Six is less than or equal to the sum of 4 and -2x

Answers

Answer 1

Answer: 6 ≤ 4 + (-2x)
6 (-4) ≤ 4 - 2x - 4
4 and 4 cancels out
2 ≤ -2x

-1≥x

When you divide by a negative number, the inequality sign turns to the other side.

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Help with line equations?

Answers

First question

$line:~~~~y=x+3$

$curve:~~~~x^2+y^2=29$

now we have to replace the y of curve by the y of line, therefore

$x^2+(x+3)^2=29$

$x^2+x^2+6x+9=29$

$2x^2+6x+9-29=0$

$2x^2+6x-20=0$

we can multiply each member by $(1)/(2)$

$\boxed{\boxed{x^2+3x-10=0}}$

Now we have to find the roots of this funtion

$x^2+3x-10=0$

Sum and produc or Bhaskara

Then we find two axis

$\boxed{x_1=2~~and~~x_2=-5}$

now we replace this values to find the Y, we can replace in curve or line equation, I'll prefer to replace it in line equation.

$y=x+3$

$y_1=x_1+3$

$y_1=2+3$

$\boxed{y_1=5}$

$y_2=x_2+3$

$y_2=-5+3$

$\boxed{y_2=-2}$

Therefore

$\boxed{\boxed{P_1(2,5)~~and~~P_2(-5,-2)}}$
_______________________________________________________________

The second question give to us

$y=ax+b$

$P_1(2,13)$

$P_2(-1,-11)$

We just have to replace the value then we'll get a linear system.

point 1

$13=2a+b$

point 2

$-11=-a+b$

then our linear system will be

$\begin{Bmatrix}2a+b&=&13\n-a+b&=&-11\end{matrix}$

I'll multiply the second line by -1 and I'll add to first one

$\begin{Bmatrix}2a+(a)+b+(-b)&=&13+(-11)\n-a+b&=&-11\end{matrix}$

$\begin{Bmatrix}3a&=&24\n-a+b&=&-11\end{matrix}$

$\begin{Bmatrix}a&=&8\n-a+b&=&-11\end{matrix}$

therefore we can replace the value of a, at second line

$\begin{Bmatrix}a&=&8\n-8+b&=&-11\end{matrix}$

$\begin{Bmatrix}a&=&8\nb&=&-11+8\end{matrix}$

$\boxed{\boxed{\begin{Bmatrix}a&=&8\nb&=&-3\end{matrix}}}$

then our function will be

$\boxed{\boxed{y=8x-3}}$

_________________________________________________________________

The third one, we have

$line:~~~~y=3x-4$

$curve:~~~~y=x^2-2x-4$

This resolution will be the same of our first question.

Let's replace the y of curve by the y of line

$3x-4=x^2-2x-4$

$0=x^2-2x-4-3x+4$

therefore

$\boxed{\boxed{x^2-5x=0}}$

now we have to find the roots of this function.

$x^2-5x=0$

put x in evidence

$x*(x-5)=0$

$\boxed{x_1=0~~and~~x_2=5}$

then

$y=3x-4$

$y_1=3x_1-4$

$y_1=3*0-4$

$\boxed{y_1=-4}$

$y_2=3x_2-4$

$y_2=3*5-4$

$y_2=15-4$

$\boxed{y_2=11}$

our points will be

$\boxed{\boxed{P_1(0,-4)~~and~~P_2(5,11)}}$

I hope you enjoy it ;)

If a hospital patient is given 50 milligrams of medicine which leaves the bloodstream at 10% per hour, how many milligrams of medicine will remain in the system after 6 hours? Use the function A(t) = Iert. A) 12.39 mg
B) 27.44 mg
C) 45.24 mg
D) 91.11 mg

Answers

A(t) = 50 e^-(0.1 x 6) = 50 e^-0.6 = 50 x 0.5488 = 27.44 mg

I think the answer is B.

5/12 expressed as a decimal fraction is? (Round to the nearest thousandths)

Answers

The required decimal fraction is 0.417.

Given that,
To express 5/12 as a decimal fraction.

What is a recurring decimal?

A recurring Decimal is described as also called repeating decimal, which is a decimal digit that only consists of repeating digits after a certain interval after the decimal. For example, 94.642642642..., 213.569569... etc.

What is the fraction?

Fraction is defined as the number of compositions that constitute the Whole.

Here,
Given fraction = 5 / 12
= 0.4166667
Round to thousand
= 0.417

Thus, the required decimal fraction is 0.417.

For more information about recurring decimal check it out here:

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5/12 expressed as a fraction is 0.42

amanda drove to the mountains last weekend. there was heavy traffic on the way there, and the trip took 7 hours. when amanda drove home, there was no traffic and the trip only took 5 hours. if her average rate was 18 miles per hour faster on the trip home, how far away does amanda live from the mountains?

Answers

The distance between the mountains and her residence is 315 miles.

What is speed?

Speed is defined as the ratio of the time distance traveled by the body to the time taken by the body to cover the distance. Speed is the ratio of the distance traveled by time. The unit of speed in miles per hour.

Given that Amanda drove to the mountains last weekend. there was heavy traffic on the way there, and the trip took 7 hours. when Amanda drove home, there was no traffic and the trip only took 5 hours. if her average rate was 18 miles per hour faster on the trip home.

The distance will be calculated as,

Distance = S x 7

The other distance is,

Distance = 5 ( S + 18 )

7S = 5S + 90

S = 45 miles

Distance = 45 x 7

Distance = 315 miles

To know more about Speed follow

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90 miles away since you multiply 18 times 5 would equal 90 miles away.

Select the proper order from least to greatest for 1/2 ,5/6 , 2/7 , 4/2a) 4/2 , 5/6, 1/2, 2/7

b) 4/2, 2/7, /6, 1/2

c) 2/7, 1/2, 5/6, 4/2

d) 2/7, 5/6, 1/2, 4/2

Answers

C. 2/7, 1/2, 5/6, 4/2

Can you solve 64x³+y³ by factoring?

Answers

$64x^3+y^3=(4x)^3+y^3\n\n=(4x+y)[(4x)^2-4xy+y^2]=(4x+y)(16x^2-4xy+y^2)$

$a^3+b^3=(a+b)(a^2-ab+b^2)\n-----------------\n64x^3+y^3=(4x)^3+y^3=(4x+y)[(4x)^2-4x\cdot y+y^2]=\n\n=(4x+y)(16x^2-4xy+y^2)$

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