3x + y = 4 6x + 4y = 6 equivalent equation and solution

[tex]~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ J^3=0.125\implies J^3=\cfrac{0125}{1000}\implies J^3=\cfrac{1}{8}\implies J^3=\cfrac{1}{2^3} \\\\\\ J^3=2^{-3}\implies J^3=(2^{-1})^3\implies J=2^{-1}\implies J=\cfrac{1}{2}[/tex]

Answer:

Step-by-step explanation:

A corresponds to angle P, so angle P measues 70 degrees.

Similarly, angle Q measures 60 degrees and angle R measures 50 degrees.

Answer:

283 m^2

Step-by-step explanation:

To find the area of a circle, you need to times pi, in this case 3.14, by the radius,9.5 here, squared.

A= π (r^2)

Answer:

200+10×12=320

Step-by-step explanation:

Answer:

1 is 9 sq units

2 is 12

3 is 24cm^2

Step-by-step explanation:

Answer:  "How do u calculate the diameter of a circle"?

Step-by-step explanation:  Calculating diameter is easy you just need the radius, the circumference, or the area. Even if you don't have any of those dimensions, you can still find the diameter if you have a drawing of the circle.

The best chance is an illustration of probability

The 21st position in line gives you the best chance of being the first duplicate birthday

Assume you are in the nth position, the probability of getting a free ticket is:

P(n) = P'(first n - 1 people share a birthday) * P(birthday with first n -1 people)

Mathematically, the above can be represented as:

P(n) = [365/365 * 364/365 * 363/365 * ... * (365 - (n -2))/365] * [(n -1)/365]

Such that: n [tex]\le[/tex] 365

When simplified, the equation becomes

p(n)/p(n+1) = 365/(366 - n) * (n - 1)/n

Where

p(n)/p(n+1) > 1

So, we have:

365/(366 - n) * (n - 1)/n > 1

Evaluate the product

(365n -365)/(366n - n²) > 1

Cross multiply

365n -365 > 366n - n²

Collect like terms

n² + 365n - 366n - 365 > 0

Evaluate the difference

n²  - n - 365 > 0

Solve for n using a graphing calculator;

n > - 18.6 or n >19.6

n cannot be negative.

So, we have:

n > 19.6

Approximate to nearest integer

n > 20

The least integer value of n is:

n = 21

Hence, the 21st position in line gives you the best chance of being the first duplicate birthday

Read more about probability at:

https://brainly.com/question/25870256

IJKL is a rectangle, so opposite sides have the same length:

• IJ = KL   ⇒   6y - 6 = 2x + 20

• JK = IL   ⇒   3x + 21 = 6y

Substitute the second equation into the first and solve for x :

6y - 6 = 2x + 20

(3x + 21) - 6 = 2x + 20

3x + 15 = 2x + 20

x = 5

Solve for y :

3x + 21 = 6y

15 + 21 = 6y

36 = 6y

y = 6

Answer:

32

Step-by-step explanation:

Answer:

32

Step-by-step explanation:

Answer:

122 and 58

Step-by-step explanation:

Answer:

7⁵-3=7⁵x- 19

Step-by-step explanation:

16807 - 3 = 7⁵x - 19

16804 = 7⁵x - 19

16804 = 16807x - 1

adding 19 on both sides

16804 + 19 = 16807x - 19 + 19

16823 = 16807x

x = 16823 / 16807

16823 upon 16807 is the x

Answer: 1/2

Step-by-step explanation: This is a coin. Having heads three times in a row will never change that a coin is two sided and random, meaning it will never affect the coin to always be heads. They were most likely just lucky to get heads all the time. It will always be 1/2 since the coin is inanimate and is not like selecting classmates from a team, it cannot know it's probabilities and affect it. Thus it is 1/2 probability.

This can be simplified in the equation: P(H) = 1/2, P(T) = 1/2, P(H | T) = 1/2

Answer: 75 Degrees

Step-by-step explanation: 1. Due to the law of opposite adjacent angles, we can determine angle 1 is congruent to angle 4 and therefore is 15 degrees 2. Angle 3 is shown to be a right angle (90 degrees) 3. Since angles 1,2, and 3 are on a flat line, the sum of all 3 is 180 4. 15+90 is 105 5. 180-105 is 75 which is the measure of angle 2

Directly solving the linear equations, we will see that:

Let's start with the first one:

3 - x = 11 + x

First, move all the terms with x to the left side and the ones without to the right side:

-x -x = 11 - 3

-2x = 8

Now we divide both sides by -2

x = 8/-2 = -4

x = -4

2) 2x + 7 = 3x + 1

Same procedure:

2x - 3x = 1 - 7

-x = -6

x = -6/-1 = 6

x = 6

3) 8 - 2x = 4 + x

-2x - x = 4 - 8

-3x = -4

x = -4/-3 = 4/3

4) 4x + 2 = 2x + 6

4x - 2x = 6 - 2

2x = 4

x = 4/2 = 2

x = 2

So we solved all linear equations.

If you want to learn more about linear equations, you can read:

https://brainly.com/question/1884491

Answer:

See below, please

Step-by-step explanation:

The right：

[tex] {(y + c)}^{2} - b \times (x + a) \\ = ( {y}^{2} + 2yc + {c}^{2} ) - bx - ba = [/tex]

[tex] = {y}^{2} - bx + 2cy + {c}^{2} - ab[/tex]

The left:

[tex] = {y}^{2} - 7x - 18y + 109[/tex]

So, after comparing the right side and the left side of this equation, we know

1)

[tex]b = 7[/tex]

2)

[tex]2c = - 18 \\ so \\ c = - 9[/tex]

3)

[tex] {c}^{2} - ab = 109[/tex]

So,

[tex]a = \frac{ {c}^{2} - 109}{b} = \frac{ { (- 9)}^{2} - 109}{7} = \frac{ - 28}{7} = - 4[/tex]

Answer:

Your answer is 8.75 or 8 ¾

Step-by-step explanation:

3 ½ × 2 ½ = 8 ¾

Have a nice day! :)

Answer:

the answer is 6 1/2

Step-by-step explanation:

I solved using calculator

Answer:

6 1/2

Step-by-step explanation:

Answer:

8 1/2

Step-by-step explanation:

14 inch - 5 1/2 inches = 8 1/2 inches

Aba's dog grew 8 1/2 inches.

Answer:

8.5 Inches, 2.78 pounds approximately

Step-by-step explanation:

14- n = 5.5. In this case you will have to subtract 5.5 from 14. 14 - 5.5 = 8.5. You get 2.5 pounds because, 1.10 x 2 = 2.20. 2.75 - 2.20= .55. $1.10 is 70 cents. 55/70 = 11/14= is around .78. 2+.78 = 2.78

Answer:

Step-by-step explanation:

where is the prism???

   i can't answer without seeing the question

Answer: [tex]12\pi[/tex]

Step-by-step explanation:

The formula for area of a circle is [tex]\pi r^2=A[/tex]

The formula for circumference of a circle is [tex]2r\pi=C[/tex]

Where r is the radius

A is area

C is circumference

Knowing this we can sub our values in and solve for r in the formula for area

Divide both sides by [tex]\pi[/tex] to isolate r

[tex]\pi r^2=A\\\pi r^2=36\pi \\\frac{\pi r^2}{\pi } =\frac{36\pi }{\pi } \\r^2=36[/tex]

Take the square root of both sides

[tex]r^2=36\\\sqrt{r^2} =\sqrt{36} \\r=6[/tex]

Now sub the value of r into the formula for circumference

[tex]2r\pi =C\\2(6)\pi =C\\12\pi[/tex]

Answer:

[tex]12\pi \: c \: m[/tex]

step by step explanation:

[tex]area \: of \: a \: cirle = \pi \: r {}^{2} \\ circmferene \: of \: a \: circle = 2 \:\pi \: r \\ 36\pi = \pi \: r {}^{2} \\ 36 = r {}^{2} \\ r = 6 \\ for \: circmference \\ 2 \times \pi \: \times 6 = 12\ \: \pi \: cm [/tex]

Answers:

Reason 23: Given

Reason 24: Reflexive Property

Reason 25: AAS

========================================================

Explanation:

Reason 23 is given because we simply restate the initial facts word for word. Whatever is said at the top "given" is copy/pasted into the table below. This explains why the second reason is "given" as well.

Reason 24 is "Reflexive Property" because any segment is congruent to itself. Think "reflexive" as in "mirror reflection".

For reason 25, we will use the AAS (angle angle side) congruence theorem. This is because we have two pairs of congruent angles (statement 1 and statement 2) as well as a pair of congruent sides (statement 3). We don't use ASA because the side FY is not between the angles mentioned. The order is important. Check out the diagram below. Take note of the color coding for the angles.

Answer:

The answer would be 20.97273616 or (rounded to the nearest cent) would be $20.97

Step-by-step explanation:

The reason for this is that the formula for compounded interest is [tex]A=P(1+\frac{r}{n})^\frac{t}{n}[/tex] where A is the total amount, P is the initial amount, r is the growth factor or the percent, n is the number of compounding periods, and t is the time. You would substitute P for 16, r for 0.14 (14%), n for 2 as it compounded semiannually so it for every 6 months instead of 1 year (annual) so is compounded 2 times per year, and t for 2. And just solve the equation and you get that A is equal to 20.97273616 but since we are talking about money( only round if asked) then it would be 20.97.

Hope this helps!!!!  

[tex]\bull[/tex]Total number of seats in theatre = 4500

[tex]\bull[/tex]Total number of seats left vacant = 3105

[tex]\longrightarrow[/tex]Number of seats occupied = Total number of seats in theatre - Total number of seats left vacant

[tex]\longrightarrow[/tex]Number of seats occupied

[tex]\quad[/tex]= 4500 - 3105

[tex]\longrightarrow[/tex] 1395

[tex]\\[/tex]

Now,

[tex]\begin{gathered}\bull \sf Percentage \:of \:seats \:filled = \frac{Seats \: filled \: by \:6th \:grader }{Total \:number \:of \:seats} \times 100 \% \\\end{gathered} [/tex]

[tex]\begin{gathered}\bull \sf Percentage \: of \:seats \: filled = \frac{1395}{45\cancel{00}} \times \cancel{100} \% \\\end{gathered} [/tex]

[tex]\begin{gathered}\implies\quad \sf \frac{1395}{45} \% \\\end{gathered} [/tex]

[tex]\begin{gathered}\implies\quad \sf 31 \% \\\end{gathered} [/tex]

[tex]\longrightarrow[/tex]Thus , 31 % of seats in the theater were filled by the 6th graders on the trip

Answer:

5.575

Step-by-step explanation:

divide it by 2 its easy

Hi again! The answer is 200 students

Would you like me to help explain so you can do these questions on your own? :)

Answer:

Step-by-step explanation:

7) Volume of the shape = Volume of triangular prism - volume of cylinder

Triangular prism:

[tex]\boxed{ \text{Volume of triangular prism = base area * h }}[/tex]

b = 6 ft & height of the triangle = 5 ft

[tex]\sf Base \ area = \dfrac{1}{2}* 6* 5[/tex]

               = 3*5

               = 15 ft²

Volume of prism = 15 * 4

                           = 60 ft³

Cylinder:

r = 2÷2 = 1 ft & h = 4 ft

Volume of cylinder = 3.14 * 1 * 1 * 4

                                = 12.56 ft³

Volume of the shape = 60 - 12.56

                                    = 47.44 ft³

8) Volume = Volume of Pyramid -  Volume of cone

[tex]\boxed{\text{Volume of the Pyramid = base area * h} }[/tex]

[tex]\text {base area = length * width}\\\\\\[/tex]

                = 9 * 9

                = 81 m²

Volume of Pyramid = 81 * 8

                                = 648 m³

[tex]\boxed{ \text{Volume of cone = \dfrac{1}{3} \pi r^{2}h}}[/tex][tex]\boxed{ \text{Volume of cone = $\dfrac{1}{3} \pi r^{2}h$}}[/tex]

r = diameter ÷ 2 = 6÷2

r = 3 m & h = 8 m

[tex]\text{ Volume of cone =$\dfrac{1}{3}*3.14* 3*3*8$}[/tex]

                        = 3.14 * 3 * 8

                        = 75.36 m³

Volume of the shape = 648 - 75.36

                                     = 572.64 m³

9) Volume of the shape = volume of cylinder + volume of cone

Cylinder:

h = 7 in ; r = 3

[tex]\boxed{\text{Volume of cylinder =$ \pi r^{2}h$}}[/tex]

                                [tex]=\dfrac{22}{7}*3*3*7[/tex]

                                  = 22 *3 * 3

                                   = 198 in³

Cone:

r = 3 in & h = 4 in

[tex]\text{Volume of cone = $ \dfrac{1}{3}*3.14*3*3*4$}[/tex]

                         = 3.14 * 3 * 4

                          = 37.68 in³

Volume of the shape = 198 + 37.68

                                     = 235.68 in³

10) Volume of the shape = Volume of outer cyliner - volume of inner cylinder

Volume of outer cylinder:

R = 9 m  & h = 3 m

Volume of outer cylinder = 3.14 * 9 * 9 * 3

                                          = 763.02 m³

Volume of inner cylinder:

r = 5 m & h = 3 m

Volume of inner cylinder = 3.14  * 5 * 5 * 3

                                          = 235.5 m³

Volume of the shape = 763.02 - 235.5

                                    = 527.52 m³

Answer:

x ^5/3 y ^1/3 (the second option listed)

Step-by-step explanation:

So without even solving the expression, you can find the correct option. If you're finding the cube root (or really any square root), you know it will be less than your original number (unless you are working with imaginary numbers, but you aren't).

So, if you are finding the cube root of an expression, you're finding the cube root of each number separately.

You wouldn't be cubing y, you would be finding the cube root. You wouldn't be leaving y the same, you are finding the cube root.

This means that without even solving (which I will explain),

the correct option is the second one on the screen.

Here's how to actually solve the equation:

So, if we are finding the cube root of a variable with an exponent, we can divide that exponent by 3 (because it is a cube root).

When we have a square root, you know that we are breaking down each number/variable into an even exponent to solve the expression. When taking the square root of an even exponent, such as 4, you would divide by 2.

This same strategy applies to cube roots. You are dividing the exponent of both variables by 3.

[remember: the exponent of a variable without an exponent is essentially an invisible exponent of 1.]

Answer:

She will pay $40 more.

Step-by-step explanation:

I used the equation y=27.50x + 25 to find this out and made x = 12 to represent how many months she is paying.

now putting x into the equation, y = 27.50(12) + 25

First i did the multiplication, 27.50 x 12 = $330.

Then I added 25 to 330 for the down payment, 330 + 25 = 355

I then did 355 - 315 to find out how much more you would pay,

355 - 315 = $40

Hope this helps!

Step-by-step explanation:

Domain of a rational function is everywhere except where we set vertical asymptotes. or removable discontinues

Here, we have

[tex] \frac{x(2x - 3)}{(x + 2)x} [/tex]

First, notice we have x in both the numerator and denomiator so we have a removable discounties at x.

Since, we don't want x to be 0,

We have a removable discontinuity at x=0

Now, we have

[tex] \frac{2x - 3}{x + 2} [/tex]

We don't want the denomiator be zero because we can't divide by zero.

so

[tex]x + 2 = 0[/tex]

[tex]x = - 2[/tex]

So our domain is

All Real Numbers except-2 and 0.

The vertical asymptors is x=-2.

To find the horinzontal asymptote, notice how the numerator and denomator have the same degree. So this mean we will have a horinzontal asymptoe of

The leading coeffixent of the numerator/ the leading coefficent of the denomiator.

So that becomes

[tex] \frac{2}{1} = 2[/tex]

So we have a horinzontal asymptofe of 2

Answer:

1020 cans

Step-by-step explanation:

100-25

=75%

0.75x1600

1200cans

100-15

=85%

0.85x1200

=1020 cans