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3 years ago

Solve using substitution y=1/2x x+4y=18

Mathematics

1 answer:

Aleks [24]3 years ago

7 0

Answer:

The solution set is (6,3)

Step-by-step explanation:

Begin by multiplying equation 1 by 2. You'll see why in a moment

2y = 2*(1/2) x

2y = x

Substitute this value into equation 2.

2y + 4y = 18 Combine like terms on the left

6y = 18 Divide both sides by 6

6y/6 = 18/6 Do the division

y = 3

To solve for x just use the top equation

y = 1/2x

3 = 1/2x Multiply by 2

3*2 = x

x = 6

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Using the definition of an even function , show that y = - cos x is even

motikmotik

A function is even if, for each x in the domain of f, f (- x) = f (x). The even functions have reflective symmetry through the y-axis.
We have then:
f (x) = - cos x
f (-x) = - cos (-x)
On the other hand:
cos (-x) = cos x
So:
- cos (-x) = - cos x
Therefore, it is fulfilled:
f (- x) = f (x)
Example:
cos (pi / 2) = 0
cos (-pi / 2) = 0

5 0

4 years ago

Solve for the letter A. ab+d=c

Eddi Din [679]

Answer:

a=c/b-d/b

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

#1. Factor the expression. 4g^2+21g-49

juin [17]

1. You want to find factors of 4×(-49) that add to 21. Those would be +28 and -7. Replacing the term 21g with the sum 28g -7g, we get an expression that can be factored by grouping.

... (4g² +28g) + (-7g -49)

... = 4g(g +7) -7(g +7) = (4g-7)(g+7)

2. After you factor out 5, you have 5(64y² -16y -15). As in the previous problem, you're looking for factors of 64×(-15) = -960 that sum to -16. There are 14 factor pairs of 960, so it can take a little bit of effort to find the right pair. That pair is -40 and 24. As in the previous problem you replace the term -16y with the sum -40y +24y and factor by grouping.

... = 5(64y² -40y +24y -15) = 5(8y(8y -5) +3(8y -5))

... = 5(8y +3)(8y -5)

3. False. It is perhaps easiest to check this by multiplying out the offered factors. Doing that gives you 36k² -36k +8k -8. The collected k terms add to -28k, not -44k.

4 0

4 years ago

An oval track is made by erecting semicircles on each end of a 44 m by 88 m rectangle. Find the length of the track and the area

Dmitry_Shevchenko [17]

Answer:

The length of the track is 247 m.

The area enclosed by the track is 5391 . 76 sq m.

Step-by-step explanation:

The length of the rectangle = 88 m

The width of the rectangle = 44 m

Now, as we know the semicircles are at the end of rectangular track.

So, the diameter of semicircles = Width of the rectangle

⇒ The diameter of the semi circle = 44 m

⇒Radius of the semi circle = 44/2 = 22 m

TOTAL LENGTH OF TRACK

= 2 ( Length of rectangle) + 2 (Circumference of 1 semicircle)

= 2 x (88 m) + 2 ( $\frac{2\pi r}{2}$ )

= 176 m + 2 (3.14)(22 m) = 176 + 71.08 = 247 m

Hence, the length of the track is 247 m

TOTAL AREA OF TRACK

= (Area of rectangle) + 2 (Area of 1 semicircle)

= (Length x Width) + 2 ( $\frac{\pi r^2}{2}$ )

= (44 m x 88 m) + (3.14)(22 m)(22 m) = (3872 + 1519.76) sq m

= 5391 . 76 sq m

Hence, the area enclosed by the track is 5391 . 76 sq m.

7 0

3 years ago

Games Galore Super Store buys the latest video game at a wholesale price of $30.00. The markup rate at Game's Galore Super Store

marishachu [46]

Answer:

Step-by-step explanation:

By definition, Markup is the difference between a product's selling price and cost as a percentage of the cost.

For example, if a product sells for $125 and costs $100, the additional price increase is ($125 – $100) / $100) x 100 = 25%.

Given data

firstly let us solve for 40% of $30

=40/100*30

=0.4*30

=$12

therefore the sale price will be the markup rate plus the initial price

<em>Hence the you will have to pay 12+30=$42</em>

6 0

3 years ago