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3 years ago

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Mathematics

2 answers:

Ulleksa [173]3 years ago

8 0

Answer:

Step-by-step explanation:

Solving simultanius equation by elimination

2x + 5y = 7 -------------(I)

3x + 4y = 6 ---------------(II)

To eliminate x, multiply equation (I) by (-3) and equation (II) by 2. Then add the two equations. Now, 'x' will be eliminated and we can find the value of 'y'.

(I) *(-3) -6x - 15y = -21

(II)*2 6x + 8y = 12 {Now add}

- 7y = -9

y = -9/-7

y = 9/7

Oduvanchick [21]3 years ago

7 0

Answer:

I'd times the first equation by 3 and the second equation by 2. Giving:

6x + 15y = 21

6x + 8y = 12

then I'd subtract the second from the first

6x-6x + 15y-8y = 21-12

7y = 9

y = 7/9

then sub y into one of the equations and solve for x.

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Answer not submitted

tensa zangetsu [6.8K]

The customer drawing a 30% discount card then the next customer 20% discount card has a probability of 5/40 for the 30% which = 12.5% and 20% is 15/40 which = 37.5% add them together then divide by 2 for a total of 25%.

The customer drawing a 10% card has a 20/40 which = 50% then a customer drawing a 20% card is 15/40 = 37.5% add them together then divide by 2 = 43.75%

The customer drawing a 10% card has a 20/40 which is 50%. Then another customer drawing another 10% is another 50% add them together and divide by 2 = 50%

The customer drawing a 20% card has a 5/40 which is 12.5% and another customer drawing a 20% card again is 12.5%. Add together and divide by 2 = 12.5%. So your answer is the 1st three.

5 0

3 years ago

The rectangular floor of a storage shed has an area of 580 square feet. The length of the floor is 9 feet more than its width (s

Marysya12 [62]

9514 1404 393

Answer:

length: 29 ft
width: 20 ft

Step-by-step explanation:

Assuming the dimensions are integer numbers of feet, you're looking for factors of 580 that have a difference of 9.

580 = 1×580 = 2×290 = 4×145 = 5×116 = 10×58 = 20×29

The last pair of factors differs by 9, so ...

the length is 29 feet; the width is 20 feet.

8 0

3 years ago

Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval. Then find all numbers c that s

ivolga24 [154]

Answer:

$c=1.215$

Step-by-step explanation:

Rolle's theorem states that if f is a continuous function defined on a closed interval [a, b] differentiable on the open interval (a, b) and f (a) = f (b), then:

There is at least one point c in the open interval (a, b) such that f '(c) = 0

Given a function:

$f(x)=x^3-x^2-2x+1$

and a interval:

$[0,2]$

Is f(x) continuous over [0,2]?

Yes, it is, because the domain of this function is $(-\infty, \infty)$

Is f'(x) differentiable on the open interval (0,2) ?

First, let's find f'(x):

$f'(x)=3x^2-2x-2$

Therefore f'(x) is differentiable on the open interval (0,2) because the domain of f'(x) is $(-\infty, \infty)$

Is f(0)=f(2) ?

$f(0)=0^3-0^2-2(0)+1=1$

$f(2)=2^3-2^2-2(2)+1=8-4-4+1=1$

Hence:

$f(0)=f(2)=1$

Now, we have verified that the function satisfies the three hypotheses of Rolle's Theorem on the given interval. So, let's find all numbers c that satisfy the conclusion of Rolle's Theorem:

$f'(x)=0\\\\3x^2-2x-2=0$

Let's find the roots using the quadratic equation:

$x=\frac{-(-2) \pm\sqrt{(-2^2)-4(3)(-2)} }{2(3)} =\frac{2\pm \sqrt{4+24} }{6} =\frac{2\pm 2\sqrt{7} }{6} \\\\Hence\\\\x=\frac{1}{3} +\frac{\sqrt{7} }{3}\approx1.215 \\\\or\\\\x=\frac{1}{3} -\frac{\sqrt{7} }{3} \approx -0.549$