Determine the value of the trigonometric ratio.

Using an exponential function, it is found that it would take 80.12 minutes for the element to decay to 6 grams.

An exponential function is defined according to the following rule:

[tex]y = a(b)^{\frac{t}{n}}[/tex]

In which:

Considering the half life of the substance, and the initial amount of 430 grams, the parameters are given as follows:

a = 430, b = 0.5, n = 13.

Then the amount of the substance after t minutes is given by:

[tex]y = 430(0.5)^{\frac{t}{13}}[/tex]

The time it will take for the element to 6 grams is t when y = 6, hence:

[tex]6 = 430(0.5)^{\frac{t}{13}}[/tex]

[tex](0.5)^{\frac{t}{13}} = \frac{6}{430}[/tex]

[tex]\log{((0.5)^{\frac{t}{13}})} = \log{\left(\frac{6}{430\right)}[/tex]

[tex]\frac{t}{13}\log{0.5} = \log{\left(\frac{6}{430\right)}[/tex]

[tex]t = 13\frac{\log{\left(\frac{6}{430}\right)}}{\log{0.5}}[/tex]

t = 80.12 minutes.

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The X- intercept of the graph of the function at x =>-4 and x = 2.

The provided function is g(x)=-1(x-4)(x+2).

The x intercept of the function means, that point at which the graph of function will have the y coordinate as zero.

So, the x intercept of the function will be at the point where the function g(x) will be equal to zero.

g(x) = 0

-1(x-4)(x+2) = 0

(4-x)(x+2) = 0

Here,

We will get two values of x at which g(x) will be zero,

X = 4 and -2.

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a. The slopes of lines C and B are the same, therefore, they are parallel.

b. y = 30

c. x = 11

The slope of a line (m) = change in y/change in x.

Two lines having the same slope (m) value means they are parallel to each other.

a. Slope of line A = change in y/change in x = (9 - 0)/(3 - 0) = 9/3

Slope of line A = 3

Slope of line B = (15 - 1)/(8 - 1) = 14/7

Slope of line B = 2

Slope of line C = (21 - 3)/(12 - 3) = 18/9

Slope of line C = 2

Slope of line D = change in y/change in x = (14 - 2)/(9 - 1) = 12/8

Slope of line D = 3/2

Lines C and B have the same slope, therefore they are parallel.

b. 3 = (9 - y)/(3 - 10)

3 = (9 - y)/-7

-21 = 9 - y

-21 - 9 = -y

-30 = -y

y = 30

c. 2 = (15 - 21)/(8 - x)

2 = -6/(8 - x)

2(8 - x) = -6

16 - 2x = -6

-2x = -6 - 16

-2x = -22

x = 11

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Answer:

10+5y

Step-by-step explanation:

5(2+y)

distribute

=5(2)+5(y)

simplify

=10+5y

I hope this is clear enough , although I did not arrive at the same answer using x in both equation .

Answer:

True

Step-by-step explanation:

Answer:

g(7) = 21

Explanation:

To calculated g(7), we need to replace x by 7 in g(x) as:

Therefore, g(7) is equal to 21

Explanation

iven the points (-1,-4) and t(3,2). The points slope form of the equation can be found using the formula

We would then substitute the value into the formula;

Answer: Option 3

Part A) The tank's water level is changing at a rate of -[tex]\frac{2}{3}[/tex] gallons per minute.

Part B) The tank will finish draining in 7.5 minutes.

Part C) Jada arrived 4.5 minutes before the water tank was empty.

The rate of change (ROC) measures how quickly a variable alters over a predetermined amount of time.

Given Data

Up to 10 gallons can be stored in a water tank.

A drain continuously drains water from the tank when it is operational.

When Jade first noticed the tank, there were 7 liters of water inside.

3 minutes later, there were 5 gallons of water remaining.

Part A: How quickly is the tank's water level changing?

In three minutes, the gallons were reduced from seven to five. It indicates that 2 gallons were lost in three minutes.

Thus, gallons Change in gallons per minute would be -[tex]\frac{2}{3}[/tex]. As a result, the tank's water level is changing at a rate of -[tex]\frac{2}{3}[/tex] gallons per minute.

Note that a negative sign means there are less gallons of water available.

Part B) How long will it take for the tank to entirely drain?

The amount of time it will take the tank to entirely empty is denoted by the letter "m."

As,

2.3 gallons per second (5 gallons) in (m minutes).

So,

m = 5 ([tex]\frac{3}{2}[/tex])

= [tex]\frac{15}{2}[/tex]

= 7.5 min.

As a result, the tank will finish draining in 7.5 minutes.

Part C: How long did it take the water tank to fill up entirely before Jada arrived?

When there are 10 gallons of water, r is complete. This means that there are now 7 gallons more of water than there were when Jada arrived, an increase of 3 gallons.

Let 'm' be the time in minutes when the water tank was full and before Jada arrived.

So,

([tex]\frac{2}{3}[/tex]) (m) = 3

m = 3([tex]\frac{3}{2}[/tex]) = [tex]\frac{9}{2}[/tex]

= 4.5 min.

The water tank was thus full before to Jada's arrival by 4.5 minutes.

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Answer:

8/6*(8)=32/3 or 10.66666.... or 10.7 rounded

Step-by-step explanation:

They are similar triangles

so we cam compare the size of the big triangle DIR to the smaller triangle DEZ

More specifically

EZ:DZ=IR:DR

8:6=IR:(6+2)

4:3=IR:8

the to solve for IR

we multiply by 8 each side

4/3*8=32/3

Answer: x+6 and x+7

Step-by-step explanation:

[tex]x^{2} +13x + 42 = 0\\D = b^{2} - 4ac = 169 - 4*42 = 169 - 168 = 1\\x_{1} = (-13 + 1)/2 = -6\\x_{2} = (-13 -1)/2 = -7\\\\So, x^{2} + 13x + 42 = (x+6)(x+7) \\\\\\[/tex]

Hence, the possible dimensions are x+6 and x+7.

Answer: (x + 6) and (x + 7)

Step-by-step explanation: Determine if the polynomial terms contain a common factor. In this case, there's no common factor. Next, find two numbers whose product is 42 and whose sum is 13. The only pair of numbers that satisfies these conditions is 6 and 7. Finally, write the polynomial in factored form as (x + 6)(x + 7). Therefore, the possible dimensions of the rectangle are (x + 6) by (x + 7).

Answer:

A

Step-by-step explanation:

if you feel cold your body will tell your brain or give feedback to make you think or say its cold

The component form of vector is (-6,8)

Geometrical objects with magnitude and direction are called vectors. A line with an arrow pointing in its direction can be used to represent a vector, and the length of the line corresponds to the vector's magnitude. As a result, vectors are depicted as arrows and have starting and ending points. It took 200 years for the idea of vectors to develop. Physical quantities like displacement, velocity, acceleration, etc. are represented by vectors.Additionally, the development of the field of electromagnetic induction in the late 19th century marked the beginning of the usage of vectors. Here, we'll examine the definition of vectors as well as their characteristics, mathematical formulas, and uses.

The component form of vector is (-6,8)

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The given equation written in standard format is 3x - 2y = -6

From the question, we are to write the given equation in standard format.

The given equation is

2y = 3x + 6

The standard form of a linear equation with two variables is

Ax + By = C

Where x and y are the variables

A is the coefficient of x

B is the coefficient of y

and C is the constant

Now, we will write the given equation in the format

2y = 3x + 6

Subtract 3x from both sides of the equation

2y - 3x = 3x - 3x + 6

-3x + 2y = 6

Multiply through by -1

3x - 2y = -6

The standard format of the equation is 3x - 2y = -6

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1. Using estimation shows that Stephen's answer is incorrect because when the whole number 3 is subtracted from 154, it gives 151 and not 119.  The actual result should be between 150 and 151.

2. The strategy that Stephen could use to solve this subtraction problem is an approximation. Approximately, 3.48 is 3.5, but for a quick estimation, the decimals are eliminated or appropriated.

Estimation means a rough calculation or an approximation.

Estimation provides a quick means of arriving at number solutions without going into detailed calculations.

Estimates are used for decision-making when complete information is not required or available.

The minuend = 154.2

The subtrahend = 3.48

The estimated value of the minuend reduces it to 154.

The estimated value of the subtrahend reduces it to 3.

Using estimation, the difference = 151 (154 - 3)

Actual difference = 150.72 (154.2 - 3.48)

The actual difference can be approximated to 151.

Thus, using appropriate estimation, Stephen can easily solve this subtraction problem without difficulty.

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Answer:

a. Using a graphing calculator: 4.486089611

b. To 2 decimal places: 4.49

The value of k = -10 in f(x).

Algebraic expressions called polynomials include coefficients and variables. Indeterminates are another name for variables. For polynomial expressions, we can do mathematical operations like addition, subtraction, multiplication, and positive integer exponents but not division by variables.

The amount "left over" after a calculation is the remainder. The integer that remains after multiplying one integer by another to create an integer quotient is known as the remnant in mathematics.

Given that,

f(x) = x³ + kx + 13

The remainder when f(x) is divided by x + 1 is 22,

Here, the f(x) is divided by x+1

Hence, x = -1

Substitute x = -1 in f(x)

22 = f(x) = x³ + kx + 13

22 = f(-1) = (-1)³ + k(-1) + 13

22 = -1 –k +13

22 = -k +12

K = -10

Therefore, the value of k = -10 in f(x).

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Answer

Option C is correct.

The equation has infinitely many solutions.

Explanation

To know the nature of the solutions, we need to solve the given equation

3 (4g + 6) = 2 (6g + 9)

12g + 18 = 12g + 18

12g - 12g = 18 - 18

0 = 0

Any equation that results in 0 = 0, is known to have infinitely many solutions because any number will fit in for g and still work for the given equation.

Hope this Helps!!!

Answer:

x= 12

Step-by-step explanation:

8/4 = 2

2x6 = 12

Answer:

(4,8) x=4/y=8

Step-by-step explanation:

the four is the x line  and the 8 the y line.

4 laying down line to the right (positive four)

8 straight up line top(positive 8)

The explicit formula of the given geometric sequence is a(n) = 8(1/2)ⁿ⁻¹.

Every term in a geometric series is obtained by multiplying the term before it by the same number aₙ= aₙ₋₁ + d is the general phrase for it. The common ratio is denoted by the number r. Any term in the sequence can be used to find it by dividing it by the word before it.

Any number series in which the ratio of succeeding terms is constant is referred to as a geometric sequence. where r is the proportion shared by all following terms. For instance, "2,6,18,54,162,486,1458,...

We have a sequence: 8, 4, 2, 1

The above sequence represents the geometric sequence with common ratio:

r = 4/8 = 1/2

First term a = 8

nth term:

a(n) = 8(1/2)ⁿ⁻¹

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From the statement, we know that:

0. the company sells 1000 packs of cards per day for $5 per pack,

1. with every $0.02 reduction in price, 10 more packs a day are sold.

To solve this problem, we define the following variables and functions:

• r = # of price reductions,

• n(r) = # of packs sold by the company as a function of r,

• p(r) = price per pack (in $) as a function of the # of price reductions,

• I(r) = income (in $) as a function of the # of price reductions.

Using points 1 and 2, we write the following functions: function of # of packs sold n(r) as:

• the i

• the function of the price per pack p(r):

• the function for the income I(r) is given by the product of the # of packs sold n(r) and the price per pack p(r):

(1) To find the maximum income, we must maximize the function I(r) for r. To do that, we compute and make equal to zero its first derivative:

Solving for r, we get:

We have found that the maximum income is achieved when the # of price reductions is equal to r = 75.

(2) s

We have found that the maximum possible income per day is $6125.

(3) s

We have found that the price per pack that maximizes the income is $3.5.

(4) s

With this new price structure, the company wins $6125 s

• The maximum possible income per day is $6125.

• The price per pack that maximizes the income is $3.5.

• The company makes $1125 extra with this new price structure.

Using it's concept, the probabilities are given as follows:

a) Type A die and orange: 1/10 = 0.1.

b) Blue: 23/30

c) Type B, if blue: 8/23.

A probability is calculated as the number of desired outcomes in the experiment divided by the number of total outcomes in the experiment.

For item a, the probability that a type A dice is chosen is:

3/5.

As there are 5 dices, 3 of type A and 2 of type B.

The probability that a type A dice comes up orange is:

1/6.

As it has six faces, one of which is orange.

Then the probability of an orange type A dice being chosen is:

3/5 x 1/6 = 1/10 = 0.1.

For item b, the probability of blue is divided as follows:

Hence the probability of a blue dice is:

p = 5/6 x 3/5 + 4/6 x 2/5 = 23/30

For item c, we apply the conditional probability, hence the probability is given as follows:

p = (4/6 x 2/5)/(23/30) = (8/30)/(23/30) = 8/23.

Dividing the probabilities of type B and blue by the probability of blue.

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The percentage that equivalent to 15/50 is 30%

The given term is 15/50

The percentage is defines as a relative value indicating hundredth parts of any number. It is denoted using the percentage symbol "%". We can also say that percentage is a number or ratio expressed as a fraction of 100.

The given term is 15/50

Here the denominator is 50 and numerator is 15

To find the equivalent percentage, first we have to divide 15 by 50, then multiply the result by 100

15/50 = 0.3

Multiply the result by 100

0.3×100 = 30%

Hence, the percent that equivalent to 15/50 is 30%

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ANSWER

x = 4 or x = -9

STEP-BY-STEP EXPLANATION:

As you can see from the question provided, you were given the following logarithms equation

Recall that,

The next thing is to replace the values and simplify

As you can see from the last process, the logarithms function resulted in a quadratic equation.

The next thing is to solve the equation using the factorization method.

Note that, the general quadratic function is given below as

Relating the two equations, you will have the following data

• a = 1

• b = 5

• c = -36

The next thing is to find the value of ac

Hence, the values of x are 4 and -9

Answer:

On sixth week , she collects 2⁶ = $64.

She saves 2(1+2+4+8+16+32) = $126 in all.

Given model is

Substitute A=12981 to find the value of t, we get

Subtracting 8000 from both sides, we get

Multiplying 8000 and 0.045, we get

Dividing both sides by 360, we get

Round off nearest tenth, we get

Hence it would take 13. 8 years for the loan amount to $ 12981.

Answer:

72 m

Step-by-step explanation:

We observe that 7y+6=18, and thus y=12/7.

So, the perimeter is:

[tex]2(18+7y+6) \\ \\ =14y+48 \\ \\ =14(12/7)+48 \\ \\ =72[/tex]

Given -

2m² + m +3 = 0​

To Find -

2m² + m +3 = 0

Step-by-Step Explanation -

2m² + m +3 = 0​

We will first calculate the roots of the equation:

So, Both the roots are imaginary.

having d = -23

Final Answer:

Graph :