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Kitty [74]
3 years ago
5

Complete The Square: (Z^2)-19z=66

Mathematics
1 answer:
Musya8 [376]3 years ago
8 0
To solve the equation using complete square method we proceed:
z^2-19z=66
but
 c=(-b/2a)^2
c=(-19/2)^2
c=361/4
thus:
z^2-19z+361/4=66+361/4
factoring the LHS we get:
1/4(2z-19)^2=625/4

(2z-19)^2=625
getting the square root of both sides we get:
2z-19=+/-25
2z=+/-25+19
2z=44 or -6
z=22 or -3
Answer: z=22 or z=-3



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Evaluate the expression –0.4(3x – 2) + 2x+4/3 for x=4
fomenos

Answer:

-1.07

Step-by-step explanation:

–0.4(3x – 2) + 2x+4/3

–0.4(24 – 2) + 8+4/3

–0.4(24 – 2) + 8+4/3

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8 0
3 years ago
Please help it's urgent.
arlik [135]

Answer:

It is the second triangle.

Step-by-step explanation:

This is because the area of the square is given as 25^2 as the perpendicular, 144^2 as the base, and the hypotenuse is 169^2.

Length of the perpendicular = 5^2 (Because 25^2 / 5^2)

Length of the base = 12^2

Length of the hypotenuse = 13^2

So, the Pythagoras theorem is,

=> H^{2} = P^{2} + B^{2}

=> 13^{2} =12^{2} +5^{2}

This is true, because, 13*13 = 12*12 + 5*5

=> 169 = 144 + 25

=> 169 = 169

If my answer helped, kindly mark me as the brainliest!!

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3 0
3 years ago
Theo can paint a fence three times as fast as his sister can. Working together, they can paint a fence in 9 hours. How many hour
Deffense [45]

Answer:

12 hours

Step-by-step explanation:

Let Theo's siste can paint a fence in x times

Given.

Theo can paint a fence three times as fast as his sister can. Working together, they can paint a fence in 9 hours.

\frac{1}{x}+\frac{1}{3x} =\frac{1}{9}\\\frac{3+1}{3x} =\frac{1}{9} \\\frac{4}{3x}=\frac{1}{9}

Apply cross multiplication

x=\frac{9\times 4}{3}\\x=\frac{36}{3} \\x=12hours

Theo’s sister to paint the fence in 12 hours.

8 0
3 years ago
write about which method you prefer to use to divide by 5 counting up, counting back on a number line, or dividing by 10, and th
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Answer:

In First method : counting up, counting back on a number line,

If we want the quotient after dividing the number by 5 then we count how many 5 we get from 0 to the dividend.

For example :  \frac{30}{5}

Since, from 0 to 30 there are six 5's obtained. ( because 5 × 6 = 30 )

Thus,  \frac{30}{5}=6

In Second Method : dividing by 10, and then doubling the quotient.

First we divide the number by 10 then multiply the quotient by 2.

For Example: \frac{30}{5}

Since, \frac{30}{10}=3

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Thus, \frac{30}{5}=6

Now, when we compare the above methods then we conclude that for the smaller numbers first method is appropriate because for small numbers we can easily count total 5's from 0. While for large numbers Second method is appropriate because it is hard to count the total 5's for the large number.


4 0
3 years ago
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