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3 years ago

Which equation is equivalent to 2^4x= 8^x-3

Mathematics

1 answer:

rosijanka [135]3 years ago

7 0

Answer:

2^4x=8^x-3?

2x^4=2^(2x-3)

2x^4=2^(2x-6)2x^4=2^(3x-3)

2x^4=2^(3x-9).

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Write a function to represent the set of ordered pairs.

77julia77 [94]

Answer:

Option C $f (x) = x^ 2 - 2$

Step-by-step explanation:

Note that the relation describing the set of ordered pairs does not change at a costing rate

$y_2 -y_1 = 7-2 = 5\\\\y_3 -y_2 = 14- 7 = 7\\\\y_4 - y_3 = 23- 14 = 9$

Therefore the relationship is not linear.

However, the exchange rate $y_n- y_{n-1}$ increases by a factor of 2 units when n increases 1 unit. This allows us to conclude that the relationship is quadratic

Note that the following ordered pairs belong to the function

$y = x ^ 2$

A = {(2, 4), (3, 9), (4, 16), (5, 25)}

The set of ordered pairs that we have is:

B = {(2, 2), (3, 7), (4, 16), (5, 23)}

Note that there is a similarity between both sets of ordered pairs.

In set B the values of y are always 2 units less than the values in y of the set A.

Then we deduce that since the function that models the set A is $y = x ^ 2$ then the function that contains the ordered pairs of the B set is:

$y = x ^ 2 -2$

The correct option is option C) $f (x) = x^ 2 - 2$

8 0

3 years ago

Solve the one-variable equation using the distributive property and properties of equality.

Tanzania [10]

Answer:

a=6

Step-by-step explanation:

-6(2+(6)=-48

-6(2+6)=-48

(-6X2)+(-6+6)=-48

(-12)+(-36)=-48

-48=-48

They are equal. Tell me if I made a mistake. Thanks!

6 0

3 years ago

Read 2 more answers

Help me please 12 and f

zimovet [89]

Answer:

It is not equivalent.

Step-by-step explanation:

You have to expand the brackets :

(x-4)(x+3)

= x(x) + x(3) - 4(x) - 4(3)

= x² + 3x - 4x - 12

= x² - x - 12

Therefore, x² - x - 12 / (x-4)(x+3) is not equivalent to x² - 4x - 12.

6 0

3 years ago

Find the surface area and round to the nearest hundredths place when necessary.

pashok25 [27]

Answer:

First lets find the area of the bottom circle:

7.2 is your radius so:

7.2^2 = 51.84 the reason why you square your radius is because thats apart of the formula when finding the are of a circle.

lets continue:

51.84 x 3.14(pi) = 162.7776

Now we need to find the area of the round surface but first we need to find the circumference of one circle and multiply it by the height.

2 x 3.14 x 7.2 = 45.216

Now lets multiply it by the height:

45.216 x 17 = 768.672

Now lets add both areas:

768.672 + 162.7776 = 931.4496 dont forget to round to the nearest hundredths place! 931.4496 rounded up = 931.45 square meters is your answer.

6 0

3 years ago

A ladder that is 13 meters long is leaning against a wall. The distance between the foot of the ladder and the wall is 7 meters

Maksim231197 [3]

<h2>Answer:</h2>

The equation that is used to model the length of ladder in terms of x is:

$x^2-7x-60=0$

<h2>Step-by-step explanation:</h2>

We can model this problem with the help of a right angled triangle whose hypotenuse is 13 meters and the other two legs are x meters and (x-7) meters.

where x is the distance between the top of the ladder and the ground.

and (x-7) is the distance between the foot of the ladder and the wall.

Hence, using Pythagorean Theorem we have:

$13^2=x^2+(x-7)^2\\\\i.e.\\\\169=x^2+x^2+49-14x\\\\i.e.\\\\169=2x^2-14x+49\\\\i.e.\\\\2x^2-14x+49-169=0\\\\i.e.\\\\2x^2-14x-120=0\\\\i.e.\\\\x^2-7x-60=0$

Hence, the answer is:

$x^2-7x-60=0$

7 0

3 years ago

Read 2 more answers