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2 years ago

12

I am four times as old as my brother and in two years time i will be just three times as old. in how many years will i be twice

as old as my brother?

1 answer:

GaryK [48]2 years ago

5 0

In 8 years you will be twice as old as your brother.

Right now, your brother is 4 years old, and 4 x 4 is 16, so you are 16.
In two years, your brother would be 6, and you would be 18, making you 3 times as old.

So, in 8 years, your brother will be 12 years old, making you 24. 12 is half of 24.

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Find the set of values of k for which the line y=kx-4 intersects the curve y=x²-2x at 2 distinct points?

Sonbull [250]

Answer:

$-6 < k < 2$

Step-by-step explanation:

Given

$y = x^2 - 2x$

$y =kx -4$

Required

Possible values of k

The general quadratic equation is:

$ax^2 + bx + c = 0$

Subtract $y = x^2 - 2x$ and $y =kx -4$

$y - y = x^2 - 2x - kx +4$

$0 = x^2 - 2x - kx +4$

Factorize:

$0 = x^2 +x(-2 - k) +4$

Rewrite as:

$x^2 +x(-2 - k) +4=0$

Compare the above equation to: $ax^2 + bx + c = 0$

$a = 1$

$b= -2-k$

$c =4$

For the equation to have two distinct solution, the following must be true:

$b^2 - 4ac > 0$

So, we have:

$(-2-k)^2 -4*1*4>0$

$(-2-k)^2 -16>0$

Expand

$4 +4k+k^2-16>0$

Rewrite as:

$k^2 + 4k - 16 + 4 >0$

$k^2 + 4k - 12 >0$

Expand

$k^2 + 6k-2k - 12 >0$

Factorize

$k(k + 6)-2(k + 6) >0$

Factor out k + 6

$(k -2)(k + 6) >0$

Split:

$k -2 > 0$ or $k + 6> 0$

So:

$k > 2$ or k $> -6$

To make the above inequality true, we set:

$k < 2$ or $k >-6$

So, the set of values of k is:

$-6 < k < 2$

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2 years ago

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2 years ago

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The function h is defined by h (y) = 2y-7.<br> What is the value of h(8) ?<br> ooo

kozerog [31]

Answer:

The value of h(8) = 9

Step-by-step explanation:

Given function as

h(y) = 2y - 7

For y = 8

Put the value of y in given function

So, h(8) = 2 (8) - 7

OR , h(8) = 16 - 7

∴ h(8) = 9

Hence the value of h(8) = 9 Answer

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2 years ago

Jose equation is -4(x+2) = 8x+16 says to jill “I can solve for the variable in this equation in at least 4 different ways

erastovalidia [21]

Answer:

that is step 1 and step 2 and step3

step 4

Let's solve your equation step-by-step.

−4(x+2)=8x+16

Step 1: Simplify both sides of the equation.

−4(x+2)=8x+16

(−4)(x)+(−4)(2)=8x+16(Distribute)

−4x+−8=8x+16

−4x−8=8x+16

Step 2: Subtract 8x from both sides.

−4x−8−8x=8x+16−8x

−12x−8=16

Step 3: Add 8 to both sides.

−12x−8+8=16+8

−12x=24

Step 4: Divide both sides by -12.

−12x

−12

=

24

−12

x=−2

Answer:

x=−2

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3 years ago