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3 years ago

Suppose LCM(a,b) = 20160, a=60. Find the smallest possible value of b.

Mathematics

2 answers:

Black_prince [1.1K]3 years ago

7 0

Answer:

Step-by-step explanation:

1260=22*32*5*7

60=22*3*5

Therefore we need the smallest number divisible by seven and nine, which is 7*9=63.

Mars2501 [29]3 years ago

5 0

Answer:

see below

Step-by-step explanation:

given:

LCM(a,b) = 20160, a=60

find:

smallest possible value of b

solution;

60, b = 20,160

b = 20,160 / 60

b = 336

60 x 336 = 20,160

= 2⁶ x 3² x 5 x 7

= (2² x 3 x 5) x (2⁴ x 3 x 7)

= (60) x (336)

LCM(60,336) = 1680

consider the 2² x 3 to get the prime number:

= 336 x 12

= 4032

therefore,

LCM(60,4032) = 20160

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The number 1,054 is:

viktelen [127]

Answer:

Step-by-step explanation:

4 0

3 years ago

A (0, 2) and B (6,6) are points on the straight line ABCD.

elena-14-01-66 [18.8K]

Answer:

(18, 14)

Step-by-step explanation:

We know that C and D lie on the line AB and BC = CD = AB. Then we need to use the distance formula and equation of the line AB to find the other two coordinates.

The distance formula states that the distance between two points $(x_1,y_1)$ and $(x_2,y_2)$ , the distance is denoted by: $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$ . Let's find the distance between A and B:

d = $\sqrt{(6-0)^2+(6-2)^2}=\sqrt{6^2+4^2} =\sqrt{36+16} =\sqrt{52} =2\sqrt{13}$

Now say the coordinates of D are (a, b). Then the distance between D and B will be twice of 2√13, which is 4√13:

4√13 = $\sqrt{(6-a)^2+(6-b)^2}$

Square both sides:

208 = (6 - a)² + (6 - b)²

Let's also find the equation of the line AB. The y-intercept we know is 2, so in y = mx + b, b = 2. The slope is (6 - 2) / (6 - 0) = 4/6 = 2/3. So the equation of the line is: y = (2/3)x + 2. Since (a, b) lines on this line, we can put in a for x and b for y: b = (2/3)a + 2. Substitute this expression in for b in the previous equation:

208 = (6 - a)² + (6 - b)²

208 = (6 - a)² + (6 - (2/3a + 2))² = (6 - a)² + (-2/3a + 4)²

208 = a² - 12a + 36 + 4/9a² - 16/3a + 16 = 13/9a² - 52/3a + 52

0 = 13/9a² - 52/3a - 156

13a² - 156a - 1404 = 0

a² - 12a - 108 = 0

(a + 6)(a - 18) = 0

a = -6 or a = 18

We know a can't be negative so a = 18. Plug this back in to find b:

b = 2/3a + 2 = (2/3) * 18 + 2 = 12 + 2 = 14

So point D has coordinates (18, 14).

8 0

4 years ago

Read 2 more answers

Help meeeeeeeeeeeeeeeeeee <br><br> >_

nignag [31]

Answer:

good news, the second one is relatively easy because it can be factored to (2x+1)(2x-3) which means that number two has solutions of -1/2 and 3/2

but for number one you have to either use the quadratic equation cause I've tried using synthetic division or just use the second equation to derive the first solutions so I tried move the graph up by two units and found that the intercepts are approximately (1+-√2)/2 or 1/2+-1/√2 for 4x^2-4x-1

7 0

3 years ago

ΔPQR has angle measurements of 80°, 50°, and 50°. What kind of triangle is ΔPQR?

trasher [3.6K]

Answer:

Isosceles Triangle; Acute Triangle

Step-by-step explanation:

Review your definitions of the different types of triangles:

acute triangle- a triangle that has three acute (less than 90 degrees) angles

obtuse triangle- a triangle that has an obtuse (greater than 90 degrees) angle.

right triangle- a triangle that had one right (90 degrees) angles

isosceles triangle- a triangle with two congruent sides and one unique side and angle.

equilateral triangle- a triangle with three congruent sides and three congruent angles.

scalene triangle- a triangle with no congruent sides and no congruent angles.

With these definitions, we can classify ΔPQR as an isosceles acute triangle.

8 0

3 years ago

Which of the following is a solution of 4x^2=-9x-4

NeTakaya

Answer:

(-9+√17)/8

Step-by-step explanation:

its an example of quadratic

4 0

3 years ago