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3 years ago

HELP PLEASEEE I HAVE A QUIZ RIGHT NOW

Mathematics

1 answer:

Sergeeva-Olga [200]3 years ago

4 0

Answer:

a=3 b=5

Step-by-step explanation:

They will equal each other and make infinite solutions

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Y intercept <br> x intercept<br> and the slope

masha68 [24]

Answer:

y-intercept = (0, - 3)

x-intercept = (-6, 0)

slope = - 1/2

Step-by-step explanation:

The y intercept is the value of y when the x = 0. By looking at the graph, we can tell that when x = 0, y = - 3. Likewise for the x-intercept.

We can use the slope formula to determine the slope.

m = y2 - y1/ x2 - x1

You can choose any 2 points on the line and substitute in the formula. I chose the y and x intercepts for easier calculations.

m = - 3 - 0/ 0 - (- 6)

m = - 3/ 6

m = - 1/2

6 0

3 years ago

Prove that 1³+2³+....n³=n²(n+1)²/4. principle of mathematics induction

alex41 [277]

<h3>The Simplified Question:-</h3>

$\sf 1^3+2^3\dots n^3=\dfrac{n^2(n+1)^2}{2}$

$\\ \sf\longmapsto 1^3+2^3+\dots n^3=\left(\dfrac{n(n+1)}{2}\right)^2$

<h3>Solution:-</h3>

Let

$\\ \sf\longmapsto P(n)=1^3+2^3\dots n^3=\left(\dfrac{n(n+1)}{2}\right)^2$

For n=1

$\\ \sf\longmapsto P(1)=\left(\dfrac{1(1+1)}{2}\right)^2$

$\\ \sf\longmapsto P(1)=\left(\dfrac{1(2)}{2}\right)^2$

$\\ \sf\longmapsto P(1)=\left(\dfrac{2}{2}\right)^2$

$\\ \sf\longmapsto P(1)=(1)^2$

$\\ \bf\longmapsto P(1)=1=1^3$

Let k be any positive integer.

$\\ \sf\longmapsto P(k)= 1^3+2^3\dots k^3=\left(\dfrac{k(k+1)}{2}\right)^2$

We have to prove that p(k+1) is true.

consider

$\sf 1^3+2^3\dots k^3+(k+1)^3$

$\\ \sf\longmapsto \left(\dfrac{k(k+1)}{2}\right)^2+(k+1)^3$

$\\ \sf\longmapsto \dfrac{k^2(k+1)^2}{4}+(k+1)^3$

$\\ \sf\longmapsto \dfrac{k^2(k+1)^2+4(k+1)^3}{4}$

$\\ \sf\longmapsto \dfrac{k+1)^2\left\{k^2+4k+4\right\}}{4}$

$\\ \sf\longmapsto \dfrac{(k+1)^2(k+2)^2}{4}$

$\\ \sf\longmapsto \dfrac{(k+1)^2(k+1+1)^2}{4}$

$\\ \sf\longmapsto \left(\dfrac{(k+1)(k+1+1)}{2}\right)^2$

$\\ \sf\longmapsto (1^3+2^3+3^3\dots k^3)+(k+1)^3$

Thus P(k+1) is true whenever P(k) is true.

Hence by the Principal of mathematical induction statement P(n) is true for $\bf n\epsilon N.$

Note:-

We can solve without simplifying the Question .I did it for clear steps and understanding .

<h3>Learn More:-</h3>

brainly.com/question/13253046?

brainly.com/question/13347635?

6 0

3 years ago

Read 2 more answers

Help pls

GarryVolchara [31]

Answer:

x^2-6x

Step-by-step explanation:

Let's start by factoring the top, or numerator of the fraction.

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

Now, you can divide this by (x-1):

$\dfrac{x((x-6)(x-1))}{(x-1)}=x(x-6)=\boxed{x^2-6x}$

6 0

3 years ago

Solve for x.<br><br> 3x - 4 = 13

mario62 [17]

X = 17/3 :) :)

add 4 to both sides
then divide both sides by 3

6 0

3 years ago

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8 x 5 ÷ 2 - (5+3) Please help

pshichka [43]

The answer is 12.
First you multiply 8 by 5, which gives you 40. Then, you divide 40 by 2, which gives you 20.
Finally, you subtract 20 by 8 because 5 + 3 = 8.

4 0

3 years ago

Read 2 more answers