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3 years ago

Factor completely 2x2 − 50.

Mathematics

2 answers:

Dafna11 [192]3 years ago

6 0

Answer:

b) 2(x - 5)(x + 5)

Step-by-step explanation:

2x² - 50

2(x² - 25)

(x² - 25) is a difference of squares and it equals (x - 5)(x + 5)

So the answer is;

2(x - 5)(x + 5)

Ede4ka [16]3 years ago

3 0

Answer:

(B) 2(x+5)(x−5)

Explanation:

Factor 2x²−50

2(x+5)(x−5)

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In a ΔPQR, ∠Q = 90 , PQ = 5 cm, QR = 12cm. If QS is the altitude then QS is equal to?

ryzh [129]

Answer:

QS EQUAL TO IS ?

Step-by-step explanation:

In a ΔPQR, ∠Q = 90 , PQ = 5 cm, QR = 12cm. If QS is the altitude then QS is equal to?

4 0

3 years ago

Problem 4: Solve the initial value problem

pishuonlain [190]

Separate the variables:

$y' = \dfrac{dy}{dx} = (y+1)(y-2) \implies \dfrac1{(y+1)(y-2)} \, dy = dx$

Separate the left side into partial fractions. We want coefficients a and b such that

$\dfrac1{(y+1)(y-2)} = \dfrac a{y+1} + \dfrac b{y-2}$

$\implies \dfrac1{(y+1)(y-2)} = \dfrac{a(y-2)+b(y+1)}{(y+1)(y-2)}$

$\implies 1 = a(y-2)+b(y+1)$

$\implies 1 = (a+b)y - 2a+b$

$\implies \begin{cases}a+b=0\\-2a+b=1\end{cases} \implies a = -\dfrac13 \text{ and } b = \dfrac13$

So we have

$\dfrac13 \left(\dfrac1{y-2} - \dfrac1{y+1}\right) \, dy = dx$

Integrating both sides yields

$\displaystyle \int \dfrac13 \left(\dfrac1{y-2} - \dfrac1{y+1}\right) \, dy = \int dx$

$\dfrac13 \left(\ln|y-2| - \ln|y+1|\right) = x + C$

$\dfrac13 \ln\left|\dfrac{y-2}{y+1}\right| = x + C$

$\ln\left|\dfrac{y-2}{y+1}\right| = 3x + C$

$\dfrac{y-2}{y+1} = e^{3x + C}$

$\dfrac{y-2}{y+1} = Ce^{3x}$

With the initial condition y(0) = 1, we find

$\dfrac{1-2}{1+1} = Ce^{0} \implies C = -\dfrac12$

so that the particular solution is

$\boxed{\dfrac{y-2}{y+1} = -\dfrac12 e^{3x}}$

It's not too hard to solve explicitly for y; notice that

$\dfrac{y-2}{y+1} = \dfrac{(y+1)-3}{y+1} = 1-\dfrac3{y+1}$

Then

$1 - \dfrac3{y+1} = -\dfrac12 e^{3x}$

$\dfrac3{y+1} = 1 + \dfrac12 e^{3x}$

$\dfrac{y+1}3 = \dfrac1{1+\frac12 e^{3x}} = \dfrac2{2+e^{3x}}$

$y+1 = \dfrac6{2+e^{3x}}$

$y = \dfrac6{2+e^{3x}} - 1$

$\boxed{y = \dfrac{4-e^{3x}}{2+e^{3x}}}$

7 0

2 years ago

Alan and Margot drive from City A to City B a distance of 147 miles. They take the same route and drive at constant speeds. Alan

S_A_V [24]

If one of them got there faster, who will it be?? 147 Miles keep that in mind ok. If they go on the Same route and Drive at Constant Speed. And Alan will start at 1:45 to 4:15. You will see the Difference of, 1:45 = 4:15 The 1 Has switched into the tens and the 4 Has Switched into The 100's. Alan Got there Fast. Margot Got there Faster. If you can Solve The Equation y=64x It will be 36y. 36 Miles speed. Well they need gas? we will find out later. Margot Got to City a To City B. so the Answer is. Margot Got there Fast Before Alan.

5 0

3 years ago

Help I don’t understand this appreciate any help

ella [17]

Theres nothing attached..

5 0

3 years ago

Read 2 more answers

Which point is a distance of 5 units from the point (1,9)?

Fantom [35]

You just need to plot them on a graph and see how many spaces are in between each. So if you plot (1,9) remember it's X, Y axis. Start from zero on the graph. Since it's positive go over 1 to the right and up 9. Then do the same for the rest. Then count how many units are between each point on the graph and find the one that is 5 units apart.

4 0

3 years ago