125m on the ground corresponds to 2.5 cm on a map. What is the actual distance between two objects if they are 4.2 cm apart on the map?

Final answer:

To find the value of ST, we set up the equation 3x + 7x = 10, solve for x, and then calculate ST as 3(1), which gives us ST = 3.

Explanation:

The student is asking to solve for ST, given that ST=3x, TU=7x, and SU=10. This is a segment addition problem, where ST and TU make up the whole segment SU. To solve it, you would first set up the equation ST + TU = SU. Substituting the given values, we get:

After finding the value of x, we substitute it back into the expression for ST:

So, the segment ST is 3 units long.

Final answer:

To complete the square for the equation [tex]x^2 + 6x = 15,[/tex] you must add 9 to both sides to form the perfect square [tex]trinomial (x + 3)^2 = 24.[/tex]

Explanation:

To complete the square for the equation [tex]x^2 + 6x = 15,[/tex]we need to add a number to both sides of the equation to form a perfect square trinomial on the left side.

Completing the square involves taking half of the linear coefficient (6), squaring it, and adding that value to both sides. Since half of 6 is 3, and 3 squared is 9, we must add 9 to both sides of the equation.

Therefore, our new equation would be[tex]x^2 + 6x + 9 = 15 + 9[/tex] , which simplified to [tex](x + 3)^2 = 24.[/tex]

Answer:

3x = 2x + 3.

Step-by-step explanation:

In the question it has been given that three times a number is three more than twice the number.

Let the number is x.

Then by the given statement 3x = 2x + 3

So equation formed can be used to find the value of x

3x - 2x = 3

x = 3

Therefore, the number is 3 and equation to be solved for x is 3x = 2x + 3.

Distance from point (-1,1) to line l: [tex]\( \frac{60}{\sqrt{74}} \)[/tex] units.

To find the distance from point P to line l, we can use the formula for the distance between a point and a line in the coordinate plane.

The formula to find the distance from a point (x1, y1) to a line Ax + By + C = 0 is given by:

[tex]\[ \text{Distance} = \frac{|Ax_1 + By_1 + C|}{\sqrt{A^2 + B^2}} \][/tex]

Where A, B, and C are the coefficients of the equation of the line, and (x1, y1) are the coordinates of the point.

First, let's find the equation of the line passing through the points (11, -1) and (-3, -11).

The slope of the line, m, can be calculated using the formula:

[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]

[tex]\[ m = \frac{-11 - (-1)}{-3 - 11} = \frac{-11 + 1}{-3 - 11} = \frac{-10}{-14} = \frac{5}{7} \][/tex]

Now, we have the slope of the line. We can use the point-slope form of the equation of a line:

[tex]\[ y - y_1 = m(x - x_1) \][/tex]

Using one of the given points, let's say (11, -1):

[tex]\[ y - (-1) = \frac{5}{7}(x - 11) \][/tex]

[tex]\[ y + 1 = \frac{5}{7}(x - 11) \][/tex]

Now, let's convert this equation into the standard form Ax + By + C = 0:

[tex]\[ \frac{5}{7}x - y - \frac{5}{7} \cdot 11 + 1 = 0 \][/tex]

[tex]\[ \frac{5}{7}x - y - \frac{55}{7} + 1 = 0 \][/tex]

[tex]\[ \frac{5}{7}x - y - \frac{55}{7} + \frac{7}{7} = 0 \][/tex]

[tex]\[ \frac{5}{7}x - y - \frac{48}{7} = 0 \][/tex]

Now, we have the equation of line l:[tex]\(\frac{5}{7}x - y - \frac{48}{7} = 0\)[/tex]

Now, we can plug in the coordinates of point P (-1, 1) into the formula for the distance:

[tex]\[ \text{Distance} = \frac{| \frac{5}{7}(-1) - 1 - \frac{48}{7} |}{\sqrt{(\frac{5}{7})^2 + (-1)^2}} \][/tex]

[tex]\[ = \frac{| -\frac{5}{7} - 1 - \frac{48}{7} |}{\sqrt{\frac{25}{49} + 1}} \][/tex]

[tex]\[ = \frac{| -\frac{5}{7} - \frac{7}{7} - \frac{48}{7} |}{\sqrt{\frac{25 + 49}{49}}} \][/tex]

[tex]\[ = \frac{| -\frac{60}{7} |}{\sqrt{\frac{74}{49}}} \][/tex]

[tex]\[ = \frac{\frac{60}{7}}{\frac{\sqrt{74}}{7}} \][/tex]

[tex]\[ = \frac{60}{\sqrt{74}} \][/tex]

So, the distance from point P to line l is [tex]\(\frac{60}{\sqrt{74}}\)[/tex] units.

Answer:

Step-by-step explanation:

We have to find which type of Regular Polygons are symmetrical.

Regular Polygons are the polygons whose all sides and angles are equal.

For ex:- Equilateral triangle is a regular triangle as its all sides are equal and all angles are equal to 60°.

Square is a regular quadrilateral whose all sides are equal and all angles are equal to 90°.

Option A:

Even-sided  regular polygons are the polygons whose no of sides is an even no.

ex, quadrilateral with 4 side, hexagon with 6 sides.

They are symmetrical which no of line of symmetry equal to no of side.

Option B:

Odd-sided  regular polygons are the polygons whose no of sides is an Odd no.

ex, Triangle with 3 side, pentagon with 5 sides.

They are symmetrical which only 1 line of symmetry.

Option C:

Rectangular regular polygons are also symmetrical.

Therefore, Option D is correct .i.e., ALL regular polygons are symmetrical.

Answer:

B. 150 children

Step-by-step explanation:

Let, number of children  = x and number of adults = y.

Since, total number of people attended the fair are 350.

So, x + y = 350.

Moreover, charges per child is $2 and adult is $3.

As, total sales are given to be $900.

So, 2x + 3y = 900

Thus, we get the system of equations,

2x + 3y = 900

x + y = 350

We will now solve the equations,

x + y = 350 ⇒ y = 350 - x

So, 2x + 3y = 900 ⇒ 2x + 3(350 -x) = 900 ⇒ 2x + 1050 - 3x = 900 ⇒ -x = -150 ⇒ x = 150.

Then, y = 350 - x ⇒ y = 350 - 150 ⇒ y = 200.

Hence, number of children and adults that attended the fair are 150 and 200 respectively.

To find the two numbers, we set up a system of equations and solve for the variables using substitution.

To solve this problem, we can set up a system of equations. Let's call the smaller number 'x' and the larger number 'y'. We know that the sum of the two numbers is 32, so our first equation is x + y = 32.

We are also given that the larger number is one less than twice the smaller number. This can be written as y = 2x - 1. Now we have two equations:

We can solve this system of equations by substitution or elimination. Let's use substitution:

Starting with the second equation, we can substitute y with its value from the first equation:

2x - 1 = 32 - x

Now we can solve for x:

3x = 33

x = 11

Substituting this back into the first equation, we can find the value of y:

11 + y = 32

y = 21

Therefore, the smaller number is 11 and the larger number is 21.

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The equivalent expression to '20 - 0.35(20)', which represents the discounted price Sheldon paid for a book, is '(1 - 0.35)20', or option A.

The expression 20−0.35(20) represents the original price of the book Sheldon bought minus the 35% discount. The expression states that Sheldon is taking 35% of $20, which is the book's original price, then subtracting that amount from $20 to find the discounted price he paid.

This operation can be rewritten as multiplication by factoring out the $20 from the expression. Hence, the equivalent expression is (1−0.35)20, representing 65% of the original cost (or the amount Sheldon pays after the discount). Therefore, the answer is A.

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Final answer:

The expression for the product of 19 and a number, subtracted from the reciprocal of the number cubed, is represented as (1/x)³ - 19x. It involves finding the product of 19 and a variable, taking the reciprocal of the variable, cubing it, and then performing the subtraction.

Explanation:

The original question is asking for the expression of a mathematical operation involving a variable and its reciprocal raised to a power. Specifically, the operation is the product of 19 and a number, subtracted from the reciprocal of the number cubed. When constructing this expression, we denote the unknown number as x and perform the following steps:

Identify the product of 19 and x, which is 19x.

Find the reciprocal of x, which is 1/x.

Cube the reciprocal of x to get (1/x)³.

Subtract the product of 19 and x from the cubed reciprocal to get the final expression (1/x)³ - 19x.

This expression represents the mathematical relationship detailed in the question. To simplify or evaluate this expression, additional information about the value of x would be required.

Justin and his wife should focus on ( b) managing liquidity, as their savings are not sufficient to cover emergencies or unexpected expenses.

Based on the information provided, the area Justin and his wife should work on is b. managing liquidity. Justin's family has a set income from both his and his wife's jobs, and they have basic insurance coverage and are contributing to retirement. However, the fact that they have a relatively low balance in savings compared to their monthly outflow suggests that they may face challenges if unexpected expenses arise or if there is a disruption in their income. It’s important for them to focus on building a larger emergency fund to cover at least three to six months of living expenses to ensure they have sufficient cash on hand to handle unforeseen situations without jeopardizing their financial stability.

Titanic is no longer in existence, as it sank over a century ago and currently rests on the ocean floor.

If you are referring to combining the Atlantic Ocean with the Titanic, it would simply mean that the Titanic is traveling across the Atlantic Ocean.

The Titanic was a famous British passenger liner that sank in the North Atlantic Ocean on April 15, 1912, after hitting an iceberg during its maiden voyage from Southampton to New York City.

So, crossing the Atlantic with the Titanic would describe the journey of the Titanic as it sailed across the Atlantic Ocean.

However, it's important to note that the Titanic is no longer in existence, as it sank over a century ago and currently rests on the ocean floor.

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The Alternate Interior Angles Theorem states that if two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent.

The Alternate Interior Angles Theorem states that if two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent.

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Answer:

f(x) = [tex]x^2 (x + 7i)(x  - 7i)[/tex]

Step-by-step explanation:

The given function is f(x) = [tex]x^4 + 49x^2[/tex]

Here x^2 is a common factor, so we take out and write the remaining term inside the parenthesis.

f(x) = [tex]x^2 (x^2 + 49)[/tex]

f(x) = [tex]x^2 (x^2 - (7i)^2)[/tex]   [Here i^2 = -1]

We know that a^2 - b^2 = (a +b)(a-b) using this identity, we get

f(x) = [tex]x^2 (x + 7i)(x - 7i)[/tex]

The given in this problem are:

99% confidence level

N = 61

Mean = 2.0 kg

Standard deviation = 4.8

Z value for a 9% confidence interval is 2.576

Confidence Interval = mean ± Z s/ sqrt n

= 2.0 ± 2.576(4.8/sqrt 61)

=2.0 ± 2.576 (0.6145770236779006736364371988794)

= 2.0 ± 1.5832

= 0.4168 < x < 3.5832

No, our friend is not correct because the absolute value equation has a solution.

Given that,
Friend says that the absolute value equation ∣3x + 8 ∣ − 9 = −5 has no solution because the constant on the right side of the equation is negative.
It is to justify whether our fried is correct or not.

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

Here,
|3x + 8 | - 9 = -5
| 3x + 8 | = -5 + 9
| 3x + 8 | = 4
3x + 8 = ± 4
x = (-8 ± 4) / 3
Here, it can be seen that the given aboslute value equation has the solution that implies our friend is wrong.

Thus, no, our friend is not correct.

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Solution:

The total cost will be the sum of money spent on tickets and on soda and popcorn.

Ticket cost for:

5 year old brother = $4.25.

Grandparents = 2x($6.00)=$12.00

Myself=$7.25.

Total cost of tickets= $4.25+$12.00+$7.25=$23.50

Total money spent= Cost of ticket + cost of soda popcorn= $23.50+$20=$43.50

Total money spent=$43.50.

To classify shapes, one can use the distance formula to calculate the lengths of a shape's sides and the slope formula to determine angles between sides. Analyzing these measurements helps identify if a shape is a rectangle, square, etc., based on side length equality and perpendicular angles.

Classifying Shapes Using Distance and Slope Formulas

To classify shapes using the distance and slope formulas, you'll need to analyze the lengths of sides and the angles between them. The distance formula helps determine the length of sides by calculating the distance between two points. On the other hand, the slope formula is used to find the inclination of sides, which can indicate whether lines are parallel or perpendicular.

Here's an example. Suppose we have a quadrilateral with vertices at (1,1), (1,4), (5,4), and (5,1). We'd calculate the distance between consecutive vertices to determine if the sides are equal. If the distances are the same, our shape might be a square or a rectangle. Next, we calculate the slopes of adjacent sides using the formula (y2-y1)/(x2-x1) (rise over run). If the slopes of adjacent sides are negative reciprocals of each other, the lines are perpendicular, which is a characteristic of rectangles and squares.

Applying the slope formula to our example, the slope from (1,1) to (1,4) would be (4-1)/(1-1), which is undefined, suggesting a vertical line. Between (1,4) and (5,4), the slope is (4-4)/(5-1), which is 0, indicating a horizontal line. Therefore, the expected behavior for a square's or rectangle's sides is observed. By further calculating all side lengths and slopes, we could definitively classify our shape.

Two forces act on the fish, and these are:

1) Its weight mg, downwards and 

2) pressure in the string, T, upwards which is 22 N when the string breaks. 
In the result of these two forces, the fish had an acceleration of 2.5 m/s^2 in the upward way. 


So, T - mg = m*2.5

=> m = T / (2.5 + g)

=> m > 22 / (2.5 + 9.8) ( when the string snaps ) 

=> m > 1.79 kg. 

As a result, the mass of the fish is more than 1.79 kg as the line has been broken.

Considering Newton's second law of motion and the given parameters of force and acceleration, the fish that caused the fishing line to snap would have a mass of approximately 1.76 kg.

In order to find out the mass of the fish in this scenario, we need to consider the principles of Newton's second law of motion, which states that the force exerting on an object is equal to the mass of the object multiplied by its acceleration (F=ma).

In this case, the force before the fishing line breaks is 22 N (Newtons), and acceleration due to gravity is 10 m/s² approximately. But as the fish is pulled out with an acceleration of 2.5 m/s², we consider total acceleration to be (10+2.5) m/s² = 12.5 m/s².

Making these substitutions into Newton's law, we will solve the equation to 22 N = m* 12.5 m/s², yielding the mass of the fish m = 22 N / 12.5 m/s² = 1.76 kg

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