Triangle $ABC$ has its vertices $A$, $B$, and $C$ on the sides of a rectangle 4 units by 5 units as shown. What is the area of triangle $ABC$ in square units?

Explanation:

Each fraction reduces to 1/2, so we have six copies of 1/2 being multiplied together. A shortcut to repeated multiplication like this is to use exponents

So you're really computing (1/2)^6 to get

(1/2)^6 = (1^6)/(2^6) = 1/64

Answer:

2.35*2/3=47/30

Step-by-step explanation:

Answer:

b = 131

Step-by-step explanation:

The two angles form a straight line so they add to 180 degrees

b+49 = 180

Subtract 49 from each side

b = 180-49

b =131

Answer:

Angle b is 131°

Step-by-step explanation:

Angles on a straight line add up to 180°

To find b add 49 and b and equate it to 180°

That's

b + 49 = 180

b= 180 - 49

b = 131°

Hope this helps you

Answer:

143.81

Step-by-step explanation:

Trapezoid Area

A = 2b/2 * h

A = 9 + 23/2 * 7

A = 32/2 * 7

A = 16 * 7

A = 112

Semi-circle Area

A = πr²/2

A = π4.5²/2

A = π20.25/2

A = 63.62/2

A = 38.81

Total Area

112 + 38.81

143.81

Answer:

Second choice.

f(x) = 1/2(x - 6)^2 + 3/2.

Step-by-step explanation:

The distance of a point  (x, y) from the focus = the distance of the point from the directrix, so:

(x - 6)^2 + (y - 2)^2 = (y - 1)^2

x^2 - 12x + 36 + y^2 - 4y + 4 = y^2 - 2y + 1

x^2 -12x + 39 = 2y

y = f(x) = 1/2 (x^2 - 12x + 39)

I see you want the answer in vertex for so it is:

f(x)  = 1/2 [ (x - 6)^2 - 36)  + 39)

f(x)  = 1/2(x - 6)^2 + 3)

f(x) = 1/2(x - 6)^2 + 3/2.

A parabola is a plane that is approximately U-shaped.

The equation of the parabola is: [tex]\mathbf{y = \frac{1}{2}(x - 6)^2 + \frac 32}[/tex]

The given parameters are:

[tex]\mathbf{Focus = (6,2)}[/tex]

[tex]\mathbf{Directrix: y = 1}[/tex]

First, equate the directrix to 0

[tex]\mathbf{y - 1 = 0}[/tex]

The equation is then calculated as:

[tex]\mathbf{(x - a)^2 + (y - b)^2 = (y- 1)^2}[/tex]

Where:

[tex]\mathbf{(a,b) = (6,2)}[/tex]

So, we have:

[tex]\mathbf{(x - 6)^2 + (y - 2)^2 = (y- 1)^2}[/tex]

Expand

[tex]\mathbf{x^2 - 12x +36 + y^2 - 4y + 4 = y^2 - 2y + 1}[/tex]

Subtract y^2 from both sides

[tex]\mathbf{x^2 - 12x +36 - 4y + 4 =- 2y + 1}[/tex]

Collect like terms

[tex]\mathbf{x^2 - 12x +36 + 4 - 1 =4y - 2y}[/tex]

[tex]\mathbf{x^2 - 12x +39 =2y}[/tex]

Divide through by 2

[tex]\mathbf{y = \frac{1}{2}(x^2 - 12x +39)}[/tex]

Express 39 as 36 + 3

[tex]\mathbf{y = \frac{1}{2}(x^2 - 12x +36 + 3)}[/tex]

Factor out 3/2

[tex]\mathbf{y = \frac{1}{2}(x^2 - 12x +36) + \frac 32}[/tex]

Expand the bracket

[tex]\mathbf{y = \frac{1}{2}(x^2 - 6x - 6x +36) + \frac 32}[/tex]

Factorize

[tex]\mathbf{y = \frac{1}{2}(x(x - 6) - 6(x -6)) + \frac 32}[/tex]

Factor out x - 6

[tex]\mathbf{y = \frac{1}{2}((x - 6) (x -6)) + \frac 32}[/tex]

Express as squares

[tex]\mathbf{y = \frac{1}{2}(x - 6)^2 + \frac 32}[/tex]

Hence, the equation of the parabola is: [tex]\mathbf{y = \frac{1}{2}(x - 6)^2 + \frac 32}[/tex]

Read more about equations of parabola at:

https://brainly.com/question/4074088

Answer:

the triangle, its interior , and its exterior best describes it.

Answer:

Hello!

__________________

Your answer would be Triangle.

the term that best describes a figure formed by three segments connecting three non-collinear points is:

Triangle.

___________________

Hope this helped you!

:D

Step-by-step explanation:

[tex]8x^3-8=2^3x^3-2^3=(2x)^3-2^3\\\\\text{Use}\ a^3-b^3=(a-b)(a^2+ab+b^2)\\\\=(2x-2)\bigg((2x)^2+(2x)(2)+2^2\bigg)\\\\=(2x-2)(4x^2+4x+4)\\=2(x-1)(4x^2+4x+4)\\=4(2x-2)(x^2+x+1)\\=8(x-1)(x^2+x+1)[/tex]

The equivalent expression of 8x³ - 8 is 8(x-1) (x² + x +1)

8x³ - 8 = 2³ x³ -2³  

=  (2x)³ - 2³

Using a³ -b³ = (a - b) (a² + ab + b²)

= (2x -2) ((2x)² + (2x) (2) + 2²))

= (2x -2) (4x² + 4x + 4)

= 2(x-1)(4x² + 4x + 4)

= 4(2x -2) (x² + x +1)

= 8 (x-1) (x² + x +1)

Learn more about expression  at:

https://brainly.com/question/1859113

#SPJ2

Answer:

Rational.

Step-by-step explanation:

Irrational numbers are real numbers that can't be written as fractions.

One clue is that the decimal goes on forever (doesn't terminate) without repeating. (pi)

.14 can be written as a fraction: 14/100

Answer:

It's rational

Step-by-step explanation:

Because irrational numbers cannot be written s a fraction and rational numbers can

Answer:

a = -1/2

b = 2

Step-by-step explanation:

Step 1: Rewrite 1st equation

-b = -5 - 6a

b = 5 + 6a

Step 2: Substitution

4a - 3(5 + 6a) = -8

Step 3: Solve

4a - 15 - 18a = -8

-14a - 15 = -8

-14a = 7

a = -1/2

Step 4: Plug in a to find b

6(-1/2) - b = -5

-3 - b = -5

-b = -2

b = 2

Answer:

I think its A

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

The graph would be a curve because of the exponent.

Answer:

Las inecuaciones que pueden ayudar a calcular cuantos litros de pintura blanca se pueden tener como son [tex]\frac{4\cdot x + 7\cdot y}{500}> 5\,\frac{USD}{L}[/tex] y [tex]\frac{4\cdot x + 7\cdot y}{500}< 6\,\frac{USD}{L}[/tex].

Step-by-step explanation:

Esta situación puede ser descrita mediante una ecuación y una inecuación simultánea. La ecuación es de la capacidad del tanque, mientras que la inecuación es del coste unitario de la mezcla. Sean [tex]x[/tex] y [tex]y[/tex] las capacidades empleadas de pintura blanca y pintura azul en litros, entonces:

Capacidad del tanque (en litros)

[tex]x + y = 500\,L[/tex]

Coste unitario de la mezcla (en dólares por litro)

[tex]5\,\frac{USD}{L} < \frac{4\cdot x + 7\cdot y}{500} < 6\,\frac{USD}{L}[/tex]

Es decir:

[tex]\frac{4\cdot x + 7\cdot y}{500}> 5\,\frac{USD}{L}[/tex] y [tex]\frac{4\cdot x + 7\cdot y}{500}< 6\,\frac{USD}{L}[/tex]

Las inecuaciones que pueden ayudar a calcular cuantos litros de pintura blanca se pueden tener como son [tex]\frac{4\cdot x + 7\cdot y}{500}> 5\,\frac{USD}{L}[/tex] y [tex]\frac{4\cdot x + 7\cdot y}{500}< 6\,\frac{USD}{L}[/tex].

Answer:

Options 2, 4, and 5 are correct (from top to bottom)

Step-by-step explanation:

g(0)=0

g(1)=1

g(-1)=1

g(4)≠-2

g(4)=2

g(1)≠-1

g(1)=1

Options 2, 4, and 5 are correct (from top to bottom)

Answer:

Step-by-step explanation:

A square has equal sides. Let x represent the length of each side of the square carpet. The diagram representing the room and the carpet is shown in the attached photo. Therefore, the length of the room would be (x + 2)m while the width of the room would be (x + 1)m

Since the area of the room is 56m², it means that

(x + 2)(x + 1) = 56

x² + x + 2x + 2 = 56

x² + 3x + 2 - 56 = 0

x² + 3x - 54 = 0

x² + 9x - 6x - 54 = 0

x(x + 9) - 6(x + 9) = 0

x - 6 = 0 or x + 9 = 0

x = 6 or x = - 9

Since the dimension of the carpet cannot be negative, then x = 6

The dimension of the carpet is 6m × 6m

Answer:

it will take 0.056025 seconds to complete

Step-by-step explanation:

Here, we want to know the amount of time it will take. the computer to sort 15 items.

What to do here is simply substitute the value of 15 for x

Thus, we have

t = 0.007(15)^2 + 0.003(15)

t = 0.011025 + 0.045

t = 0.056025

answer: 1.62

step-by-step explanation: apx :)

Answer:

Step-by-step explanation:divide both sides by the coefficient of x that is the number beside x and in inequality, when dividing with a negative sign the sign would change to its opposite sign.

-6<-2x

-6/-2>-2x/-2

3>x

X<3 this is the answer.

Answer:

The answer is 13

Step-by-step explanation:

You'll say what will you multiply by itself to give you 169.

It will be 13 times itself and it will be =169.

Answer:

30.96 [tex]in^2[/tex]

Step-by-step explanation:

Given that

Side of square = 12 in

Diameter of circle = 12 in

We know that, radius is half of diameter,

So, r = 6 cm

We have to find the area of square which is not covered by the circle.

i.e. Required Area = Area of Square - Area of Circle

Please refer to the attached to have a better understanding of the given situation.

Formula:

Area of square = [tex](side)^2[/tex]

Area of circle = [tex]\pi r^2[/tex]

Required Area = [tex]12^2[/tex] - [tex]\pi \times 6^{2}[/tex]

[tex]\Rightarrow 144 - 3.14 \times 36\\\Rightarrow 144 - 113.04\\\Rightarrow 30.96\ in^2[/tex]

So, the answer is 30.96 [tex]in^2[/tex].

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

Work Shown:

Let x be the location of E on the number line.

Since C is the midpoint of E and F, this means we can find C's location by adding E and F together and dividing that sum by 2

midpoint = (endpoint1 + endpoint2)/2

C = (E+F)/2

Plug in E = x, C = -8 and F = 4. Then solve for x

C = (E+F)/2

-8 = (x+4)/2

(x+4)/2 = -8

x+4 = 2(-8) .... multiplying both sides by 2

x+4 = -16

x = -16-4 .... subtract 4 from both sides

x = -20

The location of point E on the number line is -20

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

As a check, lets add E and F to get E+F = -20+4 = -16

Then cut this in half to get -16/2 = -8, which is the proper location of point C

This confirms our answer.

Answer:

factor: 5(2x'y'+3xy)

Step-by-step explanation:

thats for factoring, i didnt know what you needed

Answer:

25xy

Step-by-step explanation:

collect like terms

Answer:

x=8 degrees y=21 degrees

Step-by-step explanation:

Answer:

A y=1/2x(powerof)2+5

B 17.5

C x=√42 or x=−√42

Step-by-step explanation:

Answer:

a. y = x^2 + 10

b. when x=5,   y  = 35

c. when y = 26,   x =  +4 or -4

Step-by-step explanation:

Given

y = k (x^2/2 + 5), and

(2,14) is on the curve.

Solution:

Substitute x=2 and y=14 in the above equation

14 = k (2^2/2 + 5)

14 = k (2+5)

14 = 7k

k = 14/7 = 2

a. equation connecting x and y is

   y = 2 (x^2/2 + 5), or

   y = x^2 + 10

b. when x=5

   y = 5^2 + 10 = 25 + 10 = 35

c. when y = 26

  26 = x^2 + 10

  x^2 = 26-10 = 16

  x= sqrt(16) = +4 or -4

Answer:

P = 0.2517

Step-by-step explanation:

In this case we must calculate the probability of event, which would be the number of specific events (that is, at least one woman and the rest men, 4), then it would be to choose 1 of 6 women by 4 of 9 men divided by the number of total events, which would be to choose 5 (committee size) out of 15 (9 men + 6 women, total number of people)

P (at least one woman) = 6C1 * 9C4 / 15C5

we know that nCr = n! / (r! * (n-r)!)

replacing we have:

6C1 = 6! / (1! * (6-1)!) = 6

9C4 = 9! / (4! * (9-4)!) = 126

15C5 = 15! / (5! * (15-5)!) = 3003

Therefore it would be:

P (at least one woman) = 6 * 126/3003

P = 0.2517

That is, approximately 1 out of 4 women.

Answer:

1. 2 pinch of salt

2. 3/2 egg =1.5 eggs

3. 33g of flour=1/3 pinch of salt

33g of flour=1/3 tbsp of oil

33g of flour=1/3 egg

33g of flour=100ml of milk

4. 24 servings

5. 300g of flour

Step-by-step explanation:

12 servings

Plain flour=100g

Salt=a pinch

Oil= 1 tbsp

Egg=1

Milk=300 ml

1. Pinches of salt in 24 servings

24

12 servings=1 pinch of salt

24 servings=24/12*1 pinch of salt

=2*1 pinch of salt

=2 pinch of salt

2. Egg needed for 18 servings

12 servings=1 egg

18 servings=18/12 * 1 egg

=3/2* 1 egg

=3/2 egg

3. If there are 33 grams of flour,

The other ingredients will be

33g/100g=1/3

The other ingredients will be 1/3 of the original measurement

Salt=a pinch

33g of flour=1/3 pinch of salt

Oil= 1 tbsp

33g of flour=1/3 tbsp of oil

Egg=1

33g of flour=1/3 egg

Milk=300 ml

33g of flour=1/3 of 300ml

=1/3*300

=300/3

=100ml of milk

4. If two eggs were used, grams of flour needed is

1 egg =12 servings

2 eggs=2* 12 servings

=24 servings

5. Flour needed if 900ml milk is used

100g flour=300ml of milk

900ml of milk=300ml * 3

Therefore,

900ml of milk=100g of flour *3

900ml of milk=300g of flour

Answer:

4.25

Step-by-step explanation:

Answer:15 I think

Step-by-step explanation:

Answer:

3x - 8

Step-by-step explanation:

9x² - 64 is a perfect square binomial

3x - 8 and 3x + 8 are the factors

First factor the 2nd degree polynomial.

[tex]9x^2-64=(3x-8)(3x+8)[/tex]

We find that polynomial is factored to two binomials:

Hope this helps.

Answer:

[tex]\boxed{BC = 11.62}[/tex]

Step-by-step explanation:

Tan 54 = [tex]\frac{opposite}{adjacent}[/tex]

Where opposite = 16, Adjacent = BC

1.376 = [tex]\frac{16}{BC}[/tex]

BC = 16/1.376

BC = 11.62

Answer:

11.62468045 or 11.6 to 1 decimal place

Step-by-step explanation:

→ We need to utilise trigonometry. The first step would be to list out the formula triangles

Tan = Opposite ÷ Adjacent

Sin =  Opposite ÷ Hypotenuse

Cos = Adjacent ÷ Hypotenuse

→ Now we need to know which triangle to use, we do that by identifying the side or length we are not given in the triangle and then finding a formula without the name of the given side. First let's identify all the sides.

Opposite = AC = 16

Adjacent = BC = We need to find this out

Hypotenuse = AB = No given value

→ Now we look for a formula with hypotenuse

Tan = Opposite ÷ Adjacent

→ The (Tan = Opposite ÷ Adjacent) is the formula we are going to be using. Since we want to find out the adjacent, we have to rearrange to get adjacent as the subject

Adjacent = Opposite ÷ Tan

→ Now we identify the Opposite and the Tan

Opposite = 16

Tan = 54°

Side note ⇒ Sin, cos and tan will always be the angles

→ Substitute in the values in the formula

Adjacent = Opposite ÷ Tan ⇔ Adjacent = 16 ÷ Tan (54) ⇔ Adjacent = 11.6

→ The adjacent is 11.6 to 1 decimal place

Answer:

I think -1,14

Step-by-step explanation:

Because you add 5

Hi Plato/Edmentum Users!

The other person is correct!

Sarah: School to mall = 21

           mall to library = 20

Total distance for Sarah = 20 + 21 = 41 miles.

Use the Pythagorean theorem to find the distance Bret traveled:

Distance = SQRT(21^2 + 20^2)

              = sqrt(441 + 400)

              = sqrt(841)

              = 29 miles

Total distance  = 41 + 29 = 70 miles

Answer is D. 70 miles.

Answer:

70

Step-by-step explanation:

i took the test

Answer:

[tex]a = 3[/tex]

Step-by-step explanation:

[tex]3 {a}^{2} = 27 \\ \frac{3 {a}^{2} }{3} = \frac{27}{3} \\ {a}^{2} = 9 \\ a = \sqrt{9} \\ a = 3[/tex]

Answer: 9

Step-by-step explanation:

First divide both sides by 3

[tex]a^2=9[/tex]

Then root both sides([tex]\sqrt{a^2}=\sqrt{9}[/tex])

a = 9

Hope it helps <3

Edit: :o this is my 250th answer

Hey there! :)

Answer:

Choices 1, 4 and 5.

Step-by-step explanation:

To solve, we can go through each answer choice and check if they are Pythagorean Triples using the Pythagorean Theorem:

1) 26² = 10² + 24²

676 = 100 + 576

676 = 676. This is correct.

2) 49² = 14² + 48²

2401 = 196 + 2304

2401 ≠ 2500. This is incorrect.

3)

16² = 12² + 9²

256 = 144 + 81²

256 ≠ 225. This is incorrect.

4)

41² = 40² + 9²

1681 = 1600 + 81

1681 = 1681. This is correct.

5)

25² = 15² + 20²

625 = 225 + 400

625 = 625. This is correct.

Therefore, choices 1, 4 and 5 are correct.

Answer:

A, D, and E.

Step-by-step explanation:

Answer:

Option (2)

Step-by-step explanation:

Volume of a prism A (preimage) = 27 cubic units

Factor of dilation of the sides of this prism (image) = [tex]\frac{1}{3}[/tex]

Volume scale factor of these prisms = [tex]\frac{\text{Volume of image}}{\text{Volume of preimage}}[/tex]

Since, Volume scale factor = (Scale factor of dilation of the sides)³

                                             = [tex](\frac{1}{3})^3[/tex]

                                             = [tex]\frac{1}{9}[/tex]

Now from the formula of volume scale factor,

[tex]\frac{1}{9}=\frac{\text{Volume of image}}{\text{Volume of preimage}}[/tex]

[tex]\frac{1}{9}=\frac{\text{Volume of image}}{27}[/tex]

Volume of the image prism = [tex]\frac{27}{9}[/tex] = 3 cubic units

Therefore, Option (2) will be the answer.                                                    

Answer:

1 cubic unit

Step-by-step explanation: