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3 years ago

Using a graphical method, solve the simultaneous equations y=2x-6 and y=-x

Mathematics

1 answer:

siniylev [52]3 years ago

5 0

Answer:

x=2

Step-by-step explanation:

both equations represent y so

2x-6= -x

rearrange the equation to bring the like terms together

2x+x= 6

3x=6

divide by 3 on both sides to get

x=2

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Find the area of the figure.

Anettt [7]

Answer: 28.5 square units.

Step-by-step explanation: Separate the figure into a rectangle and a triangle. Count the length and width of the rectangle. The length of the rectangle is 8 units and the width is 3 units. To find the area use the formula l*w. 8*3=24.

Next find the area of the triangle section. The triangle is 3 units tall and 3 units wide. To find the area use the formula 1/2(l*w). 3*3=9. 9/2=4.5.

Finally add the areas of the rectangular section and the triangular section. 24+4.5=28.5.

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4 years ago

A painter earns $15 per hour.What is the minimum number of hours he must work to earn at least $200?

babunello [35]

12 hours in order to make 200 dollars

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4 years ago

Find a degree 4 polynomial having zeros -8,-1,4 and 5 and the coefficient of x^4 equal 1.

Keith_Richards [23]

Answer:

x^4 -53x^2 +108x +160

Step-by-step explanation:

If <em>a</em> is a zero, then (<em>x-a</em>) is a factor. For the given zeros, the factors are ...

p(x) = (x +8)(x +1)(x -4)(x -5)

Multiplying these out gives the polynomial in standard form.

= (x^2 +9x +8)(x^2 -9x +20)

We note that these factors have a sum and difference with the same pair of values, x^2 and 9x. We can use the special form for the product of these to simplify our working out.

= (x^2 +9x)(x^2 -9x) +20(x^2 +9x) +8(x^2 -9x) +8(20)

= x^4 -81x^2 +20x^2 +180x +8x^2 -72x +160

p(x) = x^4 -53x^2 +108x +160

_____

The graph shows this polynomial has the required zeros.

4 0

4 years ago

Find the probability that a randomly generated bit string of length 10 does not contain a 0 if bits are independent and if:a) a

lara31 [8.8K]

Answer:

A) 0.0009765625

B) 0.0060466176

C) 2.7756 x 10^(-17)

Step-by-step explanation:

A) This problem follows a binomial distribution. The number of successes among a fixed number of trials is; n = 10

If a 0 bit and 1 bit are equally likely, then the probability to select in 1 bit is; p = 1/2 = 0.5

Now the definition of binomial probability is given by;

P(K = x) = C(n, k)•p^(k)•(1 - p)^(n - k)

Now, we want the definition of this probability at k = 10.

Thus;

P(x = 10) = C(10,10)•0.5^(10)•(1 - 0.5)^(10 - 10)

P(x = 10) = 0.0009765625

B) here we are given that p = 0.6 while n remains 10 and k = 10

Thus;

P(x = 10) = C(10,10)•0.6^(10)•(1 - 0.6)^(10 - 10)

P(x=10) = 0.0060466176

C) we are given that;

P((x_i) = 1) = 1/(2^(i))

Where i = 1,2,3.....,n

Now, the probability for the different bits is independent, so we can use multiplication rule for independent events which gives;

P(x = 10) = P((x_1) = 1)•P((x_2) = 1)•P((x_3) = 1)••P((x_4) = 1)•P((x_5) = 1)•P((x_6) = 1)•P((x_7) = 1)•P((x_8) = 1)•P((x_9) = 1)•P((x_10) = 1)

This gives;

P(x = 10) = [1/(2^(1))]•[1/(2^(2))]•[1/(2^(3))]•[1/(2^(4))]....•[1/(2^(10))]

This gives;

P(x = 10) = [1/(2^(55))]

P(x = 10) = 2.7756 x 10^(-17)

3 0

3 years ago

What is bigger 3.345 or 3.35 or 3.3

Sidana [21]

3.35 is bigger then 3.345

8 0

3 years ago