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3 years ago

5

Gary spent 48 dollars on a watch. HE spent 1/3 of remainder on a pen. If he still had 1/2 of money left, how much money did he h

ave at first?

1 answer:

givi [52]3 years ago

7 0

First we find 1/3 of 48 so 48÷3=16
now we find 1/2 of 48=24

now we add 48+16+24=88

he had 88dollars in total :)
i hope this was helpful

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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:

$-6 < k < 2$

3 0

3 years ago

Hey how to do this and what the answer

frez [133]

Answer:

5x + y - 4 = 0

Step-by-step explanation:

When we are given two points and are asked to find the equation of the line we use the two - point form.

Two - point form: $\frac{y - y_1}{y_2 - y_1} = \frac{x - x_1}{x_2 - x_1}$ .

where: $(x_1,y_1)$ and $(x_2,y_2)$ are the two points on the line.

Given the two points are: (5,21) and (-5,-29).

Substituting in the two point form:

⇒ $\frac{y - 21}{-29 - 21} = \frac{x - 5}{-5 -5}$

$\implies \frac{y - 21}{-50} = \frac{x - 5}{-10}$

$\implies y - 21 = 5x - 25$

⇒ 5x + y - 4 = 0

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3 years ago

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3 years ago

What is 3x3 – 11x2 – 26x + 30 divided by x – 5?

ahrayia [7]

Hello :
3x3 – 11x2 – 26x + 30 divided by x – 5 is :<span>3x2 + 4x – 6
because :
(x-5)(3x²+4x-6)=3x^3+4x²-6x-15x²-20x+30 =</span>3x3 – 11x2 – 26x + 30

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3 years ago

Read 2 more answers

In a bag of marbles 12% were blue 18% were green and the rest were purple if the bag has 150 marbles how many were blue or green

baherus [9]

Answer:

45

Step-by-step explanation:

12 % of the marbles are blue, and

18 % of the marbles are green, so

30 % of the marbles are either blue or green.

There are 150 marbles.

30 % × 150 = 0.30 × 150 = 45

The number of blue or green marbles is 45.

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3 years ago