Evaluate the Expression :<br> (-2 4/5) + 2 2/3 + (-3 1/2)

Write an equation of the line that is perpendicular to the line y = 1 2 x + 8 that passes through the point (4,6)

Katen [24]

Answer:

$\large\boxed{y=-2x+14}$

Step-by-step explanation:

$\text{Let}\ k:y=_1x+b_1\ \text{and}\ l:y=m_2x+b_2.\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\============================\\\\\text{We have}\ y=\dfrac{1}{2}x+8\to m_1=\dfrac{1}{2}.\\\\\text{Therefore}\ m_2=-\dfrac{1}{\frac{1}{2}}=-2.\\\\\text{The equation of the searched line:}\ y=-2x+b.\\\\\text{The line passes through }(4,\ 6).$

$\text{Put thecoordinates of the point to the equation.}\ x=4,\ y=6:$

$6=-2(4)+b\\\\6=-8+b\qquad\text{add 8 to both sides}\\\\b=14$

6 0

4 years ago

Read 2 more answers

1.) name a pair of alternate interior angles.

irina1246 [14]

1.c
2.a
c because they are on the inside and on alternate sides, and a because they are corresponding angles.

3 0

3 years ago

Read 2 more answers

Solve. If a gallon of milk costs $3 now and the price is increasing 10% each year, how long before a gallon of milk costs $10?

Lelechka [254]

Answer: 12.63 years

Step-by-step explanation:

Hi, to answer this question we have to apply the next formula:

A = P (1 + r) t

Where:

p = original price

r = increasing rate (decimal form)

t= years

A = price after t years

10= 3 (1 + 10/100) t

10= 3(1.1)^t

10/3= 1.1^t

log 10/3 = log 1.1^t

log 10/3 = t log 1.1

log (10/3)/ log 1.1 =t

t = 12.63 years

Feel free to ask for more if needed or if you did not understand something.

5 0

3 years ago

P(x) = x^4+ax^3-x^2+bx-12 has factors of (x-2) and (x+1). Solve the equation P(x)=0

Feliz [49]

Answer:

because P(x) has factors of (x-2) and (x+1) => x = 2 and x = -1 are the solutions of P(x)

so we have:

$\left \{ {{2^{4}+2^{3}a-2^{2}+2b-12 =0} \atop {1-a-1-b-12=0}} \right.\\=>\left \{ {{8a+2b=0} \atop {a+b=-12}} \right.\\\left \{ {{4a+b=0} \atop {a+b=-12}} \right.\\\left \{ {{a=4} \atop {b=-16}} \right.$