Which of the points shown below are on the line given by the equation y = 2x?

Helpppp meee plsssss

Sholpan [36]

Answer:

B

Step-by-step explanation:

1/6x+ 4/6x = -4/6

5/6x= -4/6

x=( -4/6)/ (-5/6)

x= 4/5

8 0

2 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

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

So,

$x = \frac{-26 + 32 }{2} \text{ or } x = \frac{-26 - 32 }{2}
\newline x = \frac{6 }{2} \text{ or } x = \frac{-58 }{2}
\newline \boxed{ x = 3 \text{ or } x = -29}$

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

a construction worker needs to put a rectangular window in the side of a building. He knows from measuring that the top and bott

solmaris [256]

Answer:

You can espick español y not can espick inglés

3 0

2 years ago

Read 2 more answers

There are four steps in the manufacturing process of a stuffed toy: cutting, stuffing, sealing, and packaging. There are two emp

Anit [1.1K]

Answer:

(a) 2min/15units

(b) 1min/20units

(c) The bottleneck stage is cutting. The process capacity is 450units/hour

(d) The capacity of the new employee should be 1unit/2sec. The process capacity will increase four times

Step-by-step explanation:

(a) Cycle time for stage cutting for 2 employees = 16sec/2units × 1min/60sec = 2min/15units

(b) Cycle time for stage sealing for 1 employee = 3sec/1unit × 1min/60sec = 1min/20units

(c) Process capacity of stage cutting = 15units/2min × 60min/1hour = 450units/hour

(d) If the capacity of the new employee is 1unit/2sec, the process capacity = 1unit/2sec × 3600sec/1hour = 1800units/hour. The process capacity increases 4 times (1800/450 = 4)

7 0

3 years ago

X² + y² = 34<br>x + y =8

Nataly [62]

Step-by-step explanation:

${x}^{2} + {y}^{2} = 34 \\ x + y = 8 \\ x = 8 - y \\ substitute \: x \: in \\ {x}^{2} + {y}^{2} = 34 \\ {(8 - 4)}^{2} + {y}^{2} = 34 \\ {(8 - 4) }^{2} = {y}^{2} - 16y + 64 \\ {y}^{2} - 16y + 64 + {y}^{2} = 34 \\ {2y}^{2} - 16y + 64 = 34 \\ {2y}^{2} - 16y + 64 - 34 = 0 \\ {2y}^{2} - 16y + 30 = 0 \\ 2 {y}^{2} - 6y - 10y + 30 = 0 \\ (2 {y}^{2} - 6y) - (10y + 30) = 0 \\ 2y(y - 3) - 10(y - 3) = 0 \\ (2y - 10)(y - 3) \\ 2y = 10 \\ y = \frac{10}{2} \\ y = 5 \\ or \\ y = 3 \\ if \: y = 5 \: \: x = 3 \\ if \: y = 3 \: \: x = 5$

4 0

3 years ago