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4 years ago

14

How many solutions does this equation have?

1 answer:

larisa86 [58]4 years ago

7 0

<em>Answer:</em>

<em>B) exactly one solution</em>

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Find the two horizontal and two vertical tangent lines of the equation x^2+xy+y^2=9.

valina [46]

Differentiating w.r.t y,
We get,

<span>2 x (d x/d y) + y (d x/d y) + x + 2 y = 0 </span>

<span>Put
d x/d y = 0 </span>

The equation becomes:
<span>x=2 y </span>

<span>substituting into main equation

We, get

3 y^2 =9 </span>

y= √3

x = <span>± 2√3</span>

3 0

3 years ago

Which of the following statements are true regarding functions?<br><br> Check all that apply.

Alex

Answer:

The horizontal line test may be used to determine whether a function is one-to-one.
The vertical line test may be used to determine whether a relation is a function.

Step-by-step explanation:

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2 years ago

Reason A pack of 140 stickers contains sheets of 28 stickers. Each

xxTIMURxx [149]

Answer:

you could divide

Step-by-step explanation:

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3 years ago

The total amount paid on a 35 year loan was $98,000. If the interest rate was 4.1% and compounded monthly, what was the principa

Levart [38]

Answer:

The principal amount was $23,393.45

Step-by-step explanation:

The total amount paid on a 35 year loan was $98,000 at the rate of interest 4.1%

We will calculate Principal amount by this formula

$A=P(1+\frac{r}{n})^{nt}$

Where A = amount (98,000)

P = Principal amount (P)

r = rate of interest 4.1% (0.041)

n = number of compounding interest monthly (12)

t = time (35 years)

$98,000=P(1+\frac{0.041}{12})^{(12)(35)}$

$98,000=P(1+0.003416)^{(420)}$

$98,000=P(1.003416)^{(420)}$

98,000 = P(4.189386)

= 4.189386P = 98,000

P = $\frac{98000}{4.189386}$

P = 23,392.4494 ≈ $23,392.45

The principal amount was $23,393.45

5 0

4 years ago

Read 2 more answers

What is the exact solution for the equation

Nostrana [21]

Answer:

Option C is correct.

Exact solution of $2^{x+2} = 5^{2x}$ is, $\frac{2\ln 2}{2\ln 5 - \ln 2}$

Step-by-step explanation:

Given the equation: $2^{x+2} = 5^{2x}$

Using logarithmic rules:

$a^x=b^y$ ⇒ $x \ln a =y \ln b$

$\ln x^a = a\ln x$

Given: $2^{x+2} = 5^{2x}$

Taking logarithmic both sides:

$\ln 2^{x+2} = \ln 5^{2x}$

By logarithmic rules;

$(x+2) \ln 2 = (2x) \ln 5$

Using distributive property i.e $a\cdot (b+c) = a\cdot b + a\cdot c$

$x \ln 2 +2 \ln 2 = 2x \ln 5$

Subtract $x \ln 2$ from both sides we get;

$x \ln 2 +2 \ln 2 - x \ln 2= 2x \ln 5 - x \ln 2$

Simplify:

$2 \ln 2= 2x \ln 5 - x \ln 2$

or

$2 \ln 2= x (2\ln 5 - \ln 2)$

Divide both sides by $(2\ln 5 - \ln 2)$ we get;

$\frac{2\ln 2}{2\ln 5 - \ln 2} = x$

Therefore, the exact solution of the given equation is $\frac{2\ln 2}{2\ln 5 - \ln 2}$

7 0

3 years ago