In our Solar system six of the eight planets have moons what percentage of the planets have moons

Graph the line given by 2x+y=1 and the circle given by x²+y²=10.Find all solutions to the system of equations. Verify your resul

Aleksandr-060686 [28]

Answer:

(1.8, -2.6) and (-1, 3)

Step-by-step explanation:

$2x+y=1$

$x^2+y^2=10$

From the first equation

$y=1-2x$

Applying to the second equation

$x^2+(1-2x)^2=10\\\Rightarrow x^2+1+4x^2-4x=10\\\Rightarrow 5x^2-4x-8=0$

Solving the equation we get

$x=\frac{-\left(-4\right)+\sqrt{\left(-4\right)^2-4\cdot \:5\left(-9\right)}}{2\cdot \:5}, \frac{-\left(-4\right)-\sqrt{\left(-4\right)^2-4\cdot \:5\left(-9\right)}}{2\cdot \:5}\\\Rightarrow x=1.8, -1$

At x = 1.8

Applying in first equation

$2\times 1.8+y=1\\\Rightarrow y=1-3.6\\\Rightarrow y=-2.6$

At x = -1

Applying in first equation

$2\times -1+y=1\\\Rightarrow y=1+2\\\Rightarrow y=3$

∴ The circle and line intersect at points (1.8, -2.6) and (-1, 3)

3 0

3 years ago

Calculus= Integrate 5^x dx please break down how answer is 1/6x^6+C

aleksley [76]

Answer:

$\int\limits {5^x} \, dx = \frac{5^x}{ln\ x} + c$

Step-by-step explanation:

Note that the integral of $5^x$ is not $\frac{1}{6}x^6 + c$

The solution is as follows:

Given

$5^x$

Required

Integrate

Represent the given expression using integral notation

$\int\limits {5^x} \, dx$

This question can't be solved directly;

We'll make use of exponential rules which states;

$\int\limits {a^x} \, dx = \frac{a^x}{ln\ x} + c$

By comparing $\int\limits {5^x} \, dx$ with $\int\limits {a^x} \, dx$ ;

we can substitute 5 for a;

Hence, the expression $\int\limits {a^x} \, dx = \frac{a^x}{ln\ x} + c$ becomes

$\int\limits {5^x} \, dx = \frac{5^x}{ln\ x} + c$

-------------------------------------------------------------------------------------

However, the integral of $x^5$ is $\frac{1}{6}x^6 + c$

This is shown below:

Given that $x^5$

Applying power rule;

Power rule states that

$\int\limits{x^n}\ dx = \frac{x^{n+1}}{n+1} + c$

In this case ( $x^5$ ), n = 5;

So, $\int\limits{x^n}\ dx= \frac{x^{n+1}}{n+1} + c$

becomes

$\int\limits{x^5}\ dx = \frac{x^{5+1}}{5+1} + c$

$\int\limits{x^5}\ dx = \frac{x^{6}}{6} + c$

$\int\limits{x^5}\ dx= \frac{x^{6}}{6} + c$

4 0

3 years ago

Please help I’ll give brainliest

Tanzania [10]

Answer:

it answer would be 50% coz we take out percentage from 100.

Step-by-step explanation:

first add 17% and 33% it would be 50%

then subtract 50%from 100%

answer would be 50%

8 0

3 years ago

Read 2 more answers

( 1 2 x− 3 8 )÷ 1 3 + 4 7 (5− 1 4 x) PLS ASAP

Ugo [173]

Answer:

12x-3+ 235-658x

-646x+232

HOPE THIS HELPS!!!!!!!!

4 0

3 years ago

In ΔABC, c = 630 inches, ∠C=165° and ∠A=11°. Find the length of a, to the nearest inch.

Dvinal [7]

Answer:

464

Step-by-step explanation:

Find other angle:

<B = 180 - 165 - 11 = 4

Then plug in (opposite sides go together):

$\frac{a}{sin 11}$ = $\frac{630}{sin 165}$

$a = \frac{630 sin 11}{sin 165} = 464.454 = 464$

8 0

3 years ago