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2 years ago

Second part need help ASAP

Mathematics

1 answer:

jarptica [38.1K]2 years ago

7 0

statements 13-L , 15-F , 6-G , and 10-C are true statements

hope this helps!

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wo lines, R and M, are represented by the following equations: Line R: 2x + 2y = 18 Line M: x + y = 9 Which statement is true ab

yanalaym [24]

There is an infinite number of solutions being as they are the same line. You can tell this because the first is simply the second line divided by 2.

3 0

2 years ago

HELP? .................................................

joja [24]

Answer:

the last option

Step-by-step explanation:

I'm smart

4 0

2 years ago

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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

What is the y-intercept of a line that has a slope of 1/4 and passes through point (8, 3)? 1 3 5 11

Paha777 [63]

Slope (m) = 1/4
slope-intercept format is: y = mx + b
point-slope format is: y-k = m (x-h), where the point is at (h, k)
So we plug in for that using the point (8, 3):
y-3 = 1/4(x-8)
y-3 = 1/4x - 2 --> solve for y:
y-3+3 = 1/4x -2 +3
y = 1/4x + 1 --> now it's in slope-intercept format where the b is the y-intercept, which is +1

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2 years ago

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Find the 7th term of the geometric sequence -2, 6, -18, 54, -162, ...

AlladinOne [14]

Answer:

-1458

Step-by-step explanation:

Let's find the rule of the sequence. It seems that each term is -3 times the previous term.

Let's continue the sequence.

486, -1458

-1458 is the 7th term

4 0

2 years ago