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2 years ago

20 points

Mathematics

2 answers:

gavmur [86]2 years ago

6 0

Answer:

Michael buys 800 hockey cards from jackson

bezimeni [28]2 years ago

3 0

Answer:

480 cards

Step-by-step explanation:

Step 1: No. of cards Jackson is selling

=> 1000 x 60%

=> 1000 x 0.6

=> 600 cards

Step 2: No. of cards Michael buys

=> 600 x 80%

=> 600 x 0.8

=> 480 cards

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12 7/12 subtracted by 5 14/5

Leni [432]

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4 0

3 years ago

Rose and chi are training for a bike race if They both start the park gate and Rosa starts at 4 PM and chi starts at 4:30 PM Ros

Drupady [299]

Answer:

yes at 6pm

Step-by-step explanation:

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3 years ago

In each diagram, line p is parallel to line f, and line t intersects lines p and f. Based on the diagram, what is the value of x

ololo11 [35]

X would be 84 degrees, since its corresponding angle would be worth 84.
Hope this helped!

4 0

3 years ago

You are designing a rectangular garden. the garden will be enclosed by fencing on three sides and by a house on the fourth side.

RUDIKE [14]

Suppose the dimensions of the rectangle is x by y and let the side enclosed by a house be one of the sides measuring x, then the sides that is to be enclosed are two sides measuring y and one side measuring x.

Thus, the length of fencing needed is given by

P = x + 2y

The area of the rectangle is given by xy,

i.e.

$xy = 288 \\ \\ \\ \\ \Rightarrow y= \frac{288}{x}$

Substituting for y into the equation for the length of fencing needed, we have

$P=x+2\left( \frac{288}{x} \right)=x+ \frac{576}{x}$

For the amount of fencing to be minimum, then

$\frac{dP}{dx} =0 \\ \\ \Rightarrow1- \frac{576}{x^2} =0 \\ \\ \Rightarrow \frac{576}{x^2} =1 \\ \\ \Rightarrow x^2=576 \\ \\ \Rightarrow x=\sqrt{576}=24$

Now, recall that

$y= \frac{288}{x} = \frac{288}{24} =12$

Thus, the length of fencing needed is given by

P = x + 2y = 24 + 2(12) = 24 + 24 = 48.

Therefore, 48 feets of fencing is needed to enclose the garden.

8 0

3 years ago

Determine the angles made by the vector v = (67)i + (-15)j with the positive x- and y-axes. write the unit vector n in the direc

vivado [14]

Consider the picture attached.

From right triangle trigonometry:

tan(α)=(opposite side)/(adjacent side)=15/67=0.2239

using a scientific calculator we find that arctan(0.2239)=12.62°

thus α=12.62°, is the angle that the vector makes with the positive x-axis.

The angle made with the + y-axis is 12.62°+90°=102.62°.

The length of the vector v can be determined using the Pythagorean theorem:

$|v|= \sqrt{ 67^{2} + 15^{2} }= \sqrt{4489+225}= \sqrt{4714}=68.8$

Thus, to make v a unit vector, without changing its direction, we need to divide v by |v|=68.8.

This means that the x and y components will also be divided by 68.8, by proportionality.

So, the unit vector in the direction of v is:

(67/68.8)i + (-15/68.8)j=0.97 i + (- 0.22)j


Answer: 12.62°; 102.62°; 0.97 i + (- 0.22)j

6 0

3 years ago