If g(x) is a function that represents the cost if x packs of pens, write an equation which shows that 8 packs of pens costs $30

What is the area of triangle DEF?

FrozenT [24]

Answer:

$A=2\sqrt{14}\ units^2$

Step-by-step explanation:

we know that

Heron's Formula is a method for calculating the area of a triangle when you know the lengths of all three sides.

so

$A=\sqrt{s(s-a)(s-b)(s-c)}$

where

a, b and c are the length sides of triangle

s is the semi-perimeter of triangle

we have

$a=5\ units,b=6\ units,c=3\ units$

<em>Find the semi-perimeter s </em>

s= $\frac{5+6+3}{2}=7\ units$

Find the area of triangle

$A=\sqrt{7(7-5)(7-6)(7-3)}$

$A=\sqrt{7(2)(1)(4)}$

$A=\sqrt{56}\ units^2$

simplify

$A=2\sqrt{14}\ units^2$

3 0

2 years ago

Determine whether the three segment lengths will produce a triangle. Type yes or no in the space provided.

tresset_1 [31]

Answer:

20 , 20 , 30 will produce a triangle

Step-by-step explanation:

* Lets study how to know if the lengths of the three segments

can formed a triangle

- It is a fact that in any triangle the sum of the smallest two sides

must be greater than the largest side

- Lets study some examples

# If the lengths of the three segments are 5 , 6 , 7

∵ 5 and 6 are the smallest

∴ 5 + 6 = 11

∵ 11 > 7 ⇒ the sum greater than the 3rd side

∴ 5 , 6 , 7 can formed a triangle

# If the lengths of the three segments are 5 , 7 , 12

∵ 5 and 7 are the smallest

∴ 5 + 7 = 12

∵ 12 = 12 ⇒ the sum equal the 3rd side

∴ 5 , 7 , 12 can not formed a triangle

# If the lengths of the three segments are 10 , 12 , 24

∵ 10 and 12 are the smallest

∴ 10 + 12 = 22

∵ 22 < 24 ⇒ the sum less than the 3rd side

∴ 10 , 12 , 24 can not formed a triangle

* Now lets solve the problem

∵ The length of the three segments are 20 , 20 , 30

∵ 20 and 20 are the smallest

∴ 20 + 20 = 40

∵ 40 > 30 ⇒ the sum greater than the 3rd side

∴ 20 , 20 , 30 will produce a triangle

5 0

2 years ago

A lottery game has balls numbered 1 through 21. What is the probability of selecting an even numbered ball or an 8? Round to nea

Viktor [21]

Answer: 0.476

Step-by-step explanation:

Let A = Event of choosing an even number ball.

B = Event of choosing an 8 .

Given, A lottery game has balls numbered 1 through 21.

Sample space: S= {1,2,3,4,5,6,7,8,...., 21}

n(S) = 21

Then, A= {2,4,6,8, 10,...(20)}

i.e. n(A)= 10

B= {8}

n(B) = 1

A∪B = {2,4,6,8, 10,...(20)} = A

n(A∪B)=10

Now, the probability of selecting an even numbered ball or an 8 is

$P(A\cup B)=\dfrac{n(A\cup B)}{n(S)}$

$=\dfrac{10}{21}\approx0.476$

Hence, the required probability =0.476

7 0

2 years ago

What is the value of x in 16 to the 2nd power = x

Zepler [3.9K]

16^2 is 16•16 so x would equal 256

4 0

3 years ago

Read 2 more answers

Find the length of the segment with endpoints of (3, 2) and (-3, -6).

nevsk [136]

The distance between (3, 2) and (-3, -6) is 10 units

The correct answer is B) 10

Further explanation:

Given points are:

(x1,y1) = (3,2)

(x2,y2)=(-3,-6)

The distance formula is given by:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Putting the values

$d=\sqrt{(-3-3)^2+(-6-2)^2}\\=\sqrt{(-6)^2+(-8)^2} \\=\sqrt{36+64}\\ =\sqrt{100}\\d=10$

The distance between (3, 2) and (-3, -6) is 10 units

Keywords: Magnitude, Distance

Learn more about magnitude at:

#LearnwithBrainly

8 0

3 years ago