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Arlecino [84]
3 years ago
9

How many solutions does the following system of equations have?

Mathematics
1 answer:
True [87]3 years ago
6 0
We will use a method of substitution.
y = 5/2 x + 2 
2 y = 5 x + 4   ⇒  2 ( 5/2 x + 2 )= 5 x + 4
5 x + 4 = 5 x + 4
0 x = 0            ⇒  x, y ∈ R
Answer: D)   
This system has infinitely many solutions.
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Give all solutions if the nonlinear system of equations, including those with no real complex components.
konstantin123 [22]
\left\{\begin{array}{ccc}y=x^2+6x\\4x-y=-24\end{array}\right\\\\substitute:\\\\4x-(x^2+6x)=-24\\\\4x-x^2-6x+24=0\\\\-x^2-2x+24=0\\\\a=-1;\ b=-2;\ c=24\\\\\Delta=b^2-4ac

\Delta=(-2)^2-4\cdot(-1)\cdot24=4+96=100\\\\x_1=\frac{-b-\sqrt\Delta}{2a};\ x_2=\frac{-b+\sqrt\Delta}{2a}\\\\\sqrt\Delta=\sqrt{100}=10\\\\x_1=\frac{2-10}{2\cdot(-1)}=\frac{-8}{-2}=4;\ x_2=\frac{2+10}{2\cdot(-1)}=\frac{12}{-2}=-6\\\\y_1=4^2+6\cdot4=16+24=40;\ y_2=(-6)^2+6\cdot(-6)=36-36=0\\\\Answer:\\x=4\ and\ y=40\ or\ x=-6\ and\ y=0
4 0
3 years ago
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There are 9 players on a baseball team. In how many different ways can the coach choose players for first base, second base, thi
butalik [34]

1 player can play 4 different positions...

answer:36 different ways

7 0
3 years ago
35% is 7 out of what number?
o-na [289]

Answer:

The number is <u>20</u>.

Step-by-step explanation:

In this question, it is said that 35% of a number is equal to 7, then what is that number?

So, let the number be <em>x</em>.

Now, according to the question :

\begin{gathered} \begin{array}{l} \quad{\dashrightarrow{\sf{35 \% \: of \: x = 7}}}\\\\\quad{\dashrightarrow{\sf{\dfrac{35}{100} \: of \: x = 7}}}\\\\\quad{\dashrightarrow{\sf{\dfrac{35}{100}  \times x = 7}}}\\\\\quad{\dashrightarrow{\sf{\dfrac{35 \times x}{100} = 7}}}\\\\\quad{\dashrightarrow{\sf{\dfrac{35x}{100} = 7}}}\\\\\quad{\dashrightarrow{\sf{x = 7 \times \dfrac{100}{35}}}}\\\\\quad{\dashrightarrow{\sf{x =\dfrac{700}{35}}}}\\\\ \quad{\dashrightarrow{\sf{x = \cancel{\dfrac{700}{35}}}}}\\\\ \quad{\dashrightarrow{\sf{x =20}}}\\\\ \quad{\star{\underline{\boxed{\tt{\red{x =20}}}}}} \end{array}\end{gathered}

Hence, the number is 20.

\rule{300}{2.5}

3 0
2 years ago
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The radius of one sphere is twice as great as the radius of a second sphere. Find the ratio of their volumes. 1/2 1/4 1/8 1/16
Anton [14]

Let's pick some simple points with which to set up an example for ourselves for this. Let's let the smaller radius be 1, and the larger, twice that, be 2. The radius itself is a single unit measure; in other words, it's measured as inches, feet, cm, etc., while the volume is a cubed measure. Volume is measured in inches cubed, feet cubed, cm cubed, etc. Therefore, if we have the radii measuring 1:2, we simply cube those single unit measures to find the ratio of their volumes. 1 cubed is 1, and 2 cubed is 8. So your answer for this is 1/8.

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90(squared) + 90 (squared) = C (squared)
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127.3/2 = 67.7 ft.
67.7 ft is the distance from the pitcher<span> to the 2nd base.</span>
5 0
3 years ago
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