Triangle A C D is shown. A line is drawn from point D to point B on side A C to form a right angle. Line A D is labeled s. The length of A B is 8, the length of B C is 5, and the length of B D is 15.
What is the value of s?

units

BB's parents should choose Grandpa's option, where Baby Bertha (BB) receives $1000 at birth plus an additional 4% of the accumulated amount each year.

In Grandpa's option, the annual contribution grows dynamically with the accumulated amount, creating compounding growth. Let's denote the accumulated amount at the end of year \(n\) as A_n. The contribution at year \(n\) can be expressed as \(0.04 \times A_n\). BB's total amount at the end of year \(n\) can be written as:

\[A_n = 1000 \times (1 + 0.04)^{n}.\]

This formula considers the initial $1000 and the 4% annual growth on the accumulated amount. With compounding, this option ensures that BB's fund grows significantly over time.

Grandma's option, on the other hand, provides a fixed annual amount of $50, which does not consider the potential growth through interest or investment. Over time, the fixed contribution might not keep up with inflation, and the fund may not accumulate as much as Grandpa's option.

In summary, Grandpa's option is financially advantageous due to compounding growth, allowing BB's fund to grow more substantially over the years. This strategy aligns with long-term financial planning, providing a better financial foundation for Baby Bertha's future.

Answer:

5 peices of pizza for $4 each

and 4 drinks for $2

Step-by-step explanation:

Answer:

She needs to work 8 hours

Answer:

-2

Step-by-step explanation:

f(x) = –2x^2 + 5x – 4.

            A        B     C

Leading coefficient is always a which is -2x^2

Answer:

angle 1

Step-by-step explanation:

[tex] \angle \: 1 \: is \: complementary \: to \: \angle \: 2 \\ [/tex]

Answer:  [tex](-9,-3)[/tex]

Step-by-step explanation:

Given the following system of equations:

[tex]\left \{ {{2x=-78-20y} \atop {-x=-51-20y}} \right.[/tex]

In order to solve the System of equations, you can use the Substitution method. The steps are:

1. You can solve for "x" from the second equation:

[tex]-x=-51-20y\\\\x=51+20y[/tex]

2. Substitute the equation obtained into the first original equation:

[tex]2x=-78-20y\\\\2(51+20y)=-78-20y[/tex]

3. Now you must solve for "y":

[tex]102+40y=-78-20y\\\\40y+20y=-78-102\\\\60y=-180\\\\y=\frac{-180}{60}\\\\y=-3[/tex]

4. Substitute the value of "y" into the equation [tex]x=51+20y[/tex] and evaluate:

[tex]x=51+20(-3)\\\\x=51-60\\\\x=-9[/tex]

Then, the solution is:

[tex](-9,-3)[/tex]

The area of the largest circular fire pit is 452 square inches.

Explanation:

Given that at a campground, a rectangular fire pit is 3 feet by 2 feet

The radius is given by 1 feet.

Area:

The area of the largest circular fire is given by

[tex]A=\pi r^2[/tex]

Substituting the values in the formula, we get,

[tex]A=(3.14)1^2[/tex]

[tex]A=3.14 \ ft^2[/tex]

Thus, the area of the largest circular fire is 3.14 square feet.

To convert feet to inches:

The feet can be converted into inches by multiplying by 12.

Thus, we have,

[tex]1 \ft= 12 \ inches[/tex]

Hence, we have,

[tex]Area= 3.14\times 12^2[/tex]

Simplifying,we get,

[tex]Area= 3.14\times144[/tex]

[tex]Area=452.16 \ in^2[/tex]

Rounding off to the nearest square inch.

Thus, we have,

[tex]Area= 452 \ in^2[/tex]

Thus, the area of the largest circular fire pit is 452 square inches.

Answer:

see explanation

Step-by-step explanation:

The n th term of a geometric sequence is

[tex]a_{n}[/tex] = a[tex](r)^{n-1}[/tex]

where a is the first term and r the common ratio

Here a = 15, thus

[tex]a_{5}[/tex] = 15[tex](r)^{4}[/tex] = [tex]\frac{243}{125}[/tex] ( divide both sides by 15 )

[tex]r^{4}[/tex] = [tex]\frac{243}{1875}[/tex], thus

r = [tex]\sqrt[4]{\frac{243}{1875} }[/tex] = [tex]\frac{3}{5}[/tex]

Multiply the previous term by [tex]\frac{3}{5}[/tex] to obtain the next term

15 × [tex]\frac{3}{5}[/tex] = 9

9 × [tex]\frac{3}{5}[/tex] = [tex]\frac{27}{5}[/tex]

[tex]\frac{27}{5}[/tex] × [tex]\frac{3}{5}[/tex] = [tex]\frac{81}{25}[/tex]

[tex]\frac{81}{25}[/tex] × [tex]\frac{3}{5}[/tex] = [tex]\frac{243}{125}[/tex]

Thus the sequence is

15, 9, [tex]\frac{27}{5}[/tex], [tex]\frac{81}{25}[/tex], [tex]\frac{243}{125}[/tex]

Step-by-step explanation:

[tex]0.031 \times 1000000 \\ = 31000 \\ moves \: 4 \: places \: to \: the \: right[/tex]

Answer:

y = 1/5x

Graph Below:  

Answer:

There is only one triangle with the degrees

Step-by-step explanation:

All angles must add up to 180 degrees

Solution:

Given expression is:

[tex]4s + \frac{1}{6}s + 2\frac{3}{5}s[/tex]

We have to simplify by combining the like terms

From given,

[tex]4s + \frac{1}{6}s + 2\frac{3}{5}s[/tex]

Convert the mixed fraction to improper fraction

[tex]4s + \frac{1}{6}s + \frac{13}{5}s[/tex]

Make the denominator same

[tex]\frac{4s \times 30 }{30} + \frac{1s \times 5}{6 \times 5} + \frac{13s \times 6}{5 \times 6}\\\\\frac{120s}{30} + \frac{5s}{30} + \frac{78s}{30}\\\\\frac{203}{30} = 6.7667[/tex]

Thus the solution is 6.7667

Answer:

Model B is wider car I think for the question which ones wider

Answer:

$1,367

Step-by-step explanation:

The compound amount formula applying to continuous compounding is

A = Pe^(r*t), where P is the principal, r is the interest rate as a decimal fraction, and t is the time in years.

Here we have A = $920e^(0.036*11), or $1,367

                            =

Answer:

The correct answer would be 1367.

Step-by-step explanation:

Answer:

23

Step-by-step explanation:

log27(9) can be interpreted as " 27 to what power is equal to 9 . Since 2723=32=9,log27(9)=23

Answer:

2/3

Step-by-step explanation:

Answer:

[tex] \frac{1}{ {4}^{3} } [/tex]

Step-by-step explanation:

[tex] \frac{ {4}^{2} }{ {4}^{5} } = \frac{1}{ {4}^{ - 2} \times {4}^{5} } = \frac{1}{ {4}^{(5 - 2)} } = \frac{1}{ {4}^{3} } [/tex]

Answer:

Option 1

Step-by-step explanation:

1/6 × 5/3

Step-by-step explanation:

[tex] \frac{1}{6} \div \frac{3}{5} [/tex]

[tex] \frac{1}{6} \times \frac{5}{3} [/tex]

a= 6,b=5,c=3 option A

When a programmer works for 10 hours and earns $70, the rate of dollars per hour earned by the programmer is $7.

A computer programmer worked for 10 hours and earned $70.

To calculate the rate per hour, we divide the total earnings by the number of hours worked. In this case,

$70 ÷ 10 hours = $7 per hour.

Therefore, the programmer earned $7 per hour.

Answer: -121

Step-by-step explanation:

Answer:

x = -8

Y = -11

Step-by-step explanation:

Given

Y = 3x + 13

Y = x - 3

Substitute x - 3 for Y in the first equation

We have

Y = 3x + 13

x - 3 = 3x + 13

Add 3 to both sides

x - 3 + 3 = 3x + 13 + 3

x = 3x + 16

Subtract 3x from both sides

x - 3x = 3x - 3x + 16

-2x = 16

Divide both sides by -2

x = 16/-2

x = -8

Now substitute -8 for x in any of the above equations to get Y.

Using the second equation, we have

Y = x - 3

Y = -8 - 3

Y = -11

Hi

72 Hours before 2:12 am, Monday is 2:12 am, Friday, because 72 hours before is 3 days in the past.

Answer:

40000

Step-by-step explanation:

[tex](2 \times {10}^{2} )^{2} \\ = {2}^{2} \times {10}^{2 \times 2} \\ = 4 \times {10}^{4} \\ = 40000[/tex]

Answer:

1440 degrees

Step-by-step explanation:

The sum of the interior angles of a polygon can be found by

(n-2)*180

where n is the number of sides

a decagon has 10 sides, so n=10

(10-2) *180

8*180

1440

The sum of all the interior angles of a decagon is calculated as (n-2) × 180°. For a decagon, where n is 10, the sum is 1440°.

The correct option is (C).

The sum of all the interior angles of a decagon can be found using the formula for calculating the sum of interior angles of any polygon, which is (n-2) × 180°, where n is the number of sides of the polygon. In the case of a decagon, n is 10. Therefore, the sum of all the interior angles of a decagon is (10-2) × 180° = 8 × 180° = 1440°. Thus, the correct answer is C.1440°.

complete question given below:

The sum of all the interior angles of a decagon is

A.1000∘

B.960∘

C.1440∘

D.1200∘

Answer:

X=7 and y=45

Step-by-step explanation:

5(7)+10=45

35+10=45

I have attached a graph

Answer:

V≈44602.24

Step-by-step explanation:

The volume of a sphere is  V=4/3πr^3. All you have to do is replace 22 for r and calculate it

Answer:

5575.28

Step by step explanation:

Two mixed numbers as [tex]\frac{5}{6}[/tex] and [tex]\frac{5}{12}[/tex] the least common denominator (LCD) is 12.

Step-by-step explanation:

The least common denominator (LCD) is the smallest number that can be a common denominator for a set of fractions. Also known as the lowest common denominator, it is the lowest number you can use in the denominator to create a set of equivalent fractions that all have the same denominator.

Steps to find the LCD of fractions, integers and mixed numbers:

Let's us have two mixed numbers as [tex]\frac{5}{6}[/tex] and [tex]\frac{5}{12}[/tex].

Equivalent Fractions with the LCD

[tex]\frac{5}{6}[/tex] = [tex]\frac{10}{12}[/tex]

[tex]\frac{5}{12}[/tex] = [tex]\frac{5}{12}[/tex]

For the denominators (6, 12) the least common multiple (LCM) is 12. Therefore, the least common denominator (LCD) is 12.

Final answer:

The mixed numbers 1 1/4 and 2 1/3 can be converted to have the lowest common denominator of 12, resulting in 1 3/12 and 2 4/12 respectively.

Explanation:

To write two different mixed numbers where the lowest common denominator (LCD) is 12, we can choose denominators that are factors of 12 and numerators that result in proper fractions (where the numerators are less than the denominators). An example would be 1 1/4 and 2 1/3. Here's how these mixed numbers have 12 as their common denominator:

Now we have two mixed numbers with the LCD of 12.

Answer: 11/30

Step-by-step explanation: looking at this question that was given to us and to find the probability, then we will go by saying that;

Probability of an event (E) = number of outcome of Event E/total number of all event

Prob(Basebase player)=11/30

Going by this, then we are going to have our answer as 11/30

The probability that a randomly selected person from the group is a Toronto Blue Jays fan is 11/30.

The question asks for the probability that a randomly selected person from the group of 30 people at a baseball game is a Toronto Blue Jays fan, given that 11 out of the 30 people are fans of that team. To calculate the probability, you divide the number of Blue Jays fans by the total number of people in the group.

Probability = Number of Toronto Blue Jays fans ÷ Total number of people

Probability = 11 ÷ 30

The probability can be simplified into the simple fraction form of:

Probability = 11/30

Answer: A 1 million

Step-by-step explanation:

The amount of the lump sum that the insurance company must put

into a bank account is $1 million.

Option A is the correct answer.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

We can use the present value formula for an annuity to find the lump sum that the insurance company must put into a bank account:

PV = PMT / r

where PV is the present value, PMT is the annual payment, and r is the interest rate.

Substituting the given values, we get:

PV = 40,000 / 0.04

= $1,000,000

Therefore,

The amount of the lump sum that the insurance company must put

into a bank account is $1 million.

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ7

Answer:

Step-by-step explanation:

4(x+2) = 16

4x + 8 = 16

4x =16-8

4x = 8

x = 8/4

x = 2

The solution to the equation 4(x + 2) = 16 is x = 2.

The Distributive Property states that a(b + c) = ab + ac. Apply this to the equation:

4(x + 2) = 4 * x + 4 * 2.

Thus, the equation becomes:

4x + 8 = 16.

To solve for x, first subtract 8 from both sides of the equation:

4x + 8 - 8 = 16 - 8

4x = 8.

Divide both sides of the equation by 4:

4x / 4 = 8 / 4

x = 2.