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Ann [662]
3 years ago
6

If the mean (average) of five consecutive numbers is 21, the smallest of three five numbers will be...

Mathematics
1 answer:
Vitek1552 [10]3 years ago
7 0
Consecutive numbers are 1 apart
they are
x,x+1,x+2,x+3,x+4

average is 21
(x+x+1+x+2+x+3+x+4)/5=21
(5x+10)/5=21
times both sides by 5
5x+10=105
minus 10 both sides
5x=95
divide both sides by 5
x=19
x+1=20
x+2=21
x+3=22
x+4=23


the smallest number is 19
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Antonia incorrectly solves the equation −2(14−54a)=6 . Her work is shown below.
bekas [8.4K]

Answer:

For the yes/no bit:

step 1: no

step 2: no

step 3: yes

step 4: yes

step 5: no

for the final answer bit: a = 2  3/5 (the last option)

Step-by-step explanation:

yes/no bit:

step 1 is wrong because she didn't multiply -\frac{5}{4}a by -2

step 2 is wrong because she subtracted 1/2 instead of adding it

step 3 is correct because 6 - 1/2 = 11/2

step 4 is correct because she correctly multiplied both sides by 4

step 5 is wrong because she added 5 instead of dividing by -5.

for the final answer bit, I've attached an image below with my working out. hope this helps!

6 0
3 years ago
The height of an object tossed upward with an initial velocity of 120 feet per second is given by the formula h = −16t2 + 120t,
AleksAgata [21]

Answer:

7.5 seconds

Step-by-step explanation:

h =  - 16 {t}^{2}  + 120t \\  \because \:  we \: have \: to \: find \:  the  \:  time  \: required  \:  \\ for \:  the \:  object \:  to \:  return to \:  its  \:  \\ point \:  of  departure. \\  \therefore \: plug \: h = 0 \: in \: the \: given \: euation. \\  \therefore \: 0 =   - 16 {t}^{2}  + 120t \\ \therefore \:16 {t}^{2}  - 120t = 0 \\ \therefore \:8t(2t - 15) = 0 \\ \therefore \:8t = 0 \:  \: or \:  \: (2t - 15) = 0 \\ \therefore \:t =  \frac{0}{8}  \: or \: t =  \frac{15}{2}  \\ \therefore \:t = 0 \: or \: t = 7.5 \\  \because \: t = 0 \: is \: not \: possible \\ \huge \purple{ \boxed{  \therefore \: t = 7.5 \: seconds}}

Thus, the time required for the object to return to its point of departure is 7.5 seconds.

4 0
3 years ago
An integer is 8 more than 5 times another. If the product of the two integers is 36, then find the integers
Harman [31]

Answer:

see below

Step-by-step explanation:

1st:  x

2nd:  5x + 8

x(5x + 8) = 36

5x² + 8x = 36

5x² + 8x - 36 = 0

(x - 2)(5x + 18) = 0

(x - 2) = 0

x - 2 = 0

x = 2

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2nd:  5x + 8 = 5(2) + 8 = 18

(5x + 18) = 0

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5x = -18

x = -3.6

1st:  x = -3.6

2nd:  5x + 8 = 5(-3.6) + 8 = -18 + 8 = -10

7 0
3 years ago
The volume of cube x divided by the volume of cube y is 27. What is the side length of cube x divided by side length of cube y
Svetach [21]
If the volume of cube x divided by the volume of cube y is 27, then <span>he side length of cube x divided by side length of cube y would be 3. This is computed by solving the cube root of 27, since the side of the cube was multiplied thrice to get the volume so when geeting the side of the cube it is best to have the number be in cube root form.</span>
4 0
3 years ago
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