MATHEMATICS HIGH SCHOOL

Find the value of x.

Answers

Answer 1

Answer:

Answer:

104 degrees

Step-by-step explanation:

71 degrees is one corner

Opposite corner is equal

Middle angle: 180-71-71 = 38

isosceles triangle bottom angle = 38 and 38

top angle = 180 - 38 - 38 = 104 degrees

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The blue figure is a translation image of the black figure what write a rule to describe the translation

Answers

The translation rule from the blue figure to the black figure is -

$(x, y) \rightarrow (x - 4, \ y + 3)$

What are the types of translation of a graph?

There are three types of translations -

Reflection
Rotation
Dilation

Given is that the blue figure is a translation of the black image.

We can write the translation rule as -

$(x, y) \rightarrow (x - 4, \ y + 3)$

Hence, the translation rule from the blue figure to the black figure is -

$(x, y) \rightarrow (x - 4, \ y + 3)$

Answers

Answer:

Jaden has to plant the geranium in the circumcentre of the triangular yard in order such that it is equidistant from all its vertices.

Step-by-step explanation:

In Jaden’s yard, there is a triangular garden patch. He wants to plant a geranium in the patch at a point equidistant from all its vertices.

" The CIRCUMCENTER (C) of a triangle is the point in the plane equidistant from the three vertices of the triangle "

Hence Jaden has to plant the geranium in the circumcentre of the triangular yard in order such that it is equidistant from all its vertices.

Answer:

It’s b

Step-by-step explanation:

The line y =3x-5 meet x-axis at the point M. The line 3y+2x=2 meets y-axis at point N. Find the equation of the line joining M and N in the form ax + by + c = 0 where: a,b,c are integers.

Answers

Answer-

The line equation is,

$\boxed{\boxed{6x+15y-10=0}}$

Solution-

The line $y =3x-5$ meets x-axis at the point M, i.e M is the x-intercept of this line. At the x-intercept y=0, so

$\Rightarrow 0 =3x-5$

$\Rightarrow 3x=5$

$\Rightarrow x=(5)/(3)$

So, coordinate of M is $((5)/(3),\ 0)$

The line $3y+2x=2$ meets y-axis at point N, i.e N is the y-intercept of this line. At the y-intercept x=0, so

$\Rightarrow 3y+2(0)=2$

$\Rightarrow 3y=2$

$\Rightarrow y=(2)/(3)$

So, coordinate of N is $(0,\ (2)/(3))$

The line joining M and N can be found out by applying two point formula of straight line,

$\Rightarrow (y-y_1)/(y_2-y_1)=(x-x_1)/(x_2-x_1)$

$\Rightarrow (y-0)/((2)/(3)-0)=(x-(5)/(3))/(0-(5)/(3))$

$\Rightarrow (y)/((2)/(3))=(x-(5)/(3))/(-(5)/(3))$

$\Rightarrow -(5)/(3)y=(2)/(3)(x-(5)/(3))$

$\Rightarrow -5y=2(x-(5)/(3))$

$\Rightarrow -5y=2x-(10)/(3)$

$\Rightarrow 2x+5y-(10)/(3)=0$

As it is given that all the coefficients are integers, so multiplying with 3

$\Rightarrow 6x+15y-10=0$

Solution: As given line y =3x-5 meet x-axis at the point M.

On x axis y coordinate is zero.

Put y =0 in above equation, we get →x = 5/3

∴ Coordinate of M is (5/3,0).

As, also given , line 3y+2x=2 meets y-axis at point N.

On y axis , x coordinate is zero.

Substituting , x=0 in above equation, gives y =2/3.

Coordinate of point N is (0,2/3).

Equation of line passing through two points (a,b) and (p,q) is given by

→ $(y-b)/(x-a) =(q-b)/(p-a)$

Or as X intercept = 5/3, and Y intercept = 2/3

Equation of line in intercept form is → $(x)/(a) + (y)/(b) =1$ , where a and b is X intercept and y intercept respectively.

So, line passing through (5/3,0) and (0,2/3) is given by

→ $(x)/((5)/(3)) + (y)/((2)/(3))=1$

→ $(3x)/(5) + (3y)/(2) =1$

→ 6 x + 15 y =10 [Taking LCM of 5 and 2 which is 10]

→ 6 x + 15 y -10=0, which is equation of the line joining M and N in the form ax + by + c = 0 where: a,b,c are integers.

What is the sum of the infinite geometric series?.

1/2+1/4+1/8+1/16+...

Answers

Answer:

The sum of the given geometric series is, 1

Step-by-step explanation:

Geometric sequence states that a sequence of numbers that follows a pattern were the next term is found by multiplying by a constant called the common ratio (r).

The sum of the infinite terms of a geometric series is given by:

$S_\infty = (a)/(1-r)$ ......[1] ;where $0<r<1$

Given the series: $(1)/(2)+(1)/(4)+(1)/(8)+(1)/(16)+.....$

Since, this series is geometric series with constant term(r) = $(1)/(2)$

Since,

$((1)/(4))/((1)/(2) ) =(2)/(4) = (1)/(2)$ ,

$((1)/(8))/((1)/(4)) =(4)/(8) = (1)/(2)$ and so on....

Here, first term(a) = $(1)/(2)$

Substitute the values of a and r in [1] we get;

$S_\infty = ((1)/(2))/(1-(1)/(2))$ where r = $(1)/(2)< 1$

$S_\infty = ((1)/(2))/((2-1)/(2))$

$S_\infty = ((1)/(2))/((1)/(2))$

Simplify:

$S_\infty = 1$

Therefore, the sum of the infinite geometric series is, 1

$1/2+1/4+1/8+1/16+...=\sum\limits_(n=1)^\infty ((1)/(2))^n = ((1)/(2))/(1-(1)/(2))=1$

We can see that consecutive fractions are made from 1/2 to consecutive powers. Because we begin with 1/2, n=1
We will infinitely add fractions , hence Lemniscate sign.

In other words you cannot find a number which needs to be added to the geometric series to get "1", therefore the answer is 1. I remember the teacher explaining it this way :)

Find the slope of the line passing through the points (5, 4) and (5, -5)