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monitta
1 year ago
6

Given the lines AB and CD, determine the slope of line CD. Type a numerical answer in the space provided. If necessary, use the

/ key to represent a fraction bar.
Mathematics
1 answer:
adell [148]1 year ago
8 0

Answer:

The answer is Slope of CD = -5/4.

Step-by-step explanation:

The question is missing important information like the values for which the slope has to be find

Points A(0,-1), B(5,3), C(2,3), D(6,-2) is missing in the question

Formula for slope:

                        Slope = (y_{2}- y_{1})/(x_{2} -x_{1})

C(2,3), is  (x_{1},y_{1})

D(6,-2) is (x_{2},y_{2}). for slope of CD.

Putting values in the formula.

                          Slope = (-2-3) / (6-2)

                          Slope = -5/4

This formula can be used for for finding slope for  values of A and B similarly.

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On a coordinate plane, a piecewise function has 2 lines. The first line has a closed circle at (0, 3) and then goes down through
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Answer:

f(-2) = 2

f(0) = 3

f (4) = -1

Step-by-step explanation:

The equation of the straight line passing through the points (0,3) and (-4,1) is  

\frac{y - 1}{1 - 3} = \frac{x - (- 4)}{-4 - 0}

⇒ 2(y - 1) = x + 4

⇒ 2y - 2 = x + 4

⇒ 2y = x + 6

⇒ y = \frac{1}{2} x + 3

Again, the equation of the line passing through the points (0,1) and (4,-1) is

\frac{y - (- 1)}{- 1 - 1} = \frac{x - 4}{4 - 0}

⇒ - 2 ( y + 1) = x - 4

⇒ - 2y = x - 2

⇒ y = 1 - \frac{1}{2}x

Therefore, the function is defined as

f(x) = \frac{1}{2} x + 3 for x ≤ 0 ........... (1) and  

f(x) = 1 - \frac{1}{2}x for x > 0 ............ (2)

Therefore, f(-2) = 2 from equation (1).

f(0) = 3 from equation (1)

And f (4) = -1 from equation (2). (Answer)

6 0
2 years ago
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Suppose that D(r) is a function which gives the population density, in hundreds of people per square mile, within r miles of the
borishaifa [10]

Answer:

a) T(r) = r.D(r)

b) 975 people per square mile.

Step-by-step explanation:

(a)

The units of D(r) are  

\frac{hundreds\;of\;people}{mile^2}

when multiplying the density by the area we get the amount of people in that area, so

T(r)=rmile^2D(r)\frac{hundreds\;of\;people}{mile^2}=rD(r)\;hundreds\;of\;people

(b)

The average rate of change of T(r) over the interval [5,7] is

\frac{T(7)-T(5)}{7-5}=\frac{7D(7)-5D(5)}{2}

but D(7) = 350 and D(5) = 100, so

\frac{7D(7)-5D(5)}{2}=\frac{7*350-5*100}{2}=975

and the average rate of change of T(r) over the interval [5,7] is 975 people per square mile.

5 0
2 years ago
What is the constant of proportionality in the equation y = StartFraction x over 9 EndFraction? 0 StartFraction 1 over 9 EndFrac
Sonja [21]

Answer:

The answer is C.

Step-by-step explanation:

You only need the answer.

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What is the degree of the sin of .19
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Use your calculator.

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Fertiliser is sold in 100kg bags labelled with the amount of nitrogen (N), phosphoric acid (P2O5), and potash (K2O) present. The
anzhelika [568]

Answer:

We need 5 bags of Vigoro Ultra Turf and 4 bags of Parkers Premium fertilizer.

Step-by-step explanation:

Let's first list the percentage compositions of each fertilizer type:

<u>Vigoro Ultra Turf:</u>

Nitrogen (N) = 29 kg

Phosphoric Acid (P2O5) = 3 kg

Potash (K2O) = 4 kg

<u>Parkers Premium</u>

Nitrogen (N) = 18 kg

Phosphoric Acid (P2O5) = 25 kg

Potash (K2O) = 6 kg

We can set up simultaneous equations to find out the amount of 100 kg bags of each fertilizer needed:

x = Vigoro Ultra turf (one bag)

y = Parkers Premium (one bag)

29x + 18y = 217   -Equation 1

3x + 25y = 115     -Equation 2

4x + 6y = 44        -Equation 3

Solving for x and y, we get:

x = 5

y = 4

This means we need 5 bags of Vigoro Ultra Turf and 4 bags of Parkers Premium fertilizer.

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