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Mathematics

1 answer:

katovenus [111]2 years ago

7 0

Answer:

Points Q, J and M are not collinear

Step-by-step explanation:

Three points cannot be collinear if they are not coplanar (on the same plane), and M is on a different plane than Q. J is located on both planes.

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The sides of a triangle are 3x+2 6x-1 and 7-x express the perimeter in terms of x

Strike441 [17]

Answer:

x=3

Step-by-step explanation:

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3 years ago

Select the quadratic equation that has roots x=8 and x=-5

stellarik [79]

Step-by-step explanation:

Since, x=8 and x=-5 are the roots.

Therefore, (x - 8) & (x - 5) will be factors.

Hence, required quadratic equation can be given as:

$(x - 8)(x - 5) =0 \\ \\ \therefore {x}^{2} + ( - 8 - 5) x+ ( - 8) \times ( - 5) = 0 \\ \\ \therefore {x}^{2} + ( - 13) x+ 40= 0 \\ \\ \huge \red{ \boxed{ \therefore {x}^{2} - 13x+ 40= 0 }} \\ is \: the \: required \: quadratic \: equation.$

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2 years ago

Write the following sum using summation notation -2/5+3/6-4/7........11/14

horrorfan [7]

Answer:

$\sum_{n=1}^{10}(-1)^n\left ( \frac{n+1}{n+4} \right )$

Step-by-step explanation:

Given: $\frac{-2}{5}+\frac{3}{6}-\frac{4}{7}+...+\frac{11}{14}$

To write: the given expression using summation notation

Solution:

Summation notation helps to write a long sum as a single expression.

In the summation notation, the variable $\sum$ is called the index of summation.

Let $x_1,x_2,x_3,...,x_n$ denote a set of n numbers.

Then in summation notation,

$x_1+x_2+x_3+...+x_n=\sum_{i=1}^{n}x_i$

$\frac{-2}{5}=(-1)^1\left ( \frac{1+1}{1+4} \right )\\\frac{3}{6}=(-1)^2\left ( \frac{2+1}{2+4} \right )\\\frac{-4}{7}=(-1)^3\left ( \frac{3+1}{3+4} \right )\\.\\.\\.\\\frac{11}{14}=(-1)^10\left ( \frac{10+1}{10+4} \right )\\\therefore \frac{-2}{5}+\frac{3}{6}-\frac{4}{7}+...+\frac{11}{14}=\sum_{n=1}^{10}(-1)^n\left ( \frac{n+1}{n+4} \right )$