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3 years ago

Write the slope-intercept form of the line that passes through the point (1, 0) and is parallel to x-y=7.

1 answer:

6 0

The slope-intercept form of x - y = 7 is y = x - 7. The slope of that line is 1. That means the slope of the line that also goes through (1, 0) is also 1. If you use the point-slope formula, the answer you will receive is y = x - 1.

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14 100 000 in scientofic notation

Ann [662]

1.41 x 10^7 you move the decimal over to the left until you have a number between 1-9

8 0

3 years ago

Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used. Consider the functions given below. SEE F

Wewaii [24]

Answer:

1. $P(x)$ ÷ $Q(x)$ ---> $\frac{-3x + 2}{3(3x - 1)}$

2. $P(x) + Q(x)$ ---> $\frac{2(6x - 1)}{(3x - 1)(-3x + 2)}$

3. $P(x) - Q(x)$ ---> $\frac{-2(12x - 5)}{(3x - 1)(-3x + 2)}$

4. $P(x)*Q(x)$ --> $\frac{12}{(3x - 1)(-3x + 2)}$

Step-by-step explanation:

Given that:

1. $P(x) = \frac{2}{3x - 1}$

$Q(x) = \frac{6}{-3x + 2}$

Thus,

$P(x)$ ÷ $Q(x)$ = $\frac{2}{3x - 1}$ ÷ $\frac{6}{-3x + 2}$

Flip the 2nd function, Q(x), upside down to change the process to multiplication.

$\frac{2}{3x - 1}*\frac{-3x + 2}{6}$

$\frac{2(-3x + 2)}{6(3x - 1)}$

$= \frac{-3x + 2}{3(3x - 1)}$

2. $P(x) + Q(x)$ = $\frac{2}{3x - 1} + \frac{6}{-3x + 2}$

Make both expressions as a single fraction by finding, the common denominator, divide the common denominator by each denominator, and then multiply by the numerator. You'd have the following below:

$\frac{2(-3x + 2) + 6(3x - 1)}{(3x - 1)(-3x + 2)}$

$\frac{-6x + 4 + 18x - 6}{(3x - 1)(-3x + 2)}$

$\frac{-6x + 18x + 4 - 6}{(3x - 1)(-3x + 2)}$

$\frac{12x - 2}{(3x - 1)(-3x + 2)}$

$= \frac{2(6x - 1}{(3x - 1)(-3x + 2)}$

3. $P(x) - Q(x)$ = $\frac{2}{3x - 1} - \frac{6}{-3x + 2}$

$\frac{2(-3x + 2) - 6(3x - 1)}{(3x - 1)(-3x + 2)}$

$\frac{-6x + 4 - 18x + 6}{(3x - 1)(-3x + 2)}$

$\frac{-6x - 18x + 4 + 6}{(3x - 1)(-3x + 2)}$

$\frac{-24x + 10}{(3x - 1)(-3x + 2)}$

$= \frac{-2(12x - 5}{(3x - 1)(-3x + 2)}$

4. $P(x)*Q(x) = \frac{2}{3x - 1}* \frac{6}{-3x + 2}$

$P(x)*Q(x) = \frac{2*6}{(3x - 1)(-3x + 2)}$

$P(x)*Q(x) = \frac{12}{(3x - 1)(-3x + 2)}$

4 0

3 years ago

Chloe and Libby want to tie Ryan to a bunch of approximately spherical helium balloons of diameter 0.3m. The volume of each ball

dem82 [27]

Answer: Aproximately 2,525 balloons

Step-by-step explanation:

1. Find the volume of a balloon with the formula given in the problem, where $r$ is the radius ( $r=\frac{0.3m}{2}=0.15m$ ), then:

$V=4(0.15m)^{3}=0.0135m^{3}$

2. Convert the volume from m³ to lliters by multiplying it by 1,000:

$V=0.0135m^{3}*1000=13.5L$

3. You know that that 1 liter of helium can lift 1 gram and that Ryan weighs 5 stone and 5 pounds. So you must make the following conversions:

1 g=0.0022 lb

From 5 stones to pounds

$(5stone)(\frac{14pounds}{1stone})=70pounds=70lbs$

4. Then Ryan's weigh is:

5lb+70lb=75lb

5. Then, if 1 liter of helium can lift 0.0022 lb, to lift 75 lb (which is the weight of Ryan) they need:

$\frac{75lb*1L}{0.0022lb}=34,090.90L$

6. Then, to calculate the aproximated number of balloons they need to make him float (which can call $n$ ), you must divide the liters of helium needed to lift the weight of Ryan by the volume of a balloon, then the result is:

$n=\frac{34,090.90L}{13.5L}$

$n=2,525.25$ ≈2,525 balloons.

5 0

3 years ago

How did astronomer Yi Xing (A.D. 683-727) contribute to the development of mathematics in china?

SSSSS [86.1K]

Answer:

Yi Xing invented the astronomical clock and introduced some new methods of interpolation in mathematics.

Step-by-step explanation:

Yi Xing was both an astronomer and a mathematician during the era. He invented the astronomical clock which was more accurate than the initial water and Sun's clock in use.

Furthermore, Yi Xing also discovered some new methods of interpolation in mathematics of which the meaning and interpretation became controversial. Interpolation is a method majorly in mathematics that can be used to estimate a value of a function from its discrete values. It involves first order differences and second order differences.

Also, Yi Xing was able to design a calendar in A.D. 727.

4 0

3 years ago

Can any one help please :)

Gemiola [76]

Answer:

Step-by-step explanation:

First, subtract 3 by the numbers

-8 > 4x > 4

Remember to flip the inequality signs

Second, divide all the numbers by 4

-2 < x < 1

Flip the inequality signs again

-2 > x > 1

I am not very experienced with these problems so I might be wrong.

7 0

3 years ago

Read 2 more answers