Given that the equation of line one (L1) is 2x-y=3 and equation of line two (L2) is kx+2y=3 where k is a constant.

(a) Find the value of k such that L1 and L2 are parallel.

(b) Find the value of k such that L1 and L2 are perpendicular.


This question is related to Linear functions, Answers: (a) k = -4, (b) k=1. Someone pls tell me how to get there though

Answer:

1 and 2 are functions, 3 is not a function.

Step-by-step explanation:

One x-value can lead to one y-value. If the x-value leads to more than one y-value like #3, then the relation is not a function.

If each input value leads to only one output value, classify the relationship as a function. If any input value leads to two or more outputs, do not classify the relationship as a function.

The probability that x is either less than 3 or greater than 8 is 0.375   .

In the question ,

it is given that ,

a continuous random variable X , is uniformly distributed between 2 and 10 ,

So , alpha(α) = 2 and beta(β) = 10 .

the probability that x is either less than 3 or greater than 8 can be calculated by :

P(X < 3  or X > 8) = 1 - (8 - 3)/(β - α)

= 1 - (8 - 3)/(10 - 2)

= 1 - 5/8

On simplifying further ,

we get ,

= 0.375

Therefore , the probability P(X < 3  or X > 8) is = 0.375   .

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Answer:

2nd equation

Step-by-step explaination:

1st. -7≠-2(3)

2nd. Sastifies all

3rd. -10≠-3(4)

4th. -4≠-2(2)-3

Answer: A

Step-by-step explanation:

The abscissa or x-coordinate of any point on Y-axis is zero.

Which line is the x-coordinate?

Two parallel lines, known as axes (pronounced AX-eez), that are perpendicular to each other make up a coordinate grid. Typically, the term "x-axis" refers to the horizontal axis. The y-axis is the common name for the vertical axis.

The ordinate and abscissa are other names for the x-axis and y-axis, respectively. These two axes can be used to find or represent any point on the coordinate plane as an ordered pair of the form (x,y).

The equation of a line is typically written as y=mx+b where m is the slope and b is the y-intercept.

In order to represent the equation in y-intercept (y=mx+b) form, the slope and y-intercept must be included. The slope is the ratio of the y-to-x change. Draw a sloping triangle connecting the two spots you find on the line.

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Answer:3/5

Step-by-step explanation:

(y2-y1)/(x2-x1)

(2-(-1))/(6-1)=3/5

Answer: 19120 Toaster

Step-by-step explanation: We just need to take $478000 divided by 25, equal to 19120 Toaster!

Answer:

8

Step-by-step explanation:

16 divided by 2 is 8.

Answer: 8 students

Step-by-step explanation: 16/2=8

Answer:

  a. The proof is in your picture

  b. Yes

  c. All four triangles are congruent by the HL theorem

Step-by-step explanation:

Given AB≅CB in ∆ABC with BD⊥AC, you want to show ∆ABD≅∆CBD, and you want to know if these are congruent to ∆CEG and ∆FEG.

Your picture correctly shows a proof that ∆ABD≅∆CBD by the HL postulate.

Sides CE and FE are marked congruent to each other and sides AB and CB. The altitudes BD and EG of these isosceles triangles are marked as congruent. Hence all four triangles, ∆ABD, ∆CBD, ∆CEG, and ∆FEG are congruent by the HL theorem.

The same HL theorem reasoning applies to all of the triangles.

__

Additional comment

The distance from the light to the stage is said to be the same for both lights. That would be measured perpendicular to the stage, and is the shortest such distance. We are assuming that BD and EG are those perpendicular distances, as we see no markings on the diagram indicating right angles.

By solving the two equations, the values of x , y and x-y are found to be 1, 25/3 and -22/3 respectively.

Given two equations are;

5x+3y=30..........(1)

−5x−2y=−25.........(2)

Now , from (2)

−5x−2y=−25

⇒ 5x +2y = 25 (multiply both sides with '-' sign)

⇒ y = [tex]\frac{(25 -5x)}{2}[/tex]

Solving the system;

substitute the above vale of y in eq (1)

5x + 3y = 30

⇒ 5x + 3 ( [tex]\frac{(25 -5x)}{2}[/tex]) = 30

⇒  5x + ([tex]\frac{(75 - 15x)}{2}[/tex]) = 30

⇒  [tex]\frac{10x+75-15x}{2}[/tex] = 30

⇒ -5x + 75 = 60

⇒  -5x = -5

⇒ x = 1

∴ x = 1

Now substitute the value of x in (1)

5x + 3y = 30

⇒ 5 × 1 + 3y = 30

⇒ 3y = 25

⇒ y = 25/3

∴ y = 25/3

Now using the value of x and y , we can find the value of x - y

x - y = 1 -25/3 = (3 - 25)/ 3 = -22/3

∴ x - y = -22/3

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The table is attached below.

What are table entries?

Entities are gathered at tables. A group of properties makes up an entity. Each object may contain up to 252 name-value pairs for its properties.

From the information given, we can make a table to display all the options available for Michael to choose clothing options.

The table is attached as follows:

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There are 12 clothing options for Michael to choose from in his closet. By the fundamental principle of counting, the possible number of options is calculated.

The fundamental principle of counting states that an operation/event can be performed in 'm' ways and a second operation/event can be performed in 'n' ways. Then there are (m × n) ways for the two operations to be performed together.

It is given that,

Michael is having three shirts - yellow, green, and orange; two pairs of shorts: navy, gray and two footwear: tennis shoes and sandals.

So, we can write

the number of shirts = 3

the number of shorts = 2

the number of footwear = 2

Then, according to the fundamental principle of counting, all these are multiplied to get the total number of ways that he can wear them together.

I.e., 3 × 2 × 2 = 12

Therefore, there are 12 combinations for him to choose one among these.

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The solution for f(11) in the function when the function f(x) = 12|x + 8| is 228

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

f(x) = 12|x + 8|

The above equation is an absolute value equation

An absolute value equation has the following representation

f(x) = a|x - h| + k

So, we have the following representation

f(x) = 12|x + 8|

Also from the question, we have

f(11)

This means that the value of x is 11, and we calculate f(x) when x = 11

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

f(11) = 12|x + 8|

So, we have the following equation

f(11) = 12|11 + 8|

There are constants to add or subtract to both sides of the equation

Also, there are factors to multiply or divide from both sides of the equation

So, we have the following representation

f(11) = 12|19|

Solving further, we have

f(11) = 12 * 19

Evaluate the products

f(11) = 228

Hence, the solution is 228

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Answer:

Step-by-step explanation:

He made a mistake in step one turning the 7 into a -7

[tex]x^{2}[/tex] - 3x + 7 = 0

Solving:

[tex]1x^{2}[/tex] - 3x + 7 = 0  ← If the term doesn't have a coefficient, it is considered that the coefficient is 1.

[tex]1x^{2}[/tex] + (-3x) + 7 = 0 ← Identify the coefficients a, b, and c of the quadratic equation.

a = 1, b = -3, c = 7

x = - (-3) ±√[tex](-3)^{2}[/tex] - 4 x 1 x 7

                 2 x 1

x = 3 ± √[tex](3)^{2}[/tex] - 4 x 7

                2

x = 3 ± √9 - 4 x 7

                2

x = 3 ±√9 - 28

             2

x = 3 ± √-19

         2

The square root of a negative number does not exist in the set of real numbers.  

x = ∉ R

Answer: omg never seen somthing dat complex :O

Step-by-step explanation:

Answer:

f(x) = ³√(x–1) + 4

f-¹(x) = (x + 1)³ + 4

Step-by-step explanation:

i hope this helped

The correct order to solve the equation is given below .

In the question ,

it is given that ,

the equation is 3*([tex]2^{2 t - 5}[/tex]) - 4 = 10  ,

Step(1) , adding 4 to each side of the equation ,

3*([tex]2^{2 t - 5}[/tex]) = 14

Step(2) , dividing both sides of the equation by 3 ,

we get ,  ([tex]2^{2 t - 5}[/tex]) = 14/3  .

Step(3) , taking log on each side ,

log([tex]2^{2 t - 5}[/tex]) = log(14/3)

Step(4) , Using the Exponential Property and writing 14/3 in decimal form ,

we get ,

(2t - 5)*log(2) = log(4.67)

Step(5) , Dividing each side by log(2)  ,

we get ,  2t-5 = log(4.67)/log(2) .

Step(6) , Add 5 to each side of equation

we get , 2t = 2.23 + 5  ;

Step(7) , Simplifying we get  ,

we get , t = 3.625  .

Therefore , the the solution of the given equation is t = 3.625   .

The given question is incomplete , the complete question is

Arrange the steps in the correct order to solve the equation,

3*([tex]2^{2 t - 5}[/tex]) - 4 = 10  .

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Answer:

(-1, 3), (3, 3), (5, 3), (1, 0)

Step-by-step explanation:

A translation of 4 units to the right means adding 4 to every x-coordinate.

The new coordinates are:

(-1, 3), (3, 3), (5, 3), (1, 0)

Answer:

a) CE=PR

b) TR=FE

c) <F=<T

d) <P=<C

e) RPT=ECF

Step-by-step explanation:

Answer:

Step-by-step explanation:

since $68 is your total, let's use the example z=y+x

z is our total, and we know that he made a total of $68, therefore z is the number 68.

We also know that James made a total of $48 washing cars, which gives us the answer 48 as y. So in order to find x, we would need to subtract 68 and 48, which is called using the communtative property. Thsi answer would give us the remaining amount of money we do not yet know.

So 68-48= 20. therefore James made $20 at the art contest.

Answer:

28.27 sq. units or 9π sq.

Step-by-step explanation:

The probability that at least one of the cubes will have the face labeled 5 showing and that the sum of the showing faces will be greater than 8 is 5/36.

A probability is a numerical representation of the possibility or chance that a specific event will take place. Probabilities can be written as percentage between 0 and 1.

Number of sample spaces that are labeled 5 and display a sum more than 8 / total sample space gives the likelihood that at least one of the cubes will have the face labeled 5 showing and that the sum of the faces showing will be greater than 8.

When two cubes are rolled, the total sample space is 36.

The sample space that is labelled 5 and has a sum greater than 5 are: (4,5) , (5, 4) , (5, 5), (5, 6) , (6,5) = 5

The probability = 5/36

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Answer:

9.1 units

Step-by-step explanation:

See diagram below ....using pythagorean theorem

Answer: it’s B

Step-by-step explanation: Look at the graph clearly

and you will see the value of x and y

Therefore the solution of this question is Sam can draw 2 lines of reflection.

If a figure is reflected in a line or a point, the image and preimage are consistent. A reflection converts each point in a figure into an image along a predetermined line. Line of Reflection refers to the fixed line.

To determine the quantity of lines that will reflect a rectangle back onto itself.

Due to the fact that the line of reflection is the perpendicular bisector of the segment connecting a point with its image. The perpendicular bisector of a side must be the line of reflection if one side of the rectangle is to map to itself.

A rectangle has two distinct perpendicular bisectors of its sides, leading to two lines of reflection that map a rectangle to itself.

Therefore Sam can draw 2 lines of reflection.

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Answer:

y = -2x - 4

Step-by-step explanation:

y = mx +b is the slope intercept form of a line.  The m is the slope and the b is the y intercept.

The y intercept is where the line crosses the y axis.  It crosses at the point (0,-4).  The -4 is where the line crosses the y axis.  It is the b.

The slope is the change in y over the change in x.  To go from point (0,-4) to the point (-2,0)  You go up 4 units and the left 2 units.  Up is positive and left is negative. 4/-2 which simplifies to -2.  This is your m.

Answer:

25

Step-by-step explanation:

first add the degrees: 50+30+25=105, then 180-105 is 75, 75=3s, s is 25

(im not sure completely im only in 7th grade)

Answer:

p=12345

Step-by-step explanation:

Answer:

  see attached

Step-by-step explanation:

You want the graphed triangle rotated 90° CW about the point (2, -1).

After rotation 90° CW, points will be as far to the south and west of the center of rotation as they are east and south in the original image. This is shown by the blue triangle in the attachment.

Based on the given parameters, the value of the money to invest initially is $99341.383

The given parameters about the compound interest are

Amount, A = $181000

Interest Rate, R = 5%

Time, t = 19 years

Number of times, n = 365 i.e. continuously

To calculate the amount, we have:

A = P + CI

Where

C = P(1 + R)^t

So, we have

A = P(1 + R)^t

This can be rewritten as

A = P(1 + R/n)^nt

Substitute the known values in the above equation

181000 = A * (1 + 5%/365)^(12*365)

So, we have

A = 181000 /[(1 + 5%/365)^(12*365)]

Evaluate the expression

A = 99341.383

Hence, the amount of the investment is $99341.383

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