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The value of x in the intersecting secant and tangent lines is 40 degrees

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

Intersecting secant and tangent lines

Using the theorem of intersecting secant and tangent lines, we have

x = 1/2 * difference of the arcs

Substitute the known values in the above equation, so, we have the following representation

x = 1/2 * (170 - 90)

Evaluate

x = 40 degrees

Hence, the value of x is 40

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3. The factored polynomial is p(x) = (x - 1)(x - 5)

4. The factored polynomial is p(x) = (x + 3)²

A polynomial is a mathematical expression in which the power of the unknown is greater than or equal to 2.

3. To factorize the polynomial using the graph, we see that the polynomial cuts the x - axis at x = 1 and x = 5.

This implies that its factors are (x - 1) and (x - 5)

So, the factored polynomial is p(x) = (x - 1)(x - 5)

4. To factorize the polynomial using the graph, we see that the polynomial touches the x - axis at only one point x = -3. So,it has repeated roots

This implies that its factors are (x - (-3)) = (x + 3) twice

So, the factored polynomial is p(x) = (x + 3)²

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The total investment done by Lydia when her total annual interest is $420 at 11% dividend and 14% interest is equal to $3360.

Total annual interest = $420

Half of the investment in stock paying = 11% dividend

Half of the investment in stock paying = 14% interest

Let x be the amount Lydia has invested in each stock.

Since she has half of her investments in each stock,

The following system of equations to represent the situation,

Total annual interest is $420.

This implies ,

0.11x + 0.14x = 420

And  total investment is,

x + x = 2x

Simplifying the first equation, we get,

⇒ 0.25x = 420

Dividing both sides by 0.25, we get,

⇒ x = 1680

So, Lydia has invested $1680 in each stock, for a total investment of,

⇒ 2x = 2(1680)

        = 3360

Therefore, Lydia has a total investment of $3360.

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The new drug appears to reduce epileptic seizures since the rerandomized mean differences are close to the mean difference found between the two groups studied.

The rerandomized mean differences are:

1.2, 2.4, 1.8, 1.3, 2.1, 0.9, 1.5, 0.7, 2.1, and 2.3.

Several of these values are close to the observed mean difference of 1.8, which suggests that the observed difference could be due to chance alone.

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Answer:

6.324555320336759

Step-by-step explanation:

To find a missing leg in a right triangle use Pythagorean Theorem.

a^2 + b^2 = c^2                        Substitution

6^2 + 2^2 = c^2                         Simplify

36 + 4 = c^2                               Simplify

40 = c^2                                     Simplify
6.324555320336759 = c

The quantity of candy that Eric ate would be = 14/15

The quantity of Candy Kim had = 2⅓ pounds.

The quantity of Kims candy that Eric ate = 2/5

That is 2/5 of 2⅓.

The actual quantity of candy that Eric ate = 2/5× 7/3 = 14/15

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Answer:

(2,2), (4,8), (3,4)

Step-by-step explanation:

Plug in the x-coodinate and it should equal your desired y value

The evaluation of the function gives 16.

A function is an expression that shows the relationship between the independent variable and the dependent variable.  A function is usually denoted by letters such as f, g, etc.

To evaluate the  function f(x) =80/4x-3, we need to substitute the value of the input (i.e. x = 2). Thus:

f(x) = 80/(4x-3)

f(2) = 80/(4*2 - 3)

f(2) = 80/(8 - 3)

f(2) = 80/5

f(2) = 16

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The number of suspects had less than two prior arrests are 3.

Given that, While reviewing the previous day’s arrest report.

Let x be the number of suspects have been arrested once before and y be the number of suspects arrested twice before.

Here, x+y=5 -----(i)

2x+3y=12 -----(ii)

From equation (i), x=5-y in equation (ii), we get

2(5-y)+3y=12

10-2y+3y=12

10+y=12

y=2

Substitute y=2 in equation (i), we get

x+2=5

x=3

Therefore, the number of suspects had less than two prior arrests are 3.

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Since the dimensions of Lesley's bedroom are 7m by 6m, the area is 42 square meters.

The area is the space occupied by a two-dimensional object or space.

The dimensions for the measurement of the area are length and width.

Area is always stated in square units, for example, meters, miles, kilometers, centimeters, etc.

Dimensions of Lesley's bedroom:

Length = 7 m

Width = 6 m

Thus, the area of the bedroom = 42 m² (7 x 6).

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Answer: The coordinates of K' and M' are (-2,3) and (-4,1)

The crime that is often alcohol related is domestic violence. That is option D.

Domestic violence is defined as an abusive relationship that exist between two or more individuals that are closely related by blood or marriage.

The causes of domestic violence include the following:

Therefore, alcohol intake can lead to domestic violence because it can cause the abusive partner to have a reduction in cognitive and physical functions that impair self-control, with the consequent effect of reducing the ability to resolve conflicts nonviolently.

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The height of the planter box is 15 inches.

We have,

The volume of a rectangular prism is given by the formula:

V = l w h

where V is the volume, l is the length, w is the width, and h is the height.

In this case, we know that the length is 12 1/2 inches and the width is 10 inches, and the volume is 1,875 cubic inches.

So we can plug these values into the formula and solve for the height:

[tex]1,875 = (12 \frac{1}{2})\cdot 10 \cdot h[/tex]

Multiplying the length and width, we get:

1,875 = 125h

Dividing both sides by 125, we get:

h = 15

Therefore,

The height of the planter box is 15 inches.

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The rectangular piece of paper has a perimeter of 48.34 units.

The perimeter of a rectangle is given by the sum of the lengths of all its sides.

To find the perimeter of this rectangular sheet of paper, we need to add up the lengths of its four sides.

The length of the rectangle is 12 + 1 by 2 = 13.5 units, and its width is 10 + 2 by 3 = 11.67 units.

Therefore, the perimeter of the rectangle is:

P = 2(length + width)

P = 2(13.5 + 10.67)

P = 2(24.17)

P = 48.34 units

So the perimeter of the rectangular sheet of paper is 48.34 units.

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The final amount in the retirement account in which the rate or return and the regular contributions change over time is $33,844.51.

To determine the final amount in the retirement account, we first compute the future value of the periodic deposits of $213 for 4 years, using an online finance calculator.

The future value of $213 deposited for 48 months is used as the present value of the investment for the next 4 years or 48 months.

Then, with the present value and the periodic deposits, the final amount (future value) of the retirement account is determined as follows:

N (# of periods) = 48 months (4 years x 12)

I/Y (Interest per year) = 4%

PV (Present Value) = $0

PMT (Periodic Payment) = $213

Results:

FV = $11,067.40

Sum of all periodic payments = $10,224.00

Total Interest $843.40

N (# of periods) = 48 months (4 years x 12)

I/Y (Interest per year) = 7%

PV (Present Value) = $11,067.40

PMT (Periodic Payment) = $348

Results:

Final Value (FV) = $33,844.51

Sum of all periodic payments = $16,704.00

Total Interest = $6,073.11

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Answer:

The correct equation that initially models the value of Rob's boat is option A, y = 40,000(0.93)*.

Since the value of the boat decreased by 7% each year, the value of the boat after three years can be represented by:

y = 40,000(0.93)^3

where y is the value of the boat after three years, and 40,000 is the initial value of the boat.

Simplifying this equation, we get:

y = 40,000(0.7951)

y = 31,804

However, we know that the actual value of the boat after three years was $32,174.28. This means that our initial assumption that the boat decreased by 7% each year is incorrect and we need to adjust the equation accordingly.

To find the correct equation, we can use the formula for exponential decay:

y = a(1 - r)^t

where y is the final value, a is the initial value, r is the rate of decay (expressed as a decimal), and t is the time in years.

In this case, we know that the final value of the boat is $32,174.28, and that the boat was owned for three years. We also know that the value of the boat decreased by 7% each year.

So we can set up an equation:

32,174.28 = 40,000(0.93)^3

Simplifying this equation, we get:

32,174.28 = 31,804.00

This equation is approximately true, which means that the initial value of the boat was $40,000 and the correct equation that initially models the value of Rob's boat is:

y = 40,000(0.93)^t

where t is the time in years.

The coupon rate of the bonds by King of Diamonds Industries would be 7 %.

The formula for the bond price shows the coupon payment and so can be used to find the coupon rate:

= (Coupon payment  x ( 1 - ( 1 + r ) ^ ( - number of years till maturity ) ) ) / r + Face value /  (1  + rate )^ number of years

1,482.01 = (C x (1 - (1 + 0.07 )^ (- 14) ) ) / 0.07 + F / (1 + 0.07 ) ^ 14

103.7407 - 0.07 x (F / (1 + 0.07) ^14 ) = C x  (1 - ( 1 + 0.07) ^ ( - 14) )

Using a calculator, C is $ 70.

This means that the coupon rate is:

= 70 / 1, 000

= 7 %

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According to the information, It's important to acknowledge both of their perspectives and try to find a way to resolve the situation and move forward positively.

The situation is: two friends are having an argument because one of them forgot to invite the other to a party.

I can imagine that it must be really difficult for both of your friends right now. One of them might be feeling hurt and left out because they didn't get an invitation to the party, while the other might be feeling guilty and regretful for forgetting to invite them. It's important to acknowledge both of their perspectives and try to find a way to resolve the situation and move forward positively.

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Answer: (-3^4^-7)^-3 can be expressed with positive exponents as (-1/3^4^7)^3.

Step-by-step explanation:

First, we need to evaluate the exponents of the expression from the highest power to the lowest power. Since the exponent of 7 is negative, we need to apply the rule that a negative exponent indicates a reciprocal. Therefore, we can rewrite the expression as (-3^4^-1/7)^-3.

Next, we can simplify the expression -1/7 by flipping it to 7^-1. Therefore, we now have (-3^4^7^-1)^-3.

We can now evaluate the exponent of 4, which gives us (-3^16384^-1)^-3.

Finally, we can simplify 16384^-1 by flipping it to 1/16384, which gives us (-1/3^1/16384)^3.

This expression can be written using only positive exponents as (-1/3^4^7)^3.

The model y = 200(0.65)ⁿ represents exponential decay because the value of the bike decreases over time as t increases.

The value of the bike decreases by approximately 40.67% per year.

The value of the bike will be $50 approximately 5.2 years after it was purchased.

a. A = Peⁿ = 200e⁻⁰.⁴³⁰⁷≈ 118.66

The value of the bike after one year is approximately $118.66.

b. percent decrease = (initial amount - final amount) / initial amount * 100%

percent decrease = (200 - 118.66) / 200 * 100% ≈ 40.67%

c. We can set y = 50 in the model and solve for t:

50 = 200(0.65)ⁿ

0.65ⁿ = 0.25

Taking the natural logarithm of both sides, we get:

ln(0.65ⁿ) = ln(0.25)

t ln(0.65) = ln(0.25)

t = ln(0.25) / ln(0.65) ≈ 5.20

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We do not need both the Celsius and Fahrenheit formulas

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

The temperature equations

The general rule is that we need any of the temperature units to find the other temperature unit

This in other words means that we do not need both temperature units to find any of these two temperature units

Hence the statement is false

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The maximum value above is 46 at (2, 6). The production output goal which refers to the maximisation of profits relative to production is described by the objective function.

The production output goal which refers to the maximisation of profits relative to production is described by the objective function, which is a mathematical equation. The quantity of the final result is then calculated using the correlation between the variables. In other words, it's a formula that companies employ to meet their production and profitability objectives.

F = 5x + 6y

The coordinates of the feasible region are (0, 6), (1, 6.5) and (2, 6)

Substitute (0, 6), (1, 6.5) and (2, 6) in the above equation

F(0, 6) = 5(0) + 6(6) = 36

F(1, 6.5) = 5(1) + 6(6.5) = 44

F(2, 6) = 5(2) + 6(6) = 46

The maximum value above is 46 at (2, 6)

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a: $145,912,000,000

b: 4.6 bn shares

c: $31.72/per share (divide in half)

Tom traveled for 4 hours by train and 4 hours by plane, for a total trip time of 8 hours.

We have,

Let's call the number of hours Tom traveled by train t.

Since he traveled the same number of hours by plane, he also traveled for t hours at 275 mph.

The total distance he traveled is given by the sum of the distances traveled by train and by plane:

Distance by train = 50t

Distance by plane = 275t

Total distance = 1300

So we can set up the equation:

50t + 275t = 1300

Simplifying and solving for t, we get:

325t = 1300

t = 4

Therefore,

Tom traveled for 4 hours by train and 4 hours by plane, for a total trip time of 8 hours.

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Answer:

2.25 units³

Hope this helps!

Step-by-step explanation:

The formula, base, and height are already given so all you have to do is multiply 2 with [tex]3\frac{3}{8}[/tex].

2 × [tex]\frac{9}{8}[/tex]  =  [tex]\frac{9}{4}[/tex]  =  2.25 units³

Answer: B. (1, 8)

Step-by-step explanation:

Hope this helps! :)

Answer:

Given equations are,

5x+2y=−2        (1)

3x−5y=17.4      (2)

Multiply equation (1) by 5 and equation (2) by 2, we get,

5(5x+2y)=5×−2

∴25x+10y=−10          (3)

2(3x−5y)=2×17.4

∴6x−10y=34.8          (4)

Adding equations (3) and (4), we get,

31x=24.8

∴x=

31

24.8

​

Put this value in equation (1), we get,

5(

31

24.8

​

)+2y=−2

∴

31

124

​

+2y=−2

∴2y=−2−

31

124

​

∴2y=

31

−186

​

∴y=

31

−93

​

Step-by-step explanation:

Answer:

P((1 + r)^4) = 1,300

P((1 + r)^7) = 1,525

-----------------------

(1 + r)^3 = 61/52, so r = .0547 = 5.47%

P(1.0547^4) = 1,300, so P = $1,050.78