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3 years ago

Hi I was a little confused on dilation can anyone help me (will mark Brainly)

Mathematics

1 answer:

Westkost [7]3 years ago

7 0

Just divide the distance of each to point P by 2.

C would be 1 unit above and 2 units to the right of P.

D would be 1 unit below and 2 units to the right of P.

And so on...

Hope this helps

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A woman is q years old while her son is p years old. the sum of their ages is equal to twice the difference of their ages. the p

Allisa [31]

Step-by-step explanation:

Given

$q + p = 2(q - p)$

as equation 1.

I used q-p as the difference as logically the woman will be older than her son.

Also given,

$qp = 675$

as equation 2.

Using equation 2,

$q = \frac{675}{p}$

substitute this equation into equation 1.

$\frac{675}{p} + p = 2( \frac{675}{p} - p) \\ \frac{675}{p} + p = \frac{1350}{p} - 2p \\ \frac{675}{p} - \frac{1350}{p} = - 2p - p \\ - 3p = - \frac{675}{p} \\ - 3p \times p = - 675 \\ - 3 {p}^{2} = - 675 \\ {p}^{2} = - 675 \div - 3 \\ {p}^{2} = 225 \\ p = \sqrt{225} \\ = 15$

Substitute P into equation 2.

$15q = 675 \\ q = 675 \div 15 \\ = 45$

Therefore the woman is 45 years old while her son is 15 years old.

3 0

3 years ago

Suppose a, b denotes of the quadratic polynomial x² + 20x - 2022 & c, d are roots of x² - 20x + 2022 then the value of ac(a

Alja [10]

<h3><u>Correct Question :- </u></h3>

$\sf\:a,b \: are \: the \: roots \: of \: {x}^{2} + 20x - 2020 = 0 \: and \: \\ \sf \: c,d \: are \: the \: roots \: of \: {x}^{2} - 20x + 2020 = 0 \: then \:$

$\sf \: ac(a - c) + ad(a - d) + bc(b - c) + bd(b - d) =$

(a) 0

(b) 8000

(d) 16000

$\large\underline{\sf{Solution-}}$

Given that

$\red{\rm :\longmapsto\:a,b \: are \: the \: roots \: of \: {x}^{2} + 20x - 2020 = 0}$

We know

$\boxed{\red{\sf Product\ of\ the\ zeroes=\frac{Constant}{coefficient\ of\ x^{2}}}}$

$\rm \implies\:ab = \dfrac{ - 2020}{1} = - 2020$

And

$\boxed{\red{\sf Sum\ of\ the\ zeroes=\frac{-coefficient\ of\ x}{coefficient\ of\ x^{2}}}}$

$\rm \implies\:a + b = - \dfrac{20}{1} = - 20$

Also, given that

$\red{\rm :\longmapsto\:c,d \: are \: the \: roots \: of \: {x}^{2} - 20x + 2020 = 0}$

$\rm \implies\:c + d = - \dfrac{( - 20)}{1} = 20$

and

$\rm \implies\:cd = \dfrac{2020}{1} = 2020$

Now, Consider

$\sf \: ac(a - c) + ad(a - d) + bc(b - c) + bd(b - d)$

$\sf \: = {ca}^{2} - {ac}^{2} + {da}^{2} - {ad}^{2} + {cb}^{2} - {bc}^{2} + {db}^{2} - {bd}^{2}$

$\sf \: = {a}^{2}(c + d) + {b}^{2}(c + d) - {c}^{2}(a + b) - {d}^{2}(a + b)$

$\sf \: = (c + d)( {a}^{2} + {b}^{2}) - (a + b)( {c}^{2} + {d}^{2})$

$\sf \: = 20( {a}^{2} + {b}^{2}) + 20( {c}^{2} + {d}^{2})$

$\sf \: = 20\bigg[ {a}^{2} + {b}^{2} + {c}^{2} + {d}^{2}\bigg]$

We know,

$\boxed{\tt{ { \alpha }^{2} + { \beta }^{2} = {( \alpha + \beta) }^{2} - 2 \alpha \beta \: }}$

So, using this, we get

$\sf \: = 20\bigg[ {(a + b)}^{2} - 2ab + {(c + d)}^{2} - 2cd\bigg]$

$\sf \: = 20\bigg[ {( - 20)}^{2} + 2(2020) + {(20)}^{2} - 2(2020)\bigg]$

$\sf \: = 20\bigg[ 400 + 400\bigg]$

$\sf \: = 20\bigg[ 800\bigg]$

$\sf \: = 16000$

Hence,

$\boxed{\tt{ \sf \: ac(a - c) + ad(a - d) + bc(b - c) + bd(b - d) = 16000}}$

<em>So, option (d) is correct.</em>

4 0

2 years ago

3.0035 into a fraction

cupoosta [38]

35 is in the ten-thousandths place, so write it as a fraction over 10,000:

35/10000

Simplify:

7/2000

So we have:

3 7/2000 in mixed number form or 6007/2000 in improper fraction form.

6 0

4 years ago

Read 2 more answers

Hurry!! MATH TEST <br> Ill make brainlest and pls show work if you can!

padilas [110]

Answer:

option 1

Step-by-step explanation:

if it goes up 6 then it means plus 6

8 0

3 years ago

Find the area of ABCD

cricket20 [7]

Answer:

640 cm²

Step-by-step explanation:

The ratio of the area of 2 similar polygons = the ratio of the square of their corresponding lengths

Thus:

Area of Trapezoid ABCD to Area of Trapezoid EFGH = AB² to EF²

Area of Trapezoid ABCD = ? = x

Area of Trapezoid EFGH = 40 cm²

AB = 20 cm

EF = 5 cm

Substitute

x:40 = 20²:5²

x/40 = 400/25

x/40 = 16

Cross multiply

x = 16*40

x = 640

Area of trapezoid ABCD = 640 cm²

5 0

3 years ago