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2 years ago

Circle A has been enlarged to create circle A'. The table below shows the circumference of both circles.

Mathematics

1 answer:

stich3 [128]2 years ago

8 0

Answer:

Option (2) 1.5

Step-by-step explanation:

Rule for the dilation of an image by a scale factor is,

Scale factor = $\frac{\text{Radius of image circle A'}}{\text{Radius of pre-image A}}=\frac{r'}{r}$

= $\frac{(2\pi) r'}{(2\pi) r}$

= $\frac{\text{Circumference of image}}{\text{Circumference of pre-image}}$

= $\frac{10.5}{7}$

= 1.5

Therefore, scale factor was used to create a circle A' = 1.5

Option (2) will be the correct option.

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If the sum of the zereos of the quadratic polynomial is 3x^2-(3k-2)x-(k-6) is equal to the product of the zereos, then find k?

lys-0071 [83]

Answer:

Step-by-step explanation:

So I'm going to use vieta's formula.

Let u and v the zeros of the given quadratic in ax^2+bx+c form.

By vieta's formula:

1) u+v=-b/a

2) uv=c/a

We are also given not by the formula but by this problem:

3) u+v=uv

If we plug 1) and 2) into 3) we get:

-b/a=c/a

Multiply both sides by a:

-b=c

Here we have:

a=3

b=-(3k-2)

c=-(k-6)

So we are solving

-b=c for k:

3k-2=-(k-6)

Distribute:

3k-2=-k+6

Add k on both sides:

4k-2=6

Add 2 on both side:

4k=8

Divide both sides by 4:

k=2

Let's check:

$3x^2-(3k-2)x-(k-6) \text{ with }k=2$ :

$3x^2-(3\cdot 2-2)x-(2-6)$

$3x^2-4x+4$

I'm going to solve $3x^2-4x+4=0$ for x using the quadratic formula:

$\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$\frac{4\pm \sqrt{(-4)^2-4(3)(4)}}{2(3)}$

$\frac{4\pm \sqrt{16-16(3)}}{6}$

$\frac{4\pm \sqrt{16}\sqrt{1-(3)}}{6}$

$\frac{4\pm 4\sqrt{-2}}{6}$

$\frac{2\pm 2\sqrt{-2}}{3}$

$\frac{2\pm 2i\sqrt{2}}{3}$

Let's see if uv=u+v holds.

$uv=\frac{2+2i\sqrt{2}}{3} \cdot \frac{2-2i\sqrt{2}}{3}$

Keep in mind you are multiplying conjugates:

$uv=\frac{1}{9}(4-4i^2(2))$

$uv=\frac{1}{9}(4+4(2))$

$uv=\frac{12}{9}=\frac{4}{3}$

Let's see what u+v is now:

$u+v=\frac{2+2i\sqrt{2}}{3}+\frac{2-2i\sqrt{2}}{3}$

$u+v=\frac{2}{3}+\frac{2}{3}=\frac{4}{3}$

We have confirmed uv=u+v for k=2.

4 0

2 years ago

3x- 5=1 what does x represent

V125BC [204]

Answer:

x=2

Step-by-step explanation:

3x=5+1

3x=6

x=6/3

x=2

8 0

2 years ago

Read 2 more answers

Explain in words how to find the product of -4 (-1.5) using a number line.where do you end up

Ierofanga [76]

Answer:

To multiply two minus numbers they will result as a positive number.

the product of any numbers when there is a negtive will always have 2 negtives invlved form three numbers including the answer.

-4 x -1.5 is the same as 4 x 1.5

the answer is 6

Three numbers like -1 x 4 will also be 2 numbers of negative.

= -4

We change this to -4 x 1.5 and shows the answer as -6

But the question had 2 negative numbers already and the answer is just positive 6.

8 0

2 years ago

Read 2 more answers

1. Evaluate x2 + 10 if we let x= 3

snow_tiger [21]

Answer:

Step-by-step explanation:

$x2 + 10 \\ = 3 \times 2 + 10 \\ = 6 + 10 \\ = 16$

4 0

2 years ago

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What does y=5x+4 look like on slope intercept form?

valentina_108 [34]

Beachside it is supposed to be 619 into that form

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2 years ago