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2 years ago

What is the value of x? If necessary leave your answer in the simplest radical form.

Mathematics

1 answer:

frutty [35]2 years ago

4 0

<h3>Answer: 32</h3>

Explanation:

This is a 30-60-90 triangle as shown by the angles. These types of triangles have their shortest leg opposite the smallest angle, and the connection between the short and long legs is

long = short*sqrt(3)

We see that the long leg is 16*sqrt(3) units long, which must mean the short leg is 16 units. This doubles to 32 when we go from short leg to hypotenuse

hypotenuse = short*2

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Consider the following expression and determine which statements are true.

Serhud [2]

Given:

$$\frac{7}{r}+2^{3}+\frac{s}{3}+11$

To find:

Which statement are true?

Solution:

Option A: The entire expression is a sum.

It is true because it performed addition operation.

Option B: The coefficient of s is 3.

$$\frac{7}{r}+2^{3}+\frac{s}{3}+11=\frac{7}{r}+2^{3}+\frac{1}{3}s+11$

It is not true because the coefficient of s is $\frac{1}{3}$ .

Option C: The term $\frac{7}{r}$ is a quotient.

If we divide 7 by r, we obtain a quotient.

So it is true.

Option D: The term $2^3$ has a variable.

It is not true because it does not contain any variable.

Therefore the entire expression is a sum and the term $\frac{7}{r}$ is a quotient are true statement.

3 0

2 years ago

Can anyone help me with this

Likurg_2 [28]

7/13 = about 0.54
-1 1/2 = -1.5

The answer is
-1.7, -1 1/2, 0.04, 0.1, 7/13

5 0

3 years ago

Read 2 more answers

Noah manages a buffet at a local restaurant. He charges $10 for the buffet. On average, 16 customers choose the buffet as their

kicyunya [14]

Answer:

$3 max

Step-by-step explanation:

Charge= b, Customer= c, Revenue= r

r= bc, currently, r= 16*10= $160

We know that: b+1 ⇒ c-2 and the target is r ≥ 130

So, this will all be reflected as:

b=10+x ⇒ c= 16-2x

(10+x)(16-2x) ≥ 130
160 -20x +16x - 2x² ≥ 130
-2x² - 4x + 30 ≥ 0
x² + 2x -15 ≤ 0
(x+1)² ≤ 4²
x+1 ≤ 4 (negative value not considered)
x ≤ 3

As we see the max increase amount is $3, when the revenue will be:

(10+3)*(16-3*2)= 13*10= $130

8 0

2 years ago

A cricular arena is lit by 5 lights equally spaced around the perimeter of the arena. What is the measure of each angle formed b

Kitty [74]

Answer:

108°

Step-by-step explanation:

Suppose that circle with center A is a circular arena. Points B, C, D, E and F are 5 lights. These 5 points form regular pentagon (because these 5 lights are equally spaced around the perimeter of the arena).

The sum of all interior angles of pentagon can be calculated using following formula

$(n-2)\cdot 180^{\circ},\\ \\(5-2)\cdot 180^{\circ}=3\cdot 180^{\circ}=540^{\circ}$

All interior angles in regular pentagon are of equal measure, so

$\dfrac{540^{\circ}}{5}=108^{\circ}$

Thus, the measure of each angle formed by the lights on the perimeter is 108°.

7 0

3 years ago

Triangle L N M is shown. Angle L N M is a right angle. An altitude is drawn from point N to point O on side L M, forming a right

zaharov [31]

Answer:

Therefore the value of k = 6.

Step-by-step explanation:

Given:

LN = m

NM = l

OM = k

NO = 4

LO = 8

LM = 8 + k and

Δ LNM ,Δ LON and Δ MON are right Triangle.

To Find :

Om = k = ?

Solution:

In Right angle Triangle By Pythagoras Theorem we have,

$(\textrm{Hypotenuse})^{2} = (\textrm{Shorter leg})^{2}+(\textrm{Longer leg})^{2}$

So, In Right angle Triangle Δ LON we have,

LN² = ON² + OL²

m² = 4² + 8²

m² = 80 ............( 1 )

Now in Right angle Triangle Δ MON we have,

MN² = ON² + MO²

l² = 4² + k² ....................( 2 )

Now In Right angle Triangle Δ LNM we have,

LM² = LN² + MN²

(8 + k)² = m² + l² .................( 3 )

Substituting equation 1 and equation 2 in equation 3

(8+k)² = 80 + 4² + k²

Applying (A+B)² = A² +2AB + B² we get

$64 + 16k+k^{2} = 80+ 16 +k^{2} \\\\16k=96\\\\\therefore k=\frac{96}{16} \\\\\therefore k=6$

Therefore the value of k = 6.

4 0

2 years ago

Read 2 more answers