What is 16 to the one billionth power

The sum of two numbers is 9.9, and the sum of the squares of the numbers is 53.21. What are the numbers?

Snezhnost [94]

Answer:

There are two possibilities:

$x_{1} = 3.5$ and $y_{1} = 6.4$

$x_{2} = 6.4$ and $y_{2} = 3.5$

Step-by-step explanation:

Mathematically speaking, the statement is equivalent to this 2-variable non-linear system:

$x + y = 9.9$

$x^{2} + y^{2} = 53.21$

First, $x$ is cleared in the first equation:

$x = 9.9 - y$

Now, the variable is substituted in the second one:

$(9.9-y)^{2} + y^{2} = 53.21$

And some algebra is done in order to simplify the expression:

$98.01-19.8\cdot y +2\cdot y^{2} = 53.21$

$2\cdot y^{2} -19.8\cdot y +44.8 = 0$

Roots are found by means of the General Equation for Second-Order Polynomials:

$y_{1} \approx \frac{32}{5}$ and $y_{2} \approx \frac{7}{2}$

There are two different values for $x$ :

$y = y_{1}$

$x_{1} = 9.9-6.4$

$x_{1} = 3.5$

$y = y_{2}$

$x_{2} = 9.9 - 3.5$

$x_{2} = 6.4$

There are two possibilities:

$x_{1} = 3.5$ and $y_{1} = 6.4$

$x_{2} = 6.4$ and $y_{2} = 3.5$

5 0

3 years ago

An __________ is a mathematical sentence in which two sides are not equal and are separated with the symbols <, >, ≥, ≤

Artist 52 [7]

Answer: An inequality is a mathematical or arithmetic phrase that is not equal; this inequality prohibits the equal sign. Instead, inequalities are expressed with greater than (>), less than (<), equal to or greater than (≥) or equal to or less than (≤).

7 0

3 years ago

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What is the solution to -1/6 + (-3/7)

BartSMP [9]

Answer:

-25/42

Step-by-step explanation:

4 0

3 years ago

Identify a benchmark to find the equivalent percent for 6/10

Oxana [17]

60%=6/10

Hope this helps please mark this as brainliest answer

4 0

3 years ago

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You make $25000 a year, and you get a 10% raise. Your new salary is $____ The next year you get a 10% cut. Your new salary is $_

gtnhenbr [62]

Firstly, we have to find out what 10% of $25000 is. To do this, multiply $25000 by 0.1 (10% in decimal form): $\$25000 \times 0.1=\$2500$ . $2500 is the 10% raise.

Next, to find your first new salary, add $25000 and $2500 together: $\$25000+\$2500=\$27500$ . $27500 is your new salary after the 10% raise.

Next, we need to find 10% of $27500. It's a similar process as to finding 10% of $25000. $\$27500 \times 0.1=\$2750$ . $2750 is your 10% cut.

Next, since this is a cut, subtract $2750 from $27500. $\$27500-\$2750=\$24750$ . $24750 is your new salary after the 10% cut.

Next, to find the percentage change, firstly divide $24750 by $25000. $\frac{\$24750}{\$25000}=0.99\ \textsf{or}\ 99\%$ . Now this shows that your current salary is 99% of what you used to make. It is not how much less you make. To find how much less it is, subtract 99% from 100%: $100\%-99\%=1\%$ . Your current salary is 1% less than what you used to make.

6 0

4 years ago