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3 years ago

X+7=2y+1 3x-y=7 solve for x and y

Mathematics

1 answer:

vovangra [49]3 years ago

6 0

{x+7=2y+1 ⇔ x-2y=1-7 ⇔ x-2y=-6

{3x-y=7 /*(-2)

{x-2y=-6

{-6x+2y=-14 (+)

x-6x-2y+2y=-6-14

-5x=-20 /:(-5)

x=4

x -2y=-6

4-2y=-6 /-4

-2y=-10 /:(-2)

y=5

Solution: (4; 5)

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What is the area of a triangle when the sides are 17, 8 and 9

sleet_krkn [62]

Answer:

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Step-by-step explanation:

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3 years ago

Suppose h(x)=3x-2 and j(x) = ax +b. Find a relationship between a and b such that h(j(x)) = j(h(x))

sergejj [24]

Answer:

$\displaystyle a = \frac{1}{3} \text{ and } b = \frac{2}{3}$

Step-by-step explanation:

We can use the definition of inverse functions. Recall that if two functions, f and g are inverses, then:

$\displaystyle f(g(x)) = g(f(x)) = x$

So, we can let j be the inverse function of h.

Function h is given by:

$\displaystyle h(x) = y = 3x-2$

Find its inverse. Flip variables:

$x = 3y - 2$

Solve for y. Add:

$\displaystyle x + 2 = 3y$

Hence:

$\displaystyle h^{-1}(x) = j(x) = \frac{x+2}{3} = \frac{1}{3} x + \frac{2}{3}$

Therefore, a = 1/3 and b = 2/3.

We can verify our solution:

$\displaystyle \begin{aligned} h(j(x)) &= h\left( \frac{1}{3} x + \frac{2}{3}\right) \\ \\ &= 3\left(\frac{1}{3}x + \frac{2}{3}\right) -2 \\ \\ &= (x + 2) -2 \\ \\ &= x \end{aligned}$

And:

$\displaystyle \begin{aligned} j(h(x)) &= j\left(3x-2\right) \\ \\ &= \frac{1}{3}\left( 3x-2\right)+\frac{2}{3} \\ \\ &=\left( x- \frac{2}{3}\right) + \frac{2}{3} \\ \\ &= x \stackrel{\checkmark}{=} x\end{aligned}$

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2 years ago

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yan [13]

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3 years ago

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3 years ago

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Alenkasestr [34]

Answer:

65 square yards

Step-by-step explanation:

5x5=25

5x4=20

20+20+25= 65

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1 year ago