What is pi rounded to the nearest 15th

F divides HJ in the ratio 3:1. If H = (-11,7) and J = (5,3), what are the<br> coordinates of F?

Hatshy [7]

Answer:

The coordinates of HF are (1, 4)

Step-by-step explanation:

The parameters of the line are;

The coordinate of the end points are H = (-11, 7), and J = (5, 3)

The ratio by which the point F divides the line = 3:1

The segments in the line are HF, and FJ

Therefore;

The fraction of the length of HJ that is represented by HF = 3/(3 + 1) × HJ = 3/4 × HJ

HF = 3/4 × HJ

Which gives the coordinates of the point F as follows;

Coordinate of F = (-11 +(5 - (-11))×3/4, 7 + (3 - 7)×3/4) = (1, 4)

The coordinates of F are (1, 4)

We check the length of HF, from the equation for the length to of a line to get;

$l = \sqrt{\left (y_{2}-y_{1} \right )^{2}+\left (x_{2}-x_{1} \right )^{2}}$

$l_{HF} = \sqrt{\left (4-7 \right )^{2}+\left (1-(-11) \right )^{2}} = \sqrt{\left (-3 \right )^{2}+\left (12 \right )^{2}} = 3\cdot \sqrt{17}$

Similarly, we check the length of HJ, to get;

$l_{HF} = \sqrt{\left (3-7 \right )^{2}+\left (5-(-11) \right )^{2}} = \sqrt{\left (-4 \right )^{2}+\left (16 \right )^{2}} = 4\cdot \sqrt{17}$

The length of HF = 3·√(17)

The length of HJ = 4·√(17)

Therefore, from HF = 3/4× HJ, we have;

HF = 3/4 × 4·√(17) = 3·√(17)

Therefore, the coordinates of HF are (1, 4)

7 0

3 years ago

Ratio, proportion, percent 52 plates to 24 bowls

AleksAgata [21]

So to get a ratio of plates to bowl, you divide both the numbers by a common multiple, which I found the greatest to be 4. So you divide 52 by 4 and 24 by for to get a ratio of 13 plates to 6 bowls. (Also written as: 13:6, 13/6, or 13 to 6)

8 0

3 years ago

How to do graphs of quadratic functions

Anastaziya [24]

Answer:

The Graph of a Quadratic Function

A quadratic function is a polynomial function of degree 2 which can be written in the general form.

Step-by-step explanation:

Example: Graph: f(x)=−x2−2x+3.

Solution:

Step 1: Determine the y-intercept. To do this, set x=0 and find f(0).

f(x)f(0)===−x2−2x+3−(0)2−2(0)+33

The y-intercept is (0,3).

Step 2: Determine the x-intercepts if any. To do this, set f(x)=0 and solve for x.

f(x)000x+3x======−x2−2x+3−x2−2x+3x2+2x−3(x+3)(x−1)0−3orx−1x==Set f(x)=0.Multiply both sides by −1.Factor.Set each factor equal to zero.01

Here where f(x)=0, we obtain two solutions. Hence, there are two x-intercepts, (−3,0) and (1,0).

Step 3: Determine the vertex. One way to do this is to first use x=−b2a to find the x-value of the vertex and then substitute this value in the function to find the corresponding y-value. In this example, a=−1 and b=−2.

x====−b2a−(−2)2(−1)2−2−1

Substitute −1 into the original function to find the corresponding y-value.

f(x)f(−1)====−x2−2x+3−(−1)2−2(−1)+3−1+2+34

The vertex is (−1,4).

Step 4: Determine extra points so that we have at least five points to plot. Ensure a good sampling on either side of the line of symmetry. In this example, one other point will suffice. Choose x=−2 and find the corresponding y-value.

x −2 y 3f(−2)=−(−2)2−2(−2)+3=−4+4+3=3Point(−2,3)

Our fifth point is (−2,3).

Step 5: Plot the points and sketch the graph. To recap, the points that we have found are

y−intercept:x−intercepts:Vertex:Extra point:(0,3)(−3,0) and (1,0)(−1,4)(−2,3)

Answer:

4 0

3 years ago

a purse contains 25p coins and 50 p coins. the total amount in the purse is rs.25. if the number of 50 p coins is double the num

erica [24]

Let the total no. of 25 p coins be x
50p coins = 2x

Value of 25 p coins ( in rupees) = 0.25*x =0.25x
Value of 50p coins ( in rupees) = 0.5*2x = x

0.25x+x = 25
1.25x =25
x = 25/1.25 = 20

no. if 25p coins = 20
and 50p coins = 2*20 = 40

4 0

3 years ago

Whats the distance between (-1,4) and (1,-5)

Bess [88]

Answer:

11

Step-by-step explanation:

8 0

3 years ago