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In a function, any x-value is related to at most 1 y-value.

In the first table, x = 20 and x = 17 are related to 2 different y-values. Then, it is not a function.

In the second table, x = 9 is related to 2 different y-values. Then, it is not a function.

The third and fourth tables are functions

Two lines are parallel if:

Two lines are perpendicular if:

---------------------

Let's rewrite the given equations in the slope-intercept form:

Since:

We can conclude that the lines are parallel.

We will have the following:

*First: We have that the equation of the circle will be given by:

Here (h, k) is the coordinate of the center of the circle and r is the radius of the circle.

*Second: We will replace the center of the circle and determine the radius:

*Third: We determine the radius of the circle by using the point given:

*Fourth: We have the following expression representing the circle:

So, we replace the point (-2, sqrt(5)) to determine whether or not it belongs to the circle, that is:

Thus proving that the point (-2, sqrt(5)) does lie in the circle.

To convert decimal numbers to percentage, what we need to do is to multiply the decimal number by 100, and we will get the representation as a percentage.

In this case we have the decimal number:

We multiply that number by 100 to write is as a percentage:

Answer: 75.1%

We will investigate how to determine the end behaviours of polynomial functions.

The function given to us is:

Whenever we try to determine the end-behaviour of any function. We are usually looking for value of f ( x ) for the following two cases:

The most important thing to note when dealing with end-behaviour of polynomial functions is that the behaviour is pre-dominantly governed by the highest order term of a polynomial. The rest of the terms are considered small or negligible when considering end-behaviours of polynomials.

The highest order terms in the given function can be written as:

Then the next step is to consider each case for the value of ( x ) and evaluate the value of f ( x ) respectively.

Similarly repeat the process for the second case:

Combining the result of two cases we get the following solution:

Correct option is:

The equation of the line that goes through the point (5, -1) and is parallel to the given equation is; 3x + 2y = -7.

Recall from line geometry that parallel lines have equal slopes.

Therefore, by computing the slope of the equation given as follows; we have;

3x + 2y = 19.

By rearranging the equation in the slope-intercept form; y = mx + c; we have;

y = (-3/2)x + 19/2

Therefore, the slope of both lines is same and is; -3/2.

Therefore, By using the point slope equation of a straight line; (y - y1) = m (x - x1); we have;

(y - (-1)) = -3/2(x - 5)

2y + 2 = -3x - 5

3x + 2y = -7.

Ultimately, the required equation is; 3x + 2y = -7.

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This is a simultaneous system of equations, we would need both equations, to solve for the variables.

we have

2x - 3y = 6 - ---i

x +7y = 2------ii

Let's modify equation ii, x +7y = 2 means x = 2 - 7y

Anywhere we see x in equation i, lets put in 2 - 7y instead

2( 2 - 7y) - 3y = 6

4 - 14y - 3y = 6

4 - 17y = 6

-17y = 2

y = -2/17

Lets put this result in equation ii

a) y = 3/5x + 11/5

b) y = -5/3x + 9

For a line to be parallel to another line. the slope of the 1st line will be equalt to the slope of the 2nd line:

slope of 1st line = 3/5

So, the slope of the 2nd line = 3/5

Given point: (3, 4) = (x, y)

To get the y-intercept of the second line, we would insert the slope and the point into the equation of line

The equation of line parallel to y = 3/5x - 3:

For a line to be perpendicular to another line, the slope of one will be the negative reciprocal of the second line

Slope of the 1st line = 3/5

reciprocal of 3/5 = 5/3

negative reciprocal = -5/3

slope of the 2nd line (perpendicular) = -5/3

We need to get the y-intercept of the perpendicular line:

The equation of line perpendicular to y = 3/5x - 3:

ANSWER:

STEP-BY-STEP EXPLANATION:

We have the following expression:

When you raise an exponent to another exponent, multiply therefore:

Solution

We want to find the equation of the line given in the graph

We can see the four points on the graph where the line pass through

The points are

We first obtain the slope (m)

The formula for finding the slope is given as

Using the points (0,2) and (-4,0) (indeed we can pick any two points, we will still obtain the same answer)

Here

We can use any of the points above to find the equation

Equation of a line is given by

Using (4,4)

Option D is correct

Using (2,3)

The transformation required to transform the preimage in purple to the image in white is

Transformation is the term used to  describe when a body is repositioned  or makes some movement.

Some of the movements involved in transformation are:

The movement can start in several ways however we stick to this as described

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Probability of Debra unlocking the treasure chest, P(unlocking) = 3/10

Probability of Debra not unlocking the treasure chest,

P( not unlocking) = 1 - 3/10

P( not unlocking) = 7/10

As shown in the figure:

AB || CD

AD || CB

We need to prove AB = CD

So, the proof will be as follows:

Statements Reasons

0. AB || CD Given

1. m∠BAC = m∠DCA Alternate angles are congruent

2. AD || CB Given

3. m∠BCA = m∠DAC Alternate angles are congruent

4. AC = CA Reflexive property

5. ΔBAC ≅ ΔDCA By A.S.A [angle-side-angle] postulate

6. AB ≅ CD CPCTC

If the two figures are similar, then the missing angle equals 70°.

Given

A digital picture frame with a border of 3 cm. The actual length of the frame is x

Answer

a) The actual side of the picture is x-3

Area of picture

b) Area of frame

c) Area of border = Area of frame - area of picture

We are given the following word problem

"61 less than twice Vidy's score​"

Let us translate the word problem into an algebraic expression

Let v represents Vidy's score

twice Vidy's score means 2 times v

61 less than means to subtract 61 from 2 times v

So, the algebraic expression becomes

Let:

• A ,be the number of millilitres (mL) of solution A used.

• B ,be the number of mL of solution B used.

We know that Dale uses four times as much solution A as solution B, meaning

Now, we know that we will end up with 570 mL of pure alcohol in the final solution. Using the dilution of both A and B (20% means 0.2 and 15% is 0.15) we would have that:

We would have the following system of equations:

Substituting equation 1 in equation 2 and solving for B :

Substituting in equation 1 and solving for A:

This way, we can conclude that 2400 mL of solution A and 600mL of solution B were used.

The endpoints are a side of a rectangle ABCD in the coordinate plane at A(3,4), B(6,1) Find the equation of the line the given segment

The line segment is line Segment AB​

step 1

Find the slope of segment AB

m=(1-4)/(6-3)

m=-3/3

m=-1

step 2

Find the equation of the line in slope intercept form

y=mx+b

we have

m=-1

point (3,4)

substitute

4=(-1)*(3)+b

4=-3+b

b=4+3

b=7

therefore

the equation of segment AB is

Answer:

4nx5=n-7

-7/19

Step-by-step explanation:

Let's Write this equation step by step.

The sum of 4 times a number and 5

That means: 4nx5

The difference of the number and 7

That means: n-7

Now, combine:

4nx5=n-7

-7/19

For the division, notice that we can multiply both numbers by 100, to get the following:

then, we can make the long division:

therefore, the result of 59.25 ÷ 0.75 is 79

For the multiplication, we can write the following:

notice that since both factors have 2 digits and 1 digit each after the decimal point, the final result will have 3 digits after the decimal point,

Therefore, the result of 1.06 × 7.3 is 7.738

Solution:

Let the total field to plow be 100 %

According to the question,

The field plowed before lunch is shown below:

15 acres field = 30%

30 % field = 15 acres

1 % field = 15/30 acres

The field plow after lunch is 70%.

Final Answer:

Therefore, the field to plow after lunch in order to finish the field is 35 acres.

Step-by-step explanation:

based on the expression you wrote here, the correct answer is

1, 2, -5, -1, 3

since none of your answer options show this, you must have made a mistake either with the expression itself or with the answer options.

please choose in your original the one matching my answer above.

When we're dilating a line, we can either multiply the function value by a constant

or the argument of the function

Since the y-intercept of both functions is the same, then the multiplied quantity was the argument of the function.

We want to know the constant associated to the transformation

We have the following values for both functions

For the same y-value, we have the following correlations

and this is our answer.

We will have the following:

So:

Then we will have that:

So, the width is 14 inches and the length will then be 17 inches.

To find the inverse of a function:

We will follow the steps below

Step 1: Replace f(x) witth y

Step 2: interchange x with y

Step 3: Make y the subject of the formula

Thus, the inverse of the function is:

The percent of change is​ computed as follows:

Substituting with data:

Answer:

-105$

Step-by-step explanation:

Given:

The cost of the car is $14,000.

Then 1/10 of the cost of the car is

Hence, the down payment is $1400.

Answer

The amount of flour left in the bag = 1.82 kg

Explanation

Concetta had 2 kg of flour.

She uses 180 g of the flour to make biscotti.

We are then asked to calculate how much flour is left in kilograms.

Amount of flour left = (Initial Amount of flour) - (Amount of flour used)

Initial amount of flour = 2 kg

Amount of flour used = 180 g = 0.18 kg

Amount of flour left = (Initial Amount of flour) - (Amount of flour used)

Amount of flour left = 2 - 0.18 = 1.82 kg

Hope this Helps!!!

We have here a special case where the line is vertical. In this case, the line has an "infinite" slope (or it is not defined). Therefore, since the line is vertical and contains the point (10, 14), the line is given by the equation:

The standard form of the line is given by the general equation:

Then, we can rewrite the equation as follows:

We can see that this line contains the point (10,14):

We can see that the vertical line, x + 0y = 10 passes through the point (10, 14).

In summary, the line is given by x + 0y = 10 (A = 1, B = 0, C = 10).