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kiruha [24]
3 years ago
8

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

Mathematics
1 answer:
denis-greek [22]3 years ago
7 0

−24/5+22/3+−31/2

=38/15+−31/2

=−389/30

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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.

=> P(x)=x^{4} + 4x^{3}-x^{2} -16x-12

With P(x) = 0

=> x^{4}+4x^{3}-x^{2} -16x-12 = 0

=> ........

Step-by-step explanation:

5 0
3 years ago
Given the points (-2, 0), (-1,0), (0, – 8), (2, 0), write the polynomial in factored form.
Ket [755]

As per given by the question,

There are given that four point.

The point is,

(-2,\text{ 0), (-1, 0), (0, -8), (2, 0)}

Now,

From given point,

(-2,\text{ 0), (-1, 0), (0, -8), (2, 0)}

Then, the factor is,

(x+2)(x+1)(x-2)

Now, solve the above equation,

(x+2)(x+1)(x-2)

The factorial formd will be,

y=a\times(x+2)\times(x+1)\times(x-2)

Now, find the value of "a" with the help of given point (0, -8).

So,

Puth the value of x =0, and y=-8 in above equation,

Then,

\begin{gathered} y=a\times(x+2)\times(x+1)\times(x-2) \\ -8=a\times(0+2)\times(0+1)\times(0-2) \\ -8=a(2)(1)(-2) \\ a=\frac{-8}{-4} \end{gathered}

Then, a=2.

Now,

The value of a is 2.

And,

The polynomial in the factored form is,

y=2(x+2)(x+1)(x-2)

Hence, the value of a is 2 and the polynomial in the factored form is,

y=2(x+2)(x+1)(x-2)_{}

8 0
1 year ago
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