An oak tree casts a shadow that is 16 yards long. A wooden column near the oak tree casts a
shadow that is 8 yards long. If the oak tree is 12 yards tall, how tall is the wooden column?
Write your answer as a whole number or a decimal. Do not round.

Label the points A,B,C

Let's find the distance from A to B, aka find the length of segment AB.

We use the distance formula.

[tex]A = (x_1,y_1) = (1,2) \text{ and } B = (x_2, y_2) = (4,5)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(1-4)^2 + (2-5)^2}\\\\d = \sqrt{(-3)^2 + (-3)^2}\\\\d = \sqrt{9 + 9}\\\\d = \sqrt{18}\\\\d = \sqrt{9*2}\\\\d = \sqrt{9}*\sqrt{2}\\\\d = 3\sqrt{2}\\\\[/tex]

Segment AB is exactly [tex]3\sqrt{2}[/tex] units long.

Now let's find the distance from B to C

[tex]B = (x_1,y_1) = (4,5) \text{ and } C = (x_2, y_2) = (8,9)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(4-8)^2 + (5-9)^2}\\\\d = \sqrt{(-4)^2 + (-4)^2}\\\\d = \sqrt{16 + 16}\\\\d = \sqrt{32}\\\\d = \sqrt{16*2}\\\\d = \sqrt{16}*\sqrt{2}\\\\d = 4\sqrt{2}\\\\[/tex]

Segment BC is exactly [tex]4\sqrt{2}[/tex] units long.

Adding these segments gives

[tex]AB+BC = 3\sqrt{2}+4\sqrt{2} = 7\sqrt{2}[/tex]

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

Now if A,B,C are collinear then AB+BC should get the length of AC.

AB+BC = AC

Let's calculate the distance from A to C

[tex]A = (x_1,y_1) = (1,2) \text{ and } C = (x_2, y_2) = (8,9)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(1-8)^2 + (2-9)^2}\\\\d = \sqrt{(-7)^2 + (-7)^2}\\\\d = \sqrt{49 + 49}\\\\d = \sqrt{98}\\\\d = \sqrt{49*2}\\\\d = \sqrt{49}*\sqrt{2}\\\\d = 7\sqrt{2}\\\\[/tex]

AC is exactly [tex]7\sqrt{2}[/tex] units long.

Therefore, we've shown that AB+BC = AC is a true equation.

This proves that A,B,C are collinear.

For more information, check out the segment addition postulate.

[tex] \qquad \qquad \huge \underline{\boxed{ \sf {Answer}}}[/tex]

Let's solve ~

The given equations are :

[tex] \qquad \dashrightarrow \bf \: 3x + 4y = 36 \sf \: \: \: \: \: \: \: \: \: \: (1)[/tex]

and

[tex] \qquad \dashrightarrow \sf \:y = - \frac{1}{2} x + 8[/tex]

[ multiply each sides by 2 ]

[tex] \qquad \dashrightarrow \sf \: 2y = - x + 16[/tex]

[tex] \qquad \dashrightarrow \sf \:x + 2y = 16[/tex]

[ multiply both sides by 2 ]

[tex] \qquad \dashrightarrow \bf \: 2x + 4y = 32 \: \: \: \: \: \: \: \: \: \: \: \sf(2)[/tex]

Now, subtract equation (2) from (1)

[tex] \qquad \dashrightarrow \sf \: 3x + 4y - (2x + 4y) = 36 - 32[/tex]

[tex] \qquad \dashrightarrow \sf \: 3x + \cancel{4y }- 2x - \cancel{4y }= 4[/tex]

[tex] \qquad \dashrightarrow \bf \: x = 4[/tex]

Now, as we got the value of x, let's solve for y :

[tex] \qquad \dashrightarrow \sf \: y = - \dfrac{1}{2} x+ 8[/tex]

[tex] \qquad \dashrightarrow \sf \: y = -\dfrac{1}{2} (4)+8[/tex]

[tex] \qquad \dashrightarrow \sf \: y = - 2 + 8[/tex]

[tex] \qquad \dashrightarrow \bf \: y = 6[/tex]

Answer:

i think its a or d

Step-by-step explanation:

Answer:

no clue but thanks for the points!

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

there are 30 buildings...

#1

Just follow the naming

#2

Note the adjacent angles of JK

Answer:

8.2 cm x 6.5 cm = an area of 53.3 cm

Answer:

53.3

Step-by-step explanation:

Multiply: 8.2cm*6.5cm

Answer: 53.3

Answer:

0.56

Step-by-step explanation:

edu 2022

Answer:

17.5

Step-by-step explanation:

8 : 10 = 14 : x

8x = 10*14 = 140

x = 140/8 = 17.5 cm

Answer:

[tex]\left|a\right|[/tex]

Step-by-step explanation:

Write the distance formula

[tex]\left|x_2-x_1\right|[/tex]

Find the distance

Find the distance between [tex]None(-1,a) and ():[/tex] [tex]\left|a\right|[/tex]

I hope this helps you

:)

Answer:

The distance between the pair of numbers is the absolute value of [tex]a[/tex], or [tex]|a|[/tex].

Step-by-step explanation:

Use the distance formula: [tex]d=|x_2-x_1|[/tex]. The [tex]x[/tex]s represent points one and two. Point one is [tex]-a[/tex], and point two is 0. Plug these into the equation, then solve:

[tex]d=|x_2-x_1|\\d=|(0)-(-a)|\\d=|a|[/tex]

Therefore, the distance between the pair of numbers is the absolute value of [tex]a[/tex], or [tex]|a|[/tex].

Answer:

4

Step-by-step explanation:

PLEASE MARK ME AS BRAINLIEST

Answer:

Ali is about 5-6 due to him having a larger stomach capacity.

Step-by-step explanation:

5-6 year olds would definitely eat about 4 cookies if somebody held 5, since they are open to sugary things, and they would eat possibly anything.

PLEASE MARK ME AS THE BRAINLIEST.

Answer:

8

Step-by-step explanation:

10 percent of 80 is 8

80 x 0.1 = 8

4 is 16 percent of 25

25/4 = 0.16

0.16 = 16%

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{10\% of 80}}{\left( \cfrac{10}{100} \right)80}\implies 8 \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{4\% of 25}}{\left( \cfrac{4}{100} \right)25}\implies 1[/tex]

Answer: 3

Step-by-step explanation:

Triangle DCB is similar to Triangle ECA by AAA.

Since EA and DB are parallel lines, that makes Angle CDB = Angle CEA and Angle CBD = Angle CAE because they are corresponding angles.

Since the two triangles are parallel, we can set up a ratio.

[tex]\frac{CD}{CE} = \frac{CB}{CA}[/tex]

Now we plug in the numbers given.

[tex]\frac{6}{8} = \frac{9}{CA}[/tex]

Now we can cross multiply

6CA = 72

Therefore, CA = 12.

AB = CA - CB

So AB = 12 - 9

AB = 3

Answer:

y = 23

Step-by-step explanation:

5y - 4 + 3y = 180

8y = 180 + 4

8y = 184

y = 184/8

y = 23

Answer:

Yes

Step-by-step explanation:

6/12 is 1/2 when you simplify

7/10 is more than 5/10 (one half of ten)
Please mark brainlest

Answer : Yes

Explanation : 6/12 Is 1/2 When You Simplify

7/10 Is More Than 5/10 (One Half Of Ten)

5/10 Is The Same As 1/2 Btw

Please Mark Brainliest

◊ YusuCr ◊

Answer:

1.26 m cubed or D

Step-by-step explanation:

Multiply the Length x Height x width

hope you have a great day!

if it helped mark me as brainliest!

The volume of the rectangular prism is 1.26 [tex]m^3[/tex] .

                      V = 1.4 × 0.5 × 1.8

                      V = 1.26 [tex]m^3[/tex]

Thus, the volume of the given rectangular prism is 1.26 [tex]m^3[/tex] .

Learn more about rectangular prism here:

https://brainly.com/question/24284033

#SPJ2

Answer:

The replicas will have a surface area of 3 m2, 2.4 m2 and 2 m2.

Step-by-step explanation:

You would have to multiply:

24 x 1/8 = 3

24 x 1/10 = 2.4

24 x 1/12 = 2

Answer:

A

Step-by-step explanation:

because it reflects

Answer: 2.5 and 87.5 degrees

Step-by-step explanation:

Answer:

[tex] \displaystyle{8 \frac{3}{4} \div 2 \frac{7}{8} }[/tex]

Convert the mixed fractions into improper fractions.

[tex]\displaystyle{ \frac{8 \times 4 + 3}{4} \div \frac{8 \times 2 + 7}{8} }[/tex]

[tex]\displaystyle{ \frac{32 + 3}{4} \div \frac{16 + 7}{8} }[/tex]

[tex]\displaystyle{ \frac{35}{4} \div \frac{23}{8} }[/tex]

[tex]\displaystyle{ \frac{35}{4} \times \frac{8}{23} }[/tex]

[tex]\displaystyle{ \frac{35}{ \cancel4} \times \frac{ \cancel8 {}^{2} }{23} }[/tex]

[tex] \displaystyle{ \frac{35 \times 2}{23} }[/tex]

[tex] \displaystyle{ \frac{70}{23} }[/tex]

[tex] \displaystyle{3 \frac{1}{23} }[/tex]

15x + 17y = 31

17x + 15y = 21

- - -

───────

-2x + 2y = 10

→ -2 (x -y) = 10

→ x - y = -5

Value of (x - y) is -5

In this exercise we have to use the knowledge of equation to find the value, so:

[tex]x-y=-5[/tex]

The solution of a linear system is every ordered and finite set that satisfies all the equations of the system at the same time. The number of elements in the solution set is always equal to the number of unknowns in the system.

So we have:

[tex]15x + 17y = 31\\17x + 15y = 21\\-2x + 2y = 10\\-2 (x -y) = 10\\x - y = -5[/tex]

See more about system at brainly.com/question/9061107

Answer:

-4, -1, 3, 5, 6

Step-by-step explanation:

-4, -1, 3, 5, 6

Answer:

Least to greatest would be:

-4, -1, 3, 5, and then 6.

In the history of Nepal, Rana Regime is known as Dark Age as it lacked freedom, public sovereignty, and public literacy.  

I would do the opposite of the things listed.

Considering the median, the missing value of the data-set is of 31.

The median of the data-set separates the bottom half from the upper half, that is, it is the 50th percentile.

In this problem, since the set has even cardinality, the median is the mean of the middle elements, which are 23 and x. Since it is of 27, we have that:

(23 + x)/2 = 27

23 + x = 54

x = 31

Hence, the missing value of the data-set is of 31.

More can be learned about the median of a data-set at https://brainly.com/question/24732674

Answer:

80 + 9x + 4 + 16x - 4 =180

25x = 180 - 80 + 4 - 4

25x = 100

x = 4

I can't see the question on the image...so not sure about final answer

Answer: y = 9x - 14

Step-by-step explanation:

The equation of a line is y = mx + b

We know the slope is 9 so so far the equation we have is y = 9x + b.

Since we know (1,-5) is a point on the line, we can plug in the x and y values into the equation and we get:

-5 = 1*9 + b

-5 = 9 + b

b = -14.

Therefore, the equation of the line is y = 9x - 14

Hello.

Here we have a point that the line passes through: (1, -5)

We also have the line's slope: 9

Now, we have enough information to write the line's equation in Point-Slope Form:

[tex]\mathrm{y-y1=m(x-x1)}[/tex]

Plug in the values and solve:

[tex]\mathrm{y-(-5)=9(x-1)}[/tex]

[tex]\mathrm{y+5+9(x-1)}[/tex]

[tex]\mathrm{y+5=9x-9}[/tex]

[tex]\mathrm{y=9x-9-5}[/tex]

[tex]\mathrm{y=9x-14}[/tex]

Therefore, the answer is

[tex]\mathrm{y=9x-14}[/tex]

I hope it helps.

Have a nice day.

[tex]\boxed{imperturbability}[/tex]

Answer:

 (a)  A and B are similar but not congruent

Step-by-step explanation:

All of the rectangles have sides in the ratio of 2:1, so are all similar. Only the rectangles that are the same size are congruent: A and C.

 A and B are similar, but not congruent.