If an = n(an-1) and a1 = 1, what is the value of as?
1) 5
2) 20
3)
120
4) 720

 m∠1 + m∠2 = m ∠4 , under the exterior angle property of a triangle which says that sum of the interior opposite angles of an exterior angle will be equal to the measure of the exterior angle .

To prove that m∠3 + m ∠1 +  m∠2 = 180° , let us use the angle sum property .

= Angle sum property = Sum of the three interior angles in a triangle will be equal to 180° .

= Since  ∠1 ,  ∠2 and  ∠3 are the interior angles of this triangle , their sum will be equal to 180° .

Hence proved that m∠1 +  m∠2 + m∠3 = 180°

∴ m∠1 +  m∠2 + m∠3 = 180° under the angle sum property of a triangle .

Answer:

3 green apples and 7 red apples.

Step-by-step explanation:

1. Start with the ratio of green apples to red apples, which is 3 to 7.

2. Multiply 3 (the number of green apples) by any number to get a number that is divisible by 7 (the number of red apples).

3. In this case, multiplying 3 by 2 gives 6, which is divisible by 7.

4. Since 6 is divisible by 7, that means that the solution is 3 green apples and 7 red apples.

Answer:

14.3

Step-by-step explanation:

Since this is a right triangle, we can use the Pythagorean theorem

a^2 + b^2 = c^2   where a and b are the legs and c is the hypotenuse

14^2 + 3^2 = c^2

196 + 9 = c^2

205 = c^2

Take the square root of each side

sqrt(205) = sqrt(c^2)

14.31782106 = c

Rounding to the nearest tenth

14.3 = c

Answer :

⠀

Explanation :

⠀

Solution :

where,

We know that,

\({\longrightarrow \pmb{\mathbb {\qquad (XZ) {}^{2} = (XY) {}^{2} +( YZ) {}^{2} }}} \\ \\ \)

Now, we will substitute the given values in the formula :

\({\longrightarrow \sf{\pmb {\qquad (XZ) {}^{2} = (3) {}^{2} +( 14) {}^{2} }}} \\ \\ \)

We know that, (3)² = 9 and (14)² = 196. So,

\({\longrightarrow \sf{\pmb {\qquad (XZ) {}^{2} = 9 +196 }}} \\ \\ \)

Now, adding 9 and 196 we get :

\({\longrightarrow \sf{\pmb {\qquad (XZ) {}^{2} = 205 }}} \\ \\ \)

Now, we'll take the square root of both sides to remove the square from XZ :

\({\longrightarrow \sf{\pmb {\qquad \sqrt{(XZ) {}^{2}} = \sqrt{205 }}}} \\ \\ \)

When we take the square root of (XZ)² , it becomes XZ,

\({\longrightarrow \sf{\pmb {\qquad XZ = \sqrt{205 }}}} \\ \\ \)

We know that, square root of 205 is 14.317 (approx) .

\({\longrightarrow { \mathbb{\pmb {\qquad XZ }}}} \approx \pmb{\mathfrak{14.317 } }\\ \\ \)

So,

We can compute various descriptive statistics such as the mean, median, mode, range, variance, standard deviation, sum of values, and sum of squared deviations.

The sample mean, also known as the average, provides information about the central tendency of the variable X. It represents the typical or average number of coupons used by the shoppers in the sample. In this case, calculating the mean of the given data would provide an estimate of the average number of coupons used over the 6-month period.

The sample standard deviation measures the dispersion or variability of the data points around the mean. It indicates how much the individual observations deviate from the mean value. A higher standard deviation implies greater variability, indicating a wider range of coupon usage among the shoppers in the sample.

By computing the sample mean and standard deviation, we can understand the average coupon usage and the degree of variability in the data. These statistics help us summarize and interpret the characteristics of the variable X, allowing us to make comparisons, identify outliers, assess the spread of the data, and make inferences about the larger population from which the sample was drawn.

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a.  4 is an extraneous root. , b. 0 is an extraneous root. , c. -3 is an extraneous root. , d. -13.21 is an extraneous root. , e. 9.22 is an extraneous root.

To solve the equation, we can begin by finding a common denominator for the fractions on the left-hand side. The common denominator is (x + 3)(x - 4). We can then rewrite the equation as follows:

[4x(x - 4) + 3(x + 3)] / [(x + 3)(x - 4)] = 5

Expanding and simplifying the numerator, we have:

[4x^2 - 16x + 3x + 9] / [(x + 3)(x - 4)] = 5

Combining like terms, we obtain:

(4x^2 - 13x + 9) / [(x + 3)(x - 4)] = 5

To eliminate the fraction, we can cross-multiply:

4x^2 - 13x + 9 = 5[(x + 3)(x - 4)]

Expanding the right-hand side, we get:

4x^2 - 13x + 9 = 5(x^2 - x - 12)

Simplifying further:

4x^2 - 13x + 9 = 5x^2 - 5x - 60

Rearranging the equation and setting it equal to zero, we have:

x^2 - 8x - 69 = 0

To solve this quadratic equation, we can factor or use the quadratic formula. Factoring the equation may not yield rational roots, so we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

For the equation x^2 - 8x - 69 = 0, we have a = 1, b = -8, and c = -69. Substituting these values into the quadratic formula, we get:

x = (-(-8) ± √((-8)^2 - 4(1)(-69))) / (2(1))

= (8 ± √(64 + 276)) / 2

= (8 ± √340) / 2

= (8 ± 2√85) / 2

= 4 ± √85

So, the possible solutions for x are x = 4 + √85 and x = 4 - √85.

Now, let's check which of the given options (a, b, c, d, e) are extraneous roots by substituting them into the original equation:

a. 4: Substitute x = 4 into the equation: 4(4)/(4 + 3) + 3/(4 - 4) = 5. This results in a division by zero, which is undefined. Therefore, 4 is an extraneous root.

b. 0: Substitute x = 0 into the equation: 4(0)/(0 + 3) + 3/(0 - 4) = 5. This also results in a division by zero, which is undefined. Therefore, 0 is an extraneous root.

c. -3: Substitute x = -3 into the equation: 4(-3)/(-3 + 3) + 3/(-3 - 4) = 5. Again, we have a division by zero, which is undefined. Therefore, -3 is an extraneous root.

d. -13.21: Substitute x = -13.21 into the equation and evaluate both sides. If the equation does not hold true, -13.21 is an extraneous root.

e. 9.22: Substitute x = 9.22 into the equation and evaluate both sides. If the equation does not hold true, 9.22 is an extraneous root.

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Answer:

\(x^{2}\) + 2x

Step-by-step explanation:

Helping in the name of Jesus.

Answer:

x^{2} + 2x

Step-by-step explanation:

The person who answered above me is correct

the answer is 5 hope this helps lol

Answer:

2n-4

Step-by-step explanation:

Answer:

2n -4

Step-by-step explanation:

1. Remove the parenthesis

n + 8 + n - 12

2. Simplify

n + 8 + n - 12 = 2n -4

Etta needs to add the source of the information to better arrange these notes.

A note is a place where information about a specific item is recorded for later reference. The main goals of taking notes are to promote active learning and create study materials for tests. You should be able to organise material into an understandable format that will aid in your learning process by developing note-taking skills.

As a result, it is clear from the question that Etta is making notes for the purpose of creating a webpage about healthy eating. Once her notes have been organised with the relevant facts and information, Etta will need to cite her sources.

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Answer:

56y+32

Step-by-step explanation:

please mark me as brainlist

Answer:

52

Step-by-step explanation:

The minimum of the data set is the smallest number. Therefore, the minimum is 52.

Lydia earns $52.5 more than Gabrielle after 3 years.

percentage, a relative value indicating hundredth parts of any quantity.

we can use the formula for compound interest:

\(A = P(1 + r/n)^n^t\)

where A is the final amount,

P is the principal (initial investment),

r is the annual interest rate (as a decimal),

n is the number of times the interest is compounded per year, and

t is the number of years.

For Lydia (n=365)

A=1000(1+0.0525/365)¹⁰⁹⁵

A=1115.7

For Gabrille, we use the same formula but with n = 2 (compounded semi-annually):

A = 1000(1 + 0.0525/2)⁶

A = 1000(1.0265625)⁶

A = 1168.2

To find the difference in the amounts earned, we subtract Gabrielle's amount from Lydia's:

1168.2- 1115.7 = 52.5

Hence, Lydia earns $52.5 more than Gabrielle after 3 years.

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ANSWER

Option B

EXPLANATION

We want to find the graph that represents the exponential function given:

To do this, we simply have to check for which of the graphs has the correct y-intercept. The y-intercept is the point where the graph touches the y-axis.

We can calculate the y coordainte of the y-intercept from the given function by finding the value of f(x) when x = 0.

That is:

Hence, the y-intercept is (0,4).

Therefore, the correct answer is Option B.

On solving the the provided question we can say that -  in the equation we have 12a - 3b = 84 - 30 = 54

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.

here, we have

a = 7 and b = 10

so, 12a - 3b

84 - 30 = 54

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The mathematical statement is true when the value of t is 22

The equation is given as:

\((4x^3- 5)(2x^3 -3) = 8x^6 -tx^3 +15\)

Expand the expression on the left-hand side

\(4x^3(2x^3 -3)- 5(2x^3 -3) = 8x^6 -tx^3 +15\)

Distribute the expression

\(8x^6 -12x^3- 10x^3 +15 = 8x^6 -tx^3 +15\)

Evaluate like terms

\(8x^6 -22x^3 +15 = 8x^6 -tx^3 +15\)

By comparing the expressions on both sides of the equation, we have:

\(-22x^3= -tx^3\)

Divide both sides of the equation by -x^3

\(22= t\)

Rewrite as:

\(t =22\)

Hence, the mathematical statement is true when the value of t is 22

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Answer:

22

Step-by-step explanation:

Betrys needs another 400 grams of diced potatoes to make her vegetable stew for 8 people.

We know that Betrys is cooking for 8 people, and we know that a recipe for 2 people needs 10 ounces.

8 people is 4 times 2 people, then for 8 people you need 4 times 10 ounces, this is 4*10 oz = 40 ounces.

Now we can apply a change of units, remember that:

1 oz = 28 grams

Then the total amount she needs is:

40 oz = 40*28 g = 1,120 g

So she needs in total 1,120 grams, and in the balance, she already has 720 grams, so the amount that she needs is given by the subtraction:

1,120 g - 720g = 400

Betrys needs another 400 grams of diced potatoes to make her vegetable stew for 8 people.

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The laptop will be worth $0.001286 after 15 years if its worth becomes 1/3 each year.

We can solve this problem by using the formula for geometric sequences,

an = a₁r^(n-1), here in this case, an is the worth of the laptop after n years, r is the rate at which the worth is changing that 1/3 in this case and a₁ is the value of the laptop currently. Substituting the given values, we get:

a₁₅ = 600(1/3)¹⁵⁻¹

a₁₅ = 600(1/3)¹⁴

a₁₅ = 600x0.0000021433

a₁₅ = 0.001286

Therefore, after 15 years, the laptop is worth approximately $0.001286.

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The correct statement is that F(x) < 0 over the intervals (-0.7, 0.76) and (2.5, ∞).

Value of subjective concept that refers to the word of important that an individual group of people places on the something it is often associated with principal beliefs and the standard that are accepted by society when you can be seen as a matter of how important something is true person of organization it is often seen as a reflection of funds for view and can help to save decision.

This can be seen by looking at the function's minimum and maximum values and its points of intersection with the x- and y-axes. The minimum value of (1.9, negative 5.7) is to the left of the x-axis, indicating that the function is negative over the interval (-0.7, 0.76). The maximum value of (0, 2) is above the x-axis, indicating that the function is negative over the interval (2.5, ∞).

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Answer:

they are similar cuz it resembles a "z" pattern. The angles are so the same.

\((∃x)Hx\) is true. Hence, the conclusion "Prove valid: \((∃x)Hx\)" is valid.

Given that the premises are:\((1) (∃x)Hx v (Ja ⋅ Kb) (2) (∃x) [(Ja ⋅ Kb) ⊃ ∼ (x=x)] /\\∴ (∃x)Hx\)

We are required to show that the conclusion \(" (∃x)Hx"\)is valid.

It can be done using the Proof of contradiction technique.

For the proof of contradiction, let us assume the opposite of what we need to prove. i.e, assume that(∃x)Hx is false.

Then, we get∀x ∼HxFrom premise (1), we get \((∃x)Hx v (Ja ⋅ Kb)\)

When we assume the opposite, the above expression becomes:∀x ∼Hx v (Ja ⋅ Kb)

Since we have already assumed that ∀x ∼Hx, the above expression becomes: \(∀x ∼Hx\)

Here, we will use Universal Instantiation to substitute the value of x in premise (2).

So, from premise (2), we get \((∃x) [(Ja ⋅ Kb) ⊃ ∼ (x=x)]\)

Assuming \((∃x)Hx\) to be false, we get \(∀x ∼Hx\)

Using this and the above expression, we can say that \([Ja ⋅ Kb] ⊃ ∼(x=x)\) is true for all x.

As x cannot be equal to itself,\([Ja ⋅ Kb]\) should be false.

Thus, we can say that the negation of the premise is true.i.e, \(∼[(∃x)Hx v (Ja ⋅ Kb)]\)

We will simplify the above expression using De Morgan's law.

\(∼ (∃x)Hx ⋅ ∼ (Ja ⋅ Kb)\)

When we assume that ∃xHx is false, the above expression becomes:∀x ∼Hx ⋅ (Ja ⋅ Kb)Using Universal Instantiation, we can substitute the value of x in the above expression.

From premise (2), we can say that \((Ja ⋅ Kb) ⊃ ∼ (x=x)\) is true.

Thus, the expression ∀x ∼Hx ⋅ (Ja ⋅ Kb) becomes false.

Thus, we get

\(∼ [(Ja ⋅ Kb) ⊃ ∼ (x=x)]\)

Therefore, we have reached a contradiction to our assumption that \((∃x)Hx\) is false.

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Considering they're getting 2 more each wave, we can apply simple math to this.

6+2 and onwards,

0+3 and onwards until it surpasses the first value.

I calculated this, and it seems it takes around 6 minutes to catch up to the friend at 18 exercises.

It will take you 6 minutes to catch up to your friend.

Given that when you started your homework assignment, your friend already had 6 exercises done.

You can do about 3 exercises per minute, whereas your friend can only do 2 exercises per minute.

So, your friend is ahead by 6 exercises, and you can complete 3 exercises per minute while your friend can complete 2 exercises per minute.

This means you're gaining on your friend's lead at a rate of 3 - 2 = 1 exercise per minute.

To catch up to your friend's lead of 6 exercises, you'll need 6 minutes, because you'll be closing the gap by 1 exercise per minute.

So, it will take you 6 minutes to catch up to your friend.

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The volume of any rectangular prism (or solid) is given by:

Given that the dimnsions of the rectangular prism in question is:

Length = 62cm

Width = 3.5cm

Height = 10cm

Therefore, the volume is:

Therefore, the volume (in cubic centimeters) of the given rectangular prism is 2170

Answer: 2170cm3

Step-by-step explanation:

The volume of any rectangular prism (or solid) is given by:

Given that the dimensions of the rectangular prism in question is:

Length = 62cm

Width = 3.5cm

Height = 10cm

Answer:

-7/9

Step-by-step explanation:

To solve this equation you must isolate the variable.

First, add like terms (terms with the same variable and degree)

2x+2=11x+9

Then, subtract 2x from both sides

2=9x+9

Next, subtract 9 from both sides

-7=9x

Finally, divide both sides by 9

\(\frac{-7}{9}=x\)

The general solution is : Y = Yc + Yp = c1 cos(4t) + c2 sin(4t) – 6 Sec(4t)

We can use the method of undetermined coefficients to find a particular solution to the differential equation Y'' + 16y = –24 Sec(4t).

First, we need to find the complementary solution by solving the characteristic equation:

r^2 + 16 = 0

This gives us the roots r = ±4i.

The complementary solution is then:

Yc = c1 cos(4t) + c2 sin(4t)

To find the particular solution, we guess that Yp has the same form as the forcing function, i.e.,

Yp = A Sec(4t)

where A is a constant to be determined.

Taking the first and second derivatives of Yp, we have:

Y'p = 4A Sec(4t) Tan(4t)

Y''p = 4A [Sec(4t) Tan(4t)]' = 4A [Sec^2(4t)]

Substituting these into the original differential equation, we get:

4A [Sec^2(4t)] + 16A Sec(4t) = –24 Sec(4t)

Simplifying, we get:

4A = –24

A = –6

Therefore, the particular solution is:

Yp = –6 Sec(4t)

The general solution is then:

Y = Yc + Yp = c1 cos(4t) + c2 sin(4t) – 6 Sec(4t)

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Answer:

A) 24

Step-by-step explanation:

Answer:

m = 24

Step-by-step explanation:

Step-by-step explanation:

what ? nothing makes any sense here.

please read your problem statement again and type it here again, letter by letter, digit by digit, symbol by symbol.

Answer:

36 : 6 and -6

12 = \(2\sqrt{3} , -2\sqrt{3}\)

1.96 =1.4 and -1.4

0.64 : 0.8 and -0.8

400 : 20 and -20

25/36 = 5/6 and -5/6

Step-by-step explanation:

we know that

(-x)^2 = x^2

ALSO

(x)^2 = x^2

thus, square of both negative and positive number is same positive number.

_________________________________________________

36 = 6*6

36 = -6*-6

hence

square roots of 36 is both -6 and 6

12 = 4*3 = \(2^2*\sqrt{3} *\sqrt{3}\)

\(\sqrt{12} = 2\sqrt{3}\)

also

12 = \(-2\sqrt{3} *-2\sqrt{3}\)

\(\sqrt{12} = -2\sqrt{3}\)

___________________________________

1.96 = 196/100 = (14/10)^2

1.96 = 196/100 = (-14/10)^2

hence

\(\sqrt{1.96} = 14/10 \ or -14/10\)

_______________________________

0.64 = 64/100 = (8/10)^2 = 0.8^2

0.64 = 64/100 = (-8/10)^2 = (-0.8)^2

Thus, square root of  0.64 = 0.8 and -0.8

_________________________________

400 = 20^2

400 = (-20)^2

\(\sqrt{400} = 20\\\sqrt{400} = -20\\\)

__________________________________

25/36 = (5/6)^2

25/36 = (-5/6)^2

\(\sqrt{ 25/36} = 5/6 \\\sqrt{ 25/36} = (-5/6\)

Answer: 350 \(\sqrt{3\)

Step-by-step explanation:

700^0.5 = 10 \(\sqrt{7\\\)

525^0.5 = 5 \(\sqrt{21\)

10\(\sqrt{7\) x 5\(\sqrt{21\) = 50 x 7 x \(\sqrt{3\) = 350\(\sqrt{3\\\)