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2 years ago

If a(12)= x/3+2 and b(x)=12x, what is a(12)+b(1)?

Mathematics

1 answer:

bonufazy [111]2 years ago

5 0

Answer:

$a(12) = 12 \div 3 + 2 \\ + b(1) = 12 \times 1 \\ = 4 + 2 + 12 = 18$

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In the triangle above, Eight-fifteenths represents which ratio?

Alecsey [184]

The answer is AC/AB or tanB.

tangent is opposite over adjacent, and the opposite of angle B is 8 and the adjacent is 15, which gives you 8/15.

6 0

2 years ago

What is the simplified form of (x+9)/8 minus (x+3)/(x+2)?

Murrr4er [49]

Here is the work to help you understand the problem.
$\frac{x+9}{8}-\frac{x+3}{x+2}$

$\mathrm{Find\:the\:least\:common\:denominator\:} \ \textgreater \ 8\left(x+2\right)$

$\mathrm{Adjust\:Fractions\:based\:on\:the\:LCD} \ \textgreater \ \frac{\left(x+9\right)\left(x+2\right)}{8\left(x+2\right)}-\frac{\left(x+3\right)\cdot \:8}{8\left(x+2\right)}$

$\mathrm{Since\:the\:denominators\:are\:equal,\:combine\:the\:fractions}: \frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}$

$\frac{\left(x+9\right)\left(x+2\right)-8\left(x+3\right)}{8\left(x+2\right)}$

$Expand \left(x+9\right)\left(x+2\right)-8\left(x+3\right)$

$\left(x+9\right)\left(x+2\right)$
$\mathrm{Distribute\:parentheses\:using}: \left(a+b\right)\left(c+d\right)=ac+ad+bc+bd$
$Where\; a=x,\:b=9,\:c=x,\:d=2$

$x\cdot \:x+x\cdot \:2+9\cdot \:x+9\cdot \:2 \ \textgreater \ \mathrm{Add\:similar\:elements:}\:2x+9x=11x$

$xx+11x+2\cdot \:9 \ \textgreater \ \mathrm{Apply\:exponent\:rule}: \:a^b\cdot \:a^c=a^{b+c}$

$xx=\:x^{1+1}=\:x^2 \ \textgreater \ x^2+11x+2\cdot \:9 \ \textgreater \ \mathrm{Multiply\:the\:numbers:}\:9\cdot \:2=18$

$x^2+11x+18 \ \textgreater \ x^2+11x+18-8\left(x+3\right)$

$-8\left(x+3\right) \ \textgreater \ \mathrm{Distribute\:parentheses\:using}: \:a\left(b+c\right)=ab+ac$
$Where\;a=-8,\:b=x,\:c=3$

$-8\cdot \:x-8\cdot \:3 \ \textgreater \ \mathrm{Multiply\:the\:numbers:}\:8\cdot \:3=24 \ \textgreater \ -8x-24$

$x^2+11x+18-8x-24 \ \textgreater \ \mathrm{Group\:like\:terms} \ \textgreater \ x^2+11x-8x+18-24$

$\mathrm{Add\:similar\:elements:}\:11x-8x=3x \ \textgreater \ x^2+3x+18-24$

$\mathrm{Add/Subtract\:the\:numbers:}\:18-24=-6 \ \textgreater \ x^2+3x-6$

$\frac{x^2+3x-6}{8\left(x+2\right)}$

Hope this helps!

6 0

3 years ago

Read 2 more answers

Draw a rectangle that has a perimeter of 20 units and an area of 25 square units

marissa [1.9K]

<h2>Explanation:</h2><h2></h2>

For any rectangle the dimensions are given by:

$w:width \\ \\ l:Length$

So the perimeter (P) is given by the following equation:

$P=2(w+l)$

And the area is:

$A=w\times l$

We know that:

$P=20units \\ \\ A=25units^2$

By substituting:

$20=2(w+l) \\ \\ \therefore w+l=10 \ \ldots eq1 \\ \\ \\ 25=w\times l \ldots eq2$

Solving for $w$ from eq1:

$w=10-l$

Substituting into eq2:

$25=(10-l)\times l$

Then:

$\text{Solving for l:} \\ \\ \\ 10l-l^2=25 \\ \\ 10l-l^2-25=25-25 \\ \\ -l^2+10l-25=0 \\ \\ x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a} \\ \\ \\ a=-1,\:b=10,\:c=-25 \\ \\ \\ l_{1,\:2}=\frac{-10\pm \sqrt{10^2-4\left(-1\right)\left(-25\right)}}{2\left(-1\right)} \\ \\ l_{1,\:2}=\frac{-10\pm \sqrt{0}}{2\left(-1\right)} \\ \\ l=5$

Solving for w:

$w=10-5=5$

So this rectangle is a square and is shown below.

8 0

3 years ago

What is the algebraic expression of 3 divided by q please answer grade 6 way

Marizza181 [45]

Answer: 3/q

Step-by-step explanation:

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3 years ago

Read 2 more answers

Is (-3.4) a rational number? And why is (-3.4) a rational number?

KIM [24]

Answer:

Yes

Step-by-step explanation:

a rational number is a number that can be written as a fraction. Rational numbers are all real numbers, and can be positive or negative. A number that is not rational is called irrational. Most of the numbers that people use in everyday life are rational. These include fractions and integers.

- 3.4 is a integer and also a rational number.

4 0

3 years ago