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3 years ago

Find x and y, given that line KL and line MN are parallel. Please show how you got your answer.

Mathematics

1 answer:

Olegator [25]3 years ago

8 0

Answers:
x = 19/2 = 9.5
y = 44/3 = 14.667
The decimal value of y is approximate

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The triangles are similar. So the corresponding sides form a proportion

KM/KJ = LN/LJ
(x-2)/5 = 12/8
8(x-2) = 5*12
8x-16 = 60
8x = 60+16
8x = 76
x = 76/8
x = 19/2
x = 9.5

Similarly,
MN/KL = LN/LJ
22/y = 12/8
22*8 = 12y
12y = 176
y = 176/12
y = 44/3
y = 14.667 (value is approximate)

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Ace Truck leases its 10-ft box truck at $20/day and $0.50/mi, whereas Acme Truck leases a similar truck at $15/day and $0.55/mi.

Masja [62]

Answer:

a) $f(x) = 0.5 \frac{dollars}{day} x + 20$

$g(x) = 0.55 \frac{dollars}{mi} x + 15$

b) $f(70)=0.5*70 +20 =55$

$g(70)= 0.55*70 + 15 =53.5$

If we want to minimize the cost then we should rent the Acme Truck company.

Step-by-step explanation:

Assuming the following questions.

(a) Find the daily cost of leasing from each company as a function of the number of miles driven and sketch the graph of these functions.

For the Ace truck we know that leases its 10-ft box truck at $20/day and $0.50/mi. So then f(x) representing the daily cost is given by:

$f(x) = 0.5 \frac{dollars}{day} x + 20$

Where x represent the number of miles driven

For the Acme Truck we know that leases a similar truck at $15/day and $0.55/mi, so then the g*x( representing daily cost would be given by:

$g(x) = 0.55 \frac{dollars}{mi} x + 15$

Where x represent the miles driven.

We can see the plot on the figure attached.

(b) Which company should you rent a truck from for 1 day if you plan to drive 70 miles and wish to minimize cost?

If we replace the value x=70 for both functions we got:

$f(70)=0.5*70 +20 =55$

$g(70)= 0.55*70 + 15 =53.5$

If we want to minimize the cost then we should rent the Acme Truck company.

7 0

3 years ago

10. (a) Consider the following matrices: A = ( 2 ) B = (3) and C = (-3) w = Find the det(A). [1] (ii) Is the matrix A singular?

Viefleur [7K]

i) We have to find the determinant of A.

We can do this as:

$\det(A)=|\begin{bmatrix}{3} & {6} \\ {1} & {-2}\end{bmatrix}|=3*(-2)-6*1=-6-6=-12$

ii) We have to find if the matrix A is singular.

Singular matrix have determinant equal to 0.

This is not the case for A, as its determinant is -12. Then, A is not a singular matrix.

iii) We have to find the values of x and y so that AB = C.

We have to write the matrix multiplication and we will obtain a system of linear equations:

We can now solve the system of equations by adding 3 times the second equation to the first equation:

$\begin{gathered} 3(x-2y)+(3x+6y)=3(-3)+(-3) \\ 3x-6y+3x+6y=-9-3 \\ 6x+0y=-12 \\ x=\frac{-12}{6} \\ x=-2 \end{gathered}$

We can now use the second equation to find the value of y:

$\begin{gathered} x-2y=-3 \\ x+3=2y \\ y=\frac{x+3}{2} \\ y=\frac{-2+3}{2} \\ y=\frac{1}{2} \end{gathered}$

The values are x = -2 and y = 1/2.

iv) When we want to multiply two matrices, the required condition is that the number of columns of the matrix on the left is equal the number of rows of the matrix on the right.

In the case of A(2x2) and B(2x1), when we do A*B this condition is satisfied.

But when we try to multiply BA, the number of columns of B is not equal to the number of rows of A, so the matrix mulitplication is not possible.

Answer:

i) det(A) = -12

ii) A is not singular because singular matrices have determinant equal to zero.

iii) x = -2 and y = 1/2.

iv) Is not possible because the number of columns of the first matrix has to be equal to the number of rows of the second matrix.

6 0

1 year ago

3/5 + 4/15 = in simply

maksim [4K]

You have to get a common denominator so

3 x 3 = 9
5 x 3 = 15

So now we have 9/15 + 4/15 which is 13/15.

The answer is 13/15

7 0

3 years ago

Read 2 more answers

A $40 backpack is in sale for $28. What is the % of change

aliya0001 [1]

$ 40 ..... 100 %
$ 28 ..... x %

$x = \frac{28 \cdot 100}{40} = 70$

The % of change is 70 %.

This is equivalent with:
- the final price ($ 28) is 70 % from the initial price ($ 40)
- the initial price ($ 40) was reduced with 30% giving the new price as:
$40 - 40 \cdot \frac{30}{100} = 28$

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3 years ago

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In triangle JKL, sin(b°) = three fifths and cos(b°) = four fifths. If triangle JKL is dilated by a scale factor of 2, what is ta

scoundrel [369]

Answer:

Tan(b°) = 3/4 = three fourths (C)

Step-by-step explanation:

Triangle JKL is a right angled triangle in which angle K is a right angle and angle L= b°

We would apply SOHCAHTOA from trigonometry to determine the value for each sides.

For ∆JKL

Sin(b°) = opposite/hypotenuse

Sin(b°) = 3/5

Cos(b°) = adjacent/hypotenuse

Cos(b°) = 4/5

Tan(b°) = 3/4

From the above we know the value of each sides of ∆JKL

Find attached the diagram of the above triangle (1)

∆JKL is dilated by a scale factor = 2

Meaning we would multiply each sides of ∆JKL by 2. The values of the new triangle become:

Opposite = 2(3) = 6

Adjacent = 2(4) = 8

Hypotenuse = 2(5) = 10

To find tan(b°) of the new triangle, we would apply tangent ratio

Tan(b°) = opposite/adjacent

Tan(b°) = 6/8

Tan(b°) = 3/4

Find attached the diagram for the new triangle (2)

Diagram 3 shows the drawing of both triangles together.

From the above, we can see the angle doesn't change when a shape is dilated by a scale factor.

Therefore, tan(b°) = three fourths (C)

6 0

4 years ago