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Genrish500 [490]
3 years ago
13

An archaeological site is to be made accessible for viewing by the public. To do this, archaeologists built two straight paths f

rom point A to point B and from point B to point C as shown in the following diagram. The length of path AB is 185 m, the length of path BC is 250 m, and angle B is 125°, diagram not to scale Archaeological Site a. Find the length of AC​

Mathematics
1 answer:
Jobisdone [24]3 years ago
5 0

Answer:

387 km

Step-by-step explanation:

The length of AC, b can be obtained using the cosine rule ; using the cosine relation:

b² = a² + c² - 2ac CosB

b² = 250² + 185² - 2(250*185) Cos125

b² = 62500 + 34225 - 92500 * −0.573576

b² = 96725 + 53055.820

b² = 149780.82

b = sqrt(149780.82)

b = 387.01527

b = 387 km (nearest whole number)

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Discounted price before sales tax = 75/100 x (40 + 24 + 18 x 3) = 3/4 x (64 + 54) = 3/4 x 118 = $88.5

Total price inclusive of sales tax = 107/100 x 88.5 = $94.69

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3 years ago
Solve: 2x-3=6 I am stuck
Leni [432]
   
\displaystyle  \\  
2x - 3 = 6 \\  \\ 
2x = 6+3 \\  \\ 
2x = 9 \\  \\ 
x =  \boxed{\frac{9}{2}} = \boxed{4\frac{1}{2}} = \boxed{4,5}



6 0
3 years ago
Read 2 more answers
Evaluate the discriminant of -3x2+5-4=0
krok68 [10]

Answer:

-23

Step-by-step explanation:

A quadratic equation is given to us and we are interested in finding the discriminant of the quadratic equation . As we know that ,

If the quadratic equation is in Standard form ,

\sf\longrightarrow ax^2+bx + c = 0

The discriminant is ,

\sf\longrightarrow D = b^2-4ac

The given quadratic equation is ,

\sf\longrightarrow -3x^2 +5x - 4 = 0

On comparing it with the Standard form , we have ,

  • a = (-3)
  • b = 5
  • c = (-4)

So that ,

\sf\longrightarrow D = (5)^2 - 4(-3)(-4)\\

\sf\longrightarrow D = 25 - 48\\

\sf\longrightarrow \bf D = -23

Also note that if D < 0 , then the roots are complex conjugates .

<h3>Hence the discriminant is (-23).</h3>

5 0
2 years ago
Suppose that a household's monthly water bill (in dollars) is a linear function of the amount of water the household uses (in hu
notsponge [240]

The monthly cost for 17 hundred of cubic feet is $52.13.

<h3>What is a linear equation?</h3>

A linear equation is in the form:

y = mx + b

Where y,x are variables, m is the rate of change and b is the initial value of y.

Let y represent the bill paid for x HCF of water.

The slope is 1.45, hence m = 1.45.

The monthly cost for 13 HCF is $46.33, hence:

46.33 = 1.45(13) + b

b = 27.48

y = 1.45x + 27.48

For 17 HCF:

y = 1.45(17) + 27.48 = 52.13

The monthly cost for 17 hundred of cubic feet is $52.13.

Find out more on linear equation at: brainly.com/question/14323743

6 0
2 years ago
Which graph represents the given equation?<br> y<br> =<br> NICO<br> + 4r – 2
guajiro [1.7K]

Equations can be represented on graphs by plotting the corresponding x and y values. The graph of y = \frac{3}{2}x^2 + 4x - 2 is option (B).

Given that:

y = \frac{3}{2}x^2 + 4x - 2

First, we check the y intercept of y = \frac{3}{2}x^2 + 4x - 2

This is when x = 0

So, we have:

y = \frac{3}{2}x^2 + 4x - 2

y = \frac{3}{2} \times 0^2 + 4\times 0 - 2

y = - 2

This point is represented as: (0,-2)

Next, check the equation when x = 1

So, we have:

y = \frac{3}{2}x^2 + 4x - 2

y = \frac{3}{2} \times 1^2 + 4\times 1 - 2

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This point is represented as: (1,3.5)

From the list of given options (see attachment).

Only graph B has the (0,-2) and (1,3.5) on its curve.

Hence, option (B) is correct.

Read more about equation of graphs at:

brainly.com/question/1971145

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