the sum of the present age of a father and his son is 40 years 4 years has father will be three times as old as his son will be find their present age​

Answer:

-15/4 = y

Step-by-step explanation:

3x-8y=39

3*3-8y=39

9-8y=39

y=-15/4

The value of x calculated by using the Pythagorean theorem is equal to 6.

This can be found by using the Pythagorean theorem to solve for the length of side bc, which is the base of the triangle. By using the two given side lengths of 8 and 12, we can find that the length of the hypotenuse (bc) is equal to the square root of 8^2 + 12^2, which is equal to 16.

Since the base is divided into two equal parts, we can divide 16 by 2 and get 8. We then subtract the given length of 2x + 1 from 8 and get 7, which means x is equal to 6.

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Answer:

7.5

Step-by-step explanation:

8x÷4=12÷4

2x=3

x=3/2=1.5

2y+10=22

2y=12

y=6

1.5+6=7.5=7½

Answer:

7.5 or 7½

Step-by-step explanation:

8x = 12

x = 12/8 (12/4 / 8/4)

x = 3/2

x = 1.5

2y + 10 = 22

2y = 12

y = 6

1.5 + 6 = 7.5 = 7½

The solutions to the given equation on the interval 0≤x<2π. −8sin(5x)=−4√ 3 The solutions to the equation -8sin(5x) = -4√3 on the interval 0 ≤ x < 2π are:

x = π/3 and x = 2π/3.

To find the solutions to the equation -8sin(5x) = -4√3 on the interval 0 ≤ x < 2π, we can start by isolating the sine term.

Dividing both sides of the equation by -8, we have:

sin(5x) = √3/2

Now, we can find the angles whose sine is √3/2. These angles correspond to the angles in the unit circle where the y-coordinate is √3/2.

Using the special angles of the unit circle, we find that the solutions are:

x = π/3 + 2πn

x = 2π/3 + 2πn

where n is an integer.

Since we are given the interval 0 ≤ x < 2π, we need to check which of these solutions fall within that interval.

For n = 0:

x = π/3

For n = 1:

x = 2π/3

Both solutions, π/3 and 2π/3, fall within the interval 0 ≤ x < 2π.

Therefore, the solutions to the equation -8sin(5x) = -4√3 on the interval 0 ≤ x < 2π are:

x = π/3 and x = 2π/3.

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Answer:

see below

Step-by-step explanation:

sine typically intercept at (0,0)

cosine starts at an intercept on Y

The graphs of sine and cos trigonometric functions differ by the waves. The graphs are plotted.

What is trigonometric function?

Simply put, trigonometric functions also referred to as circular functions are the functions of a triangle's angle. This means that these trig functions provide the relationship between the angles and sides of a triangle.

A positive cosine trigonometric function graph starts at maximum value, descends to minimum value, and then rises back to maximum value.

When a graph is negative cosine, it starts at the minimum, climbs to the maximum, and then descends back to the minimum.

For a positive sine trigonometric function graph, the graph starts at the midline, rises to the maximum, descends to the midline again until it reaches the minimum, then rises to the midline again to finish.

In the case of a negative sine graph, the graph starts at the midline, descends to the minimum, then ascends to the midline once again until it reaches the maximum, before returning to the midline where it started.

Therefore, graphs of sine and cos differ with respects to wave formed.

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Answer:

he could invite 19 friends

Step-by-step explanation:

125 (buget) - 30 (cost for 1st ticket) = 95

95/5 = 19

AB is the answer. :)

The interval of convergence is (-2, 14)., the radius of convergence is 8.

To find the radius of convergence, we take half the length of the interval of convergence: Radius of Convergence = (14 - (-2))/2 = 16/2 = 8. Hence, the radius of convergence is 8.

To find the radius of convergence and interval of convergence of the series, we will use the ratio test. Consider the series:

∑ [(√n)/(8^n)] * [(x-6)^n]

Let's apply the ratio test:

lim┬(n→∞)⁡(|(√(n+1))/(8^(n+1)) * ((x-6)^(n+1))| / |(√n)/(8^n) * ((x-6)^n)|)

Simplifying this expression, we get:

lim┬(n→∞)⁡(|√(n+1)/(√n) * ((x-6)/(8))|)

Since we are interested in finding the radius of convergence, we want to find the limit of this expression as n approaches infinity:

lim┬(n→∞)⁡(|√(n+1)/(√n) * ((x-6)/(8))|) = |(x-6)/8| * lim┬(n→∞)⁡(√(n+1)/(√n))

Now, let's evaluate the limit term:

lim┬(n→∞)⁡(√(n+1)/(√n)) = 1

Therefore, the simplified expression becomes:

|(x-6)/8|

For the series to converge, the absolute value of (x-6)/8 must be less than 1. In other words:

|(x-6)/8| < 1

Simplifying this inequality, we have:

-1 < (x-6)/8 < 1

Multiplying each part of the inequality by 8, we get:

-8 < x-6 < 8

Adding 6 to each part of the inequality, we have:

-8 + 6 < x < 8 + 6

Simplifying, we obtain:

-2 < x < 14

Therefore, the interval of convergence is (-2, 14).

Finally, to find the radius of convergence, we take half the length of the interval of convergence:

Radius of Convergence = (14 - (-2))/2 = 16/2 = 8

Hence, the radius of convergence is 8.

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Answer:

$36,075

Step-by-step explanation:

Cheryl's annual rent as a function of her annual sales is:

\(R = 1,400*2*12+(x-100,000)*0.055\)

Where x are her annual sales, if x > $100,000. This function considers her fixed rent of $2 per square foot for 12 months, and her sales dependent rent.

Since she made $145,000 last year, her annual rent is:

\(R = 1,400*2*12+(145,000-100,000)*0.055\\R=\$36,075\)

Her annual rent is $36,075.

Answer:

104 degrees

Step-by-step explanation:

90 + 54 + 132 = 276

360 - 276 = 104

The acceleration function is a(t) = 6(t - 3).

Acceleration is the rate at which an object changes its velocity. The acceleration function is a mathematical function that gives the acceleration of an object at any given time

To find the acceleration function, we need to take the second derivative of the given velocity function f(t).

f(t) = (t - 3)^3 + t

First, let's find the first derivative of f(t)

f'(t) = 3 × (t - 3)^2 + 1

Now, let's find the second derivative of f(t) ( the acceleration function )

a(t) = f''( t )

= d/dt [3 × (t - 3)^2 + 1]

Do the derivation

= 6(t - 3)

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The given question is incomplete, the complete question is:

The velocity (in meters per second) with which a roller coaster moves can be given by the function f(t) = (t - 3)^3 + t. find the acceleration function a(t).

Answer:

9 feet

Step-by-step explanation:

2 1/4 can be written as an improper fraction 9/4

we are given:

1 inch ----> corresponds to 4 feet

hence,

2 1/4 inch ---> corresponds to 4 feet x 2 1/4 = 4 x (9/4) = 9 feet

Answer:

5 students

Step-by-step explanation:

.............,

Answer:

D. SSS

Step-by-step explanation:

SSS (Side-Side-Side) is a proof of congruence where two triangles share three sides.

Answer:

SSS

Step-by-step explanation:

We are given that the triangle has all congruent sides therefore we can prove that the triangles are similar by the SSS theorem ( side - side - side )

The scale factor of the dilation is equivalent to 2.

        [k] = (final dimensions)/(original dimensions)

        [k] = (A/B)

Given is that blue triangle is a dilation of the black triangle.

Since both the triangles are similar, we can write -

FG/MN = scale factor [k]

k = 4/2

k = 2

Therefore, the scale factor of the dilation is equivalent to 2.

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Answer:

Step-by-step explanation:

the scale factor is 2 : 1 (FG : MN = 4 : 2 = 2 : 1)

therefore the LM side that the question asks is also in 2 : 1 scale

LM = EF : 2

LM = 5 : 2

= 2.5

a. The probability that the sample mean will be within ±5 of the population mean is the area under the normal curve between these two z-scores. b. The lower bound z-score is (-10 - 0) / 10 = -1, and the upper bound z-score is (10 - 0) / 10 = 1. We can use the same normal distribution table or technology to find the probability associated with these z-scores.

(a) To find the probability that the sample mean will be within ±5 of the population mean, we can use the Central Limit Theorem (CLT) and the properties of a normal distribution.

The sample mean, is an unbiased estimator of the population mean, μ. According to the CLT, the distribution of sample means approaches a normal distribution with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.

     = 200 / √400

     = 200 / 20

     = 10

To find the probability that the sample mean will be within ±5 of the population mean, we can standardize the interval using the z-score:

For the lower bound (-5), the z-score is (-5 - 0) / 10 = -0.5.

For the upper bound (+5), the z-score is (5 - 0) / 10 = 0.5.

We can now use a standard normal distribution table or technology (such as a calculator or statistical software) to find the probability associated with the z-scores -0.5 and 0.5. The probability that the sample mean will be within ±5 of the population mean is the area under the normal curve between these two z-scores.

(b) To find the probability that the sample mean will be within ±10 of the population mean, we follow the same steps as in part (a).

The lower bound z-score is (-10 - 0) / 10 = -1, and the upper bound z-score is (10 - 0) / 10 = 1. We can use the same normal distribution table or technology to find the probability associated with these z-scores.

Note: Since the question mentions rounding answers to four decimal places, please use the appropriate table or technology to obtain the precise probabilities for parts (a) and (b).

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Yes, $9 for 4 visitors and $18 for 8 site visitors are proportional.

To determine whether or not $9 for 4 visitors and $18 for 8 visitors are proportional, we need to test if the ratio of the value to the number of visitors is the equal for both cases.

The ratio of cost to the quantity of visitors for $9 and four visitors is:

$9/4 visitors = $2.25/ visitors

The ratio of value to the quantity of visitors for $18 and eight visitors is:

$18/8 visitors = $2.25/ visitors

We are able to see that both ratios are equal to $2.25 per visitor.

Therefore, $9 for 4 visitors and $18 for 8 site visitors are proportional.

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Statements are False: 1. interchanging rows changes determinant. 2. determinant zero not implies specific rows. 3. determinant not product of diagonal entries. 4. determinant is scalar not matrix.

What is matrix ?

A matrix is a rectangular array of numbers or other mathematical objects, typically arranged in rows and columns. Matrices are often denoted using capital letters, such as A, B, and C. Each element of a matrix is identified by its row and column indices,

1) False, If two row interchanges are made in succession, the determinant of the new matrix is the negative of the determinant of the original matrix.

2) False, If the determinant of a matrix is zero, it does not necessarily mean that two rows or two columns are the same or a row or column is zero, it only means that the matrix is singular, i.e. non-invertible and it also can mean that the matrix is linearly dependent.

3) False, The determinant of a matrix is not always equal to the product of the diagonal entries, it is a scalar value calculated through a specific method called matrix expansion which is based on the entries of the matrix and it depends on the size of the matrix.

4) False, The determinant of a matrix is a scalar value, it cannot be equal to another matrix.

Statements are False: 1. interchanging rows changes determinant. 2. determinant zero not implies specific rows. 3. determinant not product of diagonal entries. 4. determinant is scalar not matrix.

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Answer:

$48

Step-by-step explanation:

Divide:

27 ÷ 4.5

= 6

Multiply:

6 × 8 = 48

Therefore, Andrew would make $48 if he shovel for 8 hours.

Based on the given information, the claim that can be made about f(x) is that it has a vertical asymptote at x = 4.

The limit of f(x) as x approaches 4 is infinity, which suggests that f(x) becomes arbitrarily large as x gets closer to 4. This behavior indicates that there is a vertical asymptote at x = 4. A vertical asymptote is a vertical line that a function approaches but never crosses. In this case, as x approaches 4, f(x) goes to infinity, indicating that the function becomes unbounded near x = 4.

The other claims, such as f(x) having a horizontal asymptote at y = 4 or being continuous at x = 4, cannot be deduced from the given information. The limit of f(x) as x approaches infinity is not specified, so it is unknown whether f(x) approaches infinity or any other value as x tends to infinity. The continuity of f(x) at x = 4 cannot be determined solely based on its limits; it requires additional information about the function's behavior in the vicinity of x = 4. Therefore, the only valid claim that can be made is the presence of a vertical asymptote at x = 4.

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Step-by-step explanation:

Let's start by writing down Eric's score after each event:

- Starting score: 31,500 points

- Earns 2,450 additional points: 31,500 + 2,450 = 33,950 points

- Loses 3,310 points: 33,950 - 3,310 = 30,640 points

- Score doubles: 30,640 x 2 = 61,280 points

Therefore, the expression for the number of points Eric has at the end of the game is:

2(31,500 + 2,450 - 3,310)

Simplifying the expression:

2(30,640)

61,280

Therefore, Eric has 61,280 points at the end of the game.

If Station 1 (at 74, 41) is 44 km away and Station 2( at 0,43 ) is 38 km away. The required approximate location of the GPS receiver is (42, 10).

The location of the GPS receiver can be determined with the help of trilateration. Trilateration is a process of determining absolute or relative locations of points by measurement of distances, using the geometry of circles, spheres, or triangles. If three stations (or more) are in known locations, with a known distance from the point of interest, we can determine the position of the GPS receiver with the help of trilateration.

It can be determined by the following method:

1: Plot the given stations on a coordinate plane. Stations are:

Station 1: (74, 41)

Station 2: (0, 43)

2: Calculate the distance of the GPS receiver from each station using the distance formula.

Distance Formula: The distance formula is used to find the distance between two points in the coordinate plane. The distance between points (x1,y1) and (x2,y2) is given by

d = √[(x2 - x1)² + (y2 - y1)²]

Station 1: Distance from station 1 = 44 kmSo, d1 = 44 km

Station 2: Distance from station 2 = 38 kmSo, d2 = 38 km

3: Plot the given distances as the circle on the coordinate plane.

Circle 1: Centred at (74, 41) with a radius of 44 km.

Circle 2: Centred at (0, 43) with a radius of 38 km.

4: The intersection of two circles. Circle 1 and Circle 2 intersect at point P (approx) (42, 10). So, the approximate location of the GPS receiver is (42, 10).

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Answer:

Step-by-step explanation:

Applying the Pythagoras Theorem, the length of RS = 8 units.

According to the figure,

Diameter = 16 +4 = 20 units

So, the Radius = Diameter/2 = 20/2 = 10 units

Now,

Let the center be M, then

MT = 10 - 4 = 6 units

RT = x units

The radius is perpendicular to the chord,

So, MTR will be a right-angled triangle,

We will apply the Pythagoras theorem,

So, we have :

\(RT^{2} +TM^{2} =RM^{2}\)

Here, RT = x units

TM = 6 units and RM = radius = 10 units

Putting these values in the Pythagoras theorem,

\(x^{2} +6^{2} =10^{2}\\x^{2} + 36 = 100 \\x^{2} = 100 - 36 = 64\\x^{2} = 64 \\x = 8\)

Thus, the length of RS = 8 units.

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The length of AB will be 10 units. Option B is corect. The formula for the distance between the two points is applied in a given problem.

The length of the line segment connecting two places is the distance between them.

The distance between two places is always positive, and equal-length segments are referred to as congruent segments.

The given coordinate in the problem is;

(x₁,y₁)=(-2,-4)

(x₂, y₂)= (-8, 4)

The distance between the two points is found as;

\(\rm d= \sqrt{(-8-(-2))^2+(4-(-4))^2}\\\\ d=10 \ units\)

Hence, option B is corect.

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Answer:

An equation in the form y = mx + b is in the 'slope y-intercept' form where m is the slope and b is the y-intercept. We can rewrite our equation, y = 4, in slope y-intercept form as follows: y = 0x + 4. Here, it is clear that the slope, or m, is zero. Therefore, the slope of the horizontal line y = 4 is zero

Answer:A student pays for 8.9 pounds of apples with a $10 bills. How much change does the student receive?

Step-by-step explanation:

Answer:the answer is 2 dollar

Step-by-step explanation: