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Nina [5.8K]
3 years ago
10

Please help please please

Mathematics
1 answer:
Liula [17]3 years ago
5 0

Length of shorter piece is 13 ft

Length of longer piece is 61 - 13 => 48 ft

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5 - 4k = -7<br> please help
Lina20 [59]

Answer:

k = 1.75

Step-by-step explanation:

5 - 4k = -7

k = 1.75, because if you subtract 4 from both sides, you are left with 1.75 = -7.

4 0
1 year ago
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A high school football pennant is in the shape of an isosceles triangle. The base is 18 inches long. The sides meet at an angle
Oksanka [162]

Answer:

The length of each side is 26.3 cm

Step-by-step explanation:

Opposite sides of an isoceles triangle are equal

The isoceles triangle is divided into 2 right-angled triangles so the length of one side can be calculated using trigonometric ratio

When the isoceles triangle is divided, the angle in the right-angled triangle is 20° (1/2 of 40°) and the base is 9cm (1/2 of 18 cm), the hypotenuse side is calculated using trigonometric ratio

Let the length of the hypotenuse side be y

9/y = sin 20°

y = 9/0.3420 = 26.3

Length of each side is 26.3 cm

3 0
3 years ago
The veterinarian weighed Oliva's new puppy, Benz, on a defective scale.
Mrrafil [7]

Answer:

\boxed{x = 10.28 \%}

Step-by-step explanation:

\frac{(26.75)x}{100} = 2.75 \\  \boxed{x = 10.280373832}

5 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
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musickatia [10]
You got to Round it to the 10 & all that
6 0
3 years ago
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