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mr Goodwill [35]

3 years ago

14

A sign at the entrance to a bridge reads: Maximum allowable weight 2.25 tons Jason truck weighs 2150 pounds how much additional

weigh can he carry

1 answer:

Bezzdna [24]3 years ago

8 0

Hi there!

First, we must know that 1 ton=2000 pounds

2.25×2000=4500 pounds (maximum allowable weight)
4500-2150=2350

Therefore Jason can carry 2350 pounds more weight if he wanted to.

Hope this helps!

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PLEASE HELP! MULTIPLE CHICE!

Furkat [3]

1- is they have distinct values
2- variables referring to x or y

hope this helps you out.

6 0

4 years ago

Given that f(x) = √(ax + 1) , with x ≥ -1/a and a > 0

padilas [110]

Answer:

$\displaystyle 7$

Step-by-step explanation:

first thing I assume by f~¹ you meant $f^{-1}$ however

we want to find <u>a²</u><u>+</u><u>3</u><u>x</u><u>-</u><u>3</u><u> </u>for the given condition. with the composite function condition we can do so

<u>Finding</u><u> the</u><u> </u><u>inverse</u><u> of</u><u> </u><u>f(</u><u>x)</u><u>:</u>

$\displaystyle f(x) = \sqrt{ax + 1}$

substitute y for f(x):

$\displaystyle y= \sqrt{ax + 1}$

interchange:

$\displaystyle x= \sqrt{ay + 1}$

square both sides:

$\displaystyle ay + 1 = {x}^{2}$

cancel 1 from both sides:

$\displaystyle ay = {x}^{2} - 1$

divide both sides by a:

$\displaystyle y = \frac{{x}^{2} - 1 }{a}$

substitute f^-1 for y:

$\displaystyle f ^{ - 1} (x) = \frac{{x}^{2} - 1 }{a}$

<u>finding</u><u> the</u><u> </u><u>inverse</u><u> of</u><u> </u><u>g(</u><u>x)</u><u>:</u>

$\displaystyle g(x) = \frac{x + 1}{x}$

substitute y for g(x)

$\displaystyle y= \frac{x + 1}{x}$

interchange:

$\displaystyle \frac{y + 1}{y} =x$

cross multiplication

$\displaystyle y + 1= xy$

cancel 1 from both sides

$\displaystyle y - xy= - 1$

factor out y:

$\displaystyle y(1 - x)= - 1$

divide both sides by 1-x:

$\displaystyle y= - \frac{1}{ 1 - x}$

substitute g^-1 for y:

$\displaystyle g ^{ - 1} (x)= - \frac{1}{ 1 - x}$

remember that

$\displaystyle (f \circ g)x = f(g(x))$

therefore we obtain:

$\rm \displaystyle (f ^{ - 1} \circ g ^{ - 1} ) (3) = \frac{{ \bigg(- \dfrac{1}{1 - 3} } \bigg)^{2} - 1 }{a}$

since (f~¹•g~¹)(3)=-⅜ thus substitute:

$\rm \displaystyle \frac{{ \bigg(- \dfrac{1}{1 - 3} } \bigg)^{2} - 1 }{a} = - \frac{3}{8}$

simplify parentheses:

$\rm \displaystyle \frac{{ \bigg( \dfrac{1}{2} } \bigg)^{2} - 1 }{a} = - \frac{3}{8}$

simplify square:

$\rm \displaystyle \frac{{ \dfrac{1}{4} } - 1 }{a} = - \frac{3}{8}$

simplify substraction:

$\rm \displaystyle \frac{ - \dfrac{3}{4} }{ a}= - \frac{3}{8}$

simplify complex fraction:

$\rm \displaystyle - \dfrac{3}{4a} = - \frac{3}{8}$

get rid of - sign:

$\rm \displaystyle \dfrac{3}{4a} = \frac{3}{8}$

divide both sides by 3:

$\rm \displaystyle \dfrac{1}{4a} = \frac{1}{8}$

cross multiplication:

$\rm \displaystyle 4a= 8$

divide both sides by 4:

$\rm \displaystyle \boxed{ a= 2}$

as we want to find <u>a²</u><u>+</u><u>3</u><u>a</u><u>-</u><u>3</u><u> </u>substitute the got value of a:

$\displaystyle {2}^{2} + 3.2 - 3$

simplify square:

$\displaystyle 4 + 3.2 - 3$

simplify multiplication:

$\displaystyle 4 +6 - 3$

simplify addition:

$\displaystyle 10 - 3$

simplify substraction:

$\displaystyle 7$

and we are done!

7 0

3 years ago

Dave ran 3.52 miles in the same time

Lisa [10]

Subtract 3.52 - 2.44= 1.08 miles

8 0

3 years ago

Can you write 0.02 as tenths? Explain

Murljashka [212]

No, because 0.02 is in hundred thousandth, not ten thousand

6 0

4 years ago

What is it im cunfusd

lozanna [386]

Answer:

B

Step-by-step explanation:

the signs under the questions are greater than, less than, and equal to signs. And 1/5 is greater than -4/5

8 0

3 years ago