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weeeeeb [17]
3 years ago
11

Seahorses change color and swim together in predetermined ways before mating. These behaviors are called

Mathematics
2 answers:
Anastasy [175]3 years ago
7 0
The answer is c.
i have sea horses
grin007 [14]3 years ago
4 0
Courtship rituals.

so C.
You might be interested in
I am a 3 digit number. The sum of my digits is 14. My ones place is 3 times as much as my hundreds place.
Murrr4er [49]

Answer:

329

Step-by-step explanation:

4 0
2 years ago
(n + 12) x 5 + 7n Need equivalent expression
astraxan [27]

Answer:

12n + 60

General Formulas and Concepts:

<u>Pre-Algebra</u>

Distributive Property

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right

<u>Algebra I</u>

  • Terms/Coefficients

Step-by-step explanation:

<u>Step 1: Define</u>

(n + 12) × 5 + 7n

<u>Step 2: Simplify</u>

  1. Distribute 5:                     5(n) + 5(12) + 7n
  2. Multiply:                            5n + 60 + 7n
  3. Combine like terms:        12n + 60
6 0
3 years ago
1. The height of a triangle is 6 m more than its base. The area of the triangle is 56 m². What is the length of the base? Enter
Elodia [21]
Answers:
1. 8 m 
2. 17 m
3. 7 cm
4. 2 s

Explanations:

1. Let x = length of the base
          x + 6 = height of the base

    Then, the area of the triangle is given by

    (Area) = (1/2)(base)(height)
       56 = (1/2)(x)(x + 6)
       56 = (1/2)(x²  + 6x) 
     
    Using the symmetric property of equations, we can interchange both sides      of equations so that 

    (1/2)(x²  + 6x) = 56
    
    Multiplying both sides by 2, we have
   
    x² + 6x = 112
    
    The right side should be 0. So, by subtracting both sides by 112, we have 

    x² + 6x - 112 = 112 - 112
    x² + 6x - 112 = 0

    By factoring, x² + 6x - 112 = (x - 8)(x + 14). So, the previous equation           becomes

    (x - 8)(x +14) = 0

   So, either 

    x - 8 = 0 or x + 14 = 0

   Thus, x = 8 or x = -14. However, since x represents the length of the base and the length is always positive, it cannot be negative. Hence, x = 8. Therefore, the length of the base is 8 cm.

2. Let x = length of increase in both length and width of the rectangular garden

Then,

14 + x = length of the new rectangular garden
12 + x = width of the new rectangular garden

So, 

(Area of the new garden) = (length of the new garden)(width of the new garden) 

255 = (14 + x)(12 + x) (1)

Note that 

(14 + x)(12 + x) = (x + 14)(x + 12)
                          = x(x + 14) + 12(x + 14)
                          = x² + 14x + 12x + 168 
                          = x² + 26x + 168

So, the equation (1) becomes

255 = x² + 26x + 168

By symmetric property of equations, we can interchange the side of the previous equation so that 

x² + 26x + 168 = 255

To make the right side becomes 0, we subtract both sides by 255:

x² + 26x + 168 - 255 = 255 - 255
x² + 26x - 87 = 0 

To solve the preceding equation, we use the quadratic formula.

First, we let

a = numerical coefficient of x² = 1

Note: if the numerical coefficient is hidden, it is automatically = 1.

b = numerical coefficient of x = 26
c = constant term = - 87

Then, using the quadratic formula 

x =  \frac{-b \pm  \sqrt{b^2 - 4ac} }{2a} =  \frac{-26 \pm  \sqrt{26^2 - 4(1)(-87)} }{2(1)}  &#10;\newline x =  \frac{-26 \pm  \sqrt{1,024} }{2}&#10;\newline&#10;\newline x =  \frac{-26 \pm  32 }{2}

So, 

x = \frac{-26 + 32 }{2} \text{  or } x = \frac{-26 - 32 }{2}&#10;\newline x = \frac{6 }{2} \text{  or } x = \frac{-58 }{2}&#10;\newline \boxed{ x = 3 \text{  or } x = -29}

Since x represents the amount of increase, x should be positive.

Hence x = 3.

Therefore, the length of the new garden is given by 

14 + x = 14 + 3 = 17 m.

3. The area of the shaded region is given by

(Area of shaded region) = π(outer radius)² - π(inner radius)²
                                       = π(2x)² - π6²
                                       = π(4x² - 36)

Since the area of the shaded region is 160π square centimeters,

π(4x² - 36) = 160π

Dividing both sides by π, we have 

4x² - 36 = 160

Note that this equation involves only x² and constants. In these types of equation we get rid of the constant term so that one side of the equation involves only x² so that we can solve the equation by getting the square root of both sides of the equation.

Adding both sides of the equation by 36, we have

4x² - 36 + 36 = 160 + 36
4x² = 196 

Then, we divide both sides by 4 so that

x² = 49

Taking the square root of both sides, we have

x = \pm 7

Note: If we take the square root of both sides, we need to add the plus minus sign (\pm) because equations involving x² always have 2 solutions.

So, x = 7 or x = -7.

But, x cannot be -7 because 2x represents the length of the outer radius and so x should be positive.

Hence x = 7 cm

4. At time t, h(t) represents the height of the object when it hits the ground. When the object hits the ground, its height is 0. So,
 
h(t) = 0   (1)

Moreover, since v_0 = 27 and h_0 = 10, 

h(t) = -16t² + 27t + 10   (2)

Since the right side of the equations (1) and (2) are both equal to h(t), we can have

-16t² + 27t + 10 = 0

To solve this equation, we'll use the quadratic formula.

Note: If the right side of a quadratic equation is hard to factor into binomials, it is practical to solve the equation by quadratic formula. 

First, we let

a = numerical coefficient of t² = -16 
b = numerical coefficient of t = 27
c = constant term = 10

Then, using the quadratic formula 

t = \frac{-b \pm \sqrt{b^2 - 4ac} }{2a} = \frac{-27 \pm \sqrt{27^2 - 4(-16)(10)} }{2(-16)} \newline t = \frac{-27 \pm \sqrt{1,369} }{-32} \newline \newline t = \frac{-27 \pm 37 }{32}

So, 

t = \frac{-27 + 37 }{-32} \text{ or } t = \frac{-27 - 37 }{-32} \newline t = \frac{-10}{32}  \text{ or } t = \frac{-64 }{-32}   \newline \boxed{ t = -0.3125 \text{ or } t = 2}

Since t represents the amount of time, t should be positive. 

Hence t = 2. Therefore, it takes 2 seconds for the object to hit the ground.


 




 





3 0
3 years ago
Read 2 more answers
Explain how you can find the simplest form of 100/1000
Elina [12.6K]

You can find the simplest form by dividing both the numerator and denominator by the GCF (greatest common factor). 100 divides into 100 and 1,000 equally so that can be the GCF used to reduce the fraction into its simplest form.


\frac{100/100}{1000/100}

\frac{1}{10}


The simplest form is \frac{1}{10}.

8 0
3 years ago
Read 2 more answers
How many solutions 4(x-5)=3x+7
ohaa [14]
4(x-5)=3x+7 \\ \\ 4x - 20 = 3x + 7 \\ \\ 4x = 3x + 7 + 20 \\ \\ 4x = 3x + 27 \\ \\ 4x - 3x = 27 \\ \\ x = 27 \\ \\

The final result is: x = 27
5 0
3 years ago
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