a train starting from rest moves with uniform acceleration of 5 m/s2 .find its velocity when it has travelled a distance of 1 km

Answer:

n-5

 2

Steps:

subtract n ny 5 and then hind half of the difference.

A binomial is a factor of a polynomial has been determined by using the

polynomial division method.

To determine if a binomial is a factor of a polynomial, you can use the polynomial division method. The basic idea is to divide the polynomial by the binomial and check if the remainder is zero. If the remainder is zero, then the binomial is a factor of the polynomial. Here's the step-by-step process:

Write the polynomial and the binomial in standard form, with the terms arranged in descending order of their exponents.

Perform the long division of the polynomial by the binomial, similar to how you would divide numbers. Start by dividing the highest degree term of the polynomial by the highest degree term of the binomial.

Multiply the binomial by the quotient obtained from the division and subtract the result from the polynomial.

Repeat the division process with the new polynomial obtained from the subtraction step.

Continue dividing until you reach a point where the degree of the polynomial is lower than the degree of the binomial.

If the remainder is zero, then the binomial is a factor of the polynomial. If the remainder is non-zero, then the binomial is not a factor.

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Answer: the answer is 126.6

Step-by-step explanation:

Answer:

  AC ≈ 126.6

Step-by-step explanation:

The law of sines can be used to find the side length of interest in this triangle. It tells you ...

  a/sin(A) = b/sin(B) = c/sin(C)

__

In order to use the law of sines, we must have a side length and its opposite angle. Here, the angle opposite the given side is unmarked, so we need to compute it using the angle sum theorem.

  A +B +C = 180°

  A +85° +53° = 180°

  A = 42° . . . . . . . . . . . . . subtract (85°+53°)

Then side AC can be found from ...

  AC/sin(B) = BC/sin(A)

  AC = BC·sin(B)/sin(A) = 85·sin(85°)/sin(42°)

  AC ≈ 126.547

The closest answer choice is 126.6.

The rank of a matrix is the number of linearly independent rows or columns. Since A is a 6x6 matrix, the maximum possible rank is 6, which means that all 6 rows or columns are linearly independent.

The nullity of a matrix is the dimension of the null space, which is the set of all solutions to the equation Ax=0. By the rank-nullity theorem, the nullity of A is equal to the dimension of the column space (range) minus the rank of A. Since the rank of A can be at most 6, the smallest possible value for the nullity of A is 0, which occurs when the column space (range) is the entire 6-dimensional space.

Therefore, the largest possible value for the rank of A is 6, and the smallest possible value for the nullity of A is 0.

Given that A is a 6x6 matrix, the largest possible value for the rank of A is 6, which occurs when all rows (or columns) are linearly independent. The smallest possible value for the nullity of A is 0, which happens when there are no non-trivial solutions in the null space of A. In this case, the rank-nullity theorem states that rank(A) + nullity(A) = 6, which holds true when rank(A) = 6 and nullity(A) = 0.

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Since the distribution of the 10 distances is not uniform, Raul should use the median to determine his total performance.

The median is the value that divides a data sample, a population, or a probability distribution's upper and lower halves in statistics and probability theory.

It could be referred to as "the middle" value for a data set.

The fundamental difference between the mean and the median when describing data is that the median is more representative of the "normal" value because it is not skewed by a tiny fraction of exceptionally big or small values.

Due to the fact that income distribution can be very skewed, the median income, for instance, might be a better indicator of what is considered a "normal" income.

Given that it is the most resilient statistic, the median is crucial to strong statistics.

According to our question-

The home run is an outlier in the data set even if nine lengths are grouped together.

The median is the most accurate indicator of the middle of a data collection including outliers.

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A sketch of the angle is attached and the  six trigonometric functions for each angle are;

sinθ = -½

cosθ = -(√3)/2

tanθ = (√3)/3

cscθ = -2

secθ = -(2√3)/3

cotθ = √3

We can use the unit circle to figure out the trigonometric functions of θ.

Both the x- and y- coordinates are in the third quadrant, so θ is an obtuse angle (210°), as seen in the figure below.

An angle in standard position is an angle measured with respect to the +x semi-axis. In this question we must derive the six trigonometric functions from the distances between a given point and the origin. The trigonometric functions are described below:

sinθ = -2/4 = -½

cosθ = (-2√3)/4  = -(√3)/2

tanθ = -2/(-2√3) = 1/√3  = (√3)/3

cscθ = 1/sin θ  = 1/-½  = -2

secθ = 1/cosθ = 4/(-2√3)  = -2/√3 = -(2√3)/3

cotθ = 1/tan θ = -2√3/(-2) = √3

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If an invertible symmetric n×n matrix A has a nonzero vector v in R^n such that Av is orthogonal to v, then it means that the dot product of Av and v is equal to zero. In other words, Av . v = 0. Using th peroperties of the dot product, we can rewrite this equation as:
v . A^T v = 0

Since A is symmetric, A^T = A, and we can rewrite the equation as:
v . A v = 0
This equation can be further simplified using the properties of the dot product:
v . A v = (A v) . v = 0
From this equation, we can see that the eigenvalues of A must be either positive or negative. If the eigenvalues of A are all positive, then v . A v > 0, which contradicts the equation v . A v = 0. Similarly, if the eigenvalues of A are all negative, then v . A v < 0, which also contradicts the equation v . A v = 0.
Therefore, the only way for there to exist a nonzero vector v in R^n such that Av is orthogonal to v is if the eigenvalues of A are both positive and negative. In other words, A must have both positive and negative

eigenvalues.

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Answer:

15.012

Step-by-step explanation:

tan(theta) = opposite/adjacent

tan65 = x/7

x = 7tan65

x = 15.012

hope this helped!

Answer:

It is 271.25

Answer:

271.25

Step-by-step explanation:

Answer:

$54.26

Step-by-step explanation:

Convert the percentage into a decimal by moving the decimal point 2 places to the left or divide by 100.

This will give you .0825.

Multiply this number by $50 and add it to it

$54.26

Hope this helps! Good luck!! :)

Answer:

The values of x is -7 and 7.

Step-by-step explanation:

First, you have to make the equation equals to 0 :

x² = 49

x² - 49 = 0

Given that x² and 49 are perfect square of x and 7 so you have to apply (a + b)(a - b) = a² - b² :

x² - 49 = 0

(x + 7)(x - 7) = 0

Lastly, you have to solve it :

(x + 7)(x - 7) = 0

x + 7 = 0

x = -7

x - 7 = 0

x = 7

If you choose the rebate offer, your monthly payment for the car loan at the bank will be approximately $557 (rounded to the nearest dollar).

To calculate the monthly payment for each financing option, we'll use the information provided:

1. 0% financing for 48 months:

Since the financing is offered at 0% interest, the monthly payment can be calculated by dividing the total purchase price by the number of months.

Purchase Price: $26,050

Number of Months: 48

Monthly Payment = Purchase Price / Number of Months

Monthly Payment = $26,050 / 48 ≈ $543

Therefore, the monthly payment for the 0% financing option for 48 months is approximately $543.

2. Rebate offer and car loan at the bank:

If you choose the rebate offer, you'll need to finance the remaining balance after deducting the rebate amount. Let's calculate the remaining balance:

Purchase Price: $26,050

Rebate Offer: $2,900

Remaining Balance = Purchase Price - Rebate Offer

Remaining Balance = $26,050 - $2,900 = $23,150

Now, we'll calculate the monthly payment using the remaining balance and the loan terms from the local bank:

Remaining Balance: $23,150

Interest Rate: 5.24% (compounded monthly)

Number of Months: 48

Monthly Payment = (Remaining Balance * Monthly Interest Rate) / (1 - (1 + Monthly Interest Rate)^(-Number of Months))

First, let's calculate the Monthly Interest Rate:

Monthly Interest Rate = Annual Interest Rate / 12

Monthly Interest Rate = 5.24% / 12 ≈ 0.437%

Now, we can calculate the Monthly Payment using the formula mentioned above:

Monthly Payment = ($23,150 * 0.437%) / (1 - (1 + 0.437%)^(-48))

Monthly Payment ≈ $557

Therefore, if you choose the rebate offer, your monthly payment for the car loan at the bank will be approximately $557 (rounded to the nearest dollar).

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We have the following:

Answer:

a. 45 degrees

b. 315 degrees

c. 8π

d. π

e. 7π

f. 16π

g. 2π

Original Cost - $82

First part: Apply the 60% off discount

Convert first the 60% into decimal form

60% ÷ 100% = 0.6

Multiply it to the original cost to determine the discount

$82 ˣ 0.6 = $49.2

Subtract the discount to the original price, to determine the discounted price.

$82 - $49.2 = $32.8

Second part:

The discounted price is now $32.8 for which we will apply another 10% discount.

Again, convert 10% into decimal

10% ÷ 100% = 0.1

Multiply it to the discounted price, to determine the second discount.

$32.8 ˣ 0.1 = $3.28

Subtract the discount to the already discounted price.

$32.8 - $3.28 = $29.52

Therefore, the final sale price of the watch is at $29.52.

The quantity of more flour that she needs to add would be = 3/4

A fraction is defined as the representation of the part of a whole data in a form of numerator and denominator.

The quantity of flour Ryan needs for baking = 3¼

The quantity of flour she has already added = 2½

The remaining amount that she needs to add;

= 3¼-2½

= 3/4

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After solving the given  logarithmic expression we get

1. \(log_5 k + log_5 2 = log_5 (k\times2)\)

2. \(2 log_5 k = log_5 k^2\)

3. \(log_5 k - log_5 7 = log_5 (k/7)\)

4. \(log_3 k/log_3 5 = log_5 k/log_5 3\)

5. \(log_5 k + log_25 k = log_5 k^3\)

6.  \(log_3 k^2\)/\(log_3\) 25 = \(2 log_3 (k/5)\)

The power to which a number must be increased in order to obtain another number is known as a logarithm.

Following are the Four Basic Properties of Logs by using which we can solve the given expressions.

\(log_b(xy) = log_bx + log_by\\log_b(x/y) = log_bx - log_by\\log_b(xn) = n log_bx\\log_bx = log_ax / log_ab\)

Using logarithmic properties, we can rewrite each expression as follows:

1. \(log_5 k + log_5 2 = log_5 (k\times2)\)

2. \(2 log_5 k = log_5 k^2\)

3. \(log_5 k - log_5 7 = log_5 (k/7)\)

4. \(log_3 k/log_3 5 = log_5 k/log_5 3\)

5. \(log_5 k + log_25 k = log_5 k + 2 log_5 k\)

\(log_5 k + log_25 k = 3 log_5 k\)
\(log_5 k + log_25 k = log_5 k^3\)

6.  \(log_3 k^2\)/\(log_3\) 25 = \(2 log_3 k - 2 log_3 5\)

 \(log_3 k^2\)/\(log_3\) 25 = \(2 log_3 (k/5)\)

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Question

For each expression, give an equivalent expression that is of the form \(log_5(*)\), where * is an expression with numbers and possibly the variable k.

1. \(log_5\) k + \(log_5\) 2 =          2. 2 \(log_5\) k =

3. \(log_5\) k - \(log_5\) 7 =          4. \(log_3\)k / \(log_3\) 5 =

5. \(log_5\) k + \(log_{25}\) k =       6. \(log_3 k^2\)/\(log_3\) 25 =

The requried simplest form of 1764 is given as (42)², as per the given condition.

A number or algebraic expression that evenly divides another number or expression—i.e., leaves no remainder—is referred to as a factor.

The factor tree for 1,764 is:

1,764 ÷ 2 = 882

882 ÷ 2 = 441

441 ÷ 3 = 147

147 ÷ 3 = 49

49 ÷ 7 = 7

So, the prime factorization of 1,764 is 2 × 2 × 3 × 3 × 7 × 7 = 2² × 3² × 7².

The simplest form of 1,764 is 2² × 3² × 7²,
which can also be written as (2 × 3 × 7)² = (42)² = 1,764.

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Answer: square root of 144 = 12 miles

Square root of 134 = 11,57 miles

The set of free variables found in the expression (λx.λy.y (λz.x)) (λx.z) is { } (the empty set).

To find the set of free variables in the given lambda calculus expression, we need to identify all variables that are not bound by any lambda abstraction.

Starting from the innermost expression (λx.z), we see that x is bound by the lambda abstraction, so x is not a free variable. Moving outward to the next expression (λy.y (λz.x)), we see that y is also bound by the lambda abstraction, so y is not a free variable. Finally, we reach the outermost expression (λx.λy.y (λz.x)), where the only occurrence of x is bound by the lambda abstraction.

Since there are no variables in the expression that are not bound by any lambda abstraction, the set of free variables is { } (the empty set).

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Answer:

6.7234724... ; ✓7

Step-by-step explanation:

In the most simplest of terms, we can explain irrational numbers as numbers which cannot be expressed as a ratio of two integers usually because they cannot give an exact value when evaluated.

Using the values given :

6.7234724... - - >This is an irrational number because the '...' depicts that the values are unending and as such an exact expression in the form of a ratio (p/q) cannot be determined.

315, 26, 17, 8 - - - > Is a rational number, it could be express in ratio form as : 315/1. 315 is an integer and all integers are rational.

-0.25 - - > it could be expressed as - 1 /4. Hence it is a rational number.

✓7 - irrational as the simplification gives : 2.6457513...

Answer:

The answer to the question is A.

Step-by-step explanation:

Plug in both equations to the graph!

Answer:  A

Step-by-step explanation:

In order to find the intersections you must graph the lines.

slope - intercept form:

y=mx + b

b is where the line hits the y-axis.

y=3x-4

y=-2x+2

The y-intercepts for each line is -4 and +2 respectively

The only graph that has lines going through those points at y-axis is A

The measure of angle y is 52.81 degrees.

In this geometry problem, we are asked to determine the measure of angle y. After performing the necessary calculations, we find that the measure of angle y is 52.81 degrees. This answer has been rounded to the nearest hundredth.

To arrive at this result, we likely had access to a diagram or description of the given angles and their relationships. By applying the appropriate geometric principles, such as the properties of supplementary or complementary angles, we were able to identify the relevant information needed to find the measure of angle y.

It is important to note that without a specific diagram or further context, it is challenging to provide a detailed explanation of the specific steps involved in solving this problem. The answer of 52.81 degrees represents the final outcome based on the given information, calculations, and rounding instructions.

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Below is the answer

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Tthe difference of depths between them is 1 foot, and the trench which is deeper is the Japan Trench

The depths of the trenches are given as

Japan Trench = 9 km below sea level

Peru-Chile Trench = 8 km below sea level

Both trenches are below the sea level

This means that the deeper trench will have the higher absolute value

The trench with the higher absolute value is the Japan Trench

This is so because 9 is greater than 8

The difference of depths between the trenches is

Difference = 9 - 8

Evaluate

Difference = 1

Hence, the difference of depths between them is 1 foot, and the trench which is deeper is the Japan Trench

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Answer:

42 reds.

Step-by-step explanation:

There are 72 marbles in the bag.

P(Red) = 1 - Blue = 1 - 5/12 = 7/12

P(red) = 7/12 * 72 = 42

If 1 - 5/12 confuses you, then find the blue first

5/12 * 72 = 5 * 72/12 = 5 * 6 = 30

The rest must be red.

72 - 30 = 42

The point (9, -7) is the only solution to the system of linear inequalities given.

To determine which point would be a solution to the system of linear inequalities, let's substitute the given points into the inequalities and see which point satisfies both inequalities.

The system of linear inequalities is:

y > -4x + 6

y > (1/3)x - 7

Let's test each given point:

For the point (9, -7):

Substituting the values into the inequalities:

-7 > -4(9) + 6

-7 > -36 + 6

-7 > -30 (True)

-7 > (1/3)(9) - 7

-7 > 3 - 7

-7 > -4 (True)

Since both inequalities are true for the point (9, -7), it is a solution to the system of linear inequalities.

For the point (-12, -2):

Substituting the values into the inequalities:

-2 > -4(-12) + 6

-2 > 48 + 6

-2 > 54 (False)

-2 > (1/3)(-12) - 7

-2 > -4 - 7

-2 > -11 (False)

Since both inequalities are false for the point (-12, -2), it is not a solution to the system of linear inequalities.

For the point (12, 1):

Substituting the values into the inequalities:

1 > -4(12) + 6

1 > -48 + 6

1 > -42 (True)

1 > (1/3)(12) - 7

1 > 4 - 7

1 > -3 (True)

Since both inequalities are true for the point (12, 1), it is a solution to the system of linear inequalities.

For the point (-12, -7):

Substituting the values into the inequalities:

-7 > -4(-12) + 6

-7 > 48 + 6

-7 > 54 (False)

-7 > (1/3)(-12) - 7

-7 > -4 - 7

-7 > -11 (True)

Since one inequality is true and the other is false for the point (-12, -7), it is not a solution to the system of linear inequalities.

In conclusion, the point (9, -7) is the only solution to the system of linear inequalities given.

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9514 1404 393

Answer:

  36

Step-by-step explanation:

"Varies directly" means the relationship is proportional:

  y/9 = 16/4

  y = 9·16/4 = 36

The value of y is 36 when x = 9.

Step-by-step explanation:

x2-7x-34-10=0

x2-7x-44=0

(x-11)(x+4)=0

x= 11 or x= -4

Answer:

x = 11 or x = -4

Step-by-step explanation:

x^2 - 7x - 44 = 0

-11 + 4 = -7, -11 × 4 = -44

(x -11)(x + 4) = 0 or (x + 4)(x - 11) = 0 Both are same way: O

x = 11 or x = -4 would be the answer : )