Given the equation F=95C+32 where C is the temperature in degrees Celsius and F is the corresponding temperature in degrees Fahrenheit, and the following ordered pairs:

(25,F1), (−30,F2)

[tex](\stackrel{x_1}{-6}~,~\stackrel{y_1}{-3})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{0}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{0}-\stackrel{y1}{(-3)}}}{\underset{run} {\underset{x_2}{2}-\underset{x_1}{(-6)}}} \implies \cfrac{0 +3}{2 +6} \implies \cfrac{ 3 }{ 8 }[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-3)}=\stackrel{m}{ \cfrac{3 }{ 8 }}(x-\stackrel{x_1}{(-6)}) \implies {\large \begin{array}{llll} y +3 = \cfrac{3 }{ 8 } ( x +6) \end{array}}[/tex]

My answer and step by step explanation is provided as an attachment.

Difference quotient for f(x) = √x at (16,4) is  √16+h - 4 / h

Difference quotient is mathematical operation used to solve derivation of function by using following formula :

difference quotient = [tex]\frac{f(x+ h) - f(x) }{h}[/tex]

For the function f(x) =  √x at point (16,4)

f(x +h) = [tex]\sqrt{x+h}[/tex]  

putting value in formula

difference quotient =  [tex]\frac{\sqrt{x+h} -\sqrt{x} }{h}[/tex]

now , putting x = 16 ,

difference quotient = √16+h - √16 / h

taking square root of 16 ,

= √16+h - 4 / h

So, the required Difference quotient for the function at (16,4) is √16+h - 4 / h

option (d) is correct

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How to find the vertex?

The general form of an absolute value function:

Given function is:

Its vertex is (- 3, - 2), this is our first point to plot, point A.

How to find x-intercepts?

Set y = 0 and solve for x:

So the x-intercepts are ( - 5, 0) and (- 2, 0), points B and C.

Connect the vertex (- 3, - 2) with points ( - 5, 0) and (- 2, 0) and here is your graph.

The two expressions equivalent to v are:

Here we have the equation:

5*(3a - 1) - 2*(3a + 2) = 3*(a + 2) + v

And we want to find expressions equivalent to v, so to do that, we just need to isolate the variable v in one side of the equation, if we subtract:

3*(a + 2) in both sides we will get:

5*(3a - 1) - 2*(3a + 2) = 3*(a + 2) + v

5*(3a - 1) - 2*(3a + 2) - 3*(a + 2) = v

That is one of the equivalent expressions, to get the other, we can just simplify the left side.

5*(3a - 1) - 2*(3a + 2) - 3*(a + 2) = v

15a - 5 - 6a - 4 - 3a - 6 = v

Now we can group like terms:

15a - 6a - 3a - 5 - 4 - 6

6a - 15 = v

That is the other equivalent expression to v.

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Answer:

Step-by-step explanation:

Formula for geometric sequence is:

[tex]a_{n} =a_{1} (r)^{n-1}[/tex]

Now we substitute the values in:

[tex]165=a_{1} (3)^{3-1}[/tex]

165=a1(-2x3)^2

165=a1x9

Answer is 23

Answer:

Domain: (negative infinity, positive infinity)

Range: (negative infinity, 1]

Step-by-step explanation:

The expected value for the game is -12.

Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1.

The probability of rolling a 2 or 5:

= P(2 or 5)

= 1/6 + 1/6 = 1/3

The probability of not rolling a 2 or 5:

= 1 - 1/3

= 2/3

The expected return:

= (1/3)(36) + (2/3)(-36)

= 12 - 24

= -12

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Answer: 22

Step-by-step explanation:

3 times 5 then add 7

Answer:

9.37

Step-by-step explanation:

twelve surgeons

112.44 / 12 = 9.37

Answer:

$9.37

Step-by-step explanation:

112.44 ÷ 12

24 pints of 55% pure fruit juice and 16 pints of 80% pure fruit juice will be required to make 40 pints of a mixture that is 65% pure fruit juice.

According to the question,

We have the following information:

The first type is 55% pure fruit juice, and the second type is 80% pure fruit juice. The company is attempting to produce a fruit drink that contains 65% pure fruit juice.

Now, let's take x pints of 55% pure fruit juice and y pints of 80% pure fruit juice will be required to make 40 pints of a mixture that is 65% pure fruit juice.

So, we have:

x+y = 40

x = 40-y ...(1)

55x/100+80y/100 = 40*65/100

55x+80y = 40*65

Putting the value of x from equation 1:

55(40-y)+80y = 2600

2200-55y+80y = 2600

2200+25y = 2600

25y = 2600-2200

25y = 400

y = 400/25

y = 16 pints

Putting this value in equation 1:

x = 40-y

x = 40-16

x = 24 pints

Hence, 24 pints of 55% pure fruit juice and 16 pints of 80% pure fruit juice will be required to make 40 pints of a mixture that is 65% pure fruit juice.

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The values that make the inequality -2h ≤ -40 true are

Equivalent form of the inequality is written as

Inequality is a means of representing the relationship existing between the positive and negative parts of equations, using other terms aside exactly using only "equal to"

solving the inequality

-2h ≤ -40

dividing through by a negative number changes the inequality

diving through by -2 gives

h ≥ 20

Therefore, h are values greater than 20 and 23, 25, and 30 are all greater than or equal to 20

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The unknown side and angle of the triangle is as follows:

A right angle triangle is a triangle that has one of its angles as 90 degrees. The side of a right angle triangle can be found using trigonometric ratios.

Hence, let's find x, y and z.

The sum of angles in a triangle is 180 degrees.

Hence,

180 - 27 - 90 = x

x = 63 degrees.

sin 63° = opposite / hypotenuse

sin 63 = y / 35

cross multiply

y = 35 sin 63

y = 31.1852283466

y = 31.19 units

sin 27 = z / 35

z = 35 sin 27

z = 15.8896674909

z = 15.89 units

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Answer: base = 23  height = 31

Step-by-step explanation:

Area of triangle = (bh)/2

A = 356.5 cm2

h = b+8

356.5 = (b(b+8)) / 2

2(356.5) = b2 + 8b

0 = b2 + 8b - 713

Use quadratic equation to solve for b (there are on-line quadratic equation solvers, or you can do it manually)

b = -31 , 23

23 is the base    23 + 8 = 31 = height

After flipping a fair coin, when 'H' represents the heads and 'T' represents the tails the probability of heads P(H) = 1/2 and probability of tails P(T) = 1/2.

As given in the question,

After flipping a fair coin, when 'H' represents the heads and 'T' represents the tails ,

Number of total outcomes = { H , T }

Total number of outcomes = 2

Number of favourable outcomes to represent heads = 1

Number of favourable outcomes to represent tails = 1

Probability =(Number of favourable outcomes)/ (Total number of outcomes)

Probability of getting heads from the total outcomes is equal to

P(H) = 1 / 2

Probability of getting tails from the total outcomes is equal to

P(T) = 1/2

Therefore, after flipping a fair coin, when 'H' represents the heads and 'T' represents the tails the probability of heads P(H) = 1/2 and probability of tails P(T) = 1/2.

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Answer:

Step-by-step explanation:

so if it takes 42 days and 44 days just add them up

42 plus 42 = 82 plus 42=124 plus 42= 166plus 42= 208 plus 42 = 250 plus 42 = 292 plus 42= 334 plus 42= 376 plus 42=418

44 plus 44= 88 plus 44=132 plus 44=176 plus 44 = 220 plus 44= 274 plus 44= 318 plus 44= 362 plus 44=406 plus 44= 450 plus

just keep going

Answer:$12

Step-by-step explanation:

1.75/3= 0.6 (1dp)

0.6 x 20 = 12

Answer:

$11.67

Step-by-step explanation:

3 oranges = 1.75

1 orange = 0.58333333333

20*0.58333333333 = 11.6666667

Rate Pratap can row in still water is 6.75 and Rate of current is 2.25

Step: 1

Let's y = speed of water and x = his speed of rowing in still water

Speed = Distance/Time (or)

Rate = Distance/Time

Step: 2

he row downstream in 2 hours

Rate in downstream = 18/2

Rate in downstream = 9

i.e.

x + y = 9

x = 9 - y ---(i)

Now, time taken by min to row in upstream = 4 hours

Rate in upstream = Distance/Time = 18/4

Rate in upstream = 4.5

i.e., x-y = 4.5 ---(ii)

Putting the value of x from equation (i) in equation(ii)

9 - y - y = 4.5

9 - 2y = 4.5

9 - 4.5 = 2y

y = 4.5/2

y = 2.25

Putting the value of y in equation (ii)

x - 2.25 = 4.5

x = 4.5 + 2.25

x = 6.75

x = Rate Pratap can row in still water = 6.75

y = Rate of current = 2.25

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Answer:

3 * (8 + (n - 1)*x*1/3 ) = 3 * ( 0 )

..

According to the trignonmentry of half angles, the value of sin(x/2) is  √(1-5/6)/2, cos(x/2) is √(1+5/6)/2 and the value of tan(x/2) is √11/6/(√(1 + 5/6)

Trigonometry of half angles

Trigonometry of half-angle formula is used to determine the exact values of the trigonometric ratios of angles such as 15° that is half of the standard angle 30° and 22.5° that is the half of the standard angle 45 and so on. So if θ is an angle, then the half angle is represented by θ/2.

Given,

Here we need to find if cos(x)=5/6 , and x is in quadrant I, determine the exact value of each of the following.

sin(x/2), cos(x/2), tan(x/2).

According to the concepts in trigonometry,

We know that the following formulas.

=> sin(x/2) = √(1-cosx)/2

=> cos(x/2) = √(1+cosx)/2

=> tan( x/2)=sin x/1+cosx

Here we know that cos (x) = 5/6

Thus implies that 5 is the opposite and 6 is the hypotenuse, then the adjacent is

Therefore, we can calculate the value of the adjacent a as,

=> a = √(6²-5²)

=> a = √36-25

=> a= √11

Therefore the value of sin x= √11/6

So, the value of sin(x/2)= √(1 - 5/6)/2

And the value of cos(x/2)= √(1 + 5/6)/2

Finally, the value of tan(x/2)=√11/6/(√(1 + 5/6)

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The positive difference the  numbers is given as 6.

We are told here that there is a pair of natural numbers whose sum is 52 and whose product is 667. We have to make use of the idea of simultaneous equations to obtain the numbers.

Let the numbers be x and y thus we have;

x + y = 52 ---- (1)

xy = 667 ------ (2)

x = 52 - y ------ (3)

Substituting (3) into (2)

(52 - y)y = 667

52y - y^2 = 667

y^2 - 52y + 667 = 0

Solving the quadratic equation we have;

y=23 or y=29

The difference between the numbers then becomes 29 - 23

= 6

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The product of the quotient of a and b and the quotient of c and d is ac/bd.

In mathematics, a quotient simply means a quantity produced through the division of two numbers.

From the information, the product of the quotient of a and b and the quotient of c and d.

The product will be:

= a/b × c/d

= ac / bd

The product is ac/bd.

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The graph of the  absolute value function is attached below.

The absolute value function is defined by the following piecewise rule, depending on the input of the function:

|x| = x, x ≥ 0.

|x| = -x, x < 0.

The absolute value measures the distance of a point x to the origin, hence, for example, |-4| = |4| = 0, and has vertex(turning point) at (0,0).

We have to grpah the absolute value function of y = 5x.

Thus, the function is linear function.

The graph of the function is attached below.

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Answer:

45

Step-by-step explanation:

Number of Latvian footballers(n¹) = 36

Numer of footballers of other nationalities(n²)=36/4=9

Now total number of footballers= n¹+n²= 36+9 =45

Answer:

2nd one is the best division

The perimeter of the triangle ABC with respect to the given information is 78.

Whether it be a two-dimensional shape or a one-dimensional length, a perimeter is a closed path that contains, surrounds, or delineates it. A circle's or an ellipse's circumference is its furthest boundary. Numerous real-world uses exist for calculating perimeter. Adding the lengths of all the sides and edges that surround a shape yields its perimeter. It is calculated using linear length units like centimeters, meters, inches, and feet.

Given,

In triangle QRS,

A is the midpoint of QR, B is the midpoint of RS, and C is the midpoint of SQ.

And also given that QA=10, BR=15, SQ=28

Let p represent the triangle ABC's perimeter.

QR + RS +SQ = p

2(QA) + 2(BR) + SQ = p

2(10) +  2(15)+ 28 = p

20 + 30+ 28 = p

78=p

Therefore, the perimeter of triangle ABC is 78

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Answer:

She needs 8 cups of soil
one cup per pot

Step-by-step explanation:

Answer:

Question 1:

The angle m∠DOX is greater than 90 degrees, but less than 135 degrees.

Looking at the diagram we see that:

m∠DOX = 120 degrees.

Question 2:

The angle m∠COX is the sum of two angles that in total are 80 degrees.

Therefore, the equation is:

m∠COX = m∠AOX + m∠COA

Question 3:

The BOA angle measurement is given by:

BOA = 60 - 40

BOA = 20 degrees

Therefore, an angle that measures 20 degrees is:

BOA.

Question 4:

From the previous question we have:

m∠BOA = 60 - 40

m∠BOA = 20

The measure of m∠BOA is 20 degrees

Question 5:

The measure of the angle EOD is given by:

m∠EOD = 140 - 120

m∠EOD = 20 degrees

THANKS

50

4.8

(41 votes)

Step-by-step explanation:

The equation of the graph is y = 2[tex]x^{2}[/tex] + 9x + 4

A quadratic equation is a second-order polynomial equation in a single variable x

a[tex]x^{2}[/tex]+bx +c=0

with a ≠ 0 . Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.

From the graph the roots of the equation are -4 and -1/2

so if x = -4, them x + 4 = 0 is a factor,

Also, if x = -1/2, then x + 1/2 = 0 is a factor

Multiply and expand the two factors

(x + 4)(x + 1/2) = 0

[tex]x^{2}[/tex] + x/2 +4x + 2 = 0

multiply through by 2

2[tex]x^{2}[/tex] + x +8x + 4 = 0

2[tex]x^{2}[/tex]  +9x +4 = 0

In conclusion, the equation of the function in standard form is 2[tex]x^{2}[/tex]  +9x +4 = 0

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