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3 years ago

Find the solution of this system of equations.

Mathematics

1 answer:

Drupady [299]3 years ago

4 0

{x= 0 + y ⇒ x=y
{3x + 12y= 15

3y + 12y = 12
15y = 15
y = 1

x = y = 1

Answer: x=1, y=1

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A submarine travels 6.6 km due West from its base and then turns and travels due South for 3.9

geniusboy [140]

Answer:

$7.7$ km

Step-by-step explanation:

The submarine's path from its base forms a right triangle when its final position is "connected" to the base. We know that the right triangle has legs of $6.6$ km and $3.9$ km, and we need to find the length of its hypotenuse. To do so, we can use the Pythagorean Theorem, which states that in a right triangle, $a^{2}+b^{2} =c^{2}$ , where $a$ and $b$ are the lengths of the triangle's legs and $c$ is the length of the triangle's hypotenuse. In this case, we know what $a$ and $b$ are, and we need to solve for c, so after substituting the given values of $a$ and $b$ into $a^{2}+b^{2} =c^{2}$ to solve for c, we get:

$a^{2}+b^{2} =c^{2}$

$6.6^{2} +3.9^{2} =c^{2}$ (Substitute $a=6.6$ and $b=3.9$ into the equation)

$43.56+15.21=c^{2}$ (Evaluate the squares on the LHS)

$58.77=c^{2}$ (Simplify the LHS)

$c^{2}=58.77$ (Symmetric Property of Equality)

$\sqrt{c^{2} } =\sqrt{58.77}$ (Take the square root of both sides of the equation)

$c=7.7,c=-7.7$ (Simplify)

$c=-7.7$ is an extraneous solution because you can't have negative distance, if that makes sense, so therefore, the submarine is approximately $7.7$ km away from its base. Hope this helps!

7 0

3 years ago

A caterer needs to buy 21 pounds of pasta to cater a wedding. At a local store, 8 pounds of pasta cost $12. How much will the ca

Serggg [28]

Answer:

1. 8/$12=21/$x then cross multiply.

2. 1/$1.5, we're looking for cost so $1 is more reasonable

3. $31.5

Step-by-step explanation:

12x 21/ 8 = 31.5

7 0

3 years ago

Read 2 more answers

Connor is constructing square ABCD. He has plotted A at (−2, 4), C at (−1, 1) and D at (−3, 2). Which coordinate could be the lo

xeze [42]

Answer: The answer is B(0,3)

Step-by-step explanation: I took the test and made sure it was correct

8 0

3 years ago

Read 2 more answers

Can anyone help me about question 2

madreJ [45]

9514 1404 393

Answer:

3(4/3)^2543

Step-by-step explanation:

Using logarithms base 2, we have ...

$(a_n)^{\log{a_n}}=(a_{n+1})^{\log{a_{n-1}}}\\\\(\log{a_n})(\log{a_n}) = (\log{a_{n-1}})(\log{a_{n+1}}) \\\\ \dfrac{\log{a_{n+1}}}{\log{a_{n}}}=\dfrac{\log{a_n}}{\log{a_{n-1}}}=\dots\dfrac{\log_2{16}}{\log_2{8}}=\dfrac{4}{3}$

That is, the ratio of each term to the previous is a constant equal to 4/3. This is the definition of a geometric sequence. This sequence has first term 3 and common ratio 4/3, so the general term is ...

$\log_2 a_n=3\left(\dfrac{4}{3}\right)^{n-1}$

and the 2544th term is ...

$\boxed{\log_2{a_{2544}}=3\left(\dfrac{4}{3}\right)^{2543}}$

8 0

3 years ago

Given: AC – AR <1 = <2 Prove: <3 =<4

Katena32 [7]

Answer:

ΔCTA ≅ ΔDRA

Step-by-step explanation:

Triangles CTA and DRA are congruent by ASA postulate. This is because:

∠1 ≅ ∠2 (given)

AC ≅ AR (given)

∠A is the same for both triangles (they are opposite angles)

Then, correspondent angles and sides are congruent, for example, ∠3 ≅ ∠4

8 0

4 years ago