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3 years ago

5th term in expansion of (x-2)^7

Mathematics

1 answer:

jeka943 years ago

7 0

Answer:

560x^3

Step-by-step explanation:

The formula is

(r + 1)th term of (a + x)^n = nCr a^(n-r)x^r

So 5th term = (4 + 1)th term

= 7C4 x^(7-4) (-2)^4

= 35x^3*16

= 560x^3

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How many real solutions does this system of equations have? x^2 + y^2 = 36

Vinvika [58]

Answer:

C: there are two real solutions

Step-by-step explanation:

x^2 + y^2 = 36 is the equation of a circle centered at the origin and with radius √36, or 6. Even a rough sketch of this circle would enable you to visualize what is happening here.

3x – y + 1 = 0 may be solved for y: y = 3x + 1. The y-intercept of this straight line is (0, 1). Plot this point inside the circle of radius 6 mentioned above and then draw a straight line with slope m = 3 through it. This line will intersect the circle in two places; they represent real solutions.

Alternatively, substitute 3x + 1 for y in x^2 + y^2 = 36:

x^2 + (3x + 1)^2 = 36, or

x^2 + 9x^2 + 6x + 1 = 36, or

10 x^2 + 6x + 1 - 36 = 0, or

10 x^2 + 6x - 35 = 0. This is a quadratic equation. We'll use the quadratic formula to find solutions which represent the intersections of this line with this circle:

The coefficients are a = 10, b = 6 and c = -35. Thus, the discriminant is

b^2 - 4ac, or 6^2 - 4(10)(-35), or 1436.

Because the discriminant is positive, we can safely conclude that there are two real solutions, that is, two different, real x-values, each representing the x-coordinate of a point of intersection of the circle and the line.

The correct answer to this prolem is C: there are two real solutions.

4 0

3 years ago

Which equation represents the line that is perpendicular to and passes through (-40,20)?

emmasim [6.3K]

The equation of the perpendicular line to the given line is: y = -5/4x - 30.

<h3>What is the Equation of Perpendicular Lines?</h3>

The slope values of two perpendicular lines are negative reciprocal of each other.

Given that the line is perpendicular to y = 4/5x+23, the slope of y = 4/5x+23 is 4/5. Negative reciprocal of 4/5 is -5/4.

Therefore, the line that is perpendicular to it would have a slope (m) of -5/4.

Plug in m = -5/4 and (x, y) = (-40, 20) into y = mx + b to find b:

20 = -5/4(-40) + b

20 = 50 + b

20 - 50 = b

b = -30

Substitute m = -5/4 and b = -30 into y = mx + b:

y = -5/4x - 30

The equation of the perpendicular line is: y = -5/4x - 30.

Learn more about about equation of perpendicular lines on:

brainly.com/question/7098341

#SPJ1

8 0

1 year ago

Which equations show the identity property of multiplication?

Lady bird [3.3K]

My answer is a and c becuase they equal the same on each side

3 0

3 years ago

Which would be the best method to use to solve the following equations? Explain your reasoning.

o-na [289]

A. square root property

$3x^2-192=0\\x^2-66=0\\x^2=66\\x= -\sqrt{66} or \sqrt{66}$

it has one value with x which is x^2 and it cn be easily solved without having to factorise, quadratic formula cant be used as it need ax^2+bx+c=0 format

B. factorising

$x^2-x-6=0\\x^2+2x-3x-6=0\\(x+2)(x-3)=0\\x+2=0 and x-3=0\\x= -2 \\x= 3$

i just felt like this was easier to factorise than the other 2 options left

C. Completing the square

$x^2-6x-7=0\\(x-3)^2=0\\x= -1\\x= 7$

same reason personal preference

D- Quadratic

$x^2-17x-7=0\\x=\frac{-(-17)+\sqrt{(-17)^2-4(1)(-7)} }{2(1)} \\x=\frac{-(-17)-\sqrt{(-17)^2-4(1)(-7)} }{2(1)}\\x=17.4\\x=-0.402$

the 17 kinda threw me off and i didnt wanna get on factorising or doing completing the square so quadratic formal

7 0

2 years ago

Find the equation of a circle that has its center at (-4, 3) and has a radius of 5. (x + 4) 2 + (y - 3) 2 = 25

Andreas93 [3]

Answer:

$(x+4)^2 + (y-3)^2 = 25$

Step-by-step explanation:

You can use the center of a circle to write an equation in vertex form. Vertex form is $(x-h)^2+(y-k)^2 = r^2$ and the vertex is (h,k). Notice (h,k) are the opposite sign in the equation then as the point.

Here h = -4 and k = 3. Substitute these values and the value r = 5.

$(x--4)^2 + (y-3)^2 = 5^2\\(x+4)^2 + (y-3)^2 = 25$

3 0

3 years ago