A shadow 12 meters long is cast by a water tower that is 16 meters tall. What is the length of the shadow cast by a nearby utility pole that that is 12 meters tall?

A. 6
B. 9
C. 13
D.16

[tex](\stackrel{x_1}{0}~,~\stackrel{y_1}{-3})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{4}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{4}-\stackrel{y1}{(-3)}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{0}}}\implies \cfrac{4+3}{3}\implies \cfrac{7}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-3)}=\stackrel{m}{\cfrac{7}{3}}(x-\stackrel{x_1}{0})[/tex]

we can always find the y-intercept by simply setting x = 0, or namely

[tex]y-(-3)=\cfrac{7}{3}(0-0)\implies y+3=\cfrac{7}{3}(0)\implies y+3=0\implies y=-3 \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \stackrel{\textit{y-intercept at}}{(0~~,~-3)}~\hfill[/tex]

Answer:

first one is 7/3

second one is -3

third one is g(x) = 7/3x-3

Step-by-step explanation:

I got it right

Answer:

When selecting physics students at random, there is a 60% chance to select a student who also studies math.

Step-by-step explanation:

27 students studied math and physics.

27 + 18 = 45 students studied physics.

You can ignore the rest of the numbers because of this:

"given that they study physics".

Physics students are our total population now, and 27 of the 45 physics students study both math and physics.

[tex]\frac{27}{45} =0.6[/tex]

When selecting physics students at random, there is a 60% chance to select a student who also studies math.

Answer:

8

Step-by-step explanation:

Answer:

25-10  (25 - A and 10 - B)

Step-by-step explanation:

25 - 10 equals the 15 point margin

25 plus 10 equals the 35 point score combined

Hope it helps

Answer:both involving 6 and 7. (-6,-7) would be in quadrant 3 while point (-6,7) would be on top of it in quadrant 2.

Step-by-step explanation:

Step-by-step explanation:

1 x 18, 2 x 9, dan 3 x 6. Jadi, faktor dari 18 adalah 1, 2, 3, 6, 9, dan 18.

well, let's take 2 points from it and get it :) , say let's use (4 , 5) and (-1 , 5)

[tex](\stackrel{x_1}{4}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{-1}~,~\stackrel{y_2}{5}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{5}-\stackrel{y1}{5}}}{\underset{run} {\underset{x_2}{-1}-\underset{x_1}{(4)}}}\implies \cfrac{0}{-5}\implies 0[/tex]

bearing in mind that for any horizonal line it's always 0.

Answer:

21000,14000,and14000

Step-by-step explanation:

3x+2x+2x=49000

7x=49000

x=7000

3×7000=21000

2×7000=14000

2×7000=14000

Answer:

Definitely rational because 576 and 684 are both natural numbers

Step-by-step explanation:

Answer:

C. Both statements are true

Answer:

1.  D

2. B

3. The six in the first one is in the tenths place, the second is in the thousandths. But the answer is A.

4. 5, 0.9, 0.85, 0.438, 0.42, 0.341, 0.253, 0.13, 0.1, 0.087, 0.042, 0.03, 0.023, 0.01, 0.006, 0.002, 0 Sorry, I did greatest to least on accident.

5. 0.9, 0.853, 0.82, 0.51, 0.238, 0.2, 0.187, 0.11, 0.106, 0.103, 0.072, 0.053, 0.05, 0.03 greatest to least.

Uhm, sorry if I ordered some wrong on accident.

I think is the B, tell me if it's correct OK i'm trying to help

Answer:

5√7-5x√7

Step-by-step explanation:

9514 1404 393

Answer:

  (x, y) = (1.25, 8.5)

Step-by-step explanation:

I choose to put these equations into reduced general form, then use the "cross multiplication method" to solve.

  2x -y +6 = 0

  10x -y -4 = 0

d1 = 2(-1) -10(-1) = 8

d2 = -1(-4) -(-1)(6) = 10

d3 = 6(10) -(-4)(2) = 68

Solutions are ...

  x = d2/d1 = 10/8 = 1.25

  y = d3/d1 = 68/8 = 8.5

The solution is (x, y) = (1.25, 8.5).

_____

Additional comment

I like a graphing calculator for a quick and easy solution. When the values are not integers, I like an algebraic solution to see what the exact values are.

__

The "cross multiplication method" is similar to Cramer's rule in that determinants of pairs of coefficients are computed. If you look up this method, videos will show you a variation that is slightly different. Here, we determined d1, d2, and d3 as the 2×2 determinant of the coefficients in adjacent columns of the array you get from the general form equations with the first column repeated:

  [tex]\begin{array}{cccc}2&-1&6&2\\10&-1&-4&10\end{array}[/tex]

In each pair, the determinant is the difference between the product of numbers on the down-diagonal and the product of numbers on the up-diagonal.

The determinants relate to the x- and y-values by ...

  1/d1 = x/d2 = y/d3   ⇒   x = d2/d1, y = d3/d1

There is a Vedic solution method for linear equations that is similar to this, but starts from equations in standard form. As a consequence, the cross-differences are done in a different order.

__

Standard form: ax +by = c

General form: ax +by +c = 0

Answer:

B. Q′ (−2, −1)

Step-by-step explanation:

I looked at the graph, this is as close as I could get to my answer. I'm so sorry if it is wrong.

Answer:

D

Step-by-step explanation:

Commutative switchs the numbers but not with subtraction or divion

Answer:

it is D I know because it is the opposite

Answer:

6[tex]\frac{2}{3}[/tex] inches tall

Step-by-step explanation:

4:6 = x:10

We can set it up like this:

[tex]\frac{4}{6}=\frac{x}{10}[/tex]

And then cross multiply & solve:

40 = 6x

6[tex]\frac{2}{3}[/tex] = x

Have a nice day!

     I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)

- Heather

Step-by-step explanation:

The area of a parallelogram is just base x height, same as a rectangle.

[tex]a=b*h\\a=ir*r[/tex]

If ir is 2 separate variables rather than just 1, that can be simplified to this:

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

Answer:

Arithmetic, common difference is -11

Step-by-step explanation:

19, 8, -3, -14

common difference = d = 8 - 19 = -11

-3 - 8 = -11

-14 - (-3) = -11

Arithmetic, common difference is -11

Answer:

$their down payment is $280 the percentage of the purchase is $2.8

this is best solved using algebra

let the width be 4x (since it is 4 times more the length)

let the length be x

the formula for perimeter is (l+b)2 let us sub these variables in our formula

(x + 4x)2 = 64

expand brackets

2x + 8x = 64

combine like terms

10x = 64

make x the subject

x = 64/10 = 6.4

the length is 6.4 m

now let's find the width, the width is 4 times more the length so we simply substitute our value we found for x in 4x

we get:

4(6.4) = 25.6

the length is 25.6m

let's check our answers to see if its correct

25.6 + 6.4 = 32

32 × 2 = 64

the answer is correct

Answer:

Where are the values I can't read your qn properly my friend may the lord assist you

1 4/9 ÷ 2/3 = 13/9 x 3/2 = 13/6

ok done. Thank to me :>

Answer:

okay

Step-by-step explanation:

Bearing in mind that when the base is omitted, base 10 is assumed, or namely log(x) = log₁₀(x).

[tex]\begin{array}{llll} \textit{Logarithm of rationals} \\\\ \log_a\left( \frac{x}{y}\right)\implies \log_a(x)-\log_a(y) \end{array}~\hfill \begin{array}{llll} \textit{Logarithm of exponentials} \\\\ \log_a\left( x^b \right)\implies b\cdot \log_a(x) \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]

[tex]\log_{10}(2)=0.3010\qquad \qquad \log_{10}(3)=0.4771 \\\\[-0.35em] ~\dotfill\\\\ \log_{10}\left( \cfrac{4}{9} \right)\implies \log\left( \cfrac{4}{9} \right)\implies \log\left[ \cfrac{2^2}{3^2} \right]\implies \log\left[ \left( \cfrac{2}{3} \right)^2 \right]\implies 2\log\left[ \cfrac{2}{3}\right] \\\\\\ 2[\log(2)-\log(3)]\implies 2[0.3010~~ - ~~0.4771]\implies -0.3522[/tex]

Answer:

yeah is that all?

Step-by-step explanation:

i feel like I'd understand if there was more to this

Answer:

The negatives are at the bottom and the positives are at the top, if you need help with the (x,y) let me know!!!

Step-by-step explanation:

Answer:

right and above side of graph are positive

and

left and bottom side of graph are negative