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Tju [1.3M]
3 years ago
7

Michael wants to find the length of the shadow of a tree. He measures the height of a fencepost and the length of the shadow it

casts. The fencepost is 3.5 feet tall, and its shadow is 10.5 feet long. Next, Michael measures the height of the tree, and finds it is 6 feet tall. How long is the shadow of the tree? ______________________________________
Mathematics
1 answer:
Irina18 [472]3 years ago
6 0
10.5÷3.5 = 3
6x3 = 18
18 feet is your answer (hope this helps)
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The amount of caffeine consumed from a glass of Diet Pepsi is proportional to the number of ounces that was drank. The table bel
Vilka [71]

Answer:

Constant of proportionality: k=3

Equation: c=3d

Step-by-step explanation:

By definition, Direct proportion equations have the following form:

y=kx

Where "k" is the Constant of proportionality.

In this case, let be "c"  the the amount of caffeine consumed  (in mg) from a glass of Diet Pepsi and "d" the number of ounces that was drank.

So, the equation that represents this relationship will have this form:

c=kd

Then, the first step is to find the Constant of proportionality "k".

Knowing that:

c=24;d=8

We can substitute values into the equation:

24=k(8)

Now, solving for "k", we get:

\frac{24}{8}=k\\\\k=3

Therefore, we can write the following equation that represents that proportional relationship:

c=3d

6 0
3 years ago
What is the sum of series is numbers 64&amp;66 ?<br> Using the summation notation
iragen [17]

Answer:

64. 6138

66. 8.078125

Step-by-step explanation:

Let's take it one number at a time.

For number 64:

6(2)^{1-1}=6

6(2)^{2-1}=12

6(2)^{3-1}=24

6(2)^{4-1}=48

6(2)^{5-1}=96

6(2)^{6-1}=192

6(2)^{7-1}=384

6(2)^{8-1}=768

6(2)^{9-1}=1536

6(2)^{10-1}=3072

Sum = 6 + 12 + 24 + 48 + 96 + 192 + 384 + 768 + 1536 + 3072

Sum = 6138

For number 66:

12(-\frac{1}{2})^{0}=12

12(-\frac{1}{2})^{1}=-6

12(-\frac{1}{2})^{2}=3

12(-\frac{1}{2})^{3}=-1.5

12(-\frac{1}{2})^{4}=0.75

12(-\frac{1}{2})^{5}=-0.375

12(-\frac{1}{2})^{6}=0.1875

12(-\frac{1}{2})^{7}=-0.0078125

12(-\frac{1}{2})^{8}=0.046875

12(-\frac{1}{2})^{9}=-0.0234375

Sum = 12 + -6 + 3 + -1.5 + 0.75 + -0.375 + 0.1875 + -0.0078125 + 0.046875 + -0.0234375

or to make things simpler:

Sum = 12 - 6 + 3 - 1.5 + 0.75 - 0.375 + 0.1875 - 0.0078125 + 0.046875 - 0.0234375

Sum = 8.078125

4 0
3 years ago
Do the points A(-2,1), B(-2,4), C(3, 4), D(3, 1) form a square?
monitta

Answer: i don't think they do

Step-by-step explanation: tell me if i wrong

8 0
3 years ago
Read 2 more answers
Solve the equation for x, where x is a real number (5 points): <br> -5x^2 + 7x + 41 = 32
wel
Subtract 32 to both sides to the equation becomes -5x^2 + 7x + 9 = 0.

To solve this equation, we can use the quadratic formula. The quadratic formula solves equations of the form ax^2 + bx + c = 0
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                   x = [ -7 ± √(7^2 - 4(-5)(9)) ] / ( 2(-5) )
                   x = [ -7 ± √(49 - (-180) ) ] / ( -10 )
                   x = [ -7 ± √(229) ] / ( -10)
                   x = [ -7 ± sqrt(229) ] / ( -10 )
                   x = 7/10 ± -sqrt(229)/10
The answers are 7/10 + sqrt(229)/10 and 7/10 - sqrt(229)/10.
6 0
3 years ago
PLS HELP !!! I NEED HELP PLS ILL APPRECIATE IT SM!
bazaltina [42]

Answer:

\frac{3}{4}

Step-by-step explanation:

ok so first you want to find a common factor. For instance, 3. So divide the numerator and denominator by 3. This will give you the fraction of \frac{3}{4}.

5 0
2 years ago
Read 2 more answers
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