Suppose that y varies directly with x and y 12 when x--2. What is x when y -6?

For this case we have the following function:

[tex]c (f) = \frac {5} {9} (f-32)[/tex]

We must find the inverse function. For this we follow the steps below:

Replace c (f) with y:

[tex]y = \frac {5} {9} (f-32)[/tex]

We exchange variables:

[tex]\frac {5} {9} (y-32) = f[/tex]f = \frac {5} {9} (y-32)

We solve for "y":

[tex]\frac {5} {9} (y-32) = f[/tex]

We multiply by[tex]\frac {9} {5}[/tex]on both sides of the equation:

[tex]y-32 = \frac {9} {5} f[/tex]

We add 32 to both sides of the equation:

[tex]y = \frac {9} {5} f + 32[/tex]

We change y by[tex]c^{ -1} (f):[/tex]

[tex]c^{-1} (f) = \frac {9} {5} f + 32[/tex]

Answer:

[tex]c^{-1} (f) = \frac {9} {5} f + 32[/tex]

Answer:

[tex]f(c)=\frac{9}{5}c+32[/tex]

Step-by-step explanation:

Given function that is used to convert degrees to Fahrenheit to degrees Celsius,

[tex]c(f)=\frac{5}{9}(f-32)[/tex]

Let y represents the output value of the function and x represents the input value,

[tex]y=\frac{5}{9}(x-32)[/tex]

Switch x and y,

[tex]x=\frac{5}{9}(y-32)[/tex]

Isolate y,

[tex]9x=5(y-32)[/tex]

[tex]\frac{9}{5}x=y-32[/tex]

[tex]\implies y = \frac{9}{5}x+32[/tex]

[tex]\implies f(c)=\frac{9}{5}c+32[/tex]

Which is the required function.

Answer:

B. Irrational.

Step-by-step explanation:

√99 is irrational.

Its value  just below 10 as √100 = 10.

Hello!

It’s important to keep PEMDAS in mind (order of operations) when solving this.

PEMDAS stands for: Parentheses, exponents, multiplication, division, addition, subtraction.

So when doing this problem we can see that there are two multiplication problems (8 • 9) and (2 • 5) so let’s put those to the side and solve those.

8 • 9 = 72

2 • 5 = 10

Now we can put the problem back together as 72-10

So ... 72-10=62

The scenarios provided represent different types of sampling methods, such as stratified, cluster, simple random, and systematic, based on how the samples are selected from the population.

The type of sampling can be determined based on how the samples are chosen from the population. Here, we discuss different sampling methods using the provided scenarios.

Answer:

The answer is 6 schools.

In a box and whisker plot, every piece of whisker or box represents 25% of the whole number of schools.

The schools participated 1 year or less are represented by the left part of the whisker. Which stands for 25%.

BOOM

Step-by-step explanation:

On analyzing the boxplot, we find that 6 schools have participated for 1 year or less.

A boxplot is a standardized way of displaying the distribution of data based on a five number summary (minimum, first quartile (Q1), median, third quartile (Q3), and maximum).

The box extends from 1 to 6 on the number line. This implies first quartile (Q1) = 1 and third quartile (Q3) = 6.

There is a vertical line at 3.5, median = 3.5.

The whiskers end at 0 and 8, i.e., minimum = 0 and maximum = 8.

Since, Q1 = 1, this implies 25% of the schools participated for 1 year or less.

(First quartile (Q1) is the value under which 25% of data points are found when they are arranged in increasing order.)

Number of schools that have participated for 1 year or less = 25% of 24 = [tex]\frac{25}{100} * 24 = 6[/tex]

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General vertex formula is

(X-h)^2 +k=y

where (h,k) is the vertex

X^2 +6X+14=y

X^2 +6x +9 +14-9=y

Answer is :

(X+3)^2 +5=y

Answer:

x=-2

Step-by-step explanation:

Answer:

x = - 2

y = 7

Step-by-step explanation:

4x - 2y = - 20

Now substitute - 3x for y.

4x - 2(-3x) = -20           combine the xs in the brackets

4x + 6x = - 20               Make the addition      

10x = - 20                      Divide by 10

x = - 20/10                     Do the division

x = - 2                            

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

3x - 2y = - 20                 Put - 2 in for x  

3(-2) - 2y = - 20              remove the brackets              

- 6 - 2y = - 20                 Add 6 to both sides

-2y = - 20 + 6                 Combine

-2y = - 14                         Divide by - 2

y = - 14/-2                        

y = 7

7x + 12 = 3(5x - 12)

Step 1: Distribute the 3 to the numbers in the parentheses (5x and -12)

7x + 12 = (3 × 5x) + (3 × (-12))

7x + 12 = 15x + (-36)

Step 2: Combine like terms

x's go with x's (7x and 15x)

Subtract 7x to both sides

(7x - 7x) + 12 = (15x - 7x) + (-36)

(0) + 12 = 8x - 36

12 = 8x - 36

Normal numbers go with normal numbers

Add 36 to both sides

12 + 36 = 8x + (-36 + 36)

48 = 8x

Step 3: Isolate x by dividing 8 to both sides

48/8 = 8x/8

6 = x

Hope this helped!

Answer:

x = 6

Step-by-step explanation:

Eliminate parentheses using the distributive property.

7x +12 = 15x -36

You have x-terms and constants on both sides of the equal sign. One way to approach this is to find the x-term with the least coefficient (it is 7x) and subtract everything on that side of the equation.

(7x +12) -(7x +12) = (15x -36) -(7x +12)

Simplify, also known as "collect terms."

0 = 8x -48

Now, divide by the coefficient of x: 8.

0 = x -6

Add the opposite of the constant: 6.

6 = x

__

Alternate solution

By looking for the x-term with the smallest coefficient, we get a positive result when we subtract that term. If we were to subtract 15x from both sides of the equation, it would be ...

-8x +12 = -36 . . . . . . . with a negative x-coefficient

You can still work the problem this way, but it can introduce errors if you're not careful with signs. To finish this, we would subtract 12 to get the x-term by itself:

-8x = -48

Then we would divide by the x-coefficient, -8.

x = -48/-8 = 6 . . . . . same solution; same number of steps

_____

Whenever you add, subtract, multiply, divide, you do the same thing to both sides of the equation.

To find out when Ava and Kelly will be 3/4 mile apart, we can set up a distance equation based on their average speeds. The time it takes for Ava and Kelly to be 3/4 mile apart is 22.5 minutes.

To find out when Ava and Kelly will be 3/4 mile apart, we can set up a distance equation based on their average speeds.

Let's assume that the time it takes for Ava and Kelly to be 3/4 mile apart is t. Ava's distance can be represented by the equation 6t, while Kelly's distance would be 8t. We can set up the equation:

6t - 8t = 3/4

Simplifying, we have -2t = 3/4. To solve for t, we can multiply both sides of the equation by -1/2 to eliminate the negative sign:

t = (3/4) * (-1/2) = -3/8

Since time cannot be negative, we can conclude that Ava and Kelly will be 3/4 mile apart after 3/8 of an hour or 22.5 minutes.

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Answer:

They will 3/4 miles apart after 3/8 hours.

Step-by-step explanation:

To find out when Ava and Kelly will be 3/4 miles apart, we can set up an equation.

[tex]d = 8t-6t=2t[/tex]

t is the time in hours and d is the distance between the two girls in miles. Kelly runs at 8 miles/hour (represented by 8t) and Ava runs at 6 miles/hour (represented by 6t), and the distance between them can be calculated by subtracting Ava's distance from Kelly's distance.

To find out when they will be 3/4 miles apart, set d to 3/4 and solve for t.

[tex]\frac{3}{4} =2t\\\frac{3}{8}=t[/tex]

So, they will 3/4 miles apart after 3/8 hours.

Find the Least Common Multiple (LCM) of the denominator in order to find the Least Common Denominator (LCD).

LCM = 6/5 * (x^2y^2)

Answer = B. 10x^2y^2

Answer:

Your answer is option B. 10x^2y^2

Step-by-step explanation:

Firstly, Find the Least Common Multiple of the denominator.

Then you'll get your Least Common Denominator.

You'll get LCM as :

LCM = 6/5 * ( x^ 2y ^2 )

Your answer you'll get is 10x^2y^2

Answer:

9 bottles of soda can be bought.

Step-by-step explanation:

Let chips represented by x

and soda represented by y

then

x + y = 14     eq(1)

and

5x + 3y = 52    eq(2)

Solving the equations simultaneously we can find the value of x and y

Multiplying eq(1) with 5 and subtracting from eq(2)

5x + 3y = 52

5x + 5y = 70

-     -        -

___________

-2y = -18

y = -18/-2

y = 9

Putting value of y in eq(1)

x + y =14

x + 9 = 14

x = 14 - 9

x = 5

As y represents the soda, so 9 bottles of soda can be bought.

Answer:

518.4 in³

Step-by-step explanation:

The ratio of the sides of the prisms = 5 : 6, hence

the ratio of their volumes = 5³ : 6³ = 125 : 216

let x be the volume of the larger prism then by proportion

[tex]\frac{125}{300}[/tex] = [tex]\frac{216}{x}[/tex] ( cross- multiply )

125x = 216 × 300 ( divide both sides by 125 )

x = [tex]\frac{216(300)}{125}[/tex] = 518.4

The volume of the larger prism is 518.4 in³

Answer:

parenthesis

Step-by-step explanation:

A common technique that is being used in solving with several arithmetic operations is the PEMDAS. It stands for "Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction". It is the order to be followed when calculating involving more than one arithmetic operation.

The correct first operation to perform in a calculation involving multiple arithmetic operations is parentheses, as per the order of operations, known as PEMDAS or BEDMAS.

The correct operation that should be performed first for calculations involving more than one arithmetic operation is parentheses. According to order of operations, the sequence you would follow is: Parentheses (or grouping symbols), Exponents, Multiplication and Division (from left to right), and finally Addition and Subtraction (from left to right). This is also commonly remembered by the acronym PEMDAS in the American system or BEDMAS in the Canadian system, indicating the sequence: Parentheses/Brackets, Exponents, Multiplication/Division, and Addition/Subtraction.

Answer:

55mph

Step-by-step explanation:

car A distance, d1= 220

car b distance, d2= 260

speed of car A, s1= speed of car B- 10

let speed of car B be s2

s1= s2-10

speed = distance/time

time= distance/speed

As time of car A= time of car B

     distance of Car A/speed of Car A=distance of Car B/speed of Car B

220/s2-10= 260/s2

s2=(s2-10)260/220

s2=65

s1= s2- 10

  = 65-10

   =55

hence speed of first car is 55mph !

Answer: 55 mph

Step-by-step explanation:

Answer:

The domain is all real numbers.

The range is y ≥ −25

Step-by-step explanation:

The equation has no domain restrictions.

The input (-1/5 1/5 -7/5) without specified operations and unused variables a, b, and c, make it difficult to evaluate as a standard mathematical question. There may likely be a mistake in the original question.

Given the numbers a = -3, b = 4 and c = -5, the provided expression (-1/5 1/5 -7/5) appears to be a sequence of standalone fractions, not a standard mathematical operation or equation. To evaluate fractions, generally, we perform a calculation like addition, subtraction, multiplication, or division. However, the query lacks any specified mathematical operation to apply to these fractions. It seems there might be a mistake in the original question since the given values a, b, and c are also unused. To make it a valid mathematical question, we need to know what needs to be done with the fractions and variables given.

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Final answer:

The question appears to involve solving a quadratic equation using the quadratic formula, but there seems to be a typo in the provided figures. Nevertheless, the solution process entails substituting the given values into the quadratic formula and solving for x, which may result in two possible solutions depending on the discriminant.

Explanation:

The question involves solving a quadratic equation of the form ax² + bx + c = 0 using the quadratic formula, which is x = (-b ± √(b² - 4ac)) / (2a). Based on the provided values of a, b, and c, we would substitute these into the quadratic formula to find the solutions to the equation. It seems there may be a typo in the original question, as the given values do not match any standard form of a quadratic equation nor the matrix form of a linear system. However, I will provide a general step-by-step solution for the quadratic equation based on the format provided in the reference information.

First, calculate the discriminant using the formula √(b² - 4ac). Then, use the values of a, b, and c to evaluate the positive and negative solutions of x using the quadratic formula. For example, if a = 1, b = 0.0211, and c = -0.0211, the solutions would be found as follows:

-0.0211 ± √(0.0211)² - 4(1)(–0.0211)

2(1)

It is important to note that this structure is indicative of the process and the actual computations will differ with the correct values provided for a, b, and c.

the set of 6 consecutive integers starting with -3:

{ -3,-2,-1,0,1,2 }

Answer:

Step-by-step explanation:

let :

x , x+1 , x +2 , x + 3 , x+4 , x+5 ....... ( 6  consecutive integers )

x +( x+1 ) + (x +2) + (x + 3)+ (x+4) + ( x+5) = - 3

6x+16 = - 3

6x = - 3 - 16

6x = - 18

x v= -18/6

x = - 3

6  consecutive integers  are : -3  ; - 2 ; - 1 ; 0 ; 1 ; 2

Answer: as·sume

verb

past tense: assumed; past participle: assumed

1.

suppose to be the case, without proof.

"it is reasonable to assume that such changes have significant social effects"

synonyms: presume, suppose, take it, take for granted, take as read, take it as given, presuppose, conjecture, surmise, conclude, come to the conclusion, deduce, infer, draw the inference, reckon, reason, guess, imagine, think, fancy, suspect, expect, accept, believe, be of the opinion, understand, be given to understand, gather, glean; More

2.

take or begin to have (power or responsibility).

"he assumed full responsibility for all organizational work"

synonyms: accept, shoulder, bear, undertake, take on, take up, take on oneself, manage, handle, deal with, get to grips with, turn one's hand to

"the children are to assume as much responsibility as possible"

seize (power or control).

"the rebels assumed control of the capital"

synonyms: seize, take, take possession of, take over, take away, appropriate, commandeer, expropriate, confiscate, requisition, hijack, wrest, usurp, preempt, arrogate to oneself, help oneself to, claim, lay claim to

"Edward I used the conflict to assume control of Scotland"

Step-by-step explanation:

suppose to be the case, without proof.

"I assumed you were done with the dishes"

Answer:

Graph = Cardioid

Axis of symmetry = y-axis

Critical points= [tex]\frac{\pi}{2} , \frac{3\pi }{2}[/tex]

Step-by-step explanation:

General equation for this type of cardioid is:

a ± b sinθ

Condition for a cardioid = [tex]\frac{a}{b} = 1[/tex]

Axis of symmerty according to the graph of 2 + 2 sinθ is along y-axis.

Critical points:

r = 2 + 2 sinθ  ⇒ r = 2(1 + sinθ) ⇒ r' = 2 cosθ  

 ∵derivative of 1 + sinθ = cosθ

For finding critical point the derivative is equal to zero,

2 cosθ = 0    ⇒    cosθ = 0

the value of cosθ is equal to zero at intervals: [tex]\frac{\pi}{2} , \frac{3\pi }{2}[/tex]

So, critical points = [tex]\frac{\pi}{2} , \frac{3\pi }{2}[/tex]

Answer: 24-11=a

Step-by-step explanation:

The answer is the third one because the answer to 4-4 is 0.

The Number line which shows the solution 4 + (-4) is the third number line.

The solution to the statement 4 + (-4) is correctly given by the third number line.

The solution given by plot 1 is : (-4) + (-4) as both arrows points 4 units to the left.

The solution given by plot 2 is : ( 4 + 4) as both arrows points 4 units to the right.

The solution given by plot 3 is (4) + (-4) as one arrow points 4 units to the left and the other points 4 units to the right.

The solution given by the plot 4 is (-4 + 8) as one arrow points 4 units to the left and the other points 8 units to the right.

Therefore, the Number line which shows the solution 4 + (-4) is the third number line.

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Answer:

The area of the deck that surrounds the hot tub is 17.9 m².

Step-by-step explanation:

Base of deck = 5 m

Height of deck = 5 m

Area of deck = base*height

= 5*5

= 25 m²

A circular hot tub is placed in the deck whose diameter is 3 m.

Radius = diameter/2

= 1.5 m

Area of the circular hot tub = πr²

= 3.14*(1.5*1.5)

= 7.07 m²

Area of the deck that surrounds the hot tub = Area of deck - Area of tub

= 25 - 7.07

= 17.93 m²

= 17.9 m²

Answer:

17.9

Step-by-step explanation:

A.3.3

B.7.1

C.17.9

D.18.8

Answer: 51 feet

Since we know George's height, the length of George's shadow, and the length of the flagpole's shadow we have all the information we need

Now we can set up a relationship between George and the flagpole:

[tex] \frac{6}{10} = \frac{x}{85} [/tex]

6 represents George's height

10 represents the length of George's shadow

x is the unknown height of the flagpole

85 is the length of the flagpole's shadow

Now you solve for x:

[tex]x = \frac{85 \times 6}{10} \\ x = \frac{510}{10} \\ x = 51[/tex]

So, the height of the flagpole is 51 feet

Answer: $42

Step-by-step explanation:

Answer:

$0.50

Step-by-step explanation:

We have been given that Jack sold magazine subscriptions for $2 each receiving 25% commission on his sales. We are asked to find Jack's income for each subscription.

Jack's income for each subscription will be equal to 25% of $2.

[tex]\text{Jack's income}=\$2\times \frac{25}{100}[/tex]

[tex]\text{Jack's income}=\$2\times 0.25[/tex]

[tex]\text{Jack's income}=\$0.50[/tex]

Therefore, Jack's income for each subscription will be $0.50.

Answer:

D

Step-by-step explanation:

Well, we know that for every 2 strawberries are 5 grapes.

What times 2 is 16? 8.

so, it would be 40 grapes.

(This is now making me hungry.)

rolling a 5= 11/100

getting tails=71/29

i’m pretty sure you times the fractions together to get an overall probability

The probability of rolling a 5 on number cube and tail on coin is:

            [tex]P(A\bigcap B)=\dfrac{781}{10000}[/tex]

                                      or

          [tex]P(A\bigcap B)=0.0781[/tex]      

Let A denote the event of rolling a 5 on the number cube.

and B denote the event of coin landing on tails.

Let P denote the probability of an event.

Also, event A is independent of event B.

( Since, both the events are not affected by happening of each other )

We are asked to find the probability:  P(A∩B)

We know that:

[tex]P(A\bigcap B)=P(A)\cdot P(B)[/tex]

( Since, both the events are independent )

Also,

[tex]P(A)=\dfrac{11}{100}[/tex]

( Since, 5 occurs 11 times out of a total of 100 times on the number cube )

and

[tex]P(B)=\dfrac{71}{100}[/tex]

Hence, we have:

[tex]P(A\bigcap B)=\dfrac{11}{100}\times \dfrac{71}{100}[/tex]

i.e.

[tex]P(A\bigcap B)=\dfrac{781}{10000}[/tex]

i.e.

[tex]P(A\bigcap B)=0.0781[/tex]

Answer:

The answer is 5 people.

Step-by-step explanation:

.25 * 20 people surveyed = 5.