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ryzh [129]
3 years ago
8

Question #1. factor completely p^4-13p^2+40

Mathematics
1 answer:
dsp733 years ago
3 0

Answer:

Step-by-step explanation:

#1

(p^2-8) (p^2-5)

#2

(p-2) (4p-1)

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Which equation represents a circle that contains the point (-5, -3) and has a center at (-2, 1)?
Evgen [1.6K]

The equation (x + 2)² + (y - 1)² = 25 represents a circle that contain the point (-5 , -3) and has a center at (-2 , 1)

Step-by-step explanation:

The equation of a circle of center (h , k) and radius r is:

(x - h)² + (y - k)² = r²

The given is:

  • The center of the circle is (-2 , 1)
  • The circle passes through point (-5 , -3)

The length of the radius is the distance from the center of the circle

to a point on the circle

∵ The formula of the distance is d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}

∵ The center of the circle is (-2 , 1)

∵ The circle passes through point (-5 , -3)

∴ r=\sqrt{[(-5)-(-2)]^{2}+[(-3)-(1)]^{2}}

∴ r=\sqrt{[-3]^{2}+[-4]^{2}}

∴ r=\sqrt{9+16}

∴ r=\sqrt{25}

∴ r = 5

∵ The equation of the circle is (x - h)² + (y - k)² = r²

∵ The center of the circle is (-2 , 1)

∴ h = -2 and k = 1

∵ r = 5

∴ r² = (5)² = 25

- Substitute the values of h , k , r² in the equation of the circle

∴ (x - -2)² + (y - 1)² = 25

∴ (x + 2)² + (y - 1)² = 25

The equation (x + 2)² + (y - 1)² = 25 represents a circle that contains

the point (-5 , -3) and has a center at (-2 , 1)

Learn more:

You can learn more about the equation of the circle in brainly.com/question/9510228

LearnwithBrainly

7 0
2 years ago
Write the quadratic equation y= x^2 -6x = 7 in vertex form.
lapo4ka [179]

Answer:

(x - 3)² - 16 = 0

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

Subtract 7 from both sides

x² - 6x + 7 = 0 ← in standard form

with a = 1, b = - 6

Given a quadratic in standard form then the x- coordinate of the vertex is

x_{vertex} = - \frac{b}{2a} = - \frac{-6}{2} = 3

Substitute x = 3 into the equation for y

y = 3² - 6(3) - 7 = 9 - 18 - 7 = - 16 ⇒ (h, k) = (3, - 16)

y = (x - 3)² - 16 = 0

7 0
2 years ago
Can someone help me out on questions 6, 7, and 8?
PolarNik [594]
For #6 draw a triangle between the points and find the middle by drawing the lines to the middle. There should be triangles within the triangles which finding the hypotenuses should be the same.
6 0
2 years ago
Ms. Turner drove 825 miles in March. She drove 3 times as many miles in March as she did in January. She drove 4 times as many m
navik [9.2K]
825/3 = 275 which is how many miles she drove in January.

275*4= 1100 which is how many miles she drove in February. 

Ms. Turner drove 1100 miles in February. 
4 0
3 years ago
What fraction is greater than 1/2. 4/6 3/8 1/3 2/5?
Andrei [34K]
1/2 = 0.5
4/6 =0.67
3/8=0.375
1/3=0.33
2/5=0.4 
There fore 1/2 is bigger :)
7 0
3 years ago
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