Which equation represents a linear function??

The segment joining the midpoints of the diagonals of a trapezoid is parallel to the bases

From the figure, we have the following coordinates

B = (a, 0)

D = (d, c)

The midpoint of line segment BD is calculated as

BD = 1/2 * (x1 + x2, y1 + y2)

So, we have

BD = 1/2 * (a + d, 0 + c)

This gives

BD = ((a + d)/2, c/2)

Also, we have:

Lines MN and AB are horizontal lines

This means that they have a slope of 0

i.e.

Slope of AB = Slope of MN = 0

Parallel lines have equal slope

Hence, the segment joining the midpoints of the diagonals of a trapezoid is parallel to the bases

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Answer:

Step-by-step explanation:

Part A: No. The line would have to be straight in order for the graph to be linear.

Part B:

Linear: y=2x-4.

Nonlinear: y=x^2-6.

The cash advance fee for the credit card account is $3.00

What is the basis for computing cash advance fee?

The basis for determining the cash advance fee is on the amount borrowed not that 2% is charged annually on the credit card account, in other words, the cash advance fee in this case is the cash advance multiplied by the advance fee of 2% as shown explicitly below:

cash advance fee=cash advance*cash advance fee %

cash advance=$150

cash advance %=2%

cash advance fee=$150*2%

cash advance fee=$3.00

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Full question:

Sidney took a $150 cash advance by using checks linked to her credit card account. The bank charges a 2 percent cash advance fee on the amount borrowed and offers no grace period on cash advances. Sidney paid the balance in full when the bill arrived.

What was the cash advance fee? (Round your answer to 2 decimal places.)

Answer:

The first option

Step-by-step explanation:

Answer:

1st one

Step-by-step explanation:

Opposite of positive 3 is negative 3.

Answer:

116, 117, 118

Step-by-step explanation:

Consecutive numbers are numbers that come after each other, such as 1, 2 and 3.

Find the expressions for the integers:

Let the smallest integer be x.

2nd integer= x +1

3rd integer= x +1 +1= x +2

Form an equation:

x +x +1 +x +2= 351

Solve for x:

3x +3= 351

3x= 351 -3

3x= 348

x= 348 ÷3

x= 116

Find the other 2 integers:

2nd integer= 116 +1= 117

3rd integer= 117 +1= 118

Hence, the three consecutive integers are 116, 117 and 118.

Answer:

B

Step-by-step explanation:

(look up limit calculator)

a has a limit

b does not exist

c  has a limit

d has a limit

e has a limit

Option D is correct one. Limit doesn't exist for [tex]\lim_{x\to \ 2} \frac{x^{2}-6x +8 }{x-2}[/tex].

The limit of f(x) at x = a is said to be exist if the function approaches the same value from both the sides i.e. LHL =RHL (left hand limit = right hand limit)

According to the question we have,

A. [tex]\lim_{x \to \ 1} \frac{2-x}{x+1}[/tex]

at x =1

LHL = [tex]\lim_{h \to \ 0 } \frac{2- (1-h)}{(1-h)+1}[/tex] = [tex]\frac{1}{2}[/tex]

RHL = [tex]\lim_{h \to \0} \frac{(2-(1+h) }{(1+h)+1)} =\frac{1}{2}[/tex]

Here, RHL = LHL

Hence, limit exist.

B. [tex]\lim_{x \to \ 2} \frac{x^{2} -8}{x-2}[/tex]

at x =2

LHL = [tex]\lim_{h \to \ 0} \frac{(2-h)^{2}-9 }{(2-h)-2}[/tex] =[tex]\lim_{h \to \ 0} \frac{4+h^{2} -9-4h}{2-h-2}[/tex] = [tex]\lim_{h \to \ 0 }\frac{2h-4}{-1} =\frac{-4}{-1} =4[/tex]

RHL = [tex]\lim_{h \to \ 0} \frac{(2+h)^{2} -9}{(2+h)-2}[/tex] = [tex]\lim_{h \to \ 0} \frac{4h +4 +h^{2}-9 }{h} = \lim_{h \to \ 0} \frac{2h+4}{1}[/tex]=4

Here, RHL = LHL

Hence, the limit exist.

C. [tex]\lim_{x \to \ 1} (x^{2} -2x-5)[/tex]

at x =1

LHL = [tex]\lim_{h \to \ 0} (( 1-h)^{2} -2(1-h)-5)= \lim_{h \to \ 0} (1 -2-5)=-6[/tex]

RHL = [tex]\lim_{h \to \ 0} ((1+h)^{2} -2(1+h)-5) = (1-2-5)=-6[/tex]

Here, LHL = RHL = -6

Hence, the limits exist.

D. [tex]\lim_{x \to \ 2} \frac{x^{2}-6x + 8 }{x - 2}[/tex]  

at x =2

LHL = [tex]\lim_{h \to \0} \frac{(2-h)^{2} -(2-h)+8}{(2-h)-2} = \lim_{h \to \ 0} \frac{4+h^{2}-4h-2+h+8 }{(2-h)-2}[/tex] =[tex]\lim_{h \to \ 0} \frac{2h-4+1}{1} =-3[/tex]

RHL = [tex]\lim_{h \to \ 0} \frac{(2+h)^{2} -(2+h) +8}{(2+h)-2} = \lim_{h \to \ 0} \frac{4+h^{2}+4h -2-h+8}{h} = \lim_{h \to \ 0} \frac{2h+4-1}{1} =3[/tex]

Here, RHL≠LHL

Hence, the limit doesn't exist.

E. [tex]\lim_{x \to \ 3} (x^{2} -3x-1)[/tex]

at x = 3

LHL = [tex]\lim_{h \to \ 0} ((3-h)^{2} -3(3-h)-1)[/tex] = [tex]9-9-1=-1[/tex]

RHL= [tex]\lim_{h \to \ 0} ((3+h)^{2} -3(3+h)-1)= 9-9-1 =-1[/tex]

Here, RHL = LHL

Hence, the limit exist.

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The following rigid transformations are done on each figure:

We find two pictures, each with one case of rigid transformation done on a polygon. Rigid transformations are transformations done on geometric loci such that Euclidean distance at every point of the loci are conserved.

If we consider that the Euclidean distance is the radial distance with respect to the origin of the Cartesian plane, then we find the rigid transformation corresponding to each case:

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Answer:

5

Step-by-step explanation:

To find the slope we will use the slope formula:

[tex]slope = \frac{y2 - y1}{x2 - x1}[/tex]

They give us the points of (0,1) and (-2,-9) in the equation. Let's label each thing to fit the equation:

y2 = -9

y1 = 1

x2 = -2

x1 = 0

Now, plug it all in to the equation:

[tex]\frac{-9-1}{-2-0} = \frac{-10}{-2} = 5[/tex]

Therefore, the slope is 5.

I hope this helps!!

- Kay :)

Answer:

1/8

Step-by-step explanation:

I've done this before.

Answer:

it's c i did this a week ago

Answer:

2x-1+y

---------- (meant to be a fraction line)

2x+y+1

Answer:

[tex] \frac{2 x - 1 + y }{2x + y + 1} [/tex]

Step-by-step explanation:

In the expression:

[tex] \frac{4 {x}^{2} - {y}^{2} - 4x + 1 }{4 {x}^{2} - {y}^{2} - 2y - 1 } [/tex]

Reorder the terms

[tex]⟹\frac{(4 {x}^{2} - 4x + 1) - {y}^{2} }{4 {x}^{2} - {y}^{2} - 2y - 1 } [/tex]

Rewrite the expression

[tex]⟹ \frac{(2x {)}^{2} - 2 \times 2x + {1}^{2} - {y}^{2} }{ {4x}^{2} - {y}^{2} - 2y - 1 } [/tex]

Factor the expression

[tex]⟹ \frac{(2x - 1 {)}^{2} - {y}^{2} }{4 {x}^{2} - {y}^{2} - 2y - 1 } [/tex]

[tex]⟹ \frac{((2x - 1) + y)((2x - 1) - y)}{4 {x}^{2} - {y}^{2} - 2y - 1} [/tex]

Reorder terms

[tex] \frac{((2x - 1) + y)((2x - 1) - y)}{ {4x}^{2} + ( - {y}^{2} - 2y - 1} [/tex]

Factor greatest common factors out

[tex] \frac{((2x - 1) + y)((2x - 1) - y)}{ {4x}^{2} - ( {y}^{2} + 2y + 1) } [/tex]

Rewrite the expression

[tex] \frac{((2x - 1) + y)((2x - 1) - y)}{ {4x}^{2} - ( {y}^{2} + 2y + {1}^{2}) } [/tex]

Factor the expression

[tex] \frac{((2x - 1) + y)((2x - 1) - y)}{ {4x }^{2} - (y + 1)} [/tex]

Answer:

The mass of an object is directly proportional to its inertia.

[tex]m\alpha I[/tex]

Where

m = mass

I = inertia

Step-by-step explanation:

We can first of all start by defining the two key terms present here - mass and inertia.

The mass of an object is the quantity of matter contained in the object.

The inertia of an object is the resistance of an object which is in a state of rest to motion

The mass of an object is directly proportional to its inertia.

The heavier an object is, the more inertia it has. To put things into perspective, you can easily push a bicycle because it does not really have a lot of mass, as opposed to pushing an eighteen-wheeler trailer.

Answer:

-1

Step-by-step explanation:

y = mx + c

m is the slope/gradient

to find slope = y2 - y1 / x2 - x1

= -8 - -10 / 4 - 6

m = -1

Answer:

11/12

Step-by-step explanation:

15/12-4/12= 11/12

Answer:

11/12

Step-by-step explanation:

5/4 -1/3 first make the equation easier to look at so take the 1 and add it as 4/4

15/12-4/12 then make the bottom the same with multipulcation and tops are multiples as well

11/12 subtract

Answer:

9/26

Step-by-step explanation:

2/159÷2/477=2/53÷2/159=6/52÷2/53=3

x÷6/52=3

x=18/52

x=9/26

Answer:

f(t) = -300t + 20,700

Step-by-step explanation:

2000 is the starting year, so 20,700 is our y-intercept or our constant.

Each year, represented by t, student enrollment decreases by 300. This is the slope of the equation.

Answer:

It is a function

Step-by-step explanation:

A function is of the form:

[tex]\left[\begin{array}{c}x_1&x_2&x_3\\-&-&-\\x_n\end{array}\right][/tex]            [tex]\left[\begin{array}{c}y_1&y_2&y_3\\-&-&-\\y_n\end{array}\right][/tex]

Where each of the x values must be distinct.

The x values are referred to as domain while the y values are called range.

Having said that, the given data can be represented as follows:

[tex]\left[\begin{array}{c}-3&1&6\\7&12\end{array}\right][/tex] ----------- [tex]\left[\begin{array}{c}7&-8&-6\\-8&2\end{array}\right][/tex]

From the representation above, none of the x values are repeated.

Hence, it is a function

The graph of the derivative of a quadratic function will always be a straight line.

A quadratic function is a a function of degree 2 or an equation in which the highest power of any variable in the equation is 2. The derivative of a function denotes the sensitivity to change of the given function with respect to a change in its argument.

When we differentiate any quadratic equation to find its derivative, we get a linear equation, or an equation with degree 1. The graph of a linear equation is a straight line. Thus, the graph of the quadratic equation will also be a straight line. This will hold for all quadratic functions.

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Answer:

goood luccccccckkkk...

Answer:

Ratio: [tex]=\mathbf{\frac{6}{11}}[/tex]

The decimal form (showing up to four  decimal places): 0.5454

The decimal is a repeating decimal i.e 0.54545454..

Step-by-step explanation:

We need to find ratio of hockey players to soccer players

Number of players playing Hockey= 6

Number of players playing Soccer = 11

Ratio: [tex]\frac{Hockey\:Players}{Soccer\:Players} =\mathbf{\frac{6}{11}}[/tex]

The decimal form (showing up to four  decimal places): 0.5454

Tell whether the decimal is a terminating or a repeating decimal.

The decimal is a repeating decimal i.e 0.54545454..

Answer:

7/8

Step-by-step explanation:

Using the binomial distribution, it is found that there is a [tex]\frac{7}{8}[/tex] probability that at least one of the coins comes up heads.

The formula is:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

In this problem:

The probability that at least one of the coins comes up heads is given by:

[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]

In which:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{3,0}.\left(\frac{1}{2}\right)^{0}.\left(\frac{1}{2}\right)^{3} = \frac{1}{8}[/tex]

Then:

[tex]P(X \geq 1) = 1 - P(X = 0) = \frac{8}{8} - \frac{1}{8} = \frac{7}{8}[/tex]

[tex]\frac{7}{8}[/tex] probability that at least one of the coins comes up heads.

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Answer: yes they are equivalent

Step-by-step explanation: When you distribute both equations, you end up with 5m-10.

Answer:  No.

Step-by-step explanation: Unless the tenth place is a 0, a product of a 2 numbers with 1 decimal place cannot have a product for a whole number, even if you went on forever.

When two decimal places add up to one whole, the total of the two decimal places is a whole number. The addition of relocating the decimal point after the multiplication when multiplying decimals is the only difference between multiplying whole numbers and multiplying decimals.

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Answer:

HAHAHAHH

Step-by-step explanation:

Answer:

24964

Step-by-step explanation:

hope this works : ) - btw this is not including 2 and 33