what is the total surface area of 12ft, 4ft and 5ft

Answer:

[tex]\angle m + \angle t + \angle n = 180[/tex]

Step-by-step explanation:

Required

Show that:

[tex]\angle m + \angle t + \angle n = 180^o[/tex]

To make the proof easier, I've added a screenshot of the triangle.

We make use of alternate angles to complete the proof.

In the attached triangle, the two angles beside [tex]\angle m[/tex] are alternate to [tex]\angle t[/tex] and [tex]\angle n[/tex]

i.e.

[tex]\angle 1 = \angle t[/tex]

[tex]\angle 2 = \angle n[/tex]

Using angle on a straight line theorem, we have:

[tex]\angle 1 + \angle m + \angle 2 = 180[/tex]

Substitute values for (1) and (2)

[tex]\angle t + \angle m + \angle n = 180[/tex]

Rewrite as:

[tex]\angle m + \angle t + \angle n = 180[/tex] -- proved

Answer:

25%

Step-by-step explanation:

1 ÷ 4 = 0.25

0.25 x 100 = 25 = 25%

Answer:

f(x) -5x

g(x) -85x²

f(x) . g(x)

-90x

Answer:

36x³ + 25x² + 12x + 2

Step-by-step explanation:

f(x) × g(x)

= (- 4x - 1)(- 9x² - 4x - 2)

Each term in the second factor is multiplied by each term in the first factor

- 4x(- 9x² - 4x - 2) - 1 (- 9x² - 4x - 2) ← distribute parenthesis

= 36x³ + 16x² + 8x + 9x² + 4x + 2 ← collect like terms

= 36x³ + 25x² + 12x + 2

Answer:

384 square units

Step-by-step explanation:

Square prism = Cube

Formula for finding the surface area of a cube = L x L (6)

Surface area = 8 x 8 (6)

Surface area = 64(6)

Surface area = 384 square units

Answer:

384 units squared

Step-by-step explanation:

Square 8 and then multiply by 6.

Answer:

60

would be right

Step-by-step explanation:

Total length of cable required is 466.18 m.

Pythagoras theorem states that In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides.

According to the question

A 100m mast is supported by six cables in two sets of three cables.

They are anchored to the ground at an equal distance from the mast.

The top set of three cables is attached at a point 20m below the top of the mast.

Each cable in the lower set of three cables is 60m long and is attached at a height of 30m above the ground.

One set of guy wires (1 upper and one lower have two right triangles which can solve

The lower right triangle

a = distance from the pole to guy tie point

b = 30 m

c = 60 m the lower guy wire (the hypotenuse)

Using Pythagoras theorem

[tex]a^{2} +30^{2} =60^{2}[/tex]

⇒ [tex]a^{2} = 3600 - 900[/tex]

⇒ [tex]a^{2} =2700[/tex]

⇒ [tex]a = \sqrt{2700}[/tex]

⇒ [tex]a = 51.96[/tex] m from the pole to the tie point.

The other triangle using upper guy wire as the hypotenuse (h) tied to a point on the pole 80 m from the ground (20 m from the top) and also 50m from the tie point.

Using Pythagoras theorem

[tex]h^{2} =(51.96)^{2} +80^{2}[/tex]

⇒ [tex]h^{2}=2700+6400[/tex]

⇒ [tex]h^{2}=9100[/tex]

⇒ [tex]h = \sqrt{9100}[/tex]

⇒ [tex]h = 95.39[/tex] m , the length of the upper guy wire

For one set of guy wires (1 upper & 1 lower):

= 95.39 + 60

= 155.39 m

For 3 sets of guy wires :

= 3(155.39)

= 466.18 m of wire required

Hence, total length of cable required is 466.18 m.

Find out more information about Pythagoras theorem here

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Answer:

-6/-2<-2x/-2

divide both sides by-2 to remain with the x variable on one side

I hope this helps

Answer:

Yes it can be right angle triangle

Answer:

b

Step-by-step explanation:

area of triangle = 1/2 x c x d =cd/2

area of semicircle = 1/2 x π x r^2 = 1/2 x π x (a/2)^2 = 1/2 x π x a^2/4 =πa^2/8

area of shape = area of triangle + area of semicircle

Answer:

Hence the answer is Letter B.

Step-by-step explanation:

° ° °

Answer:

here,

3x-3x=

[tex] {x}^{2} - {x}^{2} [/tex]

x=0

Answer:

A'(-3,0), B'(0,-3) and C'(4,7)

Step-by-step explanation:

We are given that the vertices of triangle are A(0,-3), B(3,0) and C(-7,4).

We have to find the coordinates of the image of triangle under a rotation of 90° clockwise about the origin.

90° clockwise about the origin

Rule:[tex](x,y)\rightarrow (y,-x)[/tex]

Using the rule

The coordinates of A'

[tex]A(0,-3)\rightarrow A'(-3,0)[/tex]

The coordinates of B'

[tex]B(3,0)\rightarrow B'(0,-3)[/tex]

The coordinates of C'

[tex]C(-7,4)\rightarrow C'(4,7)[/tex]

Hence, the vertices of image of triangle is given by

A'(-3,0), B'(0,-3) and C'(4,7)

Answer:

x = 37.3

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

tan theta = opp/ adj

tan 63 = x /19

19 tan 63 =x

x=37.28959

To the nearest tenth

x = 37.3

Answer:

x - 3y = 24

B. y = -3x - 1

Step-by-step explanation:

Hope it helped.

° ° °

Answer:

A

or

the top right option

or

0.5 + 0.1875

Step-by-step explanation:

We know D or 9 divided by 16 is the same as 9/16, so just solve for that.

Then solve for the others and find the ones that doesn't equal 9/16.

Answer:

x = 27°

Step-by-step explanation:

180° - 72° = 108°

108° / 4 = 27°

72° + (27° * 4) = 180°

Hope it helps!

Answer:

4x^3

Step-by-step explanation:

20 x^5 + 28 x^4 + 12x^3

4*5*x^5  + 4*7*x^4 + 4*3*x^3

Factor out 4x^3

4x^3 ( 5x^2 + 7x +3)

Answer:

V = 8 m/s

Step-by-step explanation:

 Assuming that the object was at rest, so μ = 0

Equations

F=ma - Newtons 2nd law

[tex]v^{2} = u^{2} + 2a[/tex]Δx - 4th kinematic equatioin

Step 1 - find "a"

F=m/a

a=F/m

a=80/10

a=8m/s^2

Step 2 - find "v"  

v^2 = 0 + 2 * 8 * 4

v^2 = 64    

v=8m/s

Answer:

3rd option

Step-by-step explanation:

Using the identity

sin²x + cos²x = 1  ( subtract sin²x from both sides )

cos²x = 1 - sin²x ( take the square root of both sides )

cosx = ± [tex]\sqrt{1-sin^2x}[/tex]

Given

sinθ = [tex]\frac{21}{29}[/tex] and 0 < θ < 90 , then

cosθ

= [tex]\sqrt{1-(\frac{21}{29})^2 }[/tex]

= [tex]\sqrt{1-\frac{441}{841} }[/tex]

= [tex]\sqrt{\frac{400}{841} }[/tex] = [tex]\frac{\sqrt{400} }{841}[/tex] = [tex]\frac{20}{29}[/tex]

Answer:

Both Ava and Finn are correct

Step-by-step explanation:

There are 4 tables and 9 pencils at each table

4 ( 9) = 36

9 * 4 = 36

Both Ava and Finn are correct

Answer:

Step-by-step explanation:

This is simple, but the extra numbers given in the form of the specific times might throw you off.

If Garrett leaves at noon and at 7 Ben is some distance ahead of him, that means that Garrett has been driving for 7 hours. Ben left at 2, so at 7 pm he has been driving for 5 hours. That's part of what's confusing. We'll put that in a table to hopefully make things easier:

              d      =       r      *        t

G                                             7

B                                             5

We also know that Garrett is driving at 10 km/h, so:

              d        =        r        *        t

G                               10       *        7

B                                 r                 5

The r is because Ben's rate is our unknown. Look at the top of the table. That is the formula we are going to use to solve this problem: d = rt.

If Garrett drives for 7 hours at 10 km/hr, then the distance he has traveled is 70 km (that's found by multiplying the rate of 10 km/h by the time of 7 hours). Ben's rate, along those same lines of reasoning, is 5r. Fill that in:

            d        =        r        *        t

G         70       =       10       *       7

B         5r        =        r        *       5

Ok now the table is filled out. Let's look at the rest of the problem. It says that at 7 pm Ben's distance is 15 km more than Garrett's distance. The words "more than" indicate addition. In words that is

"Ben's distance is Garrett's distance plus 15 km" which translates to, mathematically speaking:

5r = 70 + 15 and

5r = 85 so

r = 17

Ben's rate is 17 km/h, choice a.

===========================================================

Explanation:

Your teacher shows that minor arc BD is 129 degrees. Recall that any minor arc is always less than 180 degrees.

Let's say that we had point A at the center of the circle. This would mean angle DAB is 129 degrees. This central angle subtends or cuts off minor arc BD.

Now focus entirely on quadrilateral DABC. The goal is to find the unknown angle C. The angle A was found earlier at 129 degrees. The angles B and D are 90 degrees each since tangents are perpendicular to the radius at the point of tangency.

We have this so far

Adding all four angles of any quadrilateral will always get us 360 degrees. It's similar to how adding the angles of a triangle gets us 180 degrees. In fact, any quadrilateral can be cut into two triangles (aka the process of triangulation). So adding two triangles gets us 180+180 = 360 more or less.

--------------

Anyways, the four angles A,B,C,D must add to 360. So,

A+B+C+D = 360

129+90+C+90 = 360

C+309 = 360

C = 360-309

C = 51

--------------

As a shortcut, note how B+D = 90+90 = 180

Also note that A+C = 360-(B+D) which becomes A+C = 180

So, C = 180-A = 180-129 = 51

Answer:

b = 7/2

x = 11/2

y = 21/2

z = -4

Step-by-step explanation:

2x + 2y + 2z = 24

x + y + z = 12

b + 2x + y + z = 21

2b + 2y = 28

b + y = 14

3x + y + z = 23

we can start anywhere by transforming these equations in a way that always one variable is excised by others.

so, e.g.

b = 14 - y

14 - y + 2x + y + z = 21

2x + z = 7

z = 7 - 2x

3x + y + 7 - 2x = 23

x + y = 16

16 + z = 12

z = -4

-4 = 7 - 2x

-11 = -2x

11 = 2x

x = 11/2

11/2 + y = 16

y = 16 - 11/2 = 32/2 - 11/2 = 21/2

b = 14 - 21/2 = 28/2 - 21/2 = 7/2

Answer:

(√366 - 3)/24

Step-by-step explanation:

Given the following:

cos∝ = √3/8 and sinβ = √3/3

Sin(∝-β) = sin∝cosβ - cos∝sinβ

Get sin∝

Since cos∝ = √3/8

adj = √3

hyp = 8

opp = √8² - (√3)²

opp = √64 - 3

opp = √61

Recall that sin∝ = opp/hyp  

sin∝ = √61/8

Get cosβ

Since sinβ =  √3/3

opp = √3

hyp = 3

adj =√3² - (√3)²

adj = √9-3

adj = √6

Recall that cosβ = adj/hyp

cosβ = √6/3

Substitute the gotten values into the formula

Sin(∝-β) = sin∝cosβ - cos∝sinβ

Sin(∝-β) = ( √61/8)(√6/3)- (√3/8)(√3/3)

Sin(∝-β) = √366/24 - √9/24

Sin(∝-β) = (√366 - 3)/24

Answer:

B, [tex]-\frac{1}{2}[/tex]

Step-by-step explanation:

This problem is essentially asking one to envision a line passing through the set of points on the coordinate plane, then to find the constant of proportionality of that line. The constant of proportionally, also known as the rate of change, or the slope, is a number that can be used to describe the range that happens between points on a line. The following formula can be used to find the slope of a line passing through a set of points.

[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Where the points ([tex]x_1,y_1[/tex]) and ([tex]x_2,y_2[/tex]) are points on the line.

As one can see, on the given coordinate plane, the points ([tex]2,-1[/tex]), and ([tex]4,-2[/tex]) are on the coordinate plane. Substitute these points into the formula to find the slope of the line, then simplify to evaluate the equation and find the slope,

[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

([tex]2,-1[/tex]),  ([tex]4,-2[/tex])

[tex]=\frac{-2-(-1)}{(4)-(2)}[/tex]

[tex]=\frac{-2+1}{4-2}\\\\=\frac{-1}{2}\\\\=-\frac{1}{2}[/tex]

Answer:

3×5×7×11=1155

a.1155 the answer

3×5×7×11=1155

A natural number other than 1 whose only factors are 1 and itself is said to have a prime factor. In actuality, the first few prime numbers are 2, 3, 5, 7, 11, and so forth.

Given

3×5×7×11=1155

To learn more about prime factors refer to:

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Answer:

A) Q(x) = (x + 3)² + 5, and the vertex is (-3, 5)

B) R(x) = (x - 3)² + 2, and the vertex is (3, 2)

C) S(x) = (x - 1)² - 5, and the vertex is (1, -5)

Step-by-step explanation:

The given function is P(x) = (x + 3)² + 2

The given function is a parabolic function in vertex form, f(x) = a·(x - h)² + k, and vertex, (h, k)

By comparison, the vertex of the function P(x) = (x + 3)² + 2 is (-3, 2)

A) A function f(x) translated α units UP gives

f(x) (translated α units UP) → f(x) + α

A translation of the function 3 units UP is given by adding 3 to the given function as follows;

Q(x) = P(x) + 3

∴ Q(x) = (x + 3)² + 2 + 3 = (x + 3)² + 5

Q(x) = (x + 3)² + 5, and the vertex by comparison to f(x) = a·(x - h)² + k, and vertex, (h, k) is (-3, 5)

B) A function f(x) translated b units RIGHT gives;

f(x) translated b units right → f(x - b)

∴ P(x) = (x + 3)² + 2 translated 6 units RIGHT gives;

P(x) = (x + 3)² + 2 (translated 6 units RIGHT) → R(x) = (x + 3 - 6)² + 2 = (x - 3)² + 2

R(x) = (x - 3)² + 2, and the vertex by comparison is (3, 2)

C) A function translated α units DOWN and b units RIGHT is given as follows;

[tex]f(x) \ translated \ by\ \dbinom{b}{a} \rightarrow f(x - b) - a[/tex]

Therefore, the given function, P(x) = (x + 3)² + 2, translated 7 units DOWN and 4 units RIGHT gives;

[tex]P(x) = (x + 3)^2 + 5 \ translated \ by\ \dbinom{4}{-7} \rightarrow P(x - 4) - 7 = S(x)[/tex]

S(x) = P(x - 4) - 7 = (x + 3 - 4)² + 2 - 7 = (x - 1)² - 5

[tex]P(x) = (x + 3)^2 + 5 \ translated \ by\ \dbinom{4}{-7} \rightarrow (x - 1)^2 - 5= S(x)[/tex]

S(x) = (x - 1)² - 5, and the vertex by comparison is (1, -5)

Answer:

Step-by-step explanation:

Answer:

UWUNOE BRO HUUZEM HIHUDHS

Step-by-step explanation: