Instructions: Use the ratio of a 30-60-90 triangle to solve for the variables.
Make sure to simplify radicals. Leave your answers as radicals in simplest
form.
60°
x
10
y =
ㄷ

Answer:

30 60 90 triangle

the hypotenuse is twice the length of the shorter leg length.

Answer:

e =7.1

Step-by-step explanation:

[tex]Hypotenuse = 10\\Opposite =e\\Adjacent =7\\\\Using\:Pythagoras\:Theorem\\Hypotenuse^2=Opposite^2+Adjacent^2\\10^2 =e^2 + 7^2\\100 =e^2+49\\100-49=e^2\\\\51 =e^2\\\sqrt{51} =\sqrt{e^2}\\ e = 7.141\\\\e = 7.1[/tex]

Answer:

45°

Step-by-step explanation:

This is right triangle with equal legs of √31

Since two sides are equal and the angle between them is 90°, other angles are equal and their value is:

Answer is m∠V= 45°

Answer:

Step-by-step explanation:

y = -|x| + 1

Start with the absolute value function: y = |x|. Reflect it over the x-axis by making it y = -|x|. Finally, shift up 1 unit by adding one, getting a final answer of y = -|x| + 1.

Answer:

Hey there!

6 increased by a scale factor of 1.5 is 9.

9 increased by a scale factor of 1.5 is 13.5.

Thus, the area would be 9 times 13.5, or 121.5

Hope this helps :)

Answer:

Step-by-step explanation:

Let's find the enlarged area:

[tex] = {(scale \: factor)}^{2} \times original \: area[/tex]

Plug the values

[tex] = {(1.5)}^{2} \times 6 \times 9[/tex]

Evaluate the power

[tex] = 2.25 \times 6 \times 9[/tex]

Calculate the product

[tex] = 121.5 \: {in}^{2} [/tex]

Hope this helps...

Best regards!!

Answer:

f(x) =  3x⁴ - [tex]\frac{2X^{3} }{3}[/tex] - 17x +  [tex]\frac{68}{3}[/tex]

Step-by-step explanation:

To find f'(x), we will follow the steps below:

We will start by integrating both-side of the equation

∫f'(x) = ∫(12x^3 - 2x^2 - 17)dx

f(x)  = 3x⁴ - [tex]\frac{2X^{3} }{3}[/tex] - 17x + C

Then we go ahead and find C

f(1) = 8

so we will replace x by 1 in the above equation and solve for c

f(1)  = 3(1)⁴ - [tex]\frac{2(1)^{3} }{3}[/tex] - 17(1) + C

8 = 3 - [tex]\frac{2}{3}[/tex] - 17 + C

C =8 - 3 + 17 + [tex]\frac{2}{3}[/tex]

C = 22 +  [tex]\frac{2}{3}[/tex]

C =[tex]\frac{66 + 2}{3}[/tex]

C = [tex]\frac{68}{3}[/tex]

f(x) =  3x⁴ - [tex]\frac{2X^{3} }{3}[/tex] - 17x +  [tex]\frac{68}{3}[/tex]

Answer:

Four unique planes

Step-by-step explanation:

Given that the points are non co-planar, triangular planes can be formed by the joining of three points

The points will therefore appear to be at the corners of a triangular pyramid or tetrahedron such that together the four points will form a three dimensional figure bounded by triangular planes

The number of triangular planes that can therefore be formed is given by the combination of four objects taking three at a time as follows;

₄C₃ = 4!/(3!×(4-3)! = 4

Which gives four possible unique planes.

Answer:

a) (-4). (-7/8) = 28/8

b) (-4). (-7/8)= 28/8

c) (-4).(+ 3/5) = -12/5

d) (-2).(-3/4). (-1/7) = (6/4)(-1/7)= -6/28

Step-by-step explanation:

a) (-4). (-7/8) = 28/8

b) (-4). (-7/8)= 28/8

c) (-4).(+ 3/5) = -12/5

d) (-2).(-3/4). (-1/7) = (6/4)(-1/7)= -6/28

É repetido talvez com sinal alterado para mostrar a diferença na resposta. Se o sinal for alterado, a resposta também se tornará negativa. Seria - 28/8.

Quando um número negativo é multiplicado por um número negativo, obtém um número positivo. Mas quando um número positivo é multiplicado por um número negativo, dá uma resposta negativa.

Sempre se lembre

negativo * negativo = positivo

positivo * negativo = negativo

negativo * positivo = negativo

positivo * positivo = positivo

Em palavras simples, dois sinais diferentes dão um sinal negativo e dois sinais semelhantes dão um sinal positivo na multiplicação.

English

a) (-4). (-7/8) = 28/8

b) (-4). (-7/8)= 28/8

c) (-4).(+ 3/5) = -12/5

d) (-2).(-3/4). (-1/7) = (6/4)(-1/7)= -6/28

Its repeated maybe with a changed sign to show the difference in the answer. If the sign is changed the answer would also become negative . It would become - 28/8.

When a negative number is multiplied with a negative number it gives a positive number. But when a positive number is multiplied with a negative number it gives a negative answer.

Always remember  

negative * negative= positive  

positive *negative=negative

negative *positive =negative

positive * positive =  positive

In simple words two unlike signs give a negative sign and two similar signs give a positive sign in multiplication.

Answer:

36°

Step-by-step explanation:

<U + < V + <W = 180° (sum of angles in a triangle)

<W = 54°

The tangent is always perpendicular to the radius drawn to the point of tangency...

therefore,

<U = 90°

90° + <V + 54° = 180°

144° + <V = 180°

<V = 180° - 144°

<V = 36°

Answer:

V=36

Step-by-step explanation:

tangent makes rigt angle with radius angle U=90

W+V+U=180

V=180-90-54

V=36

Answer:

1

Step-by-step explanation:

Answer:

18

Step-by-step explanation:

Answer:

18.

Step-by-step explanation:

[4 + (3 - 1)] * 3

= (4 + 2) * 3

= 6 * 3

= 18

Hope this helps!

Answer:

no you need 10.5cm

Step-by-step explanation:

so convert 0.895m to cm by multiplying it by 100 to get 89.5 which is less

so take the required 100-89.5

Subtraction is a mathematical operation. The ribbon is not enough. 10.5 cm of ribbon is more needed.

Subtraction is a mathematical operation that reflects the removal of things from a collection. The negative symbol represents subtraction.

It is known that 1 meter is equal to 100cm, therefore, the length of the ribbon will be equal to,

[tex]\rm 1\ m =100\ cm\\\\0.895\ m = 0.895 \times 100 = 89.5\ cm[/tex]

Now, as the ribbon needed is 100 cm, therefore, the length of ribbon that is needed more is

[tex]\rm \text{length of the ribbon needed} = 100\ cm - 89.5\ cm = 10.5\ cm[/tex]

No, the ribbon is not enough. 10.5 cm of ribbon is more needed.

Learn more about Subtraction:

https://brainly.com/question/1927340

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Answer:

Dimensions to minimize surface are is 28 ft x 28 ft x 14 ft

Step-by-step explanation:

The Volume of a box with a square base of say;x cm by x cm and height

h cm is;

V = x²h

Now, the amount of material used is directly proportional to the surface area, hence we will minimize the amount of material by minimizing the surface area.

The formula for the surface area of the box described is given by;

A = x² + 4xh

However, we need A as a function of

only x, so we'll use the formula;

V = x²h

V = x²h = 10,976 ft³

So,

h = 10976/x²

So,

A = x² + 4x(10976/x²)

A = x² + 43904/x

So, to minimize the area, it will be at dA/dx = 0.

So,

dA/dx = 2x - 43904/x² = 0

Factorizing out, we have;

2x³ = 43904

x³ = 43904/2

x³ = 21952

x = ∛21952

x = 28 ft

since, h = 10976/x²

h = 10976/28² = 14 ft

Thus,dimension to minimize surface are is 28 ft x 28 ft x 14 ft

Answer:

In terms of figures, up to 12 nautical miles (22 km) from the coast, the sea belongs to the coastal state. In these territorial waters, anyone who fishes, finds an object or even an offense must submit to its laws. The coastal state can even suspend the right of a foreign country to navigate there

Step-by-step explanation:

The integer 12 can be written as -12 for 12 miles below sea level​ the answer is -12.

A number is a mathematical entity that can be used to count, measure, or name things. For example, 1, 2, 56, etc. are the numbers.

An integer can be defined as a whole number it can be a negative whole number or a positive whole number for example: 2, 4, 1, -8, 0, etc.

It is given that:

The integer number is 12

Thus, the integer 12 can be written as -12 for 12 miles below sea level​ the answer is -12.

Write an integer for the situation: 12 miles below sea level

Learn more about the number here:

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Answer:

x = 4

Step-by-step explanation:

5x-9 = 2x+3

3x = 12

x = 4

Answer:

4

Step-by-step explanation:

Answer:

120 miles

Step-by-step explanation:

Distance in 2nd hour: 40 miles

Distance in 1st hour:  

40/(4/3) = 30 miles

Distance in 3rd hour:  

(5/4) * 40 = 50 miles

Total distance:  

40 + 30 + 50 = 120 miles

5c-4c+c=2c

Step-by-step explanation:

Since there is only addition and subtraction and no other operations, just work from left to right.

5c-4c = c

c+c=2c

Done!

Answer:

2c

Step-by-step explanation:

Because this whole equation consists of numbers with c's and addition and subtraction, you can just add and subtract as if they were regular numbers!

5c-4c+c

c+c

2c

Hope this helped!! :)

Answer:  A, C, D

(3/20)*20 = 0.15*20 = 3

0.15*20 = 3

(15/100)*20 = 0.15*20 = 3

all expressions lead to the same result of 3

another thing to notice

3/20 = 15/100 = 0.15 = 15%

which are multiple ways to say the same thing just in a different form

Answer:

  B. secondary roads

Step-by-step explanation:

While all of streets, county roads, and secondary roads are generally designed to carry less traffic and/or have lower speed limits than interstate highways, the generic name for such roads is ...

  secondary roads.

CHECK THE COMPLETE QUESTION BELOW

Island A is 250 miles from island B. A ship captain travels 260 miles from island A and then finds that he is off course and 160 miles from island B. What bearing should he turn to, so he is heading straight towards island B?

A. 111.65

B. 119.84

C. 21.65

D. 135.53

Answer:

OPTION A IS CORRECT

A. 111.65

Step-by-step explanation:

This question can be explained using a triangle, let us say triangle ABD

and let us say A and B represent the islands and D is the particular point from where the captain is standing at a distance of 160 miles from B island .

We will be making use of cosines rule to calculate our angles, and we know that from cosine rule

D² = a² + b² -2abCosD

Where, a= 160 b = 260 and d = 250 then we can substitute in order to calculate our angles

250²= 60² + 260² - 2(160*260)Cos(D)

62500= 625600+ 67600- 83200CosD

83200CosD= 25600+ 67600 - 625600

83200CosD= 30700

CosD= 30700/83200

CosD= 0.369

D= cos⁻¹ (0.369)

D=68.35

Therefore, the angle inside the triangle is 68.35°

Now we can now find the bearing the captain supposed to turn , if he is heading to island B which will be the external angle of the triangle, but we know that The external angle =180°(supplimentary angles )

Then the angle he would turn will be external angle of the triangle - 68.35°

= (180 - 68.35)

= 111.65°

Therefore, the bearing the captain should turn is 111.65° for him to be heading straight towards island B.

Answer:

[tex]\displaystyle x = \frac{\pi}{3} +k\, \pi[/tex] or [tex]\displaystyle x =- \frac{\pi}{3} +2\,k\, \pi[/tex], where [tex]k[/tex] is an integer.

There are three such angles between [tex]0[/tex] and [tex]2\pi[/tex]: [tex]\displaystyle \frac{\pi}{3}[/tex], [tex]\displaystyle \frac{2\, \pi}{3}[/tex], and [tex]\displaystyle \frac{4\,\pi}{3}[/tex].

Step-by-step explanation:

By the double angle identity of sines:

[tex]\sin(2\, x) = 2\, \sin x \cdot \cos x[/tex].

Rewrite the original equation with this identity:

[tex]2\, (2\, \sin x \cdot \cos x) - 2\, \sin x + 2\sqrt{3}\, \cos x - \sqrt{3} = 0[/tex].

Note, that [tex]2\, (2\, \sin x \cdot \cos x)[/tex] and [tex](-2\, \sin x)[/tex] share the common factor [tex](2\, \sin x)[/tex]. On the other hand, [tex]2\sqrt{3}\, \cos x[/tex] and [tex](-\sqrt{3})[/tex] share the common factor [tex]\sqrt[3}[/tex]. Combine these terms pairwise using the two common factors:

[tex](2\, \sin x) \cdot (2\, \cos x - 1) + \left(\sqrt{3}\right)\, (2\, \cos x - 1) = 0[/tex].

Note the new common factor [tex](2\, \cos x - 1)[/tex]. Therefore:

[tex]\left(2\, \sin x + \sqrt{3}\right) \cdot (2\, \cos x - 1) = 0[/tex].

This equation holds as long as either [tex]\left(2\, \sin x + \sqrt{3}\right)[/tex] or [tex](2\, \cos x - 1)[/tex] is zero. Let [tex]k[/tex] be an integer. Accordingly:

Any [tex]x[/tex] that fits into at least one of these patterns will satisfy the equation. These pattern can be further combined:

Answer: C.) - 896

Step-by-step explanation:

Given the explicit formula :

An = 7 × (-2)^(n-1)

The 8th term of the geometric sequence using the formula will be :

n = 8

A8 = 7 × (-2)^(8-1)

A8 = 7 × (-2)^7

A8 = 7 × (-128)

A8 = - 896

Answer:

60men

Step-by-step explanation:

300 men - 15 days - 1 work

men? - 15 days - 1/5 of work

When 1 man does 1/5 of work,

how many days needed = (15 × 1/5) × 300 = 900days

Men needed to complete 1/5 work in 15 days = 900 ÷ 15 = 60men

Answer:

$3300 at 4%

$11700 at 7%

Step-by-step explanation:

Total investment = $15000

Total simple interest on investment = $951

Investment A:

Rate = 4% =0.04

Investment B:

Rate = 7% =0.07

Simple interest (S. I) = principal * rate * time

(S. I on investment A + S. I on investment B)

Let principal amount in investment A = A

principal amount in investment B = B

(A * 0.04 * 1) + (B * 0.07 * 1) = $951

0.04A + 0.07B = $951 - - - - (1)

A + B = $15000 - - - - (2)

from (2)

A = 15000 - B

Substitute A = 15000 - B into (1)

0.04(15000 - B) + 0.07B = 951

600 - 0.04B + 0.07B = 951

600 + 0.03B = 951

0.03B = 951 - 600

0.03B = 351

B = 351 / 0.03

B = $11700

From (2)

A + B = $15000

A + $11700 = $15000

A = $(15000 - 11700)

A = $3300

Answer:

A

Step-by-step explanation:

Just like in the last problem, we have a right triangle but in this case, x is a leg, 10 / 2 = 5 is the other leg, and 13 is the hypotenuse. Using the 5 - 12 - 13 Pythagorean Triple, we know that x = 12.

Answer:

1 = 4 = 38°, 2 = 3 = 90°

Step-by-step explanation:

Because the diagonals of rhombi are perpendicular, ∠2 = ∠3 = 90°. Since the sum of angles in a triangle is 180°, ∠1 = 180° - 52° - 90° = 38°. If we look at the triangle with 1 and 4 as its base angles, we notice that it's an isosceles triangle, therefore ∠1 = ∠4 = 38°.

Answer:

Step-by-step explanation:

In rhombus, diagonals are perpendicular to each other.

∠2 = ∠3 = 90°

52° + ∠1 + ∠ 2 = 180°    { Angle sum property of triangle}

52 + ∠1 + 90 = 180

∠1 + 142 =  180

∠1 = 180 - 142

∠1 = 38°

∠4 = ∠1 = 38°  { Isosceles triangle}

answer:

choice letter b

Answer:

Amount of Discount: 85,  Discounted cost of item: 340

Step-by-step explanation:

You Start by dividing the main price of the item by 100

You then multiply your answer from that by however much the discount is.

We divide by 100 because there is 100 percent when you are paying full price, dividing by 100 gives you the amount that is equal to 1 percent of that price

You then multiply the answer from that by 20, this will give you 20% of the full price, this will give you a discount of 85 Dollars.  

To find the Discounted price you then subtract 85 from 425 and you will have an answer of 340 dollars.  Hope this helps!

4/5 recommend, so about 4/5(120) = 96 doctors recommend the brand.

Answer:

x=-1.30068.......

Step-by-step explanation:

x( 3x^2 - 2) = -4

Distribute

3x^3 - 2x = -4

Add 4 to each side

3x^3 - 2x +4 = 0

Plot using a graphing calculator

x=-1.30068.......