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2 years ago

Identify the factors of x^2+16y^2

Mathematics

1 answer:

Soloha48 [4]2 years ago

6 0

Answer:

Prime

Step-by-step explanation:

This expression is actually impossible to factor. To get rid of the middle term, you would need two equal and opposite x values, such as in (x+4y)(x-4y). However, in that case, the expanded expression would be x^2-16y^2, not plus. If you go for the first option, then you are left with a middle term, such as 8xy. Therefore, this expression is prime. Hope this helps!

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Mariulka [41]

Answer:

$(x-5)^2+(y+4)^2=100$

Step-by-step explanation:

step 1

Find the radius of the circle

we know that

The distance between the center and any point that lie on the circle is equal to the radius

we have the points

(5,-4) and (-3,2)

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

substitute the values

$r=\sqrt{(2+4)^{2}+(-3-5)^{2}}$

$r=\sqrt{(6)^{2}+(-8)^{2}}$

$r=\sqrt{100}\ units$

$r=10\ units$

step 2

Find the equation of the circle

we know that

The equation of a circle in standard form is equal to

$(x-h)^2+(y-k)^2=r^2$

where

(h,k) is the center

r is the radius

we have

$(h,k)=(5,-4)\\r=10\ units$

substitute

$(x-5)^2+(y+4)^2=10^2$

$(x-5)^2+(y+4)^2=100$

6 0

2 years ago

A jar is filled with only dimes and quarters. The jar contains a total of 60 coins and the value of the jar is $11.25. How many

inessss [21]

Answer:

35 quarters

Step-by-step explanation:

This situation has two unknowns - the total number of dimes and the total number of quarters. Because we have two unknowns, we will write a system of equations with two equations using the two unknowns.

$d+q=60$ is an equation representing the total number of coins
$0.10d+0.25q=11.25$ is an equation representing the total value in money based on the number of coin. 0.10 and 0.25 come from the value of a dime and quarter individually.

We write the first equation in terms of q by subtracting it across the equal sign to get $d=60-q$ . We now substitute this for d in the second equation.