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3 years ago

Determine if the point (5, 7) is on the line of Equation 5x + 6y = 67

Mathematics

1 answer:

alexgriva [62]3 years ago

6 0

Answer: The point (5,7) is on the line 5x+6y = 67

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Explanation:

(5,7) means x = 5 and y = 7 pair up

Plug in those values to get...

5x + 6y = 67

5*5 + 6*7 = 67

25 + 42 = 67

67 = 67

We get the same number on both sides after fully simplifying. This means the equation is true. A true equation in the last step means the first equation is true when (x,y) = (5,7).

Therefore, the point (5,7) is a solution and it is on the line 5x+6y = 67.

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Which is the graph of f (x) = 4 (1/2) Superscript x?

miss Akunina [59]

Answer:

Option (2) is correct graph.

Step-by-step explanation:

Given:

The function to graph is given as:

$f(x)=4(\frac{1}{2})^x$

Now, the above function is an exponential function of the form $f(x)=ka^x$

Where, 'k' and 'a' are constants.

The range of an exponential function is always greater than 0.

The domain is all real numbers.

Now, for graphing it, we need to find some points on it and its end behaviour.

Now, for x = 0, the function value is given as:

$f(0)=4(\frac{1}{2})^0=4$

So, (0, 4) is a point on the graph.

Now, for x = 1, the function value is given as:

$f(1)=4(\frac{1}{2})^1=4\times\frac{1}{2}=2$

So, (1, 2) is another point on the graph.

Now, for x = 2, the function value is given as:

$f(2)=4(\frac{1}{2})^2=4\times\frac{1}{4}=1$

So, (2, 1) is another point on the graph.

Now, as 'x' tends to ∞, the function value tends to:

$f(x\to\infty)=4\cdot\frac{1}{2}^{\infty}=\frac{4}{\infty}=0$

So, as

$x\to\infty,f(x)\to0\\\\x\to-\infty,f(x)\to\infty$

Now, from among all the options, only option (2) fulfills all the conditions given above.

So, option (2) is correct graph.

5 0

4 years ago

A middle school took all of its 6th grade students on a field trip to see a symphony. The students filled 300 seats, which was 1

prisoha [69]

Answer:

3,000

Step-by-step explanation:

Basically, there are 300 seats filled which is 10%

100% is 10x10

300=10%

multiply both sides by 10

300x10=3000 and 10x10=100

therefore, the total number of seats is 3000 since 100% represents the whole thing.

Hope this was helpful!

5 0

3 years ago

How to expand and evaluate

Nana76 [90]

(-1.1)*(-1.1)*(-1.1)=-1.331

8 0

4 years ago

Change 0.307 to a percent

Nookie1986 [14]

It would be 30.7% because when you change a decimal to a percent, the decimal point moves 2 places to the right. For a percent to a decimal, move the decimal point 2 places to the left

4 0

3 years ago

Suppose a-b=0 which one of these expressions equals ab

I am Lyosha [343]

Answer:

E) b^2

Step-by-step explanation:

Solving the first equation for a, we get ...

a - b = 0

a = b . . . . . . add b to both sides

Now, the expression ab can be rewritten as

ab = bb = b^2 . . . . . . substitute b for a

6 0

3 years ago