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4 years ago

What is the slope of the line that passes through (0,12) and (3,9)

2 answers:

8 0

Hey there!
We can use our slope given two points formula:
y2-y1/x2-x1
If we plug in our values, we get:
9-12/3-0 =
-3/3 =
-1
Hope this helps!

k0ka [10]4 years ago

5 0

The slope formula is y2 - y1 / x2 - x1. So that would be 9 - 12 / 3 - 0. The answer is -3/3, which simplifies to -1. -1 is the slope.

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Use induction to prove: For every integer n > 1, the number n5 - n is a multiple of 5.

nignag [31]

Answer:

we need to prove : for every integer n>1, the number $n^{5}-n$ is a multiple of 5.

1) check divisibility for n=1, $f(1)=(1)^{5}-1=0$ (divisible)

2) Assume that $f(k)$ is divisible by 5, $f(k)=(k)^{5}-k$

3) Induction,

$f(k+1)=(k+1)^{5}-(k+1)$

$=(k^{5}+5k^{4}+10k^{3}+10k^{2}+5k+1)-k-1$

$=k^{5}+5k^{4}+10k^{3}+10k^{2}+4k$

Now, $f(k+1)-f(k)$

$f(k+1)-f(k)=k^{5}+5k^{4}+10k^{3}+10k^{2}+4k-(k^{5}-k)$

$f(k+1)-f(k)=k^{5}+5k^{4}+10k^{3}+10k^{2}+4k-k^{5}+k$

$f(k+1)-f(k)=5k^{4}+10k^{3}+10k^{2}+5k$

Take out the common factor,

$f(k+1)-f(k)=5(k^{4}+2k^{3}+2k^{2}+k)$ (divisible by 5)

add both the sides by f(k)

$f(k+1)=f(k)+5(k^{4}+2k^{3}+2k^{2}+k)$

We have proved that difference between $f(k+1)$ and $f(k)$ is divisible by 5.

so, our assumption in step 2 is correct.

Since $f(k)$ is divisible by 5, then $f(k+1)$ must be divisible by 5 since we are taking the sum of 2 terms that are divisible by 5.

Therefore, for every integer n>1, the number $n^{5}-n$ is a multiple of 5.

3 0

3 years ago

Question 4

Elanso [62]

Answer:

a $A = 30 + 0.45 n$

b $A = 90.3$

c 0 customers

Step-by-step explanation:

Given

$Base\ Amount = 30$

$Rate = 0.45$ per customer

Solving (a): Amount (A) on n customers

This is calculated as:

$A = Base\ Amount + Rate * n$

$A = 30 + 0.45 * n$

$A = 30 + 0.45 n$

Solving (b): Amount on 134 customers

In this case: n = 134

So:

$A = 30 + 0.45 * 134$

$A = 30 + 60.3$

$A = 90.3$

Solving (c): Customers at noon.

At noon, the amount is 30.

So:

$A = 30 + 0.45 n$

$30 = 30 + 0.45n$

Collect like terms

$0.45n = 30 - 30$

$0.45n =0$

$n = 0$

6 0

3 years ago

The white Christmas tree is 7.55m tall.the green Christmas tree is twice as tall as the white Christmas tree which is 0.454m tal

Alja [10]

The white Christmas tree is 7.55m

Green Christmas tree is twice as tall as white Christmas tree: 7.55 * 2 = 15.1m

High golden Christmas tree: 15.1m - 0.454m = 14.646m

The total height of 3 Christmas trees is: 7.55m + 15.1m + 14.646m = 37.296m

Choose: A 37.296m

8 0

3 years ago

Molly tried to evaluate 93\times5193×5193, times, 51 using partial products. Her work is shown below.

Mrac [35]

Since molly's solution tally's with the given solution, hence <em>Molly's solution is correct.</em>

Given the working on a partial product of 93 and 51 carried out by Molly as shown:

$\begin{array}{llrr} &&93 \\ &&\underline{{}\times51} \\ &\blueD{\text{Step 1}}&\blueD{3}& \blueD{1\times3\text{ ones}}\\ &\greenD{\text{Step 2}}&\greenD{90}& \greenD{1\times 9\text{ tens}}\\ &\maroonD{\text{Step 3}}&\maroonD{150}& \maroonD{50\times 3\text{ ones}}\\ &\goldE{\text{Step 4}}&\underline{{}+\goldE{ 4{,}500}}& \goldE{50\times 9\text{ tens}}\\ &\purpleD{\text{Step 5}}&\purpleD{4{,}743}& \end{array}$

This partial product can also be solved as shown below:

$93 \times 51 = (90+3)\times (50+1)$

Applying the distributive law:

$93 \times 51 = 90(50) + 90(1) + 3(50) + 3(1)\\93 \times 51 =4500 + 90 + 150 + 3\\93 \times 51 =4500+240+3\\93 \times 51 =4740+3\\93 \times 51 =4743$

Since molly's solution tally's with the given solution, hence <em>Molly solution is correct.</em>

Learn more about partial product at: brainly.com/question/24716925

5 0

2 years ago

Why is f(x)=0 the only odd and even function?

kupik [55]

F is odd if and only f f(-x) = -f(x) so f(x) = 0 works because 0 = 0 always.

f is even if and only if f(-x) = f(x) so f(x) = 0 works because there's no x term so nothing changes. 0 = 0.

6 0

3 years ago

Read 2 more answers