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leonid [27]
2 years ago
12

Please. Help me solve this

Mathematics
1 answer:
nikklg [1K]2 years ago
5 0

Answer:

1 < a < 13/5

Step-by-step explanation:

2 < 2a - 3(1 -a) < 10

2 < 2a - 3 + 3a < 10

2 < 5a - 3 < 10

2 + 3 < 5a - 3 + 3 < 10 + 3

5 < 5a < 13

5/5 < 5a/5 < 13/5

1 < a < 13/5

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Which property does x2+2x=2x+x^2
Naya [18.7K]
Im pretty sure its the commutative property.
8 0
3 years ago
Divide and simplify<br><br><br> 28 yd 2 ft 6 in ÷ 6
LUCKY_DIMON [66]

Answer:

   4 yd 2 ft 5 in

Step-by-step explanation:

One straightforward way to do this is to convert to inches and back:

  28 yd 2 ft 6 in = (28 yd)(36 in/yd) + (2 ft)(12 in/ft) + 6 in

  = 1008 in + 24 in + 6 in = 1038 in

Then your division problem looks like ...

  (1038 in)/6 = 173 in

Converting this back to yards, feet, and inches can proceed like this ...

  (173 in)/(36 in/yd) = 4 yd remainder 29 in . . . . . find the number of yards first

  = 4 yd + (29 in)/(12 in/ft) = 4 yd 2 ft 5 in . . . . . then find feet and inches

3 0
2 years ago
Find the mean absolute deviation to the nearest cent. Explain what this value represents.
emmasim [6.3K]

Answer:

134.38

This value represents 134.38

Step-by-step explanation:

Find the mean.

950+620+545+810+775+1120+905+775=6500

6500/8=812.5

Subtract the mean of numbers.

950-812.5=137.5

812.5-620=192.5

812.5-545=267.5

812.5-810=2.5

812.5-775=37.5

1120-812.5=307.5

905-812.5=92.5

812.5-775=37.5

Find the mean.

137.5+192.5+267.5+2.5+37.5+307.5+92.5+37.5=1075

1075/8≈134.38

This means that 134.38 is $134.38

8 0
3 years ago
Read 2 more answers
Let a=(1,2,3,4), b=(4,3,2,1) and c=(1,1,1,1) be vectors in R4. Part (a) [4 points]: Find (a⋅2c)b+||−3c||a. Part (b) [6 points]:
love history [14]

Solution :

Given :

a = (1, 2, 3, 4) ,    b = ( 4, 3, 2, 1),    c = (1, 1, 1, 1)     ∈   R^4

a). (a.2c)b + ||-3c||a

Now,

(a.2c) = (1, 2, 3, 4). 2 (1, 1, 1, 1)

         = (2 + 4 + 6 + 6)

         = 20

-3c = -3 (1, 1, 1, 1)

     = (-3, -3, -3, -3)

||-3c|| = $\sqrt{(-3)^2 + (-3)^2 + (-3)^2 + (-3)^2 }$

        $=\sqrt{9+9+9+9}$

       $=\sqrt{36}$

        = 6

Therefore,

(a.2c)b + ||-3c||a = (20)(4, 3, 2, 1) + 6(1, 2, 3, 4)  

                          = (80, 60, 40, 20) + (6, 12, 18, 24)

                         = (86, 72, 58, 44)

b). two vectors \vec A and \vec B are parallel to each other if they are scalar multiple of each other.

i.e., \vec A=r \vec B   for the same scalar r.

Given \vec p is parallel to \vec a, for the same scalar r, we have

$\vec p = r (1,2,3,4)$

$\vec p =  (r,2r,3r,4r)$   ......(1)

Let \vec q = (q_1,q_2,q_3,q_4)   ......(2)

Now given \vec p  and  \vec q are perpendicular vectors, that is dot product of \vec p  and  \vec q is zero.

$q_1r + 2q_2r + 3q_3r + 4q_4r = 0$

$q_1 + 2q_2 + 3q_3 + 4q_4  = 0$  .......(3)

Also given the sum of \vec p  and  \vec q is equal to \vec b. So

\vec p + \vec q = \vec b

$(r,2r,3r,4r) + (q_1+q_2+q_3+q_4)=(4, 3,2,1)$

∴ $q_1 = 4-r , \ q_2=3-2r, \ q_3 = 2-3r, \ q_4=1-4r$   ....(4)

Putting the values of q_1,q_2,q_3,q_4 in (3),we get

r=\frac{2}{3}

So putting this value of r in (4), we get

$\vec p =\left( \frac{2}{3}, \frac{4}{3}, 2, \frac{8}{3} \right)$

$\vec q =\left( \frac{10}{3}, \frac{5}{3}, 0, \frac{-5}{3} \right)$

These two vectors are perpendicular and satisfies the given condition.

c). Given terminal point is \vec a is (-1, 1, 2, -2)

We know that,

Position vector = terminal point - initial point

Initial point = terminal point - position point

                  = (-1, 1, 2, -2) - (1, 2, 3, 4)

                  = (-2, -1, -1, -6)

d). \vec b = (4,3,2,1)

Let us say a vector \vec d = (d_1, d_2,d_3,d_4)  is perpendicular to \vec b.

Then, \vec b.\vec d = 0

     $4d_1+3d_2+2d_3+d_4=0$

     $d_4=-4d_1-3d_2-2d_3$

There are infinitely many vectors which satisfies this condition.

Let us choose arbitrary $d_1=1, d_2=1, d_3=2$

Therefore, $d_4=-4(-1)-3(1)-2(2)$

                      = -3

The vector is (-1, 1, 2, -3) perpendicular to given \vec b.

6 0
2 years ago
The sum of two numbers is 100. Five times the smaller number is eight more than the larger
crimeas [40]

Answer:The larger of two numbers is 8 more than 4 times the smaller if the larger number is increased by four times the smaller the result is 40. From this statement, we can calculate the values of the numbers where you get the value of the larger number to be 24 and that of the smaller number to be 4.

Step-by-step explanation:

4 0
2 years ago
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