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1 year ago

Solve the following quadratic by completing the square.

Mathematics

1 answer:

lianna [129]1 year ago

4 0

Answer:

$x = -5 \pm \sqrt{26}$

Step-by-step explanation:

$x^2+10x-1=0\\\\\implies x^2+2\cdot 5 x +5^2-5^2-1=0\\\\\implies (x+5)^2-25-1=0\\\\\implies (x+5)^2 -26=0\\\\\implies (x+5)^2 = 26\\\\\implies x +5 = \pm\sqrt{26}\\\\\implies x = -5 \pm \sqrt{26}$

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A square napkin is folded in half on the diagonal and placed on the diameter of a round plate (see diagram below). If the folded

Crank

Answer:

$A=81(\pi-1)\ in^2$

Step-by-step explanation:

step 1

Find the area of the plate

The area of a circle is given by the formula

$A=\pi r^{2}$

we have

$r=18/2=9\ in$ ---> the radius is half the diameter

substitute

$A=\pi (9)^{2}\\A=81\pi\ in^2$

step 2

Find the area of the square napkin folded (is a half of the area of the square napkin)

we know that

The diagonal of the square is the same that the diameter of the plate

Applying Pythagorean theorem

$D^2=2b^2$

where

b is the length side of the square

we have

$D=18\ in$

substitute

$18^2=2b^2$

solve for b^2

$b^2=162\ in^2$ -----> is the area of the square

Divide by 2

$162/2=81\ in^2$

step 3

Find the area of the space on the plate that is NOT covered by the napkin

we know that

The area of the space on the plate that is NOT covered by the napkin, is equal to subtract the area of the square napkin folded (is a half of the area of the square napkin) from the area of the plate

$A=(81\pi-81)\ in^2$

simplify

$A=81(\pi-1)\ in^2$

8 0

2 years ago

Can someone explain the meaning of the Spiral of Theodorus?

drek231 [11]

Answer:

The Spiral of Theodorus is a construction of continuous right triangles, and each triangle has a side length of one representing the of the Pythagorean theorem, with the other sides filling in the spaces for the and in the theorem. hope that helped :)

Step-by-step explanation:

8 0

3 years ago

A rectangular pyramid has a volume of 1,296 mc014-1.jpg, a height of 24 in., and a base length of 6 in. What is the width of its

stiks02 [169]

V=L X W X H

1,296=6 x w x 24
1,296=144 x w
1296/144=w
9=width

3 0

3 years ago

Read 2 more answers

The sum of the first 6 terms of a geometric series is

jekas [21]

Answer:

Step-by-step explanation:

The sum to n terms of a geometric sequence is

$S_{n}$ = $\frac{a(r^n-1)}{r-1}$

where a is the first term and r the common ratio

Here r = 5 and a has to be found, thus

$S_{6}$ = $\frac{a(5^6-1)}{5-1}$ , so

$\frac{a(15625-1)}{4}$ = 15624

Multiply both sides by 4

15624a = 62496 ( divide both sides by 15624

a = 4

7 0

2 years ago

the ratio of reds to greens was 5 to 16 and six times the number of reds exceeded the number of greens by 112. how many were red

Masja [62]

Call red as X then X/Green =5/16 => green = 16X/5.
six times the number of reds exceeded the number of green by 112 => 6X-16X/5=112 => 14X/5=112 => X= 40 => reds:40 => green = 128

7 0

3 years ago