Which equation represents a line passing through the point (8, 16) with a slope of 3?


A y=3x – 15


B)
y=3x + 33


C)
y=3x – 8


D)
y=3x + 9

The possible heights of the students in the surf club will be -  

73 inches ≥ h > 60 inches

Given is the University of Florida that has a surf club. It has 11 females and 12 males and [h] represents the height of a team member.

The given inequality is -

300 < 5.25h - 15 ≤ 368.25

So, we can write -

5.25h - 15 > 300

5.25h > 315

h > (315/5.25)

h > 60 inches

and

5.25h - 15 ≤ 368.25

5.25h ≤ 368.25 + 15

5.25h ≤ 383.25

h ≤ 73 inches

So, we can write the range as -

73 inches ≥ h > 60 inches.

Therefore, the height range of the students in the surf club will be between 73 inches ≥ h > 60 inches.

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When both riders have stopped, the person that is further away from the parking lot is; The second rider.

Let the required distance be represented by x.

Using Pythagoras theorem, we have:

hypotenuse² =  opposite² + adjacent²

x = √(8² + 15²)

x = √289

x = 17 km

This means that the first biker is 17.0 km from the starting point.

Using the law of cosine which is given by the expression;

c² = a² + b² - 2ab cos C

x² = 8² + 15² - 2(8*15) cos (160)

x = 20.22 km

This means that the second biker is 20.22 km from the starting point.

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The yaw mark's radius is 11.2 feet, or one foot to the nearest tenth.

11.1634 miles per hour is considered the minimum speed.

Yaw marks are always curved. They are, initiated by a steering input. They're the remains of a tire that's still moving while also slapping sideways.

Using a chord and middle ordinate, you can calculate the radius using the following formula:

We must apply the algorithm to get the yaw mark's radius.

where the middle ordinate is m and the chord's length is c

With a 31 foot chord and a 3 foot middle ordinate, the tires leave a yaw mark.

so,

[tex]r^{2}=\frac{31^{2} }{8*3} + \frac{3}{2}[/tex]

[tex]r^{2} =[/tex] 40.041 + 1.5

[tex]r^{2}[/tex] = 41.041

We will now apply the following formula to get the minimum speed:

where 'f' is the drag factor and 'r' is the radius

0.2 is the drag factor, hence f=0.2

and r=41.541 feet

[tex]s= \sqrt{15*0.2*41.041}[/tex]

[tex]s=\sqrt{124.623}[/tex]

s= 11.1634 mph

11.1634 miles per hour was the lowest speed at which the brakes could be applied.

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Values that will satisfy the given inequality be 5,6 and 7.

What do you mean by natural number?

All positive numbers from 1 to infinity are considered natural numbers and are therefore a component of the number system. Because they don't contain zero or negative numbers, natural numbers are also known as counting numbers. They are a subset of real numbers, which only include positive integers and exclude negative, zero, fractional, and decimal numbers.

Given inequality:

n > 4

Values that will satisfy the given inequality be 5,6 and 7.

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Answer: -3

Step-by-step explanation:

Answer:

$7,096.55

Step-by-step explanation:

[tex]\frac{1}{6}[/tex] = [tex]\frac{7}{42}[/tex]

[tex]\frac{1}{7}[/tex] = [tex]\frac{6}{42}[/tex]

[tex]\frac{6}{42}[/tex] + [tex]\frac{7}{42}[/tex] = [tex]\frac{13}{42}[/tex]  This Son A and Son B's portion

Son C must be [tex]\frac{42}{42}[/tex] - [tex]\frac{13}{42}[/tex] = [tex]\frac{29}{42}[/tex]

[tex]\frac{29}{42}[/tex] of some number is 29400

[tex]\frac{29}{42}[/tex] x = 29400  Multiple by sides  by [tex]\frac{42}{29}[/tex]

x = [tex]\frac{42}{29}[/tex] x 29400

x = 42579.31  Rounded to the nearest penny

This number is the total

42579.31 x 1/6 = 7096.55 Rounded to the nearest penny

By using the concept of data structure, it can be concluded that-

First option is correct

What is data structure?

Data structure is a group of elements that provides an efficient way of storing and organizing data so that the data can be accessed and used efficiently. Data structure is a very important tool for computer science and computer engineer and especially in IT industry. Nowadays, lots of research work is being done on data structure.

The three main components of data model structure in SAP S/4HANA are,

configuration data, master data and transaction data

First option is correct

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The answer to ½ ½ is ¼.

The mentioned symbol is representative of fraction. It can be read as 1 by 2 or 1 over 2. It can be interpreted as the ratio or comparative quantity.

For calculating the answer to this problem, we need to multiply the mentioned two fractions. As per the known rule, the multiplication of numerator values and denominator values takes place to multiply the fraction.

Value = ½ × ½

Multiplying the numerators and denominators as 1×1 and 2×2

Value = ¼

Thus, the answer to given symbols is ¼.

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The  ratio of the sides for triangle HIL is 1:1:√3.

A triangle is a three-sided polygon that consists of three edges and three vertices.

We need to find the ratio of HIL triangle.

In the triangle JKL, IL is perpendicular to the JH.

At I the angle is 90 degrees.

The length of JI is 11cm.

The angle of JKL is x degrees.

JK is 22 cm and the angle of ILJ is y degrees.

the ratio of the sides for triangle HIL is 1:1:√3.

Hence,  1:1:√3 is the  ratio of the sides for triangle HIL

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[tex]3^4x=9^3x+7[/tex]

Simplify:

[tex]81x=729x+7[/tex]

Subtract 729x from both sides:

[tex]81x-729x=729x+7-729x[/tex]

[tex]-648x=7[/tex]

Divide both sides by -648:

[tex]\dfrac{-648x}{-648} =\dfrac{7}{-648}[/tex]

[tex]\fbox{x = $\dfrac{-7}{-648}$}[/tex]

The Rule of translation of the point is (x, y) → (x+8, y - 12)

The translation is a transformation of a figure on the coordinate plane without changing its shape, or size.

The Coordinate rule for translation is (x, y) → (x ± h, y ± k)

where h and k are the units of horizontal and vertical shifting. Here if the movement is left then h will be negative. If movement is downwards then k will be negative.

Here we have

Point A(7, 3) is translated to A'(16, -9)

If we plot the given points in a graph the will as given below the graph

There we can observe that,

The x coordinate is moved left 8 units further and y is moved 12 units  downward

Therefore,

The Rule of translation of the point is (x, y) → (x+8, y - 12)

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The correct answer is option D, which states tan∝ = 1/2

What is Trigonometry?

The field of mathematics concerned with the relationships between triangle sides and angles, as well as the pertinent functions of any angles is Trigonometry.

Solution:

we are given that tanθ = 1/2

this implies θ = 45°

We know that the sum of all interior angle of triangle is 180°

so, it can be calculated that the value of

angle ∝ = 45°

Therefore, tan∝ = 1/2

The correct answer is option D, which states tan∝ = 1/2

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A contingency is defined by miles as " a requirement of the activities belongs to one subunit which is affected by the activities of other subunits.

Step to Step Explanation:

Therefore, the contingency is defined by miles as " a requirement of the activities of one given subunit which is affected by the activities of other subunits.

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The first term of the geometric progression= 1/5

What is common ratio?

In a geometric sequence, ratio of each term to its immediately preceding term is always constant and is known as common ratio.

Given:

The second term = 3/10

The sixth term = 243/ 160

The formula for the nth term of geometric sequence is given by

an = a1 r^(n-1 ) , a1 = first term , r= common ratio

Substitute n=2

a2 = a1 r^(2-1 ) ..................(1)

3/10 = a1* r

Substitute n=6

243 / 160 = a1 r^5 ..............(2)

dividing equation 2 by 1 , we get

r^4 = 5.0625

=> r = 1.5

Substitute this value of r into equation 1

3/10 = a1 * (1.5)

a1 = 0.2

So, the first term = 1/5

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A quadrilateral has angles of 4x, 7x, 15x, and 10x.The smallest angle of the quadrilateral is 4x and the largest angle is 15x.

A quadrilateral is a polygon with four vertices, four sides, and four angles, all of which add up to 360 degrees. The quadrilateral is formed into two triangles when the diagonals are drawn. The angle total for these two triangles is 180°. As a result, the quadrilateral has a 360° total angle. TA quadrilateral has angles that total 360 degrees. This information can be used to find the value of x.

360

= 4x + 7x + 15x + 10x

x = 360 / 36

x = 10

Therefore, the smallest angle is 40 degrees and the largest angle is 150 degrees.

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The scale factor of the dilation of the triangle ABC is equal to 2.5.

We know that the triangles ABC and A'B'C' are similar.

The scale factor of the dilution is given by -

scale factor = measure of A'B' / measure of AB.

Now, let's find the measure of AB and the measure of A'B' from the graph given below, using the distance formula as follows-

The distance formula is = [tex]\sqrt{(y_{2} - y_{1})^{2} + (x_{2} - x_{1})^{2}}[/tex]

Hence, the distance AB =[tex]\sqrt{(2-2)^{2} + (2-0)^{2}}[/tex]

                                       = [tex]\sqrt{(0)^{2} + (2)^{2}}[/tex]

                                       = [tex]\sqrt{2^{2}}[/tex]

                                       = 2 units

Similarly, we can find the distance A'B'

The distance A'B' = [tex]\sqrt{(-1+1)^{2} + (1+4)^{2}}[/tex]

                             = [tex]\sqrt{(0)^{2} + (5)^{2}}[/tex]

                             = [tex]\sqrt{(5)^{2}}[/tex]

                             = 5 units

Now, the scale factor = measure of A'B' / measure of AB

                                       = 5/2

                                       =2.5

Thus, the scale factor of the dilation is 2.5.

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The complete question is -

Triangle ABC was dilated and translated to form a similar triangle A'B'C'.

What is the scale factor of the dilation?

Answer:

233

Step-by-step explanation:

Number at the beginning: 137

Additional number per week: 2

Number of weeks: 48

Additional number: 2 × 48 = 96

Total number at end of 48 weeks: 137 + 96 = 233

Answer: 233

Answer:

25

Step-by-step explanation:

Answer:25

Step-by-step explanation:

7x²-45x-28

ac=196

[tex]7x^{2}-49x+4x-28[/tex]

[tex]7x(x-7)+4(x-7)[/tex]

(7x+4) (x-7)

[tex]x=-\frac{4}{7}, 7[/tex]

1. The expression can be simplified as follows: 4 × 5 – 32 × 2 ÷ 6 = 20 – 16 ÷ 6 = 20 – 2 = 18.

2. The expression can be simplified as follows: -2(-9 + 3) = -2(-6) = 12.

3. To solve this equation, we need to isolate the variable a. We can do this by dividing both sides of the equation by -13: -a/13 = 18. Dividing both sides of the equation by -13 gives us a = -18 * 13 = -234.

4. To solve this equation, we need to isolate the variable x. We can do this by moving all terms involving x to one side of the equation and all constants to the other side. This gives us: 7 = 5x + 3(x – 2). We can then distribute the 3 to get 7 = 5x + 3x – 6. Combining like terms, we get 7 = 8x – 6, which we can solve by adding 6 to both sides to get 13 = 8x. Dividing both sides of the equation by 8 gives us x = 13/8.

5. To solve this equation, we need to isolate the variable w. We can do this by moving all terms involving w to one side of the equation and all constants to the other side. This gives us: 11w + 2(3w - 1) = 15 w. We can then distribute the 2 to get 11w + 6w - 2 = 15w. Combining like terms, we get 17w - 2 = 15w, which we can solve by adding 2 to both sides to get 17w = 15w + 2. Subtracting 15w from both sides gives us 2w = 2, which we can solve by dividing both sides by 2 to get w = 1.

6. N' is the complement of the set N. This means that N' contains all elements that are not in the set N. Since the set N contains all factors of 18, N' will contain all natural numbers less than 20 that are not factors of 18. Some elements of N' are 1, 2, 4, 5, 7, 8, 11, 13, 14, 16, and 17.

7. The solution to the inequality 17 - 2a ≤ 29 is all values of a that satisfy the inequality. To find these values, we can first subtract 17 from both sides of the inequality to get -2a ≤ 12. Dividing both sides of the inequality by -2 gives us a ≥ -6. This means that the solution is the set of all values of a that are greater than or equal to -6. This solution can be represented on a number line

8.To solve the inequality 17 – 2a ≤ 29, we first need to isolate the variable on one side of the inequality. To do this, we need to subtract 17 from both sides, which gives us -2a ≤ 12. Dividing both sides by -2, we get a ≥ -6. To graph this inequality, we can use a number line. We would draw a solid line at -6 and shade the region to the right of the line, since a is greater than or equal to -6.

9. To solve the inequality 12c + 6 > 9c – 15, we first need to isolate the variable on one side of the inequality. To do this, we need to subtract 9c from both sides, which gives us 3c + 6 > -15. Next, we need to add 15 to both sides, which gives us 3c + 21 > 0. Finally, we can divide both sides by 3 to get c > -7. To graph this inequality, we can use a number line. We would draw a solid line at -7 and shade the region to the right of the line, since c is greater than -7.

Answer:

x = -15

Step-by-step explanation:

[tex]\frac{x - 9}{3}[/tex] = -8  Multiply all the say through by 3

x - 9 = -24  Add 9 to each sides

x = -15

The value of (x,y) on the given points of the function will be (-2,10),(-1,7),(0,4),(1,1), and (2,-2).

A certain kind of relationship called a function binds inputs to essentially one output.

In other words, the function is a relationship between variables, and the nature of the relationship defines the function for example y = sinx and y = x +6 like that.

As per the given function,

f(x) = 3(2 – x) –2

Put x = -2

f(-2) = 3(2 + 2) - 2 = 10 thus, (-2,10)

Put x = -1

f(-1) = 3(2 + 1) - 2 = 7 thus, (-1,7)

Put x = 0

f(0) = 3(2 - 0) - 2 = 4 thus, (0,4)

Put x = 1

f(1) = 3(2 - 1) - 2 = 1 thus, (1,1)

Put x = 2

f(2) = 3(2 - 2) - 2 = -2 thus, (2,-2)

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The answer is 7h and 12m

Step-by-step explanation:

To solve for time, divide the distance traveled by the rate. For example, if Sergio continues reading the total of 216 pages, then he had finish reading for 7 hours and 12 minutes!

The terminal ray of an angle measuring negative startfraction 10 over 9 endfraction pi lies in the Second quadrant. this angle measures 200°.

The standard Cartesian coordinate plane is divided into four quadrants as shown in the figure above.

Angle measure: This is the unit of measure used to determine the distance between two lines joined at a common vertex. Subtract 360 to find the quadrant in degree units.

We have given that,

the angle = - 10π/9°

As we know that , π = 180°

so, - 10π/9° = (-10×180/9)° = - 200°

Now, we check the quadrant for angle - 200°

For this follow the above steps,

So, the required quadrant is second .

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For a BOAT isosceles trapezoid. The length of the median is 9 ..

An isosceles trapezoid must have two non-parallel sides of equal length. Therefore, use the information provided to apply the following formula: circumference = base 1 base 2 (legs), where the length of the "leg" is one of the two equivalent non-parallel sides . The base angles of an isosceles trapezoid are equal. The center line or median of the trapezoid is parallel to the base and its length is half the total length of the base. We have given that,

length of side BO = 12

length of side TA = 6

The length of Median = 1/2(12+6)

= 1/2(18) = 9

Hence, the required length is 9 .

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3 enlargement is the scale factor of the dilation.

What is dilation?

resizing an object is accomplished through a change called dilation. The objects can be enlarged or shrunk via dilation. A shape identical to the source image is created by this transformation. The size of the form does, however, differ. A dilatation ought to either extend or contract the original form. The scale factor is a phrase used to describe this transition.

The scale factor is defined as the difference in size between the new and old images. An established location in the plane is the center of dilatation. The dilation transformation is determined by the scale factor and the center of dilation.

The options for this question are missing. Here are the missing options:

enlargement; 6

enlargement; 3

reduction; 3

reduction; 1/3

Hence, 3 enlargement is the scale factor of the dilation.

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While virtually all time series exhibit a random​ component, not all time series exhibit other components is a true statement.

It's accurate to say that while almost all time series show a random component, not all time series show additional components.

A time series is a collection of observations of discrete data points gathered over a period of time by repeated measurements. For instance, calculating the quantity of retail sales for each month of the year would be a time series. This is because sales income is consistently and precisely measured at regular times. Data collected once or irregularly are not time series data.

A time series observation can be divided into three categories: trend (long-term direction), seasonal (systematic, calendar-related motions), and irregular (unsystematic, short term fluctuations).

A time series is a group of data points that have been arranged chronologically in mathematics. Typically, a time series is a sequence that was captured at many equally spaced intervals in time. As a result, it is a collection of discrete-time data.

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The Question is based on concept of Cost Price and selling Price is 5.2$

What is Cost PRice and Selling PRice?

Cost price is the actual price of an object where as selling price is the price in which seller sells it to customer

Solution

Cost Price of batteries = 4$

and shopkeeper can charge upto 30% interest

hence selling price will be 4$ + 30% of 4$

= 4 + 30/100(4)

= 4 + 1.2

5.2$

Hence answer to this Question is 5.2$

and this 5.2$ is the selling price of duracell batteries whereas 4$ was the cost price for the same

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