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irinina [24]
3 years ago
11

What is the factored form of the expression?

Mathematics
1 answer:
Georgia [21]3 years ago
7 0

Answer: The answer is (d) (4x+7)(7x+8).


Step-by-step explanation: Given equation to be factored is

28x^2+81x+56.

The given expression is quadratic, so we can factor it into two linear factors, by using the following factorisation rule.

x^2+(a+b)x+ab=(x+a)(x+b).

So, the given equation can be factorised using the above rule. The factorisation is as follows.

28x^2+81x+56\\\\=28x^2+49x+32x+56\\\\=7x(4x+7)+8(4x+7)\\\\=(4x+7)(7x+8).

Thus, the correct option is (d).





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5 0
3 years ago
You bake 42 chocolate cupcakes and 28 red velvet cupcakes.You package them in boxes that have the same ratio of chocolate to red
blondinia [14]

Answer: 16 red velvet cupcakes.

Step-by-step explanation:

To solve this problem you can apply the following proccedure:

- Let's call the number of red velvet cupcakes in a box that has 24 chocolate cupcakes: x

- Based on the information given in the problem, you can set up the following proportion and Solve for x<em>:</em>

\frac{42}{28}=\frac{24}{x}\\\\1.5x=24\\x=16

There are 16 red velvet cupcakes in a box that has 24 chocolate cupcakes.

5 0
3 years ago
The newly elected president needs to decide the remaining 7 spots available in the cabinet he/she is appointing. If there are 13
Alexxx [7]

Answer: 8648640 ways

Step-by-step explanation:

Number of positions = 7

Number of eligible candidates = 13

This can be done by solving the question using the combination Formula for selection in which we use the combination formula to choose 7 candidates amomg the possible 13.

The combination Formula is denoted as:

nCr = n! / (n-r)! * r!

Where n = total number of possible options.

r = number of options to be selected.

Hence, selecting 7 candidates from 13 becomes:

13C7 = 13! / (13-7)! * 7!

13C7 = 1716.

Considering the order they can come in, they can come in 7! Orders. We multiply this order by the earlier answer we calculated. This give: 1716 * 7! = 8648640

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