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3 years ago

State the angle relationship and state the measure of each angle indicated that makes lines u and v

Mathematics

1 answer:

vlabodo [156]3 years ago

7 0

Answer:

Q9. ?=53° (corr angles, u//v)

Q10. ?=58° (alt angles, u//v)

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A store received a shipment of soup cans. The clerk put an equal number of cans on each of 4 shelves. Write an equation to repre

icang [17]

To represent the number of cans in each shelf you will divide the total number of cans by the number of shelves.

This is represented as
t/4 = n.

8 0

3 years ago

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A ship leaves port at noon and has a bearing of S29oW. The ship sails at 20 knots. How many nautical miles south and how many na

ira [324]

Answer:

Approximately $58.2\; \text{nautical miles}$ (assuming that the bearing is ${\rm S$29^{\circ}$W}$ .)

Step-by-step explanation:

Let $v$ denote the speed of the ship, and let $t$ denote the duration of the trip. The magnitude of the displacement of this ship would be $v\, t$ .

Refer to the diagram attached. The direction ${\rm S$29^{\circ}$W}$ means $29^{\circ}$ west of south. Thus, start with the south direction and turn towards west (clockwise) by $29^{\circ}$ to find the direction of the displacement of the ship.

The hypothenuse of the right triangle in this diagram represents the displacement of the ship, with a length of $v\, t$ . The dashed horizontal line segment represents the distance that the ship has travelled to the west (which this question is asking for.) The angle opposite to that line segment is exactly $29^{\circ}$ .

Since the hypotenuse is of length $v\, t$ , the dashed line segment opposite to the $\theta = 29^{\circ}$ vertex would have a length of:

$\begin{aligned}& \text{opposite (to $\theta$)} \\ =\; & \text{hypotenuse} \times \frac{\text{opposite (to $\theta$)}}{\text{hypotenuse}} \\ =\; & \text{hypotenuse} \times \sin (\theta) \\ =\; & v\, t \, \sin(\theta) \\ =\; & v\, t\, \sin(29^{\circ})\end{aligned}$ .

Substitute in $\begin{aligned} v &= 20\; \frac{\text{nautical mile}}{\text{hour}}\end{aligned}$ and $t = 6\; \text{hour}$ :

$\begin{aligned} & v\, t\, \sin(29^{\circ}) \\ =\; & 20\; \frac{\text{nautical mile}}{\text{hour}} \times 6\; \text{hour} \times \sin(29^{\circ}) \\ \approx\; & 58.2\; \text{nautical mile}\end{aligned}$ .

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2 years ago

Percentages

Kay [80]

People who said yes: $24-18=6$

Decimal: $\frac{6}{24} = \frac{6/6}{24/4} = \frac{1}{4} =0.25$

Percentage: $0.25*100=25$ --> 25%

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3 years ago

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3/8 as a decimal and as a fraction

lesya692 [45]

Answer:

0.375 is the correct answer

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3 years ago

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Match the following items by evaluating the expression for x = -6.

Kryger [21]

Step-by-step explanation:

Put the value of x = -6 to all expressions:

$x^{-2}=(-6)^{-2}=\dfrac{1}{(-6)^2}=\dfrac{1}{6}\qquad\text{used}\ a^{-n}=\dfrac{1}{a^n}\\=====================\\x^{-1}=(-6)^{-1}=\dfrac{1}{(-6)^1}=-\dfrac{1}{6}\\=====================\\x^0=(-6)^0=1\qquad a^0=1\ \text{for all real numbers except 0}\\=====================\\x^1=(-6)^1=-6\qquad a^1=a\ \text{for all real numbers}\\=====================\\x^2=(-6)^2=36$

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3 years ago