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AlekseyPX
3 years ago
11

5X exponent 2 + 10x- 45=

Mathematics
1 answer:
Slav-nsk [51]3 years ago
4 0
I’ll assume the question is asking us to factor the above polynomial:
5x^2 + 10x - 45

Factor out a 5:
5(x^2 + 2x - 9)

This appears to be an irreducible quadratic polynomial, so let’s leave it alone.
5x^2 + 10x - 45 = 5(x^2 + 2x - 9)
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Quadrilateral PQRS is a square whos side length is 10. Let X and Y be points outside the square so that XQ = YS = 6 and XP = YR
erik [133]

Answer:

392

Step-by-step explanation:

Triangles XQP and YRS are right triangles because triples 6, 8, 10 are Pythagorean triples.

Extend lines XQ, YR, YS and XP and mark their intersection as A and B.

Quadrilateral XAYB is a square because all right triangles PXQ, QAR, RYS and SBP are congruent (by ASA postulate) and therefore

  • all angles of the quadrilateral XAYB are right angles
  • all sides of XAYB are congruent and equal to 6 + 8 = 14 units.

Segment XY is the diagonal of the square XAYB, by Pythagorean theorem,

XY^2=XA^2+AY^2\\ \\XY^2=14^2+14^2\\ \\XY^2=196+196\\ \\XY^2=392  

3 0
3 years ago
Which lines are perpendicular to the line y - 1 = 1/3 (x+2)? Check all that apply.
ioda

Answer: Options 1, 3, 5

Step-by-step explanation:

Perpendicular lines have slopes that are negative reciprocals, so since the slope of the given line is 1/3, we need to find lines with a slope of -3.

  • Option 1 has a slope of -3.
  • Option 2 has a slope of 3.
  • Option 3 has a slope of -3.
  • Option 4 has a slope of 1/3.
  • If we subtract 3x from both sides, we get y=-3x+7, so option 5 has a slope of -3.
7 0
2 years ago
Express 1+√2/√2 in the form p+q√2​
scoundrel [369]

\frac{1+\sqrt{2}}{\sqrt{2}} = \frac{1}{\sqrt{2}} + \frac{\sqrt{2}}{\sqrt{2}} = 1 + \frac{1}{\sqrt{2}}

3 0
3 years ago
the slope of the line below is -5. which of the following is the point slope of the line? y intercept = (2, -8)
umka2103 [35]

Answer:

Step-by-step explanation:

The y-intercept cannot be (2,-8). The x-coordinate of the y-intercept is 0.

Point-slope equation for line of slope -5 that passes through (2,-8):

y+8 = -5(x-2)

3 0
3 years ago
Suppose a simple random sample of size nequals45 is obtained from a population with muequals64 and sigmaequals14. ​(a) What must
jeka94

Answer:

Step-by-step explanation:

Given that sample size = n=45

mu = 64 and sigma =14

a) Sample mean will follow a normal distribution irrespective of the original distributions provided

i) samples are randomly drawn

ii) samples represent the population

iii) Sample size is sufficiently large

b) Here we have sample std dev= \frac{\sigma}{\sqrt{n} } \\=\frac{14}{\sqrt{45} } \\=2.09

P(X bar>68.1) = P(Z>\frac{68.1-64}{2.09} \\=P(Z>1.96)\\=0.25

c) P(X bar>66.3) = P(Z>\frac{66.3-64}{2.09} \\=P(Z>1.10)\\=0.136

7 0
3 years ago
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