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4 years ago

Which expression is equivalent to 0.2n + 2n + 4?

Mathematics

1 answer:

VashaNatasha [74]4 years ago

4 0

0.2n + 2n + 4
= 2.2n + 4
answer

D. 2.2n+4

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An explosion causes debris to rise vertically with an initial speed of 120 feet per second. The formula h equals negative 16 t s

Novay_Z [31]

Answer:

The debris will be at a height of 56 ft when time is 0.5 s and 7 s.

Step-by-step explanation:

Given:

Initial speed of debris is, $s=120\ ft/s$

The height 'h' of the debris above the ground is given as:

$h(t)=-16t^2+120t$

As per question, $h(t)=56\ ft$ . Therefore,

$56=-16t^2+120t$

Rewriting the above equation into a standard quadratic equation and solving for 't', we get:

$-16t^2+120t-56=0\\\textrm{Dividing by -8 throughout, we get}\\\frac{-16}{-8}t^2+\frac{120}{-8}t-\frac{56}{-8}=0\\2t^2-15t+7=0$

Using quadratic formula to solve for 't', we get:

$t=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\\\t=\frac{-(-15)\pm \sqrt{(-15)^2-4(2)(7)}}{2(2)}\\\\t=\frac{15\pm \sqrt{225-56}}{4}\\\\t=\frac{15\pm\sqrt{169}}{4}\\\\t=\frac{15\pm 13}{4}\\\\t=\frac{15-13}{4}\ or\ t=\frac{15+13}{4}\\\\t=\frac{2}{4}\ or\ t=\frac{28}{4}\\\\t=0.5\ s\ or\ t=7\ s$

Therefore, the debris will reach a height of 56 ft twice.

When time $t=0.5\ s$ during the upward journey, the debris is at height of 56 ft.

Again after reaching maximum height, the debris falls back and at $t=7\ s$ , the height is 56 ft.

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3 years ago

The cost of renting a sailboat at a lake is $20 per hour plus $14 for lifejackets. Write an equation in slope-intercept form tha

aalyn [17]

Answer:

y=20x+14, where:

y is the total amount you would pay for using the sailboat

x is the number of hours the sailboat is used

Step-by-step explanation:

An equation in slope-intercept form is set up as y=mx+b. From the information provided, the equation would indicate that the cost of renting the boat would be equal to the price per hour for the number of hours plus the cost of lifejackets and the equation in slope-intercept form that can be used is:

y=20x+14, where:

y is the total amount you would pay for using the sailboat

x is the number of hours the sailboat is used

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3 years ago

explain how you could use a number line to show that -4 + 3 and 3 + (-4) have the same value. Which property of addition states

brilliants [131]

They are able to have the same value as the negative sign is simply transferred to the inside. Either way 4 is being subtracted from 3.

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3 years ago

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Would it be 11 and 12?

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A pair of reading glasses shows you an image of an object that is 3.1 times the object's actual size. So the scale factor of the

KiRa [710]

When given the scale factor and the factored size of the object, to find the original size, divide the factored size by the scale factor:

0.8 / 3.1 = 0.258 inches

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