All categories

3 years ago

What expression is equivalent to the expression (4x+12) + 7x?

Mathematics

2 answers:

pochemuha3 years ago

8 0

Answer:

11x + 12

Step-by-step explanation:

( 4x + 12 ) + 7x

Remove parentheses.

= 4x + 12 + 7x

Group like terms.

= 4x + 7x + 12

Add similar elements: 4x + 7x = 11x

= 11x + 12

Kitty [74]3 years ago

7 0

Answer: 4(x+3) + 7x

Step-by-step explanation:

4(x+3) + 7x

You might be interested in

What is the triangle sum Theorem ?

vovangra [49]

Answer:

The sum of the interior angles of any triangle is equal to 180 degrees.

6 0

3 years ago

Prove that $5^{3^n} + 1$ is divisible by $3^{n + 1}$ for all nonnegative integers $n.$

Viktor [21]

When $n=0$ , we have

$5^{3^0} + 1 = 5^1 + 1 = 6$

$3^{0 + 1} = 3^1 = 3$

and of course 3 | 6. ("3 divides 6", in case the notation is unfamiliar.)

Suppose this is true for $n=k$ , that

$3^{k + 1} \mid 5^{3^k} + 1$

Now for $n=k+1$ , we have

$5^{3^{k+1}} + 1 = 5^{3^k \times 3} + 1 \\\\ ~~~~~~~~~~~~~ = \left(5^{3^k}\right)^3 + 1^3 \\\\ ~~~~~~~~~~~~~ = \left(5^{3^k} + 1\right) \left(\left(5^{3^k}\right)^2 - 5^{3^k} + 1\right)$

so we know the left side is at least divisible by $3^{k+1}$ by our assumption.

It remains to show that

$3 \mid \left(5^{3^k}\right)^2 - 5^{3^k} + 1$

which is easily done with Fermat's little theorem. It says

$a^p \equiv a \pmod p$

where $p$ is prime and $a$ is any integer. Then for any positive integer $x$ ,

$5^3 \equiv 5 \pmod 3 \implies (5^3)^x \equiv 5^x \pmod 3$

Furthermore,

$5^{3^k} \equiv 5^{3\times3^{k-1}} \equiv \left(5^{3^{k-1}}\right)^3 \equiv 5^{3^{k-1}} \pmod 3$

which goes all the way down to

$5^{3^k} \equiv 5 \pmod 3$

So, we find that

$\left(5^{3^k}\right)^2 - 5^{3^k} + 1 \equiv 5^2 - 5 + 1 \equiv 21 \equiv 0 \pmod3$

QED

5 0

2 years ago

The sales tax in your city is 4.4%, and an item costs $3

Aloiza [94]

Answer:

We would pay $.13 or 13 cents

Step-by-step explanation:

To find the tax on an item, multiply the amount by the tax rate

tax =3 * 4.4%

Change to a decimal form

= 3 *.044

=.132

We round to the nearest cent

=.13

We would pay $.13 or 13 cents

7 0

3 years ago

Collins Middle School has 240 sixth grade students. If the sixth grade is 30% of the total school, how many students are in the

Masteriza [31]

Answer:

800

Step-by-step explanation:

We can set up a proportion using the information we are given. We know that 240 students corresponds to 30% and that the total number of students, x, corresponds to 100%

$\frac{240}{x} = \frac{30}{100}$

Cross multiply and solve:

240 * 100 = 30x

24000 = 30x

800 = x

6 0

3 years ago

Is the relationship shown by the data linear? If so, model the data with an equation.

Svet_ta [14]

Yes it is linear, you go up my fours in the y side and go down by two on the x side. The equation is y=2x+19

4 0

3 years ago