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Lana71 [14]
3 years ago
11

The sum of two numbers is 21. The larger number is 6 less than twice the smaller number. Find the two numbers.

Mathematics
1 answer:
never [62]3 years ago
5 0
The sum of two numbers
 x + y = 21
x = smaller number
y = larger number

Larger Number = y = (2x -6)
Substitute  (2x - 6) for y
x + y = 21
x + (2x - 6) = 21
3x - 6 = 21
3x = 21 + 6
3x = 27
3x / 3 = 27 / 3
x =  9
Smaller number = x = 9
Find the larger number by inserting 9 into (2x - 6)
(2x - 6)
(2(9) - 6)
18 - 6
12

So 
x = 9
y =12

Check our answer by inserting x = 9 and y = 12 into  x + y = 21
x + y =21
9 + 12 = 21
21 = 21 
So since we have 21 = 21 we know our answer is correct. 
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Rainbow [258]

Answer:

x = -10

Step-by-step explanation:

x + 75 + x + 125 = 180

2x + 200 = 180

2x = -20

x = -10

(In this problem a negative number is okay because the end value will be a whole number still.)

8 0
3 years ago
Find an explicit rule for the nth term of the sequence. <br><br> 2, -8, 32, -128, ...
Akimi4 [234]
A1=2
a2=-8
a3=32
a4=-128

a2/a1=(-8)/2→a2/a1=-4
a3/a2=32/(-8)→a3/a2=-4
a4/a3=(-128)/32→a4/a3=-4

a2/a1=a3/a2=a4/a3=r=-4

an=a1*r^(n-1)
an=2*(-4)^(n-1)

The explicit rule for the nth term of the given sequence is an=2*(-4)^(n-1) 
8 0
3 years ago
in a game involving a pair of fair dice a player rolls the dice until he gets a sum of 7 let z equal the number of rolls it take
Anarel [89]

Answer:

z = 36 rolls , probability for getting 7 = 1/6

Step-by-step explanation:

A die has 6 possible outcomes, which sums to 36 for two dice for every value on both dice.

The outcomes for rolling both dice for 36 times gives 6 possible outcomes summing to 7, that is, (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), and (6, 1).

There the probability of getting a sum dice of 7 is:

= 6 / 36 = 1/6

8 0
3 years ago
An arrow is shot vertically upward at a rate of 210 feet per second. Use the projectile formula h = −16t2 + v0t to determine at
Klio2033 [76]

Answer:

Time equal to 3.30 seconds when the arrow was going up.

Time equal to 7.94 seconds when the arrow was going down.

Step-by-step explanation:

Trust me

7 0
2 years ago
HELP, I’M STUCK !
vaieri [72.5K]

Since P(<em>X</em> = <em>x</em>) = 0.3 for all 0 ≤ <em>x</em> ≤ <em>α</em>, we have

\displaystyle\int_{-\infty}^\infty P(X=x)\,\mathrm dx=1\implies0.3\int_0^\alpha\mathrm dx=0.3\alpha=1\implies\alpha=\dfrac{10}3

So,

P(X>2) = \displaystyle\int_2^\infty P(X=x)\,\mathrm dx=0.3\int_2^{\frac{10}3}\mathrm dx

P(X>2)=0.3\left(\dfrac{10}3-2\right)=\boxed{\dfrac25}

6 0
3 years ago
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