Simplify radical. Intermediate Algebra

Answers

Answer 1

Answer: 180 ÷ 2 = 90; 90 ÷ 2 = 45 ; 45 ÷ 3 = 15 ; 15 ÷ 3 = 5 ; 5 ÷ 5 = 1 => 180 = (2^2) * (3^2) * 5 => $√(180) = 2*3 * √(5 )=6 √(5) ;$

In the same way we have $√(245)=7 √(5) ;$ and $√(320 )=8 √(5) ;$

Finally, $6 √(5)+7 √(5) - 8 √(5) = 13 √(5) - 8 √(5) =7 √(5).$

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The diagram below shows the graph of which inequality?
Dad is 4 times as old as his son Jim. In 10 years, Dad's age will be 20 years more than twice Jim's age. How old is Jim?If D = dad's age now and J = Jim's age now, which of the following systems could be used to solve the problem? a. D = 4J and D + 10 = 2J + 20 b. D = 4J and D + 10 = 2(4J + 10) + 20 c. D = 4J and D + 10 = 2(J + 10) + 20
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-(4x - 7) + 1 = 2 (5 - 2x) solve for x

Answers

Answer:

No solution

Step-by-step explanation:

-(4x - 7) + 1 = 2(5 - 2x)

-4x + 7 + 1 = 10 - 4x

-4x + 8 = 10 - 4x

-4x + 8 ≠ -4x + 10

No solution

A soccer coach is marking the lines for soccer field on a large recreation field. The dimensions of the field are to be 90 yards by 48 yards. Describe a procedure she could use to confirm that the sides of the field meet at the right angles.

Answers

Hello,

Diagonals of a rectangle must have the same measure.
You don't need to know the dimension of the diagonal but only if they are equals.

(√(90²+48²)=102 (yd))

Answer:

Step-by-step explanation:

The graph of a quadratic function is shown. What is the minimum value of the function?

A. 1
B. 2
C. 3
D. -3
E. -2

Answers

Answer: E

Step-by-step explanation:

-2

Two bicyclists leave the center of town at the same time. One heads due north and the other heads due west. Later, the two cyclists are exactly 25 mi apart. The cyclist headed north has traveled 5 mi farther than the cyclist going west.How far has the cyclist going west traveled?

Answers

Answer:

Distance traveled by bicyclist traveling west = 15 miles

Step-by-step explanation:

These two cyclists travel at angle 90°

Relative displacement can be calculated using Pythagoras theorem.

Let d be the distance traveled by bicyclist traveling west

Distance traveled by bicyclist traveling north = d + 5

$25^2=d^2+(d+5)^2\n\nd^2+d^2+10d+25=625\n\n2d^2+5d-600=0\n\nd^2+5d-300=0\n\nd=(-5\pm √(5^2-4* 1* (-300)))/(2* 1)\n\nd=(-5\pm √(25+1200))/(2)\n\nd=(-5\pm √(1225))/(2)\n\nd=(-5\pm 35)/(2)\n\nd=15miles\texttt{ or }d=-20miles$

Negative displacement is not possible.

Hence d = 15 miles

Distance traveled by bicyclist traveling west = d = 15 miles

This situation is represented in annex.
From Pythagorean theorem you've got equation:
$x^2+(x+5)^2=25 \n \n \hbox{From formula} \ \ \ (a+b)^2 = a^2+2ab+b^2: \n \n x^2+x^2+10x+25=25 \n 2x^2+10x=0 \n \n \hbox{Factor out} \ \ 2x: \n 2x(x+5)=0 \n \n \hbox{So you've got:} \n \n x_1=0 \n x_2=-5$

There isn't any solutions where x>0, so this situation is IMPOSSIBLE.

Did you write correctly this question....?

Decrease £270 by 25%

Answers

the answer is 269.75

Anthony bought a rug for his office. He made a scale drawing of the office using a scale of 1 in = 4 ft.What is the area of the office floor not covered by the rug?

Answers

464 ft
28 times 28 = 784
20 times 16 = 320
784-320 =464 ft
So the first one

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