Which of the following is a rational function?

Answer:

3.61 sec

Step-by-step explanation:

Set the given d= 3t + 3t ^2 equal to 50 and solve for t:

3t^2 + 3t - 50 = 0

This is a quadratic equation with coefficients 3, 3 and -50.  The discriminant is b^2 - 4ac, or 3^2 - 4(3)(-50), or 9 + 600 = 609

The roots of this quadratic are therefore:

     -(3) ± √609           -3 ± 24.68           21.68

t = --------------------  =  -------------------  =  ----------- = 3.61 sec

           2(3)                           6                     6

Answer: 27 miles in 1 gallon

Step-by-step explanation:

297/11

The unit rate of 297 miles in 11 gallons will be 27 miles/gallons.

The ratio is the division of the two numbers.

For example, a/b, where a will be the numerator and b, will be the denominator.

We will be used when division is not possible wholly

For example 4/2 is divisible so we write 2 instant of 4/2 while 1/3 is not divisible so we write 1/3 instant of 0.33.

Proportion is the relation of a variable with another. It could be direct or inverse.

The ratio is very useful to determine complex calculation where decimal number become tough to solve.

Given,

297 miles in 11 gallons

297 miles ⇔ 11 gallons

Divide by 11 on both sides

297/11 miles ⇔ 11/11 gallons

27 miles ⇔ 1 gallon

So, 27 miles in 1 gallon.

Hence unit rate is 27 miles/gallon will be correct.

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Answer:

[tex](\sqrt[2]{32})^{9}[/tex]=5931641.60152

Step-by-step explanation:

:)

Answer: angles 1 and 7

Answer:

A

Step-by-step explanation:

(-4-3, 7+7)

(-7, 14)

Answer: A

Step-by-step explanation:

Answer:

Jason has 75 pencils.

Step-by-step explanation:

In order to get from 4 to 100, you must multiply by 25 (100/4 = 25). And in order to find the amount of pencils Jason has, you must have an equivalent ratio. So you have to also multiply 3 by 25, 3 * 25 = 75. Jason has 75 pencils.

Answer:

if the solution to the system is  1.5 and 2

Then the mistake was in line 2 the student should have subtracted the eqations instead of adding them.

Step-by-step explanation:

if y = 2

Then 8y -5y = 3y

4x -x = (4 = 1.5 x 2 2/3) =4   if x = 1.5

3y = 2 2/3 = 3   if y = 2

The ratio stays the same.

The student mistake was in line 2, the student forgot to multiply the

right side of the equation by 2.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Given:

2x + 5y = 13

-x + 4y = 13

The first steps are correct.

In second step the LHS and RHS both should be multiplied by 2.

So,

-2x + 8y = 26

But, the student only multiply 2 on the LHS side.

Hence, the student mistake was in line 2, the student forgot to multiply the right side of the equation by 2.

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Answer:

y - 32 = 4(x - 4)

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

y - 1 = 4(x + 3) ← is in point- slope form

with slope m = 4

Parallel lines have equal slopes.

Using m = 4 and (a, b) = (4, 32), then

y - 32 = 4(x - 4) ← equation of parallel line

Answer:

A

Step-by-step explanation:

Hyperbolic geometry is defined as a non-Euclidean geometry.

(invalidating the fifth postulate of Euclid's five fundamental postulates)

Choice B and D can be eliminated because this has nothing to do with perpendicular lines.

Choice C should be eliminated as well since that's exactly the fifth postulate of Euclid's five fundamental postulates

We are left with A by the process of elimination

Answer:

A. There are an infinite number of lines parallel to a given line through a given point.

Hope this Helps!

Answer:

The answer is option 2.

Step-by-step explanation:

Given that the equation of a straight line is y = mx + c where m represents gradient and c is the y-intercept which touches the y-axis.

By looking at the graph, we know that it is a positive gradient and it touches -1 at y-axis.

Answer:

Answer:

Option B.

Step-by-step explanation:

We take a point D from the figure attached,

Coordinates for the point D → (-1.5, 3.5)

And coordinates of D' → (3.5, 1.5)

Coordinates of D when rotated about the origin,

Option A. Rotated by 270° clockwise.

Rule to be followed,

D(x, y) → D'(-y, x)

D(-1.5, 3.5) → D'(-3.5, -1.5)

Therefore, Option A. is incorrect

Option B. rotation by 90° clockwise

Rule to be followed

D(x, y) → D'(y, -x)

D(-1.5, 3.5) → D'(3.5, 1.5)

Therefore, Option B. is correct.

Option C. 90° counterclockwise

Rule to be followed,

D(x, y) → D'(-y, x)

D(-1.5, 3.5) → D'(-3.5, -1.5)

This option C is incorrect.

Option D. 180° counterclockwise

Rule to be followed,

D(x, y) → D'(-x, -y)

D(-1.5, 3.5) → D'(1.5, -3.5)

Therefore, option D is incorrect.

Answer:

B. 90 clockwise

Step-by-step explanation:

Answer:

15.94490514

Step-by-step explanation:

First, work out the average, or arithmetic mean, of the numbers:

Count: 5(How many numbers)

Sum: 357(All the numbers added up)

Mean: 71.4(Arithmetic mean = Sum / Count)

Then, take each number, subtract the mean and square the result:

Differences:

4.6, -26.4, -7.4, 8.6, 20.6

(Every Number minus Mean)

Differences^2:

21.16, 696.96, 54.76, 73.96, 424.36

(Square of each difference)

Now calculate the Variance:

Sum of Differences2:1271.2(Add up the Squared Differences)

Variance:254.24(Sum of Differences2 / Count)

Lastly, take the square root of the Variance:

Standard Deviation:15.94490514 (The square root of the Variance)

Answer:

1/4

Step-by-step explanation:

3 and 6 are both multiples of 3, so there is a 2/8 chance of spinning a multiple of 3, which can be simplified to 1/4.

Answer:

1. (-1/4,0)(1.5,0)

2.(-1/2,2)(6/4,2)

Step-by-step explanation:

just locate the numbers on the graph

Answer:

A,D

Step-by-step explanation:

I'm taking the test

The first and the fourth graph do not represent constant rates of change. Hence, option A and option D are correct.

A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.

In the first and the fourth graph the function follows a curved graph because of it, it does not follow linearity. In the second and third graphs, the function follows a linear line, therefore, it shows a constant rate of change.

Hence, option A and option D are correct.

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The question is incomplete! Complete question along with answer and step by step explanation is provided below.

Question:

The Whispering Lakes  Neighborhood Association is  having a hamburger cookout.  Each family can choose whether  to order the hamburgers or  bring their own. Use the  information in the table to solve  the number stories. Use  drawings, tables, or equations  to show what you did.

Mrs. Ward found 80-ounce packages of hamburger on sale. If she needs to make  2 of each size hamburger, how many packages of meat will she need to buy?

Answer:

The number of meat packages is

100/80 = 1.25 = 5/4

Assuming that the number of packages cannot be in fraction, then she would need at least 2 packages of meat.

Number of meat packages = 2

Step-by-step explanation:

Please refer to the attached table where we are given size of hamburgers and the weight of corresponding hamburger patty in pounds.

small = 1/8 lb

medium = 1/4 lb

large = 1/2 lb

jumbo = 3/4 lb

king of burgers = 1 1/2 lb = 3/2 lb

To make 1 of each hamburger we need

Total weight of patty = 1/8 + 1/4 + 1/2 + 3/4 + 3/2

Total weight of patty = 25/8 = 3.125 lb

But she needs to make  2 of each size hamburger so,

Total weight of patty = (25/8)×2 = 25/4 = 6.25 lb

Mrs. Ward found 80-ounce packages of hamburger on sale

first we have to convert pounds into ounces

We know that 1 pound has 16 ounces

6.25×16 = 100 ounces

So the number of meat packages required is

100/80 = 1.25 = 5/4

Assuming that the number of packages cannot be in fraction, then she would need at least 2 packages of meat.

Number of meat packages = 2

Answer:

The image of the circle is 9·x² + 9·y² - 42·x + 33·y = 22

Step-by-step explanation:

We convert the equation to the form (x - h)² + (y - k)² = r²

Where:

(h, k) = Coordinates of the center of the circle

We therefore have;

x² + y² - 2·x + 3·y = 8 which gives;

x² - 2·x + 1 - 1 + y² + 3·y + (3/2)² - (3/2)² = 8

(x - 1)² + (y + 3/2)² - 1 - (3/2)² = 8

(x - 1)² + (y + 3/2)²  = 8 +  1 + (3/2)² = 45/4

Therefore, the center = (1, -3/2) and the radius = √5 × 3/2

The line joining the centers of the actual (1, -3/2) and reflected circle (h, k) is bisected by the line of reflection, therefore the midpoint of the line is on the line of reflection with coordinates;

Midpoint between (1, -3/2) and  (h, k) = [tex]\left (\dfrac{{h - 1}}{2}, \, \dfrac{k - 3/2}{2} \right )[/tex]

Which gives;

y = 2·x - 3 being equivalent to [tex]\dfrac{k - 3/2}{2} = 2\times\dfrac{{h - 1}}{2} - 3[/tex]

Which gives;

4·h -2·k -13 = 0.......(1)

Similarly the slope of the reflecting line is perpendicular to the line joining the centers of the actual and reflected circles

Therefore;

The slope of the line, y = 2·x - 3 = 2, hence we have;

[tex]\dfrac{\left ( \dfrac{k - 3/2}{2} \right ) + 3/2}{\left (\dfrac{{h - 1}}{2}-1 \right )} = \dfrac{1}{2}[/tex]

Which gives;

2·h -4·k -12 = 0.......(2)

Multiplying equation (2) and subtracting from equation (1) gives

4·h -2·k -13 - 2×(2·h -4·k -12) = 0

6·k + 11 = 0

k = -11/6

From which we have;

2·h -4×(-11/6) -12 = 0

Hence;

h = 7/3

Therefore, the center of the reflected circle = (7/3, -11/6)

The equation of the reflected circle is therefore;

(x - 7/3)² + (y + 11/6)² = 45/4

Which gives;

9·x² + 9·y² - 42·x + 33·y - 22 = 0

or x² + y² - 42/9·x + 33/9·y = 22/9.

Answer:

the difference would be 28 degrees.

Step-by-step explanation:

The question says difference so we subtract the two following temperatures 30 and -2 which would be 28 degreees.

Answer: The difference between the high and low temperature in the thermometer is 32°F.

Step-by-step explanation:

Given information: Highest temperature = 30°F and the lowest temperature = -2°F.

We need to find the difference between the high and low temperature in the thermometer.

Difference between the high and low temperature is

Difference = Highest temperature - Lowest temperature

Difference = 30°F - (-2°F)

Difference = 30°F + 2°F

Difference = 32°F

Answer:

x = -2, x= -5 , x= +5

Step-by-step explanation:

x^3 + 2x^2 -25x - 50 = 0

Factor by grouping

x^3 + 2x^2        -25x - 50 = 0

x^2(x+2)   -25( x+2) = 0

(x+2) ( x^2 -25) =0

Using the zero product property

x+2 =0     x^2 -25 =0

x=-2            x^2 = 25

x= -2            Taking the square root of each side

                     x = ±5

Answer:

X=4

Step-by-step explanation:

Solution: x equals 4

x/14-(6/21)=0

1. Simplify 2/7

x/14- 2/7 is 0

It’s too much steps

Step-by-step explanation:

Explanation:

The formula for volume of a sphere is:

V=43πr3

Since we know the volume, and have to find the diameter (twice the radius), we need to determine the radius first.

Hence, using the given data:

2304π=43πr3

We can cancel π from each side.

2304=43r3

Multiply both sides by 34.

2304×34=34×43r3

2304×34=34×43r3

2304×34=r3

5762304×34=r3

576×3=r3

To find the cube root, we separate the factors of the number on the left.

3⋅3⋅3⋅4⋅4⋅4=r3

(3⋅4)(3⋅4)(3⋅4)=r3

12×12×12=r3

12=r

Since the radius (r) is 12, the diameter, which is 2r, will be:

2×12=24

Answer:

the slope is zero because

Step-by-step explanation:

this is a perfect horizontal line passing through y=-3

I've been thought

hope it helps

Answer:

Slope = 0

This is because the line does not go up or down. And the line is horizontal leading to the factor of the slope being 0.

Answer:

A

Step-by-step explanation:

17/12 = 1  5/12

1×12+5=17

Answer:

Acute and Scalene.

Step-by-step explanation:

By definition, an acute triangle is one that has three angles that are less than 90 degrees. This triangle falls under the category.

By definition, a scalene triangle is one that has three sides with different measurements. This triangle falls under the category.

Hope this helps!

Answer:

x = - [tex]\frac{2}{9}[/tex]

Step-by-step explanation:

Given

[tex]\frac{2}{5}[/tex] (x - 2) = 4x

Multiply both sides by 5 to clear the fraction

2(x - 2) = 20x ( divide both sides by 2 )

x - 2 = 10x ( subtract x from both sides )

- 2 = 9x ( divide both sides by 9 )

- [tex]\frac{2}{9}[/tex] = x

Answer:

60 possible sequences.

Step-by-step explanation:

That would be 6! / 3! 2!

   6*5*4*3*2*1

=  ------------------

     3*2*1*2*1

= 5*4*3

= 60.

The volume is 15/16 cubic meters.

please see the attached picture for full solution

hope it helps

Answer:

4+2.4=6.4+1.44=7.84

The infinite geometric sum of 4+2.4+1.44+... will be 10.

At each point in the sequence, you multiply or divide by the common ratio. Divide two sets of phrases that follow one another to find it. Whichever pair of terms is picked, as long as they appear next to one another in the sequence, is irrelevant.

It is given that, the sequence is 4+2.4+1.44+...

The sequence is defined as the systematic way of representing the data that follows a certain rule of arithmetic.

Divergent sequences are those in which the terms never stabilize; instead, they constantly increase or decrease as n approaches infinity, approaching either infinity or -infinity.

It is obtained that the common ratio is,

r=2.4/4

r=0.6

The Sum of an infinite geometric sequence is,

S = a / (1-r)

S=4 / (1-0.6)

S=10

Thus, the infinite geometric sum of 4+2.4+1.44+... will be 10.

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