Finding the area of a triangle is straightforward if you know the length of the base and the height of the triangle. But is it possible to find the area of a triangle if you know only the coordinates of its vertices? In this task, you’ll find out. Consider ΔABC, whose vertices are A(2, 1), B(3, 3), and C(1, 6); let line segment AC represent the base of the triangle.
Part A
Find the equation of the line passing through B and perpendicular to AC .

Answer:

m∠1 = 83

m∠2 = 97

m∠3 = 83

m∠4 = 97

m∠5 = 83

m∠6 = 97

m∠7 = 83

Step-by-step explanation:

When two lines are parallel,

m∠8 = m∠4 = 97 ( Alternate interior angles )

m∠8 = m∠2 = 97 ( Alternate interior angles )

m∠6 = m∠4 = 97 ( Vertically opposite angles )

m∠2 and m∠3 are linear pair angles,

m∠2 + m∠3 = 180

97 + m∠3 = 180

m∠3 = 180 - 97

m∠3 = 83

m∠1 = m∠3 = 83 ( Vertically opposite angles )

m∠3 = m∠7 = 83 ( Alternate interior angles )

m∠7 = m∠5 = 83 ( Vertically opposite angles )

Answer:

  0.16 liters of water

Step-by-step explanation:

Samantha's recipe makes 0.06 liters of solution. She wants 0.48 liters of solution, an amount 0.48/0.06 = 8 times as great as made by one recipe.

The recipe calls for 0.02 liters of water. To make 8 times the amount of solution, Samantha will use 8 times as much water: 0.16 liters.

Samantha will use 0.16 liters of water to make 0.48 liters of solution.

__

Alternate solution

The fraction of solution that is water is (0.02 L)/(0.06 L) = 1/3. For 0.48 L of solution, the water needed is 1/3×0.48 L = 0.16 liters.

Answer:

0.16L

Step-by-step explanation:

Answer:

Step-by-step explanation:

full price of the phone in terms of percentage

= 100%

percentage discount = (100-35)% = 65%

let the price of the phone before discount= X

therefore,

65%-----------78

100%----------X

cross multiplying

65×X = 100×78

dividing bothsides by X

X = 100×78/65

X = 7800/65

X = 120

price of the phone before discount=€120

Answer:

15 rides for each horse

Step-by-step explanation:

60 minutes in an hour

   90 minutes in an hour and a half

6 minutes per ride (counting the re-saddle time )

   90 min / 6 min/ride = 15 rides     for each horse

Answer:

1. 6.75x or (6.75, 1)

2.  buys 9 sandwiches.

Step-by-step explanation:

hope this helps if not let me know have a blessed day

Answer: E ; (0,12) , (9,0)

Explanation: To find coordinates by a scale factor is by multiplying.
What we need to do is to multiply the coordinate points by the scale factor.

Find A' is use A 's coordinate.  A 's coordinates are (0,4)
3 x 0 = 0
3 x 4 = 12

A' coordinates are : (0,12)

Using the same technique with C'.
3 x 3 = 9
3 x 0 = 0

C' coordinates are : (9,0)

Answer:

Both of the prism are similar , Then

prism A is 10m and it's surface area is 880m²

Now,

prism B is 3m and it's surface area will be = 264m²

Answer:

yes

Step-by-step explanation:

the slope stays constant throughout

The area of the composite figure is 1152 square meters

A rectangular prism and 2 triangular prisms. The rectangular prism has a length of 20 meters, width of 6 meters, and height of 8 meters. The triangular prisms each have 2 triangular sides with a base of 6 meters and height of 8 meters. The rectangular sides are 20 meters by 6 meters, 20 meters by 10 meters, and 20 meters by 8 meters.

The composite figure shown is made up of 2 triangular prisms and one rectangular prism. If the area of each triangle base of the triangular prisms has an area of 24 m2, what is the total surface area of the composite figure?

The given parameters are:

Rectangular prism :

Length = 20 meters; Width = 6 meters; Height = 8 meters

Triangular prism :

The area of the rectangular prism is:

Area = 2 * (Length * Width + Length * Height + Width * Height)

So, we have:

Area = 2 * (20 * 6 + 20 * 8 + 6 * 8)

Area = 656

The area of the triangular prism is:

Area = 2 * Base Area + Areas of Rectangular sides

So, we have:

Area = 2 * 24 + (20 * 6 + 20 * 10 + 20 * 8)

Area = 528

The common area between the prisms is:

Common area = 8 * 4

Common area = 32

Subtract the common area from the sum of the areas of the triangular prism and the rectangular prism to get the area of the composite figure

Composite figure = 656 + 528 - 32

Evaluate the sum

Composite figure = 1152

Hence, the area of the composite figure is 1152 square meters

Read more about areas at:

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Answer: D, 1152 m2

Step-by-step explanation: I got it correct

Answer:

x+2

Step-by-step explanation:

Given polynomial:

1x+2

x can be written as 1x, which is

Same case is here as well.

Rewrite 1x as x:

There isn't any like terms so we can't simplify.

Answer:

1516

Step-by-step explanation:

hope can help you

2000x 2%=40

9000x 5%= 450

(30000-9000-2000) x 5.4% = 1026

total tas 40+450+1026=

Answer:

Nice to hear that, congrats with practice 7.3

Answer:

WHAT ARE WE SUPPOSE TO ANSWER...?

The function which represents a graph which has been vertically shifted by 3 units is; y= log (x) + 3.

It follows from the task content that the graph which has been shifted vertically is to be identified.

For a vertical shift, it means that the y value of such graphs must have increased or decreased. This is However, evident in the equation y= log (x) + 3 and hence, is the solution.

Read more on function shift;

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So probability of red rose is 1/24

Probability of white rose is 1/28

TOTAL roses= 50

P(A$\cap$ B)=1/24+1/28-1/50

So Probability of white is

Answer:

29/4

Step-by-step explanation:

7/1/4 = 7 1/4 = (4/4 x 7) + 1/4 = 28/4 + 1/4 = (28/4 + 1)4 = 29/4

The quick rule is:

Multiply the integer by the denominator: 7 x 4 = 28

Add the numerator to this product: 28 + 1 = 29

Put this result over the denominator: 29/4

Answer:

Step-by-step explanation:

draw ⊥ from B cutting  AC.

let it be D.

[tex]\frac{BD}{BC} =sin 30\\BD=\frac{1}{2} \times BC=\frac{1}{2} \times 2x=x\\area=\frac{1}{2} \times 3x \times BD=\frac{1}{2} \times 3x \times x\\T=\frac{3x^2}{2} \\2T=3x^{2} \\x^{2} =\frac{2T}{3} \\x=\sqrt{\frac{2T}{3} }[/tex]

Answer:

See below ....none of your answer choices  'fit'

Step-by-step explanation:

Break it into two pieces....a triangular prism and a square pyramid

prism volume = (area) * length

                      ( 1/2 base * height)     *  length  

     Use pythagorean theorem to find height of triangular prism = 12

                            1/2 * 12 * 9   * 21 = 1134 km^3

Pyramid volume = 1/3 base * height =

               =   1/3  *   (9*21)    *    7 = 441 km^3

Summed = 1575 km ^3          

Answer:

1) They will stop 10 times for a break

2) A baker can make 10 cakes

3) Tammy will distrubute 36 bags with 2 1/2 pounds of candy

Step-by-step explanation:

Let me know if you have any questions !

Hope it helps

Answer:

is this required answer

Step-by-step explanation:

AB=3x-2

=3*8-2

=22

Answer:

[tex]\huge\boxed{\textbf{AB = 22}}[/tex]

Step-by-step explanation:

Given that:

AB = 3x - 2

Put x = 8

AB = 3(8) - 2

AB = 24 - 2

AB = 22

[tex]\rule[225]{225}{2}[/tex]

Answer: can i get

Step-by-step explanation:

Answer:

Step-by-step explanation:

Remeber range is the difference between the highest and lowest values in a set of numbers.  so 79 right rounded to the nearst tenth the answer will be 80

If the coordinate is reflected over the x-axis, the resulting coordinate point will be at (8, 7)

If the coordinate (x, y) is reflected over the x-axis, the resulting coordinate will be at (x,-y).

Given the coordinate point (8, -7), if the coordinate is reflected over the x-axis, the resulting coordinate point will be at (8, 7)

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Answer:

  see attached

Step-by-step explanation:

The related function we like to graph is the one that has the solutions as its zeros.

__

Subtract 5 from both sides.

  x² -9 = 0

This is now in the form ...

  f(x) = 0

The related function is then ...

  f(x) = x² -9

and its zeros are the solutions to the original equation. The zeros (x-intercepts) of f(x) are x = -3 and x = 3.

__

Additional comment

The second attachment shows a graph of the given equation. Essentially, its graph is two points on the number line: x = -3 and x = 3.

Answer:

i belive 7

Step-by-step explanation:

becuse 3+6 in one line = 9 so 2 + 7= 9

Answer:

∠CED = 70°

∠BCE = 134°

Step-by-step explanation:

Finding z :

Finding ∠CED :

Finding y :

Finding ∠BCE :

Answer:

∠CED = 70°

∠BCE = 134°

Step-by-step explanation:

We don't know if AB and DE are parallel (since there are no arrows on these line segments), therefore we cannot use the Alternate Interior Angles Theorem at this point to definitively say that ∠CDE = ∠ABC.

Angles around a point sum to 360°

Angles on a straight line sum to 180°

⇒ ∠ACB + ∠BCE = 180

⇒ ∠ACB + (7y - 6) = 180

⇒ ∠ACB = 180 - (7y - 6)

⇒ ∠ACB = 180 - 7y + 6

⇒ ∠ACB = 180 - 7y + 6

⇒ ∠ACB = 186 - 7y

The interior angles of a triangle sum to 180°

⇒ ∠ACB + ∠CBA + ∠BAC= 180

⇒ 186 - 7y + 64 + 3y + 10 = 180

⇒ 260 - 4y = 180

⇒ 4y = 80

⇒ y = 20

Using the found value of y to find ∠BCE:

⇒ ∠BCE = 7(20) - 6

⇒ ∠BCE = 134°

Angles on a straight line sum to 180°

⇒ ∠DCE + ∠BCE = 180

⇒ ∠DCE + 134 = 180

⇒ ∠DCE = 46°

The interior angles of a triangle sum to 180°

⇒ ∠DCE + ∠CED+ ∠EDC = 180

⇒ 46 + (9z - 2) + 8z = 180

⇒ 17z + 44 = 180

⇒ 17z = 136

⇒ z = 8

Using the found value of z to find ∠CED:

⇒ ∠CED = 9(8) - 2

⇒ ∠CED = 70°

Answer:

True, (-∞, ∞)           0 > -12

Step-by-step explanation:

8 > −4

8 - 8 > −4 - 8

0 > -12

Hope it helps :)

If you have any questions or anymore help lmk, happy to help with any school work!!

Have a nice day, you’ll make it thru :)

(shhhh i added your deleted question to this one as well, Image below)

Answer:

16 girls.

Step-by-step explanation:

Ignoring for a second the strict gender binary here, let's break down what this problem is telling us. A ratio of 3 boys to 4 girls means that for every 3 + 4 = 7 students, 3 are boys and 4 are girls. A class of 28 students is 4 times bigger than 7, so we can multiply each number in the ratio by 4 to get the count for this larger class. Doing that math, we find 3 · 4 = 12 boys and 4 · 4 = 16 girls.

Answer:

y = 5

Step-by-step explanation:

An equation can be written in two forms: point-slope form or slope-intercept form.

When you write an equation in point-slope form, you only need two things: a point and a slope.

Given:

The standard point-slope equation is

y - y₁ = m(x - x₁)

Plug in what you know.

y - (5) = 0(x - (-4))

Simplify.

y - 5 = 0(x + 4)

y - 5 = 0

y = 5

This is your equation.

Let's now represent this in slope-intercept form.

The standard equation is

y = mx + b

Plug in what you know.

5 = 0(-4) + b

Simplify.

5 = 0 + b

5 = b

Therefore,

y = 0x + 5 or y = 5

Hope this helps!

Learn with another example:

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