Classify the following real numbers as rational or irrational:

Answer:

[tex] \frac{2x - 5}{x + 5} [/tex]

Step-by-step explanation:

Firstly, you have to factorize the expressions on the numerator and denorminator :

Numerator :

[tex]2 {x}^{2} - 3x - 5[/tex]

[tex] = 2 {x}^{2} + 2x - 5x - 5[/tex]

[tex] = 2x(x + 1) - 5(x + 1)[/tex]

[tex] = (2x - 5)(x + 1)[/tex]

Denorminator :

[tex] {x}^{2} + 6x + 5[/tex]

[tex] = {x}^{2} + x + 5x + 5[/tex]

[tex] = x(x + 1) + 5(x + 1)[/tex]

[tex] = (x + 1)(x + 5)[/tex]

Next, you have to put the factorized-form in the fraction and cut out the similar expressions :

[tex] \frac{(2x - 5)(x + 1)}{(x + 1)(x + 5)} [/tex]

[tex] = \frac{2x - 5}{x + 5} [/tex]

Answer:

It'll take approximately 34 years from today.

Step-by-step explanation:

in order to solve this problem we first need to find the rate of change, "k", to do that we will use the given information where the population was 1400 five years ago and its now 1000. Applying this data to the equation gives us:

[tex]A = A_0*e^{k*t}\\1000 = 1400*e^{5*k}\\1400*e^{5*k} = 1000\\e^{5*k} = \frac{1000}{1400}\\ln(e^{5*k}) = ln(\frac{1000}{1400})\\5*k = ln(1000) - ln(1400) \\k = \frac{ln(1000) - ln(1400)}{5} = -0.06729[/tex]

We now know the value for "k", we can estimate how many years it will take for the bird population to dip below 100. We have:

[tex]100 = 1000*e^{-0.06729*t}\\e^{-0.06729*t} = \frac{100}{1000}\\ln(e^{-0.06729*t} = \frac{1}{10}\\-0.06729*t = ln(0.1)\\t = -\frac{ln(0.1)}{0.06729} = 34.22[/tex]

It'll take approximately 34 years from today.

Answer:  (b) x = -2/3

Step-by-step explanation:

The vertical asymptote is the restriction on x.

The denominator cannot be equal to zero so that it the restriction.

Set the denominator equal to zero and solve for x to find the asymptote.

3x + 2 = 0

3x       = -2

 x       = -2/3

Answer: 79/4

Step-by-step explanation:

The kettle contains 20 3/8 cups of soup = 163/8 cups

A server scoops 5/8 cup from the kettle

So,

163/8 - 5/8 = 158/8 = 79/4

Answer:

1.08

Step-by-step explanation:

1.01 < x < 1.17

x ≠ 1.20

x ≠ 1.008

x = 1.08

x ≠ 1.18

x ≠ 1.8

The number that completes the inequality is 1.08:

1.01 < 1.08 < 1.17, < 1.20

Option C is the correct answer.

We have,

To determine which number completes the inequality, we need to find the number that is greater than 1.01 but less than both 1.17 and 1.20.

Among the given options, the number that satisfies this condition is 1.08.

Thus,

The number that completes the inequality is 1.08:

1.01 < 1.08 < 1.17, < 1.20

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Answer:

y = [tex]\frac{4\sqrt{3} }{3}[/tex]

Step-by-step explanation:

We are working with 30-60-90 triangles, and to solve for y we need to know the hypotenuse of the smaller triangle.

You can get that by finding the smaller value of the larger triangle.

[tex]\frac{8}{\sqrt{3} } =\frac{x}{1}[/tex]

x[tex]\sqrt{3}[/tex] = 8

x = [tex]\frac{8}{\sqrt{3} }[/tex]

x = [tex]\frac{8\sqrt{3} }{3}[/tex]

That is the hypotenuse of the smaller triangle. To find y...

[tex]\frac{(\frac{8\sqrt{3} }{3}) }{2} =\frac{y}{1}[/tex]

2y = [tex]\frac{8\sqrt{3} }{3}[/tex]

y = [tex]\frac{4\sqrt{3} }{3}[/tex]

Hope this helps!

Answer: The vertex of the function is (-1, -7).

Step-by-step explanation: We are given to find the vertex of the following function.

We know that the vertex of the function is given by (h, k).

So, for the given function f(x), the vertex will be (-1, -7).

The graph of the function f(x) is shown in the attached figure, where the vertex is at the point (-1, -7).

Thus, the vertex of the function is (-1, -7).

The vertex of the function  f(x) = |x + 1| - 7 is (-1,-7)

The function is given as:

f(x) = |x + 1| - 7

The above function is an absolute value function

An absolute value function is represented as:

f(x) = a|x – h| + k

Where, the vertex is (h,k)

So, we have:

(h,k) = (-1,-7)

Hence, the vertex of the function  f(x) = |x + 1| - 7 is (-1,-7)

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Answer:

y = (-2/125)(x - 50)² + 40

Step-by-step explanation:

The total length of the bridge is 100 meters.

Maximum height always occurs at midpoint of x.

So for x=50 meters , y = 40 meters.

As the vertex is given at the maximum height,  Vertex can be defined at the point (50,40)

We know that the general equation for vertical parabola is:

y = a(x - h)² + k

Where (h,k) = Vertex = (50,40)

Substitute in the equation:

y = a(x - 50)² + 40 ⇒ Equation (i)

We know 2 more points on the parabola. We know that when x=0 , y=0 and we also know that when x=100m, y=0 meters.

Substitute any point in the above equation

Substituting (100,0) in the equation

0 = a(100 - 50)² +40

Solve the equation for a:

a = - 2/125

Substitute a in Equation (i)

y = (-2/125)(x - 50)² + 40

Answer:

93 hamburgers

Step-by-step explanation:

let cheeseburgers=c

let hamburgers=h

c=3h

c+h=372

Substitute c for 3h

3h+h=372

4h=372

h=93

c=h*3=93*3=279

279 cheeseburgers 93 hamburgers

Answer:

99

Step-by-step explanation:

(99^2-98^2)/197+(98^2-97^2)/195+(97^2-96^2)/193+ ... +(2^2-1^2)/3

each term can be written as:

so the sum will look as:

(all middle terms get cancelled leaving only 99 and -1 in the equation)

Answer:

Proportion of blue marbles in in sample = 9/40

Step-by-step explanation:

Total number of blue marbles in a jar is given by 25%

Lets find the probability of blue marble in the jar of the given sample:

Proportion of blue marbles in in sample = Total number of blue marbles in sample/ Total number of marbles in sample

Where

Total number of blue marbles in sample = 9

Total number of marbles in sample = 9 + 15 + 16

Total number of marbles in sample = 40

SO

Proportion of blue marbles in in sample = 9/40

or

Proportion of blue marbles in in sample = 9/40

Answer:

10% of the people at the picnic are neither.

Step-by-step explanation:

To get the answer,

1/2 + 2/5 = 9/10

10/10 - 9/10 = 1/10

1/10 = 10%

Thanks, I hope I got this right!

Answer:

Step-by-step explanation:

Answer:

The y-intercept would be 6.25

Step-by-step explanation:

I found this by taking the two points and making it into a y = mx + b line.

Answer:

(0,3)

Step-by-step explanation:

We can use the slope-intercept form to find the y-intercept.

First, we need to find the slope of the line.

We are given the points (-1,7) and (1,-1).

[tex]m=\frac{rise}{run}=\frac{-1-7}{1+1}=\frac{-8}{2}=-4[/tex]

The slope is -4.

Slope-intercept is [tex]y=mx+b[/tex].

We can replace 'y' and 'x' with one of the points given, 'm' with the slope, and solve for 'b'. "B" would be the y-intercept.

I will use (-1,7):

[tex]7=-4(-1)+b\\\\7=4+b\\\\7-4=4-4+b\\\\\boxed{3=b}[/tex]

The line's equation is [tex]y=-4x+3[/tex].

Therefore, the y-intercept is '3'. The coordinates of the y-intercept is (0,3).  

Yes they are independent because P(California) = 0.55 approximately and P(California | Brand B) = 0.55 approximately as well

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

Explanation:

P(California) is notation that means "probability the person is from California". There are 150 people from California out of 275 total. Therefore, the probability is 150/275 = 0.5454 approximately which rounds to 0.55

Now if I told you "this person prefers brand B", then you would focus your attention solely on the brand B column. The other columns are ignored because you know they don't prefer anything else. With this narrower view, we see that 54 Californians prefer this brand out of 99 total. The probability becomes 54/99 = 0.5454 which rounds to 0.55. We get the same as before.

The notation P(California | Brand B) means "the probability they are from California given they prefer brand B". The vertical line is not the uppercase letter i or lowercase letter L. It is simply a vertical line. In probability notation that vertical line means "given".

We've shown that P(California | Brand B) = 0.55 approximately. The fact that they prefer brand B does not change the original probability. So the two events are independent. If liking brand B did change the probability, then the events would be dependent.

Answer:

-7

Step-by-step explanation:

[tex]x^2+x+2=0 \\\\b^2-4ac= \\\\1^2-4(1)(2)= \\\\1-8= \\\\-7[/tex]

Hope this helps!

The value of the discriminant for the quadratic equation 0 = x + 2 + x² is -7.

Quadratic equations are polynomial equations of second degree.

The general form of a quadratic equation is ax² + b x + c = 0.

Given quadratic equation is,

x² + x + 2 = 0

The discriminant of a quadratic equation of the form ax² + bx + c = 0 is,

Discriminant = b² - 4ac

Here, a = 1, b = 1 and c = 2

Substituting,

Discriminant = 1² - (4 × 1 × 2)

                     = 1 - 8

                     = -7

Hence the discriminant of the given equation is -7.

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Answer:

C) None of the above

Step-by-step explanation:

Reason is V is a shorter distance and q is longer they need to be subtraction but the other way round to enable the correct subtraction we can show (q-V) which means the longer distance minus the shorter distance.

Answer:

median, mode, range, mean

Step-by-step explanation

the median is found by putting the data in order and selecting the middle value

the mode is the value that occurs the most often

the range is the difference between the greatest and least value

and the mean is the sum of all the values divided by the number of values

Answer:

The  ✔ median   is calculated by putting the data in order and selecting the middle value.

The  ✔ mode   is the data value that occurs the most in a set of data.

The  ✔ range  is the difference between the maximum and minimum values of a data set.

The  ✔ mean  is the sum of the data divided by the number of data values.

Students were asked how many pairs of shoes they owned. Their responses were 8, 2, 1, 5, 7, 6, 2, 2, 8, and 3.

The mean of the data is 4.4.

The median of the data is  4 .

The mode of the data is  2 .

The range of the data is  7 .

Step-by-step explanation:

Just took the test from E D G E N U I T Y....

hope this helps :P

Answer:

Step-by-step explanation:

Common ratio = 2nd term/1st term = 4/-16 = -1/4

[tex]a_{n}=a_{n-1}*r\\a_{n}=a_{n-1}*\frac{-1}{4}\\\\a_{n}=\frac{-1}{4}a_{n-1}[/tex]

Answer:

Common ratio = 2nd term/1st term = 4/-16 = -1/4

Step-by-step explanation:

Answer:

[tex]Dina= 35[/tex]

Step-by-step explanation:

Given

[tex]Ratio = 4:2:5[/tex]

Peter = 14 more A's than Chris

Required

How many A’s did Dina get?

The order of the ratio is Peter: Chris: Dina

This implies that

[tex]Peter: Chris: Dina = 4:2:5[/tex]

Considering Peter and Chris

[tex]Peter: Chris = 4:2[/tex]

Let the number of Chris' A's be represented by A

This implies that:

Peter's = 14 + A

And as such;

[tex]14 + A : A = 4 : 2[/tex]

Convert ratio to division

[tex]\frac{14 + A}{ A} = \frac{4}{ 2}[/tex]

Multiply both sides by A

[tex]A * \frac{14 + A}{ A} = \frac{4}{ 2}* A[/tex]

[tex]14 + A = \frac{4}{ 2}* A[/tex]

[tex]14 + A = 2* A[/tex]

[tex]14 + A = 2 A[/tex]

Subtract A from both sides

[tex]14 + A-A = 2 A-A[/tex]

[tex]14 = A[/tex]

This means that;

Chris answered 14 while Pete answered 28 (14 + 14)

Considering Chris and Dana

[tex]Chris :Dana = 2:5[/tex]

Replace Chris with 14

[tex]14:Dana = 2:5[/tex]

Convert ratio to division

[tex]\frac{14}{ Dina} = \frac{2}{5}[/tex]

Cross Multiplication

[tex]Dina * 2 = 14 * 5[/tex]

Divide both sides by 2

[tex]\frac{Dina * 2}{2} = \frac{14 * 5}{2}[/tex]

[tex]Dina= \frac{14 * 5}{2}[/tex]

[tex]Dina= \frac{70}{2}[/tex]

[tex]Dina= 35[/tex]

Hence, Dina had 35 A's

Answer:

x + y ≥ 3

x + y ≤ 3

Step-by-step explanation:

In the picture attached, the problem is shown.

The solution to the system:

x + y ≥ 3

x + y ≤ 3

is the line x + y = 3

In order to get a solution to a system of inequalities that is a line, we need the same equation on the left (here, x + y), the same constant on the right (here, 3), and the ≥ sign in one inequality and the sign ≤ in the other one.

Answer:

None. (or B)

Step-by-step explanation:

A)  AC≅ZY

B) AZ≅

C) ∠A ≅ ∠C

D) ∠B ≅ ∠X

Options C and D are not true and Options A is wrong and B is incomplete but using process of elimination, the answer is probably B.

The resulting information will be ∠ A ≅ ∠ X, ∠ B ≅ ∠ Y and ∠ C ≅ ∠ Z and AB ≅ XY, BC ≅ YZ and AC ≅ XZ

A translation is a type of transformation that takes each point in a figure and slides it the same distance in the same direction.

Given that, Δ ABC has been translated right to create triangle Δ XYZ

We know that in translation transformation, in translation, only the position of the object changes, its size remains the same.

That means Δ ABC ≅ Δ XYZ Therefore, we get,

Congruent parts are;

Angles:-

∠ A ≅ ∠ X,

∠ B ≅ ∠ Y and

∠ C ≅ ∠ Z

Side:-

AB ≅ XY,

BC ≅ YZ and

AC ≅ XZ

Hence, The resulting information will be ∠ A ≅ ∠ X, ∠ B ≅ ∠ Y and ∠ C ≅ ∠ Z and AB ≅ XY, BC ≅ YZ and AC ≅ XZ

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Answer:

Choice D

Step-by-step explanation:

[tex]3\dfrac{1}{2}\cdot 5 \cdot \dfrac{1}{2}= 3.5\cdot 5\cdot 0.5=8.75 = 8\dfrac{3}{4}[/tex]

Hope this helps!

Cubic feet would be volume.

Volume = length x width x height

Volume = 3 1/2 x 5 x 1/2 = 8 3/4 cubic feet.

Answer:

Step-by-step explanation:

Perimeter of the rectangle = 332m

Perimeter of a rectangle = 2(L+b)

Breadth = 75m

= 2 ( L + 75) = 332

2L + 150 = 332

2L = 332-150

L = 182/2

L= 91m

Answer:

  5

Step-by-step explanation:

The number of cells in a tile is 4, so the board dimension cannot be odd, but must be a multiple of 2 in order to have the number of cells divisible by 4.

If the tiles are colored in an alternating pattern, tiles must have 3 of one color and 1 of the alternate color. Hence the total number of tiles used to cover a board must be even (so the numbers of each color match). Then the board dimension must be divisible by 4.

In the given range, there are 5 such boards:

  4×4, 8×8, 12×12, 16×16, and 20×20

Answer:

c

Step-by-step explanation:

In the given line the relationship between angle w and z is Measure of angle w + measure of angle z = 180 degrees.

This is the type of angle that when measured, two of the angles would sum up to 180 degrees.

The supplementary angle is the sum of angle w + angle z = 180 degrees. Hence c is correct.

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Answer:

The correct option is;

Substitute x = 0 in the function  and solve for f(x)

Step-by-step explanation:

The zeros of a function are the values of x which produces the value of 0 when substituted in the function

It is the point where the curve or line of the function crosses the x-axis

A. Substituting x = 0 will only give the point where the curve or line of the function crosses the y-axis,

Therefore, substituting x = 0 in the function  can't be used to find the zero's of a function

B. Plotting a graph of the table of values of the function will indicate the zeros of the function or the point where the function crosses the x-axis

C. The zero product property when applied to the factors of the function equated to zero can be used to find the zeros of a function

d, The quadratic formula can be used to find the zeros of a function when the function is written in the form a·x² + b·x + c = 0

Answer: Substitute x = 0 in the function and solve for f(x).

Step-by-step explanation:

Answer: 430 miles

Step-by-step explanation:

Distance = speed x time

1) D = 50 x 3 = 150

2) D = 40 x 7 = 280

Total distance travelled = 150+280 = 430

Answer:

About 2.7 feet

Step-by-step explanation:

The tangent of an angle is equivalent to the length of the opposite side divided by the length of the adjacent side:

[tex]\tan 44=\dfrac{x}{2.8}\\\\x=2.8 \cdot \tan 44\approx 2.7[/tex]

Hope this helps!

Answer:

x = 2.7 feet

Step-by-step explanation:

Use tan to find the value of x

tan 44 = [tex]\frac{x}{2.8}[/tex]      Simplify

0.9657 = [tex]\frac{x}{2.8}[/tex]    Multiply both sides by 2.8

x = 2.70396    Round this answer to the nearest tenth of a foot

x = 2.7 feet