Arc measurement with equations

Answer:

she invest $18,500 at the 17% rate and $15,500 at the 20% rate.

Step-by-step explanation:

Suppose that you invest some quantity A to an invest rate of x%

At the end, the amount you will have is given by:

Amount = A + A*(x%/100%)

Where:

A*(x%/100%)  is the interest income

So, here she initially has $34,000

And she invest some quantity X to a 17% and a quantity Y to 20%

Then we have:

X + Y = $34,000

And we know that her total anual income is $6245

X*(17%/100%) + Y*(20%/100%) =  $6245

Then we have a system of two equations:

X + Y = $34,000

X*(17%/100%) + Y*(20%/100%) =  $6245

First we can rewrite the second one to a more simpler form:

X*(0.17) + Y*(0.20) =  $6245

Now we can isolate one of the variables in the first equation to get:

X = $34,000 - Y

Now we can replace that in the other equation to get:

( $34,000 - Y)*0.17 + Y*0.20 = $6245

Now we can solve this for Y:

$34,000*0.17 + Y*(0.20 - 0.17) = $6245

$5,780+ Y*0.03 =  $6245

Y*0.03 = $6245 - $5,780 = $465

Y = $465/0.03 = $15,500

And X = $34,000 - Y = $34,000 - $15,500 = $18,500

So she invest $18,500 at the 17% rate and $15,500 at the 20% rate.

Answer:

x^5+5x^4+10x³+10x²+5x+1

Step-by-step explanation:

Divide 8 by 4

Because is PEDMAS, division comes first.

Answer:

divide 8 by 4

Step-by-step explanation:

PEMDAS or BODMAS

I'm assuming you meant to say "it reaches a height that is 2/3 the height of the previous bounce".

We have a geometric sequence with a = 9 as the first term and r = 2/3 as the common ratio.

The nth term is a*(r)^(n-1) = 9*(2/3)^(n-1)

Set this equal to 3 and solve for n. You'll need logs to isolate the exponent.

9*(2/3)^(n-1) = 3

(2/3)^(n-1) = 3/9

(2/3)^(n-1) = 1/3

log[ (2/3)^(n-1) ] = log(1/3)

(n-1)*log(2/3) = log(1/3)

(n-1)*(-0.17609) = -0.47712

n-1 = (-0.47712)/(-0.17609)

n-1 = 2.7095235

n = 2.7095235+1

n = 3.7095235

Unfortunately we don't get a whole number. We can see that the terms of the sequence are:

9, 6, 4, 2.667

Each term is found by multiplying 2/3 by the previous term.

We don't land exactly on "3". The closest we get is 2.667 approximately.

So to answer the question, there is no way to get to exactly 3 feet above the ground based on a whole number of bounces.

Answer:

6[tex]\sqrt{34}[/tex]

Step-by-step explanation:

[tex]\sqrt{1224}\\[/tex] = [tex]\sqrt{36*34}[/tex] = 6[tex]\sqrt{34}[/tex]

Answer:

i think the first one- bc it should be 11x5pi but it would still end up as 55pi

Step-by-step explanation:

sorry if that doesnt help

Answer:I would sayif the planet earth was making a shadown on it. when u on other side

Step-by-step explanation:

That is the best i got

Answer:

Different times

Step-by-step explanation:

The closer you could get to the moon, the faster the phases will move. If you are about half way it should cut the time it takes to get through a season. Since you get closer to the object.

Answer:

y = 3x - 27

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = 3 , then

y = 3x + c ← is the partial equation

To find c substitute (6, - 9) into the partial equation

- 9 = 18 + c ⇒ c = - 9 - 18 = - 27

y = 3x - 27 ← equation of line

Answer:

[tex]7.4km[/tex]

Step-by-step explanation:

[tex]24.6km - 17km \\ = 7.4km[/tex]

hope this helps you.

Answer:

8

Step-by-step explanation:

LINE DC =BD

because line AD is a bisector of CAB

Dividing line CAD into two equal half's

Answer:

A=35 degrees, B=55 degrees, C=110 degrees

Step-by-step explanation:

The 35 degree given angle is vertical angles with A, so they are congruent

The sum of angles in a triangle is 180, and we already have 2 angles (35 and 90) so subtract those and you get 55

angle c and the other given angle (70 degrees) are supplementary so subract 70 from 180

Answer:

A) 800 seats

Step-by-step explanation:

Notice that an arithmetic sequence is formed with the number of seats. Since we're adding one seat each row, the last (25th) row will have 44 seats since the first row has 20 seats.

The sum of an arithmetic sequence is given by:

[tex]S_n=n\left(\frac{a_1+a_n}{2}\right)[/tex], where [tex]n[/tex] is the number of terms, [tex]a_1[/tex] is the first term, and [tex]a_n[/tex] is the last term

Therefore, substituting [tex]a_1=20[/tex], [tex]a_n=44[/tex], and [tex]n=25[/tex], we get:

[tex]S_n=25(\frac{20+44}{2}),\\s_n=25\cdot 32=\boxed{800}[/tex]

Answer:

336

Step-by-step explanation:

2x7=14, so 200-14=186, then 186+150=336

the answer is on the photo

Answer:

3 : 8

Step-by-step explanation:

The ratio of the radii is equal to the ratio of the circumference, then ratio is

12π : 32π ( divide both parts by 4π )

= 3 : 8

Answer:

Step-by-step explanation:

Table for function 1,

         x                      y              Difference 1          Difference 2        

         2                    10                      -                             -

         3                     1                 1 - 10 = -9                     -

         4                    10                10 - 1 = 9                9 - (-9) = 18

         5                    37               37 - 10 = 27            27 - 9 = 18

         6                    82               82 - 37 = 45          45 - 27 = 18

Since, difference 2 is common as 18,

Table will represent a quadratic function.

Table for function 2,

        x                    y               Difference 1            Difference 2

        5                    16                       -                               -

        6                    19              19 - 16 = 3                        -

        7                    28             28 - 19 = 9                  9 - 3 = 6

        8                    43             43 - 28 = 15              15 - 9 = 6

        9                    64             64 - 43 = 21              21 - 15 = 6

Since, difference 2 is common as 6,

Table will represent a quadratic function.

Table for function 3,

        x                    y                   Ratio

        1                   112                     -

        2                  56               56 ÷ 112 = [tex]\frac{1}{2}[/tex]  

        3                  28               28 ÷ 56 = [tex]\frac{1}{2}[/tex]

        4                   14               14 ÷ 28 = [tex]\frac{1}{2}[/tex]

        5                    7                7 ÷ 14 = [tex]\frac{1}{2}[/tex]

Since, ratio is common as [tex]\frac{1}{2}[/tex].

Table will represent an exponential function.

Discount percent = 33%

Sale price = $268

Let the original price be $x.

So,

[tex]x - (33\% \: of \: x) = 268 \\ = > x - ( \frac{33}{100} \times x) = 268 \\ = > x - ( \frac{33x}{100}) = 268 \\ = > \frac{100x}{100} - \frac{33x}{100} = 268 \\ = > \frac{(100x - 33x)}{100} = 268 \\ = > \frac{67x}{100} = 268 \\ = > 67x = 268 \times 100 \\ = > 67x = 26800 \\ = > x = \frac{26800}{67} \\ = > x = 400[/tex]

So, yesterday the price was $400.

The height of a juice cylinder container with base area of 100 cm² and volume of 1500 cm³ is 15 cm

Base area = πr²

base area = 100 cm²

100 = π × r²

r² = 100 / π

r = √100 / π

volume = πr²h

1500 = π (√100 / π)² × h

1500 = π(100 / π) × h

1500 = 100h

divide both sides by 100

h = 1500 / 100

h = 15 cm

learn more on cylinder here: https://brainly.com/question/27342403

Answer:

See explanation

Step-by-step explanation:

Required

The significance of "b" in exponential function

An exponential function is represented as:

[tex]y = ab^x[/tex]

In the above equation, parameter "b" is the rate of the function

In other words, the constant multiplier of the function.

Take for instance;

[tex]y = 2*4^x[/tex]

By comparison:

[tex]b = 4[/tex]

Another instance is:

[tex]y = 2(-4)^x[/tex]

By comparison

[tex]b = -4[/tex]

Other significance of parameter b are:

If [tex]b > 0[/tex] then b represents a growth factor

If [tex]b < 0[/tex] the b represents the factor of decay

[tex]b \ne 0[/tex] i.e. b is never 0

Answer:

r = d/t

Step-by-step explanation:

Given:

d = r * t

where,

d = distance

r = rate

t = time

Rewrite the equation to determine Dave's rate

d = r * t

d = rt

Divide both sides by the

d / t = rt / t

d / t = r

r = d/t

Average rate, r = d/t

The linear inequality that represents the graph is y > (2/3)x + 3.

Option C is the correct answer.

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal = ≤

Greater than and equal = ≥

We have,

y < (2/3)x + 3

y > (3/2)x + 3

y > (2/3)x + 3

y < (3/2)x + 3

The graph is on the positive side of the y-coordinate so,

We can consider:

y > (3/2)x + 3

y > (2/3)x + 3

Now,

Plotting in a graph we see that,

We need to have the y-intercept at y = 3 and the x-intercept at x = 4.5.

So,

y > (2/3)x + 3 satisfied.

Thus,

y > (2/3)x + 3 represents the graph.

Learn more about inequalities here:

https://brainly.com/question/20383699

#SPJ7

Answer:

A: 18

Step-by-step explanation:

1. 4(5) - 2

2. 20 - 2

3. 18

Answer:

herlojffhgdxvjdxhyeb olis the tim view on the euros 2020 final

Answer:

0.11

Step-by-step explanation:

Strongest correlation:

The strongest correlations happen for [tex]r = -1[/tex] and [tex]r = 1[/tex], that is, when r has the higher absolute value.

In this question:

The value of r with the lowest correlation is the one with the lowest absolute value(absolute value of -0.75 is 0.75 for example), so it is 0.11, which is the answer.

Answer:

it's C on edg

Step-by-step explanation:

.11

Answer:

35

Step-by-step explanation:

Since the triangles are similar, we can write a ratio

25      ?

---- = -----

5       7

Using cross products

25*7 = 5 ?

Divide each side by 5

25*7/5 = 5?/5

35 = ?

Answer:

[tex]1.86 \div 2 = 0.93[/tex]

Step-by-step explanation:

The correct form of the question is:

Complete the equations below.

[tex]1.86 \div 2 =[/tex]

Required

Solve

Start from left to right

[tex]1 \div 2 = ??[/tex] --- this will give a fraction.

So, we append the next digit

[tex]1.8 \div 2 = 0.9[/tex]

Next:

[tex]0.06 \div 2 = 0.03[/tex]

Bring the results together:

[tex]1.86 \div 2 = 0.9+ 0.03[/tex]

[tex]1.86 \div 2 = 0.93[/tex]

Answer:

z =86

Step-by-step explanation:

The exterior angle of a triangle is the sum of the opposite interior angles

z + z-39 = z+47

2z-39 = z+47

Subtract z from each side

z-39 = 47

Add 39 from each side

z = 47+39

z =86

The given information is,

To find the required value of z.

Property we use,

The exterior angle of a triangle is the sum of the opposite interior angles.

Now we can get the value of z,

→ z + z-39 = z + 47

→ 2z-39 = z + 47

→ 2z -z = 47 + 39

→ z = 47 + 39

→ [z = 86]

Thus, the required value of z is 86.