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3 years ago

Is 10 a solution to the following inequality? -2 (x-13)-7+5x<0

Mathematics

1 answer:

zlopas [31]3 years ago

6 0

Answer:

10 is NOT a solution for -2 (x - 13) - 7 + 5 x <0

Step-by-step explanation:

Here, the given expression is : -2 (x - 13) - 7 + 5 x <0

To check : If it holds true for x = 10

Put x = 10 in the lefts side, we get:

-2 (x - 13) - 7 + 5 x = -2 ( 10 -13) - 7 + 5 (10)

= -2 (-3) -7 + 50

= 6 - 7 + 50 = -1 + 50

= 49

⇒ at x = 10 , -2 (x - 13) - 7 + 5 x = 49

and Right side of the inequality is 0.

49 < 0 is a contradiction , as 49 ≮ ( is not less than) 0

Hence, 10 is NOT a solution for -2 (x - 13) - 7 + 5 x <0

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Find the equation of a sphere if one of its diameters has endpoints: (-9, -12, -6) and (11, 8, 14).

baherus [9]

Answer:

Hence, the equation of a sphere with one of its diameters with endpoints (-9, -12, -6) and (11, 8, 14) is $(x-1)^{2}+(y+2)^{2}+(z-4)^{2} = 30$ .

Step-by-step explanation:

There are two kew parameters for a sphere: Center ( $h$ , $k$ , $s$ ) and Radius ( $r$ ). The radius is the midpoint of the line segment between endpoints. That is:

$C(x,y,z) = \left(\frac{-9+11}{2},\frac{-12+8}{2},\frac{-6+14}{2} \right)$

$C(x,y,z) = (1,-2,4)$

The radius can be found by halving the length of diameter, which can be determined by knowning location of endpoints and using Pythagorean Theorem:

$r = \frac{1}{2}\cdot \sqrt{(-9-11)^{2}+(-12-8)^{2}+(-6-14)^{2}}$

$r = 10\sqrt{3}$

The general formula of a sphere centered at (h, k, s) and with a radius r is:

$(x-h)^{2}+(y-k)^{2}+(z-s)^{2} = r^{2}$

Hence, the equation of a sphere with one of its diameters with endpoints (-9, -12, -6) and (11, 8, 14) is $(x-1)^{2}+(y+2)^{2}+(z-4)^{2} = 30$ .

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3 years ago

A box of cereal states that there are 81 cal in a 3/4 cup serving what is the unit rate for calories per cup how many calories a

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Answer:

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Step-by-step explanation:

A box of cereal states that there are 81 cal in a 3/4 cup serving what is the unit rate for calories per cup how many calories are there in 3 cups of cereal

The unit rate for calories per cup = calories per cup

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We Cross Multiply

3/4 × x = 81 × 3

x = (81 × 3) ÷ 3/4

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