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10 pts

Answer:

d)  3, 4, 5, 6

Step-by-step explanation:

Given recursive rule:

\(\begin{cases}a_n=2a_{n-1}-n\\a_1=3\end{cases}\)

First four terms of the sequence:

\(\implies a_1=3\)

\(\begin{aligned}\implies a_2 & =2a_{(2-1)}-2\\& = 2a_1-2\\& = 2(3)-2\\& = 6-2\\& = 4\end{aligned}\)

\(\begin{aligned}\implies a_3 & =2a_{(3-1)}-3\\& = 2a_2-3\\& = 2(4)-3\\& = 8-3\\& = 5\end{aligned}\)

\(\begin{aligned}\implies a_4 & =2a_{(4-1)}-4\\& = 2a_3-4\\& = 2(5)-4\\& = 10-4\\& = 6\end{aligned}\)

Therefore, the first four terms of the sequence are 3, 4, 5, 6.

Answer:

I won’t bother putting on the same answer as the other person.

Step-by-step explanation:

This is a linear sequence, as it has no indices in the nth term.

It starts with 3.

Thus, we only need to work out the 2nd term to have our answer.

3,4…

We know it will continue to be 3,4,5,6

There’s your answer

Answer:

The length of AB is 18

Step-by-step explanation:

Do the pygotham theorem

24^2 + 7^2 = 625

Square root the answer

\(\sqrt{625}\) = 25

Line BO equals 7 because CO is 7 and they are both radiuses

Subtract the answer to the length BO

25 - 7 = 18

18 is the length of AB bro

It takes longer for one person to flip five batches of two pennies than one batch of ten pennies, mainly for a simple reason: although 5 x 2 is equal to 10, that is, it will take the same time to flip the coins, 5 batches is greater than 1 batch, which will take longer to manipulate each of these, increasing the total time.

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The nearest tenth, 44.5 minutes have gοne by.

Time is the οngοing prοgressiοn οf existence and events that take place in what appears tο be an irreversible οrder frοm the past thrοugh the present tο the future. It is οne οf the quantities that make up variοus measurements that are used tο cοmpare the lengths οf events οr the gaps between them, tο cοmpare hοw lοng they last, tο οrder events, and tο measure hοw quickly certain quantities in the physical wοrld οr in cοnsciοus experience change. The fοurth dimensiοn, in additiοn tο the three spatial dimensiοns, is frequently referred tο as time.

If Teresa has finished 57% οf her run, then she has 43% left tο cοmplete.

Let x be the number οf minutes that have gοne by.

Since 57% οf the run is cοmpleted in 78 minutes, we can set up the fοllοwing prοpοrtiοn:

57/100 = x/78

Sοlving fοr x, we get:

x = (57/100) * 78

x = 44.46

Therefοre, tο the nearest tenth, 44.5 minutes have gοne by.

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Answer:

x = 16°

H = 46°

I = 55°

J = 39°

Step-by-step explanation:

Since the whole figure is 180°

Deduct 180 by the numbers mentioned above in order to find x.

180 - 2 - 9 - 9 = 160

3x + 4x + 3x = 10x

10 x = 160

x = 160 ÷ 10 = 16

Since we know what x is, we can find all the angles in the figure.

Angle at H = 3 x 16 - 2 = 46°

Angle at I = 4 x 16 - 9 = 55°

Angle at J = 3 x 16 - 9 = 39°

The value of x is 20.

The total of a triangle's three internal angles is 180 degrees, as stated by the angle sum feature of a triangle. A closed shape with both inner and exterior angles, a triangle is created by three line segments. When the values of the other two angles are known, one can utilise the angle sum property to determine the measure of an unknown interior angle.

Given:

Angles are: 3x-2, 3x-9 , 4x-9

Using Angle Sum Property

3x-2 + 3x -9 + 4x- 9 = 180

10x - 20 = 180

10x = 200

x= 200/10

x= 20

Hence, the value of x is 20.

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The expression for the perimeter of the quadrilateral is 4a + 21 and the value of a is 9.75 cm when perimeter is 60 cm.

Perimeter of a straight sided figures or objects is the total length of it's boundary.

1. Given is a quadrilateral made up of 1 blue, 2 black and 1 red sticks.

Length of the sides according to the figure are a cm, (a + 6) cm, (a + 6) cm and (a + 9) cm.

Perimeter = a + (a + 6) + (a + 6) + (a + 9)

                 = 4a + 21

2. Let the perimeter of the shape be 60 cm.

4a + 21 = 60

4a = 39

a = 9.75 cm

Hence the value of a is 9.75 when the perimeter of the quadrilateral is 60 cm.

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To solve for the length of a side of such a pyramid, given its three sides, we can use the Pythagorean theorem.

A triangular pyramid with three right angles is known as a right triangular pyramid or a tetrahedron.

1. Identify the three sides of the pyramid:

The sides can be labelled a, b, and c.

2. Determine which sides form the right angles:

In a right triangular pyramid, two sides will be perpendicular to each other, forming the right angles. Let's assume sides a and b form the right angles.

3. Apply the Pythagorean theorem:

Using the Pythagorean theorem, we can write the equation:

  a² + b² = c²

4. Substitute the given values:

Plug in the lengths of sides a and b into the equation.

5. Solve for c:

Simplify and solve the equation to find the length of side c, which represents the length of the remaining side of the triangular pyramid.

By following these steps, you can determine the length of the side of a right triangular pyramid when the lengths of the other three sides are given.

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A pair of corresponding angles, alternate interior angles, and alternate exterior angles include the following:

Corresponding angles: ∠1 ≅ ∠5.

Alternate interior angles: ∠4 ≅ ∠6.

Alternate exterior angles: ∠2 ≅ ∠8

In Mathematics, corresponding angles can be defined as a postulate (theorem) which states that corresponding angles are always congruent when the transversal intersects two (2) parallel lines:

∠1 ≅ ∠5

By applying the alternate interior angles theorem to parallel lines m and n, we have the following congruent angles:

∠4 ≅ ∠6

By applying the alternate exterior angles theorem to parallel lines m and n, we have the following congruent angles:

∠2 ≅ ∠8

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The expression of "The difference of -10 and the product of p and q" in algebraic notation is pq + 10

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

The difference of -10 and the product of p and q

The numbers are given as

p and q

The product of p and q means pq

So, we have the following

The difference of -10 and pq

The difference of -10 and pq means

pq + 10

Hence, the expression is pq + 10

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The required reverse Euclidean algorithm is the solution to the modular equation (5x) mod 91 is

x = 6(mod 91).

Given that (5*x) mod 91 =32.

To solve the modular equation (5*x) mod 91 =32 using reverse Euclidean algorithm is to find the modular inverse of 5 modulo 91.

Consider  (5*x) mod 91 =32.

5x = 32(mod 91)

Apply the Euclidean algorithm to find GCD of 5 and 91 is

91 = 18 * 5 + 1.

Rewrite it in congruence form,

1 = 91 - 18 *5

On simplifying the equation,

1 = 91 (mod 5)

The modular inverse of 5 modulo 91 is 18.

Multiply equation by 18 on both sides,

90x = 576 (mod91)

To obtain the smallest positive  solution,

91:576 = 6 (mod 91)

Divide both sides by the coefficient of x:

x = 6 * 90^(-1).

Apply the Euclidean algorithm,

91 = 1*90 + 1.

Simplify the equation,

1 + 1 mod (90)

The modular inverse of 90 modulo 91 is 1.

Substitute the modular inverse in the given question gives,

x = 6*1(mod 91)

x= 6 (mod91)

Therefore, the solution to the modular equation (5x) mod 91 is

x = 6(mod 91).

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The plane flew at the first speed (111 mph) for 2 hours, and the remaining time of the trip (5 - 2 = 3 hours) was flown at the second speed (122 mph).

Let's assume the plane flew at the first speed (111 mph) for x hours.

Since the total duration of the trip was 5 hours, the time flown at the second speed (122 mph) can be calculated as (5 - x) hours.

To find the time flown at each speed, we can set up an equation based on the distance traveled.

The total distance traveled during the trip is 588 miles.

The distance covered at the first speed is given by the formula: Distance = Speed \(\times\) Time.

So, for the first part of the trip, the distance covered is 111x miles.

The distance covered at the second speed is: Distance = Speed \(\times\) Time.

For the second part of the trip, the distance covered is 122(5 - x) miles.

Since the total distance is 588 miles, we can set up the equation:

111x + 122(5 - x) = 588

Simplifying the equation:

111x + 610 - 122x = 588

-11x + 610 = 588

-11x = -22

x = 2.

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Answer: no one cares

Step-by-step explanation:

Answer: 6.7% 0.67 6
                                 -
                                9

Step-by-step explanation:

Answer:

\(\sf 6.7\% < 6/9 < 0.67\)

Explanation:

You would think 6.7% is a lot bigger than both, but it is not. Remember 6.7 is a percentage out of 100, thus, 6.7% actually is 0.067.

The nominal rate per annum compounded half-yearly, equivalent to an effective rate of 14.5% per annum, is approximately 14.900625%.

To convert an effective rate to a nominal rate compounded half-yearly, we can use the formula:

Nominal rate \(= (1 + r/m)^m - 1\)

Where:

r = effective rate

m = number of compounding periods per year

In this case, the effective rate is 14.5% per annum, and we want to convert it to a nominal rate compounded half-yearly.

Since compounding is done semi-annually, m would be 2.

Plugging in the values:

Nominal rate \(= (1 + 0.145/2)^2 - 1\)  

Simplifying the expression inside the parentheses:

Nominal rate \(= (1 + 0.0725)^2 - 1\)

Calculating the exponent:

Nominal rate \(= (1.0725)^2-1\)

Performing the calculations:

Nominal rate = 1.14900625 - 1

Nominal rate = 0.14900625

Converting the nominal rate to a percentage:

Nominal rate = 14.900625%

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The dimensions of the garden that create the maximum area are 5 meters by 15 meters, and the maximum possible area is 75 square meters

What is measurement?

Measurement is the process of assigning numerical values to physical quantities, such as length, mass, time, temperature, and volume, in order to describe and quantify the properties of objects and phenomena.

Let's assume that the rock wall is the width of the garden and the wire fencing is used for the length and the other two sides. Let's denote the length of the garden as L and the width as W.

Since we have 30 meters of fencing available, the total length of wire fencing used is:

L + 2W = 30 - W

Simplifying this equation, we get:

L = 30 - 3W

The area of the garden is:

A = LW

Substituting the expression for L from the previous equation, we get:

A = W(30 - 3W)

Expanding the expression, we get:

A = 30W - 3W²

To find the maximum area, we need to take the derivative of A with respect to W and set it equal to zero:

dA/dW = 30 - 6W = 0

Solving for W, we get:

W = 5

Substituting this value back into the expression for L, we get:

L = 15

Therefore, the dimensions of the garden that create the maximum area are 5 meters by 15 meters, and the maximum possible area is:

A = 5(15) = 75 square meters

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Answer:

\(g'(y)=3y^2-4y-8\)

Step-by-step explanation:

start by foiling out the given function

\(g(y)=(y-4)(2y+y^2)\\=2y^2+y^3-8y-4y^2\\=y^3-2y^2-8y\)

next, use the power rule to find the derivative

power rule: To use the power rule, multiply the variable's exponent n, by its coefficient a, then subtract 1 from the exponent. If there's no coefficient (the coefficient is 1), then the exponent will become the new coefficient.

\(g'(y)=3y^2-4y-8\)

Answer:

A. √16

Step-by-step explanation:

A perfect square is any number that can be expressed as a product of an integer and itself. i.e. 4 can be represented as 2 × 2. Therefore, 4 is a perfect square.

From the options given, the only radical expression that has two perfect square is √16.

√16 consists of two perfect squares, which are 4 and 4.

4 can be expressed as 2 × 2.

Thus: √16 = √(2 × 2)(2 × 2).

Therefore, √16 consists of two perfect squares.

Answer:

$880

Step-by-step explanation:

Use the equation:

\(P=(1-d)x\) with d being the discount in a decimal form, and P being the price that was bought at.

220=(1-0.75)x

simplify parenthesis terms

220=0.25x

divide both sides by 0.25

880=x

So, the original price was $880.

Hope this helps! :)

Let's start by assigning variables to represent the unknowns in the problem.

Let's use "c" to represent the number of crayons Manuel had in the beginning and "m" to represent the number of markers he had in the beginning.

From the problem, we know that:

Manuel had 4 times as many crayons as markers in the beginning, so:

c = 4m

After he bought 250 crayons and 100 markers, he had 3 times as many crayons as markers, so:

c + 250 = 3(m + 100)

Now we can use algebra to solve for c:

c + 250 = 3m + 300 // distribute the 3

c = 3m + 300 - 250 // simplify by combining like terms

c = 3m + 50

Substitute c = 4m from the first equation into the second equation:

4m = 3m + 50 // subtract 3m from both sides

m = 50

So Manuel had 4 times as many crayons as markers in the beginning, which means he had:

c = 4m = 4(50) = 200 crayons in the beginning.

The calculated measure of m∠PNM is 87 degrees

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

The circle

Where, we have

PM = 360 - 64 - 122

Evaluate

PM = 174

Next, we have

m∠PNM = 1/2 * 174

So, we have

m∠PNM = 87

Hence, the measure of m∠PNM is 87 degrees

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Answer:

1,5 answer of 1 St questions

1,2,5,7,9,12 answer 2nd questions

Step-by-step explanation:

1.A ∩ B

A { 1, 2, 5, 7 } and B = { 1, 5, 9, 12 }.

                They have both five and one so the answer is

A ∩ B= {1,5}

2. A ∪ B

           You only need to list everything(but no repetition) so the answer is

{ 1, 2, 5, 7, 9, 12 }

The sec 132 degrees 15 minutes in degrees is approximately -1.638 degrees.

The secant function, denoted as sec(x), is a trigonometric function that is defined as the reciprocal of the cosine function, cos(x).

In other words,

sec(x) = 1 / cos(x)

The secant function is defined for all values of x except for those where the cosine function is equal to zero, which corresponds to the values x = (2n+1)π/2 where n is an integer. At these points, the secant function is undefined.

To convert sec(132 degrees 15 minutes) to degrees, we first need to convert the angle to decimal degrees.

We know that 1 degree is equal to 60 minutes, so 15 minutes is equal to 15/60 = 0.25 degrees.

Therefore, the angle 132 degrees 15 minutes is equal to 132 + 0.25 = 132.25 degrees.

Now we can find the secant of this angle:

sec(132.25 degrees) = 1/cos(132.25 degrees) ≈ -1.638

So the answer is approximately -1.638 degrees.

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Answer:

17

Step-by-step explanation:

Shape: Isosceles Right Triangle.

Isosceles Right Triangles always have two sides of equal length. In this case, the sides of equal length include 17 and 17. The third side (9) would refer to the base, so it would not count.

Also, if you turn the shape sideways, you can see that the unknown side would be 17.

Hope this helps!

Answer:

Step-by-step explanation:

d is the answeru got it right

Answer:

The question is incomplete, but if I had to guess, it's an exercise in using the intermediate value theorem. The IVT says that for a continuous function , there is some value of  within any interval , i.e. , in the domain of such that  when , or  when .We're told that  and . The IVT then guarantees the existence of some value of  between -2 and 8 such that .It looks like  is one of several possible answer choices. We can't say anything about the value of  because we only know how  behaves between -2 and 8; the number 13 falls outside of this range. So this choice is not correct.

Step-by-step explanation:

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Explanation:

The ratio we want is in the format green:red:total which means we list the number of green first, then the number of red next, then the number total last. The order is very important. This is because we'll simply list the numbers without saying the color name or "total". So the reader will imply what the numbers refer to, based on this order mentioned.

We have:

The ratio of green to red to total is 70:50:162

To reduce the ratio, we divide all three parts of that ratio by the GCF 2

The ratio 70:50:162 fully reduces to 35:25:81 which is the final answer.

This says that for every 35 green marbles, we have 25 red marbles and 81 total marbles.

Answer:

24

Step-by-step explanation:

Basically, for every 5 boys there is 3 girls. A simple way to solve this, but longer, yet the one I personally use count up, go 5*2 3*2 and find which one adds up to 64. Once you get to 64, total including the product of both, you will have the amount of boys and girls. In this case

5*8 and 3*8 = 64

3*8 = 24

5*8 = 40

There are 24 girls

The value of each variable is:

x = 11 units

y = 11√2 units

Trigonometry deals with the relationship between the ratios of the sides of a right-angled triangle with its angles.

We can find the value of each variable using trigonometric ratios:

tan 45° = x/11 (tan = opposite/adjacent)

1 = x/11

x = 11 units

sin 45° =  9/y (sine = opposite/hypotenuse)

(√2)/2 = 11/y

y = 11/ (√2)/2

y = 11√2 units

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