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3 years ago

David writes down the sequence 2, 6, 10, 14he says the sequence is n+4 is he correct

Mathematics

2 answers:

Sonja [21]3 years ago

7 0

He is, since each number is 4 more in value than the previous number

gavmur [86]3 years ago

7 0

Yes
looks right to me i did the work on a piece of paper and it was right

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8x-5y= 14<br> – 5х+бу = -3

podryga [215]

Answer:

y= 34/23

x= 123/46

Step-by-step explanation:

Solve for x

8x-5y= 14

x= 14/8 +5/8y

Sub x into second equation

– 5х+бу = -3

-5(14/8 +5/8y) + 6y= -3

-29/4 +23/8y = -3

y= 34/23

Sub y into any equation and solve for x

8x=483/23

x= 123/46

4 0

3 years ago

Write an equation of the perpendicular bisector of the segment with the endpoints (8,10) and ( -4,2).

ale4655 [162]

Answer:

The required equation is:

$y = -\frac{3}{2}x+9$

Step-by-step explanation:

To find the equation of a line, the slope and y-intercept is required.

The slope can be found by finding the slope of given line segment. A the perpendicular bisector of a line is perpendicular to the given line, the product of their slopes will be -1 and it will pass through the mid-point of given line segment.

Given points are:

$(x_1,y_1) = (8,10)\\(x_2,y_2) = (-4,2)$

We will find the slope of given line segment first

$m = \frac{y_2-y_1}{x_2-x_1}\\= \frac{2-10}{-4-8}\\=\frac{-8}{-12}\\=\frac{2}{3}$

Let m_1 be the slope of perpendicular bisector then,

$m.m_1 = -1\\\frac{2}{3}.m_1 = -1\\m_1 = \frac{-3}{2}$

Now the mid-point

$(x,y) = (\frac{x_1+x_2}{2} , \frac{y_1+y_2}{2})\\= (\frac{8-4}{2} , \frac{10+2}{2})\\=(\frac{4}{2}, \frac{12}{2})\\=(2,6)$

We have to find equation of a line with slope -3/2 passing through (2,6)

The equation of line in slope-intercept form is given by:

$y = m_1x+b$

Putting the value of slope

$y= -\frac{3}{2}x+b$

Putting the point (2,6) to find the y-intercept

$6 = -\frac{3}{2}(2)+b\\6 = -3+b\\b = 6+3 =9$

The equation is:

$y = -\frac{3}{2}x+9$

7 0

3 years ago

<img src="https://tex.z-dn.net/?f=%20%5Cfrac%7Bx%20%7B%7D%5E%7B2%7D%20-%204%20%7D%7B%20%5Csqrt%7Bx%20%7B%7D%5E%7B2%7D%20-%206x%2

Nimfa-mama [501]

First of all, we can observe that

$x^2-6x+9 = (x-3)^2$

So the expression becomes

$\dfrac{x^2-4}{\sqrt{(x-3)^2}} = \dfrac{x^2-4}{|x-3|}$

This means that the expression is defined for every $x\neq 3$

Now, since the denominator is always positive (when it exists), the fraction can only be positive if the denominator is also positive: we must ask

$x^2-4 \geq 0 \iff x\leq -2 \lor x\geq 2$

Since we can't accept 3 as an answer, the actual solution set is

$(-\infty,-2] \cup [2,3) \cup (3,\infty)$

7 0

3 years ago

Is this a linear function ?<br><img src="https://tex.z-dn.net/?f=y%20%3D%20%20-%203%20%5E%7B2%7D%20%20%2B%202" id="TexFormula1"

Slav-nsk [51]

No its not a linear function i think

8 0

3 years ago

A semicircle is drawn next to the base of an isosceles triangle such that its diameter is perpendicular to the triangle's

irina1246 [14]

The total area of the semicircle and triangle is 30 + 4.5π .

The diameter of the semicircle is perpendicular to the base of the triangle.

Given diameter length = 6 cm

radius = 6 /2 = 3cm

Area of the semicircle = 1/2 πr² = 1/2π3² = 4.5π

height of the triangle = 10 cm

Area of the triangle = 1/2 × 6 × 10 =30cm

Total area of the figure = 30 + 4.5π

hence the total area of the resulting figure is 30 + 4.5π

A semicircle with one locus of points is referred to as a half-circle in mathematics, more specifically geometry. A semicircle's complete arc is always equal to 180 degrees, radians, or a half-turn.

It only contains one reflectional symmetry line. A half-disk, a twofold geometric entity that includes both the circumferential segment from one end of the arc towards the other and all the inner points, is typically referred to as a "semicircle" in non-technical language.

Disclaimer: The complete question is :

A semicircle is drawn next to the base of an isosceles triangle such that its diameter of 6 cm is perpendicular to the triangle's altitude of 10 cm

To learn more about semicircle visit:

brainly.com/question/29393120

#spj9

7 0

1 year ago