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3 years ago

A rectangle has the

Mathematics

1 answer:

SVEN [57.7K]3 years ago

6 0

Answer:

15.5 inches

Step-by-step explanation:

Length of rectangle = 22 inches
Perimeter = 75 inches

To calculate : Width of the rectangle.

★ Perimeter of rectangle = 2( l + w )

→ 75 = 2(22 + w)

→ 75 = 44 + 2w

→ 75 – 44 = 2w

→ 31 = 2w

→ 31 ÷ 2 = w

→ 15.5 inches = Width

Therefore, width of the rectangle is 15.5 inches.

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If p(x) = 2x2 – 4x and q(x) = x – 3 what is (p*q)(x)

igomit [66]

The correct answer is 2x²-16x+30.

Explanation:
(p*q)(x) is a composition of the two functions p(x) and q(x); it is the same as p(q(x)). We replace every x in p(x) with our value of q(x), x-3:
instead of 2x², we have 2(x-3)², and instead of -4x, we have -4(x-3).

This gives us 2(x-3)²-4(x-3). This is the same as 2(x-3)(x-3)-4(x-3).

Multiplying, we have
2(x*x-3*x-3*x-3(-3))-(4*x-4*3)
=2(x²-3x-3x+9)-(4x-12)
=2(x²-6x+9)-4x+12.

Using the distributive property gives us
2*x²-2*6x+2*9-4x+12
=2x²-12x+19-4x+12.

Combine like terms, and we have 2x²-16x+30.

6 0

3 years ago

Read 2 more answers

Under certain conditions, the number of bacteria present in a colony is approximated by f(t) = Age 0.023t, where t is in minutes

AleksandrR [38]

Answer:

5 min: 3,029,058
10 min: 3,398,220
60 min: 10,732,234

Step-by-step explanation:

The given function is evaluated by substituting the given values of t. This requires using the exponential function of your calculator with a base of 'e'. Many calculators have that value built in, or have an e^x function (often associated with the Ln function).

<h3>5 minutes</h3>

The number of bacteria present after 5 minutes is about ...

f(5) = 2.7×10^6×e^(0.023×5) ≈ 3,029,058

<h3>10 minutes</h3>

The number of bacteria present after 10 minutes is about ...

f(10) = 2.7×10^6×e^(0.023×10) ≈ 3,398,220

<h3>60 minutes</h3>

The number of bacteria present after 60 minutes is about ...

f(60) = 2.7×10^6×e^(0.023×60) ≈ 10,732,234

8 0

2 years ago

Deluxe River Cruises operates a fleet of river vessels. The fleet has two types of vessels: A type-A vessel has 60 deluxe cabins

bixtya [17]

Answer: It should be used 2 for type-A and 3 for type-B to minimize the cost.

Step-by-step explanation: As it is stipulated, x relates to type-A and y to type-B.

Type-A has 60 deluxe cabins and B has 80. It is needed a minimum of 360 deluxe cabins, so:

60x + 80y ≤ 360

For the standard cabin, there are in A 160 and in B 120. The need is for 680, so:

160x + 120y ≤ 680

To calculate how many of each type you need:

60x + 80y ≤ 360

160x + 120y ≤ 680

Isolating x from the first equation:

x = $\frac{360 - 80y}{60}$

Substituing x into the second equation:

160( $\frac{360 - 80y}{60}$ ) + 120y = 680

-3200y+1800y = 10200 - 14400

1400y = 4200

y = 3

With y, find x:

x = $\frac{360 - 80y}{60}$

x = $\frac{360 - 80.3}{60}$

x = 2

To determine the cost:

cost = 42,000x + 51,000y

cost = 42000.2 + 51000.3

cost = 161400

To keep it in a minimun cost, it is needed 2 vessels of Type-A and 3 vessels of Type-B, to a cost of $161400

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2 years ago

PLEASE HELP ME i really need help and please show your work

tester [92]

Since the graph is a straight line, we know that this equation follows some sort of y = mx + b format.

Let's take the points that are on the axes (-4,0) and (0,-3)
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this is our m in the general equations above
we now have y = (-3/4)x + b
b is the y-intercept which is where x = 0 we already have that point in (0,-3)

plug the -3 in for b to give as a final answer:
y = (-3/4)x - 3

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3 years ago

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umka21 [38]

Answer:

Step-by-step explanation:

2 csc²x-2 csc x-1=0

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2 years ago