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2 years ago

The line 2x + 5y = 1 meets the curve x² + 5xy - 4y² + 10 = 0 at the points A and B

Mathematics

1 answer:

lys-0071 [83]2 years ago

7 0

Answer:

A(3,-1) and B( -2,1)

Step-by-step explanation:

2x+5y=1. , or. y=(1–2x)/5………….(1)

x^2+5xy-4y^2+10=0…………………..(2)

Putting y=(1–2x)/5 from eqn. (1)

x^2+5x.(1–2x)/5–4/25.(1–2x)^2 +10=0

or. 25x^2+25x.(1–2x)-4.(1+4x^2–4x)+250 = 0

or. 25x^2+25x-50x^2–4–16x^2+16x+250=0

or. 41x^2–41x-246=0

or x^2– x - 6=0

or. (x-3).(x+2)=0

=> x= 3 or -2

But y=(1–2x)/5

=> y= (1–6)/5 or. (1+4)/5

hence, y= -1. or. 1

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Translate the following into an algebraic expression: A number is 30% of 20% of the number x.

bezimeni [28]

Answer: 0.06x

Step-by-step explanation:

An algebraic expression is an expression consist of integer constants, variables, and algebraic operations.

The given statement: A number is 30% of 20% of the number x.

The required algebraic expression would be:

30% of 20% of x

$=\dfrac{30}{100}\times \dfrac{20}{100}\times x$ [we divide a percentage by 100 to convert it into decimal]

$=\dfrac{6}{100}\times x\\\\=0.06x$

Hence, the required algebraic expression would be :

0.06x

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3 years ago

Simplify the expression: 2(4 + 6j)

aniked [119]

Answer:

$\boxed{ \bold{ \huge{ \boxed{ \sf{8 + 12j}}}}}$

Step-by-step explanation:

$\sf{2(4 + 6j)}$

Distribute 2 through the parentheses

$\longrightarrow{ \sf{2 \times 4 + 2 \times 6j}}$

$\longrightarrow{ \sf{8 + 12j}}$

Hope I helped!

Best regards! :D

8 0

3 years ago

v-10=-3 I don't get how this would get a negative answer I don't get it and my teacher sucks at explaining these so plz help!!!!

o-na [289]

V-10=-3

add 10 by both sides (opposite of -10)

v= 7

6 0

3 years ago

Lydia ran 10 miles in 120 minutes. How many minutes did she run per mile?

Digiron [165]

Answer:

It took Lydia 12 minutes to run each mile

Step-by-step explanation:

120/10

6 0

3 years ago

Read 2 more answers

When the sample size and the sample proportion remain the same, a 90 percent confidence interval for a population proportion p w

deff fn [24]

Answer:

A 90% confidence interval for p will be narrower than the 99% confidence interval.

Step-by-step explanation:

The formula to compute the (1 - α) % confidence interval for a population proportion is:

$CI=\hat p\pm z_{\alpha /2}\sqrt{\frac{\hat p(1-\hat p)}{n}}$

Here $\hat p$ is the sample proportion.

The margin of error of the confidence interval is:

$MOE= z_{\alpha /2}\sqrt{\frac{\hat p(1-\hat p)}{n}}$

The MOE is dependent on:

Confidence level
Standard deviation
Sample size

The MOE is directly related to the confidence level and standard deviation.

So if any of the two increases then the MOE also increases, thus widening the confidence interval.

And the MOE is inversely related to the sample size.

So if the sample increases the MOE decreases and vice versa.

It is provided that the sample size and the sample proportion are not altered.

The critical value of z for 90% confidence level is:

$z_{\alpha/2}= z_{0.10/2}=z_{0.05}=1.645$

And the critical value of z for 99% confidence level is:

$z_{\alpha/2}= z_{0.05/2}=z_{0.05}=1.96$

So as the confidence level increases the critical value increases.

Thus, a 90% confidence interval for p will be narrower than the 99% confidence interval.

6 0

3 years ago