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saw5 [17]
3 years ago
6

Sienna is solving the quadratic equation by completing the square.

Mathematics
2 answers:
VladimirAG [237]3 years ago
6 0

Answer:  The correct option is (C) 3.

Step-by-step explanation: Given that Sienna is solving the quadratic equation by completing the square as follows:

3x2+9x-4=0\\\\\Rightarrow 3x^2+9x=4\\\\\Rightarrow a(x^2+3x)=4.

We are given to find the find the value of a.

We can see that in the second step of Sienna's solution, 3 is common in both the terms, 3x2 and 9x.

So, she took 3 out and then in the third step, the expression within the bracket remais x^2+3x.

Therefore, the complete steps are as follows:

3x2+9x-4=0\\\\\Rightarrow 3x^2+9x=4\\\\\Rightarrow 3(x^2+3x)=4.

Hence, the value of a is 3.

Thus, (C) is the correct option.

kari74 [83]3 years ago
4 0
3x^2 + 9x - 4
3x^2 + 9x = 4
3(x^2 + 3x) = 4

Therefore, a = 3
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Usually, when you see a number followed by another number in parentheses, like here, that means to multiply.
3 0
3 years ago
Read 2 more answers
Jason is painting a large circle on one wall of his new apartment. The largest distance across the circle will be 8 feet. Approx
Hunter-Best [27]

Answer:

a) 50.24 ft²

b) 150.72 ft²

Step-by-step explanation:

Jason is painting a large circle on one wall of his new apartment. The largest distance across the circle will be 8 feet.

The distance across a circle is also called a diameter, Hence,

D = Diameter = 8 ft

The Area of a circle = πr²

r = Diameter/2 = 8ft/2 = 4ft

π = 3.14

Hence,

The Area of the circle = π × (4 ft)²

= 50.24 ft²

a) Approximately the amount of wall the circle will cover is 50.24 ft².

b) How much area will he cover if he painted a circle on three walls?

This is calculated as:

1 wall = 50.24 ft²

3 walls = x

Cross Multiply

x = 3 × 50.24 ft²

x = 150.72 ft²

7 0
3 years ago
If y=4x+5 how much does the tree grow each year?
Elena L [17]

Answer:

4 ( not sure what the units are)

Step-by-step explanation:

Just by looking at the slope you can figure out how much it grows per year.

y = mx + b

m = slope

Not sure what units there are in the question just place it in the end.

Hope this helps :)

6 0
3 years ago
Read 2 more answers
A solar collector is 2,0 m long by 1,5 m wide. It is held in place
icang [17]

Answer:

The width of the frame is 0.0746 meters

Step-by-step explanation:

We are told that after the frame has been attached to the solar collector, the area that is left exposed is 2.5m^2  . As we see in the figure, the dimensions of this area are

(w-2x) and  (l-2x)

where x is the width of the frame.

The product of these dimensions must equal the exposed area:

(w-2x)(l-2x)=2.5m^2

Now since w=1.5m and l=2m we have:

(1.5-2x)(2-2x)=2.5

we expand this and solve for x using the quadratic formula:

4x^2-7x+3=2.5

4x^2-7x+0.5=0

we get two solutions:

x=1.6753

x=0.0746

We take the second solution i.e x=0.0746, because first one gives a width larger than the dimensions of the solar collector which cannot be possible.

Thus the width of the frame is 0.0746 meters.

7 0
3 years ago
Peter is making new cushion covers for a chair. There are three sizes of
Lesechka [4]

Answer:

A 846 square inches

Step-by-step explanation:

Use the net:

Rectangle 1: (21 in + 3 in + 21 in + 3 in) by 15 in.

Rectangle 2: 21 in by 3 in

Rectangle 3: 21 in by 3 in

total area = sum of areas of 3 rectangles above.

total area = (48 in * 15 in) + 2(21 in * 3 in)

total area = 720 in^2 + 126 in^2

total area = 801 in^2

Answer: A 846 square inches

6 0
3 years ago
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