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4 years ago

Solve the system using elimination: 12x - 8y = -12 6x + 4y = -30

Mathematics

1 answer:

lubasha [3.4K]4 years ago

4 0

Answer: (-3,6)

Step-by-step explanation:

multiply the bottom by 2

12x-8y=-12

12x+8y=-60

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

24x=-72

x=-3

so.......

12(3)-8y=-12

36-8y=-12

-8y=-48

y=6

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The circumference of a circular painting is 59.66 feet. What is the radius of the painting? Use 3.14 for π and do not round your

Studentka2010 [4]

Answer:

9.5 feet

Step-by-step explanation:

So let's review the equations we need to know.

Circumference= π x d or π x 2r

Since we are solving for r, let's stick with the 2nd one.

Next, plug in the values.

59.66=3.14 x 2r

simplify.

59.66=6.28r

9.5=r

done!

the radius is 9.5 feet!

3 0

4 years ago

The digit 5 appears twice in the number 255,120. How does the total value of the 5 on the right compare to the total value of th

maksim [4K]

Answer:

The value of the first " $5$ " in the number $255,\!120$ is ten times that of the second " $5\!$ " in this number.

Step-by-step explanation:

What gives the number " $255,\!120$ " its value? Of course, each of its six digits has contributed. However, their significance are not exactly the same. For example, changing the first $\verb!5!$ to $\verb!6!$ would give $2\mathbf{6}5,\!120$ and increase the value of this number by $10,\!000$ . On the other hand, changing the second $\verb!5!\!$ to $\verb!6!\!$ would give $25\mathbf{6},\!120$ , which is an increase of only $1,\!000$ compared to the original number.

The order of these two digits matter because the number " $255,\!120$ " is written using positional notation. In this notation, the position of each digits gives the digit a unique weight. For example, in $255,\!120\!$ :

$\begin{array}{|r||c|c|c|c|c|c|}\cline{1-7}\verb!Digit!& \verb!2! & \verb!5! & \verb!5! & \verb!1! & \verb!2! & \verb!0!\\\cline{1-7}\textsf{Index} & 5 & 4 & 3 & 2 & 1& 0 \\ \cline{1-7} \textsf{Weight} & 10^{5} & 10^{4} & 10^{3} & 10^{2} & 10^{1} & 10^{0}\\\cline{1-7}\end{array}$ .

(Note that the index starts at $0$ from the right-hand side.)

Using these weights, the value $255,\!120$ can be written as the sum:

$\begin{aligned}& 255,\!120\\ &= 2 \times 10^{5} + 5 \times 10^{4} + 5 \times 10^{3} + 1 \times 10^{2} + 2 \times 10^{1} + 0 \times 10^{0} \\&=200,\!000 + 50,\!000 + 5,\!000 + 100 + 20 + 0 \end{aligned}$ .