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gulaghasi [49]
4 years ago
14

Find all the natural numbers, which when divided by 7, leave the same number for the quotient and the remainder.

Mathematics
1 answer:
Anna11 [10]4 years ago
5 0

Answer:

8,16,24,32,48

Step-by-step explanation:

When dividing a number by 7, only 7 different remainders are possible.

The remainders when dividing by 7 can not exceed 6, so the numbers in which we are interested can be represented as 7k+k or just 8k, where k=1, 2, ... , 6.

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You earn a fixed salary working as a sales clerk making $11 per hour. You get a weekly bonus of $100. Your expenses are $60 per
elena55 [62]
Shall we make life simpler by eliminating unnecessary numbers. 
<span>Totally, my expenses would be 60+200 = $260. Let us say that of this $100 would be met by the weekly bonus so that the residual part of the requirement is $160. </span>
<span>Let x be the number of hours I work. Then my earning would be 11x. For break even, earning should equal requirement. That is 11x = 160. And so, x = 160/11 = 14.55 hours/week </span>
6 0
4 years ago
Given the binomials (x-1), (x-3), (x+3), (x+5), which one is the factor of f(x) = x^3 + 6x^2 + 12x +35?
kari74 [83]
The given polynomial is
f(x) = x³ + 6x² + 12x + 35

According to the Remainder Theorem, if x = a is a zero, then
f(a) = 0, and (x-a) is a factor.

Test (x-1):
f(1) = 1 + 6 +12 + 35 = 54   
Not a factor.

Test (x-3):
f(3) = 3³ +6*3² + 12*3 + 35 = 152
Not a factor.

Test (x+3):
f(-3) = (-3)³ + 6*(-3)² + 12*(-3) + 35 = 26
Not a factor.

Test (x+5):
(-5)³ + 6*(-5)² + 12*(-5) + 35 = 0
It is a factor.

Answer: (x+5) is a factor.
4 0
3 years ago
Solve the system using substitution 5y-x=-5 7y-x=-23
dlinn [17]

5y-x= -5      7y-x= -23

x=5y+5

7y-(5y+5)= -23

7y-5y-5= -23

2y= -23+5

2y= -18

y= -9


x= 5y+5

x= (5*-9)+5

x= -45+5

x= -40

8 0
3 years ago
<img src="https://tex.z-dn.net/?f=solve%20%5C%3A%20this%20%5C%3A%20%20%5C%5C%20%20%5C%5C%202a%20%2B%205b%20%2B%207a%20%2B%203b%2
ozzi

Answer:

7a + 8b + 3c

Step-by-step explanation:

Group together like terms and simplifyy

7 0
3 years ago
Read 2 more answers
Can you help me on question 25?!
Y_Kistochka [10]
The answer would be C
5 0
3 years ago
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