What is the length of BD?

The equation of line parallel to -x+2y = 30 and passing through (3,6) is x - 2y + 9 = 0.

Given equation is -x+2y = 30

and passing through the point (3,6).

If two lines are parallel, their slopes will be equal.

We know that equation for parallel lines is y = 3x+c

Now, -x + 2y = 30

= 2y = 30 + x

[tex]= y = \frac{30+x}{2}[/tex]

[tex]= y = \frac{30}{2} +\frac{x}{2} \\\\= y = 15 + \frac{x}{2}[/tex]

Therefore slope = [tex]\frac{1}{2}[/tex]

Equation of line with slope and passing through (3,6)

[tex]y-y_{1} = m(x-x_{1}) \\\\y - 6 = \frac{1}{2} (x-3)\\\\[/tex]

2(y-6) = 1(x-3)

2y - 12 = x - 3

x - 2y + 9 = 0

Hence the answer is the equation of line parallel to -x+2y = 30 and passing through (3,6) is x - 2y + 9 = 0.

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AC is congruent to SU

Answer:

Step-by-step explanation:

Given

Number of servings:

Answer

0.8 ft/hr

Explanation

2 4/5 ÷ 3 1/2 = 2.8 ÷ 3.5 = 0.8

Answer:

Any of the following will work: -9,-8,-7,-6,-5,-4,-3, or -2,

Step-by-step explanation:

What does < mean?

The less than sign shows that the number being compared is LESS than the other number.

Think: 9 < 100 showing that the number 9 is less than the number 100

What does > mean?

The greater than sign shows that the number being compared is GREATER than the other number.

Think: 100 > 9 showing that 100 is greater than the number 9

What is an integer?

Integers are all whole positive and negative numbers including zero.

Think: -13 and 13 are integers but 13.445 or -13.445 are not.

How can we prove these answers?

Simply looking at a number line, we can fill in what numbers would be greater than -10 but less than -1. Remember, these numbers must be whole numbers.

Answer: 177.936.....

Step-by-step explanation:but since this number is not a natural number its not possible

The quadratic function h (x) = x^2 + 3x − 18 by completing the square is witten as h(x) = (x + 1.5)^2  - 20.25.

We are given a quadratic function:

h (x) = x^2 + 3x − 18

We need to rewrite the function by completing the square.

We can see the coefficient of x is 3.

So, we will add and subtract the square of half that.

So, find the square of half of 3, we will get;

(3 / 2)^2 = 9 / 4 = 2.25

add and subtract the square of half of 3 from the given function, we will get;

h(x) = x^2 +3x + -18 2.25 -2.25

arrange the expression, we will get;

h(x) = (x^2 +3x +2.25) -18 -2.25

write the expression in parentheses as a square, and simplify the constant, we will get;

h(x) = (x + 1.5)^2  - 20.25

So, the square function is written as h(x) = (x + 1.5)^2  - 20.25.

Thus, the quadratic function h (x) = x^2 + 3x − 18 by completing the square is witten as h(x) = (x + 1.5)^2  - 20.25.

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The number local extremas to the function is given as follows:

3.

They are classified as follows:

The local extremas of a function are the turning points of the graph of the function, and they are classified as follows:

The graph of the function has three turning points, and they are defined as follows:

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Answer:

Time 2 540 years

Step-by-step explanation:

T = 5 600 yares - Half-life

73% - Carbon content

N = 0.73·N₀

Decay constant:

λ = ln 2 / T = 0.693 / 5600 ≈ 0.000124  (years)⁻¹

Law of radioactive decay:

N = N₀·e^(-λ·t)

0.73·N₀ = N₀·e^(-λ·t)

0.73 = e^(-λ·t)

ln (0.73) = -λ·t

t = ln (0.73) / (-λ)  = ln (0.73) / (- 0.000124)  ≈ 2 540 years

702, 0.91, 0.73, 0.76  shows the decimal numbers in order from smallest to largest.

What is a decimal number?

Here are four decimal numbers:

0.702, 0.76, 0.91, 0.73

the numbers in order from smallest to largest.

702, 0.91, 0.73, 0.76

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Answer:

B)  0.702, 0.73, 0.76, 0.91

Step-by-step explanation:

The given set of decimal numbers (in any order) is:

Each number has zero units.

Comparing the digits in the tenth place, all the numbers have 7 tenths except 0.91 which has 9 tenths.  Therefore, 0.91 is the largest number as 9 > 7.

Comparing the digits in the hundredths place of the other three numbers, 0.702 is the smallest number as it has zero hundredths.

As 0.73 has 3 hundredths and 0.76 has 6 hundredths, this means that 0.73 is the second smallest number as 3 < 6.

Therefore, the given set of decimals in order from smallest to largest is:

the slope is 1 because 3/3

Answer:

1

Step-by-step explanation:

When two points are given;

= -4-(-7)/5-2

= -4+7/3

= 3/3

=1

from the reading above, doesn't seem the boric acid has any alcohol at all, so we can say 0% alcohol.

now let's see how many liters we have hmmm 2 of hazel, 1 of alcohol and the rest in boric acid, to make a total of 5 liters, so boric acid must be 2, since 2 + 1 + 2 = 5.

how much alcohol is there in 14% of 2 liters?

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{14\% of 2}}{\left( \cfrac{14}{100} \right)2}\implies 0.28[/tex]

how much alcohol is there  in 95% of 1? well, no to bore you to death, is just 0.95 liters, and we know the boric acid has no alcohol.

so in the 5 liters of the lotion, we have 0.28 liters plus 0.95 liters of alcohol total, that's 1.23 liters total.

now, if we know the 100% of the lotion is the 5 liters, how much is 1.23 liters off of it in percentage?

[tex]\begin{array}{ccll} liters&\%\\ \cline{1-2} 5 & 100\\ 1.23& x \end{array} \implies \cfrac{5}{1.23}~~=~~\cfrac{100}{x} \\\\\\ 5x=123\implies x=\cfrac{123}{5}\implies x=\stackrel{\%}{24.6}[/tex]

Answer:

Step-by-step explanation:

you'll need to know  L'Hôpital's Rule.  Obviously this problem goes to zero in the denominator if you let x go to zero, which is a big problem :P  sooo use L'Hopital's rule to solve this messy problem.  

L'Hoptial's rule takes the advantage that you can find the derivative of something but still find it's limit just like you didn't take a derivative.  soo

take derivative of numerator and denominator  separately

remember how to take derivative of  sin^2(3x) ??

pull the two down,   then chain rule

d/dx (sin^2(3x) =   2sin(3x) * cos(3x) * 3    = 6*sin(3x)*cos(3x)

d/dx (4x^2)  = 8x

we still have the same issue if we take the limit if x goes to zero :0

but it's okay... just take L'Hopitals' again :P

d/dx (6*sin(3x)*cos(3x)) =  6*cos(3x) *3 *(-sin(3x)*3 = 54*cos(3x)*(-sin(3x))

d/dx (8x) = 8

now we can let the limit go to zero

lim ( x ->0)[54*cos(3x)*(-sin(3x)) / 8]

we can see that sin(x) will get closer and closer to zero so we have 0/8

so we can fairly say,  without guessing, that yes... this limit goes to zero as X goes to zero.  :)  nice

The required amount in the savings account=$2704.05

What is simple interest?

Calculating the interest on a loan using simple interest is quick and simple. Simple interest is calculated by dividing the principle by the daily interest rate and the number of days between installments.

A quick and simple way to figure out interest on money is to use the simple interest technique, which adds interest at the same rate for each time cycle and always to the initial principal amount. Any bank where we deposit our funds will pay us interest on our investment. One of the different types of interest charged by banks is simple interest.

P=2700, r=0.3%=0.003, t= 0.5 year

A= P(1+rt)

 = 2700(1+ 0.003*0.5)

 = 2700(1+ 0.0015)

 = 2700(1.0015)

 = 2704.05

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The number is 11.

Lets assume that the P is the product of the number 'x' and 5, then the equation will become :

P = 5x .......i

now given that the product P is same as the 11 less than 6 times the number 'x'., therefore the equation will become :

P = 6x -11 ......ii

Now from i and ii,

5x = 6x -11 ,

11 = 6x - 5x

therefore, x = 11.

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Answer:

5(d)

Step-by-step explanation:

(3.0471×10⁹)/2.4×10^-4

30471×10^9-4÷24×10^-4-1

30471×10⁵÷24×10^-5

(30471÷24)×10^5-(-5)

1269.625×10^5+5

1269.625×10¹⁰

1.269625×10^10-3

1.269625×10⁷

1.2696 to 5s.f

The amount owed at the end of 1 year is $4120 and by the end of 2 years, $4243.60 when Tom borrows $4000 at an interest rate of 3% compounded each year.

The interest you earn on interest is known as compound interest. Simple math can be used to demonstrate this: if you have $100 and it earns 5% interest annually, you will have $105 at the end of the first year. You will end up with $110.25 at the end of the second year. In order to calculate compound interest, multiply the principal of the original loan by the annual interest rate multiplied by the number of compound periods minus one.

Here,

principle amount=$4000

rate of interest=3%

For first year,

A=P(1+r/n)^(nt)

A=4000(1+3/12)^12*1

A=$4,120.00

For first year,

A=P(1+r/n)^(nt)

A=4120(1+3/12)^12*1

A=$4,243.60

When Tom borrows $4000 at an interest rate of 3% compounded annually, the total amount due at the end of one year is $4120, and at the end of two years, it is $4243.60.

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Answer:

40

Step-by-step explanation:

We divide 317 by 8 to see how much for each table

317/8 is 39.625

We round up for the next whole number since the last table is probably not filled all the way

So we need 40 tables

Hopes this helps please mark brainliest

Answer:

40 tables

Step-by-step explanation:

317 divided by 8 equals 39.625

Round the answer.

Since the number after the decimal is bigger than 4, round up to the nearest whole number which is 40.

P.S. this is simple math. No offense, but you should have been able to figure this out yourself. It's not that hard. Again, not trying to offend you. Just letting you know.

Answer: 30$

Step-by-step explanation:

first you divide 420 by 35 and you get 12 times 2.50$ equals 30$

The explicit equation for the table is,

f(n) = n² + 4

Given, the values of an explicit function,

Let the function be,

f(n) = an² + bn + c

f(1) = a(1)² + b(1) + c

5 = a + b + c

f(2) = a(2)² + b(2) + c

8 = 4a + 2b + c

f(3) = a(3)² + b(3) + c

13 = 9a + 3b + c

On subtracting the equations, we get

5 = 5a + b

3 = 3a + b

Again, on subtracting we get

2 = 2a

a = 1

On putting the values we get,

b = 0.

a + b + c = 5

1 + 0 + c = 5

c = 4

Hence, the explicit equation for the table is,

f(n) = n² + 4

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The equation for the nth term of the arithmetic sequence is  [tex]a_{n}[/tex] = 25 - 4n  

An arithmetic sequence or arithmetic progression is a series of numbers with a common difference. For example 1, 2, 3, 4... is an Arithmetic sequence with a common difference 1. In an Arithmetic sequence, the difference between every two consecutive terms will be equal.

The formula for the nth term of a sequence is given below

=> [tex]a_{n}[/tex] = a + (n-1)d

where a is the first term and d is a common difference.

Here we have

21, 17, 13 ... is the arithmetic sequence

Where first term a = 21

and common difference d = term2 - term1 = 17 - 21 = - 4  

As we know the nth term of AP, [tex]a_{n}[/tex] = a + (n-1)d  

=>  [tex]a_{n}[/tex] = 21 + (n-1)(-4)

=>  [tex]a_{n}[/tex] = 21 - 4n + 4

=>  [tex]a_{n}[/tex] = 25 - 4n

Therefore,

The equation for the nth term of the arithmetic sequence is  [tex]a_{n}[/tex] = 25 - 4n  

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y<2 is the solution to the inequality

What is Linear Inequality?

The mathematical expression with unequal sides is known as an inequality in mathematics. Inequality is referred to in mathematics when a relationship results in a non-equal comparison between two expressions or two numbers. In this instance, any of the inequality symbols, such as greater than symbol (>), less than symbol (), greater than or equal to symbol (), less than or equal to symbol (), or not equal to symbol (), is used in place of the equal sign "=" in the expression. Polynomial inequality, rational inequality, and absolute value inequality are the various types of inequalities that can exist in mathematics.

The symbols "" and ">" signify tight inequalities, while "" and "" signify slack inequalities. A linear inequality looks precisely like a linear equation, but the symbol connecting two expressions is different.

According to the question

2y+3<7

subtracting 3 from both sides

we get,

2y<4

dividing both sides with 2

we get,

y<2

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Answer: 4 + (2*3)^2

Step-by-step explanation:

By writing the fractions as decimals, we will see that the numbers ordered from least to greatest are:

-5, 2/16, 23/40

The 3 numbers given are:

-5

23/40

2/16

The numbers should be ordered as they appear on a number line (from left to right)

The smaller number is, obviously, the negative one, so the thing that we need to check now is what of the two fractions is smaller.

To do so, we can write them as decimals:

23/40 = 0.575

2/16 = 0.125

So the smaller one is 2/16 and then comes 23/40

Then the numbers ordered from smaller to larger are:

-5, 2/16,  23/40

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Answer:

[tex]y = -2x-2[/tex]

Step-by-step explanation:

A line being perpendicular means that it has a slope that is an opposite reciprocal of the other line.

In this case:

[tex]x - 2y = 5\\-2y = -x + 5\\y = \frac{x}{2} - \frac{5}{2}[/tex]

The slope of this line is [tex]\frac{1}{2}[/tex] and so the perpendicular slope would be [tex]-2[/tex].

Using the point slope form:

[tex]y - y_1 = m(x-x_1)\\[/tex]

Substitute values:

[tex]y - y_1 = m(x-x_1)\\y - 2 = -2(x+2)\\y -2 = -2x-4\\y = -2x-2[/tex]

Answer:

y = 35.5x - 10

Step-by-step explanation:

If we graph the function with the help of the given table,

Since, there is a common difference in each term of 'cost of gym membership'

d = 61 - 25.5 = 35.5

d = 96.5 - 61 = 35.5

Graph will represent a linear function.

Let the equation of the line is,

y - y' = m(x - x')

where (x', y') is a point lying on the graph and 'm' is the slope.

Two points lying on the graph are (1, 25.5) and (2, 61).

Slope of the line =

                          =

                          = 35.5

Equation of the line passing through (1, 25.5) having slope 'm' = 35.5

y - 25.5 = 35.5(x - 1)

y = 35.5x - 35.5 + 25.5

y = 35.5x - 10

Here x = duration of membership

y = membership price

Therefore, equation representing Fit Zoom's membership price equation will be,

y = 35.5x - 10

The conversion of 19 pounds to grams is 8170.74 grams.

From the information illustrated, it should be noted that it was illustrated that 1 pound = 453.93 grams.

In this case, in order to fund the value of 18 pounds, we will have to multiply 18 by 453.93 grams.

This will be calculated as:

18lb = 18 × 453.93 grams.

= 8170.74 grams

The value is 8170.74 grams.

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Answer:

  -i, 1, i, -1, 1, -1

Step-by-step explanation:

You want the simplified form of various expressions involving powers of i.

The definition of i is ...

  i = √(-1)  or  i² = -1

This value can be used to find other powers:

  i³ = (i²)(i) = -i

  i⁴ = (i²)² = (-1)² = 1

This means any power of i is equivalent to that power modulo 4.

  [tex]-i^{25}=-i^1 = \boxed{-i}\\\\i^{16}=i^0=\boxed{1}\\\\i^{17}=i^1=\boxed{i}\\\\-i^{32}=-i^0=\boxed{-1}\\\\i^{-9}\times -i^{11}=-i^{-9+11}=-i^2=-(-1)=\boxed{1}\\\\\dfrac{i^{23}}{-i^{11}}=-i^{23-11}=-i^{12}=-i^0=\boxed{-1}[/tex]