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3 years ago

The cost, £C, of hiring a lorry to travel n miles is given by

2 answers:

7 0

Part A:
C= a + bn

Make the two equations out of the words:
82 = a + b100 * 2.5 = 205 = a + b250
157 = a+ b250

Subtract the two,
205 = a + b250
- ( 157 = a + b250)
48 = a

Find b by substituting in a:
82 = a + b100
82 = 48 + b100
34 = b100
b = 0.34
Answer for part a: a = 48 , b = 0.34

Part B:
C = a +bn <- when n = 300 , put in a and b, then solve
C = 48 + 0.34(300)
C = 48 + 102
C = 150

Cost when hiring a lorry to travel 300 miles is 150 pounds

Sav [38]3 years ago

4 0

Answer:

Part a) a = 32 and b = 0.5

Part b) £182 is the cost of hiring.

Step-by-step explanation:

Given expression is C = a + bn

where C is the cost of hiring a lorry, n is the distance covered and a, b are two constants.

Part a).

We have to find the constants a and b.

Now we will find the system of equations to find the value of constants.

The cost of travelling 100 miles is £82.

82 = a + 100b ---------(1)

The cost of travelling 250 miles is £157

157 = a + 250b --------(2)

Now we will subtract equation 2 from 1.

157 - 82 = (a + 250b) - (a + 100b)

75 = 150b

b = $\frac{75}{150}=0.5$

Now we put the value of b in equation 1

82 = a + 100×(0.5)

82 = a + 50

a = 82 - 50 = 32

a = 32 and b = 0.5

Part b).

We have to find the cost of hiring a lorry to travel 300 miles.

C = a + bn

C = 32 + (0.5)(300)

C = 32 + 150

C = £182

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Find the value of each variable

aniked [119]

Answer:

Answer d)

$a= 10*\sqrt{3}$ $b=5*\sqrt{3}$ , $c=15$ , and $d=5$

Step-by-step explanation:

Notice that there are basically two right angle triangles to examine: a smaller one in size on the right and a larger one on the left, and both share side "b".

So we proceed to find the value of "b" by noticing that it the side "opposite side to angle 60 degrees" in the triangle of the right (the one with hypotenuse = 10). So we can use the sine function to find its value:

$b=10*sin(60^o)= 10*\frac{\sqrt{3} }{2} = 5*\sqrt{3}$

where we use the fact that the sine of 60 degrees can be written as: $\frac{\sqrt{3} }{2}$

We can also find the value of "d" in that same small triangle, using the cosine function of 60 degrees:

$d=10*cos(60^o)=10* \frac{1}{2} = 5$

In order to find the value of side "a", we use the right angle triangle on the left, noticing that "a" s the hypotenuse of that triangle, and our (now known) side "b" is the opposite to the 30 degree angle. We use here the definition of sine of an angle as the quotient between the opposite side and the hypotenuse:

$sin(30^o)= \frac{b}{a} \\a=\frac{b}{sin(30)} \\a=\frac{5*\sqrt{3} }{\frac{1}{2} } \\a= 10*\sqrt{3}$

where we used the value of the sine function of 30 degrees as one half: $\frac{1}{2}$

Finally, we can find the value of the fourth unknown: "c", by using the cos of 30 degrees and the now known value of the hypotenuse in that left triangle:

$c=10*\sqrt{3} * cos(30^o)=10*\sqrt{3} *\frac{\sqrt{3} }{2} \\c= 5*3=15$

Therefore, our answer agrees with the values shown in option d)

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2 years ago

How the GCF of Monomials helps to factor an expression?

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2 years ago

What is f(-2) if f(x) = 1/2 x? F. 2 G. -1 H. 0 I. 1

kozerog [31]

Answer:

G) -1

Step-by-step explanation:

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f(-2)=1/2(-2)

f(-2)=-2/2

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