Form the union for the following sets. R = {10, 15, 20} S = {20, 25} R ∪ S =

Free brainleist What is the product of five square root five times six square root four ? Simplify your answer. (5 points)

SSSSS [86.1K]

Sixty square root five (simplified) There ya go hope it helps

6 0

3 years ago

Read 2 more answers

Show work please \sqrt(x+12)-\sqrt(2x+1)=1

Nesterboy [21]

Answer:

$x=4$

Step-by-step explanation:

Given $\displaystyle\\\sqrt{x+12}-\sqrt{2x+1}=1$ , start by squaring both sides to work towards isolating $x$ :

$\displaystyle\\\left(\sqrt{x+12}-\sqrt{2x+1}\right)^2=\left(1\right)^2$

Recall $(a-b)^2=a^2-2ab+b^2$ and $\sqrt{a}\cdot \sqrt{b}=\sqrt{a\cdot b}$ :

$\displaystyle\\\left(\sqrt{x+12}-\sqrt{2x+1}\right)^2=\left(1\right)^2\\\implies x+12-2\sqrt{(x+12)(2x+1)}+2x+1=1$

Isolate the radical:

$\displaystyle\\x+12-2\sqrt{(x+12)(2x+1)}+2x+1=1\\\implies -2\sqrt{(x+12)(2x+1)}=-3x-12\\\implies \sqrt{(x+12)(2x+1)}=\frac{-3x-12}{-2}$

Square both sides:

$\displaystyle\\(x+12)(2x+1)=\left(\frac{-3x-12}{-2}\right)^2$

Expand using FOIL and $(a+b)^2=a^2+2ab+b^2$ :

$\displaystyle\\2x^2+25x+12=\frac{9}{4}x^2+18x+36$

Move everything to one side to get a quadratic:

$\displaystyle-\frac{1}{4}x^2+7x-24=0$

Solving using the quadratic formula:

A quadratic in $ax^2+bx+c$ has real solutions $\displaystyle x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ . In $\displaystyle-\frac{1}{4}x^2+7x-24$ , assign values:

$\displaystyle \\a=-\frac{1}{4}\\b=7\\c=-24$

Solving yields:

$\displaystyle\\x=\frac{-7\pm \sqrt{7^2-4\left(-\frac{1}{4}\right)\left(-24\right)}}{2\left(-\frac{1}{4}\right)}\\\\x=\frac{-7\pm \sqrt{25}}{-\frac{1}{2}}\\\\\begin{cases}x=\frac{-7+5}{-0.5}=\frac{-2}{-0.5}=\boxed{4}\\x=\frac{-7-5}{-0.5}=\frac{-12}{-0.5}=24 \:(\text{Extraneous})\end{cases}$

Only $x=4$ works when plugged in the original equation. Therefore, $x=24$ is extraneous and the only solution is $\boxed{x=4}$

4 0

2 years ago

Kate has a coin collection. She keeps seven of the coins in a box, which is only 5% of her entire collection. What is the total

tia_tia [17]

Answer:

D. 140

Step-by-step explanation:

8 0

2 years ago

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The most efficient first step in the process to factor the trinomial 4x^3-20x^2+24x

USPshnik [31]

Factor out 4x <=====

7 0

2 years ago

Explain the role of the GCF in factoring a polynomial.

Ahat [919]

1. GCF is a factor that is shared by all terms within a polynomial for example, if we have a polynomial of the form A*B + A*C, the GCF is A since both terms have A as a factor 2. after we factor out the GCF, it is placed outside the parentheses, in front of the rest of the polynomial. using our previous example, A*B+A*C = A(B+C) 3. we can verify that our factoring is correct by distributing the GCF to the polynomial within the parentheses

5 0

3 years ago