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Artyom0805 [142]

1 year ago

13

Call line that passes through the point x, y with a y intercept of b and a slope of m can be represented by the equation y=mx +

b. a line is drawn on the coordinate plane that passes through the .3, -6 and has a slope of four the y-intercept of the line is

1 answer:

Sergio039 [100]1 year ago

3 0

Answer: (0, -7.2)

Step-by-step explanation:

Substituting into point-slope form, the equation is

$y+6=4(x-0.3)$

The y-intercept is when x=0, so substituting in x=0,

$y+6=4(-0.3)\\\\y+6=-1.2\\\\y=-7.2$

So, the y-intercept is (0, -7.2).

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Show that n(n+1)(n+2) is divisible by 6<br>Solution<br>(

vladimir2022 [97]

Proof by induction

Base case:

n=1: 1*2*3=6 is obviously divisible by six.

Assumption: For every n>1 n(n+1)(n+2) is divisible by 6.

For n+1:

(n+1)(n+2)(n+3)=

(n(n+1)(n+2)+3(n+1)(n+2))

We have assumed that n(n+1)(n+2) is divisble by 6.

We now only need to prove that 3(n+1)(n+2) is divisible by 6.

If 3(n+1)(n+2) is divisible by 6, then (n+1)(n+2) must be divisible by 2.

The "cool" part about this proof.

Since n is a natural number greater than 1 we can say the following:

If n is an odd number, then n+1 is even, then n+1 is divisible by 2 thus (n+1)(n+2) is divisible by 2,so we have proved what we wanted.

If n is an even number" then n+2 is even, then n+1 is divisible by 2 thus (n+1)(n+2) is divisible by 2,so we have proved what we wanted.

Therefore by using the method of mathematical induction we proved that for every natural number n, n(n+1)(n+2) is divisible by 6. QED.

6 0

2 years ago

A real estate company wants to build a parking lot along the side of one of its buildings using 800 feet of fence. If the side a

Elden [556K]

Answer:

80,00 $ft^{2}$

Step-by-step explanation:

According to my research, the formula for the Area of a rectangle is the following,

$A = L*W$

Where

A is the Area
L is the length
W is the width

Since the building wall is acting as one side length of the rectangle. We are left with 1 length and 2 width sides. To maximize the Area of the parking lot we will need to equally divide the 800 ft of fencing between the <u>Length and Width.</u>

800 / 2 = 400ft

So We have 400 ft for the length and 400 ft for the width. Since the width has 2 sides we need to divide 60 by 2.

400/2 = 200 ft

Now we can calculate the maximum Area using the values above.

$A = 400ft*200ft$

$A = 80,000ft^{2}$

So the Maximum area we are able to create with 800 ft of fencing is 80,00 $ft^{2}$

I hope this answered your question. If you have any more questions feel free to ask away at Brainly.

Read more on Brainly.com - brainly.com/question/12953427#readmore

3 0

2 years ago

What 0.356 in word form

Zina [86]

It is three hundred fifty-six thousandths.

4 0

3 years ago

Read 2 more answers

Chris invests $20,000 into a savings account that accrues 5.2% interest compounded semiannually. What is the balance of Chris' a

il63 [147K]

The amount to be paid after 3 years is $23,329.97.

<h3>What is Compound Interest?</h3>

In order to compute compound interest, multiply the principle of the original loan by the annual interest rate multiplied by the number of compound periods minus one. You will then be left with the principal amount of the loan plus compound interest.

Given:

P= 20,000

r= 5.2%

t= 3 years

r = R/100

r = 5.2/100

r = 0.052 rate per year,

Now, solve for A

A = P $(1 + r/n)^{nt$

A = 20,000.00 $(1 + 0.052/2)^{(2)(3)$

A = 20,000.00 $(1 + 0.026)^(6)$

A = $23,329.97

Learn more about Compound interest here:

brainly.com/question/14295570

#SPJ1

5 0

11 months ago

find the zeros of following quadratic polynomial and verify the relationship between the zeros and the coefficient of the polyno

Cloud [144]

Answer:

$\textsf{Zeros}: \quad x=\dfrac {\sqrt{3}}{2}, \:\:x=-\dfrac {4\sqrt{3}}{3}$

Step-by-step explanation:

Rewrite the given polynomial in the form ax² + bx + c:

$f(x)=2 \sqrt{3}x^2+5x-4 \sqrt{3}$

To find the zeros, set the function to zero and solve for x using the quadratic formula.

$\implies 2 \sqrt{3}x^2+5x-4 \sqrt{3}=0$

<u>Quadratic formula</u>:

$x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when }\:ax^2+bx+c=0$

Therefore,

a = 2√3
b = 5
c = - 4√3

Substituting the values into the quadratic formula:

$\implies x=\dfrac{-5 \pm \sqrt{5^2-4(2\sqrt{3})(-4\sqrt{3})} }{2(2\sqrt{3})}$

$\implies x=\dfrac {-5 \pm \sqrt {121}}{4\sqrt{3}}$

$\implies x=\dfrac {-5 \pm 11}{4\sqrt{3}}$

$\implies x=\dfrac {6}{4\sqrt{3}}, \:\:x=\dfrac {-16}{4\sqrt{3}}$

$\implies x=\dfrac {3}{2\sqrt{3}}, \:\:x=-\dfrac {4}{\sqrt{3}}$

$\implies x=\dfrac {\sqrt{3}}{2}, \:\:x=-\dfrac {4\sqrt{3}}{3}$

The sum of the roots of a polynomial is -b/a:

$\implies -\dfrac{b}{a}=-\dfrac{5}{2 \sqrt{3}}=-\dfrac{5\sqrt{3}}{6}$

The sum of the found roots is:

$\implies \left(\dfrac {\sqrt{3}}{2}\right)+\left(-\dfrac {4\sqrt{3}}{3}\right)=-\dfrac{5\sqrt{3}}{6}$

Hence proving the sum of the roots is -b/a

The product of the roots of a polynomial is: c/a

$\implies \dfrac{c}{a}=\dfrac{-4\sqrt{3}}{2\sqrt{3}}=-2$

The product of the found roots is:

$\implies \left(\dfrac {\sqrt{3}}{2}\right)\left(-\dfrac {4\sqrt{3}}{3}\right)=-\dfrac{12}{6}=-2$

Hence proving the product of the roots is c/a

Therefore, the relationship between the roots and the coefficients is verified.

8 0

1 year ago