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3 years ago

The ratio of the areas of two similar rectangles is 1:4. What is the ratio of the corresponding sides?

1 answer:

4 0

The ratio of linear dimensions (side lengths) is the square root of the ratio of areas.
√1 : √4 = 1 : 2

The best choice is ...
B. 1:2

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HELP!!! 15 points. picture below

vlada-n [284]

Step-by-step explanation:

$\sin( \alpha ) = \frac{ \sqrt{5} }{3} \\ \alpha = 48.19 \: degrees \\ \cos( \alpha ) = \frac{2}{3}$

7 0

3 years ago

Read 2 more answers

The function f(x) = 2x + 510 represents the number of calories burned when exercising, where x is the number of hours spent exer

riadik2000 [5.3K]

Answer: 789 calories burned while combining diet with 2 hours of exercise

Step-by-step explanation:

we have that

$f(x)=2x+510$

$g(x)=200x-125$

we know that

$(f+g)(x)=f(x)+g(x)$

substitute

$(f+g)(x)=2x+510+200x-125$

$(f+g)(x)=202x+385$

Find $(f+g)(2)$

For x=2 hours

substitute

$(f+g)(2)=202(2)+385$

$(f+g)(2)=789\ calories$

therefore

The answer is

789 calories burned while combining diet with 2 hours of exercise

8 0

3 years ago

What is the true solution to the equation below? In e^in x + in e^in x^2 = 2 in 8

mariarad [96]

To solve the given equation, w need to review some rules:
$(1) \ ln \ e = 1 \\ 
(2) \ ln \ b^{a} = a*ln \ b \\
(3) \ ln \ a + ln \ b = ln \ (ab) \\
(4) \ ln \ a - ln \ b = ln \ \frac{a}{b} \\$

The given equation is :
$ln \ e^{ln \ x} + ln \ e^{ln \ x^{2}} = 2 \ ln \ 8$
$ln \ x * ln \ e + ln \ x^{2} * ln \ e = 2 \ ln \ 8$ ⇒⇒⇒⇒ rule (2)
$ln \ x + ln \ x^{2} = ln \ 8^{2}$ ⇒⇒⇒⇒ rule (1) and rule (2)

$ln \ ( x* x^{2} ) = ln \ 64$ ⇒⇒⇒⇒ rule (3)
removing the nature logarithm from both sides

$x^{3} = 64 = 4^{3}$
∴ x = 4

So, the correct answer is option (2) ⇒⇒⇒⇒ x = 4

5 0

3 years ago

Read 2 more answers

Find the sum of a finite arithmetic sequence from n = 1 to n = 10, using the expression 3n − 8.

maw [93]

Answer:

The answer is 85

Step-by-step explanation:

The equation used to find the sum of an arithmetic series is: (n/2) * (a1 + an).

n in this case is 10 (the number of numbers in the series)

an is 22 (plug in 10 to the expression 3n-8)

and a1 is -5 (plug in 1 to the expression 3n-8)

so when you plug everything in to the final equation, you get

(10/2) * (-5 + 22)

5 * 17

8 0

3 years ago

Please help me solve this, and show your work

zlopas [31]

$6r+5=11r\ \ \ \ |\text{subtract 6r from both sides}\\\\5=5r\ \ \ \ |\text{divide both sides by 5}\\\\\boxed{r=1}\\-------------------------\\\dfrac{2x-4}{2}=6x+3\\\\\dfrac{2x}{2}-\dfrac{4}{2}=6x+3\\\\x-2=6x+3\ \ \ \ \ |\text{add 2 to both sides}\\\\x=6x+5\ \ \ \ |\text{subtract 6x from both sides}\\\\-5x=5\ \ \ \ \ |\text{divide both sides by -5}\\\\\boxed{x=-1}$

6 0

3 years ago