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Ede4ka [16]
3 years ago
10

Please help I don’t know the answer :(

Mathematics
2 answers:
gogolik [260]3 years ago
6 0

Answer:

When x=8, y=-6. When x=10, y=0

Step-by-step explanation:

y=3x-30\\x^2+y^2=100

You can plug the given y value into the second equation to get:

x^2+(3x-30)^2=100\\x^2+9x^2-180x+900=100\\10x^2-180x+800=0\\10(x^2-18x+80)=0\\10(x-8)(x+10)=0\\x= 8, 10\\y= -6, 0

Hope this helps!

GarryVolchara [31]3 years ago
4 0
-6,0 is the answer for this
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What do the vertical lines mean?
zhenek [66]
The vertical lines are absolute values, the number in between them, if negative turns positive.
3 0
3 years ago
At a pizzeria, a medium pizza which has diameter of 12 inches sells for $6.00 and a large pizza which has a diameter of 16 inche
Sidana [21]
We are comparing areas, so square of the linear dimension
Relative cost per unit area
12^2/6=24
16^2/10=256/10=25.6
Since 24<25.6, the 12" pizza is a better deal.

Note: we could compare exact area by calculating A=pi (d^2)/4, but since it is a relative comparison, the result will be the same, albeit more work.
5 0
2 years ago
When X =10, the ??? Of the expression 4x is 40
AVprozaik [17]
When x=10, the product of the expression 4x is 40

Product is defined to be the result of the multiplication. If we multiply the value of the x (which is 10) by 4 the result (called the product) will be equal to 40.
3 0
3 years ago
The diagram below shows a pennant in the shape of an isosceles triangle. The equal sides each measure 13. The altitude is x + 7
Kisachek [45]

Answer: The length of the base is 10.

Step-by-step explanation:

You can draw an isosceles triangle like the one shown attached.

An isosceles triangle has two equal sides. Then, you can divide it into two right triangles, where the base of each one of them will be:

b'=\frac{2x}{2}=x

The hypotenuse of each right triangle shown is 13 and the other legs are (x+7) and x, therefore you can apply the Pythagorean Theorem:

13^2=x^2+(x+7)^2

Simplify the expression:

169=x^2+(x^{2}+2(x)(7)+7^2)\\169=x^{2}+x^{2}+14x+49\\0=2x^{2}+14x-120

Use the quadratic formula, where:

a=2\\b=14\\c=-120

x=\frac{-b\±\sqrt{b^2-4ac}}{2a}

Then:

x=\frac{-14\±\sqrt{14^2-4(2)(-120)}}{2+2}

x_1=5\\x_2=-12

Choose the positive value, because lengths are not negative.

Substitute the value of x into the base 2x. Therefore, the answer is:

b=2x=2(5)=10

7 0
3 years ago
All of these ODEs model a system with a spring, mass and dashpot.
Wewaii [24]

Answer:

− 3 y ' ' − 3 y ' + 3 y = 0 : over-damped

− 2 y ' ' − 4 y ' + 1 y = 0 : over-damped

1 y ' ' + 7 y ' + 5 y = 0: over-damped

Step-by-step explanation:

Using the characteristic equation you can express a differential equation of order n as an algebraic equation of degree n:

a_ny^n+a_n_-_1y^{n-1}+...+a_1y'+a_oy=0

This differential equation will have a characteristic equation of the form:

a_nr^n+a_n_-_1r^{n-1}+...+a_1r+a_o=0

Now, you can classify the solution for a differential equation using a simple method. In order to do it, you just need to use the discriminant.

  • If the discriminant is greater than zero, the solution is over-damped

  • If the discriminant is less than zero, the solution is under-damped

  • If the discriminant is equal to zero, the solution is critically damped

So, given the differential equation:

-3y''-3y+3y=0

Which has characteristic equation of the form:

-3r^2-3r+3=0

The quadratic polynomial of the form:

ar^2+br+c=0

Has discriminant:

Disc=b^2-4ac

In this case:

a=-3\\b=-3\\c=3

So:

Disc=(-3)^2-4(-3)(3)=9-(-36)=45

In this case:

Disc=45>0

Therefore the solution is over-damped.

Now, given the differential equation:

-2y''-4y'+1y=0

Which has characteristic equation of the form:

-2r^2-4r+1=0

The quadratic polynomial of the form:

ar^2+br+c=0

Has discriminant:

Disc=b^2-4ac

In this case:

a=-2\\b=-4\\c=1

So:

Disc=(-4)^2-4(-2)(1)=16+8=24

In this case:

Disc=24>0

Therefore the solution is over-damped.

Finally, given the differential equation:

1y''+7y'+5y=0

Which has characteristic equation of the form:

1r^2+7r+5=0

The quadratic polynomial of the form:

ar^2+br+c=0

Has discriminant:

Disc=b^2-4ac

In this case:

a=1\\b=7\\c=5

So:

Disc=(7)^2-4(1)(5)=49-20=29

In this case:

Disc=29>0

Therefore the solution is over-damped.

6 0
3 years ago
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