Find an equation of the line with the given slope and containing the given point. Write the equation using function notation.

slope: 5/6 through (-18,6)

f(x)=

The side lengths 300 mm and 190 mm make a valid triangle because of the triangle inequality theorem

The side lengths are given as

300 mm and 190 mm

To solve this question, we make use of the triangle inequality theorem

The triangle inequality theorem states that

Given that the sides of a triangle are x, y and z.

The sum of any two sides of a triangle is greater than or equal to the third side;

This means that

x + y ≥ z

Using the above as a guide, we have the following inequality expressions

300 + 190 ≥ z

300 + z ≥ 190

z + 190 ≥ 300

Evaluate the inequality expressions

490 ≥ z

z ≥ -110

z  ≥ 110

Remove the negative value

490 ≥ z

z ≥ 110

Combine the inequalities

110 ≤ z ≤ 490

The above inequality is a valid inequality expression

Hence, the side lengths 300 mm and 190 mm make a valid triangle

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The comparison and contrast function notation and vector notation for translations are-

Function notation is a method for writing functions that are simple to comprehend and read.

Whenever a vector is simply a list of numbers, it can be represented by an arrow in space.

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The value of the indicated function would be (fg)(4t2)  = (64t⁶ - 48t⁴ - 4t² + 3)

The question has that

f(x) = x² - 1

f(g) = x -3

We have to find (fg)(4t²)

(fg)(4t²) = f(4t²) (g(4t²)

= (4t²)²-1) (4t² - 3)

we have to expand the bracket

(16t⁴ - 1) (4t² - 3)

= (64t⁶ - 48t⁴ - 4t² + 3)

Hence we can say that the value of

(fg)(4t2)  = (64t⁶ - 48t⁴ - 4t² + 3)

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Answer:

the mid point of (-3,4) and (-6,0) is (4.5,2)

Answer:

[tex]=(-4.5, 2)[/tex]

Step-by-step explanation:

Midpoint formula is:

[tex](x_m, y_m) = (\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})[/tex]

where

x1=-3, x2=-6

y1=4, y2=0

Now just plug into formula

[tex]=( \frac{-3+-6}{2}, \frac{4+0}{2})[/tex]

[tex]= ( \frac{-9}{2}, \frac{4}{2})[/tex]

[tex]=(-4.5, 2)[/tex]

When a die is rolled twice, the probability of getting a 3 and then a 5 is 1/36.

When a die is rolled twice, the following combinations are possible:

1, 1 - 1, 2 - 1, 3 - 1, 4 - 1, 5 - 1, 6

2, 1 - 2, 2 - 2, 3 - 2, 4 - 2, 5 - 2, 6

3, 1 - 3, 2 - 3, 3 - 3, 4 - 3, 5 - 3, 6

4, 1 - 4, 2 - 4, 3 - 4, 4 - 4, 5 - 4, 6

5, 1 - 5, 2 - 5, 3 - 5, 4 - 5, 5 - 5, 6

6, 1 - 6, 2 - 6, 3 - 6, 4 - 6, 5 - 6, 6

Thus, the sample space is 36.

3, 5 only occurs once in the sample space.

∴ P (3 and 5) = 1/36.

Hence, the probability of rolling a 3 and then a 5 is 1/36.

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The quadratic opens upwards, so the minimum is at the vertex.

We can see that the minimum value of g is y = -1.

By looking at the given graph, can see that g(x) is a quadratic equation.

If the quadratic equation has a positive leading coefficient (it opens upwards) the minimum of the quadratic is on the vertex, and there is no maximum (as the function end behavior tends to infinity)

If the quadratic equation has a negative leading coefficient (it opens downwards). The maximum is at the vertex, and there is no minimum (similar like the case above).

Here we can see that the quadratic opens upwards, thus, the minimum is at the vertex, which we can see is located at x = 3 and y = -1, then the minimum value of the function g(x) is y = -1

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The equation for week 1 at a high school showing collected aluminum cans and plastic bottles is; x + 4y = 2319

From the given table, we are told that;

Average number of cans and bottles collected by Sophomores in week 1 = 1

Average number of cans and bottles collected by Sophomores in week 2 = 4

Average number of cans and bottles collected by Juniors in week 1 = 4

Average number of cans and bottles collected by Juniors in week 2 = 2

Total number of cans and bottles collected by all in week 1 = 2319

Total number of cans and bottles collected by all in week 2 = 2290

Let x represent the number of sophomores, and let y represent the number of juniors. Thus, the equation for week 1 is;

x + 4y = 2319

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The equation of the line in slope-intercept form is y = (1/2)x + (-5/2) .

The equation of a line in slope-intercept form can be written as follows,

y = mx + c                                                       equation 1

m in the above equation represents slope of the line and c represents the intercept.

The given equation is 2x - 4y = 10 .

To get the equation of the line in slope-intercept form we need to convert the given equation in the format of equation of a straight line i.e., equation1. So, now we will rearrange the given equation as

   2x - 4y = 10

⇒ 4y = 2x -10

Now on dividing this equation by 4 on both sides, we will get

y = (1/2)x + (-5/2)                                               equation 2

On equating equation 1  and equation 2, we will get

Slope of the line = m = 1/2.

Intercept = c = -5/2

The equation of the line in slope-intercept form is y = (1/2)x + (-5/2) .      

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The  binary strings of length 10 are there in which the number of 0's in the string is not equal to the number of 1's in the string is 2¹⁰ - 2⁹.

Binary number:

A binary number is a number expressed in the base-2 numeral system or binary numeral system, a method of mathematical expression which uses only two symbols: typically "0" and "1".

Given,

Here we need to find How many binary strings of length 10 are there in which the number of 0's in the string is not equal to the number of 1's in the string.

Here the length of the binary string is 10.

So, it can be written in the power form as 2¹⁰.

Now we need to find the number of 0's in the string is not equal to the number of 1's in the string.

For that, we have to consider,

There are 2⁹ number of binary strings are not have same number of 0's in the string is not equal to the number of 1's in the string.

So, it can be written as,

=> 2¹⁰ - 2⁹

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Answer:

System C

Step-by-step explanation:

When we multiply both sides of the equation 4x - 3y = 9 by -2, we obtain

-8x + 6y = -18. So system C has infinitely many solutions.

Answer:

90°

Step-by-step explanation:

X = 90°

A right angle is 90° and they are all 90° (right-angles).

As well as that is, that there are 360° on a point

9x4=36 so it must be the same 90° (1 right angle) times 4

90x4 = 360

Answer:

Step-by-step explanation:

You want the quadratic expression evaluated for several different values of x.

Evaluating a polynomial is often easier when it is written in Horner form.

  f(x) = -x² -2x +3

  f(x) = (-x -2)x +3 = -(x +2)x +3

Repetitive evaluations are often easier to do by programming a spreadsheet or calculator to do them. The basic idea is to put the value where x is, then do the arithmetic.

  f(0) = -(0 +2)(0) +3 = 3

  f(1.5) = -(1.5 +2)(1.5) +3 = -(3.5)(1.5) +3 = -5.25 -3 = -2.25

  f(-0.02) = -(-0.02 +2)(-0.02) +3 = (1.98)(0.02) +3 = 3.0396

  f(-1) = -(-1 +2)(-1) +3 = 1 +3 = 4

  f(100) = -(100 +2)(100) +3 = -10200 +3 = -10197

__

Additional comment

Horner form rewrites the polynomial to minimize the number of arithmetic operations required to evaluate it.

  ax^5 +bx^4 +cx^3 +dx^2 +ex +f = ((((ax +b)x +c)x +d)x +e)x +f

Work to solve p and s

Let s = students, s is in the place of x

Let p = parents, p is in the place of y

Answer:

There were 27 student tickets sold and 35 parent tickets sold

Step-by-step explanation:

The statement "∠4 and ∠8 are corresponding angles" is true

Given,

The angles = ∠4 and ∠8

Here, ∠4 and ∠8 are lies same side of the one of two lines and both are same side of the transversal

So, ∠4 and ∠8 are corresponding angles

So the given statement is true
Hence, the statement "∠4 and ∠8 are corresponding angles" is true

Complete question is :

State whether the sentence is true or false. If false, replace the underlined word or number to make a true sentence.

∠4 and ∠8 are corresponding angles.

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The point bisector hypothesis expresses that on the off chance that a point is on the bisector of a point, the point is equidistant from the sides of the point.

In math, the point bisector hypothesis is worried about the overall lengths of the two fragments that a triangle's side is separated into by a line that cuts up the contrary point.  

The point bisector hypothesis talk expresses that on the off chance that a point is in the inside of a point and equidistant from the sides, then it lies on the bisector of that point.

According to the angle bisector theorem, PQ/PR = QS/RS or a/b = x/y. A point bisector is a line or beam that separates a point in a triangle into two equivalent measures.

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Answer:

∠ 1 = 131° , ∠ 2 = 49°

Step-by-step explanation:

∠ 1 and ∠ 4 are a linear pair and sum to 180° , that is

∠ 1 + ∠ 4 = 180°

∠ 1 + 49° = 180° ( subtract 49° from both sides )

∠ 1 = 131°

∠ 2 and ∠ 4 are vertically opposite angles and are congruent , so

∠ 2 = 49°

Jonah has chosen the greater number.

Given, Sue and Jonah chose numbers for a place value game.

As a way to express numbers, a number system is a way of expressing them. It is a method of describing numbers from a particular set mathematically by consistently employing digits or other symbols. Every number is given a distinct representation, and the figures' algebraic and mathematical structures are also shown.

Sue chose the number = one hundred fifty two thousand

= 152000

= 1.52 lakhs

Jonah chose the number = five million

= 5,000,000

we know that 10 lakhs = 1 million = 1,000,000

therefore, 5 million  = 5 × 10 lakhs

= 50 lakhs

50 lakhs > 1.5 lakhs

the greater number is 5 million.

Therefore , the greater number chose by Sue and Jonah is of Jonah's that is 5 million.

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On a number line, the possible coordinates of point E are: 10 or -12.

Given that point E on a number line has a coordinate of -1, and also, we know that the distance from point E to point G is 11 units, we would determine the possible coordinates of point G as explained below:

11 units from point E is: -1 + 11 = 10

11 units towards point E is: -1 - 11 = -12

Therefore, on a number line, the possible coordinates of point E are: 10 or -12.

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At the job, the hourly Wage was solved to be $16.94.

Given data

rate of hours worked over 40 hours = 1.5

hours worked in a week = 52

total paycheck = $982.50

let the pay hourly rate be x, and over 40 hours pay is 1.5x

finding the hours worked over 40

52 - 40 = 12

total paycheck $982.50 is gotten as follows:

$982.50 = 40 * x + 12 * 1.5x

982.50 = 40x + 18x

982.50 = 58x

x = 982.50 / 58

x = 16.9397

x = 16.94

Since x which is the hourly wage is found to be 16.94m, we can therefore say that the hourly wage is $16.94.

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The fraction is 23/27.

Let the numerator and denominator of the given fraction be x and y respectively.

According to the question,

Case 1 :-

Denominator of the fraction is 4 more than the numerator.

⇒ Numerator = Denominator - 4

⇒ x = y - 4 ...(1)

Case 2 :-

If 1 is added to numerator and 2 is subtracted from denominator fraction becomes 24/25

⇒ (Numerator + 1) / (Denominator + 2) = 4/5

⇒ (x + 1) / (y - 2) = 24/25

⇒ 25(x + 1) = 24(y - 2)

⇒ 25x + 25 = 24y - 48

⇒ 25x - 24y = -73 ...(2)

Substituting the value of x from (1) in (2), we have

⇒ 25(y - 4) - 24y = -73

⇒ 25y - 100 - 24y = -73

⇒ y = -73 + 100

y = 27

substitute the value of y in equation 1.

x = 27 - 4

x = 23

Now, At the beginning of our solution we took the numerator & denominator to be x & y respectively. So the fraction is:

⇒ x / y

⇒ 23/27

Hence the fraction is 23/27.

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Answer:LN=18

Since point M is between the two other points, you add each number, giving you the answer

The next three numbers in the pattern are 80, 85, 90....

These are the multiples of 5.

The complete pattern is 30,45,60,75,80, 85, 90....

Look at the first three or four numbers in the pattern. You might wonder what link there is between these figures. In this mathematical pattern, for instance, the first three to four numbers are 1, 3, 6, and 10. It seems like you must add to get the higher numbers as you go up the scale. Start with adding 2, then follow with 2, 3, and finally 4. So, if you write this down, you probably see a pattern starting to emerge.

Try the remaining elements of the supplied pattern to see whether your solution works.

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b ≈ 16.1 is high up on the side of the house, to the nearest tenth of a foot, does the ladder reach.

What are examples of linear equations?

8²  +  b²  = 18²

64 + b² = 324

b² = 260

b ≈ 16.1

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A proportion exists in an equation in which two ratios stand set equivalent to each other. 367 students in his school have at least one sibling.

A proportion exists an equation that sets two ratios at the same value. A mathematical comparison of two numbers is called a proportion. In terms of proportion, two sets of given numbers are said to rise or decrease in the same ratio if they are directly proportionate to one another.

Let the number of students be x, then

25/32 = x/470

simplifying the above equation, we get

25(470) = 32x

32x = 11750

Dividing both sides of the equation by 32, we get

32x / 32 = 11750 / 32

x = 367

The value of x = 367.

Therefore, 367 students in his school have at least one sibling.

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According to the question, the homeroom class wants to get a present for a student. From [tex]32[/tex]students, [tex]10[/tex] choose cards, [tex]12[/tex] choose t-shirts, [tex]6[/tex] choose a video and the remaining choose a bracelet.

Now, calculate the probability that the exchange students should get a card or a bracelet.

Let us assume, ‘C’ represents the card and ‘B’ represents the bracelet.

Using standard probability formula:

P (C or B) = P(C)+P(B) = [tex]\frac{10}{32} + \frac{4}{32} = \frac{14}{32} = \frac{7}{16} = 43.8%[/tex]

Therefore, the probability to get a card or a bracelet is [tex]43.8[/tex] percent.

What is Probability?

The term probability means the study of the occurrence or the outcomes of the event. It is the measurement of the events that occurred during events. And many uncertain events cannot be measured.

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The total surface area of the closed milk tin is 528 cm²

The shape of the closed tin of milk is cylinder.

The formula for calculating the total surface area of cylinder is the curved surface area of the cylinder + the area of the two circles(on the top and the bottom) which equals to 2πr(r+h), where r is the radius of the cylinder and h represents the height of the cylinder.

The diameter of the cylinder is 12cm and the height of the cylinder is 8cm.

The radius of the cylinder is half of the diameter of the cylinder which is 12/2=6cm

By putting the values, we get = 2×22/7×6(6+8)

    = 264/7(14)

    = 264(2)

    = 528 cm²

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Answer:

=====================

The distance between points (x₁, y₁) and (x₂, y₂) is:

So we have both segments with same length of 5 units

Answer:

  c = -3 1/4

Step-by-step explanation:

You want the solution to 3/2(2c+7) -3c =6(c+5).

Simplifying the equation gives ....

  3c +21/2 -3c = 6c +30

  21/2 -60/2 = 6c . . . . . . . . . subtract 30

  -39/2 = 6c . . . . . . . . . . combine terms

  -13/4 = c . . . . . . . . . . divide by 6

The value of c is -3 1/4.