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4 years ago

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Triangle ABC is such that AB = 3cm , BC = 4cm , angle ABC = 120 and BAC = theta : Write down in terms of theta , and expression

for angle ACB ( why is this (60-theta) and not (120-theta)? Next question asks for using the sine rule (or otherwise) show that tan theta = 2sqrt3 /(5) A diagram would be pretty cool guys

1 answer:

lakkis [162]4 years ago

8 0

1)inside the triangule is 180º .There are 3 angules, one with 120º, theta and
angle ACB, lets call it x.

x + theta + 120 = 180
x + theta= 180-120
x + theta= 60
x= 60- theta
angle ACB= 60- theta

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The formula for finding the distance traveled, based on speed and time, is

Phoenix [80]

Answer and explanation:

The formula for finding the distance traveled, based on speed and time, is $D=R\times T$

Where, D is distance , R is rate (speed) and T is time

Units must be consistent.

1) Given : If the unit for D is miles and the unit for T is minutes.

To find : What must the units for R be?

Solution :

$R=\frac{D}{T}$

Now we put unit,

$R=\frac{miles}{minutes}$

The unit of R is miles per minute.

2) Given : If a bicyclist rides for 160 minutes at an average speed of 17 miles per hour.

To find : How far was the ride ?

Solution :

Speed R=17 miles per hour

Time T=160 minutes

Convert into hours,

$1\text{ minute}=\frac{1}{60}\text{ hour}$

$160\text{ minute}=\frac{160}{60}\text{ hour}$

$160\text{ minute}=2.67\text{ hour}$

Substitute value in the formula,

$D=R\times T$

$D=17\times 2.67$

$D=45.39\text{ miles}$

The distance is 45.4 miles.

3) Given : A bicyclist ride to cover 12 miles in 1.5 hours.

To find : At what speed must a bicyclist ride ?

Solution :

Distance D=12 miles

Time T=1.5 hour

Substitute value in the formula,

$R=\frac{D}{T}$

$R=\frac{12}{1.5}$

$R=8$

The speed is 8 miles per hour.

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3 years ago

Find the percent of change round to the nearest percent original: 50 new: 70

kykrilka [37]

The percent change is 40%

Step-by-step explanation:

The percent change is given by the formula

$Percent\ change=\frac{New\ value-Original\ value}{Original} * 100$

Here

New value = 70

Original value = 50

Putting the values in the formula

$Percent\ change=\frac{70-50}{50}*100\\=\frac{20}{50}*100\\=0.4*100\\=40\%$

The percent change is 40%

Keywords: Percentage

Learn more about percentage at:

#LearnwithBrainly

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4 years ago

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Lera25 [3.4K]

Answer:

The second choice, $(-1,\, 12)$ .

Step-by-step explanation:

Note, that the expression $y = f(x)$ is an equation. A point $(x,\, y)$ is on the graph of $y = f(x)\!$ if and only if the value of $x$ and $y$ satisfy this equation; that is: in other words, the $y\!$ -coordinate of that point (the second number in the tuple) should be equal to $f(x)$ , which is equal to $(-3\, x +9)$ (evaluated where $x\!$ is equal to the first number in the tuple.

For each tuple in the choices, calculate the value of $f(x)$ where $x$ is equal to the first number of each tuple. Compare the result to the second number in that tuple. That choice corresponds to a valid point on $y = f(x)$ only if these two numbers match.

First choice: $x = 1$ , $f(x) = f(1) = -3 + 9 = 6$ . That's not the same as the second number, $-10$ . Therefore, this point isn't on the graph of $y = f(x)$ .
Second choice: $x = -1$ , $f(x) = f(-1) = (-3)\times (-1) + 9 = 3 + 9 = 12$ . That matches the second number in the tuple. Therefore, this point is on the graph of $y = f(x)$ .
Third choice: $x = 2$ , $f(x) = f(2) = (-3)\times 2 + 9 = 3$ . That's not the same as the second number, $(-3)$ . Therefore, this point isn't on the graph of $y = f(x)$ .
Fourth choice: $x = -2$ , $f(x) = f(-2) = (-3)\times (-2) + 9 = 15$ . That's not the same as the second number, $13$ . Therefore, this point isn't on the graph of $y = f(x)$ .

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