What is the value of 1 in 2.391

According to the solution we have come to find that, the equation for the line passing through point A and perpendicular to BC is y = (-5/2)x + 31/2.

what is slope?

In mathematics, slope is a measure of the steepness of a line. It is defined as the ratio of the vertical change between two points on the line to the horizontal change between those same two points.

Slope is often denoted by the letter m, and can be calculated as:

m = (y2 - y1) / (x2 - x1)

where (x1, y1) and (x2, y2) are two points on the line.

A positive slope indicates a line that is increasing from left to right, while a negative slope indicates a line that is decreasing from left to right. A slope of zero indicates a horizontal line, while a slope that is undefined (or "infinite") indicates a vertical line.

To find the equation of the line passing through point A and perpendicular to BC, we need to first find the slope of line BC.

The slope of line BC can be calculated as:

slope of BC = (y2 - y1) / (x2 - x1), where (x1, y1) = B and (x2, y2) = C

slope of BC = (3 - 5) / (2 - 7) = -2 / -5 = 2/5

Since the line we're trying to find is perpendicular to BC, its slope will be the negative reciprocal of the slope of BC. The negative reciprocal of 2/5 is -5/2.

Now, we can use the point-slope form of the equation of a line to find the equation of the line passing through point A and perpendicular to BC. The point-slope form is:

y - y1 = m(x - x1), where (x1, y1) = A and m is the slope we just calculated.

Substituting the values, we get:

y - 8 = (-5/2)(x - 3)

Simplifying this equation gives:

y - 8 = (-5/2)x + 15/2

y = (-5/2)x + 31/2

Therefore, the equation for the line passing through point A and perpendicular to BC is y = (-5/2)x + 31/2.

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let's firstly change the 1.2 to a fraction

\(1.\underline{2}\implies \cfrac{12}{1\underline{0}}\implies \cfrac{6}{5} \\\\[-0.35em] ~\dotfill\\\\ (\stackrel{x_1}{10}~,~\stackrel{y_1}{6})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{\frac{6}{5}}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{\frac{6}{5}}-\stackrel{y1}{6}}}{\underset{run} {\underset{x_2}{4}-\underset{x_1}{10}}}\implies \cfrac{~~ \frac{6-30}{5}~~}{-6}\implies \cfrac{~~ \frac{-24}{5}~~}{-6}\implies \cfrac{~~ -\frac{24}{5}~~}{-\frac{6}{1}}\)

\(-\cfrac{\stackrel{4}{~~\begin{matrix} 24 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}{5}\cdot -\cfrac{1}{\underset{1}{~~\begin{matrix} 6 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}\implies \boxed{\cfrac{4}{5}}\)

i) 3x² - 5x - 7 (option B)

ii) 3 (option D)

iii) -7 (option A)

iv) -5 (option B)

i) To write a polynomial in standard form, the terms will be arranged according to the degrees. The term with the highest degree will come first, followed by the term with the next highest and so on. That is the degrees will be arranged in descending order

From the given polynomial, the highest degree is 2 followed by 1 and then a constant

Re-arranging:

ii) The first term when arranged in standard form is 3x²

So, the first term when the polynomial is written in standard form is 3 (option D)

iii) The constant is a number without a variable (without x)

The constant is -7 (option A)

iv) The second term when re-arranged in standard form is -5x

The coefficient of the second term when the polynomial is written standard form is -5 (option B)

Answer:

an alien can fly 14.5 miles in 1 hour and a dragon can fly 440 miles in 11 hours

Step-by-step explanation:

Answer:   76.67%

Step-by-step explanation:

Joe will be able to save and invest a total of $7200 per year. Assuming he continues to invest the same amount each year with an average return of 8%, after 10 years he would have saved and invested a total of $72,000. With an 8% return, Joe would have accumulated a total of $97,764.

To calculate Joe's total savings and investments after 10 years, we must first calculate the amount he will save and invest each year. Joe earns $50,000 annually and commits to spending only 80% of his income, leaving him with an annual savings of $10,000. Joe invests the remaining 20% of his income, which is $10,000, each year. With an average return of 8%, Joe will have saved and invested a total of $72,000 after 10 years. With an 8% return, this amount will have grown to $97,764.

Annual Savings = $50,000 x 0.8 = $40,000

Annual Investment = $50,000 x 0.2 = $10,000

Total Savings & Investments after 10 years = $10,000 x 10 years = $72,000

Total Return after 10 years = $72,000 x 1.08 = $97,764

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Let's represent the number with the variable "x". According to the given property, we can write the following equation:

3(x + 4) < 7x

Now, let's solve this inequality to find the range of numbers that satisfy the property.

3x + 12 < 7x

Subtract 3x from both sides:

12 < 4x

Divide both sides by 4 (since the coefficient of x is 4):

3 < x

So, the range of numbers that satisfy the given property is x > 3.

Therefore, any number greater than 3 will satisfy the condition. For example, 4, 5, 6, 7, 8, etc.Step-by-step explanation:

At the end of 1 week, species A and species B will have the same population.

A mathematical function called an exponential function is employed frequently in everyday life. It is mostly used to compute investments, model populations, determine exponential decline or exponential growth, and so forth.

Given;

A scientist is studying the population growth rates of two different types of bacteria under the same laboratory conditions. The number of bacterial cells of type A is represented by the equation shown, where P represents the number of bacterial cells at the end of x hours.

\(P = 2^{x} + 19\)

The number of bacterial cells of type B is represented by the equation shown, where Q represents the number of bacterial cells at the end of x hours.

\(Q = 3^{x} + 19\)

Since, population of species A is represented by: P = 2ˣ + 19

Let us find the population of species A, at the end of week 1:

i.e., x = 1

i.e., P(1) = 2¹ + 19

i.e., P(1) = 2 + 19

i.e., P(1) = 21

Also, since population of species B is represented by: P = 3 ˣ+ 18

Let us find the population of species B, at the end of week 1:

i.e., x = 1

i.e., P(1) = 3¹ + 18

i.e., P(1) = 3 + 18

i.e., P(1) = 21

Thus, at the end of 1 week, species A and species B will have the same population.

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Answer:

I am on my phone and this is kinda confusing and I don't know if your asking 10x^5 or 10^5 but the answer would be

100,000 if it is 10 to the 5th power

If it is 10x to the 5th power then it's 100,000x

Step-by-step explanation:

I hope that helps :) explanation and answer is up!

Answer:

100000x

Step-by-step explanation:

When you do anything to a positve power, the decimal point goes to the right, if its negative to the left

Answer:

Domain: [-4,4]

Step-by-step explanation:

Domain is representative of the space on the graph that x occupies. Because all the points are closed, there should be closed or inclusive brackets outside of the domain. Because the lowest inclusive point is -4, that should be the first domain point. The graph continues until -2, where that line stops, but the second line begins at -2, so we include this point too, and there is no need to mention it in the domain. The second line ends at 4, so that is the highest end of the domain and would be the second domain point. Therefore the domain is [-4, 4]. Remember to keep closed brackets because of the closed points.

The perimeter of the rectangle created by the given points (-4, 4), (3, 4), (-4, -3), and (3, -3) is 28 units. The length of each side is calculated, and the sum of all four sides gives the perimeter. Option D.

To find the perimeter of the rectangle created by the given points, we need to calculate the sum of the lengths of all four sides.

Let's calculate the length of each side:

Side 1: The distance between (-4, 4) and (3, 4) along the x-axis is 3 - (-4) = 7 units.

Side 2: The distance between (-4, 4) and (-4, -3) along the y-axis is 4 - (-3) = 7 units.

Side 3: The distance between (-4, -3) and (3, -3) along the x-axis is 3 - (-4) = 7 units.

Side 4: The distance between (3, -3) and (3, 4) along the y-axis is 4 - (-3) = 7 units.

Now, let's sum up the lengths of all four sides:

Perimeter = Side 1 + Side 2 + Side 3 + Side 4

Perimeter = 7 + 7 + 7 + 7

Perimeter = 28 units

Therefore, the perimeter of the rectangle created by the given points is 28 units. Option D is correct.

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Answer:

  N263,341.50

Step-by-step explanation:

The value of the account is given by the formula ...

  A = P(1 +r/n)^(nt) . . . . principal P at rate r for t years compounded n times per year

Using the given values in the formula, we find the bank balance to be ...

  N263,341.50

The solution that is the closest estimate of the amount of glass Maria will need to construct her pyramid would be =5289.25 cm squared. That is option C.

To calculate the area of a square based pyramid, the formula that should be used would be given below as follows:

\(area = {a}^{2} + 2a \sqrt{ \frac{a2}{4} } + {h}^{2} \)

Where:

a= 44cm

height= 44²-22²= 38.1cm

Area= 44²+ 2(44) × √44²/4 + 38.1²

= 1936+88 × √ 484+1452

= 2024× √1936

= 5807.61 cm².

Therefore the closest estimate to the final answer would be 5289.25 cm squared

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Answer:

3:25

Step-by-step explanation:

The photo shows how it's solved.

Answer: 3:25

Step-by-step explanation:

Step 1) Convert the decimal number to a fraction by making 0.12 the numerator and 1 the denominator

0.12 = 0.12/1

Step 2) Multiply the numerator and denominator by 100 to eliminate the decimal point.
0.12 x 100

------------ = 12/100
1 x 100

Step 3) Simplify the fraction in the previous step by dividing the numerator and the denominator by the greatest common factor (GCF) of 12 and 100. (The GCF of 12 and 100 is 4.)

12 ÷ 4

---------  = 3/25  

100 ÷ 4

Step 4) Convert the fraction in the previous step to a ratio by replacing the divider line with a colon like this:  

3  

25   =  3:25

The expression "F = {(x, y) : φ(x, y, p)}" represents a set of ordered pairs (x, y) that satisfy a condition defined by the function φ. The interpretation and nature of the set F depend on the specific function φ and the parameter p, which determine the relationship between the variables x, y, and p.

The expression "F = {(x, y) :  φ(x, y, p)}" represents a set F consisting of ordered pairs (x, y) that satisfy a particular condition defined by the function  φ, which takes the variables x, y, and p as inputs.

To fully understand the meaning of F, we need to delve into the function  φ and its relationship with the variables x, y, and p. The function φ could represent a wide range of mathematical relationships or conditions that determine the inclusion of certain pairs (x, y) in the set F.

For instance, let's consider a specific example where vraphi(x, y, p) is defined  φ(x, y, p) = \(x^2 + y^2 - p^2.\)In this case, F = {(x, y) : \(x^2 + y^2 - p^2\)= 0} represents a set of ordered pairs (x, y) that satisfy the equation \(x^2 + y^2 - p^2 = 0.\) This equation represents a circle with radius p centered at the origin (0, 0). Consequently, F corresponds to all the points lying on the circumference of this circle.

It is important to note that the specific meaning and implications of F heavily rely on the nature of the function  φ and the parameter p. Different functions and parameters will yield distinct sets F with their own unique characteristics and interpretations.

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The ordered triple representing \(3u - 2v\) is \((13, -8, 5)\).

To find an ordered triple representing \(3u - 2v\),

where \(u = (5, -2, 3)\) and \(v = (1, 1, 2)\),

we can perform the following operations:

\(3u = 3(5, -2, 3)\)

\(3u = (15, -6, 9)\)

\(2v = 2(1, 1, 2)\)

\(2v = (2, 2, 4)\)

Now, subtracting 2v from 3u gives:

\(3u - 2v = (15, -6, 9) - (2, 2, 4)\)

\(3u - 2v = (15-2, -6-2, 9-4)\)

\(3u - 2v = (13, -8, 5)\)

Therefore, the ordered triple representing 3u - 2v is (13, -8, 5).

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Answer:

x = 110°

Step-by-step explanation:

The opposite angles are equal in a parallelogram

3x - 60 = 2x + 50

⇒ 3x - 2x = 60 + 50

⇒ x = 110°

Answer:

x = 110°

Step-by-step explanation:

As the top and bottom line segments of the given shape are the same length and parallel (indicated by the tick marks and arrows), the shape is a parallelogram.

As the opposite angles of a parallelogram are equal, to find the value of the variable x, equate the two angle expressions and solve for x:

\(\begin{aligned}3x-60^{\circ}&=2x+50^{\circ}\\3x-60^{\circ}-2x&=2x+50^{\circ}-2x\\x-60^{\circ}&=50^{\circ}\\x-60^{\circ}+60^{\circ}&=50^{\circ}+60^{\circ}\\x&=110^{\circ}\end{aligned}\)

Therefore, the value of x is 110°.

Note: There must be an error in the question. If x = 110°, each angle measures 270°, which is impossible since the sum of the interior angles of a quadrilateral is 360°.

Answer:

\(\sqrt{97} \\ \sqrt{9^{2}+4^{2} }\)

Step-by-step explanation:

Step-by-step explanation:

\( = \frac{10ab}{ {c}^{3}d } \div \frac{15a {b}^{3} }{7 {c}^{3} {d}^{4} } \)

\( = \frac{10ab}{ {c}^{3} d} \times \frac{7 {c}^{3} {d}^{4} }{15a {b}^{3} } \)

\( = \frac{70ab {c}^{3} {d}^{4} }{15a {b}^{3} {c}^{3} d} \)

\( = \frac{70}{15} {a}^{1 - 1} {b}^{1 - 3} {c}^{3 - 3} {d}^{4 - 1} \)

\( = \frac{14}{3} {a}^{0} {b}^{ - 2} {c}^{0} {d}^{3} \)

\( = \frac{14 {d}^{3} }{3 {b}^{2} } \)

Answer:

19 tables

Step-by-step explanation:

Let X represent the number of tables that have 1 student and 3 seniors

Let Y represent the number of tables that have 2 student2 and 4 seniors

Therefore number students total

1X + 2Y =23   (1)

Number of seniors total

3X + 4Y = 61   (2)

Multiply equation (1) by 2 giving

2X + 4Y = 46  (3)

Subtract (3) from (2)

3X + 4Y - (2X+4y) = 61-46

3X + 4Y - 2X -4Y  = 15

3X-2X = 15

X = 15

Plugging this value into equation (1) gives

1(15) + 2Y = 23

15 + 2Y = 23

Subtract 15 from both sides

2Y = 23 - 15

2Y = 8

Divide by 2 both sides

Y = 4

Thus total number of tables used = X +Y = 15+4 = 19

Answer: x=0

Answer:

13.00?

Step-by-step explanation:

The coordinates of point P are (5, -3.5). The equation of the circle is \((x - 5)^2 + (y + 3.5)^2 = 1.5^2\). The equation of KL is y = (-4/3)x + 22/3.

To find the coordinates of point P, we can first find the midpoint of MN, which is the center of the circle. The midpoint formula is given by:

Midpoint = ( (x1 + x2) / 2 , (y1 + y2) / 2 )

Using the coordinates of M(3,-5) and N(7,-2), we can calculate the midpoint:

Midpoint = ( (3 + 7) / 2 , (-5 + -2) / 2 ) = (5, -3.5)

Since the midpoint of MN is the center of the circle, the coordinates of P will be the same as the coordinates of the center, which are (5, -3.5).

i. To determine the equation of the circle in the form of \((x-a)^2\) + \((y-b)^2\) = \(r^2\), we can use the center and any point on the circle. We can use point N(7,-2), which lies on the circle.

The radius of the circle is half the length of PN. Therefore, the radius is given by:

Radius =\(1/2 * \sqrt((7 - 5)^2 + (-2 - (-3.5))^2) = 1.5\)

Substituting the values into the equation, we get:

\((x - 5)^2 + (y + 3.5)^2 = 1.5^2\)

ii. To determine the equation of KL in the form of y = mx + c, we can use the slope of the tangent line.

The slope of KL can be calculated as the negative reciprocal of the slope of the radius line MN. The slope of MN is given by:

m = (y2 - y1) / (x2 - x1) = (-2 - (-3.5)) / (7 - 5) = 1.5 / 2 = 0.75

The negative reciprocal of 0.75 is -4/3, which represents the slope of KL.

Using the point N(7,-2) and the slope -4/3, we can use the point-slope form of a line to find the equation of KL:

y - (-2) = (-4/3)(x - 7)

y + 2 = (-4/3)x + 28/3

y = (-4/3)x + 22/3

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Answer:

The rate of change is 1.

The equation of a line and y-intercept form is

y = mx + b, where m = the slope of the line.

and our given equation y = x - 2 the slope of the line is 1 in other words y = 1x - 2

Answer:

Day 5 ................

The probability of winning the minimum award of $100 in the lottery is \(\frac{113}{140448}\)

The probability of picking first winning number (out of 57 white balls) is \(\frac{1}{57}\)

Now, out of the remaining 56 white balls, the probability of picking second winning number is \(\frac{1}{56}\)

So total probability of the correctly matching two numbers drawn from the white balls is  \(\frac{1}{57} + \frac{1}{56}\)

Next, to match the winning number on the gold ball, probability of this event is \(\frac{1}{44}\)

Thus overall probability of winning the minimum award is calculated by multiplying the individual probabilities of aforesaid two independent events as follows:

\((\frac{1}{44}) (\frac{1}{57}+\frac{1}{56})\)

= \(\frac{113}{140448}\)

Above value is the probability of winning the minimum award of $100.

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Given statement solution is :- Carla's Catering provides the lowest total cost for 12 lunches, and the difference is $11.00.

To determine which company will provide the lowest total cost for 12 lunches, let's calculate the costs for both Carla's Catering and Dan's Diner.

Carla's Catering:

Using the equation provided, y = 6.75x + 25, where x represents the number of lunches:

For x = 12:

y = 6.75(12) + 25

y = 81 + 25

y = 106

The total cost for 12 lunches from Carla's Catering is $106.

Dan's Diner:

We are given the following data points for Dan's Diner:

Number of Lunches (x) Total Cost (y)

5 $57.50

10 $100.00

15 $142.50

From this data, we can calculate the rate at which the cost increases per lunch:

Rate = (Change in Total Cost) / (Change in Number of Lunches)

Rate = (100 - 57.50) / (10 - 5)

Rate = 42.50 / 5

Rate = 8.50

Now, let's calculate the cost for 12 lunches using the rate:

For x = 12:

y = 100 + (8.50 * (12 - 10))

y = 100 + (8.50 * 2)

y = 100 + 17

y = 117

The total cost for 12 lunches from Dan's Diner is $117.

Comparing the costs:

Carla's Catering: $106

Dan's Diner: $117

Carla's Catering provides the lowest total cost for 12 lunches, and the difference is $11.00.

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