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3 years ago

We want to factor the following expre

Mathematics

1 answer:

mote1985 [20]3 years ago

8 0

Step-by-step explanation:

$(x - 3)^{2} - 10(x - 3) + 25 \\ = (x - 3)^{2} - 5(x - 3) - 5(x - 3)+ 25 \\ = (x - 3) \{(x - 3) - 5 \} - 5 \{(x - 3) - 5 \} \\ = \{(x - 3) - 5 \} \{(x - 3) - 5 \} \\ = (x - 8)(x - 8) \\ \\ another \: way \\ \\ (x - 3)^{2} - 10(x - 3) + 25 \\ = (x - 3)^{2} - 2 \times 5 \times (x - 3) + {5}^{2} \\ = \{(x - 3) - 5 \}^{2} \\ = \{x - 3 - 5 \}^{2} \\ = \{x - 8 \}^{2} \\ = (x - 8)(x - 8)$

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An aquarium measures 61 cm long, 30.5 cm wide, and 30.5 cm high.If the tank is only filled to 80% capacity with water, how much

LiRa [457]

Answer:

$V=45396.2\ cm^3$

Step-by-step explanation:

Given that,

The dimensions of an aquarium are 61 cm long, 30.5 cm wide, and 30.5 cm high.

The tank is filled to 80% capacity with water.

We need to find the water needed for this tank.

The volume of cuboid is given by :

$V=lbh$

As it is filled to 80% capacity, so,

$V=\dfrac{80}{100}\times lbh\\\\=0.8\times 61\times 30.5\times 30.5\\\\V=45396.2\ cm^3$

So, $45396.2\ cm^3$ of water is needed for this tank.

5 0

2 years ago

Which ordered pair represents the y-intercept of the graph of the equation y = -3x - 9?

Mnenie [13.5K]

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Equation
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y = -3x - 9

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Option 1
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If I substitute x = -9, I should get y = 0

When x = -9
y = -3 (-9) - 9
= 18 (I did not get 0, wrong)

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Option 2
------------------------------------------------------------------------------------------
If I substitute x = -3, I should get y = 0
y = -3(-3) - 9
y = 9 - 9
y = 0 (Yes, I got 0, correct)

------------------------------------------------------------------------------------------
Option 3
------------------------------------------------------------------------------------------
If I substitute x = 0, I should get y = -3
y = -3 (0) - 9
y = 0 - 9
y = -9 (I did not get -3, wrong)

------------------------------------------------------------------------------------------
Option 4
------------------------------------------------------------------------------------------
If I substitute x = 0, I should get y = -9
y = -3 (0) - 9
y = 0 - 9
y = -9 (Yes, I got -9, correct)

------------------------------------------------------------------------------------------
Answer: (-3, 0) and (0, 9) are ordered pairs of the equation (Answer B, D)
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7 0

3 years ago

"Trigonometric Models" (50 POINTS) Is my graph right?

ch4aika [34]

Answer:

Yes, this graph is absolutely right for the function y = $2\sin(2x)-3$ .

Step-by-step explanation:

firstly we will calculate amplitude, period, phase shift, and vertical shift.

Use the standard form $a\sin(bx-c)+d$ to calculate the values of amplitude, period, phase shift, vertical shift.

here a = 2

b = 2

c = 0

d = -3

Amplitude = |a| = 2

period = $\frac{2\pi}{|b|}$

= $\frac{2\pi}{2}$ = $\pi$

phase shift = $\frac{c}{b}$ = 0

and vertical shift = d = -3

so, by using this information, if we plot the graph then the graph obtained will be same as the given graph.

6 0

3 years ago

Image is down below :)

zhuklara [117]

-3, 1 is the answer because the spot is on the -3 and in the first low with the Y-axis and stuff .

4 0

3 years ago

Read 2 more answers

What is the surface area of a rectangular prism? length : 3 width : 3 height = 5

elixir [45]

Since it is a rectangular prism, the front and back are the same. the sides are the same and the top and bottom are the same. You would find the area of the front and back first. Since they both have the same measurements, you can find the area of one of the faces and multiply by 2.
A=BH
A= 3x5
A=15
15x2=30
So the front and back's area is 30. Now you find the area of both sides. They are both rectangle so the formula is A=BH.
A=BH
A=3x5
A=15
15x2=30
Now you find the area of the top and bottom. It is also a rectangle so you will use the same formula.
A=BH
A=3x3
A=9
9x2=18
Finally, you add all these measurements together adn that is the surface area.
This surface area of this rectangle prism is 78.

4 0

3 years ago