Complete the following word problems using systems of equations.
1. Astronauts traveling to the International Space Station have to be very careful about
weight (it takes about 9 lbs of rocket fuel to send 1 lb of stuff to the station). Each
astronaut can bring approximately 11 lbs of personal items (mementos and clothes)
with them into space. Each memento weighs about 0.1 lb, and each item of clothing
weighs about 0.5 lbs. If an astronaut wanted to bring 30 items with them, how many
mementos and pieces of clothing would they bring?

Answer:

[tex]d = 15.620499[/tex]

Step-by-step explanation:

To solve this question, we must use the following distance equation:

[tex]\sqrt{(x_{2}-x_{1})^{2} + (y_{2}-y_{1})^{2} }[/tex]

Plug your coordinates into the equation. Remember, a coordinate is denoted as (x, y).

[tex]\sqrt{(12-2)^{2} + (13-1)^{2}}[/tex]

[tex]\sqrt{(10)^{2} + (12)^{2}}[/tex]

[tex]\sqrt{100+144}[/tex]

[tex]\sqrt{244} = 15.620499[/tex]

not rlly surw if you are supposed to be putting dots there but if you are, I would put one a little bit before the first line for the 82.4 and one in the middle of the 600 and the line in the middle

Answer:

65

Step-by-step explanation:

Answer:

f = 65

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

201.5 = f + 136.5

Step 2: Flip the equation.

f + 136.5 = 201.5

Step 3: Subtract 136.5 from both sides.

f + 136.5 − 136.5 = 201.5 − 136.5

f = 65

Answer:

B. Rectangle T, Rectangle P, Rectangle S.

Step-by-step explanation:

To determine which list shows the correct order of the length of the diagonals of the rectangles from shortest to longest, let all the lengths be in decimal form:

Rectangle P = 6.7 cm

Rectangle S = [tex] \frac{34}{5} cm [/tex] = 6.8 cm

Rectangle T = [tex] \sqrt{36.5} cm [/tex] ≈ 6.04

Thus:

6.04 cm < 6.7 cm < 6.8 cm

Therefore, from the shortest to the longest, we have:

Rectangle T < Rectangle P < Rectangle S.

ITS AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAfor real I'm serious

Draw from (3, -1.5) to (-2, 6)

Answer:78

Step-by-step explanation:

Answer:

y= -3+2x/3 ...i think

Step-by-step explanation:

Answer:

sorry don't know the answers and please follow me

Answer:

y=3/2x-5

when finding the equation of a line, we use this formula

y=mx+b

where Y= a point on the y-axis

M= ∆y/∆x

x= a point on the x-axis

and b = intercept

Step-by-step explanation:

so to in this case, we are given y= 4, x=6 and y-int = -5

substitute the value in the given equation,

therefore, 4=6m-5

4+5=6m

9/6=M

3/2=m

Answer y=3/2x-5 that is the equation of the line

Answer:

Alana bought 4 cans of paint additive

Step-by-step explanation:

Proportions

If a proportional amount of x is to be distributed between y elements, each one of them gets x/y portions.

For example, if we have 100 coins and distribute evenly between 20 boxes, each box will receive 100/20=5 coins.

Alana bought 1/2 of a liter of the special paint additive and evenly distributed it between an unknown number of cans, let's call it C. We also know each can received 1/8 of a liter of the additive. That is the proportion of the 1/2 liter of additive.

We can establish the following condition:

[tex]\displaystyle \frac{1/2}{x}=\frac{1}{8}[/tex]

Solving for x:

[tex]\displaystyle \frac{1/2}{\frac{1}{8}}=x[/tex]

Transform the division into a product:

[tex]\displaystyle x=\frac{1}{2}\cdot\frac{8}{1}=4[/tex]

Alana bought 4 cans of paint additive

Answer:

0.39

Step-by-step explanation:

Answer:39/100

Step-by-step explanation: it can't be simplified

Answer:

2      -1          -2

Step-by-step explanation:

Answer:

2/6 has a repeating decimal

Step-by-step explanation:

if x is real number then there are infinte numbers between 3 and 5.

if x is natural number then there is just one solution and that is number 4

7.810 Rounded to the nearest thousandth

Answer:

not a polynomial

Step-by-step explanation:

A polynomial is a combination of terms separated by + or − signs. A polynomial does not contain variables raised to negative or fractional exponents, variables in the denominator or under a radical, or any special features such as trigonometric functions, or logarithms

Answer:

False is a Non-polynomial

Answer:

Step-by-step explanation:

Did u get an answer???

Answer: The answer is A.  

Step-by-step explanation:

since $12 is the amount of money he gets from selling scarves you have to subtract $2 from that because that's the amount of money he losses to make the scarves. then you have to subtract $45 because he had to pay for the booth so the answer is P(x) = 10x - 45

Answer:

it's 6 cubic feet look you must count all the sides together also I took the test this cube has 6 sides so your answer will be 6 cubic feet ;)

Step-by-step explanation:

Answer:

The probability that the sample mean would differ from the population mean by greater than 2.4 gallons is 0.86558

Step-by-step explanation:

The given parameters are;

The mean, [tex]\bar x[/tex] = 101 gallons

The population mean = μ

The variance, σ² = 49

The number of racing cars, n = 43

The probability that the sample mean would differ from the population mean by greater than 2.4 gallons is given as follows;

P([tex]\left | \bar x - \mu \right |[/tex]) >2.4 = P(2.4 > [tex]\left | \bar x - \mu \right |[/tex] >-2.4)

The formula for the test of the mean, Z₀, is given as follows;

[tex]Z_0 = \dfrac{\bar x - \mu}{\dfrac{\sigma}{\sqrt{n} } }[/tex]

Therefore, we have;

[tex]P \left (\dfrac{2.4}{\dfrac{\sqrt{49} }{\sqrt{43} } } >Z> \dfrac{-2.4}{\dfrac{\sqrt{49} } {\sqrt{43} } } \right) = P \left (\dfrac{2.4}{\dfrac{7 }{\sqrt{43} } } >Z> \dfrac{-2.4}{\dfrac{7} {\sqrt{43} } } \right)[/tex]

Which gives;

P([tex]\left | \bar x - \mu \right |[/tex]) >2.4 = P(2.25 > Z > -2.25)

(We round up to 2.25 because that is the accuracy of the z-table)

From which we have;

P(Z > -2.25) - P(Z > 2.25) = (1 - P(Z < -2.25)) -  (1 - P(Z < 2.25))

P([tex]\left | \bar x - \mu \right |[/tex]) >2.4 =  (1 - 0.1222) - (1 - 0.98778) = 0.86558

The probability that the sample mean would differ from the population mean by greater than 2.4 gallons = 0.86558.

Answer:

A is incorrect

Step-by-step explanation:

Point x is negative, so you need to subtract the negative. In A, they are subtracting 5, not negative 5.

Answer:Total Weight of Bowl W = 340 + (12.5T) grams

Step-by-step explanation:

Answer:

4,360

Step-by-step explanation:

      3,178

   +

      1,452        

   =

     4,360

Answer:

The temperature at the base camp Friday evening is - 6 degrees Celsius.

Step-by-step explanation:

To get the temperature at a mountain base camp on Friday evening, we must translate statement into a mathematical form:

(i) The temperature at a moutain base camp was - 2 degress Celsius on Thursday:

[tex]T_{o} = -2\,^{\circ}C[/tex]

(ii) Friday morning, the temperature was 1 degree Celsius lower than it was on Thursday:

[tex]\Delta T_{1} = -1\,^{\circ}C[/tex]

(iii) Friday evening, the temperature was 3 degrees Celsius lower that it was that morning:

[tex]\Delta T_{2} = -3\,^{\circ}C[/tex]

The temperature at the base camp Friday evening is:

[tex]T = T_{o}+\Delta T_{1}+\Delta T_{2}[/tex]

[tex]T = -2\,^{\circ}C-1\,^{\circ}C-3\,^{\circ}C[/tex]

[tex]T = -6\,^{\circ}C[/tex]

The temperature at the base camp Friday evening is - 6 degrees Celsius.

Answer:

D) -6 degrees Celsius

Answer:

3/4

Step-by-step explanation:

We can use the formula [ y2-y1/x2-x1 ] to solve.

1-4/-4-0

-3/-4

3/4

Best of Luck!

Answer:

2.25

Step-by-step explanation:

-3x+10=5x-8

    +8       +8

-3x+18=5x

+3x     +3x

      18=8x

      _    _

      8    8

   2.25=x

Answer:

x=8

Step-by-step explanation:

Answer: 4 1/4 hours

Step-by-step explanation:

Answer:

it will take 4 hours and 30 minutes

Step-by-step explanation:

first you have to divide 4 by 17 so you would get 4 with a remainder of one. Next, four will be the number of hours and  the 1 is the 30 minutes.