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2 years ago

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