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2 years ago

2,307,419 = two million, three hundred seven thousand, four hundred nineteen

Mathematics

1 answer:

Alona [7]2 years ago

7 0

Hello!

The numbers should be written as :

1,750,064

one million, seven hundred fifty thousand, sixty-four

218,502

two hundred eighteen thousand, five hundred two

384,057

three hundred eighty-four thousand, fifty-seven

4,012,923

four million, twelve thousand, nine hundred twenty-three

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What is the range of the equation

a_sh-v [17]

The range of the equation is $y>2$

Explanation:

The given equation is $y=2(4)^{x+3}+2$

We need to determine the range of the equation.

Range:

The range of the function is the set of all dependent y - values for which the function is well defined.

Let us simplify the equation.

Thus, we have;

$y=2 \cdot 4^{x+3}+2$

This can be written as $y=2^{1+2(x+3)}+2$

Now, we shall determine the range.

Let us interchange the variables x and y.

Thus, we have;

$x=2^{1+2(y+3)}+2$

Solving for y, we get;

$x-2=2^{1+2(y+3)}$

Applying the log rule, if f(x) = g(x) then $\ln (f(x))=\ln (g(x))$ , then, we get;

$\ln \left(2^{1+2(y+3)}\right)=\ln (x-2)$

Simplifying, we get;

$(1+2(y+3)) \ln (2)=\ln (x-2)$

Dividing both sides by $\ln (2)$ , we have;

$2 y+7=\frac{\ln (x-2)}{\ln (2)}$

Subtracting 7 from both sides of the equation, we have;

$2 y=\frac{\ln (x-2)}{\ln (2)}-7$

Dividing both sides by 2, we get;

$y=\frac{\ln (x-2)-7 \ln (2)}{2 \ln (2)}$

Let us find the positive values for logs.

Thus, we have,;

$x-2>0$

$x>2$

The function domain is $x>2$

By combining the intervals, the range becomes $y>2$

Hence, the range of the equation is $y>2$

7 0

3 years ago

What is the greatest common factor of <img src="https://tex.z-dn.net/?f=24%20%7Ba%7D%5E%7B3%7D%20c" id="TexFormula1" title="

Agata [3.3K]

If you're not sure, begin by looking for any divisor that will divide into 24a^3c and 3a without leaving a remainder. Note that 3 is such a number, and a is another.

Factoring out 3a from 24a^3*c and 3a, we get 3a{8a^2*c, 1}

So the GCF is 3a.

8 0

3 years ago

How do you graph a direct variation

Artyom0805 [142]

I confirm with the answer that k is the slope of the graph. If the variables x and y vary directly when x = 3 and y = 15, then: a. Write an equation that relates x and y.

3 0

3 years ago

Read 2 more answers

Find the volume of this composite figure and explain how you got your answer

Damm [24]

To solve this, we work out the volume of the two shapes (the cuboid and the pyramid) and then add them together.

We get the volume of the cuboid by multiplying the base by the width by the length:

Volume of cuboid = 6 x 6 x 4
= 144m³

Now to get the volume of the pyramid, we multiply the base by the length by the height, and then we divide by three.

Volume of pyramid = 6 x 6 x 8 ÷ 3
= 96m³
-------------------------------------------------------------------------------------------------------------
Answer:
Now that we know the two volumes, we simply add them together:

144 + 96 = 240m³

So the volume of the composite sold is 240m³

7 0

3 years ago

Please help!!!!!! y=[?]°

coldgirl [10]

Answer:

Since there are already 2 angles shown, which are 48 and 90 (indicated by the square in the bigger triangle, we can set up an equation.

48 + 90 + y = 180

138 + y = 180

-138 + 138 + y = 180 - 138

y = 42°

7 0

3 years ago