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3 years ago

7

What is the factored form of 4x^2 + 23x – 72?

1 answer:

fomenos3 years ago

7 0

The correct answer is the last one. (4x-9) (x+8).

You might be interested in

What is the factorization of 729^15+1000?

igomit [66]

Answer:

The factorization of $729x^{15} +1000$ is $(9x^{5} +10)(81x^{10} -90x^{5} +100)$

Step-by-step explanation:

This is a case of factorization by <em>sum and difference of cubes</em>, this type of factorization applies only in binomials of the form $(a^{3} +b^{3} )$ or $(a^{3} -b^{3})$ . It is easy to recognize because the coefficients of the terms are <u><em>perfect cube numbers</em></u> (which means numbers that have exact cubic root, such as 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000, etc.) and the exponents of the letters a and b are multiples of three (such as 3, 6, 9, 12, 15, 18, etc.).

Let's solve the factorization of $729x^{15} +1000$ by using the <em>sum and difference of cubes </em>factorization.

1.) We calculate the cubic root of each term in the equation $729x^{15} +1000$ , and the exponent of the letter x is divided by 3.

$\sqrt[3]{729x^{15}} =9x^{5}$

$1000=10^{3}$ then $\sqrt[3]{10^{3}} =10$

So, we got that

$729x^{15} +1000=(9x^{5})^{3} + (10)^{3}$ which has the form of $(a^{3} +b^{3} )$ which means is a <em>sum of cubes.</em>

<em>Sum of cubes</em>

$(a^{3} +b^{3} )=(a+b)(a^{2} -ab+b^{2})$

with $a= 9x^{5}$ y $b=10$

2.) Solving the sum of cubes.

$(9x^{5})^{3} + (10)^{3}=(9x^{5} +10)((9x^{5})^{2}-(9x^{5})(10)+10^{2} )$

$(9x^{5})^{3} + (10)^{3}=(9x^{5} +10)(81x^{10}-90x^{5}+100)$

.

8 0

3 years ago

When a constant force is applied to an object, the acceleration of the object varies inversely with its mass. When a certain con

marusya05 [52]

Answer: The mass of the object is 10 kg

Step-by-step explanation:

According to Newton's second law of motion, the force $F$ applied to an object with mass $m$ is directly proportional to its acceleration $a$ :

$F=ma$ (1)

If we isolate $a$ :

$a=\frac{F}{m}$ (2) This means the acceleration of the object varies inversely with its mass

Now, we are given the following data to calculate a constant force using (1):

$m_{1}=4 kg$

$a_{1}=5 m/s^{2}$

$F=m_{1}a_{1}$ (3)

$F=(4 kg)(5 m/s^{2)$ (4)

$F=20 N$ (5)

If we apply this same force calulated in (4) in another object with an acceleration of $a_{2}=2 m/s^{2}$ , its mass $m_{2}$ will be:

$F=m_{2}a_{2}$ (6)

$20 N=m_{2}2 m/s^{2}$ (7)

Finding $m_{2}$ :

$m_{2}=10 kg$ This is the mass of the object

4 0

3 years ago

Write an inequality and solve the problem the sum of a number and 19 is at least 8.2.

Sunny_sXe [5.5K]

When you write it as an inequality you get x + 19 ≈ 8.2 and when you solve it it should look like x + 19 ≈ 8.2
19 ≈ - <u>19
</u> x ≈ -10.8<u>
</u>

4 0

3 years ago

What is the factored form of 6x^2 + 13x + 6?

LekaFEV [45]

Answer:

(3x+2)(2x+3)

Step-by-step explanation:

6x2+13x+6

6x2+13x+6

=(3x+2)(2x+3)

7 0

3 years ago

Membership at the Universal Fitness Gym offers yearly memberships for $275. Yoga classes cost an additional $5 per class. Write

Dmitry [639]

total cost = membership +cost per class* number of classes

y = 275+5*x

Choice C

6 0

3 years ago