Write the equation, in slope-intercept form, of the line that has a slope of 2 and passes through the point (3, 1).

Answers

Answer 1

Answer: From the equation of a line;
y=mx+c
m=2
y=2x+c
Replacing for;
y=1
x=3
1=2*3+c
1=6+c
c=1-6
c=-5
y=2x-5

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a ski shop has a markup rate of 50% find the selling price of skis that cost the store owner $300. tell me how you got the answer

Answers

if nthe shop has a mark up rate of 50% and they cost 300 to buy you multiply 300 by 50% convert 50% to decimal
so you do .5*300=150
then you add 150 to 300 which means that the shop sells the skis for 450 dollars.

the ages of John and Mary total 27 years. Mary's age plus twice john's age is 40. how old is each person?

Answers

so
Jon's age=j
mary age=m

m+j=27
m+2 times j=40
m+2j=40
M+j=27
ssubtract j from both sides
m=27-j
subsitute 27-j for m
27-j+2j=40
27+j=40
subtract 27 fromboth sdies
j=13

subsitue
13+m=27
subtract 13
m=14

mary=14
john=13

$J+M=27$
$2J+M=40$

$J=27-M$

$2(27-M)+M=40$
$54-2M+M=40$
$54-M=40$
$-M=-14$
$M=14$

$2J+14=40$
$2J=26$
$J=13$

John is 13 years old
Mary is 14 years old

Could somebody Please help me

Answers

Correct answer is B :)
So first you work out the total Surface area (L x W of every quadrilateral, and [L x W]÷2 for triangles)
and then for the lateral surface area, you minus the area of the vertical sides, which are the 2 triangles :)

Answer and explanation please

Answers

Answer:

$\sf log 162 = p + 4q$

Step-by-step explanation:

Given:

p = log 2
q = log 3

To find :

log 162 in terms of p and q.

Solution:

In order to find the logarithm of 162 in terms of p and q, we can use the properties of logarithms.

We can start by expressing 162 as a product of prime factors:

$\sf 162 = 2 * 3 * 3 * 3 * 3$

Now, we can use the properties of logarithms to simplify this expression:

$\sf log 162 = log (2 * 3 * 3 * 3 * 3)$

Since log(ab) = log(a) + log(b), we can split this into separate logarithms:

$\sf log 162 = log 2 + log (3 * 3 * 3 * 3)$

Now, we can use the fact that q = log 3:

$\sf log 162 = log 2 + log (3^4)$

Using the property $\sf \boxed{\sf log(a^b) = b * log(a)}$ , we get:

$\sf log 162 = log 2 + 4 log 3$

Now, substitute the values of p and q:

$\sf log 162 = p + 4q$

So, the logarithm of 162 in termsof p and q is:

$\sf log 162 = p + 4q$

Answer:

log 162 = 6p + 2q

Step-by-step explanation:

To write log 162 in terms of p and q, we can use the following steps:

- First, we can write 162 as a product of powers of 2 and 3, such as 162 = 2 x 3^4.

- Next, we can use the property of logarithms that log ab = log a + log b to write log 162 = log 2 + log 3^4.

- Then, we can use another property of logarithms that log a^n = n log a to write log 3^4 = 4 log 3.

- Finally, we can substitute p = log 2 and q = log 3 to get log 162 = p + 4q.

We can write 162 as follows:

```

162 = 2^6 * 3^2

```

Therefore,

```

log 162 = log (2^6 * 3^2)

```

Using the logarithmic properties of addition and multiplication, we can simplify this to:

```

log 162 = 6 * log 2 + 2 * log 3

```

Finally, substituting p = log 2 and q = log 3, we get the following expression:

```

log 162 = 6p + 2q

```

Therefore, log 162 can be written as **6p + 2q** in terms of p and q.

Okay, let's break this down step-by-step:

* log 162 = log (2^4 * 3^2) (by prime factorization)

* log (2^4 * 3^2) = 4log2 + 2log3 (by properties of logarithms)

* Let p = log 2 and q = log 3

* Substituting:

* log 162 = 4p + 2q

Therefore, log 162 can be written as 4p + 2q, where p = log 2 and q = log 3.

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To express log 162 in terms of p (log 2) and q (log 3), you can use logarithm properties, particularly the change of base formula. The change of base formula states that:

log_b(a) = log_c(a) / log_c(b)

In your case, you want to find log 162:

log 162 = log 2^1 * 3^4

Now, we can use the change of base formula with base 10 (or any other base):

log 162 = (log 2^1 * 3^4) / (log 10)

Since log 10 is simply 1 (logarithm of 10 to any base is 1), we can simplify further:

log 162 = (log 2^1 * 3^4) / 1

Now, apply the properties of logarithms to split the logarithm of a product into a sum of logarithms:

log 162 = (log 2^1) + (log 3^4)

Now, we can replace log 2 with p and log 3 with q:

log 162 = p + (4q)

So, log 162 in terms of p and q is:

log 162 = p + 4q

To write log 162 in terms of p and q, we can use the following steps:

- First, we can write 162 as a product of powers of 2 and 3, such as 162 = 2 x 3^4.

- Next, we can use the property of logarithms that log ab = log a + log b to write log 162 = log 2 + log 3^4.

- Then, we can use another property of logarithms that log a^n = n log a to write log 3^4 = 4 log 3.

- Finally, we can substitute p = log 2 and q = log 3 to get log 162 = p + 4q.

The function below models the correlation between the number of hours a plant is kept in sunlight (x) and the height (y), in mm, to which it grows:y = 4 + 2x
What does the y-intercept of this function represent?
The original height of the plant was 4 mm.
The original height of the plant was 2 mm.
The height of the plant increases by 2 mm for every hour of sunlight it receives.
The height of the plant increases by 4 mm for every hour of sunlight it receives.

Answers

Remember that the y-intercept is obtained when the value of x is set to zero. This means that the y-intercept is the value of the height without sunlight yet. This also refers to the original height of the plant. This gives:

y = 4 + 2(0) = 4

So, the original height of the plant is 4 mm.

The formula also indicates that when sunlight is present, a height of 2mm is increased every hour of sunlight exposure.

Answer:The original height of the plant was 4 mm.

Step-by-step explanation:

clara has £7. she buys some chocolate bars at 63p each and has 7p left over. how many chocolate bars did she buy?