A 135-page notebook has 33 writing lines on each page. What is the total number of writing lines in the entire notebook

Mathematics

1 answer:

ladessa [460]2 years ago

6 0

Answer:

4455

Step-by-step explanation:

135 pages x 33 lines a page = 4455 lines.

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If the diagonals of a quadrilateral bisect the angles, is the quadrilateral always a parallelogram? Explain your answer.

Liula [17]

Yes. If the diagonals bisect the angles, the quadrilateral is always a parallelogram, specifically, a rhombus.

Consider quadrilateral ABCD. If diagonal AC bisects angles A and C, then ΔACB is congruent to ΔACD (ASA). Hence AB=AD and BC=CD (CPCTC).

Likewise, if diagonal BD bisects angles B and D, triangles BDA and BDC are congruent, thus AB=BC and AD=CD. (CPCTC again). Now, we have AB=BC=CD=AD, so the figure is a rhombus, hence a parallelogram.

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Howard’s uncle gave him $885 for his tenth birthday. The money was invested in a savings account with interest compounded at 12%

Stella [2.4K]

Principal Amount = P = $885
Amount Accumulated = A = $3500
Interest rate = r = 12% = 0.12
Compounding period in a year = n = 2
Time in years = t = ?

The formula for compounding is:

$A=P(1+ \frac{r}{n})^{t*n}$

Using the values, we get:

$3500=885(1+ \frac{0.12}{2})^{2*t} \\ \\ 
 \frac{3500}{885} =(1.06)^{2t} \\ \\ 
log(\frac{3500}{885})=log((1.06)^{2t}) \\ \\ 
log(\frac{3500}{885})=2tlog(1.06) \\ \\ 
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t=11.80$

This means, it will take him 11.8 or approximately 12 years

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3 years ago

Which equation represents a line which is parallel to the line y = -x + 5?

ozzi

Answer:

2x + 3y = -21

Step-by-step explanation:

Parallel lines have same slope.

2x + 3y = -21

3y = - 2x - 21

y = $y = \dfrac{-2}{3}x-\dfrac{21}{3}\\\\y=\dfrac{-2}{3}x-7$

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3 years ago

A toy train car is 6in.long. if a real train car is 75 ft long , which of the following have the same constant of proportionalit

agasfer [191]

A toy train and a real train are similar shapes, then their dimensions are proportional. The ratio is $\dfrac{real}{toy} =\dfrac{75}{6} =\dfrac{25}{2}$ .