All categories

3 years ago

What is the simplified form of the expression? 2sqrt18 - 5sqrt32

Mathematics

1 answer:

Morgarella [4.7K]3 years ago

7 0

Answer

26√2

Step-by-step explanation:

The trick here lies in recognizing that both 18 and 32 have factors that are perfect squares: 18 = 2*9 and 32 = 2*16. Therefore, we can write

2sqrt18 as 2√2√9, or 6√2, and 5sqrt32 as 5√2√16, or 20√2.

Then the original expression, in simplest form, is 6√2 + 20√2, or 26√2

You might be interested in

The temperature fell from 0 Degrees Fahrenheit to 15 and one-half Degrees Fahrenheit below 0 in 5 and three-fourths hours. Wen t

Kryger [21]

Answer:

The correct answer will be:

$-\dfrac{62}{23}$

Step-by-step explanation:

It is given that :

Initial temperature, $T_1 = 0^\circ F$

Final temperature,

$T_2 = -15\dfrac{1}{2}^\circ F\\\Rightarrow T_2 = -\dfrac{15\times 2+1}{2} ^\circ F\\\Rightarrow T_2 = -\dfrac{31}{2} ^\circ F$

Time taken :

$5\dfrac{3}{4}\ hrs = \dfrac{5 \times 4+3}{4}\ hrs = \dfrac{23}{4}\ hrs$

Change in temperature per hour:

$\dfrac{\text{Difference of temperature}}{\text{Total Time Taken}}\\\Rightarrow \dfrac{T_2-T_1}{\text{Total Time Taken}}$

Putting the values of temperatures and time:

$\dfrac{\dfrac{-31}{2}-0}{\dfrac{23}{4}}\\\Rightarrow \dfrac{\dfrac{-31}{2}}{\dfrac{23}{4}}\\\Rightarrow \dfrac{-31 \times 4}{2 \times 23}} \text{---- Error done by Wen at this step}\\\Rightarrow \dfrac{-31 \times 2}{23}}\\\Rightarrow \dfrac{-62}{23}}$

The error done by Wen was during calculating the values of fraction.

So, the correct answer is : $\frac{-62}{23}}$ instead of $\frac{-713}{8}$

5 0

3 years ago

Read 2 more answers

(Photo attached) Trig question. I partially understand it, but not completely. Please explain! :) Thanks in advance.

aliya0001 [1]

Answer:

A = 2
B = 3

Step-by-step explanation:

You can start by recognizing 19/12π = π +7/12π, so the desired sine is ...

sin(19/12π) = -sin(7/12π) = -(sin(3/12π +4/12π)) = -sin(π/4 +π/3)

-sin(π/4 +π/3) = -sin(π/4)cos(π/3) -cos(π/4)sin(π/3)

Of course, you know that ...

sin(π/4) = cos(π/4) = (√2)/2

cos(π/3) = 1/2

sin(π/3) = (√3)/2

So, the desired value is ...

sin(19π/12) = -(√2)/2×1/2 -(√2)/2×(√3/2) = -(√2)/4×(1 +√3)

Comparing this form to the desired answer form, we see ...

A = 2

B = 3

5 0

3 years ago

(n + 12) x 5 + 7n Need equivalent expression

astraxan [27]

Answer:

12n + 60

General Formulas and Concepts:

Pre-Algebra

Distributive Property

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Algebra I

Terms/Coefficients

Step-by-step explanation:

Step 1: Define

(n + 12) × 5 + 7n

Step 2: Simplify

Distribute 5: 5(n) + 5(12) + 7n
Multiply: 5n + 60 + 7n
Combine like terms: 12n + 60

6 0

3 years ago

What is 90,090,010 in expanded form

tester [92]

Answer:

90,000,000 + 90,000 + 10

I hope this helped!

Step-by-step explanation:

3 0

3 years ago

If tanisha has $100 to invest at 8% annum compounded monthly, how long will it be before she has $150?

marissa [1.9K]

An exponential behavior can be observed.

Let x be the number of years she has to wait.

100((1+0.08/12)^12x) = 150

Now solve for x.

log base 1.08/12 of 1.5 = 61.02 approx

12x=61.02

x=5.09 years

4 0

3 years ago