<1 and <2 are complementary angles. The measure of <1 is 51 degrees. The measure of <2 is 3x. Find the value of x.

It should be noted that No. the value of the 9 in the hundred place is not ten times the value of 3 in the tens place.

It should be noted that the value of 3 in 1934 is 30 and the value of 9 is 900.

1934 = 1000 + 900 + 30 + 4

Therefore the value of 9 will be:

= 30 × 3

Therefore, the the value of the 9 in the hundred place is 30 times the value of 3 in the tens place.

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Answer:

Beauty algebra is not a recognized term or concept within the field of mathematics. Therefore, there is no main idea associated with it in mathematical context. It is possible that the term is used in a different context or field, but without additional information, it is not possible to provide a more accurate answer.

At x = 86 gives minimum value of surface area and the dimensions of the box that minimize the amount of material used.

The surface area of an object refers to the overall space filled by its surfaces. Different 3D shapes in geometry have various surface areas, which may be quickly estimated using the formulas we shall learn in this lesson. Two categories are used to classify the surface area:

Curved surface area or Lateral surface area

Surface area in total

V = x²h = 318028

h = 318028 / x²

∴ A( x ) = x² + 4ah = x² + 1272112 / x .

 Derivative of A(x)

= 2x - 1272112 / x² = 0

After solving

x³ = 636056

x= 86

After doing double derivative we get the point as Positive,

A''(x) = 2 + 2544224 / x³

A''(86)= 6

Hence at x = 86 gives minimum value of surface area.

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Answer:

7296 / 24 = 304

9216 / 18 = 512

Answer:

A. y=√2x

Step-by-step explanation:

Edge 2021

Answer:

The answer is B (\(\sqrt[6]{2}\))

You have guessed it correctly

The numbered spot at which all the runners will be next to one another is spot 19.

Least Common Multiple is the meaning of the acronym LCM. The lowest number that may be divided by both numbers is known as the least common multiple (LCM) of two numbers. It may also be computed using two or more real numbers.

Starting with the runner on the outside track, the provided parameters are;

The runner covered n₁ = 5 places on the outside track, which is the number of spaces.

Next, the inner runner will traverse n₂ spaces, which equals one space.

The following inner runner will cover n₃ = 3 spaces.

The subsequent runner will traverse n₄ = 2 spaces.

The Lowest Common Multiple, or LCM, of all the runners' speeds or the total number of spaces they cover in the same amount of time, determines where all the runners will be placed next to one another.

LCM(5, 1, 3, 2) = 30 is the LCM of 5, 1, 3, and 2.

Time = 30/ = 6

Consequently, when the first runner has covered 30 places, we have;

Six time units have been expended.

The runner comes to a stop at position 30- (30 -19) = Position 19.

First runner's new destination is Spot 19.

The distance covered simultaneously by runner 2 is 6 x 1 = 6.

The distance covered by two runners running simultaneously equals six spaces.

Second runner's new position: 6 spaces plus spot 13 equals spot 19.

The combined distance covered by the three runners is 6 x 3 = 18.

The distance runner 3 covers 18 spaces simultaneously.

Third runner's new position: 18 spaces + Spot 1 = 19 spaces

Runner 4 covers a distance of 6 x 2 = 12 at the same time.

Distance runner 4 journeys equals 12 spaces

Runner 4's new position is now 12 spaces Plus Spot 7 = Spot 19.

Therefore, all the runners will be next to one another is spot 19.

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Answer:

I  believe it's A)

Step-by-step explanation:

Answer:

x = 0

Step-by-step explanation:

- 3 - x = - 3

- x = - 3 + 3

- x = 0

x = 0

Based on the given information, we have a square pyramid with points M and N being the midpoints of the edges of one face. and forms a parallelogram. Option D

Since the base of the pyramid is a square, the cross section will consist of a square shape. Additionally, since the slice is made through the midpoints of the edges of the face, the resulting cross section will have parallel sides.

Considering these characteristics, we can conclude that the shape of the resulting cross section is a parallelogram. A parallelogram is a quadrilateral with opposite sides parallel. In this case, the opposite sides of the square cross section will be parallel, as the slice passes through the midpoints of the edges.

Therefore, the correct answer is D. parallelogram.

It's important to note that a triangular prism is not the correct answer because a triangular prism is a three-dimensional figure with two triangular bases and three rectangular faces. The cross section resulting from the given slice will not have the characteristics of a triangular prism. Option D.

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The graph of the function y = 2x⁴ - 5x³ + x² - 2x + 4 is plotted and attached.

We have the 4 functions as shown in the image attached.

The y - intercept is the point where the graph intercepts the y - axis.

Function [1] -

y = 4 + 2x

y - intercept is 4

Function [2] -

y = 5ˣ + 1

y - intercept is 2.

Function [3] -

the y-intercept is 1.

Function [4] -

the y - intercept is at -1.

Therefore, the greatest y-intercept is of function -

f(x) = 2x + 4

and the least y-intercept is of the function shown in graph [4] or function [4].

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Answer:

Carlos puts $3 into his bank account and it grows by 50% each year

f(x)=4^x+1

(The Table)

(The Graph)

Answer:

there would be 11 accidents of people

Step-by-step explanation:

6+3+1+1= 11

or

6+3+2= 11

or

6+5 =11

a. To withdraw $1800 a month for 10 years, you would need $311,973.14 in your amount at the beginning.

b. Of the money you withdrew, $140,619.54 would be interest.

To calculate the amount that you would need to have in your account at the beginning to withdraw the desired amount, you must first calculate the total value of each month's withdrawal. The interest rate of 2.15% compounded monthly can be converted into a monthly interest rate of 0.177%. Using the formula A = P(1 + r/n)^nt, the total value of each monthly withdrawal over 10 years can be calculated to be $18,856.41. Thus, to withdraw $1800 a month for 10 years, you would need to have $311,973.14 in your account at the beginning. Of the money withdrawn, $140,619.54 would be interest. This can be calculated by multiplying the monthly interest rate of 0.177% by the total amount withdrawn over 10 years, which is $18,856.41 x 10. Thus, the total interest earned over 10 years would be $140,619.54.

First, we need to convert the annual interest rate of 2.15% into a monthly interest rate:

r = 2.15% / 12 = 0.177%

Where r is the monthly interest rate.

Next, we can use the formula for the future value of an annuity:

A = P [\((1 + r)^n - 1\)] / r

Where A is the total value of each monthly withdrawal, P is the amount of money needed to be withdrawn each month, r is the monthly interest rate, and n is the number of months.

Given a monthly withdrawal of $1,800 over 10 years (120 months), the calculation would be as follows:

P = $1,800

r = 0.177%

n = 120

A = $1,800 [(1 + 0.177%)^120 - 1] / 0.177% = $18,856.41

So, the total value of each monthly withdrawal over 10 years would be $18,856.41.

To calculate the amount needed to be in the account at the beginning, we can use the formula for the present value of an annuity:

P = A [(1 - \((1 + r)^-n\)) / r]

Where P is the amount needed at the beginning, A is the total value of each monthly withdrawal, r is the monthly interest rate, and n is the number of months.

Given a total value of each monthly withdrawal of $18,856.41 over 10 years (120 months), the calculation would be as follows:

A = $18,856.41

r = 0.177%

n = 120

P = $18,856.41 [(1 - \((1 + 0.177%)^-120\)) / 0.177%] = $311,973.14

So, to withdraw $1,800 a month for 10 years, you would need to have $311,973.14 in your account at the beginning. And of the money withdrawn, $140,619.54 would be interest, which is calculated by multiplying the monthly interest rate of 0.177% by the total amount withdrawn over 10 years, which is $18,856.41 x 120.

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Answer:

  about 14 months

Step-by-step explanation:

Questions regarding loan payments, values, interest amounts, number of payments, and so on, are conveniently answered by the financial formulas available in many apps, calculators, and spreadsheets. Here, we want to solve for the number of payments.

__

The time-value-of-money app on a TI-84 calculator tells us the number of monthly payments is 13.98. It will take about 14 months to pay off the credit card balance.

__

Alternate solutions

You can also use a graphing calculator to find the time value needed in the amortization formula that corresponds to a monthly payment amount of $300 on a loan of $3850 at 13.99% interest compounded 12 times per year. This is shown in the second attachment.

The algebraic solution is a little messy, and involves logarithms, but you can solve it that way, too.

  A = P(r/n)/(1 -(1 +r/n)^(-nt))

gives the monthly payment A on a loan of principal P at annual rate r compounded n times per year for t years. We want to find the value of nt for P=3850, A=300, r=0.1399, n=12.

Putting in the numbers, we get ...

  300 = 3850(0.1399/12)/(1 -(1 +0.1399/12)^(-nt))

  (1.011658333...)^(-nt) = 0.8503847222... . . . . isolate nt term

  nt = -log(0.8503857222...)/log(1.011658333...) ≈ 13.982213...

Probability of randomly selecting two members who currently hold positions of chairman and ranking member and reassigning them to their current positions from a committee of 14 members is (1 /182).

As given,

Total members in the committee=14

Number of members serve as chairman and ranking member=2

Total number of ways to assigned new position

=¹⁴P₂

=(14!) / (14-2)!

=(14 × 13 × 12!) / 12!

=14 ×13

=182

Each member is equally likely to serve in any of positions.

Each position there is only one way to reassign position.

Probability of randomly selecting two members = 1 /182

Therefore, probability of randomly selecting two members who currently hold positions of chairman and ranking member and reassigning them to their current positions from a committee of 14 members is (1 /182).

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The solution to the given linear inequality, r - 6 > -11, is r > -5

From the question, we are to determine the solution of the given inequality

The given inequality is

r - 6 > -11

To determine the solution of the inequality, we will solve the inequality for the unknown variable.

In the inequality, the unknown variable is r.

Solving the inequality for r

r - 6 > -11

Add 6 to both sides

r - 6 + 6 > -11 + 6

r > -5

Hence, the solution is r > -5

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Answer:A unique line is defined by any two distinct (not identical) points. You have two distinct, which means you have a line. To find the equation for the line, we start with the slope-intercept equation for a line. This is only a template for a generic line, so we will have to find the specific values of m (slope) and b (y-intercept) that define your line.

The template: y = mx + b

b is the y-intercept, which, if you look at (0,–2), you will see is –2; it is where the line crosses the y-axis. Fill that value of b into our template to get:

y = mx – 2

Now, we only need the value of m, which is the slope. If you have two points on a line, you can calculate the slope of that line. The slope is the change (difference) of y over the change in x (difference) of x for two given points on the line. It's a fraction or ratio though sometimes it can be reduced to an integer.

So, taking your two points, you calculate the slope, m, in the following way:

(x1,y1) = (0,–2)

(x2,y2) = (5,1)

        y2 – y1                   1 – (–2)                1 + 2               3

m = ________   =     ________    =     ________  =    ____

       x2 – x1                      5 — 0            

Step-by-step explanation:

The probability that it weighs more than 51 pounds exactly 53 pounds.

Given that, mean weight of 50 pounds and a standard deviation of 0.5 pounds.

We need to find the probability that it weighs more than 51 pounds,

P(X = 53) = 0

z = (51 - 50) / 0.5 = 2.00

P(X > 51) = P(z > 2.00) = 0.0228

z1 = (49 - 50) / 0.5 = -2.00

z2 = (51 - 50) / 0.5 = 2.00

P(49 < X < 51) = P(-2.00 < z < 2.00) = P(z < 2.00) - P(z < -2.00) = 0.9772 - 0.0228 = 0.9544

Hence, the probability that it weighs more than 51 pounds exactly 53 pounds.

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The correct answer to the given postulate as required in the task content is; Choice A; True.

It follows from the task content that it is required to verify if there are values of t such that; sin t= .6 and cost=.8.

Recall from square trigonometric identities that;

sin² x + cos² x = 1.

To verify if sin t= .6 and cost=.8 satisfy the given condition;

sin² t + cos² t = 1;

i.e (.6)² + (.8)² = 1

.36 + .64 = 1.

1 = 1; True.

Ultimately, the statement that t can take values such that sin t= .6 and cost=.8 is True.

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ABC has vertices A (0, -1), B (3,4), and C (3,1). The coordinates of the image after reflection over the x axis is

Reflection is a method of transformation that creates mirror image.

The transformation rule for reflection over the x axis is as below

(x, y) → (x, -y)

Applying the rule we have

A (0, -1), B (3, 4), and C (3, 1) will result to

A' (0, 1), B' (3, -4), and C' (3, -1)

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The approximate difference in the circumferences of the two circles is: C. 61 cm.

Mathematically, the circumference of a circle can be calculated by using this mathematical expression:

C = 2πr or C = πD

Where:

Substituting the given parameters into the circumference of a circle formula, the circumference of the small circle is;

Circumference of circle, C = πD

Circumference of circle, C = 3.14 × 4.5

Circumference of circle, C = 14.13 cm.

For the larger circle, we have:

Circumference of circle, C = 3.14 × 24

Circumference of circle, C = 75.36 cm.

Difference = 75.36 cm - 14.13 cm.

Difference = 61.23 ≈ 61 cm.

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Answer:

2/35

Step-by-step explanation:

\(\frac{9}{35}-\frac{1}{5}=\frac{9}{35}-\frac{7}{35}=\frac{2}{35}\)

Answer:

c) 1

Step-by-step explanation:

Solving for the value of s,

→ 3s - 12 = -9

→ 3s = -9 + 12

→ s = 3/3

→ [ s = 1 ]

Thus, option (c) is correct.

Answer:

4 eggs, 1/2 cup water, and 1/2 cup oil

Step-by-step explanation:

The expanded form of (x²-3y)⁴ using Pascal's Triangle is x⁸ - 12x⁶y² + 54x⁴y⁴ - 108x²y⁶ + 81y⁸.

Pascal's Triangle is a triangular array of numbers in which the value in each cell is the sum of the two numbers directly above it.

To expand the given expression (x²-3y)⁴ as per Pascal's triangle:

First, write down the fourth row of Pascal's Triangle as:

1 4 6 4 1

The above numbers represent the coefficients of the terms in the expansion of (a+b)⁴, where a is x² and b is -3y. Therefore, it can be written as,

1×(x²)⁴ + 4×(x²)³×(-3y) + 6×(x²)²×(-3y)² + 4×(x²)(-3y)³ + 1(-3y)⁴

Simplify each term,

x⁸ - 12x⁶y² + 54x⁴y⁴ - 108x²y⁶ + 81y⁸

Therefore, the expanded form of (x²-3y)⁴ using Pascal's Triangle is x⁸ - 12x⁶y² + 54x⁴y⁴ - 108x²y⁶ + 81y⁸.

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