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3 years ago

What is the distance between points S and T?

Mathematics

2 answers:

Margarita [4]3 years ago

8 0

Answer: 16 units

Step-by-step explanation:

The distance between any two points $x_1$ and $x_2$ on a number line is given by :-

$d=|x_2-x_1|$

From the given picture, there is a number line where point S is at -2 and point T is at 14.

Then, the distance between points S and T will be :_

$d=|14-(-2)|\\\\\Rightarrow\ d=|14+2|=|16|=16\text{ units}$

Hence, the distance between points S and T = 16 units

Alex_Xolod [135]3 years ago

7 0

The distance between points S and T is 16.

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4 years ago

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Paul [167]

Answer:

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Step-by-step explanation:

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3 years ago

(10v^4 + 30v^3 + 2v^2) / 10v

Zina [86]

Given expression is

$\frac{10v^4+30v^3+2v^2}{10v}$

Now we need to simplify this expression. We can begin by factoring numerator and denominator if possible.

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divide numerator and denominator both by 2v

$= \frac{v(5v^2+15v+1)}{5}$

$= \frac{5v^3+15v^2+1v}{5}$

Hence final answer is $\frac{5v^3+15v^2+1v}{5}$

Or you can also keep factored form

$\frac{v(5v^2+15v+1)}{5}$

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4 years ago

Charles can do a job in 1 hour, bill can do the same job in 2 hours, and bob can do the job in 3 hours. How long does it take th

KiRa [710]

Charles can do the whole job in an hour, Bill can do 1/2 of the job in an hour, and Bob does 1/3 of the job in an hour. Therefore, they do a total of 1+1/2+1/3=11/6 of the job in an hour, meaning it takes them 6/11 of an hour. This is 6/11*60=360/11 minutes, or approximately 33 minutes.

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3 years ago

Read 2 more answers

On a coordinate plane, parallelogram R S T U has points (negative 4, 4), (2, 6), (6, 2), and (0, 0). What is the area of paralle

Ad libitum [116K]

Answer:

The area of the parallelogram is;

32 square units

Step-by-step explanation:

The given parameters are;

The coordinates of the parallelogram RSTU = R(-4, 4), S(2, 6), T(6, 2), and U(0, 0)

We note that the area of a parallelogram = Base length × Height

From the drawing of the parallelogram RSTU, we have;

The base length = The length of $\overline {TU}$ = The length of $\overline {SR}$ = √((2 - (-4))² + (6 - 4)²) = 2·√10

The height of a parallelogram is perpendicular to its base length = The line $\overline {VT}$

∴ Where, the slope of the base length = m, the slope of the height = -1/m

The slope, 'm' of $\overline {SR}$ = (6 - 4)/(2 - (-4)) = 1/3

Therefore, the slope of the height = -1/(1/3) = -3

We note that a point on the height is the point 'T', therefore, the equation of the line in point and slope form is therefore;

y - 0 = -3·(x - 0)

∴ y = -3·x

Therefore, the coordinates of the point 'V' is given by the simultaneous solution of the equations of $\overline {SR}$ and $\overline {VT}$

The equation of the line $\overline {SR}$ in point and slope form from the point 'R' and the slope 'm = 1/3' is given as follows;

y - 4 = (1/3) × (x - (-4)) = (1/3) × (x + 4)

y = x/3 + 4/3 + 4 = x/3 + 16/3

y = x/3 + 16/3

We then have the coordinate at the point 'V' (x, y) is given as follows;

-3·x = x/3 + 16/3

-9·x = x + 16

-10·x = 16

x = -16/10 = -1.6

x = -1.6

∴ y = -3·x = -3 × -1.6 = -4.8

y = 4.8

The coordinate at the point, V = (-1.6, 4.8)

The length of the line $\overline {VT}$ = The height of the parallelogram = √((-1.6 - 0)² + (4.8 - 0)²) = 8/5·√10

The height of the parallelogram = 8/5·√10

The area of the parallelogram, A = Base length × Height

∴ A = 2·√(10) × 8/5·√(10) = (16/5) × 10 = 32

The area of the parallelogram, A = 32 square units.

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3 years ago

Read 2 more answers