Could I get some help with this question on Trigonometric Identities?

To calculate the time necessary for an investment to accrue a specific amount of interest, use the simple interest formula. For this question, it would take 6 years for a $1525 investment to earn $237.90 at a 2.6% interest rate.

To find the amount of time (t) needed for an investment to earn a certain amount of interest (I), we can use the simple interest formula: Interest = Principal x rate x time. Given that Interest ($237.90), Principal ($1525), and the annual nominal interest rate (2.6% or 0.026 as a decimal) are known, we can isolate time (t) and solve for it.

The formula with the given values is: $237.90 = $1525 x 0.026 x t.

To isolate t, we divide both sides by the product of the principal and the rate:

t = $237.90 / ($1525 x 0.026)

t = $237.90 / $39.65

t = 6 years

Therefore, it would take 6 years for the investment to earn $237.90 in interest at an annual rate of 2.6%.

C. (–7x + 4)(4 – 7x)

Answer:1/4c+5

Step-by-step explanation:

Well we know that there are 20 cards as given by the equation. And there are 8 black cards.

8/20= .40 or 40% the answer for me is C. 40%

Answer: c is the answer is 40 hope u get it right goodluck

Step-by-step explanation:

Answer:

the answer is point S

~batmans wife dun dun dun...aka ~serenitybella

When [tex]\( a \)[/tex] is negative in the equation [tex]\( y = ax^2 \)[/tex], the parabola opens downwards. So, the answer is (a).

To determine the direction in which the parabola described by the equation [tex]\( y = ax^2 \)[/tex] opens, we need to understand the properties of the quadratic function. Let's analyze this step by step:

1. Identify the general form of the equation:

  The given equation is [tex]\( y = ax^2 \)[/tex].

2. Determine the effect of the coefficient [tex]\( a \)[/tex] on the parabola:

  - If [tex]\( a \)[/tex] is positive, the parabola opens upwards.

  - If [tex]\( a \)[/tex] is negative, the parabola opens downwards.

3. Evaluate the given condition:

  The problem states that [tex]\( a \)[/tex] is negative.

4. Apply the condition to the quadratic equation:

  Since [tex]\( a \)[/tex] is negative, the coefficient of [tex]\( x^2 \)[/tex] in the equation [tex]\( y = ax^2 \)[/tex] is negative.

5. Conclusion:

  When [tex]\( a \)[/tex] is negative, the parabola opens downwards.

Therefore, the correct answer is:

a. down

Answer:

[tex]cos(x)=(+/-)0.44[/tex]  

Step-by-step explanation:

we know that

[tex]sin^{2}(x)+cos^{2}(x)=1[/tex]

In this problem we have

[tex]sin(x)=0.9[/tex]

substitute and solve for cos(x)

[tex]0.9^{2}+cos^{2}(x)=1[/tex]

[tex]cos^{2}(x)=1-0.9^{2}[/tex]

[tex]cos^{2}(x)=0.19[/tex]  

[tex]cos(x)=(+/-)0.44[/tex]  

Final answer:

The value of cos x is approximately ±0.44.

Explanation:

Given that sin x = 0.9, we need to find cos x. We can use the Pythagorean identity, which states that sin2(x) + cos2(x) = 1. Since we are given sin(x), we can rearrange the identity to solve for cos(x) as follows:

sin2(x) + cos2(x) = 1

cos2(x) = 1 - sin2(x)

cos2(x) = 1 - (0.9)2

cos2(x) = 1 - 0.81

cos2(x) = 0.19

Now, take the square root of both sides to find cos(x). Since the square root has both a positive and a negative value, and we do not have information about the angle's quadrant, we consider both possibilities.

cos(x) = ±0.43589

We can round the cosine value to the nearest hundredth. However, without knowing the quadrant, we cannot definitively determine the sign of cos(x). Assuming the angle is in the first quadrant where both sine and cosine are positive, cos(x) = +0.44.

You can infer from this problem that for every 100 m that John was able to run, it takes him 9.93 seconds. To get how much time is needed for 26 – mile marathon, you need to divide 26 miles by 100 meters. But first, you need to convert 26 miles to meters first.

1 mile = 1,609.34 meters

26 miles = 41,842.84 meters

41,824.84 meters / 100 meters = 418.43 x 9.93 seconds = 4,155 seconds or 69.25 minutes

[tex] 4*e^{2x} -3 = 12 [/tex]

Step 1:

Here we have -3 in subtraction on the left side, so when we take it to the right we apply opposite operation of subtraction that is addition.

[tex] 4*e^{2x} = 12+3 [/tex]

[tex] 4*e^{2x} = 15 [/tex]

Step 2:

Next we have 4 in multiplication on left side, so dividing right side by 4,

[tex] e^{2x} = 15/4 [/tex]

[tex] e^{2x} = 3.75 [/tex]

Step 3:

taking log on both sides

[tex] ln ( e^{2x}) = ln(3.75) [/tex]

[tex] {2x} =ln 3.75 [/tex]

Step 4:

Dividing right side by 2,

x= ln (3.75) /2 = 0.66088

Answer : x = 0.66088..

The width of the patio is 4 feet.

Let's denote the width of the patio as "x" feet.

The length of the pool is given as 24 feet, and the width of the pool is given as 16 feet.

The area of the pool is the length multiplied by the width:

Area of the pool = Length * Width

Area of the pool = 24 ft * 16 ft

Area of the pool = 384 square feet

The area of the patio is also given to be equal to the area of the pool, so:

Area of the patio = 384 square feet

Now, the total dimensions of the pool and the patio together (including the patio's width on all sides) will be:

Total length = Length of the pool + 2 * Width of the patio

Total length = 24 ft + 2x

Total width = Width of the pool + 2 * Width of the patio

Total width = 16 ft + 2x

The area of the patio can also be expressed as the product of the total length and total width:

Area of the patio = Total length * Total width

Substitute the expressions for total length and total width:

384 square feet = (24 ft + 2x) * (16 ft + 2x)

Now, solve for "x" by expanding and rearranging the equation:

384 = 24 * 16 + 24 * 2x + 16 * 2x + 2x * 2x

384 = 384 + 48x + 32x + 4x²

Rearrange to get the equation in standard quadratic form:

4x² + 80x - 384 = 0

Now, we can solve this quadratic equation for "x" using the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

where a = 4, b = 80, and c = -384.

x = (-(80) ± √(80² - 4 * 4 * (-384))) / 2 * 4

x = (-80 ± √(6400 + 6144)) / 8

x = (-80 ± √(12544)) / 8

x = (-80 ± 112) / 8

Now, we get two possible values for "x":

x = (-80 + 112) / 8

x = 32 / 8

x = 4

or, we have,

x = (-80 - 112) / 8

x = -192 / 8

x = -24

Since the width cannot be negative, we discard the negative value:

The width of the patio is 4 feet.

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complete question:

attached

The width of the patio is equal to half the sum of the length and width of the pool, given by (L + W) / 2.

Let's assume the rectangular swimming pool has length L and width W. The concrete patio surrounds the pool on all sides, and its width is denoted by P.

The area of the surface of the pool is given by the product of its length and width: A_pool = L * W.

Since the area of the pool surface is equal to the area of the patio, we have:

A_pool = A_patio

L * W = (L + 2P) * (W + 2P)

Expanding the right side of the equation:

L * W = L * W + 2PL + 2PW + 4P^2

Canceling out the L * W terms:

0 = 2PL + 2PW + 4P^2

Rearranging the equation:

2PL + 2PW + 4P^2 = 0

Dividing the entire equation by 2:

PL + PW + 2P^2 = 0

Factoring out the common factor of P:

P(L + W + 2P) = 0

Since the width of the patio cannot be zero, we can conclude that:

L + W + 2P = 0

Simplifying further:

2P = - (L + W)

P = - (L + W) / 2

Since the width of the patio cannot be negative, we disregard the negative sign:

P = (L + W) / 2

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A = Layer 4..................................................

The correct decimal that represents eighteen and eight hundredths is 18.08, with the '8' in the hundredths place following the whole number 18.

The decimal that shows eighteen and eight hundredths is 18.08. This is because the number 18 represents the whole part, and the decimal part .08 represents the hundredths place. To express this, we place a decimal point after the whole number 18, followed by two digits: the first digit after the decimal point for tenths (which is 0 in this case), and the second digit for hundredths, which is 8. Thus, the correct decimal representation would be 18.08, as opposed to 18.80 which shows eighty hundredths, or .1808 which implies a number less than one with eight hundredths and eight ten-thousandths.

The piecewise function representing Tracy's cell phone charges is C(m) = {29 if m ≤ 250, 29 + (0.35)(m - 250) if m > 250.}.

Based on Tracy's cell phone plan, we want to create a piecewise function that represents the charges based on her usage. She is offered 250 free minutes at a flat rate, and any additional minutes are billed at an additional rate per minute. This piecewise function will have two parts: one for when Tracy's usage is at or below 250 minutes, and another for when her usage exceeds 250 minutes.

The first part of the function accounts for the flat rate up to 250 minutes:

If m ≤ 250, then C(m) = 29.

The second part of the function accounts for additional charges past 250 minutes:

If m > 250, then C(m) = 29 + (m - 250) * 0.35.

Therefore, the piecewise function that represents Tracy's cell phone charges based on the minutes used (m) is:

C(m) = {
 29 if m ≤ 250,
 29 + (0.35)(m - 250) if m > 250.
}

The coefficient of the x-term in the slope-intercept equation of a line represents the slope. The slope indicates how the y-value changes with each one-unit increase of the x-value. The constant term 'b' is the y-intercept, the point where the line crosses the y-axis.

In the slope-intercept equation of a line, typically written as y = mx + b, the coefficient of the x-term gives the slope of the line. The slope, represented by the letter 'm', defines the steepness of the line, or how much the y-value changes for every one-unit increase in x. The y-intercept is given by the constant term 'b', which indicates the point where the line crosses the y-axis, occurring when x equals zero.

Slope is especially important in fields like economics as it measures the relationship between two variables. A positive slope means that as x increases, y also increases, and vice versa for a negative slope. Therefore, knowing the slope allows us to predict how one variable will change in response to the other.