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FrozenT [24]
2 years ago
11

2) 8xy -- 3y + 2 ( 9x - 5y + 4 ) if x = 3, y = - 4

Mathematics
1 answer:
Scilla [17]2 years ago
4 0

Answer:

8xy-3y + 2(9x-5y+4) = 18

Step-by-step explanation:

We need to find the value of the given expression:

8xy-3y + 2(9x-5y+4) ....(1)

when x = 3 and y = -4

Put the values of a and y in equation (1)

8×3×(-4)-3(-4)+ 2(9×3-5(-4)+4)

= -96 +12 + 2(27 + 20 +4)

= -84 + 2(51)

= -84 + 102

= 18

Hence, the value of the given expression is 18.

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A vector with magnitude 9 points in a direction 190 degrees counterclockwise from the positive x axis. Write in component form
Over [174]

Answer:

\vec{v}= \text{ or } \approx

Step-by-step explanation:

Component form of a vector is given by \vec{v}=, where i represents change in x-value and j represents change in y-value. The magnitude of a vector is correlated the Pythagorean Theorem. For vector \vec{v}=, the magnitude is ||v||=\sqrt{i^2+j^2.

190 degrees counterclockwise from the positive x-axis is 10 degrees below the negative x-axis. We can then draw a right triangle 10 degrees below the horizontal with one leg being i, one leg being j, and the hypotenuse of the triangle being the magnitude of the vector, which is given as 9.

In any right triangle, the sine/sin of an angle is equal to its opposite side divided by the hypotenuse, or longest side, of the triangle.

Therefore, we have:

\sin 10^{\circ}=\frac{j}{9},\\j=9\sin 10^{\circ}

To find the other leg, i, we can also use basic trigonometry for a right triangle. In right triangles only, the cosine/cos of an angle is equal to its adjacent side divided by the hypotenuse of the triangle. We get:

\cos 10^{\circ}=\frac{i}{9},\\i=9\cos 10^{\circ}

Verify that (9\sin 10^{\circ})^2+(9\cos 10^{\circ})^2=9^2\:\checkmark

Therefore, the component form of this vector is \vec{v}=\boxed{}\approx \boxed{}

6 0
3 years ago
Jeremy lost his dog, and wants to make some signs to put up in the neighborhood. The cost to make 8 paper signs and 2 laminated
Mashcka [7]

Answer:

cost to make paper signs = $1

cost to make laminated signs = $2

Step-by-step explanation:

Let

x = cost to make paper signs

y = cost to make laminated signs

8x + 2y = 12 (1)

10x + 10y = 30 (2)

Multiply (1) by 5

40x + 10y = 60 (3)

10x + 10y = 30 (2)

Subtract (2) from (3) to solve for x

40x - 10x = 60 - 30

30x = 30

x = 30/30

x = $1

Substitute x = 1 into (1)

8x + 2y = 12

8(1) + 2y = 12

8 + 2y = 12

2y = 12 - 8

2y = 4

y = 4/2

y = $2

cost to make paper signs = $1

cost to make laminated signs = $2

5 0
3 years ago
All members of our painting team paint at the same rate. If $20$ members can paint a $4800$ square foot wall in $36$ minutes, th
Softa [21]

Answer:

It takes 70 minutes for 9 team members (painting 60 sq ft per minute) to paint a 4200 sq ft wall.

Step-by-step explanation:

According to the situation the calculation is shown below:-

= \frac{4800}{20}

= 240 sq ft each member of the team in 36 minutes

= \frac{240}{36}

= 6.67 sq ft each member of the team within 1 minute

= 6.67\times 9

= 60 sq ft for every 9 team members in one minute

= \frac{4200}{60}

= 70 minutes (or 1 hour and 10 minutes)

Hence, the 70 minutes is taken for 9 team members

8 0
3 years ago
The regular price of an item at a store is p dollars. The items is on sale for 10% off the regular price. Some of the expression
Stolb23 [73]

Answer:

<u><em>C,   </em></u>  Expression B and Expression D

Step-by-step explanation:

<h2><u><em>Step 1 : Analyzing the question:</em></u></h2>

The regular price of an item at a store is p dollars. The items is

on sale for 10% off the regular price. Some of the expressions

below represent the sale price, in dollars, of the item.

It says  " <em>item on sale for 10% off </em>". That means p-0.1p  or  0.9p.

<h2><u><em>Step 2 : Looking at the next portion of the question:</em></u></h2>

Expression A: 0.1p

Expression B: 0.9p

Expression C: 1 - 0.1p

Expression D: p - 0.1p

Expression E: p - 0.0p

<u>Expression A</u> doesn't make any sense. It only shows the how

much you save

<h3><em><u>Expression B:</u></em>   This is one of the answer. </h3><h3 /><h3>p-0.1p=0.9p</h3><h3 />

<u>Expression C: </u>  You can't subtract 0.1p from 1

<h3><em><u>Expression D: </u></em>  D makes sense.p-0.1p=0.9p</h3><h3 />

<u>Expression E: </u>   This is the same thing as p

<h2><u><em>Step 3: The answers:</em></u></h2>

<u><em>The answer is C .</em></u>

5 0
2 years ago
You choose a marble at random from a bag containing 3 yellow marbles, 8 red marbles, and 4 blue marbles. You pick a second marbl
jonny [76]
First would be Red Marbles Second would be Blue and last Yellow. (remember this is <em><u>not</u></em> exact)  
I'm sure this is good! :D
5 0
2 years ago
Read 2 more answers
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