You and a friend want to know how much rope you need to climb a large rock. Your friend is 5.5 feet tall and casts a shadow that is 18 feet long. If the rock casts a shadow that is 209.5 feet long, calculate the height of the rock from the ground. Round your answer to the nearest foot. (Hint: make a drawing) a. 64 ft b. 18 ft c. 210 ft d. 219 ft

Brooke earned $9.00 in interest over one year on her account with $90 at a 10% annual interest rate, compounded annually.

To solve this problem, we can use the formula for compound interest:

A =[tex]P(1 + r/n)^(^n^t^)[/tex]

where A is the amount of money in the account after t years, P is the principal (the initial amount of money), r is the annual interest rate as a decimal, n is the number of times the interest is compounded per year, and t is the time period in years.

In this case, we want to find the interest earned in one year, so we can set t = 1. We know that Brooke has $90 in her account, so P = 90. The annual interest rate is 10%, or 0.1 as a decimal. The interest is compounded annually, so n = 1.

We can plug these values into the formula and solve for the amount of money in the account after one year:

A = [tex]90(1 + 0.1/1)^(^1^*^1^)[/tex]

A = 90(1.1)

A ≈ 99

The amount of money in the account after one year is approximately $99. So, Brooke earned $99 - $90 = $9 in interest. To the nearest cent, this is $9.00.

In conclusion, using the formula for compound interest, we can calculate the interest earned on an account given the initial balance, annual interest rate, number of compounding periods per year, and time period.

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Answer:

Step-by-step explanation:

Answer:

24 is awnser

Step-by-step explanation:

Pls mark me as brainliest

Answer:

A

Step-by-step explanation:

Answer:

angle 3x = 78°

angle opposite (4x + 30) = 226°

Step-by-step explanation:

It has 6 sides, so:

total interior angles sum = (180° x 6) - 360° = 720°

720° = 90° + 3x + 90° + 118° + (360° - (4x + 30°)) + 118°

combine like terms:

720° = 3x + 416° + (360° - 4x - 30°)

720° = -x + 746°

x = 26°

Answer:

g

Step-by-step explanation:

the point at the intersection of the parabola and its line of symmetry

Answer:

ill be figuring this out rn, (theres a caculator thingy online if nobody helps u)

Step-by-step explanation:

44.4 is the Percent and as a fraction its

111/250 (thats what i got)

6.66 as a dec. and as a fraction its 333/50

sorry if these are wrong bur its what i got.

Answer:

.12

Step-by-step explanation:

First set up your proportion.

[tex] \frac{3}{25} = \frac{12}{100} [/tex]Multiply 3 and 25 by 4 to get 12 and 100.

the answer would be 12 hundredths or .12

Answer:

C. =

Step-by-step explanation:

whenever you have |  | It will always be positive so -6 turns to 6 and that makes it equal.

Answer:

The Pythagorean theorem states that a2 + b2 = c2 in a right triangle where c is the longest side. You can use this equation to figure out the length of one side if you have the lengths of the other two.

Answer:

10 h 55 min

Step-by-step explanation:

13 h 10 - 2h = 11 h 10

11 h 10 - 15 min = 10 h 55 min

Answer:

the 3rd one

Step-by-step explanation:

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{-12=6\sqrt{x+4}}[/tex]

[tex]\mathsf{6 \sqrt{x + 4}=-12}[/tex]

[tex]\textsf{DIVIDE your BOTH SIDES by 6}[/tex]

[tex]\mathsf{\dfrac{6\sqrt{x + 4}}{6}= \dfrac{-12}{6}}[/tex]

[tex]\textsf{Introduce the new temporary equation}[/tex]

[tex]\mathsf{\sqrt{x + 4}=-2}[/tex]

[tex]\textsf{SOLVE for your SQUARE ROOT }[/tex]

[tex]\mathsf{\sqrt{{x + 4}}=-2}[/tex]

[tex]\mathsf{Like: x + 4 = (-2)^2}[/tex]

[tex]\textsf{SQUARE EACH of your SIDES}[/tex]

[tex]\mathsf{x + 4 = 4}[/tex]

[tex]\textsf{SUBTRACT your BOTH SIDES by 4 }[/tex]

[tex]\mathsf{x + 4 -4= 4-4}[/tex]

[tex]\mathsf{Cancel\ out\ 7-7 \ because\ it\ gives\ you\ 0}[/tex]

[tex]\textsf{Solving for your last temporary question}[/tex]

[tex]\mathsf{x = 4-4}[/tex]

[tex]\mathsf{4-4 = \bf 0}[/tex]

[tex]\mathsf{\bf x = 0}[/tex]

[tex]\textsf{Plug your x-value (x = 0) to make sure it works for your original equation}[/tex]

[tex]\textsf{You will see that it doesn’t work for the original problem so this means that the}\\\textsf{original equation \bf does NOT have any solutions.}[/tex]

[tex]\boxed{\boxed{\large\text{Answer: \huge\bf No solutions}}}\huge\checkmark[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

25

Step-by-step explanation:

Find the prime factors of each term in order to find the greatest common factor (GCF),

25

Answer:

180

Step-by-step explanation:

Answer:

B. 6.2

Step-by-step explanation:

The calculation is done by hand and verified by a TI-84 calculator.

Answer:f

Step-by-step explanation:d

Answer:

k = 4/25 or 0.16

Step-by-step explanation:

Given the following data;

y = 4/5

x = 5

To find the variation constant, k;

y is directly proportional to x

Mathematically, y = kx

Substituting into the formula, we have;

4/5 = k5

Cross-multiplying, we have;

4 = 25k

k = 4/25

Answer:

the blue block 'side' is 10

the pink block ' bottom' is 9

the cream 'side' block is 13 (length)

the green back triangle next to the blue side is also 10

and the other side of the green back triangle is 8

Answer:

The answer to the question provided is 60.

Answer:

nsdjdhbdeihddjjdoeuriehdisueueeuhd

Answer:

V(x) = 4(1.35)x, and it grows.

Step-by-step explanation:

The statement that illustrates the approximate value of the bond in hundreds of dollars over time in years is:

"The value of the bond can be approximated by the quadratic equation V(x) = 0.725x² + 0.675x + 4.

An equation contains one or more terms with variables connected by an equal sign.

Example:

2x + 4y = 9 is an equation.

2x = 8 is an equation.

We have,

We can use the given data points to approximate the relationship between the value of the bond and time by fitting a curve that best fits the points.

Based on the given data,

It seems that the value of the bond is increasing at an accelerating rate over time.

We can try to approximate this relationship by fitting a quadratic equation to the data.

Let's assume that the relationship between the value of the bond and time can be approximated by the quadratic equation:

V(x) = ax² + bx + c

where V(x) is the value of the bond in hundreds of dollars after x years, and a, b, and c are constants to be determined.

To solve for a, b, and c, we can use the three data points for which we have values of V(x):

V(0) = 4, V(1) = 5.4, V(2) = 7.29

Substituting these values into the equation.

a(0)² + b(0) + c = 4

a(1)² + b(1) + c = 5.4

a(2)² + b(2) + c = 7.29

Simplifying.

c = 4

a + b + c = 5.4

4a + 2b + c = 7.29

Substituting c = 4.

a + b = 1.4

4a + 2b = 3.29

Solving for a and b.

a = 0.725

b = 0.675

Now,

The equation that approximates the relationship between the value of the bond and time is:

V(x) = 0.725x² + 0.675x + 4

This equation tells us that the value of the bond is increasing at an accelerating rate over time, starting at $400 (or 4 hundred dollars) and increasing by approximately 0.725 hundred dollars for each year squared, plus 0.675 hundred dollars for each year, plus a constant 4 hundred dollars. For example, after 5 years, the value of the bond would be approximately:

V(5) = 0.725(5)² + 0.675(5) + 4 = 23.75

Therefore,

The statement that illustrates the approximate value of the bond in hundreds of dollars over time in years is:

"The value of the bond can be approximated by the quadratic equation V(x) = 0.725x² + 0.675x + 4.

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Answer:

hi

Step-by-step explanation:

10+963=973

have a nice day

Answer:

10+963= 973

Step-by-step explanation:

Answer 973

i hope this help

Answer:

Step-by-step explanation:

Greatest common factor of 6x and 9y is 3.

6x + 9y = 3(2x + 3y)

:::::

Greatest common factor of 3c and 11c is c.

3c + 11c = (3+11)c

The general rule for the given Sequence is a_n = 1 – 2n, where n = 1, 2, 3, ... This equation allows us to calculate any term in the sequence by substituting the corresponding value of n.

The given sequence –1, –3, –5, –7, –9,... follows a specific pattern or rule. To determine the general rule for n = 1, 2, 3,..., we can observe the sequence and identify the relationship between the terms.

Looking at the sequence, we notice that each term is decreasing by 2. Starting with –1, we subtract 2 to get the next term –3. Then, we subtract 2 again to get –5, and so on. Therefore, the rule for generating the terms in this sequence is to start with –1 and subtract 2 from each subsequent term.

We can express this rule algebraically as follows:

a_n = a_1 + (n – 1) * d

Where:

a_n represents the nth term of the sequence,

a_1 represents the first term of the sequence,

n represents the position of the term in the sequence,

d represents the common difference between the terms.

In this case, a_1 = –1 and d = –2 (since each term is decreasing by 2). Plugging these values into the equation, we get:

a_n = –1 + (n – 1) * (–2)

Simplifying further, we have:

a_n = –1 – 2n + 2

a_n = 1 – 2n

Therefore, the general rule for the given sequence is a_n = 1 – 2n, where n = 1, 2, 3, ... This equation allows us to calculate any term in the sequence by substituting the corresponding value of n.

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Note the full question may be :

From the following sequence: – 1, – 3, – 5, – 7, – 9,…, What is the general rule for n=1, 2, 3,…?

Step-by-step explanation:

The given equation is :

2x = 10

We need to find the value of x.

This equation has one solution as it is a linear equation having one variable i.e. x.

Dividing both sides by 2,

x = 5

So, the value of x is equal to 5.

Put x = 5. So,

2(5) = 10

10 = 10

Hence, this is the required solution.

Answer:

3/10

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

That whole circle equals 180, so just add 99 plus 76 and subtract it from 180.