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BartSMP [9]
3 years ago
13

How do I do this qn?

Mathematics
1 answer:
denis-greek [22]3 years ago
3 0
You can take the log of the left and right hand side, and then apply the <span>logarithm rules:

log(a</span>ˣ) = x·log(a)
log(ab) = log(a) + log(b)

log(9^(x-1) * 2^(2x+2)) = log(6^(3x))
log(9^(x-1)) + log(2^(2x+2)) = 3x log(6)
(x-1) log(9) + (2x+2) log(2) - 3x log(6) = 0
x(log9 + 2log2 - 3log6) = log9 - 2log2
x = (log9 - 2log2) / (log9 + 2log2 - 3log6)

simplifying by writing log9 = 2log3 and log6 = log2+log3

x= 2(log3 - log2) / (2log3 + 2log2 - 3log2 - 3log3) = 
x= -2(log3 - log2) / (log3 + log2) = -2 log(3/2) / log(6)

So 6^x = 4/9
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Every spring the grade four students play the grade five students in softball. The graph shows their scores.
bezimeni [28]

Answer:

B

Step-by-step explanation:

3 0
3 years ago
If w = 12 units, x = 7 units, and y = 8 units, what is the surface area of the figure? Figure is composed of a right square pyra
bearhunter [10]

Answer:

720 sq units.

Step-by-step explanation:

Length and width of square prism, w = 12 units

Height of square prism, x = 7 units

Height of square pyramid, y = 8 units

Please have a look at the attached image.

Here 2 Surfaces will not be exposed which are base of the square pyramid and the top of the square prism i.e. 2 square surfaces will not be exposed.

Here, surface area of the composite figure will be:

<em>Surface Area of Composite Figure = Lateral surface area of Square Pyramid + Surface Area of 5 surfaces of the square prism</em>

For finding the lateral surface area of pyramid, we need to find the slant height of the pyramid.

Let slant height be l units.

Using pythagoras theorem, we can find out the value of l.

As per theorem:

Hypotenuse^{2} = Base^{2} + Height^{2}\\

\Rightarrow l^{2} = (\dfrac{w}{2})^{2} + y^{2}\\\Rightarrow l^{2} = (\dfrac{12}{2})^{2} + 8^{2}\\\Rightarrow l^{2} = {6}^{2} + 8^{2}\\\Rightarrow l^{2} = 36+64 =  100\\\Rightarrow l = 10\ units

Lateral surface area of square prism = 4 \times Area of triangular surface

\Rightarrow 4 \times \dfrac{1}{2}\times Base \times Slant\ Height\\\Rightarrow 4 \times \dfrac{1}{2} \times 10 \times 12\\\Rightarrow 240\ sq\ units

Surface Area of 5 surfaces of the square prism =

4 \times x \times w + w^2\\\Rightarrow 4 \times 12 \times 7 + 12^2\\\Rightarrow 336 +144\\\Rightarrow 480\ sq\ units

So, total surface area of composite figure:

240 + 480 = 720 sq units.

7 0
3 years ago
A park has a large circle painted in the middle of the playground area.thecircle is divided into 4 equal sections And each secti
lilavasa [31]

Answer:

The area of each section of the circle is 25\pi\ m^{2}

Step-by-step explanation:

we know that

The area of a circle is equal to

A=\pi r^{2}

we have

r=10\ m

substitute

A=\pi (10^{2})=100\pi\ m^{2}

To find the area of each section divide the complete area of the circle by 4

so

100\pi\ m^{2}/4=25\pi\ m^{2}

8 0
3 years ago
What is the product of (-4)(7) and why?
Evgesh-ka [11]

Answer:

The product of (-4)(7) is -28

Step-by-step explanation:

First you will multiply the number together.

This gets you -28.

The reason it is a negative number is because when you multiply a positive and a negative number together, you get a negative number.

Whereas, if it were two negative numbers, (-4)(-7), or two positive numbers,

(4)(7), the answer would have been positive, 28.

3 0
3 years ago
How many weeks and days are there in 72 days?
earnstyle [38]
72 days and 10 weeks ( 10.2857 I just rounded)
3 0
3 years ago
Read 2 more answers
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