Karl’s rectangular vegetable garden is 20 feet by 45 feet, and Makenna’s is 25 feet by 40 feet. Whose garden is larger in area?

Answer:

[tex]a_n=\frac{1}{2}a_{n-1}[/tex]

Step-by-step explanation:

Here, you can see every consecutive term is divided by 2. I think that's pretty obvious looking at it, but you can work it out like this if you'd like to. Divide each consecutive term by the one before it:

[tex]6\div12=\frac{1}{2}\\\\3\div6=\frac{1}{2}\\\\\frac{3}{2}\div3=\frac{1}{2}[/tex]

Each term is multiplied by 1/2 over the last, or divided by 2. In this case actually, we do want it in the form of "multiplied by 1/2", as the recursive equation is:

[tex]a_n=xa_{n-1}[/tex]

where x is the factor. Here, we're multiplying by x, so we want "multiplied by 1/2" as described above. x is 1/2, so you can write the equation:

[tex]a_n=\frac{1}{2}a_{n-1}[/tex]

You can simply interpret this as "each term is 1/2 of the term before it"

[tex]a(n) = {n}^{2} + 3[/tex]

Answer:

nth term is equal to n²+3

Answer:

  a) m = 60°, n = 30°

  b) m = 20°, n = 45°

Step-by-step explanation:

The top and bottom horizontal lines are parallel, so angle m is an alternate interior angle congruent to the interior angle(s) of the equilateral triangle. Those angles are all 60°.

Angle n is the complement of angle m, so is 90°-60° = 30°

  m = 60°, n = 30°

__

The base angles of the isosceles right triangle are n = 45°. (This should be a memorized fact. It is computed as (180° -90°)/2 = 45°.)

The base angles of the isosceles acute triangle are (180°-50°)/2 = 65°. Angle m is the difference between one of these and angle n.

  m = 65° -45° = 20°

  m = 20°, n = 45°

_____

Additional comment

The sum of angles of a triangle is 180°. The "base" angles of an isosceles triangle (one with two equal sides) are equal. If 'a' is the third angle, and 'b' are the base angles, you have ...

  a + 2b = 180°

  2b = 180° -a

  b = (180° -a)/2 . . . . . . the relation used above

Answer:

C

Step-by-step explanation:

5x+15+2=5x+17

2 Simplify 5x+15+25x+15+2 to 5x+175x+17.

5x+17=5x+17

5x+17=5x+17

3 Since both sides equal, there are infinitely many solutions.

Infinitely Many Solutions

Answer:

I am pretty sure it is y=22-4x/3

Step-by-step explanation:

4x+3y=22

(you need to put it in y=mx+b format)

-subtract 4x on both sides-

3y=22-4x

-divide by 3 on both sides-

y=22-4x/3

Not sure if this is correct, but I hope this helps!

The parking lot is located along the front and one side of the school

building.

Reasons:

The given dimensions in the compound are;

Length of the school and the old parking lot = 300 + 75

Width of the school and the old parking lot = 165 + 75

Length of the school, the old and new parking lot = 300 + 75 + x

Width of the school and the old and new parking lot = 165 + 75 + x

Area of the new parking lot the school wants = Double the old parking lot

In terms of areas, we have;

New compound - School = 2 × (old compound - school)

Which gives;

(300 + 75 + x) × (165 + 75 + x) - 300 × 165 = 2 × ((300 + 75) × (165 + 75) - 300 × 165)

2 × (375 × 240 - 49,500) = (375 + x) × (240 + x) - 49,500

Simplifying gives;

81,000 = x² + 615·x + 40,500

x² + 615·x + 40,500 - 81,000 = 0

x² + 615·x - 40,500 = 0

Factorizing with a graphing calculator gives;

(x - 60)·(x + 675) = 0

Therefore;

x = 60 or x = -675

Given that x is a natural number, we have, the correct value is; x = 60;

The distance with which the lot should be expanded, x = 60 feet.

Learn more about writing equations here:

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Answer:

Part A:

Gwen equation

x + 10y = 30

Part C:

Keith equation:

x + 10y = 30

Part B:

Tristan equation:

x + 15y = 40

Part D:

You would use Keith's and Tristan's equation, because Gwen and Keith have the same exact equation so you can just use Keith's equation.

Part E:

Multiply the second equation by -1, then add the equations together.

(x+10y=30)

-1(x+15y=40)

Becomes:

x + 10y = 30

-x - 15y = - 40

Add these equations to eliminate x:

-5y = -10

-5y/5 = -10/5

so y = 2

Now lets find x, so lets plug it in x + 10y = 30.

x + 10(2) = 30

x + 20 = 30 ( do 30-20)

x = 10

We used elimination to solve this problem.

The entree fee is $10 and each ticket costs $2.

Part F:

For this part search graph tool and go on the app, then put Keith's and Tristan's equation in Graph Tool. Once you do that just screenshot it and paste it to Part F, then your answer should be Yes, you get the same solution when it is solved algrebraically.

Step-by-step explanation:

I really hope this helps you!!!! :D Mark brainliest if it does!!!!

Answer: Part A:

Gwen equation

x + 10y = 30

Part C:

Keith equation:

x + 10y = 30

Part B:

Tristan equation:

x + 15y = 40

Part D:

You would use Keith's and Tristan's equation, because Gwen and Keith have the same exact equation so you can just use Keith's equation.

Part E:

Multiply the second equation by -1, then add the equations together.

(x+10y=30)

-1(x+15y=40)

Becomes:

x + 10y = 30

-x - 15y = - 40

Add these equations to eliminate x:

-5y = -10

-5y/5 = -10/5

so y = 2

Now lets find x, so lets plug it in x + 10y = 30.

x + 10(2) = 30

x + 20 = 30 ( do 30-20)

x = 10

We used elimination to solve this problem.

The entree fee is $10 and each ticket costs $2.

Part F:

For this part search graph tool and go on the app, then put Keith's and Tristan's equation in Graph Tool. Once you do that just screenshot it and paste it to Part F, then your answer should be Yes, you get the same solution when it is solved algrebraically.

Step-by-step explanation:

I really hope this helps you!!!! :D Mark brainliest if it does!!!!

Step-by-step explanation:

Answer:

Parallel: a and b

Perpendicular: none

Step-by-step explanation:

You are given the coordinates of each line.

To check if they are parallel or perpendicular, need to find slope.

In this case we can use :

m = (y2 - y1) / (x2 - x1)

So for line a:

(1,5) and (-2, -4)

slope = (-4 - 5) / (-2 - 1)

slope = -9/-3

slope = 3

Line b:

(3, 2) and (1, -4)

slope = (-4 - 2)/(1 - 3)

slope = -6/-2

slope = 3

Line C:

(6, 1) and (-4, 2)

slope = ( 2 - 1) / ( -4 -6)

Slope = 1/ -10

slope = - 1/10

Line A and B are parallel because their slopes are the same.

To check if they are perpendicular, we need to know if their slopes are reciprocals.

Here none of them are perpendicular to each other

Answer:

b= -1/5

Step-by-step explanation:

Though a variable's sign changes when it is multiplied by -1, its absolute value does not. Therefore, we can eliminate the 1:

1/5+b=0

b+1-1/5=0-1/5

b+0/5= 0 -1/5

b=0 -1/5

and you have b= -1/5 as your answer

Answer:

5

Step-by-step explanation:

3x - 5 = 10

3x = 15

x = 5

I hope it helps bye, good luck

Answer:

x=5

Step-by-step explanation:

Move all terms not containing  x  to the right side of the equation.

Add  5 to both sides of the equation.

3x = 10 + 5

Add 10 and 5

3x = 15

Divide each term in  3x = 15  by 3  and simplify.

3x/3 = 15/3

Simplify the left side

Cancel the common factor of  3

x = 15/3

Divide 15 by 3

x = 5

Answer:

divide both sides by 5

Step-by-step explanation:

y + 12 = 5

y = -7

Answer:12

Step-by-step explanation:

Hello there, this is how we would solve this problem, we can see that angle KAE equals 90° and we have an angle that equals 62° now since angle GCJ or also known as x is a vertical angle with IAD we can make the following equation

[tex]x+62+90=180[/tex] subtract 62 and 90 from both sides and we get that [tex]x=28[/tex]°

Answer:

d = 6

Step-by-step explanation:

sorry for late awenser

The value of the equation is d = 6

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

4 ( d - 5 ) - 6 = 2 ( 8 - d ) - d   be equation (1)

On simplifying the equation , we get

4d - 20 - 6 = 16 - 2d - d

On further simplification , we get

4d - 26 = 16 - 3d

Adding 3d on both sides of the equation , we get

7d - 26 = 16

Adding 26 on both sides of the equation , we get

7d = 42

Divide by 7 on both sides of the equation , we get

d = 6

Therefore , the value of d is 6

Hence , the equation is d = 6

To learn more about equations click :

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1. -2 + 15 = 13

If the temperature is -2 and it rises 15 degrees, the new temperature is 13 degrees.

2. The temperature rose 15 degrees

-6 + 9 = 15

Answer:

1 a) 13 degrees Celsius

b) By fifteen degrees

Answer:

15 Nachos and 23 Powerades were sold.

Brainliest is appreciated. (The crown)

A perfect square trinomial is represented by the equation [tex]x^2-6x+9[/tex] and this can be determined by using the factorization method.

Given :

A perfect square trinomial can be represented by a square model with equivalent length and width.

The following steps can be used in order to determine the polynomial that can be represented by a perfect square model:

Step 1 - First, check option a) [tex]x^2-6x+9[/tex] is a perfect square or not.

Step 2 - Try to factorize the above equation.

[tex]x^2-6x+9 = x^2-3x-3x+9[/tex]

[tex]x^2-6x+9 = x(x-3)-3(x-3)[/tex]

[tex]x^2-6x+9 = (x-3)^2[/tex]

Step 3 - The equation in option a) represents the perfect square trinomial.

From, the above steps, it can be concluded that the correct option is a).

For more information, refer to the link given below:

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Answer:

B and A

Step-by-step explanation:

What I did for these problems is plug in the numbers listed for the x-value. For example, in your calculator you’d put; (1/2)^3 and that’d get you 1/8. Then, try it for 8^(2 - 3) which is also 1/8. So, (1/2)^3 = 8^(2 - 3).

The same process for the second problem. 16^(2(7/3) -3) = 4^((7/3) + 1). This should give you 101.59…

I hope this helps :)!

Answer:

Good night sagey!!!! sleep well

Answer:

B, 13.2

Step-by-step explanation:

Multiply 60 by 0.22 for your answer and you get 13.2

Answer:

answer is D

Step-by-step explanation:

speed = distance divide by time.

299.8/ 7 .5

40

Answer:

488

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

That means 4.3 (2.7) = 7

The negative signs get removed because negative × negative = positive

Answer:

A=5.375

Step-by-step explanation:

46.28-3.28= 43

43÷8= 5.375

I hope this helps

Answer:

x = 4

y = 2

Step-by-step explanation:

1) y = 5x - 6

2) y = 4x - 2

sub 1 into 2

5x - 6 = 4x - 2

5x - 4x = 6 - 2

x = 4 ---> (3)

sub 3 into 2

y = (4 * 1) - 2

y = 4 - 2

y = 2

Answer:

4

Step-by-step explanation:

Since they both equal y, they are both equivinlent

[tex]5x-6=4x-2[/tex]

[tex]5x=4x+4[/tex]

[tex]x=4[/tex]

CHECK

[tex]20-6=16-2[/tex]

[tex]14=14[/tex]

Answer:

Vincent will be able to buy the sneakers, while David will not be able too.

Step-by-step explanation:

I believe this is true because for David,

6% of 86$ is 5.16$

so 86 + sales tax (which is 5.16) = 91.16$

David only has 90$ so he can't afford the sneakers. They are 1.16$ over his budget.

While for Vincent,

9% of 86$ is 7.74$

so 86 + sales tax (which in this case is 7.74) = 93.74

Vincent has 95$ to spend so he can afford the shoes.

I am not exactly sure if all calculations are correct, but I hope this helps! :)

Answer:

Vincent          

I took the test on edg

Answer:

1/6

Step-by-step explanation:

-3/4 - (-1/2) = - 1/4

-2/3 - 5/6 = - 3/2

-1/4 ÷ -3/2

(2,5) and (4,13)

y - y1 = y2 - y1

x - x1    x2 - x1

y - 5  = 13 - 5 = 8/2 = 4 x - 2     4 - 2

y - 5 = 4x - 8

y = 4x - 3

m = 4, c = -3

Answer:

525

Step-by-step explanation:

hope this helps

Answer:

526

Step-by-step explanation: