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3 years ago

Eliminate the parameter. x = 7t, y = t + 4

Mathematics

2 answers:

kenny6666 [7]3 years ago

8 0

Answer:

7y = x + 28

Step-by-step explanation:

Given x = 7t and y = t + 4

Here t is the parameter Now to remove it express one of it in terms of the variables (like x or y)

Given x = 7t

from this we can write $t=\frac{x}{7}$

Now substitute this value in the second equation

y = t + 4

$y=\frac{x}{7}+4$

Therefore the parameter is eliminated.

Rama09 [41]3 years ago

6 0

Answer:

y = x/7 + 4

Step-by-step explanation:

7y = x + 28

7y(/7) = x(/7) = 28(/7)

y = x/7 + 4

Hope this helps!

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Find the set of values of k for which the line y=kx-4 intersects the curve y=x²-2x at 2 distinct points?

Sonbull [250]

Answer:

$-6 < k < 2$

Step-by-step explanation:

Given

$y = x^2 - 2x$

$y =kx -4$

Required

Possible values of k

The general quadratic equation is:

$ax^2 + bx + c = 0$

Subtract $y = x^2 - 2x$ and $y =kx -4$

$y - y = x^2 - 2x - kx +4$

$0 = x^2 - 2x - kx +4$

Factorize:

$0 = x^2 +x(-2 - k) +4$

Rewrite as:

$x^2 +x(-2 - k) +4=0$

Compare the above equation to: $ax^2 + bx + c = 0$

$a = 1$

$b= -2-k$

$c =4$

For the equation to have two distinct solution, the following must be true:

$b^2 - 4ac > 0$

So, we have:

$(-2-k)^2 -4*1*4>0$

$(-2-k)^2 -16>0$

Expand

$4 +4k+k^2-16>0$

Rewrite as:

$k^2 + 4k - 16 + 4 >0$

$k^2 + 4k - 12 >0$

Expand

$k^2 + 6k-2k - 12 >0$

Factorize

$k(k + 6)-2(k + 6) >0$

Factor out k + 6

$(k -2)(k + 6) >0$

Split:

$k -2 > 0$ or $k + 6> 0$

So:

$k > 2$ or k $> -6$

To make the above inequality true, we set:

$k < 2$ or $k >-6$

So, the set of values of k is:

$-6 < k < 2$

3 0

3 years ago

Solve using Elimination 3x+y=-9 y=5x+7

valentinak56 [21]

Answer

x=-2 and y=-3

Step-by-step explanation:

Step: Solvey=5x+7for y:

Step: Substitute5x+7 for y in 3x+y=−9:

3x+y=−9

3x+5x+7=−9

8x+7=−9(Simplify both sides of the equation)

8x+7+−7=−9+−7(Add -7 to both sides)

8x=−16

8x/8=−16/8

(Divide both sides by 8)

x=−2

Step: Substitute−2 for x in y=5x+7:

y=5x+7

y=(5)(−2)+7

y=−3(Simplify both sides of the equation)

7 0

2 years ago

When doing blood testing for a viral infection, the procedure can be made more efficient and less expensive by combining partial

Serjik [45]

Answer:

0.1694 = 16.94% probability of a positive result for three samples combined into one mixture.

Step-by-step explanation:

For each test, there are only two possible outcomes. Either it is positive, or it is negative. The probability of a test being positive or negative is independent of any other test, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

The probability of an individual blood sample testing positive for the virus is 0.06.

This means that $p = 0.06$

If samples from three people are combined and the mixture tests negative, we know that all three individual samples are negative. Find the probability of a positive result for three samples combined into one mixture.

It will be positive if at least one of the tests is positive, that is:

$P(X \geq 1) = 1 - P(X = 0)$

In which

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{3,0}.(0.06)^{0}.(0.94)^{3} = 0.8306$

Then

$P(X \geq 1) = 1 - P(X = 0) = 1 - 0.8306 = 0.1694$

0.1694 = 16.94% probability of a positive result for three samples combined into one mixture.

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3 years ago

The volume of a cube is 1 cubic meter. What is the length of of each side of the cube

julsineya [31]

1 Metre is the length of each side of the cube.

To example, here is the Volume Of Cube Equation:

V = a^3

We are given the value for V, so just take the cube root of 1, which equates to 1.

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3 years ago

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Marat540 [252]

$2x + ( - 2x - 6) = 5 \\ - 6 = 5 \\$
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3 years ago

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