A certain compound has a half-life of 5 days. Write and use an exponential decay function to find the amount
of compound remaining from a 84-ounce sample after seven weeks.

Since ΔABC and ΔACD are similar triangles, therefore the length of AC is 18 m.

Similar triangles are triangles with corresponding sides that have the same ratio.

Thus:

AD is parallel to BC (bases of a trapezoid are parallel)

Therefore:

∠ACB = ∠CAD (alternate interior angles)

This implies that, ΔABC ~ ΔACD by AA similarity theorem.

Thus:

AC/DA = CB/AC

Substitute

AC² = 12 × 27

AC = √324

AC = 18 m

Therefore, since ΔABC and ΔACD are similar triangles, therefore the length of AC is 18 m.

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Answer:

9 and 6

Step-by-step explanation:

7x - x + 9 ← collect like terms

= (7x - x) + 9

= 6x + 9

the constant term is the numeric term, with no variable ( letter) attached

the constant term is + 9

the coefficient of x is the numeric value before x

the coefficient of x is 6

The given function is continuous at  x = 5,  RHL = LHL = F(5)

In mathematics, The function is called as continuous at the particular value of x,  if right hand limit, left hand limit and the value of function at x all are equal.

RHL   = LHL  = F(x)

Limit exist and continuous

Given that,

F(x)  =  [x² - 49]/[x² + 6x -7][x² + 14x + 49]

To check whether it is continuous at x = 3

First taking LHL,

[tex]\lim_{h \to \00 } F(x)[/tex]  

[tex]\lim_{h \to \00 }[/tex]   [(5-h)² - 49]/[(5-h)² + 6(5-h) -7][(5-h)² + 14(5-h) + 49]

⇒  -24/(48x144)

⇒   -1/288

Now, taking RHL

[tex]\lim_{h \to \00 }[/tex]   [(5+h)² - 49]/[(5+h)² + 6(5+h) -7][(5+h)² + 14(5+h) + 49]

⇒  -24/(48x144)

⇒   -1/288

The value at x = 3

F(3)  =  [(5)² - 49]/[(5)² + 6(5) -7][(5)² + 14(5) + 49]

⇒  -24/(48x144)

⇒   -1/288

Hence Proved,   RHL = LHL = F(5)

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We know from the problem that l = 3w - 5. We also know the formula for area is A = w * l. Therefore, the area of the rectangle is A = w * (3w - 5). We can then set this equation equal to 50 as the question states and solve for w.

[tex]50 = w * (3w-5)[/tex]

Expand the multiplication

[tex]50 = 3w^{2}- 5w[/tex]

Subtract 50 from both sides.

[tex]0 = 3w^{2} - 5w - 50[/tex]

We now have a quadratic equation and can solve it using the quadratic formula to find w. We find that the solutions to the equation are 5 and -3.3. We know that the width can't be negative, so the width must be 5.

Finally, we can plug this solution into the length formula we found earlier to solve for length.

[tex]l = 3w - 5[/tex]

Plug in the solution to w.

[tex]l = 3(5) - 5[/tex]

Multiply 3 and 5.

[tex]l = 15-5[/tex]

Subtract 5

[tex]l = 10[/tex]

Therefore the width is 5 and the length is 10.

Answer:

∠ A = 23.6°

Step-by-step explanation:

complementary angles sum to 90°

sum the 2 angles and equate to 90

2x - 20 + 3x + 1 = 90

5x - 19 = 90 ( add 19 to both sides )

5x = 109 ( divide both sides by 5 )

x = 21.8

Then

∠ A = 2x - 20 = 2(21.8) - 20 = 43.6 - 20 = 23.6°

Answer:

120 mph

Step-by-step explanation:

t = 35 min = (35 min)/(60 min/hr) = 0.583 hr

d = 70 mi

speed = d/t = (70 mi) / (0.583 hr) = 120 mph

The total charge for the month is given as follows:

$123.93.

The total charge for the month is obtained applying the proportions in the context of the problem.

The costs are given as follows:

For a customer with 7 lines, the charges are given as follows:

Hence the total charge is then calculated as follows:

3 x 19.99 + 4 x 15.99 = $123.93.

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The unit rate of Jana's ride is 0.3 Miles per minutes

A unit rate means a rate for one of something. We write this as a ratio with a denominator of one. For example, if you ran 70 yards in 10 seconds, you ran on average 7 yards in 1 second. Both of the ratios, 70 yards in 10 seconds and 7 yards in 1 second, are rates, but the 7 yards in 1 second is a unit rate.

The unit rate of Jane's ride is

= 15miles/50minutes

= 0.3miles per minute

therefore the unit rate of Jane's ride is 0.3 miles per minute.

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The polygon is a regular 9 sided polygon with each exterior angles as 40° and the measure of the sum of the exterior angles of the polygon is 360°

The exterior angles of a polygon added together is equal to 360°. No matter what the size of the polygon is, the sum of the exterior angles will always add up to 360°. If the polygon is regular, then each exterior angle measures 360°/n.

the polygon is a 9 sided polygon and thus

each exterior angle derived as;

360°/9 = 40°

40° + 40° + 40° + 40° + 40° + 40° + 40° + 40° + 40° = 360°

Therefore, the 9 sided polygon with each exterior angles as 40° have the measure of the sum of the exterior angles to be 360°

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The first row of a bank statement shows -

Option D : The account's balance at the beginning of the period.

What is bank statement?

A bank statement, also known as an account statement, is a record that summarises all of an account's transactions for a given month and is normally issued by the bank to the account holder each month.

The transactions for a bank account over a specific time period, typically monthly, are listed in a bank statement.

The statement provides the beginning and ending balances for the period along with deposits, charges, and withdrawals.

Every month, account holders typically analyse their bank statements to assist them keep track of their spending and costs and to check for any erroneous or fraudulent charges.

Therefore, the first row shows the balance at the beginning period.

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Answer: 3 3/8 or 3.375

Step-by-step explanation:

Answer:

3.375

Step-by-step explanation:

Answer:

6561m^4

Step-by-step explanation:

(9m)^4 =

(9 * m)^4 =

9^4 * m^4 =   ==> distribute the power 4 to 9 and m

6561 * m^4 = ==> simplify

6561m^4

A graph of the line with a slope of 3/4 and y-intercept of -9 is shown in the image attached below.

Mathematically, the standard form or slope-intercept form of the equation of a straight line is given by this mathematical expression;

y = mx + c

Where:

Next, we would write an equation of this straight line based on the slope and y-intercept as follows;

y = mx + c

y = 3x/4 + (-9)

y = 3x/4 - 9

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Answer:

C) AB, AC, AD

Step-by-step explanation:

All of the line segments stem from point A and connect to a point on the circle.

Hope this helped! :)

Answer:

third option

Step-by-step explanation:

the radius of a circle is a line segment from the centre of the circle A to a point on the circumference of the circle.

the circle shown here with centre A has 3 segments to the circle.

AB , AC and AD

Answer:

working on a answer hold up

Step-by-step explanation:

The value of the function at g = 1 and g = 4 will be 55 and 105, respectively.

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

The function is given below.

C(g) = 55          if 0 < g < 2

C(g) = 25g + 5  if g ≥ 2

The value of the function at g = 1 is given as,

C(1) = 55

The value of the function at g = 4 is given as,

C(4) = 25(4) + 5

C(4) = 100 + 5

C(4) = 105

The value of the function at g = 1 and g = 4 will be 55 and 105, respectively.

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The required solution of the given system of equations is x = 5 and y = -1/4.

Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.

Here,
3x+4y=8 - - - - - (1)

x-4y=4 - - - - (2)

Put x from equation 2 to equation 1
12y + 12 + 4y = 8
16y = -4
y = -1/4

Now,
Put y in equation 2
x - 4 {1/4} = 4

x = 5

Thus, the required solution of the given system of equations is x = 5 and y = -1/4.

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Part 1

E. There is a pair of congruent angles and a pair of congruent right triangles, so the triangles are similar by the AA [tex]\sim[/tex] postulate.

Part 2

Note that 4 ft 6 in = 4.5 ft. Using the fact that corresponding sides of similar triangles have proportional side lengths,

[tex]\frac{x}{14}=\frac{4.5}{4} \implies \boxed{x=15.75 \text{ ft}}[/tex]

The simplified expression for this problem is given as follows:

6x + 16z.

The expression for this problem is defined as follows:

2x-3z*4/(-2)+1x+10z+3x

The quotient has the higher precedence, hence it is given as follows:

3z * 4/(-2) = 12z/(-2) = -6z.

Then the expression is given as follows:

2x + 6z + x + 10z + 3z.

The like terms are given as follows:

Hence the simplified expression is given as follows:

6x + 16z.

The problem asks to simplify the expression 2x-3z*4/2z+1x+10z+3x.

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Answer:

Step-by-step explanation:

The mean depression level  for the first group is μ₁ = 16.

The mean depression level for the second group is μ₂ = 12

The weighted mean is closer to 12 than to 16.

The calculated weighted mean  for  CES-D is 13.5

The calculated weighted mean  for  MAST is 17.25 ≈ 17.0 rounded to 17.

Calculating the weighted mean μ

μ=         {where x1 =μ₁ and x2= μ₂ }

μ= 16×6 + 10×12/ 6+10

μ= 216/16

μ= 13.5

The first group has a mean score of μ₁= 18.

The second group has a mean score of μ₂ = 14

Calculating the weighted mean μ

{where x1 =μ₁ and x2= μ₂ ; w1= number of women in the first   group and w2= number of women in the second group}

μ=        

μ= 18×6 + 14×12/ 6+10

μ= 276/16

μ= 17.25≈ 17

Based on the definition of an angle bisector, the measure of angle WUT is: B. 38°.

An angle bisector is a line, ray or segment that divides an angle into two congruent angles.

Therefore:

m<VUW = m<WUT

Substitute

4x + 6 = 6x - 10

Solve for x

4x - 6x = -6 - 10

-2x = -16

x = 8

m<WUT = 6x - 10

Plug in the value of x:

m<WUT = 6(8) - 10 = 38°

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Answer:

To find the GCF of 2^5·5·11 and 2^3·5^2·7, we first prime factorize each number:

2^5·5·11 = 2^5 x 5 x 11

2^3·5^2·7 = 2^3 x 5^2 x 7

Next, we look for the highest power of each prime factor that they both have in common:

2^3 is the highest power of 2 that both numbers have.

5^2 is the highest power of 5 that both numbers have.

So, the GCF of 2^5·5·11 and 2^3·5^2·7 is 2^3 x 5^2 = 180.

Step-by-step explanation:

The algebraic expression for the area is:

A = (2H - 8)*H/2

Here we want to write the expression:

"the area of a triangle that has a base 8 inches less than 2 times wider than the height."

Remember that for a triangle of base B and height H, the area is:

A = B*H/2

So if the base is 8 inches less than 2 times the height, we can write:

B = 2*H - 8

Replacing that in the area equation we get:

A = (2H - 8)*H/2

That is the equation for the area.

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The greatest number of biscuits Habib can make is 25

From the question, we have the following parameters that can be used in our computation:

Habib has 400 g of butter

150 g of sugar

675g of flour

Factor each number to determine the GCF

So, we have

400 = 2 * 2 * 2 * 2 * 5 * 5

150 = 2 * 3 * 5 * 5

675 = 3 * 3 * 3 * 5 * 5

So, we have

GCF = 5 * 5

Evaluate

GCF = 25

Hence, the number of biscuits is 25

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The rate of increase is 150%.

A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.

Given:

Desk were on sale for $200 the sale is over,

and they have gone back up to the full price of $300.

The rate of increase,

= 300 x 100 / 200

= 150%

Therefore, the rate is 150%.

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Kevin has $3840 invested in stocks in total.

Interest is the sum of money that must be repaid on a loan or received in exchange for a loan. Principal refers to the borrowed or lent funds. The Amount is the total of the principal plus interest.

Given:

Annual interest in first investment - 11%

Annual interest in other investment - 14%

Total interest annually - $480

let the investment for each stock be x.

then total investment = 2x

We can write

0.11x + 0.14x=480

0.25x = 480

x= 480/ 0.25

x= $1920

Also, the total investment = 2x

= 2×(1920)

= 3840

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Regarding shopping for a new card, it would depend on the terms and conditions of the new card, including the annual interest rate and any fees. Rachel should compare the options available and weigh the benefits and drawbacks of each before making a decision.

The length of time it will take Rachel to pay off her credit card balance can be calculated by dividing the outstanding balance by the monthly payment amount and then adding the number of months needed to pay off the balance.

Balance = $8,281

Monthly payment = $250

Annual interest rate = 16%

To calculate the length of time it will take to pay off the balance, we would first need to calculate the monthly interest rate, which can be done by dividing the annual interest rate by 12:

Monthly interest rate = 16% / 12 = 1.33%

Next, we can calculate the monthly payment amount, including the interest:

Monthly payment amount = $250 + ($8,281 * 1.33%)

By continually subtracting the monthly payment amount from the balance and adding the monthly interest, we can determine the length of time it will take to pay off the balance.

Regarding shopping for a new card, it would depend on the terms and conditions of the new card, including the annual interest rate and any fees. Rachel should compare the options available and weigh the benefits and drawbacks of each before making a decision.

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The solution is,

* The company’s degree of operating leverage: 1.38;

* The impact on net operating income of a 22% increase in sales: it will increase by 30.4%;

* New contribution format income statement:

                                              Engberg Company

                            Contribution format income statement

                                     Amount                        Percentage of sales

Sales                             $176,900                              100%

Variable expenses            70,760                               40%

Contribution margin         106,140                               60%

Fixed expenses                 24,000

Net operating income        82,140      

A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.

here, we have,

* The company’s degree of operating leverage = Contribution / profit = 87,000/63,000 = 1.38

* The impact on net operating income of a 22% increase in sales is calculated as: Degree of operating leverage x % changes in sales revenue = 1.38 x 22% = 30.4%.

* new contribution format income statement is shown in the answer part.

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The value of x in the expression is 0.9429

From the question, we have the following parameters that can be used in our computation:

8 square root x^5 divided by square root x = 5/x^8 divided by 1/x^2

Express properly

So, we have

8√x⁵/√x = 5x²/x⁸

Evaluate the quotients

So, we have

8x² = 5/x⁶

Cross multiply

This gives

x⁸ = 5/8

Take the 8th root of both sides

x = 0.9429

Hence, the solution is 0.9429

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