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3 years ago

What is the equation of a line that is parallel to y=-4x-3 and shifted down 3 untits

Mathematics

1 answer:

Elenna [48]3 years ago

4 0

Answer:

y= -4x - 3

Step-by-step explanation:

Given

The equation of line is

The line which is parallel to the given line is

and shifted by 3 units down i.e. its y-intercept is 3 units below the given line

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The sum of the circumference of two circles is 38π cm and the sum of their areas is 193π cm². Calculate the radii of the circles

sdas [7]

Answer:

The radii of the circles are 12 cm and 7cm.

Step-by-step explanation:

Let the radii of the circles be $r_{1}\ and\ r_{2}$

Given:

Sum of circumference of two circles= 38π cm

Formula for circumference of a circle with radius r = 2πr

$2\pi r_{1}+2\pi r_{2}=38\pi \\r_{1}+r_{2}=19$ ------------1

Sum of areas of two circles= 193π cm²

Area of circle with radius r = πr²

$\pi r_{1}^{2}+\pi r_{2}^{2}=193\pi \\r_{1}^{2}+r_{2}^{2}=193$ -------2

Substituting r2 = 19 - r1 in equation 2 we get:

$r_{1}^{2}+(19-r_{1})^{2}=193\\2r_{1}^{2}-38r_{1}+168=0\\r_{1}^{2}-19r_{1}+84=0\\(r_{1}-12)(r_{1}-7)=0\\r_{1}=12\ or\ 7$

Then r2 = 19 - r1

$r_{2}=12\ or\ 7$

7 0

3 years ago

Find the value of c that makes the expression a perfect square trinomial.<br><br> x2 + 4x + c

masha68 [24]

the value of c that makes the expression a perfect square binomial is c=4 .

<u>Step-by-step explanation:</u>

Here we have , an expression x2 + 4x + c or , $x^2 + 4x + c$ . We need to find the value of c that makes the expression a perfect square binomial. Let's find out:

We have , $x^2 + 4x + c$

⇒ $x^2+4x+c$

⇒ $x^2+2(2)x+c$

Now , we know that $(a+b)^2=a^2+2(a)(b)+b^2$

Comparing above equation , to $x^2+2(2)x+c$ we get ;

⇒ $x^2+2(2)x+c$ { $c=2^2$ }

⇒ $x^2+2(2)x+2^2$

⇒ $(x+2)^2$

Therefore , the value of c that makes the expression a perfect square binomial is c=4 .

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3 years ago

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kumpel [21]

c. Tu | MN and MN || PQ I am done with the interview

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4 years ago

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3 years ago

Enter this equations key features in the table and sketch the graph. y=-1/18(x+3)^1(x-3)(x-4)

Nikitich [7]

Answer:

step below and graph

Step-by-step explanation:

y intercept: x=0 y = (-1/18) * 3 * (-3) * (-4) = - 2

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highest degree:( x³) 3

6 0

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