�
=
5
9
(
�
−
32
)

The equation above shows how temperature
�
, measured in degrees Fahrenheit, relates to a temperature
�
, measured in degrees Celsius. Based on the equation, which of the following must be true?

A temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of
5
9
degree Celsius.
A temperature increase of 1 degree Celsius is equivalent to a temperature increase of 1.8 degrees Fahrenheit.
A temperature increase of
5
9
degree Fahrenheit is equivalent to a temperature increase of 1 degree Celsius.
A) I only
B) II only
C) III only
D) I and II only



ANSWER EXPLANATION: Think of the equation as an equation for a line

�
=
�
�
+
�

where in this case

�
=
5
9
(
�
−
32
)

or

�
=
5
9
�
−
5
9
(
32
)

You can see the slope of the graph is
5
9
, which means that for an increase of 1 degree Fahrenheit, the increase is
5
9
of 1 degree Celsius.

�
=
5
9
(
�
)

�
=
5
9
(
1
)
=
5
9

Therefore, statement I is true. This is the equivalent to saying that an increase of 1 degree Celsius is equal to an increase of
9
5
degrees Fahrenheit.

�
=
5
9
(
�
)

1
=
5
9
(
�
)

(
�
)
=
9
5

Since
9
5
= 1.8, statement II is true.

The only answer that has both statement I and statement II as true is D, but if you have time and want to be absolutely thorough, you can also check to see if statement III (an increase of
5
9
degree Fahrenheit is equal to a temperature increase of 1 degree Celsius) is true:

�
=
5
9
(
�
)

�
=
5
9
(
5
9
)

�
=
25
81
(
which
is
≠
1
)

An increase of
5
9
degree Fahrenheit leads to an increase of
25
81
, not 1 degree, Celsius, and so Statement III is not true.

The final answer is D.

Answer:

r = 4

Step-by-step explanation:

17 = 9 + 2r   subtract both sides by 9

8 = 2r          divide both sides by 2

4 = r

Answer:

r=4

Step-by-step explanation:

You have to get r on one side so you subtract nine on both sides to get rid of it so 8=2r

then you divide 2 m both sides and r=4

The total area of the figure is 528 square feet, which is closest to 440 square feet, so the answer is 440 ft2.

The five-sided figure is a trapezoid with two parallel sides, so we can use the formula for the area of a trapezoid to find the total area.

Area of a trapezoid = (sum of the lengths of the two parallel sides) / 2 * height

Let's call the length of the longer parallel side "L". Then the height of the figure is 22 feet, and the length of the shorter parallel side is 16 feet.

Area = (L + 16) / 2 * 22

We also know that the portion from the vertex to the perpendicular height is 8 feet, and the portion from a point to a vertical line created by two vertices is 4 feet. These two lengths form a right triangle, so we can use the Pythagorean theorem to find the length of the longer parallel side, L.

L² = (8 + 4)² = 64

L = 8

Now we can use the formula for the area of a trapezoid to find the total area.

Area = (L + 16) / 2 * 22 = (8 + 16) / 2 * 22 = 24 * 22 = 528

The total area of the figure is 528 square feet, which is closest to 440 square feet, so the answer is 440 ft2.

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Answer:

y = -10x -6

Step-by-step explanation:

Answer:

36,900

Step-by-step explanation:

it's right I just do not know how to explain lol

Answer:

The volume is 997.62 cubic units..

Step-by-step explanation:

We are given the following details:

The pyramid has a regular hexagonal base i.e. each side of hexagon is equal.

Side of hexagonal base, a = 8 units

Altitude of pyramid, h = 18 units

We have to find the volume of pyramid.

Formula:

\(V = \dfrac{1}{3} \times B \times h\)

Where, B is the area of base of pyramid.

h is the height/altitude of pyramid

To calculate B:

Here, base is a hexagon with side 8 units.

\(\text{Area of hexagon, B }= 6 \times \dfrac{\sqrt{3}}{4}a^{2}\)

Here, a = 8 units

\(\Rightarrow B = 6 \times \dfrac{\sqrt{3}}{4}\times 8^{2}\\\Rightarrow B = 166.27\text{ square units}\)

Putting values of B and h in Formula of volume:

\(\Rightarrow V = \dfrac{1}{3} \times 166.27 \times 18\\\Rightarrow V = \dfrac{2992.89}{3} = 997.62\text{ cubic units}\)

Hence, the volume is 997.62 cubic units.

Answer:

$127.50

Step-by-step explanation:

All you have to do is $125 times 1.02 because it is adding to the price it is already.

$125 × 1.02.

Which is $127.50.

Answer:

B. 6/9 - 4/9

Step-by-step explanation:

Make sure each fraction has a common dominator

2/3 *3/3 = 6/9

4/9 = 4/9

6/9 - 4/9 = 2/9

Answer:

6/9 - 4/9, B

Step-by-step explanation:

Based on the fact that there is no country which had won more than 900 silver medals, set E using the roster method would be E = {  }.

Set E is meant to include the set of countries who have attained more than 900 silver medals in the Olympic games.

The highest number of silver medals attained is that of the United States which is 860 silver medals.

This means that no single country has attained more than 900 silver medals.

Set E would therefore be null. Using the roster method, the way to show set E would be:

E = {  }

In conclusion, set E is E = {  }.

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251

bc 15x16=240

240+11=251

Answer:

B

Step-by-step explanation:

the sum of the 3 angles in a triangle is 180° , so

∠ c + 56° + 38° = 180°

∠ c + 94° = 180° ( subtract 94° from both sides )

∠ c = 86°

After answering the presented question, we can conclude that As a rectangle result, the wall's length is approximately 18.67 metres.

In Euclidean geometry, a rectangle is a parallelogram with four small angles. It can also be described as a fundamental rule hexagon or one in which all of the angles are equal. Another option for the parallelogram is a straight angle. Four of the vertices in a square are the same length. A quadrilateral with four 90° angle vertices and equal parallel sides has a rectangle-shaped cross section. As a result, it is also known as a "equirectangular rectangle." A rectangle is sometimes referred to as a parallelogram due to the equal and parallel dimensions of its two sides.

To begin, we can use the formula for the area of a rectangle, which is:

length x width Equals area

We know the wall's area is 39.2 m2, and we want to know how long it is. We are also given the wall's breadth, which is 2.1 m.

As a result, we can rearrange the formula to find the length:

width = Area length

length = 39.2 2.1 cm

a length of 18.67

As a result, the wall's length is approximately 18.67 metres.

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Answer: Its definitely 7.2 for the first two and 4.5 on the last one to the right

Step-by-step explanation: i did the quiz

Answer:

just substitute each value of x into the function

Step-by-step explanation:

1. (x=-2) y= 4(-2)+2

2. (x=0) y= 4(0)+2

3. (x=2) y= 4(2)+2

4. (x=4) y= 4(4)+2

use the same steps but change the value of x. go ahead a use your calculator

The " Eight  further than the Quotient of a number and 7 is equal to 3," and the  result to the equation is x = -35.

The equation 8( x/ 7) =  3 represents the  judgment " Eight  further than the Quotient of a number and 7 is equal to 3," and the  result to the equation is x = -35.    

" Eight  further than" implies addition, so we've 8 " The quotient of a number and 7" means dividing a number by 7, so we've x/ 7 " is equal to" means that the expression on the left side is equal to the expression on the right side, so we've =  " 3" is the value to which the expression on the left side is equal, so we've 3  Putting it all together the  judgment " Eight  further than the quotient of a number and 7 is equal to 3" can be  restated into the equation ( x/ 7) =  3  

In this equation, x represents the number we're trying to find. To  break for x, we can manipulate the equation using algebraic operations to  insulate x on one side of the equation.  By abating 8 from both sides of the equation, we get ( x/ 7)- 8 =  3- 8  Simplifying, we have  x/ 7 = -5

To  insulate x, we can multiply both sides of the equation by 7  *( x/ 7) = -5 * 7  This gives us  x = -35  thus, the equation 8( x/ 7) =  3 represents the  judgment " Eight  further than the quotient of a number and 7 is equal to 3," and the  result to the equation is x = -35.

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The total surface area of the doghouse is 1452 ft²

The area occupied by a three-dimensional object by its outer surface is called the surface area.

The dog house has many surfaces including the roofs . The total surface area is the sum of all the area of the surfaces.

area of the roof part = 2( 13×11) + 2( 12× 10)×1/2

= 286 + 720

= 1006 ft²

surface area of the building

= 2( lb + lh + bh) -bh

= 2( 10× 11 + 10×8 + 11×8) - 10×11

= 2( 110+80+88)-110

= 2( 278) -110

= 556 -110

= 446ft²

The total surface area = 1006 + 446

= 1452 ft²

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The solution is: Piece-wise function

f(x)=x+6 , x≤1

f(x) = x^2 + 3 , x>1, the following functions is graphed below.

Option C is correct.

Explanation:

We are given a graph of piece-wise function which break at x=1

We need to choose correct option for graph.

Function is break at x=1.

We will get two function

For x≤1 and x>1

As we can see x≤1, graph is linear and x>1 graph is parabolic.

Equation of linear graph, x≤1

Take two point of graph (0,6) and (-6,0)

Equation of line:

y-y1/y2-y1 = x-x1/x2-x1

y = x+1

f(x)=x+6 , x≤1

Equation of parabolic graph, x>1

f(x) = x^2 + 3

Piece-wise function

f(x)=x+6 , x≤1

f(x) = x^2 + 3 , x>1

Please see the attached figure.

Hence, The option C is correct.

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Answer:

x-intercept: (1, 0)

Step-by-step explanation:

The x-intercept is the point on the graph where it crosses the x-axis, and has coordinates, (a, 0).  Looking at the two points on the graph, one of them crosses the x-axis at point (1, 0). This represents the x-intercept of the line.

Therefore, the x-intercept of the line is (1, 0).

Answer:

21794.495 units/month

Step-by-step explanation:

Some data are missing which i can assume as per requirement of the Question.

Let us consider that profit generated by a product is given by

p(x) =4√x

Also, consider that the profit keeps changing at a rate of $1000 per month.

Now, Using the chain rule we can write

dp/dx=(dp/dt)÷(dx/dt).

So, we  can calculate

dp/dx=2x^(-1/2)=2/√x.

As per  question we have to find out  dx/dt

Since, dx/dt= (dp/dt)/(dp/dx),

so plugging  x=1900  we get 1000√1900/2=21794.495 units/month increase in sales.

Answer:

224

Step-by-step explanation:

360.-136.

Answer:

Step-by-step explanation:

so I believe the question is

\(\frac{1}{4}\)X - \(\frac{1}{3}\)Y=1

and we want to know if that is linear, and what the standard form for the equation would be

let's move a few things around using our algebra skillz

\(\frac{1}{4}\)X-1 = \(\frac{1}{3}\)Y

\(\frac{3}{4}\)X-3 = Y

y = \(\frac{3}{4}\)x-3  (in standard form  y=mx+b)

y=\(\frac{3}{4}\)x + (-3)

we can see that this does make a line,  so it's linear, and it's in standard form now.  

Answer:

6.24 x \(10^{-7}\)

Step-by-step explanation:

0.000000624 in scientific notation is 6.24 x \(10^{-7}\)

Answer:

Step-by-step explanation:

The resulting number is in scientific notation. In this case, the number is 6.24 * 10^-7.

The number of visits before he can win a free tickets is 6.

Here are inequality signs and what they mean:

The inequality sign that would be used is ≥.

initial reward + (reward point per visit x number of visits) ≥ minimum points needed to get a free ticket

85 + (12.50  × xx) ≥ 155

85 + 12.50xx ≥ 155

In order to determine the value of xx, take the following steps:

Combine similar terms:

12.50xx ≥ 155 - 85

Add similar terms: 12.50xx ≥ 70

Divide both sides by 12.50

xx  ≥ 70 / 12.50

xx  ≥ 5.6

xx  ≥ 6.

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a) The point-slope form of a linear equation is given by y - y1 = m(x - x1), where m is the slope and (x1, y1) is any point on the line.

Given that the x-intercept is 11, we know that the line passes through the point (11, 0) on the x-axis. Similarly, given that the y-intercept is 6, we know that the line passes through the point (0, 6) on the y-axis.

Let's use (11, 0) as our point (x1, y1) and find the slope:

slope = (y2 - y1) / (x2 - x1) = (6 - 0) / (0 - 11) = -6/11

Substituting this slope and the point (11, 0) into the point-slope form, we get:

y - 0 = (-6/11)(x - 11)

Simplifying, we get:

y = (-6/11)x + 6/11

So the linear function in the form y - y1 = m(x - x1) is:

y - 0 = (-6/11)(x - 11)

And the linear function in the form y = mx + c is:

y = (-6/11)x + 6/11 (by simplifying the equation obtained from the point-slope form)

b) To find the equation of the line in slope-intercept form (y = mx + c), we need to find the slope and y-intercept of the line.

Given that the x-intercept is 11, we know that the line passes through the point (11, 0) on the x-axis. Similarly, given that the y-intercept is 6, we know that the line passes through the point (0, 6) on the y-axis.

Let's use the two points (11, 0) and (0, 6) to find the slope:

slope = (y2 - y1) / (x2 - x1) = (6 - 0) / (0 - 11) = -6/11

Now that we have the slope, we can use the y-intercept to write the equation in slope-intercept form:

y = mx + c

y = (-6/11)x + 6

So the linear function in the form y = mx + c is:

y = (-6/11)x + 6.

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Answer:

the answer is D broski

Step-by-step explanation:

trust me on this one

Answer:

63 1/4

Step-by-step explanation:

Step-by-step explanation:

4 smoothies = 2 1/2 banana

you need to make 2 more smoothies, So half of what you did already.

(2.5)/2= 1.25 then add them (2.5)+(1.25)

6 smoothies = 3.75 or 3 3/4, same thing.

cos(tan^(-1)(-2/3)) simplifies to 3√13 / 13.

To evaluate the expression cos(tan^(-1)(-2/3)), we can use the trigonometric identity:

cos(tan^(-1)(x)) = 1 / √(1 + x^2)

In this case, x is -2/3. Substituting the value into the identity:

cos(tan^(-1)(-2/3)) = 1 / √(1 + (-2/3)^2)

Now, let's calculate the value:

cos(tan^(-1)(-2/3)) = 1 / √(1 + 4/9)

                   = 1 / √(13/9)

                   = 1 / (√13/3)

                   = 3 / √13

                   = 3√13 / 13

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The possible answers for the restaurants are Three 8-hour shifts; four 6-hour shifts; six 4-hour shifts.

2. The seconds that they will blink together again is 45 seconds.

Here we have to determine the factors of 24 for the shifts i.e.  1, 2, 3, 4, 6, 8, 12, 24 .

A 1-hour shift does not make much sense; most employers will also not use a 2-hour or 3-hour shift.

Restaurants typically do not use 12-hour shifts either, and employers do not use 24-hour shifts either.

Since both signs blink as they are turned on and one blinks every 9 seconds. The other sign blinks every 15 seconds. The least common multiple is 45.

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Answer:

\(y=-8x-61\)

Step-by-step explanation:

The slope-intercept form of the equation is y=mx+b where m is the slope and b is the y intercept. We know so far, that the slope is -8. We plug that in for m.

\(y=-8x+b\)

Now, we need to find the y-intercept. The question gives us the point (-7,-5). We plug in -7 for x, and -5 for y.

\(-5=-8(-7)+b\)

Then, we solve.

\(-5=56+b\)

Subtract 56 from both sides.

\(-61=b\)

Finally, we get this equation:

y=-8x-61

Yes, 7/56 and 6/48 are proportional because 7×48 = 56×6. Therefore, the correct answer is option B.

Given that, a truck needs 7 gallons of fuel to travel 56 miles.

The truck travel 48 miles with 6 gallons of fuel.

Here, the proportion is

7:56::6:48

We know that, the proportion is product of extremes = product of means

7×48 = 56×6

336 = 336

Therefore, the correct answer is option B.

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A) A 747 Airplane is 762 inches tall. 762 inches is equal to 63.5 feet, so the airplane is 63.5 feet tall.

An airplane is a type of aircraft that is heavier than air and propelled by one or more jet engines. It is used for transport across long distances, typically carrying passengers and cargo.

The river raft ride at the amusement park can hold 12 riders at a time. 527 people divided by 12 riders per ride is 44.75. This means the ride will need to run 44 times in order to get all 527 people through the ride.
One school bus can hold 46 students. There are 24 students in each of the 5 fifth grade classes. 24 students times 5 classes is 120 students, so they will need 3 buses in order to transport everyone to the zoo for a field trip.
Write and solve a word problem that requires long division AND has a remainder.
Samantha has 192 lollipops. She wants to evenly divide them into bags of 10. How many bags will she need and how many lollipops will be left over?
192 divided by 10 is 19 with a remainder of 2. Samantha will need 19 bags and will have 2 lollipops left over.

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