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3 years ago

A triangle has sides which are consecutive odd integers and an

Mathematics

1 answer:

wolverine [178]3 years ago

8 0

Answer:

Perimeter = 15

Step-by-step explanation:

We are told that the length of each of the 3 sides of the triangle are consecutive odd integers.

Thus means that we can write the 3 terms as;

(x - 2), x, (x + 2)

Thus, perimeter is;

P = (x - 2) + x + (x + 2)

P = 3x

If an angle is 120°, it means that the corresponding side that is directly opposite the angle is the largest side of the triangle.

Thus, this side is (x + 2)

Using cosine rule, we have;

(x + 2)² = x² + (x - 2)² - 2(x(x - 2))cos 120

Expanding, we have;

x² + 4x + 4 = x² + x² - 4x + 4 - (2x² + 4x)(-½)

This reduces to;

4x = x² - 4x + x² - 2x

2x² = 10x

2x = 10

x = 10/2

x = 5

Thus, other sides are;

(x - 2) = 5 - 2 = 3

And (x + 2) = 5 + 2 = 7

So,perimeter is;

P = 3x = 3 × 5 = 15

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the radius of a circle is 9 times of the radius of a smaller circle. the area of the smaller circle is 50 square cenimeters. wha

notsponge [240]

Answer:

4050 cm²

Step-by-step explanation:

This is a question of scale factors:

The radius of the larger circle is 9× that of the smaller circle;

This is the linear scale factor of the enlargement of the smaller to larger circle;

The scale factor of the area pertains to 2 dimensions so the scale factor will be the square of the linear scale factor, which is:
9² = 81

The area of the larger circle is found by the area of the smaller circle multiplied by this number:
50 × 81 = 4050

4 0

2 years ago

Help me I've been stuck forever! it is an absolute value equation btw.

ehidna [41]

Answer:

${n=\frac{-11}{3} ,3}$

Step-by-step explanation:

Original problem: $2|n+7|=|4n+8|$

Get rid of the absolute value signs by breaking the problem down into two equations, the positive and negative cases.

The first case, the positive case, will be formed by just changing the absolute value symbols ( $|$ ) into parentheses.

$2(n+7)=(4n+8)$

The next case, the negative case, will be formed by changing the absolute value symbols into parentheses as well but the $(4n+8)$ will be multiplied by negative 1.

$2(n+7)=-(4n+8)$

Let's solve the first equation we created with the positive case. Start by getting rid of the parentheses on the right side of the equation.

$2(n+7)=4n+8$

Distribute 2 inside the parentheses.

$2n+14=4n+8$

Combine like terms by subtracting 2n and 8 from both sides of the equation.

$6=2n$

Isolate and solve for n by dividing both sides of the equation by 2.

$3=n$

One of the solutions is 3. Let's solve the second equation we created. Distribute the negative sign inside the parentheses on the right side of the equation.

$2(n+7)=-4n-8$

Now distribute 2 inside the parentheses on the left side of the equation.

$2n+14=-4n-8$

Combine like terms by adding 4n to both sides of the equation.

$6n+14=-8$

Subtract 14 from both sides of the equation.

$6n=-22$

Divide both sides of the equation by 6.

$n=\frac{-22}{6}$

This fraction can be simplified by dividing the top and bottom by 2 to $\frac{-11}{3}$ .

You can check for extraneous solutions by substituting 3 and $\frac{-11}{3}$ back into the original equation. There are no extraneous solutions in this particular problem.

This means that the two solutions of n are 3 and $\frac{-11}{3}$ .

$\boxed{n=\frac{-11}{3} ,3}$

4 0

3 years ago

A culture started with 2,000 bacteria. After 2

Ket [755]

Answer: In 10 hours, 4000 bacteria will be present.

Step-by-step explanation:

Given that 2000 bacteria grew to 2400 in 2 hours,

growth/ increase rate = 2400 - 2000

= 400 bacteria increase in 2 hours

Per hour is therefore 400/2 = 200 bacteria increase per hour

If the bacteria increases by 200 per hour

If 200 = 1 hour

X = 10 hours

We cross multiply:

X = 200 x 10

X = 2000

Therefore, a culture with 2000 bacteria at the same growth rate will have increased by additional 2000 in 10 hours

So, after 10 hours, number of bacteria will be 2000 + 2000 = 4000 bacteria

3 0

3 years ago

PLEASE HELP

densk [106]

For this case we have that by definition, a function is of the form:

$y = f (x)$

So, we have the following system of equations:

$y = -6x + 2\\y = -2x + 4$

Equating the equations we have:

$-6x + 2 = -2x + 4$

Adding 2x to both sides of the equation:

$-6x + 2x + 2 = 4\\-4x + 2 = 4$

Subtracting 2 from both sides of the equation:

$-4x = 4-2\\-4x = 2$

Dividing between -4 on both sides of the equation:

$x = \frac {2} {- 4}\\x = - \frac {1} {2}$

Thus, the value of the variable "x" is -0.5.

Answer:

-0.5

6 0

3 years ago

SOOO this jejwijsnxnJjxnndjjs

Tcecarenko [31]

Answer:

Step A) 250 times 3 months + 500 cause you already have that in your bank account= 1250

Step B) 12+12=24 so 250 times 24=6000+ 500 cause you already have that in your bank account= 6500

Step C) 8,300- 6500= 1800 then, 250 time 5 + 500= 1750, and 250 times 6 = 1500+500=2000 so you can go with whatever.

Step D) 3 years= 36 months so 250 times 36 months= 9000 so in three yrs you should have about 9500 bc you need to add the 500 on again. sry I could not do the graph but I hoped I helped. :)

Step-by-step explanation:

8 0

2 years ago