Test question........................

Answer:

[tex]3\sqrt{3}[/tex]

Step-by-step explanation:

In all 30-60-90 triangles, the side lengths are in the ratio [tex]x:x\sqrt{3}:2x[/tex], where [tex]x[/tex] is the side opposite to the 30 degree angle and [tex]2x[/tex] is the hypotenuse of the triangle. Since the side opposite to the 30 degree angle is marked as 3, the value of [tex]x[/tex] must be [tex]\boxed{3\sqrt{3}}[/tex].

Alternatively, we can use basic trig. for a right triangle to solve. In any right triangle, the tangent of an angle is equal to its opposite side divided by its adjacent side. Thus, we have:

[tex]\tan 60^{\circ}=\frac{x}{3},\\x=3\tan 60^{\circ}=\boxed{3\sqrt{3}}[/tex]

Answer:

Step-by-step explanation:

The tangent of a 60 degree angle = Sin(60) / Cos(60)

Sin(60) = Square root (3) / 2

Cos(60) = 1/2

Tan(60) = √3 / 2 // 1/2   Invert the denominator and multiply

Tan(60) = √3/2 * 2/1

Tan(60) = √3

Tan(theta) = opposite / adjacent

Tan(theta) = x/3 in this case

Tan(60) = √3 = x/3

x = 3*√3

Answer:

Step-by-step explanation:

-6 and up going left

Answer:

x = - 10

Step-by-step explanation:

7x + 40 = 5x + 20

7x + 40 - 40 = 5x + 20 - 40

7x = 5x - 20

7x - 5x = 5x - 5x - 20

2x = - 20

2x ÷ 2 = - 20 ÷ 2

x = - 10

Answer:

Lower Bound = 2.996

Upper bound = 3.244

Step-by-step explanation:

Answer:

5x^2 - 3x -5

Step-by-step explanation:

You simplify the like terms

Remember to use distributive property to do the (7x-3x^2+5) part

Answer:

10

Step-by-step explanation:

5 (2) is the same as 5 × 2 which equals 10

Answer:

Step-by-step explanation:

Given here,

(5)2

= 5 × 2.

= 10 (Ans)

Answer:

$575.71

Step-by-step explanation:

A = 960(1-.12)^4

A = 960(.88)^4

A =575.71

Answer:

$575.71

Step-by-step explanation:

100-12=88

(0.88)⁴×960= 575.707

Answer:

Step-by-step explanation:

In ABC. In DEF

AB. = DE. (Given side)

<BAC. = <EDF. (Given side)

BC. = EF. (Given side)

Hence,

Triangle ABC is congruent to Triangle DEF by SAS Congruence Theorem.

Answer:

The triangles are congruent  by HL

Step-by-step explanation:

The triangles are right triangles so we can use either HL ( hypotenuse leg) or LL (leg leg) if we know that two sides are congruent

We know one leg is equal to the other by the red line.  The hypotenuse is the same since it is the same line.

The triangles are congruent  by HL

Answer:

7/24

Step-by-step explanation:

two minuses make a +,

meaning this equation is basically

-1/12+3/8

find a common denominator by LCM.

8,16,24,32

12,24,36,48

they share 24

denominator is 24

12*2 is 24, -1*2 = -2. 8*3 = 24 so we do 3*3 = 9

-2+9/24

7/24

Answer:

35

Step-by-step explanation:

Only if u put x as 35 will the whole triangle sum equal 180 as necessary for the theorem to be true.

Answer:

Brandon is correct

Step-by-step explanation:

Brandon is running errands for his mother.

It is 1/4 mile from his house to the library and 2/3 mile from the library to the grocery store .

Brandon claims that he walked a total of 11/12 mile if he goes from his house to the library to the grocery store.

Distance from his house to the library = 1/4 mile

Distance from the library to the grocery store = 2/3 mile

Total distance Brandon walks from his house to the library to the grocery store = Distance from his house to the library + Distance from the library to the grocery store

= 1/4 + 2/3

Make both 1/4 and 2/3 have the same denominator to be able to add

The lowest common multiple (LCM) of 4 and 3 is 12

Therefore,

1/4 + 2/3

= (3+8)/12

= 11/12

Total distance Brandon walks from his house to the library to the grocery store = 11/12 mile

Answer:

Let's define East as the positive x-axis and North as the positive y-axis.

If Michelle's initial position is (0, 0)m

We know that Nathasha is 50m due East of Michelle.

Then the position of Natasha is (50, 0)m

Now we know that Natasha walks 20m due North, then the new position of her's is:

(50, 0 + 20)m = (50, 20)m

While Michelle walks 10m due South (South would be the negative y-axis, then we subtract 10 meters)

Michelle's new position will be:

(0, 0 - 10)m = (0, -10)m

Now we want to know the distance and bearing of Michelle from Natasha.

First, remember that the distance between two points (a, b) and (c, d) is given by:

Distance = √( (a - c)^2 + (b - d)^2)

Then the distance between Michelle and Natasha is:

Distance = √( (50m - 0m)^2 + (20m - (-10m))^2)

Distance = √( (50m)^2 + (30m)^2) = 58.31m

Now to find the bearing you can see the image below:

Point B is Michelle's position and point A is Natasha's position.

To find the bearing, we can make a triangle rectangle as the one shown in the image:

Also remember the relation:

Tan(a) = (opposite cathetus)/(adjacent cathetus).

Where the opposite cathetus is the difference between the x-values of each position, this is:

opposite cathetus = 50m - 0m = 50m

And the adjacent cathetus is the difference between the y-values, this is:

adjacent cathetus = 20m - (-10m) = 30m

Then:

Tan(a) = 50m/30m

Tan(a) = 5/3

Now if we apply the inverse Tan function to both sides, Atan(x) we get:

Atan(Tan(a)) = Atan(5/3)

a = Atan(5/3) = 59°

So the bearing is of 59°.

Answer:

a

Step-by-step explanation:

I think so..

Answer:

first qustion the last one .

second qustion the first one .

Answer:

12[tex]\sqrt{3}[/tex] / 24

Step-by-step explanation:

ΔXZW is a 30-60-90 triangle whose sides are in the ratio of 1 : [tex]\sqrt{3}[/tex] : 2, respectively

also, ΔXZW ≅ ΔYZW

so XW = 12

XZ = 24

WZ = 12[tex]\sqrt{3}[/tex]

cos ratio of ∡XZW is WZ/XZ which is:

12[tex]\sqrt{3}[/tex] / 24

Answer:14 m

Step-by-step explanation:

Dada

larga [tex]l=20\ m[/tex]

superficie [tex]A=280\ m^2[/tex]

Suponga que el ancho es w

La superficie está dada por el producto de la longitud y la anchura.

[tex]\therefore A=lw\\\Rightarrow 280=20\times w\\\Rightarrow w=14\ m[/tex]

Por lo tanto, el ancho es de 14 m.

The y intercept is 3 and the x intercepts are +1.3 and -1.3

The graph is given below.

In mathematics, the graph of a function f is the set of ordered pairs, where {\displaystyle f(x)=y.} In the common case where x and f(x) are real numbers, these pairs are Cartesian coordinates of points in two-dimensional space and thus form a subset of this plane.

Here, we have,

h(x)=-x^4 +3

so, The y intercept is 3 and the x intercepts are +1.3 and -1.3

The graph is given below.

To learn more on graph click:

brainly.com/question/17267403

#SPJ2

Answer:

416 feet squared

Step-by-step explanation:

Answer:

208 ft

Step-by-step explanation:

4*4+4*16+4*16+6*4+4*4+6*4

Answer

What event will cost the least for 9 tickets?

the wave pool

How much less will this event cost?

$20.25

Hope it helps :)

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

write numbers in numerical order then subtract the highest number from the lowest number and you get the range.

(1,2,3,3,4,4,6,9)

9 - 1 = 8

Answer:

A 1/5^2

Step-by-step explanation:

5^3 x 5^-5

We know that a^b* a^c = a^(b+c)

5^3 x 5^-5 = 5^(3-5)  = 5^-2

We also know that a^-b = 1/ a^b

5^-2 = 1/5^2

Answer:

18 i think

Step-by-step explanation:

Answer:

3^-6(81)^2=3^-6(6561)=9 which is 3^2

Answer:-2

Step-by-step explanation:

Answer:

sinU = 0.96

Step-by-step explanation:

sinU = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{WV}{UV}[/tex] = [tex]\frac{24}{25}[/tex] = 0.96