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2 years ago

Evaluate the expression 2ab3 + 6a3 - 4ab2 when a = 2 and b = 4.

Mathematics

2 answers:

evablogger [386]2 years ago

7 0

2(2)(4)3+6(2)3-4(2)(4)2
48 + 36 - 64
74 - 64
= 10

nalin [4]2 years ago

3 0

2(2x4)3 + 6(2)3 - 4(2x4)2
(4x8)3 + (12)3 - (8x16)2
(32)3 + (12)3 - (128)2
96 + 36 - 256
-124

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Simplify by prime factorization 15/27

Mamont248 [21]

$⟹ \: \cancel \frac{15}{27} = (3 \times 3 \times 3 \times 3 \times 3 ) \: (9 \times 9 \times 9)$

$⟹ \cancel \frac{15}{27} = 5(3) \times 9(3)$

$⟹ \cancel \frac{15}{27} = \frac{5}{9}$

<em><u>Therefore, when 15/27 is factorise using the method of prime factorization we'll get 5/9.</u></em>

7 0

3 years ago

If a, b, and c are solutions to the

Alik [6]

Answer:

$\displaystyle 10c - 6a = 110$

Step-by-step explanation:

We are given the equation:

$\displaystyle 3x^3 - 25x^2 -50x = 0$

Where <em>a</em>, <em>b</em>, and <em>c</em> are solutions to the equation and where <em>a</em> < <em>b</em> < <em>c</em>, we want to determine the value of 10<em>c</em> - 6<em>a</em>.

To find the solutions of the equation, we can factor:

$\displaystyle \begin{aligned} 3x^3 - 25x^2 -50x & = 0 \\ \\ x(3x^2 - 25x -50) & = 0 \\ \\ x(3x+5)(x-10) & = 0 \end{aligned}$

From the Zero Product Property:

$\displaystyle x = 0 \text{ or } 3x + 5 = 0 \text{ or } x - 10 = 0$

Solve for each case:

$\displaystyle x = 0 \text{ or } x = -\frac{5}{3} \text{ or } x = 10$

We can see that -5/3 < 0 < 10. Thus, <em>a</em> = -5/3, <em>b</em> = 0, and <em>c</em> = 10.

Therefore:

$\displaystyle \begin{aligned} 10c - 6a & = 10(10) - 6\left(-\frac{5}{3}\right) \\ \\ &= 100 + 10 \\ \\ & = 110 \end{aligned}$

3 0

2 years ago

Which linear inequality is represented by the graph?

svp [43]

See the explanation

<h2>Explanation:</h2>

Since you don't provide any graph I can't give you an exact answer. However, I'll give you the fourth graph for this problem. So we have:

<h3>First:</h3>

We have the inequality:

$y < 3x + 2$

The symbol < tells us that the line is dotted and the shaded region is below the line. Also, the slope is 3 and the y-intercept is 2. So as x increases one unit y increases 3, so if (0, 2) which is both a point and the y-intercept of the line, then (1, 5) will also be a point on the line. By using graphing tool we get the first graph below.

<h3>Second:</h3>

We have the inequality:

$y > 3x + 2$

This case is similar to the previous one. The only difference is that the shaded region is above the line. The graph is the second one below.

<h3>Third:</h3>

We have the inequality:

$y < \frac{1}{3}x + 2$

Again the line is shaded under the graph. Also, the slope is 1/3 and the y-intercept is 2. So as x increases one unit y increases 1/3, or in other words, as x increase 3 units y increases one unit, so if (0, 2) which is both a point and the y-intercept of the line, then (3, 3) will also be a point on the line. By using graphing tool we get the third graph below.

<h3>Fourth:</h3>

We have the inequality:

$y > \frac{1}{3}x + 2$

This case is similar to the previous one. The only difference is that the shaded region is above the line. The graph is the fourth one below.

<h2>Learn more:</h2>

Inequalities: brainly.com/question/12890742

#LearnWithBrainly

6 0

3 years ago

The sum of 8 and 5 minus 2

Masteriza [31]

(8+5)- 2
First, add 8+5 (=13)
Then, subtract 2 (=11)
So the answer is 11

7 0

2 years ago

In the diagram, ray GH bisects <FGI.

Ymorist [56]

Part a.

An angle bisector divides the angle into two congruent angles.

m<FGH = m<HGI

2x - 4 = 3x - 22

Subtract 2x from both sides. Add 22 to both sides.

18 = x

x = 18

Now that we know x = 18,

m<FGH = 2x - 4 = 2(18) - 4 = 36 - 4 = 32

m<FGH = 32

Part b.

m<HGI = 3x - 22 = 3(18) - 22 = 54 - 22 = 32

m<HGI = 32

Part c.

m<FGI = m<FGH + m<HGI = 32 + 32 = 64

m<FGI = 64

6 0

2 years ago

Read 2 more answers