Simplify: x+2/x2-6x-16 ÷ 1/9x

Answers

Answer 1
[tex]\dfrac{x+2}{x^2-6x-16}:\dfrac{1}{9x}=\dfrac{x+2}{x^2-8x+2x-16}\cdot9x=\dfrac{x+2}{x(x-8)+2(x-8)}\cdot9x\\\\=\dfrac{x+2}{(x-8)(x+2)}\cdot9x=\dfrac{1}{x-8}\cdot9x=\dfrac{9x}{x-8} [/tex]

Related Questions

For these two rules, the second number in the ordered pair is always three times greater than the first number. If the relationship between the two numbers in each ordered pair is the same, the graph will be: Not graph-able A straight line A circle An exponential curve A parabolic curve

Answers

well this factor has to the answer b.) hope I helped.

Gina is a tour boat operator and she wants to know the mean age of all the people in her tour group.

She randomly selects 8 people in the group and asks them for their ages. Their responses are 19, 27, 25, 21, 44, 22, 45, and 34.

What is the best estimate of the mean age of all the people in the tour group?



Round to the nearest whole number.

Answers

mean means average, so add all the ages together and divide by the number of people asked:

19 + 27 + 25 + 21 + 44 + 22 + 45 + 34 = 237

237 / 8 = 29.625 = 30 years

A fire truck has a ladder that can extend to 60 feet in length. the ladder can be safely raised to a maximum angle of 75o with the horizontal. disregarding the height of the fire truck itself, which is closest to the maximum height that the ladder can safely reach?

Answers

This is a problem on right triangle trigonometry. The hypotenuse is 60 feet and the unknown side is opposite the given 75-degree angle. Given these values, we will use the sine function. That is 
     [tex]sin\left(75^{\circ} \right)=\frac{h}{60}[/tex]

     [tex]h=60\cdot sin\left(75^{\circ} \right)=58\:feet[/tex]

The maximum height that the ladder can safely reach is closest to 58 feet

Final answer:

Using trigonometry and the sine function, the maximum height that the ladder can reach when raised to a 75-degree angle with a length of 60 feet is approximately 58 feet.

Explanation:

To determine the maximum height that a fire truck ladder can safely reach when it is extended to 60 feet in length and raised to a maximum angle of 75 degrees with the horizontal, we would use trigonometry, specifically the sine function. The sine of an angle in a right triangle is equal to the opposite side (height in this case) divided by the hypotenuse (the length of the ladder).
Therefore, the maximum height (h) can be calculated using the formula:

h = Ladder Length × sin(Angle)

Where:

Ladder Length is 60 feet

Angle is 75 degrees

Plugging in our values we get:

h = 60 feet × sin(75 degrees)

Using a calculator, we find that:

sin(75 degrees) is approximately 0.9659.

Therefore:

h ≈ 60 feet × 0.9659

h ≈ 57.95 feet

The maximum height the ladder can safely reach when disregarding the height of the fire truck itself is approximately 58 feet.

A survey of 1,000 people was done by New York Times. 80% of the people did not know the name of their representative in Congress. How many of the 1,000 people knew the name of the Congressman?

Answers

The answer is 20% of the 1000 people, as 100%-80%+20%. 1000 times 0.2 equals 200 people that knew the name.

Orville traveled at a speed that was twice as fast as randy, Orville traveled 240 miles in one hour less than it took randy to travel 150 miles. What were the speed and time it took for both Orville and randy?

Please answer will give brainliest

Answers

Let
x-------> Orville speed
y-------> Randy speed
t--------> Randy time

we know that
speed=distance /time
Orville traveled at a speed that was twice as fast as randy
so
x=2y------> equation 1

speed Orville
x=240/(t-1)------> equation 2

speed Randy
y=150/t------> equation 3

substitute equation 1 in equation 2
2y=240/(t-1)------> y=120/(t-1)----------> equation 4

equate equation 3 and equation 4
150/t=120/(t-1)------> 150*(t-1)=120*t----> 150*t-120*t=150
30*t=150-----> t=5 hours

Orville speed and time
x=240/(t-1)-----> 240/(4)----> 60 miles/hour
Orville speed is 60 miles/hour
Orville time is (t-1)----> 5-1-----> 4 hour

Randy speed and time
y=150/t-----> 150/5----> 30 miles/hour
Randy speed is 30 miles/hour
Randy time is t-----> 5 hours

the answers are
a) Orville speed is 60 miles/hour
b) Orville time is 4 hours
c) Randy speed is 30 miles/hour
d) Randy time is 5 hours


match each graph with its corresponding equation

Answers

The graphs match the equations as follows:

Graph A: (−x+3)^2 -2

Graph B: (x−2)^2+3

Graph C : −(x+2)^2 +3

Graph D : 2(x−2)^2 +3

Equation (−x+3)^2 -2:

This equation is in the form of a quadratic function, y=a(x−h) ^2+k, where (h ,k) is the vertex of the parabola.

The vertex of the parabola is at (3,1), which matches the vertex of Graph A.

The coefficient a is negative, which tells us that the parabola opens downward.

The constant term k is −2, which tells us that the minimum value of the parabola is −2.

Equation (x−2)^2+3 :

This equation is in the form of a quadratic function, y=a(x−h) ^2 +k, where (h, k) is the vertex of the parabola.

The vertex of the parabola is at (2,3), which matches the vertex of Graph B. The coefficient a is positive, which tells us that the parabola opens upward.

The constant term k is 3, which tells us that the minimum value of the parabola is 3.

Equation  −(x+2)^2 +3:

This equation is in the form of a quadratic function, y=a(x−h) ^2 +k, where (h, k) is the vertex of the parabola.

The vertex of the parabola is at (−2,3), which matches the vertex of Graph C.The coefficient a is negative, which tells us that the parabola opens downward.

The constant term k is 3, which tells us that the maximum value of the parabola is 3.

Equation  2(x−2)^2 +3 :

This equation is in the form of a quadratic function, y=a(x−h) ^2 +k, where (h ,k) is the vertex of the parabola.

The vertex of the parabola is at (2,3), which matches the vertex of Graph D. The coefficient a is positive and multiplied by 2, which tells us that the parabola opens upward and is stretched vertically by a factor of 2.

The constant term k is 3, which tells us that the minimum value of the parabola is 3.

What values for xx and yy make △MNO≅△PRT▵MNO≅▵PRT?
Triangles MNO and PRT

Answers

Unfortunately, you have not provided a diagram of the triangles, therefore, I cannot give a precise answer.
However, I can help you understand how to solve such problem and you can apply the explanation in the triangles you have.

Now, when writing congruent triangles, the order of the letters is very important. This is because each side/angle in the first triangle is congruent to the corresponding side/angle in the second one.

In the given, we have:
ΔMNO ≈ ΔPRT
This means that:
angle M = angle P
angle N = angle R
angle O = angle T
MN = PR
NO = RT
MO = PT

Now, to get x and y, all you have to do is make use of the above equal angles/sides.
Equate the corresponding angles/sides having the variables x and y and solve for them

Hope this helps :)

At Martina's auto shop, it takes her 15 minutes to do an oil change and 18 minutes to do a tire change. Let x be the number of oil changes she does. Let y be the number of tire changes she does. Using the values and variables given, write an inequality describing how many oil changes and tire changes Martina can do in at most 3 hours ( 180 minutes).

Answers

Hello!

You want to know how much she can do in 180 minutes

She can do an oil change in 15 minutes

She can do a tire change in 18 minutes

Based on this information you can make the inequality

[tex]15x + 18y \leq 180[/tex]

The answer is [tex]15x + 18y \leq 180[/tex]

Hope this helps!
15x + 18y ≤ 180 

It's at most 180 minutes so left side is 'less than or equal to 180'.

Two angles of a triangle have the same measure and the third angle is 72degrees greater than the measure of the other two. find the measure of each angle.

Answers

The two shorter angles = 36 degrees. 

The longer anger = 108 degrees. 

Let me know if you would like me to explain how I got this.

If an arithmetic series has a1 equals=44​, d equals 5, and n=24​, what is sn​?

Answers

Sn = 44 + 5(24-1) = 159 is the answer

In how many ways can the letters of the word BANANA be rearranged such that the new word does not begin with a B?

Answers

First arrange the words in order:

AAABNN

so there are 3 A's, 1 B and 2 N's.

If there were no constraints,

Number of permutations = (3+1+2)!/(3!1!2!)=6!/(6*1*2)=720/(6*2)=60

Number of words that begin with B is to take out the B, that leaves us with

AAANN => 3 A's and 2 N's

=> 5!/(3!2!) = 120/(6*2)=10

Therefore the number of words that do NOT begin with B is

60-10 = 50 ways

A right triangle has sides measuring 5 inches, 12 inches, and 13 inches. What is the area, in square inches, of this triangle ?

Answers

Please look up and apply Heron's Formula.  Start by calculating s, where
        a  +  b  +  c
s = -------------------
               2

Then calculate A:

A = sqrt[ s(s-a)(s-b)(s-c) ]

Final answer:

The area of a right triangle with sides of 5 inches and 12 inches as the base and height, respectively, is 30 square inches, calculated using the formula A = (base × height) / 2.

Explanation:

The area of a right triangle is calculated by multiplying one-half the base by the height: A = (base × height) / 2.

In the case of a right triangle with sides measuring 5 inches, 12 inches, and 13 inches, the 5-inch and the 12-inch sides are the legs and thus can be used as the base and height. Using the formula for the area of a right triangle:

A = (5 × 12) / 2

A = 60 / 2

A = 30 square inches

Therefore, the area of this triangle is 30 square inches.

Brainliest for correct answer!
Which strategy can be used to solve this problem? Dan has dogs named Chester and Ally. Together the two dogs weigh 40 pounds. Chester weighs 4 pounds more than Ally. How much does Ally weigh? A. Write a number sentence. Let p represent the amount that Ally weighs. (4 + 40) ÷ 2 = p B. Guess and test. Guess that Ally weighs 20 pounds. Add 4 to 20 to find out how much Chester weighs (24). Add Chester's and Ally's weights (44). Ask if the sum is more or less than 40. Revise your guess so it is 19 and test your answer again. Repeat the process until you have the correct answer. C. Draw a diagram. Draw 40 dots to represent how much the two dogs weigh altogether. Divide the dots into 2 equal groups and then divide one of the groups by 4.

Answers

Let
C = weight of Chester
A = weight of Ally

From the information given,
Both dogs weigh 40  pounds. Therefore,
C + A = 40 --- (1)

In addition, Chester weighs 4 pounds more than Ally. Therefore,
C = A + 4 ---- (2)

Substituting for C from equation (2) in equation (1);
A + 4 + A = 40
2A + 4 = 40
2A = 40 -4 = 36
2A = 36
A = 36/2
A = 18 pounds

Therefore, Ally weighs 18 pounds.

Describe the number of solutions for each system of equations graphed
below

Answers

The solution of the system of equations means that following:
1- In case we are dealing with system of equations, the solution would be the point of intersection of the two graphs
2- In case we're dealing with only one equation, the solution would be the points of intersection of the graph with the x-axis

Graph (a):
The graph is for a system of equations (two lines). Therefore, the solution would be the point of intersection of the two lines.
From the graph, we can note that there is only one point of intersection between the two lines (-3,-1). Therefore, the system of equations has only one solution

Graph (b):
The graph is for a system of equations (two lines). Therefore, the solution would be the point of intersection of the two lines.
From the graph, we can note that the two lines are parallel. This means that they will never intersect. Therefore, the system of equations has no solutions

Graph (c):
The graph is for a single line. Therefore, the solution(s) would be the point(s) that make the overall equation equal to zero, i.e. point(s) of intersection with the x-axis.
From the graph, we can note that the line intersects with the x-axis only once at point (2,0). This means that the line has only one solution.

Hope this helps :)

QUICK QUESTION PLEASE. help.

The length of a rectangle is six times its width. If the perimeter of the rectangle is 112 ft, find its area.

Answers

lw=A

2l+2w=112
l=6w
2(6w)+2w=112
12w+2w=112
14w=112
w=8
l=48
A=384 ft^2


The area of the rectangle will be 384 ft². Square feet and other similar units are used to measure area.

What is the area?

The space filled by a flat form or the surface of an item is known as the area.

The number of unit squares that cover the surface of a closed-form is the figure's area.

Let the length of a rectangle is,l and the width of a rectangle be,w

Given condition;

l=6w

The perimeter of the rectangle  = 112 ft,

⇒2l+2w=112

According to condition;

2(6w)+2w=112

12w+2w=112

14w=112

w=8

The length of a rectangle is;

l=6w

l=48

Area of rectangle = length × width

A =lw

A=6 × 48 ft

A=384 ft^2

Hence the area of the rectangle will be 384 ft².

To learn more about the area, refer to the link;

https://brainly.com/question/11952845

#SPJ2

A ceo of awesome coolers owns 8 pairs of pants, 10 shirts, 7 ties and 4 jackets. how many different outfits can he wear to the office if he must wear one of each item?

Answers

I think it is 8 because of the pants and shirts plus, the ties you can wear everytime you wear a pair the goes for the jacket too.

A) how many ways can the letters in the word computer be arranged in a row?
b.how many ways can the letters of the word computer be arranged if the letters co must remain next to each other as a unit?

Answers

A.

The are 8 total letters:
8!= 8*7*6*5*4*3*2*1
=40320

B.

The are still 8 total letters, but the 1st 2 are constants, CO. So what would scramble the remaining letters as such.

6!= 6*5*4*3*2*1
=720

Hope this helps

The permutation is defined as the arrangement number or order in which rearrangement of  element in an order list.

(a) The letters in the word computer be arranged in a row is 40320.

(b) The letters of the word computer be arranged 5040 ways.

Given:

The given latter is COMPUTER.

How to find the permutation of latter?

(a)

There are 8 letter in word COMPUTER. Calculate the number of ways in which we can arrange 8 letters.

[tex]8!=8\times7\times6\times5\times4\times3\times2\times1\\8!=40,320.[/tex]

Thus, the letters in the word computer be arranged in a row is

(b)

As per the question if we treat CO as a unit then there will only seven letters effective.

[tex]7!=7\times6\times5\times4\times3\times2\times1\\7!=5,040[/tex]

Thus, the letters of the word computer be arranged 5040 ways.

Learn more about permutation here:

https://brainly.com/question/1216161

Find the 12th term in the following geometric sequence. 0.75, 1.5, 3, 6, . . .

Answers

the pattern doubles, .75 x 2= 1.5. 1.5 x 2= 3, and so on. so the answer would be 1,536

Answer:

1536

Step-by-step explanation:

Given : A geometric sequence 0.75, 1.5, 3, 6, . . .

To Find:Find the 12th term

Solution:

0.75, 1.5, 3, 6, . . .

First term =a = 0.75

Common difference = [tex]r = \frac{a_3}{a_2} =\frac{a_2}{a_1}=\frac{1.5}{0.75}=\frac{3}{1.5}=2[/tex]

nth term of G.P. = [tex]a_n=a r^{n-1}[/tex]

Where a = First term = 0.75

r = common difference = 2

Substitute n = 12

[tex]a_{12}= 0.75 (2)^{12-1}[/tex]

[tex]a_{12}= 0.75 (2)^{11}[/tex]

[tex]a_{12}= 1536[/tex]

Hence the 12th term in the geometric sequence. 0.75, 1.5, 3, 6, . . . is 1536.

Anyone know what the answer is?

Answers

the answer is D!!! hope this helps 


a glass jar contains 1 red, 3 green, 2 blue, and 4 yellow marbles. if a single marble is chosen at random from the jar, what is the probability that it is red

Answers

To find the probability, you need to divide the amount of red marbles by the total amount of marbles. 

1/10 = 0.1. 

The probability of choosing a red marble is 0.1, or 10%

[tex] |\Omega|=10\\
|A|=1\\\\
P(A)=\dfrac{1}{10}=10\% [/tex]

please help asap 50 pts

Answers

If you factor the expression by grouping you should get (3g - 5) (2g +7)

Steps:
1. Factor 11 out of 11g
6g^2 + 11 (g) - 35

2. Rewrite 11 as -10 plus 21
6g^2 + (-10 + 21) g - 35

3. Apply the distributive property
6g^2 + (-10g + 21g) - 35

4. Remove parentheses
6g^2 - 10g + 21g - 35

5. Group the first two and the last two terms
(6g^2 - 10g) + (21g - 35)

6. Factor out the greatest common factor from each group
2g (3g - 5) + 7 (3g - 5)

7. Factor out the greatest common factor, 3g - 5
(3g - 5) (2g + 7)


Therefore the answer is A
[tex]6g^2+11g-35=6g^2+21g-10g-35=3g(2g+7)-5(2g+7)=(2g+7)(3g-5)[/tex]
Answer: A. (3g - 5)(2g + 7)

Find the surface area

Answers

if you notice, the figure has two hexagonal faces and 6 rectangles.

now the rectangles are just 4x9 each, so their area is just 6(4*9) for all 6.

the hexagons has a distance from the center perpendicular to a side of 7.8, namely the apothem is 7.8, and since each side is 9 km long, the perimeter is 9+9+9+9+9+9.

since the area of a regular polygon is (1/2)(apothem)(perimeter), we can simply get the area of those two hexagons and the area of the rectangles, sum them up, and that's the surface area of the hexagonal prism.

[tex]\bf \stackrel{\textit{6 rectangles}}{6(4\cdot 9)}~~~~+~~~~\stackrel{\textit{2 hexagons}}{2\left[ \cfrac{1}{2}(7.8)(54) \right]}[/tex]

Find the equation of the line whose x-intercept is 8 and y-intercept is -2. write the equation in slope-intercept form.

Answers

Two points on this line are (8,0) and (0,-2).  The slope is thus

         0-(-2)
m = ---------- = 1/4
         8-0

The equation of the line is then y-0 = (1/4)(x-8), or y = (1/4)X - 2 (in slope-intercept form).

To determine the equation of the line with x-intercept 8 and y-intercept -2, the slope is calculated to be 1/4. Thus, the line's equation in slope-intercept form is y = (1/4)x - 2.

To find the equation of a line with an x-intercept of 8 and a y-intercept of -2, we'll first determine the slope of the line (m) and then use the slope-intercept form (y = mx + b).

Two points on this line are (8,0) and (0,-2). The slope (m) of a line is calculated by the change in y divided by the change in x, which in this case is
(0 - (-2)) / (8 - 0) = 2 / 8 = 1 / 4.

Now we know the slope is 1/4 and the y-intercept (b) is -2, so the equation of the line in slope-intercept form is:

y = (1/4)x - 2

Mr ong spent $960 of his salary on food and transport.He spent 1/4 of his remaining money on clothes.He then had 1/3 of his salary left.How much was his salary?

Answers

I pass the solution
49601
43
culculate the value approximate
×11.53,51163

I hope his helps

Use the graphs of f(x) =2/x and g(x)=1/-3-x to determine the solutions to f(x) = g(x).

A) (-2, -1)
B) (-2, 1)
C) (2, -1)

Answers

we have that
f(x) =2/x
and
g(x)=1/(-3-x)

we know that
the solutions to f(x) = g(x) is the intersection of both graphs

the intersection of both graphs is the point (-2,-1)

the answer is the option
A) (-2, -1)

see the attached figure

which of the following are examples of exponential decay

1) the population of a florida is increasing by 43% each year

2) the pesticide DDT has half life if 15 years

3) March madness has 64 teams in the bracket. Each round half the teams are eliminated

4) after an antibiotic is added to culture of bacteria, the number of bacteria is reduced by half every three hours

5) a tree frog population doubles every three weeks

Answers

4) after an antibiotic is added to a culture of bacteria, the # of bacteria is reduced by half every 3 hours
The correct answers are:
B)
C)
D)


An ellipse has a center at the origin, a vertex along the major axis at (0, 17), and a focus at (0, −8). Which equation represents this ellipse?

Answers

we know that
Since the focus and vertex are above and below each other, rather than side by side, I know that this ellipse must be taller than it is wide.
Then 
a² will go with the y part of the equation
Also, since the focus is 8 units below the center, then c = 8
since the vertex is 17 units above, then a = 17
The equation b² = a² – c² gives me
b²=17²-8²-----> b²=225
the equation is
y²/a²+x²/b²=1------> y²/289+x²/225=1

the answer is
y²/289+x²/225=1

see the attached figure

Answer:

D

Step-by-step explanation:

Refer to the following illustration to answer this Question.

The center of a circle is at (−3, 1) and its radius is 9.

What is the equation of the circle?

Answers

The answer is (x + 3) 2 + (y − 1) 2 = 81

A plane intersects a double-napped cone such that the plane intersects both nappes through the cone's vertex. which terms describe the degenerate conic section that is formed? select each correct answer. degenerate parabola pair of intersecting lines point line degenerate hyperbola degenerate ellipse

Answers

It is both of ...
  pair of intersecting lines
  degenerate hyperbola

Answer with explanation:

It is given that, a plane intersects a double-napped cone such that the plane intersects both Nappes through the cone's vertex.It also depends on how thick or thickness of the plane:

1.We can surely say that degenerate hyperbola will be formed,whatever be the thickness of Plane.

2. Two parallel lines=pair of intersecting lines ,because both ,A double napped cone and Plane is three dimensional shape.Instead of intersecting lines ,two parallel lines which we call pair of intersecting lines,  will be formed.

Determine whether quantities vary directly or inversely and find the constant of variation. A teacher grades 25 students essays in 4 hours. Assuming he grades at the same speed, how long will it take him to grade 35 essays?

Answers

It will take him 5.6 hours to grade 35 essays

To determine whether quantities vary directly or inversely, let's first define the variables:

Let x be which student essays had been graded.

Let y be the time taken to grade those essays.

In this case, it seems that the time taken to grade essays varies inversely with the number of essays graded. This means that as the number of essays increases, the time taken to grade them decreases, assuming the grading speed remains constant.

So, we can set up an equation using the constant of variation: xy = k

where the variation in the ratio is designated by k.

Given that the teacher grades 25 essays in 4 hours, we can use this information to find the constant of variation:

25 × 4 = k

k = 100

Now that we have the constant of variation, we can use it to find the time it takes to grade 35 essays:

35y = 100

y = (100/35)

y ≈ 2.857

So, it will take approximately 2.857 hours to grade 35 essays.

To determine if quantities vary directly or inversely, we compare how changes in one quantity affect the other.

Here, as the number of essays increases, the time taken to grade them decreases, indicating an inverse relationship.

Using the formula for inverse variation, xy = k, where x is the number of essays and y is the time taken, we find the constant of variation by substituting values: 25 × 4 = k, which gives k=100.

With the constant, we can find the time to grade 35 essays: 35y = 100.

Solving for y, we get y ≈ 2.857 hours. Therefore, it will take approximately 2.857 hours to grade 35 essays.

Complete Question:

Determine whether quantities vary directly or inversely and find the constant of variation. A teacher grades 25 students' essays in 4 hours. Assuming he grades at the same speed, how long will it take him to grade 35 essays?

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