When 4x2–8x–24=0 is written in the form (x–p)2=q, what is the value of q?

Answer:

  -65°

Step-by-step explanation:

You want the angle whose tangent is -2.1.

The inverse tangent function is used to find the angle when the tangent is known. On your calculator, the key for this will likely be labeled tan⁻¹. You need to make sure the calculator mode is set to degrees.

The value of θ is about -65°.

__

Additional comment

The principal branch of the arctangent function extends from -90° to +90°. The tangent function is periodic with period 180°, so adding any integer multiple of 180° to -65° will give you another angle whose tangent is -2.1. One such angle is 115°.

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Answer:

The expression 3+4x2 can be simplified using the order of operations, which is a set of rules used to determine the sequence in which operations are performed in an expression. According to the order of operations, we first perform any calculations inside parentheses, then we perform any multiplications or divisions (from left to right), and finally we perform any additions or subtractions (from left to right).

There are no parentheses in this expression, so we move on to the next step, which is to perform any multiplications or divisions. In this case, we have 4x2, which equals 8. So, we can replace 4x2 with 8, and the expression becomes:

3+8

Finally, we perform the addition, and get the final result:

11

Therefore, 3+4x2 is equal to 11.

Step-by-step explanation:

If p(x) ⊆ p(y), then it means that every element of the power set of x is also an element of the power set of y. This implies that set x is a subset of set y, written as x ⊆ y.

Here,

Let A be the set x and B be the set y. Then the power sets of A and B are p(A) and p(B) respectively.

Suppose p(A) ⊆ p(B). This means that for every element a in p(A), a is also an element of p(B).

Now consider any element a in A. Since a is an element of A, it is also an element of its power set p(A). Thus, if p(A) ⊆ p(B), a must also be an element of p(B). This means that a is an element of B.

Therefore, we have established that every element of A is an element of B. That is, A ⊆ B.

Thus, if p(x) ⊆ p(y), then x ⊆ y.

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Answer:

X = 10

Z = 67

Step-by-step explanation:

We see that the angles are formed by the intersection of two lines.

Angles z and  67° are vertically opposite angles and therefore they are equal to each other

z°= 67°

Angles z and (7x + 43) are supplementary angles. The sum of these angles add up to 180°

z + 7x + 43 = 180

67 + 7x + 43 = 180

7x + 110 = 180

7x = 180 -110 = 70

x = 70/7 = 10

From the given information, we have:

PC = 10 (length of segment PC)

∠CBD = x°

∠BCD = x + 54°

We can determine the relationship between angles ∠CBD and ∠BCD by recognizing that they are inscribed angles intercepting the same arc CD. In a circle, the measure of an inscribed angle is half the measure of its intercepted arc. Therefore, we have:

∠BCD = 1/2(arc CD)

Since ∠BCD = x + 54° and arc CD is the diameter, which is 180°, we can set up the following equation:

x + 54 = 1/2(180)

Simplifying the equation:

x + 54 = 90

x = 90 - 54

x = 36

So, the measure of ∠CBD (m∠CBD) is 36°.

Answer:

x = 48°

Step-by-step explanation:

[tex]x=(90-42)^{0} =48^{0}[/tex]

Hope this helps

★ The sum of the angles in a triangle is always 180° ...

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Hello !

45min = 3/4h = 0,75h

[tex]\frac{45km}{0,75h} \\\\= \frac{45km*\frac{1}{0,75} }{0,75h*\frac{1}{0,75} } \\\\= \frac{60km}{1h}[/tex]

s = 60km/h

[tex]s=\dfrac{d}{t}\\\\d=45\text{ km}\\t=45\text{ min}=0.75\text{ h}\\\\s=\dfrac{45\text{ km}}{0.75\text{ h}}=60\dfrac{\text{km}}{\text{h}}[/tex]

Answer: 4.5 or A

Step-by-step explanation:

1) Find LCM of 9 and 6, which is 18.

2) Multiply x/9 by 2. (2x/18)

3) Multiply 3/6 by 3. (9/18)

4) Divide by 2 (numberator on both sides)

               x = 4.5

(x + 12)° + (5x)° = 90°

m∠1 = 25° and m∠2 = 65°

We know that the little box represents 90 degrees. We will write an equation using this information.

      (x + 12)° + (5x)° = 90°

Next, we will solve by isolating the x variable with inverse operations and combing like terms.

      (x + 12)° + (5x)° = 90°

      x° + 5x° = 78°

      6x° = 78°

      x = 13°

Lastly, we will find the value of each angle by substituting.

       m∠1 = (x + 12)° = ((13) + 12)° = 25°

       m∠2 = (5x)° = (5(13))° = 65°

Answer: a=101 b=79 c=83 d=97

Answer:

a. q^2 = sqr(225) can be solved.

q^2 = sqr(225) means q^2 = 15^2. So, q can be found by taking the square root of both sides:

q = ±15

Step-by-step explanation:

The equation that represents the direct variation between a and b in this scenario is: b = -a.

The correct option is (A).

We have,

The number b varies directly with the number a.

This equation states that b is equal to the negative value of a, which reflects the condition that b is located in the opposite direction from 0 compared to a and varies directly with a.

So, the equation cab be stated as b = -a.

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Answer:

a is g(x) b is f(x)

Step-by-step explanation:

because a increases faster

The expression implies that the number of fish that are not angelfish can be represented as 3/4

In this expression, "z" represents the total number of fish in the aquarium. The statement mentions that one-fourth of the fish are angelfish, which means that 1/4 of "z" fish are angelfish.

To determine how many fish are not angelfish, we need to subtract the number of angelfish from the total number of fish. Since 1/4 of the fish are angelfish, 3/4 of the fish must be non-angelfish.

Therefore, the expression implies that the number of fish that are not angelfish can be represented as 3/4 of "z," which can be mathematically written as (3/4)z.

In summary, the expression represents the number of fish that are not angelfish based on the total number of fish "z" in the aquarium.

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Answer:

  (c)  x³·∛x

Step-by-step explanation:

You want the simplified form of ∛(x¹⁰).

The first part of the problem tells you how to get there. After you have that expression, you need to bring the x⁹ term from under the radical.

  [tex]\sqrt[3]{x^{10}}=\sqrt[3]{x^9\cdot x}=\sqrt[3]{x^9}\cdot\sqrt[3]{x}=\boxed{x^3\cdot\sqrt[3]{x}}\qquad\text{matches choice C}[/tex]

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The minimum amount one will pay making a deposit of notes and coins is R7.25.

To determine the minimum amount one will pay when making a deposit of notes and coins, we need to consider the costs mentioned in Table 2.

According to Table 2, the cost for notes deposit is R2.25 per R100 (or part thereof) deposited, and the cost for coins deposit is R5 per R100 (or part thereof) deposited.

To calculate the minimum amount, we need to determine the lowest possible value for both the notes and coins deposit costs.

For notes deposit:

The minimum value would be R2.25, as it is the cost for depositing less than R100 worth of notes.

For coins deposit:

The minimum value would be R5, as it is the cost for depositing less than R100 worth of coins.

To calculate the total minimum amount, we sum up the costs for notes and coins deposits:

Minimum amount = R2.25 (notes deposit cost) + R5 (coins deposit cost)

Minimum amount = R7.25

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Answer:

2x squared - 5

= 2(x)^2 - 5

= 2(4)^2 - 5

= 2(16) - 5

= 32 - 5

= 27

The area of the vertical cross section through the center of the base of the paperweight is approximately 12.56 square inches.

To find the area of a vertical cross section through the center of the base of the cone-shaped paperweight, we need to determine the radius of the base first.

The circumference of a circle is given by the formula C = 2πr, where C is the circumference and r is the radius. In this case, we know the circumference is about 12.56 inches, so we can set up the equation:

12.56 = 2πr

To solve for r, we divide both sides of the equation by 2π:

r = 12.56 / (2π)

Now we can calculate the radius:

r ≈ 12.56 / (2 × 3.14)

r ≈ 12.56 / 6.28

r ≈ 2 inches

The radius of the base is approximately 2 inches.

Since the vertical cross section passes through the center of the base, the shape of the cross section is a circle. The formula for the area of a circle is A = [tex]πr^2[/tex], where A is the area and r is the radius.

Now we can calculate the area of the cross section:

A = [tex]πr^2[/tex]

A ≈ 3.14 × [tex](2^2)[/tex]

A ≈ 3.14 × 4

A ≈ 12.56 square inches

Therefore, the area of the vertical cross section through the center of the base of the paperweight is approximately 12.56 square inches.

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Answer:

8/15

Step-by-step explanation:

Assuming that a is in the 1st quadrant, based on sin a = 8/17 you can build a right triangle as in the picture. Third side you compute with Pythagoras [tex]x^2 + 8^2 = 17^2 \implies x = 15[/tex].

At this point the tangent is the ratio of the two segments, or 8/15.

Else, you can calculate cos a  based on the fact that [tex]cos\ a = \sqrt{1-sin^2\ a}[/tex] (under the same assumption as the beginning. Then it's just a matter of plugging numbers.

Answer:

5m

Step-by-step explanation:

regla de 3:

1m = 3ft

15 pies ÷ 3 = 5m

Answer:

x ≤ 4

Step-by-step explanation:

To solve the inequality x - 3 ≤ 1, we need to isolate x.

Remember that this is a linear inequality, and linear inequalities are solved the same way as a linear equation - the objective is to leave the variable alone on one side (usually the left-hand side or LHS) to find its value −

x - 3 ≤ 1

x ≤ 4

Therefore, x ≤ 4

Answer:

a. Let X be the length of a wooden pole produced for electricity networks in rural areas. The probability of a pole being rejected because it is too short is 0.02, and the probability of a pole being rejected because it is too long is 0.05. The acceptable range is between 6.3 m and 7.5 m. We can find the mean and standard deviation of X as follows:

First, we need to find the z-score corresponding to the lower bound of the acceptable range:

z1 = (6.3 - μ) / σ

Similarly, we need to find the z-score corresponding to the upper bound of the acceptable range:

z2 = (7.5 - μ) / σ

Using a standard normal table, we can find the values of z1 and z2 that correspond to the probabilities of 0.02 and 0.95, respectively:

z1 = -2.05

z2 = 1.64

Solving for μ and σ, we get:

z1 = (6.3 - μ) / σ => μ = 6.3 + 2.05σ

z2 = (7.5 - μ) / σ => σ = (7.5 - 6.3) / 1.64 = 0.74

Therefore, the mean and standard deviation of X are:

μ = 6.3 + 2.05(0.74) = 7.6 m

σ = 0.74 m

b. Let Y be the number of rejected poles in a sample of 20 poles. Y follows a binomial distribution with parameters n = 20 and p = 0.02 + 0.05 = 0.07. The probability of finding 2 rejected poles in a sample of 20 poles is:

P(Y = 2) = (20 choose 2) * 0.07^2 * 0.93^18 = 0.242

The probability of finding 2 rejected poles in a sample of 20 poles is 0.242.

The limit when n approaches infinity for the given expression is the one in option D, 21.

Here we want to take the following limit of n when it tends to infinity in the following rational expression:

[tex]\lim_{n \to \infty} 24 - 3 - \frac{24}{2n} + \frac{40}{n} + \frac{15}{3n^2}[/tex]

Notice that in all the terms where n appears, it is on the denominator. Thus, when n tends slowly to infinity, the denominator will be way larger than the numerator, and thus, all the fractions will tend to zero, then we will get:

[tex]\lim_{n \to \infty} 24 - 3 - \frac{24}{2n} + \frac{40}{n} + \frac{15}{3n^2} = 24 - 3 = 21[/tex]

The correct option is the last one, D.

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Step-by-step explanation:

Vertical angles are equal   r = 70 degrees

To find the total in the retirement account after 38 years of investing with monthly contributions and an interest rate of 4.99%, we can use the compound interest formula.

The formula for the future value of an investment with regular monthly contributions is given by:

FV = P * [(1 + r)^n - 1] / r

Where:

FV is the future value or the total in the retirement account.

P is the monthly contribution amount.

r is the monthly interest rate (annual interest rate divided by 12).

n is the number of monthly contributions (years invested multiplied by 12).

Let's calculate the total:

P = $225

r = 4.99% / 100 / 12 = 0.0041583 (monthly interest rate)

n = 38 * 12 = 456 (number of monthly contributions)

FV = $225 * [(1 + 0.0041583)^456 - 1] / 0.0041583

Using a financial calculator or spreadsheet, we can evaluate this expression to find the future value or total in the retirement account.

The calculated total may vary depending on the compounding frequency and rounding used.

Answer:

[tex]-8x^3\sqrt{7}[/tex]

Step-by-step explanation:

Step 1:  Let's start by simplifying -4x^2 * (√63x^2) using the following steps:

1.1: Separate √63x^2 into two terms:  

-4x^2 * (√63 * √x^2)

1.2:  Find the largest perfect square that we can factor out of 63.  It's 9 as 3^2 = 9 and 9 * 7 = 63.  Furthermore, √x^2 simplifies to x:

-4x^2 * (√9 * 7 * (x))

-4x^2 * (3√7 * x)

1.3:  We can multiply x and 3:

-4x^2 * (3x√7)

1.4:  We can distribute -4x^2 to 3x√7.  

-12x^3 * √7

Step 2:  Now we can work on simplifying x^3√112 using the following steps:

2.1:  Find the largest perfect square you can factor out of 112.  It's 16 since 4^2 = 16 and 16 * 7 = 112:

x^3 * √16 * 7

x^3 * 4√7

2.2:  Multiply x^3 and 4√7:
4x^3 * √7

Step 3:  Thus, -4x^2 * √63x^2 simplified individually is -12x^3 * √7 and x^3 * √112 simplified individually is 4x^3 * √7

3.1:  Add -12x^3 * √7 + 4x^3 * √7:

-8x^3√7

Optional Step 4:  We can check that we've correctly simplifed the equation by plugging in a number for x in both the radical expression not yet simplified and the simplified radical expression.  If we get the same answer, then we've simplified the expression correctly.  We can plug in 2 for x.

Plugging in 2 for x in -4x^2 * (√63x^2) + x^3 * (√112):

(1.) -4(2)^2 * √63(2)^2 + 2^3 * √112:

(2.) -4(4) * √63(4) + 8 * √112

(3.) -16 * √252 + 8 * √112

(4.) -16 * √36 * 7 + 8 *√16 * 7

(5.) -16 (6 * √7) + 8(4 *√7)

(6.) -96 * √7 + 32 * √7

(7.) -64√7

(8.) -169.3280839

Plugging in 2 for x in -8x^3√7:

(1.) -8(2)^3 * √7

(2.) -8(8) * √7

(3.) -64 * √7

(4.) -169.3280839

Therefore, we've correctly expressed the expression in simplest radical form

Answer: 2048

Step-by-step explanation: 1. Write the exponential growth model.

The population of the town doubles every year, so the growth factor is 2. The initial population is 112, so the equation is: P(t) = 112(2)^t where P(t) is the population in year t and t is the number of years since 2014.

2. Estimate the population of the town in 2023. To estimate the population of the town in 2023, we can set t=9, since 2023 is 9 years after 2014. Plugging this into the equation, we get: P(9) = 112(2)^9 = 2048

Therefore, the estimated population of the town in 2023 is 2048.