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3 years ago

How many solutions does the system have? 3x−5y=15 6x−10y=30

Mathematics

1 answer:

34kurt3 years ago

4 0

Answer:

infinite solutions

Step-by-step explanation:

3x−5y=15

6x−10y=30

Multiply the first equation by 2

2(3x-5y) = 2*15

6x -10y =30

The two equations are identical, which means they are the same line

That means they have infinite solutions

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A plastic sun visor allows light to pass through but reduces the intensity of the light. the intensity is reduced by 5% if the p

irinina [24]

Answer: The equation is f(x) = $0.95^{x}$ ;

The piece of plastic has to have 10mm of thickness.

Step-by-step explanation: It is known that with 1 mm of thickness, 5% of the intensity is reduced. So, 95% of the light is transmitted.

For each milimetre added, "more" 95% of light is transmitted.

For example, if another milimetre of plastic is added, another 0.95 of light is transmitted:

0.95.0.95 = 0.9025 of light reach the visor

So, the model that relate thickness of plastic and intensity of light is:

f(x) = $0.95^{x}$

in which:

f(x) is the intensity of light;

x is thickness in mm;

Using the equation, the thickness necessary to reduce intensity to 60% is:

f(x) = $0.95^{x}$

0.6 = $0.95^{x}$

log 0.6 = log $0.95^{x}$

x. log (0.95) = log (0.6)

x = $\frac{log 0.6}{log 0.95}$

x = 9.95

x ≈ 10

The thickness necessary to reduce intensity of light to 60% is 10mm.

6 0

3 years ago

Read 2 more answers

If the discriminant is positive how many solutions are there

ddd [48]

Answer:

$b^2-4ac>0$ yields 2 real roots

Step-by-step explanation:

To find the number of real roots for a quadratic, we apply the discriminate. The discriminate is the inside portion of the square root from the quadratic formula.

• $b^2-4ac>0$ yields 2 real roots

• $b^2-4ac=0$ yields 1 real root

• [tx]b^2-4ac<0[/tex] yields no real roots

Example:

$4x^2-7x+2=0$ where a=4, b=-7, and c=2

$b^2-4ac=(-7)^2-4(4)(2)=49-32=17$ .

It has 2 real roots

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3 years ago

What is the value of this expression? 42+3×5−(15−3×6)2 4 2 + 3 × 5 − ( 15 − 3 × 6 ) 2

kenny6666 [7]

The solution is the B. 22

6 0

3 years ago

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STION 1

Lorico [155]

Answer:

1.1.1- Michael has 200 lovebirds in total

1.1.2- There are 40 birds in each cage

1.1.3- 120/80 = 3/2

Step-by-step explanation:

120+80=200

200÷5=40

120÷40=3, 80÷40=2

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3 years ago

Cubed root x cubed root x2

Yuki888 [10]

Answer:

Final answer is $\sqrt[3]{x^1}\cdot\sqrt[3]{x^2}=x$ .

Step-by-step explanation:

Given problem is $\sqrt[3]{x}\cdot\sqrt[3]{x^2}$ .

Now we need to simplify this problem.

$\sqrt[3]{x}\cdot\sqrt[3]{x^2}$

$\sqrt[3]{x^1}\cdot\sqrt[3]{x^2}$

Apply formula

$\sqrt[n]{x^p}\cdot\sqrt[n]{x^q}=\sqrt[n]{x^{p+q}}$

so we get:

$\sqrt[3]{x^1}\cdot\sqrt[3]{x^2}=\sqrt[3]{x^{1+2}}$

$\sqrt[3]{x^1}\cdot\sqrt[3]{x^2}=\sqrt[3]{x^{3}}$

$\sqrt[3]{x^1}\cdot\sqrt[3]{x^2}=x$

Hence final answer is $\sqrt[3]{x^1}\cdot\sqrt[3]{x^2}=x$ .

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3 years ago

How many solutions does the system have? 3x−5y=15 6x−10y=30 ​

How many solutions does the system have? 3x−5y=15 6x−10y=30