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3 years ago

Which graph represents the solution to the inequality 3 + 5/2x ≥ 2 − 132?

Mathematics

1 answer:

Leno4ka [110]3 years ago

6 0

Answer:

Option D.

Step-by-step explanation:

We have the inequality:

3 + (5/2)*x ≥ 2*x - 13/2

First, let's try to isolate x in one side of the inequality:

3 + (5/2)*x ≥ 2*x - 13/2

(5/2)*x ≥ 2*x - 13/2 - 3

(5/2)*x - 2*x ≥ - 13/2 - 3

Now all the terms with an x are in the left, and the terms without are in the right.

We can rewrite this inequality as:

(5/2)*x - (4/2)*x ≥ - 13/2 - 6/2

(1/2)*x ≥ -19/2

Now, multiplying both sides by 2 we get:

2*(1/2)*x ≥ (-19/2)*2

x ≥ - 19

So the graph will be a solid point in x = -19, and a ray that extends to the right (the values that are larger than -19)

The correct option is the last graph, option D.

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Alisiya [41]

Answer:

$y = -0.75x + 9.5$

Step-by-step explanation:

Equation of a circle is given as :

$(x-a)^{2} + (y-b)^2 = r^{2} \\(x-6)^{2} + (y-5)^2 = 4^{2}\\x^{2} - 12x + 36 + y^{2} -10y + 25 = 16\\x^{2} - 12x + y^{2} -10y + 45 = 0\\$

Take the derivative of the above with respect to x

$2x - 12 + 2y dy/dx - 10 dy/dy = 0\\\frac{dx}{dy} = \frac{6 - x}{y-5} \\At (2,8) dy/dx = (6-2)/(8-5) = 4/3\\dy/dx = 4/3\\The slope of the tangent to the circle, m = \frac{-1}{dy/dx} \\m = \frac{-1}{4/3}\\m= -0.75$

The equation of the tangent is given by :

$y - y_{1} = m(x - x_{1})\\ y - 8 = -0.75(x - 2)\\y - 8 = -0.75x + 1.5\\y = -0.75x + 9.5$

8 0

3 years ago

Read 2 more answers

If there are 52 cards in a deck with four suits (hearts, clubs, diamonds, and spades), how many ways can you select 5 diamonds a

Luba_88 [7]

Answer:

$12C5 *(12C3) = 792*220 =174240 ways$

Step-by-step explanation:

For this case we know that we have 12 cards of each denomination (hearts, diamonds, clubs and spades) because 12*4= 52

First let's find the number of ways in order to select 5 diamonds. We can use the combinatory formula since the order for this case no matter. The general formula for combinatory is given by:

$nCx = \frac{n!}{x! (n-x)!}$

So then 12 C5 would be equal to:

$12C5 = \frac{12!}{5! (12-5)!}=\frac{12!}{5! 7!} = \frac{12*11*10*9*8*7!}{5! 7!}= \frac{12*11*10*9*8}{5*4*3*2*1}=792$

So we have 792 was in order to select 5 diamonds from the total of 12

Now in order to select 3 clubs from the total of 12 we have the following number of ways:

$12C3 = \frac{12!}{3! 9!}=\frac{12*11*10*9!}{3! 9!} =\frac{12*11*10}{3*2*1}=220$

So then the numbers of ways in order to select 5 diamonds and 3 clubs are:

$(12C5)*(12C3) = 792*220 =174240 ways$

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Aubrey says that the product of 104 and 10–2 is 10–8. Is she correct? If not, explain why.

konstantin123 [22]

Answer:

Step-by-step explanation:

No, she multiplied the exponents instead of adding them.