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Dmitry [639]
3 years ago
14

Solve the equation 5x^2-6x-7=0

Mathematics
2 answers:
Zepler [3.9K]3 years ago
8 0

Answer:

x = (3-2√11)/5 ; x= (3+2√11)/5

Step-by-step explanation:

Δ/4 = (b/2)^2 - ac  where b is the term that multiplies x, a is the therm that multiplies x^2 and c is the therm without x

Δ/4 = (-3)^2 - (-7*5) = 9 + 35 = 44 = 2^2 *11

x1 = (3 - √2^2 *11)/5 = (3-2√11)/5

x2 = (3+ √2^2 *11)/5 = (3+2√11)/5

Nataly [62]3 years ago
4 0

Answer:

0.37

Step-by-step explanation:

5x^2-6x-7=0

25x-6x-7=0

19x-7=0

19x=7

0.37

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Triangle PQR where P(1,4), Q(-3,-4),R(7,k) is right-angled at Q. find the value of k
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Answer:

k = -9.

Step-by-step explanation:

As the triangle is right-angled at Q, by Pythagoras:

PR^2 = PQ^2 + RQ^2

So, substituting the given data and using the distance formula between 2 points:

(7 - 1)^2 + (k - 4)^2 =  (-4-4)^2 + (-3-1)^2 + (7 - (-3))^2 + (k - (-4))^2

36 + (k - 4)^2 = 64 + 16 + 100 + ( k + 4)^2

(k - 4)^2 - (k + 4)^2 = 180 - 36

k^2 - 8k + 16 - (k^2 + 8k + 16) = 144

-16k = 144

k = -9.

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3 years ago
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3 years ago
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3 years ago
A semicircle is attached to the side of a rectangle as shown.
laiz [17]

Answer:

58.8\ mm^2

Step-by-step explanation:

we know that

The area of the figure is equal to the area of rectangle plus the area of semicircle

step 1

Find the area of rectangle

The area of rectangle is equal to

A=bh

where

b=9\ mm\\h=3\ mm

substitute

A=(9)(3)=27\ mm^2

step 2

Find the area of semicircle

The area of semicircle is equal to

A=\frac{1}{2}\pi r^{2}

we have

r=9/2=4.5\ mm ---> the radius is half the diameter

\pi =3.14

substitute

A=\frac{1}{2}(3.14) (4.5)^{2}

A=31.8\ mm^2

step 3

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