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Rom4ik [11]
2 years ago
14

Solve for u. |5u + 15| = 10

Mathematics
1 answer:
Rudiy272 years ago
6 0

Answer:

-1 and -5

Step-by-step explanation:

You must account for negative u values (which the abs nullifies).

So 5u+15=10 and 5u+15=-10 is what we have to solve for.

As for usual equations, isolate the u variable.

5u + 15 = 10

5u + 15 (-15) = 10 (-15)

5u = -5

\frac{5u}{5}=\frac{-5}{1}

u = -1

Now you can do the same operation for the other equation and you should get u = -5.

Let's make sure we did it right by replacing u with one of our solutions (-1 or -5).

|5(-1)+15| = 10\\10 = 10

That's true. What about the other one?

|5(-5)+15|=10\\10=10

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The perimeter of a rectangle is 128 cm, and the ratio of its sides is 5: 3. Find the area of ​​a rectangle
Juliette [100K]

Answer:

Area = 960 cm^2

Step-by-step explanation:

Perimeter (P) = 2 (l + w)

P = 2l + 2w

Let the length be 5x

Let the width be 3x

From the question, P = 128.

Therefore:

128 = 2l + 2w

Divide both sides by 2.

l + w = 64

Recall we said:

l = 5x

w = 3x

So then:

5x + 3x = 64

8x = 64

Divide both sides by 8

x = 64/8

x = 8.

Since x = 8

Length = 5x = 5*8 = 40cm

Width =3x = 3 * 8 = 24cm

Area of a RECTANGLE:

Area = length * width

Area = 40 * 24

Area = 960 cm^2

7 0
3 years ago
A bag contains 1p, 2p and 5p coins
garri49 [273]

Answer:

160 2p coins

Step-by-step explanation:

3/8 x 640 = 240 = 1p coins

240 = 5p coins

240 + 240 = 480

640 - 480 = 160

4 0
2 years ago
Compare the two graphs and explain the transformation that was applied to f(x) in order to look exactly like the graph of g(x).
Neporo4naja [7]

The two graphs are represented below.

Answer and Step-by-step explanation: One graph can "transform" into another through changes in the function.

There are 3 ways to change a function:

  1. <u>Shifting</u>: it adds or subtracts a constant to one of the coordinates, thus changing the graph's location. When the <em><u>y-coordinate</u></em> is<em> </em>added or subtract and the x-coordinate is unchanged, there is a <em><u>vertical</u></em> <u><em>shift</em></u>. If it is the <em><u>x-coordinate</u></em> which changes and y-coordinate is kept the same, the shift is a <em><u>horizontal</u></em> <u><em>shift</em></u>;
  2. <u>Scaling</u>: it multiplies or divides one of the coordinates by a constant, thus changing position and appearance of the graph. If the <em>y-coordinate</em> is multiplied or divided by a constant but x-coordinate is the same, it is a <em>vertical scaling</em>. If the <em>x-coordinate</em> is changed by a constant and y-coordinate is not, it is a <em>horizontal</em> <em>scaling</em>;
  3. <u>Reflecting</u>: it's a special case of scaling, where you can multiply a coordinate per its opposite one;

Now, the points for f(x) are:

(-5,0)  (0,6)  (5,-4)  (8,0)

And the points for g(x) are:

(-5,-3)  (0,-9)   (5,1)   (8,-3)

Comparing points:

(-5,0) → (-5,-3)

(0,6) → (0,-9)

(5,-4) → (5,1)

(8,0) → (8,-3)

It can be noted that x-coordinate is kept the same; only y-coordinate is changing so we have a vertical change. Observing the points:

(-5,0-3) → (-5,-3)

(0,6-15) → (0,-9)

(5,-4+5) → (5,1)

(8,0-3) → (8,-3)

Then, the vertical change is a <u>Vertical</u> <u>Shift</u>.

Another observation is that y-coordinate of f(x) is the opposite of g(x). for example: At the second point, y-coordinate of f(x) is 6, while of g(x) is -9. So, this transformation is also a <u>Reflection</u>.

<u>Range</u> <u>of</u> <u>a</u> <u>function</u> is all the values y can assume after substituting the x-values.

<u>Domain</u> <u>of</u> <u>a</u> <u>function</u> is all the values x can assume.

Reflection doesn't change range nor domain of a function. However, vertical or horizontal translations do.

Any vertical translation will change the range of a function and keep domain intact.

Then, for f(x) and g(x):

graph            translation            domain      range

f(x)                       none                 [-5,8]          [-4,6]

g(x)                vertical shift           [-5,8]          [-9,1]

<u>In conclusion, this transformation (or translation) will affect the range of g(x)</u>

5 0
2 years ago
Brand X sells 21 oz. Bags of mixed nuts that contain 29% peanuts. To make their product they combine brand A mixed nuts which co
masha68 [24]

Answer:

Brand X has to mix 8.4 oz of brand A mixed nuts which contain 35% peanuts and 12.6 oz of brand B mixed nuts which contain 25%, to obtain 21 oz. Bags of mixed nuts that contain 29% peanuts.

Step-by-step explanation:

Hi

We define

B_{A}=1oz @ 35\%, wich means Brand A has 1 oz containing 35% peanuts.

B_{B}=1oz @ 25\%, wich means Brand b has 1 oz containing 25% peanuts.

So we can build an equiation system

(1) B_{a}+B_{b}=21

(2)0.35 \times B_{a}+0.25 \times B_{b}=0.29 \times 21, after fixing it a little

(2)0.35B_{a}+0.25B_{b}=6.09

As we can use any method to solve the system, I used a calculator wich thrown the following results B_{a}=8.4 \ oz and B_{b}=12.6 \ oz.

4 0
2 years ago
Find the value of 1/3 divided by 1/2
Arisa [49]

When dividing two fractions, it is important to know to multiply the first fraction by the reciprocal of the second fraction.

Reciprocal means basically a flipped fraction. 2/3 as a reciprocal is 3/2, etc.

1/3 / 1/2= 1/3 x 2/1=2/3

8 0
2 years ago
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