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2 years ago

Write an equation in slope-intercept form of the line that passes through (7, 2) and (2, 12)

Mathematics

1 answer:

Anika [276]2 years ago

4 0

Step-by-step explanation:

the general slope intercept form is

y = ax + b

a is the slope, b is the y-intercept (when x=0).

the slope is the ratio y/x indicating how much y changes, when x changes for a certain amount of units when going from one point to another.

going from (7, 2) to (2, 12) :

x changes by -5 (from 7 to 2), y changes by +10 (from 2 to 12).

so, the slope is 10/-5 = -2

therefore, we have already

y = -2x + b

we get b by using the coordinates of one of the points as x and y. e.g. (7, 2)

2 = -2×7 + b = -14 + b

16 = b

so, the full line equation is

y = -2x + 16

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jeyben [28]

Answer:

4a)= 2.1m 4b)= 1.9 m 5)= 29.6º

Step-by-step explanation:

4a):

x is the opp

AB is the hyp

BC is the adj

thus,

sin32 = x/4

cross multiply, x= 4*sin32

x= 2.1196.......

x=2.1 m

4b).

x is the hyp

ac is the opp

bc is the adj

thus,

cos65=4.5/x

cross multiply, x= 4.5*cos65

x=1.9017....

x=1.9 m

5).

AB is the opp

bc is the adj

ac is the hyp

thus:

tanC= 2.1/3.7

C= tan^-1 (2.1/3.7)

C= 29.5778.....

C= 29.6º

5 0

2 years ago

Let $r$ and $s$ be the roots of $3x^2 + 4x - 12 = 0.$ Find $r^2 + s^2.$

Paul [167]

We can factorize the quadratic as

$3x^2 + 4x - 12 = 3 (x - r) (x - s)$

and expand the right side to get

$3x^2 + 4x - 12 = 3x^2 - 3(r + s) x + 3rs$

$\implies r + s = -\dfrac43 \text{ and } rs = -4$

Then we find

$(r + s)^2 = r^2 + 2rs + s^2 \implies r^2 + s^2 = \left(-\dfrac43\right)^2 - 2(-4) = \boxed{\dfrac{88}9}$

8 0

1 year ago

Express the situation as a system of two equations in two variables. Be sure to state clearly the meaning of your x- and y-varia

expeople1 [14]

Answer:

9 TV ads and 20 radio ads

Step-by-step explanation:

He has $37,000 to spend. He has to sum that amount of money between the TV and radio ads. Each TV ad costs $3000 while each radio ad costs $500, so the equation that represents that is 37000 = 3000x + 500y

The same happens with the amount of voters he needs to reach, the equation is 130000 = 10000x + 2000y

The system that represents this is

$\left \{ {{3000x+500y=37000} \atop {10000x+2000y=130000}} \right.$

And the augmented matrix is

$\left[\begin{array}{cc|c}3000&500&37000\\10000&2000&130000\end{array}\right]$

First we divide the first row by 3000 and the second by 10000:

$\left[\begin{array}{cc|c}1&1/6&37/3\\1&1/5&13\end{array}\right]$

Then we multiply the second row by (-1) and we add the first row:

$\left[\begin{array}{cc|c}1&1/6&37/3\\0&-1/30&-2/3\end{array}\right]$

Now we multiply the second row by -30:

$\left[\begin{array}{cc|c}1&1/6&37/3\\0&1&20\end{array}\right]$

Finally, to the first row we add the second one multiply by (-1/6):

$\left[\begin{array}{cc|c}1&0&9\\0&1&20\end{array}\right]$

So, x = 9 and y = 20

That means 9 TV and 20 radio ads will contact 130,000 voters using the allocated funds

3 0

2 years ago

What are the coordinates of the vertex of the graph of f(x)=−3|x−1|? Enter your answer in the boxes. ( , )

kykrilka [37]

Well, the cheap answer is

f(x) = -3| x - 1 | is really just f(x) = -3| x - 1 | + 0.

now, what value of "x" makes the absolute value expression to 0?

well, let's just set it to 0 and check,

x - 1 = 0

x = 1

so if "x" ever becomes 1, the | x - 1| will turn to 0, therefore, the vertex is at

f(x) = -3| (1) - 1 | + 0 --------------> ( 1, 0 )

5 0

2 years ago

Lincy is standing 20 feet from the circular wall of an above ground swimming pool and 49 feet from a point of tangency. Find the

BaLLatris [955]

Answer:

the radius of the pool is 50.025 feet

Step-by-step explanation:

From the information given:

We can have a schematic view of a diagrammatic illustration in our mind where the distance of the pool to Lincy is (20 + r ) and the distance to the tangent is 49.

So; by using pythagoras theorem, since the radius meets the tangent at a right angle; we have:

$r^2 + 49^2 = ( r + 20 )^2$

$r^2 +2401 = r^2 + 40r + 400$

$2401 = 40r + 400$

$2401- 400 = 40r$

2001 = 40 r

r = 2001/40

r = 50.025 feet

7 0

2 years ago