Question 12 (5 points)
Find the value x in the figure below and write your answer below.

We are given:

An even number 'n', multiplied by the next consecutive even number is 168

Solving for n:

From the given statement, we can say that:

n(n+2) = 168                      [n multiplied by the next even number 'n+2']

n² + 2n = 168

n² + 2n - 168 = 0               [subtracting 168 from both sides]

We can see that we now have a quadratic equation, solving using splitting the middle term

n² + 14n - 12n - 168 = 0

n(n + 14) -12(n + 14) = 0      [factoring out common terms]

(n-12)(n+14) = 0

Here, we can divide both sides by either (n-12) OR (n+14)

Checking the result in both the cases:

(n + 14) = 0/(n-12)                     (n-12) = 0/(n+14)

n + 14 = 0                                 n - 12 = 0

n = -14                                      n = 12

Both these values are even and since we are not told if the number 'n' is positive or negative, both 12 and -14 are the possible values of n

Answer:

we have:

u(1) = 18

u(2) = 21 = 18 + 3

u(3) = 24 = 18 + 3.2

u(4) = 27 = 18 + 3.3

.......

=> the sequence has: u(1) = 18

                                    d = 3

=> u(n) = 18 + 3(n - 1) = 3n + 15

so the recursive formula for the sequence is u(n) = 3n + 15

Step-by-step explanation:

Answer:

Fourth choice, 16

Step-by-step explanation:

The 2 angles are both 74 degrees, so the side that is facing each angle will be the same length, so:

9x - 73 = 3x + 23

add 73 to both sides

9x = 3x + 96

subtract 3x from both sides

6x = 96

divide by 6

x = 16

Answer:

c

Step-by-step explanation:

Answer:

8.246 units long

2sqrt(17) units long in simplest radical form

Step-by-step explanation:

Use the Pythagorean Theorem to find the missing leg length:

a^2+b^2=c^2

4^2+b^2=sqrt(84)^2

16+b^2=84

b^2=68

b=sqrt(68)

b=2sqrt(17) <-- Simplest Radical Form

b=8.246

So the third side is approximately 8.246 units long

Answer:

16.4%

Step-by-step explanation:

$1665=100%

$53.40=?

53.40×100÷1665

=16.4%

Answer:

True

Step-by-step explanation:

3n + 7 = 16 (equation)

3n = 9

n = 3 (answer

Answer:

The answer is z= 7.5

Step-by-step explanation:

Answer:

Step-by-step explanation:

56

Answer:

x=-3

x=-4

Step-by-step explanation:

-2|7+2x|=-2

|7+2x|=1

7+2x=1

x=-3

7+2x=-1

x=-4

Answer:

cross multiply

Step-by-step explanation:

Answer:

OOOoOOOOOOOOooOOooOOOoOoOoOoOoOoOooooooooOOOOFFFFFFFFFFFFFFFFFFFFF

Step-by-step explanation:

You did the same thing to me

Step-by-step explanation:

you need to mulitiply the 4 to x and -3

4x-12

if you need to solve for x: 4x=12

X=3

The answer is 4x-12

if you multiply 4 times x it is 4x, and if you multiply 4 by negative 3(-3) the answer is negative 12 (-12), so you put 4x together with -12 that would be 4x-12

Answer:

your answer would be 1kg

Step-by-step explanation:

Answer: The largest one is 1kg

Step-by-step explanation:

Answer:

x=11

Step-by-step explanation:

since the triangle is an isosceles triangle, angle 2 should be angle 42 so,

2x+20=42 degrees

2x=22

x=11

Answer:

x = 6

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Step-by-step explanation:

Step 1: Define Equation

3 - 2x = -1.5x

Step 2: Solve for x

Step 3: Check

Plug in x into the original equation to verify it's a solution.

Here we see that -9 does indeed equal -9.

∴ x = 6 is the solution to the equation.

Answer:

x= 6

Step-by-step explanation:

3-2x= -1.5x

-3       -3

-2x= -1.5x - 3

+1.5x   +1.5x

-.5x= -3

divide both sides by -.5

x = 6

Answer:

70 kg

Step-by-step explanation:

[tex]\frac{5}{8}*\frac{112}{1}kg\\\frac{5}{1}*\frac{14}{1}kg\\5 * 14kg\\70 kg[/tex]

Decreasing 112kg by 3/8 is equal to 70kg.

A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.

We have two types of fractions.

Proper fraction and improper fraction.

A proper fraction is a fraction whose numerator is less than the denominator.

An improper fraction is a fraction where the numerator is greater than the denominator.

Example:

1/2, 1/3 is a fraction.

3/6, 99/999 is a fraction.

1/4 is a fraction.

We have,

To decrease 112kg by 3/8,

we can multiply 112 by 3/8 and then subtract the result from 112:

112 - (112 x 3/8)

First, we simplify 3/8 by finding a common denominator of 8:

= 3/8

= 3/8 x 8/8

= 24/64

So we have:

112 - (112 x 24/64)

To simplify this expression, we can first divide both the numerator and denominator of 24/64 by the greatest common factor, which is 8:

= 24/64

= (24 ÷ 8) / (64 ÷ 8)

= 3/8

Substituting this value, we get:

112 - (112 x 3/8)

Multiplying 112 by 3/8, we get:

= (112 x 3/8)

= (336/8)

= 42

Substituting this value, we get:

= 112 - 42

= 70

Therefore,

Decreasing 112kg by 3/8 is equal to 70kg.

Learn more about fractions here:

https://brainly.com/question/24370499

#SPJ3

Answer:

here's how you calculate sales tax after a discount.

Sale Price = original price – (% of discount * original price)

Sales Tax = Sales Tax rate * Sale Price.

Sales Tax = 0.05 * $17.21 = $0.8605 = $0.86.

Step-by-step explanation:

Answer:

38:48=3:4

48:42= 8:7

20:30= 2:3

16:14=8:7

9:12=3:4

56:49=8:7

24:32=3:4

24:36=2:3

18:27=2:3

Answer:

He’s a good man

Step-by-step explanation:

Answer:

20 %

Step-by-step explanation:

tell me if I'm wrong , your welcome and merry Christmas !!

Answer: 20%

Step-by-step explanation: 50 times 5 is 250. If you take 5 out of 100 you get 20’s

Answer: y - $50 = $5*(x - 3)

Step-by-step explanation:

We know that each ticket is sold at $5.00

The band initially had an amount of money M.

We know that after selling 3 tickets, the band had $50

We can write this as:

M + 3*$5.00 = $50

M + $15 = $50

M = $50 - $15 = $35

We want to write the equation for the account in the point-slope form.

We know that the slope will be equal to the cost of a single ticket, and we already have the point:

x = 3

y = $50

Then we can write:

y - $50 = $5*(x - 3)

This is the equation we wanted to find.

Answer:

Step-by-step explanation:

the shaded area would be

200*75=15,000 ft^2

from this are we have to subtract the are of the house and of the  garage

house= 40*40=1600

garage=24*30=720

house and garage= 1600+720=2320

15,000-2320=12,680

Answer:

12680 ft²

Step-by-step explanation:

First we will find the area of the house and then the garage.

They're both rectangles so we should use this formula [tex]A=l*w[/tex].

Area Of The House:

[tex]A=l*w\\A=40*40\\A=1600ft^2[/tex]

Area Of The Garage:

[tex]A=l*w\\A=24*30\\A=720ft^2[/tex]

Adding the two areas:

Now we have to add the two together to find how much of the space they take up in the yard.

[tex]1600+720=2320[/tex]

Area Of The Yard:

[tex]A=l*w\\A= 200*75\\A=15000ft^2[/tex]

Subtracting The Two Areas To The Yard's Area:

[tex]15000-2320=12680ft^2[/tex] and that is it!

Answer:

x = 20

Step-by-step explanation:

The length of the segment EG can be obtained as the sum of the segments EF and FG, that is:

EG = EF + FG

We are given:

EF = 4x + 14

FG = 50

EG = 144

Thus, we set the equation:

144 = 4x + 14 + 50

Simplifying:

144 = 4x + 64

Subtracting 64:

80 = 4x

Dividing by 4:

x = 80/4 = 20

x = 20

Answer:

Step-by-step explanation:

Time taken in each lap = 4 min

Total laps = 11

Total time = 11 x 4 = 44min

Answer:

44 minutes

Step-by-step explanation:

4 minutes per lap . He is running 11 laps. Multiply 4 times 11 and it equals 44