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Hitman42 [59]
3 years ago
14

Pencils cost $.10 and erasers cost $0.25. steve bought 5 more pencils than erasers. he spent a total of $1.55. how many erasers

did steve buy?
Mathematics
1 answer:
ad-work [718]3 years ago
5 0

Answer:

Let x be the number of pencils Steve bought.

Let y be the number of erasers Steve bought.

x=y+5

0.1x + 0.25y = 1.55

Solving the system, our answer is: (8, 3)

So, she bought 3 erasers.

Let me know if this helps!

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8 0
3 years ago
Suppose that f: R --&gt; R is a continuous function such that f(x +y) = f(x)+ f(y) for all x, yER Prove that there exists KeR su
Pachacha [2.7K]
<h2>Answer with explanation:</h2>

It is given that:

f: R → R is a continuous function such that:

f(x+y)=f(x)+f(y)------(1)  ∀  x,y ∈ R

Now, let us assume f(1)=k

Also,

  • f(0)=0

(  Since,

f(0)=f(0+0)

i.e.

f(0)=f(0)+f(0)

By using property (1)

Also,

f(0)=2f(0)

i.e.

2f(0)-f(0)=0

i.e.

f(0)=0  )

Also,

  • f(2)=f(1+1)

i.e.

f(2)=f(1)+f(1)         ( By using property (1) )

i.e.

f(2)=2f(1)

i.e.

f(2)=2k

  • Similarly for any m ∈ N

f(m)=f(1+1+1+...+1)

i.e.

f(m)=f(1)+f(1)+f(1)+.......+f(1) (m times)

i.e.

f(m)=mf(1)

i.e.

f(m)=mk

Now,

f(1)=f(\dfrac{1}{n}+\dfrac{1}{n}+.......+\dfrac{1}{n})=f(\dfrac{1}{n})+f(\dfrac{1}{n})+....+f(\dfrac{1}{n})\\\\\\i.e.\\\\\\f(\dfrac{1}{n}+\dfrac{1}{n}+.......+\dfrac{1}{n})=nf(\dfrac{1}{n})=f(1)=k\\\\\\i.e.\\\\\\f(\dfrac{1}{n})=k\cdot \dfrac{1}{n}

Also,

  • when x∈ Q

i.e.  x=\dfrac{p}{q}

Then,

f(\dfrac{p}{q})=f(\dfrac{1}{q})+f(\dfrac{1}{q})+.....+f(\dfrac{1}{q})=pf(\dfrac{1}{q})\\\\i.e.\\\\f(\dfrac{p}{q})=p\dfrac{k}{q}\\\\i.e.\\\\f(\dfrac{p}{q})=k\dfrac{p}{q}\\\\i.e.\\\\f(x)=kx\ for\ all\ x\ belongs\ to\ Q

(

Now, as we know that:

Q is dense in R.

so Э x∈ Q' such that Э a seq belonging to Q such that:

\to x )

Now, we know that: Q'=R

This means that:

Э α ∈ R

such that Э sequence a_n such that:

a_n\ belongs\ to\ Q

and

a_n\to \alpha

f(a_n)=ka_n

( since a_n belongs to Q )

Let f is continuous at x=α

This means that:

f(a_n)\to f(\alpha)\\\\i.e.\\\\k\cdot a_n\to f(\alpha)\\\\Also\\\\k\cdot a_n\to k\alpha

This means that:

f(\alpha)=k\alpha

                       This means that:

                    f(x)=kx for every x∈ R

4 0
3 years ago
1. What is the factored form of q2 - 12q + 36? (1 point)
Novay_Z [31]

Step-by-step explanation:

{q}^{2}  - 12q + 36 \\  =  {q}^{2}  - 6q - 6q + 36 \\  = q(q - 6) - 6(q - 6) \\   \huge \red{ \boxed {= (q - 6)(q - 6) }}\\ is \: the \: factored \: form.

3 0
3 years ago
Find the values of x and y?
lakkis [162]

Answer:x=20 y=70

Step-by-step explanation:

4 0
3 years ago
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riadik2000 [5.3K]

Answer:

The number is 12

Step-by-step explanation:

Let x be the number

160/100 = 1.6

1.6 x = 19.2

x = 19.2 / 1.6

x = 12

7 0
3 years ago
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