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maxonik [38]
3 years ago
14

Polynomial division

Mathematics
1 answer:
Serjik [45]3 years ago
6 0
This is a great place and time to apply synthetic division.  Since you are dividing the 3rd order poly by (a+2), let the divisor in synth. div. be -2.

Then:
      _________________
 -2 /   1   6   12    8

     _____-2_-8    -8____________
          1   4     4     0

Since there is no remainder, -2 is a root and (x+2) is a factor of the poly.

The quotient comes from  those coefficinets 1  4  4  

and is    1a^2 + 4a + 4, whose factors are (a+2)^2.
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The diameter of a circle has endpoints A(1, 3) and B(4, 7), what is the
lana [24]

Answer:

The circumference of the circle is 5π

Step-by-step explanation:

First we need to calculate the diameter  

for this we have to know the distance between A(1, 3) and B(4, 7)

X =  Xb - Xa

X = 4 - 1

X = 3

Y = Yb - Ya

Y = 7 - 3

Y = 4

b - a = (3 , 4)

now that we have the distance of x and r we can calculate its distance using Pythagoras

h = hypotenuse

x = leg 1 = 3

y = leg 2 = 4

h² = x² + y²

we replace the known values

h² = (3)² + (4)²

h² = 9 + 16

h² = 25

h = √25

h = 5

The diameter of the circle is 5

Now we need to calculate the circumferencefor this we need to use the circumferenc formula of a circle:

c = circumference

d = diameter = 5

π = pi

c = π * d

we replace with the known values

c = 5  * π

c = 5π

The circumference of the circle is 5π

4 0
3 years ago
On an algebra test , the highest grade was 50 points higher than the lowest the sum of the two grades was 122 find the lowest gr
KATRIN_1 [288]

Answer:

Highest grade: 86

Lowest grade: 36

Step-by-step explanation:

Let the highest grade be h, lowest grade be l.

h = 50 + l  \\  \\ h + l = 122 \\ h = 122 - l \\  \\

Therefore,

122 - l \:  = 50 + l \\ 2l \:  = 72 \\ l = 36 \\  \\ h = 36 + 50 = 86

6 0
3 years ago
it is claimed that proportion in favor of proportion A is greater than 60%. A sample of size 100 found 69 in favor. what is the
GenaCL600 [577]

Answer:

The alternative hypothesis is H_1: p > 0.6.

The critical value is Z_c = 1.645

Step-by-step explanation:

It is claimed that proportion in favor of proportion A is greater than 60%.

This means that at the null hypothesis, we test if the proportion is of at most 60%, that is:

H_0: p \leq 0.6

At the alternative hypothesis, we test if the proportion is more than 60%, that is:

H_1: p > 0.6

What is (are) the critical value?

The critical value is the value of Z with a p-value 1 subtracted by the standard significance level of 0.05, since we are testing if the mean is more than a value, so, looking at the z-table, Z_c = 1.645

7 0
2 years ago
WILL GIVE BRAINLIEST PLEASE ANSWER If a circle is dilated by 5/3 and the area of the larger circle is 100pi square cm, then what
Simora [160]

Answer:

We have a small circle, that is dilated by a factor of 5/3 creating a larger circle.

If the smaller circle has a diameter D, then after the dilation, the larger circle will have a diameter equal to: (5/3)*D

We know that the area of the larger circle is:

A = 100*pi cm^2.

And the area of a circle of diameter d, is:

a = pi*(d/2)^2

knowing that the diameter of the large circle is (5/3)*D, we can find the value of D.

A = pi*( (5/3)*D/2)^2 = 100*pi cm^2

let's solve this for D:

pi*( (5/3)*D/2)^2 = 100*pi cm^2

( (5/3)*D/2)^2 = 100 cm^2

( (5/3)*D/2) = √(100 cm^2) = 10cm

D/2 = (3/5)*10cm

D = 2*(3/5)*10cm = 12cm.

Then the area of the smaller circle will be:

a = pi*(D/2)^2 = pi*(12cm/2)^2 = pi*(6cm)^2 = pi*36 cm^2

and pi = 3.14

a = pi*36 cm^2 = 3.14*36cm^2 = 113.04 cm^2

7 0
3 years ago
PLEASE HELP ASAP! NO SCAMS ALLOWED!
Kitty [74]

Answer:

Step-by-step explanation:

I used calculus for this, as I'm not sure there's any other way to do it and to do it as easily. This is the volume of a solid found by using the disk method of rotation:

V=\pi\int\limits^a_b {[R(x)]^2-[r(x)]^2} \, dx

where R(x) is the outer shell of the solid and r(x) is the space inbetween the solid and the axis of rotation. There is no space between the solid and the axis of rotation, so r(x) = 0. R(x) is the height of the solid which is 3. Therefore, f(x) = 3 and that's the function we put into the formula with the lower bound of 3 and the upper bound of 5:

V=\pi\int\limits^5_3 {3^2}-0^2 \, dx  and

V-\pi\int\limits^5_3 {9} \, dx  and integrating:

V=\pi(9x\left \} {{5} \atop 3}} \right. and using the First Fundamental Theorem of Calculus:

V = π(9(5) - 9(3)) and

V = π(45 - 27) so

V = 18π units cubed or in decimal format,

V = 56.549 units cubed

6 0
2 years ago
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