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2 years ago

A bucket was placed under a water leak in a ceiling. in half an hour the bucket was 1/5 of the way full. write an equation that

represents the number of buckets filled ,y, in × hours

Mathematics

1 answer:

mr_godi [17]2 years ago

8 0

$\frac{1}{5} x = y$

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What are the lengths of the legs of a right triangle in which one acute angle measures 19° and the hypotenuse is 15 units long?

pentagon [3]

The legs of a triangle with a hypotenuse that measures 15 units long have lengths that are equal to 15 times the sine or cosine of the given angle.
leg 1 = (15 units) x (cos 19) = 14.18 units
leg 2 = (15 units) x (sin 19) = 4.88 units
The lengths of the legs are 14.18 units and 4.88 units.

6 0

3 years ago

What is the slope-intercept equation of this line?

levacccp [35]

Answer:

y=-2x+8

Step-by-step explanation:

Slope=-2

Y intercept= 8

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3 years ago

Ramona owns a orange grove, and needs to harvest at least 2616 oranges to cover the costs of running the grove. If each tree bea

GuDViN [60]

Answer:

Kindly check explanation

Step-by-step explanation:

Given the following information :

Number of oranges Ramona needs to harvest in other to cover the cost of running the orange Grove = 2616

Average number of oranges each tree bears = 62

Oranges needed for charity donation = 360

Number of orange trees needed in the Grove :

Total number of oranges needed :

(Charity + running the Grove)

(360 + 2616) = 2976 oranges

Number of trees needed = total number of oranges needed / average number of oranges beared per tree

Number of trees needed = 2976 / 62

= 48 trees

Number of trees needed ≥ 48

4 0

3 years ago

Show work please<br> \sqrt(x+12)-\sqrt(2x+1)=1

Nesterboy [21]

Answer:

$x=4$

Step-by-step explanation:

Given $\displaystyle\\\sqrt{x+12}-\sqrt{2x+1}=1$ , start by squaring both sides to work towards isolating $x$ :

$\displaystyle\\\left(\sqrt{x+12}-\sqrt{2x+1}\right)^2=\left(1\right)^2$

Recall $(a-b)^2=a^2-2ab+b^2$ and $\sqrt{a}\cdot \sqrt{b}=\sqrt{a\cdot b}$ :

$\displaystyle\\\left(\sqrt{x+12}-\sqrt{2x+1}\right)^2=\left(1\right)^2\\\implies x+12-2\sqrt{(x+12)(2x+1)}+2x+1=1$

Isolate the radical:

$\displaystyle\\x+12-2\sqrt{(x+12)(2x+1)}+2x+1=1\\\implies -2\sqrt{(x+12)(2x+1)}=-3x-12\\\implies \sqrt{(x+12)(2x+1)}=\frac{-3x-12}{-2}$

Square both sides:

$\displaystyle\\(x+12)(2x+1)=\left(\frac{-3x-12}{-2}\right)^2$

Expand using FOIL and $(a+b)^2=a^2+2ab+b^2$ :

$\displaystyle\\2x^2+25x+12=\frac{9}{4}x^2+18x+36$

Move everything to one side to get a quadratic:

$\displaystyle-\frac{1}{4}x^2+7x-24=0$

Solving using the quadratic formula:

A quadratic in $ax^2+bx+c$ has real solutions $\displaystyle x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ . In $\displaystyle-\frac{1}{4}x^2+7x-24$ , assign values:

$\displaystyle \\a=-\frac{1}{4}\\b=7\\c=-24$

Solving yields:

$\displaystyle\\x=\frac{-7\pm \sqrt{7^2-4\left(-\frac{1}{4}\right)\left(-24\right)}}{2\left(-\frac{1}{4}\right)}\\\\x=\frac{-7\pm \sqrt{25}}{-\frac{1}{2}}\\\\\begin{cases}x=\frac{-7+5}{-0.5}=\frac{-2}{-0.5}=\boxed{4}\\x=\frac{-7-5}{-0.5}=\frac{-12}{-0.5}=24 \:(\text{Extraneous})\end{cases}$