The sets A and L are given below.
A = (a, b, e}
L={c, k,j}
Find the intersection of A and L.
Find the union of A and L.
Write your answer using notation (in roster form)

Answer:

[tex]\boxed{\sf a = 9 }[/tex]

Step-by-step explanation:

Two lines are given to us which are perpendicular to each other and we need to find out the value of a . The given equations are ,

[tex]\sf\longrightarrow 3x - 2y +7=0 [/tex]

[tex]\sf\longrightarrow 6x +ay -18 = 0 [/tex]

Step 1 : Convert the equations in slope intercept form of the line .

[tex]\sf\longrightarrow y = \dfrac{3x}{2} +\dfrac{ 7 }{2}[/tex]

and ,

[tex]\sf\longrightarrow y = -\dfrac{6x }{a}+\dfrac{18}{a} [/tex]

Step 2: Find the slope of the lines :-

Now we know that the product of slope of two perpendicular lines is -1. Therefore , from Slope Intercept Form of the line we can say that the slope of first line is ,

[tex]\sf\longrightarrow Slope_1 = \dfrac{3}{2} [/tex]

And the slope of the second line is ,

[tex]\sf\longrightarrow Slope_2 =\dfrac{-6}{a} [/tex]

Step 3: Multiply the slopes :-

[tex]\sf\longrightarrow \dfrac{3}{2}\times \dfrac{-6}{a}= -1 [/tex]

Multiply ,

[tex]\sf\longrightarrow \dfrac{-9}{a}= -1[/tex]

Multiply both sides by a ,

[tex]\sf\longrightarrow (-1)a = -9 [/tex]

Divide both sides by -1 ,

[tex]\sf\longrightarrow \boxed{\blue{\sf a = 9 }} [/tex]

Hence the value of a is 9 .

Given:

The sequence is:

-3, 5, -7, 9, -11,...

To find:

The correct statement about the given sequence.

Solution:

We have,

-3, 5, -7, 9, -11,...

Here, "..." means there are more terms in the sequence. So, the sequence has more than 5 terms and option A is incorrect.

From the given sequence it is clear that the 4th term is 9. So, option B is correct.

Clearly, 5th terms is -11. So, [tex]f(5)=-11[/tex] and option C is incorrect.

The domain of a sequence is always the set of natural numbers. So, option D is correct.

In the given sequence the 4th term is 9. It means the point (4,9) lies on the graph of the sequence. So, option E is correct.

Therefore, the correct options are B, D, E.

Answer:

c) x= 15

d) x= 5

Step-by-step explanation:

c)4x + 5+ 7x +10=180

solve it like usually

for d) 3x + 15+12x=90

Answer:

15 and 3

Step-by-step explanation:

the first figure total sum of angles is 180 since it is a straight line

the second figure is a right ane(90) so sum of angles is 90

Answer:

r=8

Step-by-step explanation:

Answer:

See below

Step-by-step explanation:

Step 1

x^2 – 30x = –125

-30/2 = -15

(-15)^2 = 225

Step 2

x^2 -30x+225 = -125+225

(x-15)^2 = 100

Step 3

Take the square root of each side

sqrt((x-15)^2) = sqrt(100)

Step 4

x-15 = ±10

x-15 =10    x-15 = -10

x= 10+15    x = -10 +15

x = 25      x = 5

Answer:

f(- 3) = 27 and g(6) = - 15

Step-by-step explanation:

Substitute x = - 3 into f(x) and x = 6 into g(x) , that is

f(- 3) = - 2(- 3)² - 3(- 3) = - 2(9) + 9 = 18 + 9 = 27

g(6) = - 2(6) - 3 = - 12 - 3 = - 15

Answer:

The way I would tackle these types of problems would be to make a table, then graph the points using the results I get.

Step-by-step explanation:

So explaining the table is kinda hard since I suck at explaining, so I've attached a file showing the table I've made for number 1.

First Step:

Make the table. Make it a 3x4 table. For the top row, put y, the equation (I put 'y=2x' as shown in number 1), then x. Then for the left column, go down by one box, then put: -1, 0, 1. Really, you can put any numbers, but to make it easy for yourself, just write the numbers I've listed. These will be your y-values you'll be substituting.

Second Step:

a.) Plugging in the numbers. For the middle column, I've put down y=2x in each box, as shown in my table. Then for each of those boxes, plug in the numbers to the left of them and substitute them for the y-value. For example, look at the second row. The left box has '-1', so I replaced the 'y' in the equation and got '(-1)=2x'.

b.) After substituting the y-values, solve for x. For this case, you'll need to divide both sides by 2. If it doesn't make much sense, think about a seesaw. If you have 5 pounds on both sides, the seesaw will stay balanced. Add an additional 5 pounds to one side, then the seesaw will start tipping towards the heavier sides. So in order to keep an equation balanced, you must do any action to both sides of the equation. After diving both sides by 2, you'll get the value for x.

Final Step:

After finding the x-values for each of the y-values, it's time to graph the equations. Remember, x is left to right and y is down to up. To graph them, let's use the second row for example. y=-1 and x=-0.5. So all you need to do is to start from the origin (0,0), then go half a unit to the left, as x is negative, then go a unit down, as y is negative, then make a point. The rest should be pretty straight forward.

After making all three points, just get a ruler or any straight edge, then align it along those three points, then just make a line, and boom! You've solved number 1! For the purpose of saving my time, I'm pretty sure you can solve the rest using what I've just told you. Good luck!

Answer:

A.2x+6

B.60x-20

C.8x+4

D.6x-24y

Answer:

GHI is congruent to HGW

Step-by-step explanation:

Answer:

$11,400

Step-by-step explanation:

3,000+14(600)=11,400

We know that it expands by $600 a year and we are looking for the salary during the 15th year.  During the 15th year, it could be using the salary of the 14th year since it is during not after.  We then add that to the base salary of $3,000 so then we have $11,400.

Answer:

x² - 4x - 8

General Formulas and Concepts:

Algebra I

Step-by-step explanation:

Step 1: Define

Identify

(-3 + 4x² - 4x) + (-1 - 3x² - 4)

Step 2: Simplify

Answer:

c. .01

Step-by-step explanation:

.6389 divided by 63.89

Answer:

by SAS only

Step-by-step explanation:

based on the diagram we only have one side and one angle explicitly identified as equivalent.

but we have an implicit confirmation of the second side QS to the enclosed angle, because the triangles are presented that this side is the same for both triangles.

so, SAS applies (but no other, as we don't have any information on the 3rd side).

Answer:

- 3 / 10

Step-by-step explanation:

- 9 / 10 - ( - 3 / 5 )

= - 9 / 10 + 3 / 5

= 3 / 5 - 9 / 10

= 6 / 10 - 9 / 10

= ( 6 - 9 ) / 10

= - 3 / 10

Answer:

-6

Step-by-step explanation:

The number line is created by skip counting of 2.

So, -2 ,  then -4 and then -6.

So,  blue dotted point is (-6)

Answer:

15

Step-by-step explanation:

[tex]=\frac{6!}{4!\left(6-4\right)!}[/tex]

Answer:

Maybe you can add roles, like managing, or narrating?

Step-by-step explanation:

Answer:

1) -1

2) 3

3) 2

Answer:

The customer will pay along with VAT = Rs 3767.4

Step-by-step explanation:

Cost price of an electric fan = 2800

Pirce after 30% above the cost price = 2800 + (30% of 2800 = 3640

Selling price after 10% discount = 3640 - (10% of 3640) = 3276

Now 15% VAT = 3276 x 15%

15% VAT = 491.4

The customer will pay along with VAT = 3276 + 491.4  

The customer will pay along with VAT = Rs 3767.4

Answer:

X= 7/2

Step-by-step explanation:

Multiply first equation by -2 and second equation by 1

-2(4x+7y=-14)

1(8x+5y= 8)

= -8x -14y =28

8x+5y=8

Add these equations to eliminate X:

-9y=36

-9y/-9 = 36/-9

y=- 4

Plug in Y to find X

4x + 7y = -14

4x+7(-4) = -14

4x-28+28= -14+28

4x= 14

X= 7/2

Answered by Gauthmath

Answer: x=3 and 1/2

Step-by-step explanation: Happy to Help (0.<)

Answer:

[tex]d = 3h - 6[/tex]

Step-by-step explanation:

Step 1:  Solve for d

I am assuming that you are asking for me to solve for the variable d.  Let me know if what I am doing is not what you want.

[tex]h = \frac{d}{3} + 2[/tex]

[tex]h - 2 = \frac{d}{3} + 2 - 2[/tex]

[tex](h - 2) * 3 = \frac{d}{3} * 3[/tex]

[tex]3h - 6 = d[/tex]

Answer:  [tex]d = 3h - 6[/tex]

Answer:

x-⅓y=0

Step-by-step explanation:

thats the answer

brainly please

Answer: 3x-y=0

Step-by-step explanation:

X = 1/3y

X × 3 = 1/3 y × 3

3x = y

3x - y = y- y

3x- y = 0

Answer:

Rob has saved $24.

Step-by-step explanation:

The first thing I noticed was that Rob only saved some of the money he earned. That means only x% only gets saved. To find x, I simply divided 6 by 14 and got 0.42857142857. Then to find the amount he saved from earning $56, I multiplied that number with 56 and got 24.

Answer:

20 miles

Step-by-step explanation:

10miles × 2 = 20miles

Answer:

StartFraction negative 1 Over k cubed EndFraction

Step-by-step explanation:

3k / (k + 1) × (k²- 1) / 3k³

= 3k(k² - 1) / (k + 1)(3k³)

= 3k³ - 3k / 3k⁴ + 3k³

= -3k / 3k⁴

= -1/k³

StartFraction k + 1 Over k squared EndFraction

(k + 1) / k²

StartFraction k minus 1 Over k squared EndFraction

(k - 1)/k²

StartFraction negative 1 Over k cubed EndFraction

= -1/k³

StartFraction 1 Over k EndFraction

= 1/k

Answer:

B: k - 1 / k^2

Step-by-step explanation:

Since this is a right triangle, we can use one of the three main trigonometric functions: sine, cosine, or tangent.

Remember: SOH-CAH-TOA

Looking from the angle, we know the opposite side and the hypotenuse. Therefore, we should use the sine function.

sin(x) = 21/40

x = sin^-1(21/40)

x = 32 degrees

Hope this helps!

The axis of symmetry always passes through the vertex of the parabola . The x -coordinate of the vertex is the equation of the axis of symmetry of the parabola. For a quadratic function in standard form, y=ax2+bx+c , the axis of symmetry is a vertical line x=−b2a .

Answer:

5

Step-by-step explanation:

Answer:

[tex]4=1/2gt^{2}[/tex]

Multiply equation by 2/g

4(2/g) = t²

t = √(8/g)

t = 2√(2/g)

[tex]answer:t=\sqrt{\frac{8}{g} }[/tex]

OAmalOHopeO

Answer:

Origin = (0, 0)

Gradient or slope:

[tex]{ \tt{slope = \frac{(0 - 3)}{(0 - ( - 2))} }} \\ { \tt{slope = - \frac{3}{2} }}[/tex]

General equation of line:

[tex]{ \bf{y = mx + c}}[/tex]

Consider the origin:

[tex]{ \tt{0 = ( - \frac{3}{2} \times 0) + c }} \\ c = 0[/tex]

Equation of line:

[tex]{ \tt{y = - \frac{3}{2}x }} \\ { \tt{2y = - 3x}}[/tex]

Answer:

-2y+3x=0

Step-by-step explanation:

Slop=(3-0)/(-2-0)=-3/2

(Y-Y1) =m(x-x1)

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

-2y+3x=0

Answer:

64

Step-by-step explanation:

1=879=96889=