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2 years ago

Solve the system of equations. y = 4x – 4 y = 5x

Mathematics

1 answer:

kolbaska11 [484]2 years ago

4 0

Answer:

Step-by-step explanation:

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A window is twice as long as it is wide. The area of the window is 2x where x

Alchen [17]

Answer:

When we have a rectangle of length L and width W, the area is calculated as:

A = W*L

In this case, W = x, and the area is:

A = 2*x

Then we must have L = 2.

We know that the area of the window and the frame (together) is:

a = 2*x^2 + 12*x + 16

The area of the frame alone, will be equal to the difference between the area of both objects (a) and the area of the window alone (A)

area of the frame = a - A

= (2*x^2 + 12*x + 16) - (2*x) = (2*x^2 + 10*x + 16)

This is the area of the frame

5 0

2 years ago

The lifetime of a certain type of battery is normally distributed with mean value 15 hours and standard deviation 1 hour. There

KIM [24]

Answer:

If the lifetime of batteries in the packet is 40.83 hours or more then, it exceeds for 5% of all packages.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 15

Standard Deviation, σ = 1

Sample size = 4

Total lifetime of 4 batteries = 40 hours

We are given that the distribution of lifetime is a bell shaped distribution that is a normal distribution.

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

Standard error due to sampling:

$\displaystyle\frac{\sigma}{\sqrt{n}} = \frac{1}{\sqrt4} = 0.5$

We have to find the value of x such that the probability is 0.05

P(X > x) = 0.05

$P( X > x) = P( z > \displaystyle\frac{x - 40}{0.5})=0.05$

$= 1 -P( z \leq \displaystyle\frac{x - 40}{0.5})=0.05$

$=P( z \leq \displaystyle\frac{x - 40}{0.5})=0.95$

Calculation the value from standard normal z table, we have,

$\displaystyle\frac{x - 40}{0.5} = 1.64\\x = 40.825 \approx 40.83$

Hence, if the lifetime of batteries in the packet is 40.83 hours or more then, it exceeds for 5% of all packages.

8 0

3 years ago

Parallel, orthogonal, or neither.

zzz [600]

Vectors are orthogonal, when dot product $u\cdot v=0$

$u\cdot v=\langle-1,3\rangle\cdot\langle-9,-3\rangle=(-1)\cdot(-9)+3\cdot(-3)=9-9=0$

Vectors $u$ and $v$ are orthogonal.

8 0

2 years ago

3x^+5x+2=0 need work shown plz

Alexxandr [17]

Answer:

${3x}^{2} + 5x + 2 \\ = {3x}^{2} + 3x + 2x + 2 \\ = 3x(x + 1) + 2(x + 1) \\ = (3x +2)(x + 1)$

7 0

2 years ago

Read 2 more answers

Surface area???????????

MAVERICK [17]

Answer:

The option B is the correct answer. 79.18 m²

Step-by-step explanation:

Surface area = Base area + Lateral surface area

Area of triangle = bh/2

b - base and h - height

To find the base area

We can consider the base is a hexagon.

A regular hexagon is a combination of 6 equilateral triangle

Base area = 6 * area of triangle

base b = 3

To find the height

h =√[(6.2)² - (5.6)₂] = 2.7

Area of triangle bh/2 = (3 * 2.7)/2 = 3.99

Area of base = 23.95

To find lateral surface area

Lateral surface area = 6 * area of triangle

Area of triangle = bh/2 =(3 *6.2)/2 = 9.3

Lateral surface area = 6 * 9.3 = 55.8

To find the total surface area 

Total surface area = Base area + lateral surface area = 23.95 + 55.8

= 79.75 m²

Therefore the option B is the correct answer. 79.18 m²

7 0

2 years ago