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3 years ago

6

Consider this expression.

1 answer:

schepotkina [342]3 years ago

5 0

Answer:

$9m^2 + 17m- 9$

Step-by-step explanation:

Given

$7m^2 + (2m - 1)(m + 9)$

Required:

Simplify

We start by opening the bracket

$7m^2 + (2m(m + 9) - 1(m + 9))$

$7m^2 + 2m^2 + 18m - m - 9$

Collect Like Terms

$9m^2 + 17m- 9$

Hence, the equivalent expression is $9m^2 + 17m- 9$

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State the restrictions, if any.<br> F(x)= x/x2-81

Crazy boy [7]

Answer:

f=1/x^2-81

Step-by-step explanation:

Step 1: Multiply both sides by x^2-81.

fx3−81fx=x

Step 2: Factor out variable f.

f(x3−81x)=x

Step 3: Divide both sides by x^3-81x.

f(x3−81x)

x3−81x =x x3−81x f= 1 x2−81

3 0

3 years ago

A boat leaves a dock and travels 9 miles due north and 12 miles due west. Find how far the boat is from the dock. Type the corre

adelina 88 [10]

Answer:

15 miles

Step-by-step explanation:

Let's say the dock is at the origin on a coordinate plane and each unit is 1 mile. If the boat travels 9 mile due north, that means that we move up from the origin (0, 0) 9 units to point A (0, 9). Now, this boat moves 12 miles due west, so we will go 12 units to the left of (0, 9) to point B (-12, 9). See the attached drawing (sorry for the crudeness).

Notice that this is a right triangle with legs of 9 and 12. That means the distance from the boat to the dock is just the hypotenuse, so use the Pythagorean Theorem: distance = $\sqrt{9^2+12^2} =\sqrt{81+144} =\sqrt{225} =15$

Thus, the answer is 15 miles.

Hope this helps!

3 0

3 years ago

Read 2 more answers

Problem PageQuestion Flying against the jetstream, a jet travels 3050 miles in 5 hours. Flying with the jetstream, the same jet

goblinko [34]

Answer: the rate of the jet in still air is 685 mph and the rate of the jetstream is 75 mph

Step-by-step explanation:

Let x represent the rate of the jet in still air.

Let y represent the rate of the jet jetstream.

Distance = speed × time

Flying against the jetstream, a jet travels 3050 miles in 5 hours. This means that the total speed of the jet would be (x - y) mph. Therefore,

3050 = 5(x - y)

3050/5 = x - y

x - y = 610 - - - - - - - - - - - - - -1

Flying with the jetstream, the same jet travels 3800 miles in 4 hours. This means that the total speed of the jet would be (x + y) mph. Therefore,

3800 = 4(x + y)

3800/5 = x + y

x + y = 760 - - - - - - - - - - - - - -2

Adding equation 1 to equation 2, it becomes

2x = 1370

x = 1370/2 = 685mph

Substituting x = 685 into equation 1, it becomes

685 - y = 610

y = 685 - 610 = 75mph

3 0

3 years ago

The height of a triangular window is 3 feet less than its base. The area the window is 20 ft.? find the dimensions of the window

Ivenika [448]

Let us assume base of the window = b feet.

Height is 3 feet less than base, that is = (b-3).

Given area of the triangle = 20 feet square.

We know formula for area of a triangle:

Area = $\frac{1}{2}$ × Base × Height

Plugging values in formula, we get

20 = $\frac{1}{2} b \times (b-3)$

$\mathrm{Multiply\:both\:sides\:by\:}2$

$40=b\left(b-3\right)$

$40=b^2-3b$

$b^2-3b-40=0$

Factoring quadratic, we get

$\left(b+5\right)\left(b-8\right)$ =0

b+5=0

b=-5

b-8=0

b=8.

For base we can take only positive value.

<h3>Therefore, base of the triangle = 8 feet and height = 8 -3 = 5 feet.</h3>

6 0

3 years ago

Minimum and maximum value of 2n^2+5n-25=0

Alborosie

Equations don't have minimum or maximum, functions do.

Function y=2n^2+5n-25 has minimum -28.125, has no maximum.

8 0

3 years ago