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3 years ago

12/19*.............................= -12/19

Mathematics

1 answer:

melamori03 [73]3 years ago

3 0

Answer:

$\frac{12}{19} \times \underline{\bold{-1}} = -\frac{12}{19}$

Step-by-step explanation:

$\frac{12}{19} \times ..... = -\frac{12}{19}$

= $\frac{\frac{12}{19}}{-\frac{12}{19}}$

= $\frac{12}{19} \times -\frac{19}{12}$

= $-\frac{228}{228}$

= $\bold{-1}$

So, the appropriate value to complete it is -1

#CMIIW ^^

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Santos is a lifeguard and spots a drowning child 50 meters along the shore and 60 meters from the shore to the child. Santos run

Amanda [17]

Answer:

Santos should run approximately 36.145 meters along the shore

Step-by-step explanation:

The given parameters are;

The distance along the shore of the child = 50 meters

The distance from the shore of the child = 60 meters

The rate at which Santos can run = 4 m/s

The rate he can swim = 0.9 m/s

Let 'x' represent the distance he runs along the shore

We have;

The time he spends running on the shore, t₁ = x/4

The time he spends swimming, t₂ = (√(60² + (50 - x)²)/0.9

The total time, T = t₁ + t₂ = x/4 + (√(60² + (50 - x)²)/0.9

To find the maximum, we have;

dT/dx = 0 = d(x/4 + (√(60² + (50 - x)²)/0.9)/dx = 1/4 - (50 - x)/(0.9·(√(60² + (50 - x)²) = 0

1/4 - (50 - x)/(0.9·(√(60² + (50 - x)²) = 0

Simplifying using a graphing calculator gives;

$\dfrac{x - 2000}{9} = \sqrt{x^2-100\cdot x+6,100}$

1519·x² - 151900·x + 3505900 = 0

x = (151900 ± √((-151900)² - 4×1519×3505900))/(2 × 1519)

x ≈ 63.86 m or x ≈ 36.145 m

We note that the distance from a point x = 63.83 meters and 36.145 meters from where Santos spots the girl to the location of the girl are the same

Therefore, Santos should run approximately 36.145 meters along the shore before jumping into to the water in order to save the child

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2 years ago

Alan buys 5.2 ounces of sour patch kids candy. After sharing with his friends he returns to buy an additional 6.75 ounces. How m

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2 years ago

Given that $x \le -7,$ identify all the correct conclusions. (A) $3x \le -21.$ (B) $3x \ge -21.$ (C) $-3x \le 21.$ (D) $-3x \ge

exis [7]

Answer:

Options A and D are correct choices.

Step-by-step explanation:

We have been given an inequality $x\leq -7$ and we are asked to find the correct options from our given choices.

Let us solve inequalities in our given options one by one to see which of these matches with our given inequality.

(A) $3x\leq -21$

$x\leq \frac{-21}{3}$

$x\leq -7$

We can see that option A gives the same answer as our given inequality, therefore, option A is the correct choice.

(B) $3x\geq -21$

$x\geq \frac{-21}{3}$

$x\geq -7$

This inequality represented in option C gives solution that x should be greater than or equal to -7, which is opposite to our given inequality, therefore, option B is incorrect.

Dividing inequality by a negative number swaps inequality sign.

$x\geq \frac{21}{-3}$

$x\geq -7$

This inequality gives solution that x should be greater than or equal to -7, which is opposite to our given inequality, therefore, option C is incorrect.

(D) $-3x\geq 21$