All categories

3 years ago

Does the following system have a unique solution? Why? 3x+2y= 9 14x + 10y = 14

Mathematics

1 answer:

Neko [114]3 years ago

7 0

<span>Yes, the determinant of the coefficient matrix is 2.</span>

You might be interested in

How do you solve for the quotient of (x^-1) - 1 ÷ x - 1?

Ber [7]

$\bf x^{-1}-1\div x-1\implies \implies \cfrac{1}{x}-1\div x-1\implies \cfrac{\frac{1}{x}-1}{~~x-1~~}\implies \cfrac{~~\frac{1-x}{x}~~}{\frac{x-1}{1}} \\\\\\ \cfrac{1-x}{x}\cdot \cfrac{1}{x-1}\implies \cfrac{-(\begin{matrix} x-1 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix})}{x}\cdot \cfrac{1}{\begin{matrix} x-1 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}}\implies -\cfrac{1}{x}\implies -x^{-1}$

3 0

4 years ago

There was a blizzard. Snow was falling at the rate of 4 1/2 inches per hour. If the snow keeps acclimating how long will 5 feet

Archy [21]

5 feet = 60 inches
4 1/2 inches = 1 hour
60 inches = 1 ÷ 4 1/2 x 60
= 13 1/3 hours

If the snow keeps accumulating, it would take 13 1/3 hours for 5 feet of snow to accumulate.

5 0

3 years ago

Read 2 more answers

The volume of two spheres are 327\pi in^{3} and 8829\pi in^{3}

Crazy boy [7]

A dimension of a sphere is its radius, so it correlates with its volume, thus

$\bf \qquad \qquad \textit{ratio relations}
\\\\
\begin{array}{ccccllll}
&\stackrel{ratio~of~the}{Sides}&\stackrel{ratio~of~the}{Areas}&\stackrel{ratio~of~the}{Volumes}\\
&-----&-----&-----\\
\cfrac{\textit{similar shape}}{\textit{similar shape}}&\cfrac{s}{s}&\cfrac{s^2}{s^2}&\cfrac{s^3}{s^3}
\end{array}\\\\
-----------------------------$

$\bf \cfrac{\textit{similar shape}}{\textit{similar shape}}\qquad \cfrac{s}{s}=\cfrac{\sqrt{s^2}}{\sqrt{s^2}}=\cfrac{\sqrt[3]{s^3}}{\sqrt[3]{s^3}}\\\\
-------------------------------\\\\
%The volume of two spheres are 327\pi in^{3} and 8829\pi in^{3}
\cfrac{small}{large}\qquad \cfrac{s}{s}=\cfrac{\sqrt[3]{s^3}}{\sqrt[3]{s^3}}\implies \cfrac{s}{s}=\cfrac{\sqrt[3]{327}}{\sqrt[3]{8829}}\qquad 
\begin{cases}
8829=3\cdot 3\cdot 3\cdot 327\\
\qquad 3^3\cdot 327
\end{cases}$

$\bf \cfrac{s}{s}=\cfrac{\sqrt[3]{327}}{\sqrt[3]{3^3\cdot 327}}\implies \cfrac{s}{s}=\cfrac{\underline{\sqrt[3]{327}}}{3\underline{\sqrt[3]{327}}}\implies \cfrac{s}{s}=\cfrac{1}{3}$

6 0

3 years ago

What is 1,450,000 in scientificnotation

geniusboy [140]

Answer:

The answer is 1.45*10^6

4 0

3 years ago

I need help with 12 13 and 14

nikdorinn [45]

Answer: Lines $\frac{}{BC}$ and $\frac{}{EF}$ are different lengths.

Step-by-step explanation:

The distance formula is $\sqrt{(x_1-x_2) ^{2}+(y_1-y_2) ^{2} }$ , and you can use this formula to solve for the lengths of both lines $\frac{}{BC}$ and $\frac{}{EF}$ .

For line $\frac{}{BC}$ , let $x_{1}$ = the x at point B, or 1, and let $x_{2}$ = the x at point C, or 2.

Now, let $y_{1}$ = the y at point B, or 4, and let $y_{2}$ = the y at point C, or -1.

Now, solve the formula to find the length $\frac{}{BC}$ = $\sqrt{(x_1-x_2) ^{2}+(y_1-y_2) ^{2} }\\$ .

$\frac{}{BC}$ = $\sqrt{(1-2)^{2} +(4-(-1))^2$

$\frac{}{BC}$ = $\sqrt{(-1)^{2} +(4+1)^2$

$\frac{}{BC}$ = $\sqrt{1 +5^2$

$\frac{}{BC}$ = $\sqrt{(1+25)$

$\frac{}{BC}$ = $\sqrt{26} \\$

Now, for line $\frac{}{EF}$ , let $x_{1}$ = the x at point E, or -4, and let $x_{2}$ = the x at point F, or -1.

Let $y_{1}$ = the y at point E, or -3, and let $y_{2}$ = the y at point F, or 1.

Now, solve the formula to find the length $\frac{}{EF}$ = $\sqrt{(x_1-x_2) ^{2}+(y_1-y_2) ^{2} }\\$ .

$\frac{}{EF}$ = $\sqrt{(-4-(-1))^{2} +(-3-1)^2$

$\frac{}{EF}$ = $\sqrt{(-4+1)^{2} +(-4)^2$

$\frac{}{EF}$ = $\sqrt{(-3)^2+16$

$\frac{}{EF}$ = $\sqrt{(9+16)$

$\frac{}{EF}$ = $\sqrt{25}$

$\frac{}{EF}$ = 5

Now, look back at $\frac{}{BC}$ . The two lines have different lengths, so you have now justified the fact that they are not the same.

Questions 13 and 14 would be solved in much the same way- but please let me know if you want me to show the work for those as well!

7 0

3 years ago