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erik [133]
3 years ago
13

Write a polynomial of least degree with rational coefficients and with the root -19-5 square root 2.

Mathematics
1 answer:
iogann1982 [59]3 years ago
5 0

Answer:

y = x² + 38x + 311

Step-by-step explanation:

If a polynomial has rational coefficients and irrational roots, then the roots must be conjugate pairs.

y = (x − (-19-5√2)) (x − (-19+5√2))

y = (x + 19+5√2) (x + 19−5√2)

Use FOIL to distribute:

y = x² + x (19−5√2) + x (19+5√2) + (19+5√2)(19−5√2)

y = x² + 19x − 5√2 x + 19x + 5√2 x + (19+5√2)(19−5√2)

y = x² + 38x + (19+5√2)(19−5√2)

Use FOIL to distribute the last term:

y = x² + 38x + 19² − 95√2 + 95√2 − 50

y = x² + 38x + 361 − 50

y = x² + 38x + 311

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Answer:

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Step-by-step explanation:

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8 0
2 years ago
In the circle below, if &lt; B = 46°, what is the measure of arc AB?
olganol [36]

angle B = ( arc ADB ) ÷ 2

46 = ( arc ADB ) / 2

Multiply both sides by 2

46 × 2 = 2 × ( arc ADB ) / 2

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3 years ago
34. I need to know how to write the equation in slope-intercept form and graph it. My biggest question is how to write it in slo
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8 0
3 years ago
Mateo built the skateboard ramp below and filled it with pebbles to make it more stable.
bagirrra123 [75]

Answer:

The shape can be broken into a rectangular prism and a triangular prism.

The volume of the ramp is 24 feet cubed.

Step-by-step explanation:

The ramp has a rectangular prism and triangular prism. The combined shape makes the ramp.

The volume of a rectangular prism = Bh

where

B = base area

B = length × width

h = height

volume = 1.5 × 4.8 × 2 = 14.4  ft³

The volume of a triangular prism = base area + slant height

volume = 1/2 b × h × l

where

b = base of the triangle

h = height of the triangle

l = slant height of the prism

volume = 1/2 × 2 × 2 × 4.8 = 19.2/2 = 9.6  ft³

The volume of the ramp = 14.4 + 9.6 = 24 ft³

5 0
3 years ago
Read 2 more answers
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