilogram of watermelon = $ 2.

Given:

The given function is

\(y=\sec x\)

To find:

The period of given function.

Solution:

General sec function is defined as

\(y=A\sec (Bx+C)+D\)

Where, A is amplitude, \(\dfrac{2\pi}{B}\) is period, \(-\dfrac{C}{B}\) is phase shift and D is vertical shift.

We have,

\(y=\sec x\)

Here, B=1. So,

\(Period=\dfrac{2\pi}{1}\)

\(Period=2\pi\)

Therefore, the period of given function is 2π.

The value of period of function y = sec x is, 2π.

The given function is,

y = sec x

Since, We know that,

General form of equation for sec x is,

y = A sec (Bx + C) + D

Where, A is amplitude, 2π/B is period and D is vertical shift.

Here, function is,

y = sec x

Hence, B = 1,

So, Period = 2π/B

                = 2π/1

                = 2π

Thus, The value of period of function y = sec x is, 2π.

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The value of x is 14.

We know in an isosceles triangle an isosceles polygon is a polygon with at least two sides of equal length.

We have two sides measured 2x-9 and x+ 5.

From the figure the length of sides are equal then

2x-9 = x+ 5

2x- 9- x = 5

x-9 = 5

Add 9 to both sides of the equation:

x - 9 + 9 = 5 + 9

x= 14

Thus, the value of x is 14.

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Answer:

Step-by-step explanation:

f(x) =2x - 7

f( - 3) = 2( - 3) - 7 = - 13

f(3) = 2(3) - 7 = - 1

f(a) = 2a - 7

- f(a) = - (2a - 7) = 7 - 2a

f(a + h) = 2(a + h) - 7 = 2a + 2h - 7

Answer:

f(x) =2x - 7

f( - 3) = 2( - 3) - 7 = - 13

f(3) = 2(3) - 7 = - 1

f(a) = 2a - 7

- f(a) = - (2a - 7) = 7 - 2a

f(a + h) = 2(a + h) - 7 = 2a + 2h - 7

Step-by-step explanation:

Answer:

8 and 10

Step-by-step explanation:

8+10= 18

8-10= -2

Answer: The two numbers are 8 and 10.

Hopefully this helps!

The function g(x) can be expressed as g(x) = a(x - h) + k, where a is the coefficient of x (which is 1 for f(x) = x^2), h is the horizontal shift, and k is the vertical shift.

To translate a function 6 units left, we need to shift it horizontally by -6 units. So, h = -6.

Since the function g(x) is a translation of f(x), a and k will have the same values as in f(x). In this case, a = 1 and k = 0.

Therefore, the function g(x) that represents the translation 6 units left of f(x) is:

g(x) = a(x - h) + k

= 1(x - (-6)) + 0

= 1(x + 6) + 0

= x + 6

the answer is: g(x) = x + 6

Answer:

Is there any options if so just repost with the options and i will answer it

Step-by-step explanation:

Answer: 172 ounces

Step-by-step explanation:

We are given 10 pounds and 12 ounces to convert to ounces.

There are 16 ounces in 1 pound.

We can create a proportion to find out how much ounces 10 pounds is.

10 pounds / x ounces = 1 pound / 16 ounces

We need to solve for x by isolating the variable x.

10/x = 1/16

10 = x/16

10 * 16 = x

160 ounces = x

so 10 pounds is equivalent to 160 ounces. But we are not done yet.

We were asked to convert 10 pounds and 12 ounces.

So add together the ounces to find the total ounces:

160 ounces + 12 ounces = 172 ounces.

If a and b are integers that divide c and are relatively prime, then ab divides c. If a and b are not relatively prime, then ab need not divide c.

If a and b are integers that divide c, this means that c is divisible by both a and b. Additionally, if a and b are relatively prime, this means that they have no common factors besides 1. In this case, since a and b both divide c, then it follows that their product, ab, also divides c.

However, if a and b are not relatively prime, this means that they have common factors besides 1. In this case, the common factors of a and b may not divide c, so it is not necessarily true that ab divides c.

For example, if a = 6, b = 8, and c = 24, then 6 and 8 both divide 24, but 6 and 8 are not relatively prime (they have a common factor of 2). In this case, 6 * 8 = 48 does not divide 24.

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The end-points of the line segment will be negative 1.25 and 0.25.

A number line refers to a straight line in mathematics that has numbers arranged at regular intervals or portions along its width. A number line is often shown horizontally and can be postponed in any direction.

The length of the line segment is 1.50 units and the midpoint of the line segment is negative 0.50. Then the end-points of the line segment are given as,

⇒ - 0.50 ± (1.50) / 2

Simplify the expression, then we have

⇒ - 0.50 ± (1.50) / 2

⇒ - 0.50 - (1.50) / 2, - 0.50 + (1.50) / 2

⇒ - 0.50 - 0.75, - 0.50 + 0.75

⇒ - 1.25, 0.25

The end-points of the line fragment will be negative 1.25 and 0.25.

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Answer:

40

Step-by-step explanation:

i think it is the write answer

Answer: 5

Step-by-step explanation: edge 2021

You can use the constant which if multiplied with the coefficient of x in first equation, ends up making it negative and of equal magnitude to the coefficient of x variable in second equation.

The first equation should be multiplied by the constant 5

This method is actually called method of elimination to solve a system of linear equations.

We make one specific variable's coefficients of equal magnitude so that we can subtract or add the equations and eliminate that variable to make it easy to get the value of the other variable which will then help in getting the value of the first variable (if working in dual variable system).

If we have equations:

\(a_1x + b_1y = c_1\\a_2 x + b_2y = c_2\\\)

then, if we want to eliminate variable x, then we have to multiply equation 1 with \(-\dfrac{a_2}{a_1}\) which will make coefficient of x in first equation as  \(a_1 \times -\dfrac{a_2}{a_1} = -a_1\)

Then adding both equation will eliminate the variable x.

We could've skipped that -ve sign and at then end, instead of adding, we could've subtracted the equations.

The system of equation we've got is

\(\dfrac{2}{5}x + 6y = -10\\\\-2x -2y = 40\)

Thus, we have the constant needed = \(-\dfrac{a_2}{a_1} = -\dfrac{-2}{2/5} = 5\)

The resultant system of equation we will get is:

\(2x + 30y = -50\\\\-2x -2y = 40\)

Thus,

The first equation should be multiplied by the constant 5

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Answer:

90 cm²

Step-by-step explanation:

since the ratio is 1:6 for every one little box the bigger box increases 6 times.

so  15·6= 90 cm²

Answer:

D. 90 square cm

Answer:

10000/p.

Step-by-step explanation:

r = pq/100

pq = 100r

q = 100r/p

As a percentage of r:

we have P = q * 100/r

P = 100r/p * 100/r

   = 10,000r / rp

   = 10000/p

Answer:

p=4

Step-by-step explanation:

11x4= 44  

44+10 = 54

Answer:

p = 4

Step-by-step explanation:

11p + 10 = 54

      - 10  - 10

11p = 44

44/11

4

p = 4

Answer:

nnjvg Step-by-step explanation:

Answer:

164 seats

Step-by-step explanation:

you make the equation 4+ 8X to deteremine the seats and x equals the rows and you get your answer.

An arithmetic sequence is a sequence where each consecutive term has a common constant difference. The total number of seats that the theatre has is 156 seats.

An arithmetic sequence is a sequence where each consecutive term has a common constant difference.

An arithmetic sequence, therefore, is defined by two parameters, viz. the starting term and the common difference.

Let the starting term be 'a' and the common difference be 'd', then we get the arithmetic sequence as:

a, a+d, a+2d, .....

The sum of those 'n' terms is:

\(\rm a + (a+d) + (a+2d) + \cdots + (a+(n-1)d) = \dfrac{n}{2}[2a + (n-1)d ]\)

The condition is a case of an arithmetic progression. Therefore, the common difference in the progression is of 8 and the first term of the sequence is 4. Therefore, the sum of the series for the first 20 terms will be,

aₙ = 4 + (20-1)8

   = 4 + (19)8

   = 4 + 152

   = 156

Hence, the total number of seats that the theatre has is 156 seats.

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The quantity of people in each row is = 18

The total number of people in the talent show = 380

The total number of rows in the show = 21

For every one in each row to be even the total number of people should be divided by the available number of rows. That is,

380/21 = 18.1

Therefore, the quantity of people in each row is approximately = 18.

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Answer:

The null hypothesis is  rejected

Therefore there is sufficient evidence to conclude that the professors teaching method favored the male

Step-by-step explanation:

From the question we are told that

   The sample size for each population is  \(n_1 = n_2 = n = 10\)

   The  first sample  mean is  \(\= x_1 = 82\)

    The  second sample  mean is  \(\= x_2 = 74\)

    The  first standard deviation is \(\sigma _1 = 4\)  

    The second standard deviation is  \(\sigma_2 = 8.0\)

     The  level of significance is  \(\alpha = 0.05\)

The  null hypothesis is  \(H_o : \mu_1 = \mu_2\)

The  alternative  hypothesis is  \(H_a : \mu_1 \ne \mu_2\)

Generally the standard error is mathematically represented as

           \(SE = \sqrt{ \frac{ \sigma_1^2}{n_1} + \frac{ \sigma_2^2}{n_2} }\)

=>        \(SE = \sqrt{ \frac{ 4^2}{10} + \frac{ 8^2}{10} }\)

=>        \(SE = 2.83\)

Generally the test statistics is mathematically represented as

          \(t = \frac{\= x_1 - \= x_2 }{SE}\)

=>        \(t = \frac{82 - 74}{2.83}\)

=>        t =  2.83

Generally the p-value  mathematically represented as

        \(p-value = 2 P(Z > 2.83)\)

From the z table  

           \(P(Z > 2.83) = 0.0023274\)

So

    \(p-value = 2 * 0.0023274\)

   \(p-value = 0.0047\)

Since  

      \(p-value < \alpha\)

Hence the null hypothesis is  rejected

Therefore there is sufficient evidence to conclude that the professors teaching method favored the male

Answer:
V = 180 (vans)

S = 90 (small trucks)

L = 40 (large trucks)

Step-by-step explanation:

Set up the variables: Let V represent the number of vans, S represent the number of small trucks, and L represent the number of large trucks.

Write the equations:

V + S + L = 310 (total number of vehicles)

V = 2S (twice as many vans as small trucks)

35,000V + 70,000S + 60,000L = 15,000,000 (total cost of the vehicles)

Substitute equation 2) into equation 1):

2S + S + L = 310

3S + L = 310

Simplify equation 3) by substituting V = 2S:

70,000S + 70,000S + 60,000L = 15,000,000

140,000S + 60,000L = 15,000,000

Set up a system of equations:

3S + L = 310

140,000S + 60,000L = 15,000,000

Eliminate L by multiplying equation 1) by 60,000:

60,000(3S + L) = 60,000(310)

180,000S + 60,000L = 18,600,000

Subtract equation 2) from the new equation:

(180,000S + 60,000L) - (140,000S + 60,000L) = 18,600,000 - 15,000,000

40,000S = 3,600,000

Solve for S:

S = 90

Substitute the value of S into equation 1) to solve for L:

3(90) + L = 310

270 + L = 310

L = 40

Substitute the values of S and L into equation 2) to solve for V:

V = 2S

V = 2(90)

V = 180

The final answer is:

V = 180 (vans)

S = 90 (small trucks)

L = 40 (large trucks)

Answer:

180 Vans 90 Small trucks and 40 Large trucks

Step-by-step explanation:

The  quotient of 302 ÷ (9.1 x \(10^4)\) in scientific notation is approximately 3.31868131868 x \(10^1\)

Dividing 302 by 9.1 gives:

302 ÷ 9.1 ≈ 33.1868131868

Now, to express this result in scientific notation, we need to move the decimal point to the appropriate position to create a number between 1 and 10. In this case, we move the decimal point two places to the left:

33.1868131868 ≈ 3.31868131868 x\(10^1\)

Therefore, the quotient of 302 ÷ (9.1 x \(10^4\)) in scientific notation is approximately 3.31868131868 x\(10^1\)

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Answer:

All they are doing is finding what a 20% drop would be. You do that by multiplying the value by .8 which gives you the total accounting for a 20% drop.

Step-by-step explanation:

An equation of the new graph is: A. y = ∣x - 4∣ - 9.

In Mathematics and Geometry, the translation of a graph to the right simply means a digit would be added to the numerical value on the x-coordinate of the pre-image:

g(x) = f(x - N)

Conversely, the translation of a graph downward simply means a digit would be subtracted from the numerical value on the y-coordinate (y-axis) of the pre-image:

g(x) = f(x) + N

Since the parent function y = ∣x∣ was translated 4 units to the right and 9 units down in order to produce the graph of the image, we have:

y = ∣x - 4∣ - 9

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

8x-6y

Step-by-step explanation:

(3x-2y)+(5x-4y)

put like terms together

(3x+5x)+(-2y-4y)

add together

8x           -6y

put together

8x-6y

The total combination they can wear is 56 clothings

From the question, we have the following the given parameters are

Skirts = 7

Blouses = 8

From the question, the skirts and the blouse match

This means that

The total combination they can wear is the product of the skirts and the blouses

This is represented as

Total combination = Skirts x Blouses

Substitute the known values in the above equation

So, we have the following equation

Total combination = 7 * 8

Evaluate the product

Total combination = 56

Hence, the total combination of clothings is 56

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ANSWER: y = (1/2)x - 1.

To find the equation of the tangent line to the curve y = √(x - 3) at the point (4, 1), we need to determine the slope of the tangent line and its y-intercept.

First, let's find the derivative of the function y = √(x - 3) using the power rule:

dy/dx = 1/(2√(x - 3))

Now, we can substitute x = 4 into the derivative to find the slope of the tangent line at that point:

m = dy/dx = 1/(2√(4 - 3)) = 1/2

So, the slope of the tangent line is 1/2.

Next, we can use the point-slope form of a line to find the equation of the tangent line. Given the point (4, 1) and the slope m = 1/2, the equation becomes:

y - y1 = m(x - x1)

Substituting the values (x1, y1) = (4, 1):

y - 1 = (1/2)(x - 4)

Simplifying the equation:

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

y = (1/2)x - 1

Therefore, the equation of the tangent line to the curve y = √(x - 3) at the point (4, 1) is y = (1/2)x - 1.

Answer:

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

Step-by-step explanation:

Step 1: Find the derivative of the function

The derivative of a function gives the slope of the tangent line to the curve at any point. To find the derivative of the given function y = sqrt(x - 3), we can use the power rule of differentiation which states that:

d/dx (x^n) = nx^(n-1)

Applying this rule to our function, we get:

dy/dx = d/dx sqrt(x - 3)

To differentiate the square root function, we can use the chain rule of differentiation which states that:

d/dx f(g(x)) = f'(g(x)) * g'(x)

Applying this rule to our function, we have:

g(x) = x - 3

f(g) = sqrt(g)

So,

dy/dx = d/dx sqrt(x - 3) = f'(g(x)) * g'(x) = 1/(2*sqrt(g(x))) * 1

Substituting g(x) = x - 3, we get:

dy/dx = 1/(2*sqrt(x - 3))

So, the derivative of y with respect to x is 1/(2*sqrt(x - 3)).

Step 2: Evaluate the derivative at the given point

To find the slope of the tangent line at the point (4, 1), we need to substitute x = 4 into the derivative expression:

dy/dx = 1/(2*sqrt(4 - 3)) = 1/2

So, the slope of the tangent line at the point (4, 1) is 1/2.

Step 3: Use point-slope form to write the equation of the tangent line

Now that we know the slope of the tangent line at the point (4, 1), we can use point-slope form to write the equation of the tangent line. The point-slope form of a line is given by:

y - y1 = m(x - x1)

where (x1, y1) is the point on the line and m is the slope of the line.

Substituting the values x1 = 4, y1 = 1, and m = 1/2, we get:

y - 1 = (1/2)*(x - 4)

Simplifying this equation, we get:

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

So, the equation of the tangent line to the curve y = sqrt(x - 3) at the point (4, 1) is y = (1/2)x - 1/2.

Hope this helps!

Answer:

\( \frac{3}{6} \)

Answer:

1/3

Step-by-step explanation:

2/6 divided by 2/2 equals 1/3.

Explanation: You have to find the common factor the numerator and denominator share.

Have A Great Day! :)