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siniylev [52]
3 years ago
10

Look at the picture and solve the equations

Mathematics
1 answer:
ch4aika [34]3 years ago
6 0

Answer:

1. a= 7, one solution

2. x=x, infinitely solutions

3. y=3, one solution

4. x=6, one solution

5. no solution

6. k = 2, one solution

Step-by-step explanation:

1.

7a - 6 = 43

7a = 49

one solution

a = 7

2.

3x + 4 = 3x + 4

3x = 3x

x = x

infinitely solutions

3.

4(2y - 4) = 5y + 2

8y - 16 = 5y + 2

3y -16 = 2

3y = 18

one solution

y= 6

4.

multiply 2 on both sides

5x + 6 = x + 30

4x = 24

one solution

x = 6

5.

4e - 19 = 4(e-4)

4e - 19 = 4e -16

-19 ≠ -16

no solution

6.

10k - 2(k+3) = 10

10k -2k - 6 = 10

8k - 6 = 10

8k = 16

one solution

k = 2

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The sum of two consecutive cube numbers is 341. Work out the two numbers. (2 marks)
Kobotan [32]

Answer:

63 and 53

Step-by-step explanation:

you could use trail and error. So:

13+23=9

33+43=91

63+73=559

53+63=341

3 0
3 years ago
The value
ehidna [41]

Answer:

A

Step-by-step explanation:

Check the solution by substituting x = \frac{\pi }{2} into the left side of the equation

2sin²x - sinx - 1

= 2sin²(\frac{\pi }{2} ) - sin (\frac{\pi }{2} ) - 1

= 2(1)² - 1 - 1

= 2 - 1 - 1

= 0

= right side

\frac{\pi }{2} is therefore a solution to the equation

7 0
3 years ago
How do you subtract an integer from another integer without using a number line or counters? Give an example.
Feliz [49]
An integer is all whole numbers and zero, are the numbers you are talking about negatives?
3 0
3 years ago
Determine the values of a for which the following system of linear equations has no solutions, a unique solution, or infinitely
navik [9.2K]

Answer:

Never

Never

Never

Step-by-step explanation:

The equations given are

2x1−6x2−4x3 = 6 ....... (1)

−x1+ax2+4x3 = −1 ........(2)

2x1−5x2−2x3 = 9 ..........(3)

the values of a for which the system of linear equations has no solutions

Let first add equation 1 and 2. Also equation 2 and 3. This will result to

X1 + (a X2 - 6X2) - 0 = 5

And

X1 + (aX2-5X2) + 2X3 = 8

Since X2 and X3 can't be cancelled out, we conclude that the value of a is never.

a unique solution,

Let first add equation 1 and 2. Also equation 2 and 3. This will result to

X1 + (a X2 - 6X2) - 0 = 5

And

X1 + (aX2-5X2) + 2X3 = 8

The value of a = never

infinitely many solutions. 

Divide equation 1 by 2 we will get

X1 - 3X2 - 2X3 =3

Add the above equation with equation 3. This will result to

3X1 - 8X2 - 4X3 = 12

Everything ought to be the same. Since they're not.

Value of a = never.

4 0
3 years ago
Show tan(???? − ????) = tan(????)−tan(????) / 1+tan(????) tan(????)<br> .
anyanavicka [17]

Answer:

See the proof below

Step-by-step explanation:

For this case we need to proof the following identity:

tan(x-y) = \frac{tan(x) -tan(y)}{1+ tan(x) tan(y)}

We need to begin with the definition of tangent:

tan (x) =\frac{sin(x)}{cos(x)}

So we can replace into our formula and we got:

tan(x-y) = \frac{sin(x-y)}{cos(x-y)}   (1)

We have the following identities useful for this case:

sin(a-b) = sin(a) cos(b) - sin(b) cos(a)

cos(a-b) = cos(a) cos(b) + sin (a) sin(b)

If we apply the identities into our equation (1) we got:

tan(x-y) = \frac{sin(x) cos(y) - sin(y) cos(x)}{sin(x) sin(y) + cos(x) cos(y)}   (2)

Now we can divide the numerator and denominato from expression (2) by \frac{1}{cos(x) cos(y)} and we got this:

tan(x-y) = \frac{\frac{sin(x) cos(y)}{cos(x) cos(y)} - \frac{sin(y) cos(x)}{cos(x) cos(y)}}{\frac{sin(x) sin(y)}{cos(x) cos(y)} +\frac{cos(x) cos(y)}{cos(x) cos(y)}}

And simplifying we got:

tan(x-y) = \frac{tan(x) -tan(y)}{1+ tan(x) tan(y)}

And this identity is satisfied for all:

(x-y) \neq \frac{\pi}{2} +n\pi

8 0
3 years ago
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