yo solve....14√x+15 = 71

After solving the equation, the value obtained for x will be equal to 20 in².

An object's area is how much space it takes up in two dimensions. It is the measurement of the number of unit squares that completely encompass the surface of a compact figure.

The squared unit, which is frequently expressed as inches, square feet, etc., is the accepted unit of area.

As per the given information in the question,

Let the length of the rectangular wood, l = 16 in and,

The width of the rectangular wood, w = 8 in.

Use the area of a rectangle,

A = lw

A = (16)(8)

A = 128 in².

Let the area cut from each side be x.

If the area is cutting from all sides, then it will be 4x.

The surface area left after cutting the board = 48 in²

Then, the equation will be,

128 in² - 4x = 48 in²

4x = 128 in² - 48 in²

4x = 80

x = 80/4

x = 20 in²

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Answer:

0.61 °C

Step-by-step explanation:

1. You look at all the tenths in the degrees

2.You figure out which one of the tenths fits between -0.8 and -0.1

Answer:

see explanation

Step-by-step explanation:

Expand the factored form and compare coefficients of like terms with the original polynomial

a(x + 1)(x - 2)² + b(x + 2) + c

= a(x + 1)(x² - 4x + 4) + b(x + 2) + c

= a(x³ - 4x² + 4x + x² - 4x + 4) + b(x + 2) + c

= a(x³ - 3x² + 4) + b(x + 2) + c ← distribute parenthesis

= ax³ - 3ax² + 4a + bx + 2b + c

Compare x³ terms

ax³ with 2x³ , then a = 2

Compare x terms

bx = - 3x , then b = - 3

Compare constant terms

4a + 2b + c = 6

4(2) + 2(- 3) + c = 6

8 - 6 + c = 6

2 + c = 6 ( subtract 2 from both sides )

c = 4

Thus a = 2, b = - 3, c = 4

Answer:

\(\frac{27y^6}{8x^{12}}\)

Step-by-step explanation:

1) Use Product Rule: \(x^ax^b=x^{a+b}\).

\((\frac{3x^{-5+2}{y^3}}{2z^0yx}) ^3\)

2) Use Negative Power Rule: \(x^{-a}=\frac{1}{x^a}\).

\((\frac{3\times\frac{1}{x^3} y^3}{2x^0yx} )^3\)

3) Use Rule of Zero: \(x^0=1\).

\((\frac{\frac{3y^3}{x^3} }{2\times1\times yx} )^3\)

4) use Product Rule: \(x^ax^b=x^{a+b}\).

\((\frac{3y^3}{2x^{3+1}y} )^3\)

5) Use Quotient Rule: \(\frac{x^a}{x^b} =x^{a-b}\).

\((\frac{3y^{3-1}x^{-4}}{2} )^3\)

6) Use Negative Power Rule: \(x^{-a}=\frac{1}{x^a}\).

\((\frac{3y^2\times\frac{1}{x^4} }{2} )^3\)

7) Use Division Distributive Property: \((\frac{x}{y} )^a=\frac{x^a}{y^a}\).

\(\frac{(3y^2)^3}{2x^4}\)

8) Use Multiplication Distributive Property:  \((xy)^a=x^ay^a\).

\(\frac{(3^3(y^2)^3}{(2x^4)^3}\)

9) Use Power Rule: \((x^a)^b=x^{ab}\).

\(\frac{27y^6}{(2x^4)^3}\)

10)  Use Multiplication Distributive Property:  \((xy)^a=x^ay^a\).

\(\frac{26y^6}{(2^3)(x^4)^3}\)

11) Use Power Rule: \((x^a)^b=x^{ab}\).

\(\frac{27y^6}{8x^12}\)

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Answer:

\(\displaystyle \frac{27y^{6}}{8x^{12}}\)

Step-by-step explanation:

\(\displaystyle \biggr(\frac{3x^{-5}y^3x^2}{2z^0yx}\biggr)^3\\\\=\biggr(\frac{3x^{-5}y^2x}{2}\biggr)^3\\\\=\frac{(3x^{-5}y^2x)^3}{2^3}\\\\=\frac{3^3x^{-5*3}y^{2*3}x^3}{8}\\\\=\frac{27x^{-15}y^{6}x^3}{8}\\\\=\frac{27y^{6}x^3}{8x^{15}}\\\\=\frac{27y^{6}}{8x^{12}}\)

Notes:

1) Make sure when raising a variable with an exponent to an exponent that the exponents get multiplied

2) Variables with negative exponents in the numerator become positive and go in the denominator (like with \(x^{-15}\))

3) When raising a fraction to an exponent, it applies to BOTH the numerator and denominator

Hope this helped!

Answer:

1. Given

2. Distributive Prop

3. Addition Prop

4. Division Prop

Step-by-step explanation:

Answer:

$2.10

Step-by-step explanation:

Answer:

$2.1

Step-by-step explanation:

2 x 0.05 = 0.1

5+0.1 = $2.1

Answer:

Step-by-step explanation:

a. (I) x = 65

(ii) vertically opposite angles are equal.

b. (i) 71 degrees

(ii) alternate interior angles are equal

c. (i) z = 180 - 71 = 109 degrees

(ii) angles on a line add up to 180 degrees

Answer:

x = 65°, y = 71°, z = 44°

Step-by-step explanation:

x and 65 are vertical angles and congruent, thus

x = 65°

y and 71 are alternate angles and congruent, thus

y = 71°

The sum of the 3 angles in a triangle = 180°, thus

z = 180° - (65 + 71)° = 180° - 136° = 44°

Hence

x = 65°, y = 71° and z = 44°

The dimensions of the rectangle are width = 7/2 meters and length = 4 meters.

Let's assume that the width of the rectangle is x meters. According to the given information, the length of the rectangle is 3 meters less than double the width, which can be expressed as 2x - 3.

The area of a rectangle is given by the formula: Area = Length × Width. In this case, the area is given as 14 m². Therefore, we can write the equation:

(x)(2x - 3) = 14

Expanding the equation:

2x² - 3x = 14

Rearranging the equation to standard form:

2x² - 3x - 14 = 0

To solve this quadratic equation, we can factor it or use the quadratic formula. In this case, let's use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

In our equation, a = 2, b = -3, and c = -14. Plugging in these values into the quadratic formula:

x = (-(-3) ± √((-3)² - 4(2)(-14))) / (2(2))

x = (3 ± √(9 + 112)) / 4

x = (3 ± √121) / 4

x = (3 ± 11) / 4

Simplifying further:

x = (3 + 11) / 4 or x = (3 - 11) / 4

x = 14 / 4 or x = -8 / 4

x = 7/2 or x = -2

Since the width cannot be negative, we discard the negative solution. Therefore, the width of the rectangle is 7/2 meters.

Now, we can substitute the value of x into the expression for the length:

Length = 2x - 3

Length = 2(7/2) - 3

Length = 7 - 3

Length = 4 meters

Thus, the dimensions of the rectangle are width = 7/2 meters and length = 4 meters.

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Answer:

$1,252.13 I believe  or $1,252

Step-by-step explanation:

Multiply the 1500 by .10 and you'll get 150

Now subtract that from 1500 that's 1350

.0725 multiplyed by 1350 is 97.875

Subtract that from 1350 and you'll get the answer!

Answer: Research

Step-by-step explanation:

Assuming Σ a is convergent and Σ b is divergent, we prove the divergence of Σ (a + b) by contradiction. If Σ (a + b) were convergent, Σ a - Σ b would also be convergent, contradicting the assumption. Hence, Σ (a + b) is divergent.

To prove that if Σ a is convergent and Σ b is divergent, then the series Σ (a + b) is divergent, we can use a proof by contradiction. Here are the step-by-step calculations

Assume that Σ (a + b) is convergent.

Since Σ a is convergent, we know that the series Σ (a - b) is also convergent (subtracting a convergent series from both sides).

Rewrite Σ (a + b) = Σ a + Σ (-b).

Since Σ b is divergent, we know that Σ (-b) is also divergent (the sum of a divergent series with its negative).

Assume that Σ (a + b) is convergent, so Σ a + Σ (-b) is also convergent.

Adding Σ a and Σ (-b) gives Σ (a - b).

This implies that Σ (a - b) is convergent since the sum of convergent series is convergent.

However, this leads to a contradiction because we assumed that Σ a is convergent and Σ b is divergent.

Therefore, our assumption that Σ (a + b) is convergent must be false.

Thus, the series Σ (a + b) is divergent.

By reaching a contradiction, we have proven that if Σ a is convergent and Σ b is divergent, then the series Σ (a + b) is divergent.

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The explicit formula for an, the nth term of the sequence is a(n) = 7(2)^n-1

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

7, -14,28,..

The above definitions imply that we simply multiply -2 to the previous term to get the current term

Using the above as a guide,

So, we have the following representation

First term, a = 7

Common ratio, r = -2

The sequence is represented as

a(n) = a(r)^n-1

So, we have

a(n) = 7(2)^n-1

Hence, the sequence is a(n) = 7(2)^n-1

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A function's behaviour as x approaches positive or negative infinity might reveal vertical, horizontal, and oblique asymptotes. As x approaches a value, vertical asymptotes occur. As x approaches infinity, horizontal asymptotes occur. As x approaches infinity, oblique asymptotes occur.

To identify vertical asymptotes, we examine the behavior of the function as x approaches a particular value. For example, let's consider the function f(x) = 1 / (x - 2). As x approaches 2, the denominator becomes very close to zero, causing the function to approach infinity or negative infinity. Hence, x = 2 is a vertical asymptote.

Horizontal asymptotes are determined by analyzing the behavior of the function as x approaches positive or negative infinity. For instance, let's take the function f(x) = (3x^2 + 2x - 1) / (2x^2 + x + 1). As x approaches infinity or negative infinity, the highest power terms dominate the function. In this case, both the numerator and denominator have the same highest power term (x^2), so the ratio of the coefficients determines the horizontal asymptote. Therefore, the horizontal asymptote for this function is y = 3/2.

Oblique asymptotes occur when the function approaches a non-horizontal line as x approaches positive or negative infinity. Consider the function f(x) = (3x^2 + 2x + 1) / (x + 1). By performing polynomial long division or synthetic division, we can see that the quotient is 3x + 1. As x approaches infinity or negative infinity, the function approaches the line y = 3x + 1. Hence, y = 3x + 1 is an oblique asymptote for this function.

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Answer:

y = -1/5x + 6.4

Step-by-step explanation:

Use the point-slope formula.

y-y₁ = m(x -x₁)

so...

y-7 = -1/5(x - (-3))

y = -1/5x+ 32/5

and you need you can change 32/5 to 6.4

Hope this helps!

Factor by grouping.

(2x + 3)(x − 6)

Answer:

(2x-3) (x+6)

Hope this helps :)

Answer:

Got this from the internet.

Step-by-step explanation:

The vertical line dividing the parabola into two equal portions is called the line of symmetry. All parabolas have a vertex, the ordered pair that represents the bottom (or the top) of the curve. The vertex of a parabola has an ordered pair \begin{align*}(h, k)\end{align*}.

Answer:

1 over 100

Step-by-step explanation:

Answer:

Step-by-step explanation:

If by what is the measure of angle CBD you mean the degrees then I would say it is 45 degrees.

Answer:

the answer is 75%

each dot represents 25% of the data

Below 345 meters are 3 points

so, 3 * 25% = 75%

Answer:

\(\theta \approx 61.93\textdegree\)

Step-by-step explanation:

We can solve for the measure of angle θ in this right triangle using the trigonometric ratio sine, which uses the opposite and hypotenuse sides.

\(\sin(\theta) = \dfrac{\text{opposite}}{\text{hypotenuse}}\)

↓ plugging in the given values

\(\sin(\theta) = \dfrac{15}{17}\)

↓ taking the inverse tangent of both sides

\(\sin^{-1}\left(\dfrac{}{}\sin(\theta)\dfrac{}{}\right) = \sin^{-1}\left(\dfrac{15}{17}\right)\)

↓ canceling the inverse functions on the left side ... \(f^{-1}\left(\dfrac{}{}f(x)\dfrac{}{}\right) = x\)

\(\theta = \sin^{-1}\left(\dfrac{15}{17}\right)\)

↓ evaluating using a calculator

\(\theta \approx 61.93\textdegree\)

The formula \forall x \exists y(x\oplus y=c) in first-order logic states that for any value of x, there exists a value of y such that the binary function \oplus of x and y is equal to a constant c.

To determine the interpretations for which this formula is valid, we need to consider the possible interpretations of the binary function \oplus and the constant c.

Since the formula does not provide specific information about the binary function \oplus or the constant c, we cannot determine a single interpretation for which the formula is valid. The validity of the formula depends on the specific interpretation of \oplus and the constant c.

To evaluate the validity of the formula, we need additional information about the properties and constraints of the binary function \oplus and the constant c. Without this information, we cannot determine the interpretation(s) for which the formula is valid.

In summary, the validity of the formula \forall x \exists y(x\oplus y=c) depends on the specific interpretation of the binary function \oplus and the constant c, and without further information, we cannot determine a specific interpretation for which the formula is valid.

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a. The number of student surveyed is = 12 + 7 - 4 + 47 = 62

b. The number of student that are math major but not biology major = 7

c. The number of student that are neither math major nor biology major = 47

d. The number of student that are both math and biology major = 4

The cumulative downtime per year of an SLA percentage of 99.95 is 4 hours, 21 minutes, 58 seconds.

The  SLA Downtime refers to the time duration that a machine or service is unavailable.

The SLA Uptime is the amount of time a machine or service is available.

The cumulative downtime per year of an SLA percentage of 99.95 will give the following:

An SLA percentage of 99,95 gives 43 seconds daily downtime.

In a year, cumulative downtime = 43 seconds  * 365 = 15695 seconds

Converting to hours and minutes give a downtime of 4 hours, 21 minutes, 58 seconds.

In conclusion, downtime refers to unavailability of a given machine or service.

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Therefore , the solution of the given problem of percentage comes out to be  earned 6.1% from the selling of the oranges.

In statistics, "a%" refers to a figure or a statistic that is expression as a percentage of 100. The letters "pct," "pct," and "pc" are also rare abbreviations. It is typically represented by the symbol "%," though. There are no indicators and a flat ratio to the overall amount. In reality, percentages are numbers because their sum almost always equals 100.

Here,

Let's suppose that the lady purchased x oranges.

She charged 60gp for each orange she sold, for a total of 60x gp.

She earned a profit of 3.05 GHC, making her overall profit

=> 3.05 GHC = 305p.

Her cost price (50gp) plus her profit (305p) would equal her total income (selling price), which would be 355gp.

=> 60x = 355

=> x = 355/60

=> x = 5.9167

She consequently purchased six bananas.

b) Since she paid 50gp for the container of oranges, their cost would be 50gp.

c) The total sale price of the oranges would be 360gp, or 60gp for each orange multiplied by 6.

d) She would have earned a profit of (profit/cost price) x 100%.

She made 305p, or 3.05 GHC, in earnings.

Her cost was 50gp, so

=> 6.1%  = (3.05/50) *  100%.

She thus earned 6.1% from the selling of the oranges.

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Answer: x=4/9

Step-by-step explanation:

Answer:

Step-by-step explanation:

80        40

___________

 100        50

Answer:

A is Perpendicular

B is Neither

C is Parallel

Answer:

8

Step-by-step explanation:

a) The value of z corresponding to an area of 0.1210 can be found using statistical tables or a statistical calculator.

b) Similarly, the value of z corresponding to an area of 0.9898 can be obtained using statistical tables or a statistical calculator.

c) To find the value of z at the 45th percentile, we can use the standard normal distribution table or a statistical calculator.

a) To find the value of z corresponding to an area of 0.1210, you can use a standard normal distribution table or a statistical calculator. By looking up the area of 0.1210 in the table, you can determine the corresponding z-value. For example, if you find that the z-value for an area of 0.1210 is -1.15, then -1.15 is the value of z corresponding to the given area.

b) Similarly, to find the value of z corresponding to an area of 0.9898, you can refer to a standard normal distribution table or use a statistical calculator. Find the z-value that corresponds to the area of 0.9898. For instance, if the z-value for an area of 0.9898 is 2.32, then 2.32 is the value of z corresponding to the given area.

c) To find the value of z at the 45th percentile, you can use a standard normal distribution table or a statistical calculator. The 45th percentile corresponds to an area of 0.4500. By finding the z-value for an area of 0.4500, you can determine the value of z at the 45th percentile. For example, if the z-value for an area of 0.4500 is 0.125, then 0.125 is the value of z at the 45th percentile.

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The amount of money in Lucia's account after 5 years will be $1,105.5.

A loan or deposit's interest is computed using the starting principle and the interest payments from the ago decade as compound interest.

We know that the compound interest is given as

A = P(1 + r)ⁿ

Where A is the amount, P is the initial amount, r is the rate of interest, and n is the number of years.

Lucia opened a savings account and deposited $600.00 as principal. The account earns 13% interest, compounded annually. Then the amount of money after 5 years will be given as,

A = $600 × (1 + 0.13)⁵

A = $600 × (1.13)⁵

A = $600 × 1.84

A = $1,105.5

The amount of money in Lucia's account after 5 years will be $1,105.5.

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