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Misha Larkins [42]

2 years ago

15

What is the completely factored form of 20x² – 45

1 answer:

Nina [5.8K]2 years ago

4 0

Answer:

5(2x(2x + 3) - 3 ( 2x +) or 5(2x -3) (2x + 3)

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A construction company completes two projects. The first project has $3,000 in labor expenses for 60 hours worked, while the sec

d1i1m1o1n [39]

Answer: 2,100 = 0.02(42) + b

2,100 = 50(42) + b

Step-by-step explanation: good day man

3 0

1 year ago

a baker is making bread dough.He uses 3 cups of flour for every 8 ounces of water. How many cups of flour will be use if he used

Nataliya [291]

Answer:

36 cups of flour

Step-by-step explanation:

if 3 cups of flour=8 ounces.what about 96 onces you cross multiply

7 0

2 years ago

Rewrite the equation y−2=−3/2(x+6) in standard form.

navik [9.2K]

For this case we have that by definition, the standard form of the equation of the line is given by:

$ax + by = c$

We have the following equation:

$y-2 = - \frac {3} {2} (x + 6)$

We manipulate the equation algebraically:

$y-2 = - \frac {3} {2} x- \frac {3 * 6} {2}\\y-2 = - \frac {3} {2} x \frac {18} {2}\\y-2 = - \frac {3} {2} x-9\\y-2 + 9 = - \frac {3} {2} x\\y-7 = - \frac {3} {2} x\\2 (y-7) = - 3x\\2y-14 = -3x\\3x + 2y = 14$

Finally, the equation is:

$3x + 2y = 14$

Answer:

$3x + 2y = 14$

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

(c) 8080

(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

Find the coordinates of the midpoint M of ST. Then find the distance between points S and T. Round the distance to the nearest

ololo11 [35]

Answer:

Step-by-step explanation:

M is the midpoint

=> $\left \{ {{x=\frac{6+7}{2} } \atop {y=\frac{-3-2}{2} }} \right$

⇔ $\left \{ {x=\frac{13}{2} } \atop {y=\frac{-5}{2}}} \right.$

⇒M( $\frac{13}{2}$ ; $\frac{-5}{2}$ )

ST= $\sqrt{(7-6) ^{2} +(-2+3)^{2}$ = $\sqrt{2}$ =1.414

8 0

2 years ago