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3 years ago

I need help with this fast

Mathematics

2 answers:

devlian [24]3 years ago

6 0

It whould be -1.5 for and 0.5

matrenka [14]3 years ago

3 0

2/6

Step-by-step explanation:

The two points are -3/6 and 5/6. Subtract -3 - 5 and it's 2. 2/6 :)

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Word phrase to represent 5x+2

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One of the roots of the quadratic equation dx^2+cx+p=0 is twice the other, find the relationship between d, c and p

scZoUnD [109]

Answer:

$c^2 = 9dp$

Step-by-step explanation:

Given

$dx^2 + cx + p = 0$

Let the roots be $\alpha$ and $\beta$

So:

$\alpha = 2\beta$

Required

Determine the relationship between d, c and p

$dx^2 + cx + p = 0$

Divide through by d

$\frac{dx^2}{d} + \frac{cx}{d} + \frac{p}{d} = 0$

$x^2 + \frac{c}{d}x + \frac{p}{d} = 0$

A quadratic equation has the form:

$x^2 - (\alpha + \beta)x + \alpha \beta = 0$

So:

$x^2 - (2\beta+ \beta)x + \beta*\beta = 0$

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

So, we have:

$\frac{c}{d} = -3\beta$ -- (1)

and

$\frac{p}{d} = \beta^2$ -- (2)

Make $\beta$ the subject in (1)

$\frac{c}{d} = -3\beta$

$\beta = -\frac{c}{3d}$

Substitute $\beta = -\frac{c}{3d}$ in (2)

$\frac{p}{d} = (-\frac{c}{3d})^2$

$\frac{p}{d} = \frac{c^2}{9d^2}$

Multiply both sides by d

$d * \frac{p}{d} = \frac{c^2}{9d^2}*d$

$p = \frac{c^2}{9d}$

Cross Multiply

$9dp = c^2$

$c^2 = 9dp$

Hence, the relationship between d, c and p is: $c^2 = 9dp$

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3 years ago

Find the product. (y3)^2 · y^7

Sedbober [7]

Hey there! :D

When powers are outside the parenthesis, you multiply them. When they are not, you add them.

(y^3)^2 * y^7

3*2= 6

y^6*y^7

Add the powers.

y^13= the simplest form

I hope this helps!
~kaikers

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3 years ago

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