1
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match the expressions with their simplified versions.

for a rational, we find the vertical asymptotes where its denominator is 0, thus

(x-2)(x+1) = 0, gives us two vertical asymptotes when that happens, x = 2 and x = -1.

if we expand the denominator, we'll end  up with a quadratic equation, namely a 2nd degree equation, whilst the numerator is of 3rd degree.  Whenever the numerator has a higher degree than the denominator, the rational has no horizontal asymptotes, however when the numerator is exactly 1 degree higher like in this case, it has an oblique asymptote instead.

Answer:

A

x=2,x=-1

Step-by-step explanation:

Answer:

a. 35≤x≤45 where x represents speed

b. 16≤y≤100 where y represents age

Step-by-step explanation:

a. Explain how compound inequalities can be use to describe the speed restrictions on roads.  

x represents the speed, then

the maximum speed is 45 miles

x≤45

the minimum speed is 35 miles

x≥35

Both inequalities represent the speed restrictions

The compound inequality will be:

35≤x≤45

b. Include a compound inequality describing a possible age restriction for driving on roads. Describe what this represents. (Minimum driving age is 16 years, and most drivers stop renewing their licenses by age 100.)

Let y be the age

then

Minimum driving age is 16 years

y≥16

most drivers stop renewing their licenses by age 100.)

y≤100

The compound inequality will be:

16≤y≤100 ..

Answer:

a. 35 ≤ x ≤ 45

b. 16 ≤ x ≤ 100.

Step-by-step explanation:

On a road in the city of Madison, the maximum speed is 45 miles per hour and minimum speed is 35 miles per hour.

If x represents the speed then

x ≥ 35

and x ≤ 45 are the inequalities to represent the speed restrictions.

(a) combined inequality will be 35 ≤ x ≤ 45

    which shows the combined speed limits on the road.

(b) Let the driving age of a driver is x years.

     So by the statement x ≥ 16 and x ≤ 100

When we combine these inequalities 16 ≤ x ≤ 100.

Answer: D: 672

Step-by-step explanation:

use the equation C = 2πR, where C is circumference and R is radius

re-write the equation with 107 instead of R

C=2*π*107

then solve (use 3.14 for pi and round up)

3.14*2=6.28

6.28*107=671.96

then round up to get 672

I hope this helps!

The circumference of a circular park with a radius of 107 m, calculated with the formula Circumference = 2 * π * radius, is approximately 672 m.

The circumference of a circle is calculated by using the formula: Circumference = 2 * π * radius. In this case, the radius of the circular park is given as 107 m. Substituting the radius into the formula, we obtain: Circumference = 2 * 3.14 * 107 which equals approximately 672 m. So, to the nearest meter, the circumference of the park is 672 m.

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Answer:

the answer to your question is A.

Answer:

Option A. is correct

Step-by-step explanation:

A rational fraction is an algebraic fraction such that both the numerator and denominator are polynomials.

Here, a graph is given .

We need to find which of the given rational functions is graphed in image.

On x-axis, 1 unit = 2 units

Clearly, we can see the graph is not defined at point x = - 4 and at x = 1.

Corresponding to x = - 4, factor is (x+4) .

Corresponding to x = 1, factor is (x-1) .

So, this graph is of the rational fraction [tex]F(x)=\frac{1}{(x-1)(x+4)}[/tex]

Hence, Option A. is correct

Answer:

Step-by-step explanation:

<, > - dotted line

≤, ≥ - solid line

<, ≤ - shaded region below the line

>, ≥ - shaded region above the line

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

[tex]y\leq-2x+10[/tex]

Draw the solid line [tex]y=-2x+10[/tex].

Shade region below the line.

for x = 5

[tex]y=-2(5)+10=-10+10=0\to(5,\ 0)[/tex]

for x = 0

[tex]y=-2(0)+10=0+10=10\to(0,\ 10)[/tex]

[tex]y>\dfrac{1}{2}x-2[/tex]

Draw the dotted line [tex]y=\dfrac{1}{2}x-2[/tex]

Shade region above the line.

for x = 0

[tex]y=\dfrac{1}{2}(0)-2=0-2=-2\to(0,\ -2)[/tex]

for x = 4

[tex]y=\dfrac{1}{2}(4)-2=2-2=0\to(4,\ 0)[/tex]

Look at the picture

The solutions: A, C, D, K

Answer:

15.1792 or 15.18

Step-by-step explanation:

14.32 timex 6% or .06 is 0.8592. You add .8592 to 14.32 and get 15.1792 or 15.18 :)

Answer:

$15.18

Step-by-step explanation:

To find the sales tax, you would multiply $14.32 by 6%.

6% = 0.06

0.06*14.32 =  0.8592

Then add the sales tax to the original price to find how much the total costs.

0.8592 + $14.32 = $15.1792

Round $15.1792 to the nearest cent since its money.

So its $15.18

Answer:

c) 18 + 45m

Step-by-step explanation:

9(2+5m)

We multiply the 9 by each term inside the parentheses

9*2 + 9*5m

18+45m

9(2+5m)

Multiply the bracket with 9

9(2)+9(5m)

18+45m

Answer : 18+45m-c)

Check the picture below.

make sure your calculator is in Degree mode.

Answer:

53.06°

Step-by-step explanation:

In triangle ABC, since ∠CAB is 90 degree, therefore consider AB to be the opposite and AC be the adjacent.

Now to find the angle, ∠ACB using trigonometry,

tan θ = opposite / adjacent

tan θ = AB / AC

given AC = 6 and AB = 8

tan θ = 8 / 6

tan θ = 1.33

therefore, θ = [tex]tan^{-1}[/tex] 1.33

                 θ = 53.06°

Therefore, the bearing from post C to post B is 53.06°

Final answer:

The modified surface area of a square pyramid, with the side length tripled and slant height divided by 5, is calculated as 9s^2 + 6sl/5, where 's' is the original side length and 'l' is the original slant height.

Explanation:

To find the modified surface area of the square pyramid when the side length is tripled and the slant height is divided by 5, we need to recall the formula for the surface area of a square pyramid. The original surface area formula for a square pyramid is given by the sum of the area of the base plus the area of the four triangular faces, which can be represented as:

Surface Area = base area + 4 × (1/2 × slant height × side length)

For the modified pyramid, if the original side length is 's' and the slant height is 'l', tripling the side length would make it '3s' and dividing the slant height by 5 would make it 'l/5'. Using these new values, the formula for the modified surface area becomes:

Modified Surface Area = (3s)^2 + 4 × (1/2 × (l/5) × 3s)

Simplifying, we get:

Modified Surface Area = 9s^2 + 6s(l/5)

This accounts for the nine-fold increase in the base area (since area is proportional to the side length squared) and the change in the area of the triangular faces.

Answer:

The solution is the point (-4,-2)

Step-by-step explanation:

we have

-0.1x-0.8y=2 -----> equation A

0.6x-0.5y=-1.4 ----> equation B

Solve by graphing

Remember that the solution of the system of equations by graphing is the intersection point both lines

using a graphing tool

The intersection point is (-4,-2)

see the attached figure

therefore

The solution is the point (-4,-2)

8 out of 12 people were happy.

8/12 reduces to 2/3 of the people were happy.

Multiply the total people surveyed by 2/3:

126 x 2/3 = (126 x 2) /3 = 252/3 = 84

84 people were happy.

Answer:

[tex]\sin x=1[/tex]

Step-by-step explanation:

The given function is

[tex]\cos^2x+2\sin x-2=0[/tex]

We use the identity: [tex]\sin^2x+\cos^2x=1[/tex] [tex]\implies \cos^2x=1-\sin^2x[/tex]

This implies that:

[tex]1-\sin^2x+2\sin x-2=0[/tex]

[tex]-\sin^2x+2\sin x-1=0[/tex]

[tex]\sin^2x-2\sin x+1=0[/tex]

[tex](\sin x-1)^2=0[/tex]

[tex]\sin x-1=0[/tex]

[tex]\sin x=1[/tex]

Hence the numerical value of one trigonometric function(the sine function) is 1

Answer:

Step-by-step explanation:

From

\cos^2x+2\sin x-2=0

Using the identity, we have: \sin^2x+\cos^2x=1 \implying \cos^2x=1-\sin^2x

Opperating:

1-\sin^2x+2\sin x-2=0

-\sin^2x+2\sin x-1=0

\sin^2x-2\sin x+1=0

(\sin x-1)^2=0

\sin x-1=0

\sin x=1

A numerical value for x would be for example x=90 degrees or pi/2 (radians)

And this answer is valid for every angle x=90+360n (n=0,1,2,3,etc) or x=pi/2+2pi*n (n=0,1,2,3,etc)

Answer:

0 if the function is [tex]F(x)=\frac{4-x^2}{4-x}[/tex].  Please tell me if this is not the right function.

Step-by-step explanation:

I'm assuming the function is [tex]F(x)=\frac{4-x^2}{4-x}[/tex].  Please tell me if it is not the right assumption.

F(-2) means to use the expression called F and replace x with -2.

Like this:

[tex]F(-2)=\frac{4-(-2)^2}{4-(-2)}=\frac{4-4}{4+2}=\frac{0}{6}=0[/tex]

So the value of F(-2) is 0.

F(-2)=0.

Answer:

3 gallons per mile, slope of 3

Step-by-step explanation:

To find out how many gallons the train uses per mile, look at the point (50,150). If you know that the train used 150 gallons to travel 50 miles, do 150/50 to get an answer of 3 gallons per mile.

For the second part, you know that as x increases by 1 (miles traveled) y (gallons) increases by 3, so therefore the slope is 3. You can also check this value by plugging in the points (150,450) and (50,150) into the [tex]m=\frac{x_{2}  - x_{1}}{y_{2}  - y_{1}}[/tex]

Answer:

I am sure it is D

The hexagon is made up of two trapezoids, each having the following dimensions:

[tex]a=12\text{ m}\\b=5\text{ m}\\h=4\text{ m}[/tex]

So, its total area is the sum of the areas of those two trapezoids.

[tex]A_h=2A_t=2\cdot\dfrac{1}{2}(a+b)h=(a+b)h\\A_h=(12+5)\cdot 4=68\text{ m}^2[/tex]

Answer:

Step-by-step explanation:

No, the graph fails the vertical line test.

If a vertical line intersects a curve more than once then the curve does not represent a function. If all vertical lines intersect a curve at most once then the curve represents a function.

Answer:

7 high priced speakers

21 Low priced speakers

Step-by-step explanation:

170x7 =1190

90x21=1890

1890+1190=3080

90’s are the low speaker docks, and 170’s are the high speaker docks.

3 times 90 is 270, plus 170 is 440

3080 divided by 440 is 7, the number of 170’s they sold. 7 times 3 is 21, the number of 90’s they sold.

Answer:

40 ft

Step-by-step explanation:

We can use ratios to solve this problem.  Put the scale over the actual size

1/4 inch           2 inches

-------------- = ----------------

5 ft                  x ft

Using cross products

1/4 x = 2 *5

1/4 x = 10

Multiply each side by 4

4*1/4 x = 4 * 10

x = 40

The wall is 40 ft

Answer:

[tex]x=-5/7[/tex]

Step-by-step explanation:

we have

[tex]f(x)=7x+5[/tex] ----> The degree of this polynomial is 1 (linear equation)

Remember that

The zero of the polynomial is the value of x when the value of f(x) is zero

so

For f(x)=0

[tex]0=7x+5[/tex]

solve for x

[tex]x=-5/7[/tex] ----> the zero of the polynomial or x-intercept

Answer:

The answer should become clearer once we convert everything to a common denominator:

14/15,12/15,10/15,8/15

We can now see we have an arithmetic sequence with common difference 2/5. The next term is thus

6/15=2/5

2/5 is the answer

Answer:

2/5

Step-by-step explanation:

because I someone didn't let me solve it the way I normally do;

you need to convert all of them to a common denominator;

making them [tex]\frac{14}{15}[/tex], [tex]\frac{12}{15}[/tex], [tex]\frac{10}{15}[/tex], [tex]\frac{8}{15}[/tex]

making the next one [tex]\frac{6}{15}[/tex] or [tex]\frac{2}{5}[/tex]

Answer:

[tex]\large\boxed{x\in\left(-\dfrac{13}{3},\ \infty\right)}[/tex]

Step-by-step explanation:

[tex]4(x+1)+4>x-5\qquad\text{use the distributive property}\\\\4x+4+4>x-5\\\\4x+8>x-5\qquad\text{subtract 8 from both sides}\\\\4x>x-13\qquad\text{subtract}\ x\ \text{from both sides}\\\\3x>-13\qquad\text{divide both sides by 3}\\\\x>-\dfrac{13}{3}\to x\in\left(-\dfrac{13}{3},\ \infty\right)[/tex]

Subtract the rental fee, then divide the left over amount by the cost per hour.

38-10 = 28

28 / 7 = 4

The answer is 4 hours.

Answer:

Option D is the answer.

Step-by-step explanation:

Volume of sphere is given as:

[tex]\frac{4}{3}\pi r^{3}[/tex]

Case 1:

Lets say the radius is 3 cm.

Volume = [tex]\frac{4}{3}\times3.14\times3\times3\times3[/tex]

= 113.04 cubic cm

Case 2:

Lets say the radius is twice 3 cm that is 6 cm.

Volume = [tex]\frac{4}{3}\times3.14\times6\times6\times6[/tex]

= 904.32 cubic cm.

The volume of the larger ball is [tex]\frac{904.32}{113.04}[/tex] = 8 times the smaller one.

So, the answer is option D : 8 times.

Answer:

≈ 7854 m²

Step-by-step explanation:

The surface area (A) of a sphere is calculated as

A = 4π r² ← r is the radius

here diameter = 50, hence r = 25, so

A= 4π × 25²

  = 4π × 625 = 2500π ≈ 7854 m²

Answer:

The surface area of the structure ≅ 7854 meter²

Step-by-step explanation:

* Lets revise the surface area of the sphere

- The surface area of a sphere is the same as the lateral surface area

  of a cylinder having the same radius as the sphere and a height

  equal the length of the diameter of the sphere.

- The lateral surface area of the cylinder is 2πrh

- The height of the cylinder = 2r , then the surface area of the sphere is

  2πr(2r) = 4πr²

* Now lets solve the problem

∵ The sphere has diameter = 50 meters

∵ The diameter is twice the radius

∴ 2r = 50 meters ⇒ divide both sides by 2

∴ r = 25 meters

∵ The surface area of the sphere = 4πr²

∴ The surface area of the sphere = 4π(25)² = 7853.98

∴ The surface area of the sphere ≅ 7854 meters²

Answer:

Step-by-step explanation:

Let f(x) = x^7 - 4e^x .

Then f '(x) = 7x^6 - 4e^x, and

f "(x) = 42x^5 - 4e^x, and so:

f '(-1) = 7(-1)^6 - 4e^(-1)  =  7 + 4/e

and

f "(x) = 42(-1)^5 - 4e^(-1)  =  -42 + 4/e

Answer:

Option D; (x, y) -> (x, -y); A' is at (-5, -1)

.

Step-by-step explanation:

Reflection is one of the linear transformations which reflect any object along the line of reflection. The size of the shape remains the same but the orientation changes.

Reflection along the x-axis means that the sign of y-coordinate changes but the sign of the x-coordinate remains same.

From figure we identified the coordinates of point A:

A (-5,1)

So, A' will be (x,-y)

=> A' = (x,-y) = (-5,-1)

So, Option D (x, y) -> (x, -y); A' is at (-5, -1) is correct.

Answer:

Option D (4, -5)

Step-by-step explanation:

This question can be solved by various methods. I will be using the hit and trial method. I will plug in all the options in the both the given equations and see if they  balance simultaneously.

Checking Option 1 by plugging (-4, -5) in the first equation:

-2(-4) + 6(-5) = -38 implies 8 - 30 = -38 (not true).

Checking Option 2 by plugging (-5, 4) in the first equation:

-2(-5) + 6(4) = -38 implies 10 + 24 = -38 (not true).

Checking Option 3 by plugging (1, -6) in the second equation:

3(1) - 4(-6) = 32 implies 3 + 24 = 32 (not true).

Since all the options except Option 4 have been ruled out, therefore, (4,-5) is the correct answer!!!

Answer:

Step-by-step explanation:

14n+6p-8n=18p

6n=12p

n=2p

Answer:

Step-by-step explanation:

[tex]14n+6p-8n=18p\qquad\text{combine like terms}\\\\(14n-8n)+6p=18p\qquad\text{subtract}\ 6p\ \text{from both sides}\\\\6n=12p\qquad\text{divide both sides by 6}\\\\n=2p[/tex]