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3 years ago

Find the area of rectangle ABCD. 20 10 √2+ √82 24 12

Mathematics

2 answers:

QveST [7]3 years ago

7 0

Answer:

12 units²

Step-by-step explanation:

AB = $\sqrt{(x_{2} -x_{1})^2 +(y_{2} -y_{1})^2 }$ = $\sqrt{(0-3)^2 +(0-3)^2}$ = 3√2

BC = $\sqrt{(5-3)^2 +(1-3)^2}$ = 2√2

$A_{ABCD}$ = AB × BC = 3√2 × 2√2 = 12 units²

gregori [183]3 years ago

7 0

Answer:

So I did the assignment, and the answer that you're looking for in this problem would be 12.

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In the expansion (ax+by)^7, the coefficients of the first two terms are 128 and -224, respectively. Find the values of a and b

madam [21]

Answer:

a = 2, b = 3.5

Step-by-step explanation:

Expanding $(ax+by)^7$ using Binomial expansion, we have that:

$(ax+by)^7$ =

$(ax)^7(by)^0 + (ax)^6(by)^1 + (ax)^5(by)^2 + (ax)^4(by)^3 + (ax)^3(by)^4 + (ax)^2(by)^5 + (ax)^1(by)^6 + (ax)^0(by)^7$

$= (a)^7(x)^7+ (a)^6(x)^6(b)(y) + (a)^5(x)^5(b)^2(y)^2 + (a)^4(x)^4(b)^3(y)^3 + (a)^3(x)^3(b)^4(y)^4 + (a)^2(x)^2(b)^5(y)^5 + (a)(x)(b)^6(y)^6 + (b)^7(y)^7\\\\\\= (a)^7(x)^7+ (a)^6(b)(x)^6(y) + (a)^5(b)^2(x)^5(y)^2 + (a)^4(b)^3(x)^4(y)^3 + (a)^3(b)^4(x)^3(y)^4 + (a)^2(b)^5(x)^2(y)^5 + (a)(b)^6(x)(y)^6 + (b)^7(y)^7$

We have that the coefficients of the first two terms are 128 and -224.

For the first term:

=> $a^7 = 128$

=> $a = \sqrt[7]{128}\\ \\\\a = 2$

For the second term:

$a^6b = -224$

$b = \frac{-224}{a^6}$

$b = \frac{-224}{2^6} \\\\\\b = \frac{-224}{64} \\\\\\b = 3.5$

Therefore, a = 2, b = 3.5

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3 years ago

Priscilla invests $10,000 in an account that compounds interest continuously and earns 11%. How long will it take for her money

Shkiper50 [21]

Answer:

Step-by-step explanation:

When the interest compounds continuously, our formula is

$A(t)=Pe^{rt}$

If we start with 10000 and are looking for how long, t, it takes to double, we are looking for how long it will take for our account to have 2 times 10000. That's 20000. Therefore, our equation is

$20000=10000e^{.11t}$

Divide both sides by 10000 to get

$2=e^{.11t}$

Take the natural log of both sides to "undo" that e:

$ln(2)=ln(e^{.11t})$

Again, since ln and e undo each other what we have now is

ln(2) = .11t and

$\frac{ln(2)}{.11}=t$ so

t = 6.3 years

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3 years ago

Absolute value of |9|

oee [108]

Answer:

The absolute value of 9 is... 9.

Step-by-step explanation:

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3 years ago

Factoring polynomials. Please help I suck at factoring (especially polynomials) Ill give brainiest too

BlackZzzverrR [31]

the two numbers are -36 and -2.. thier product is 72 but thier sum is -38..

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6 0

2 years ago

suppose that you plan on taking a summer job selling magazines subscriptions . the magazine company will help you pay $0.75 for

alina1380 [7]

Answer:

Money earned by selling 175 magazine subscriptions will be 3176.25

Solution:

Given that you are planning to take a summer job selling magazine subscription.

For first subscription, magazine company will help you to pay $0.75

For each additional subscription sold, magazine company will pay you $0.20 more than what was paid for previous subscription.

So for second subscription, payments will be = 0.75 + 0.20 = 0.75 + 0.20 x 1

And for third subscription, payments will be = 0.75 + 0.20 = 0.75 + 0.20 x 2

Generalizing for nth subscription we get

Payments for nth subscription = 0.75 + 0.20(n-1)

so here we can see that arithmetic sequence is formed, having first term

$a_1 = 0.75$ and common difference = d = 0.20

We need to determine sum of above arithmetic sequence for n = 175

Formula for sum of arithmetic sequence is as follows 

$\mathrm{S}_{\mathrm{n}}=\frac{n}{2}[2 a+(n-1) d]$

In our case n = 175, a = 0.75, d = 0.20

$\begin{array}{l}{=>\mathrm{S}_{175}=\frac{175}{2}[(2 \times 0.75)+(175-1) 0.20]} \\\\ {=>\mathrm{S}_{175}=\frac{175}{2}[1.5+(174 \times 0.20)]} \\\\ {\Rightarrow \mathrm{S}_{175}=\frac{175}{2} \times 36.3=3176.25}\end{array}$

Hence money earn by selling 175 magazine subscriptions will be 3176.25

6 0

3 years ago