Mathematics High School

Is the inequality always, sometimes or never true?
9(x+2) > 9(x-3)

answer is 2>3 and i said it's never true, right?

2. 6x-13 < 6(x-2)
answer is 6x-13 < 6x-12 my answer is sometimes

3. -6(2x-10) + 12x less than or equal to 180. im stuck.,

Answers

Answer 1
In order to understand if the inequalities are always, never or sometimes true, you need to perform the calculations:

A) 9(x+2) > 9(x-3)
9x + 18 > 9x - 27
the two 9x cancel out and you get:
+18 > -27
which is always true.

B) 6x-13 < 6(x-2)
6x - 13 < 6x - 12 
the two 6x cancel out and you get:
- 13 < -12
which is always true

C) -6(2x-10) + 12x ≤ 180
-12x +60 +12x ≤ 180
-12x and +12x cancel out and you get:
60 ≤ 180
which is always true.

All three cases are always true.

Related Questions

123456780-646472.657

Answers

122,810,307.343 is the answer

At the beginning of the spelling bee there were 60 participants. One-third of the participants were eliminated during the first round. One-fourth of the remaining participants were eliminate during the second round. One-sixth of the remaining participants were eliminated during the third round. How many participants were still cmpeting at the beginning of the fourth round?

Answers

Participants = 60
.
First round:
1/3 of 60 = 20
or
60 x 1/3
= 60/3
= 20
60 - 20 = 40
There are 20 participants that are eliminated on the first sound and 40 participants to move on to the second sound.
.
Participants = 40
Second round:
1/4 of 40 = 10
or
40 x 1/4
= 40/4
= 10
40 - 10 = 30
There are 10 participants that are eliminated on the second round and 30 participants that is moving on to the next round.
.
Participants = 30
Third round:
1/6 of 30 = 5
or
30 x 1/6
= 30/6
= 5
30 - 5 = 25
There are 5 participants that are eliminated on the third round and 25 participants to move on to the fourth round.
:)

By subtracting the eliminated participants in each round from the original number, it is determined that 25 participants were still competing at the beginning of the fourth round.

To find out how many participants were still competing at the beginning of the fourth round of the spelling bee, we need to perform some calculations based on the given percentages of participants eliminated in each round.

In the first round, one-third of the 60 participants were eliminated. This is 60 / 3 = 20 participants eliminated. So, 60 - 20 = 40 participants remained after the first round.In the second round, one-fourth of the remaining participants were eliminated. This is 40 / 4 = 10 participants eliminated. So, 40 - 10 = 30 participants remained after the second round.In the third round, one-sixth of the remaining participants were eliminated. This is 30 / 6 = 5 participants eliminated. So, 30 - 5 = 25 participants remained.

Therefore, 25 participants were still competing at the beginning of the fourth round.

Carpet sells for $3 per square foot and will cost you $810 to recarpet your rectangular room. if your room is 18 feet long, how many feet wide is it?

Answers

$810 ÷ 3 = 270 square feet
Area of the room is 270 square feet.

Area = 270 square feet,  length = 18 feet

Area = Length x Width
270 = 18 x width
Width = 280 ÷ 18
Width = 15 feet

The room is 15 feet wide.

Question 2: A circular picture is 8 inches in diameter. Part A What is the area of the picture in square inches? A. 4π square inches B. 8π square inches C. 16π square inches D. 32π square inches Part B A frame that is 2 inches wide surrounds the picture. What is the total area of the picture and the frame in square inches? A. 4π square inches B. 12π square inches C. 36π square inches D. 40π square inches

really important please answer correctly

Answers

Answers:
_______________________________________________________
Part A)  The correct answer is:  [C]:  " 16 [tex] \pi [/tex] square inches " .
_______________________________________________________
Part B)  The correct answer is:  [C]:  " 36 [tex] \pi [/tex] square inches " .
_______________________________________________________
Note:
_______________________________________________________
Part A)
_______________________________________________________
The formula for the area, "A", of a circle:

  A = [tex] \pi * r^2 [/tex]  ; 

    in which:
           
             " A = area of the circle" ; 
             " r = radius of the circle" ; 

            Note:  radius, "r" =  d / 2 ;  in which: "d" is the diameter of the circle ; 
 
            Given:  " d = 8 in " ;   " r = (8 in) / 2 = 4 in " ;
_________________________________________________
     A = [tex] \pi [/tex] * (4 in)² = [tex] \pi [/tex] * 4² * (in)² ;

                                                      = [tex] \pi [/tex] * (4*4) * (in²) ; 

                                                      = [tex] \pi [/tex] *  16 * in² ; 
________________________________________________________
   →   which is:  Answer choice:  [C]:  " 16 [tex] \pi [/tex] square inches " .
________________________________________________________
Part B)
________________________________________________________
       We now have a circular frame with a thickness of "2 inches" 
surrounding the original circle.  This adds "4 inches" to the diameter of that of the original circle in "Part A" —
    {Note: "2 inches on one side of the circle" ; PLUS "2 inches on the other side of the circle" ; equals "4 inches".}.

The diameter, "d", of this "new circle" ;
    =  "8 inches (that of the previous circle)" , PLUS "4 inches" , equals "12 inches" . 

  →  d = 12 in. ; 

The radius , "r" :   

   →  r = d/2 = 12 in / 2 = 6 in. 

    → r = 6 in.

The area, "A" of a circle:
______________________________________________________
   A = [tex] \pi [/tex] * r²  ; 

      = [tex] \pi [/tex] * (6 in)²  ;
 
      = [tex] \pi [/tex] * (6²) * (in²) ;

      = [tex] \pi [/tex] * (6*6) * (in²) ; 

      = [tex] \pi [/tex] * (36) * (in²) ; 
_______________________________________________________
  →  which is:  Answer choice:  [C]:  " 36 [tex] \pi [/tex] square inches " .
_______________________________________________________

You have a camera with a 16 mp resolution. how many pixels are represented by that resolution? 16 16 million 16,000 16 billion

Answers

MP equals megapixels. 1 megapixel equals 1 million pixels, so 16 MP is equal to 16 million megapixels. The more megapixels an image has, the clearer the picture will be when enlarged.

ANSWER: 16 million

Hope this helps! :)

Is it possible to take a cross section of a tetrahedron and get an octagon? Why or why not?
A.) Yes, because an octagon has eight sides, which is twice the number of faces on a tetrahedron.
B.) Yes, because a tetrahedron is symmetric about its center.
C.) No, because the only cross section that can result from a tetrahedron is a triangle.
D.) No, because the number of sides on the resulting shape cannot exceed the number of faces on the solid.

Answer: D.) No, because the number of sides on the resulting shape cannot exceed the number of faces on the solid.

Answers

Answer: The correct answer is Choice D.

A tetrahedron is another name for a triangular prism. When you look at a tetrahedron it only has 4 different sides. If you take a cross section, the largest number of sides that you could have would be 4. There is no way to get an 8 sided octagon.

Option (D) No, it is not possible to take a cross section of a tetrahedron and get an octagon because the number of sides on the resulting shape cannot exceed the number of faces on the solid. A tetrahedron, having only four faces, cannot have a cross section with eight sides like an octagon.

The question asks if it is possible to take a cross section of a tetrahedron and get an octagon. A tetrahedron is composed of four triangular faces, six edges, and four vertices. It is the simplest of all the ordinary convex polyhedra and the only one with fewer than 5 faces. The provided options suggest various reasons why an octagon could or could not result from a cross section of a tetrahedron. The correct answer is D: No, because the number of sides on the resulting shape cannot exceed the number of faces on the solid.

A cross section that intersects a solid will typically not have more sides than the number of faces of the solid itself. Since a tetrahedron has only four faces, any cross-section made through it cannot naturally have more than four sides, thus it cannot result in an octagon, which has eight sides. The concept of symmetry or the fact that an octagon has twice as many sides as a tetrahedron does not relate to the possibility of such a cross section.

A sphere is dilated by a scale factor of 1.5 to create a new sphere. How does the volume of the new sphere compare with the volume of the original sphere?
A) The volume of the new sphere is 1.5 times the volume of the original sphere.
 B) The volume of the new sphere is 3.0 times the volume of the original sphere. 
C) The volume of the new sphere is 1.52 times the volume of the original sphere. 
D) The volume of the new sphere is 1.53 times the volume of the original sphere.

Answers

Hmm, I am pretty sure the answer is A.

Answer: D


Step-by-step explanation:


find the geometric mean of the pair of numbers 36 and 4

Answers

Final answer:

The geometric mean of the pair of numbers 36 and 4 is calculated by getting the square root of the product of the two numbers, which gives us the geometric mean as 12.

Explanation:

To find the geometric mean of the pair of numbers 36 and 4, we use the formula for the geometric mean of two positive numbers, which is the square root of the product of the two numbers.

When we multiply 36 and 4 we get 144. So, the geometric mean of 36 and 4 is the square root of 144, which equals 12.

Therefore, the geometric mean of the numbers 36 and 4 is 12.

Learn more about Geometric Mean here:

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What is the domain of y = cos θ?
A. [-1, 1]
B. [0, infinity]
C. All real numbers
D. 2pi,

Answers

The domain of y = cos θ is all real numbers. This is because any real number can be plugged in for θ and y will be equal to a real number. This can be shown graphically because the y = cos θ will go on infinitely both to the right and left.

Answer:

Option C - All real numbers                                      

Step-by-step explanation:

Given : Function [tex]y=\cos \theta[/tex]

To find : The domain of given function ?

Solution :

Domain is defined as the set of values for which function is defined.

We have given the function,

[tex]y=\cos \theta[/tex]

We know, for any value of [tex]\theta[/tex] the function  [tex]y=\cos \theta[/tex] is defined.

Which means the set of all real numbers defined the given function i.e. [tex]x\in(-\infty,\infty)[/tex]

Therefore, Option C is correct.

The domain of  [tex]y=\cos \theta[/tex] is all real numbers.

Match each correlation coefficient with the type of association it indicates between the variables x and y.

r = 0.9
r = -1.0
r = -0.6
r = 0.1

a perfect linear association in which y increases as x increases

a perfect linear association in which y decreases as x increases

a strong linear association in which y increases as x increases

a strong linear association in which y decreases as x increases

a moderate linear association in which y increases as x increases

Answers

r = 0.9
A value of 0.9 would indicate that the correlation is positive. Since it's also close to the value 1, it would also tell us that the correlation of y and x is strong. Therefore, r = 0.9 would be a strong linear association in which y increases as x increases.

r = -1.0
Since the value of r is negative, this would mean that the correlation is also negative. Furthermore, the value of r is also at the minimum point which is -1.0 thus this would tell us that the correlation is a perfect linear association in which y decreases as x increases.

r = -0.6
Likewise, this r value is also negative thus allowing us to know that y will decrease as x increases. The value of r, which is -0.6, is also close to -1.0. This allows us to tell that it is a strong relationship. Therefore, r = -0.6 is a strong linear association in which y decreases as x increases.

r = 0.1
For this correlation, the r value is positive. This would indicate that the value of y will increase as x increases. Since the r value is only 0.1, we cannot say that it is a strong relationship since it is far from the maximum value for a perfect relationship which is 1. Therefore, r = 0.1 is a moderate linear association in which y increases as x increases.

r = 0.9 (a strong linear association in which y increases as x increases)

r = -1.0 (a perfect linear association in which y decreases as x increases)

r = -0.6 (a moderate linear association in which y decreases as x increases)

r = 0.1 (no linear association or a very weak association)

bracelet costs $8. Simone is also buying a necklace for her mother for $18. She believes that her total will be $98. Which expression could be used to estimate the reasonableness of Simone’s total? 8 × $8 + $10 8 × $8 + $18 10 × $8 + $20 10 × $10 + $10

Answers

she wrong is 26
 i hope i helps

For this case what we should do is write the expression step by step.
 "She believes that her total will be $ 98"
 To get to this we have:
 10 × $ 8 + $ 20
 Rewriting:
 10 × $ 8 + $ 20
 $ 80 + $ 20
 $ 100
 Rate approximately equal to $ 98 with an extra $ 2.
 Answer:
 An expression that could be used to estimate the reasonableness of Simone's total is:
 10 × $ 8 + $ 20

one method of estimating is to

Answers

One way of estimating is to Round the numbers to the nearest whole number.

Hope this helps!
The answer is "A" because whenever you round (up or down) you are only changing the value a teeny bit, which only matters if you want to measure an exact amount of something. Using a calculator gives you the exact answer. Guess and check really doesn't work because there are ∞ numbers. Any answer is not fine because if the answer is 5 and you answer with 9633, that answer is obviously wrong. So, A is right.

twice the measure of an angle's complement less 6 is equal to 124 find the measure of the angle

Answers

Answer

you work it out the same way the first guy did, except instead of

2 (180-x) - 6 = 124, it's

2(90-x) -6 = 124.

the first guy divided by the supplement instead of the complement.

Step-by-step explanation:

Final answer:

To find the measure of the angle, you can use the equation 2(90 - x) - 6 = 124, where x represents the angle. By solving for x, you can determine that the measure of the angle is 25 degrees.

Explanation:

To find the measure of the angle, we can use the information provided in the question. Let's let the measure of the angle be x degrees. The complement of the angle can be found by subtracting the measure of the angle from 90 degrees, since the sum of an angle and its complement is always 90 degrees. Therefore, the complement of the angle is 90 - x degrees.



According to the given equation, twice the measure of the angle's complement less 6 is equal to 124. We can write this as 2(90 - x) - 6 = 124. Now we can solve for x:



2(90 - x) - 6 = 124

180 - 2x - 6 = 124

-2x + 174 = 124

-2x = -50

x = 25



Therefore, the measure of the angle is 25 degrees.

Learn more about Angle Measures here:

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Find the percent of increase from 4.5 inches to 13.5 inches.

Answers

Final answer:

To calculate the percent of increase from 4.5 inches to 13.5 inches, subtract the original value from the new value, divide by the original value, and then multiply by 100, resulting in a 200% increase.

Explanation:

To find the percent of increase from one number to another, you can use the formula: (New Value - Original Value) / Original Value × 100%. Applying this to the question, the original value is 4.5 inches, and the new value is 13.5 inches.

Calculate the increase: 13.5 - 4.5 = 9 inches.Divide the increase by the original number: 9 / 4.5 = 2.Convert this to a percentage by multiplying by 100: 2 × 100% = 200%.

Therefore, the percent of increase from 4.5 inches to 13.5 inches is 200%.

PLEASE ANSWER THIS EASY MATH QUESTION!!
WILL PROVIDE THE ANSWERS BELOW!!!

Answers

The answer is A , you can use Photomath for questions like this !!

Please help me I have 2 questions.

Answers

1) You know that the area (A) of a regular polygon can be computed from the apothem (h) and the perimeter (P) by
.. A = (1/2)*h*P
You also know that a regular pentagon's perimeter (P) is 5 times the length of one side (s).
.. 37.2 m^2 = (1/2)*(3.2 m)*(5s)
.. 37.2 m^2 = (8 m)*s
.. (37.2 m^2)/(8 m) = s = 4.65 m

The length of one side is 4.65 m.


2) There are several ways you can figure this, all giving the same result.
a) The side length will be (12 cm)*√2, and the area is the square of that:
.. A = ((12 cm)*√2)^2 = 144 cm^2 * 2 = 288 cm^2

b) The area is half the product of the diagonal lengths.
.. A = (1/2)*(2*12 cm)^2 = (1/2)*576 cm^2 = 288 cm^2

c) The area is 4 times the area of the right triangle with sides of 12 cm.
.. A = 4*(1/2)*(12 cm)^2 = 2*144 cm^2 = 288 cm^2

d) The area is 4 times the area of one triangle with central angle 90°.
.. A = 4*(1/2)*(12 cm)^2*sin(90°) = 2*144 cm^2*1 = 288 cm^2

The area of the square is 288 cm^2.

A light bulb manufacturing machine produces 72 light bulbs per minute. How much time would it take to make 5400 light bulbs?

Answers

(5400 bulbs)/(72 bulbs/min) = 75 min

It would take 75 minutes for the machine to make 5400 light bulbs.

Given f(x) = 3x+4 . What is f(8)

Answers

If x=8 {f(8)=3x+4}, the answer is 28.


Comment the correct answer. 
it would be substitution then solving. step by step.

f(x)=3x+4
f(8)=3(8)+4
f(8)= 24+4
f(8)=28
hope that helps!!

Suppose you invest $500 at an annual interest rate of 8.2% compounded continuously. How much will you have in the account after 15 years? (1 point)

$1,671.74
$17,028.75
$1,710.61
$8,140.92

Answers

(1.082)^15(500)=$ 1,630.71. I do not see this figure as an option, but it is the correct response.
The formula to find the amount with principal P, rate of interest r and time t when it is compounded continuously is 
A=Pe^(rt)
 P=$500 r=8.2% n=15
 A=500*e^(0.082*15)
  =500*e^1.23
 = 1710.61476814
 Rounding off to the nearest hundredths, we have
 A= $1,710.61

PLEASE HELP ME ON THIS

Answers

The domain of the function is 80 to 180 because domain refers to the valid inputs of the function.

After receiving $42, the new domain (that Albert can afford) is from 80 to 147. 


The expanded form 700,000 + 10,000+9 represents the whole number. 701,309. 713,009. 710,309. 713,090.

Answers

it represents the whole number 710,009

maria is planning a triangular garden she wants to build a fence around the garden to keep out the rabbits. the length of one side of the garden is 29 feet. if the angles of this side are 65 and 44 find the length of the fence needed to enclose the garden

Answers

Approximately 85.323 feet of fence is needed to enclose the garden.

To find the length of the fence needed to enclose Maria's triangular garden, we can use the Law of Sines since we know one side length and its opposite angle.

The Law of Sines states that in any triangle, the ratio of the length of a side to the sine of its opposite angle is constant:

[tex]\[ \frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)} \][/tex]

Where:

- a, b, c are the side lengths of the triangle.

- A, B, C are the angles of the triangle.

Given that one side length is 29 feet and its opposite angle is 65°, let's denote the other two angles as B  and C . Since the sum of angles in a triangle is 180°, we can find angle C as 180° - 65° - 44° = 71°.

Now, we can use the Law of Sines to find the lengths of the other two sides:

[tex]\[ \frac{29}{\sin(65°)} = \frac{b}{\sin(44°)} \][/tex]

Solving for b:

[tex]\[ b = 29 \times \frac{\sin(44°)}{\sin(65°)} \][/tex]

b ≈ [tex]24.438 \text{ feet} \][/tex]

Similarly, we can find the length of side c  using the same formula:

[tex]\[ \frac{29}{\sin(65°)} = \frac{c}{\sin(71°)} \][/tex]

[tex]\[ c = 29 \times \frac{\sin(71°)}{\sin(65°)} \][/tex]

c ≈ [tex]31.885 \text{ feet} \][/tex]

Finally, to find the total length of the fence needed, we sum up the lengths of all three sides:

[tex]\[ \text{Total fence length} = 29 + 24.438 + 31.885 \][/tex]

[tex]\[ \text{Total fence length}[/tex] ≈ [tex]85.323 \text{ feet} \][/tex]

So, approximately 85.323 feet of fence is needed to enclose the garden.

Mark has 36 drawings of horses and 4 drawings of spaceships. write and solve an equation to find how many times as many drawings of horses he has as spaceships.

Answers

We need to find how many horses there are for one spaceship. So, we can set up our equation like:

4x = 36

Dividing both sides by 4:

x = 9

Hope this helps!
36 divided by 4 = 9
(I need 20 letters)

Find the two numbers whose sum is 29 and whose difference is 15

Answers

22 and 7, 22-7 is 15, and 22+7 is 29

ILL GIVE BRAINLIST TO FIRST PERSON!!! Which of these is a primary economic activity? A) tourism B) farming C) healthcare D) construction

Answers

farming c because farming is where we get all our resources well mostly all

WHAT IS 2 400 000 written as a standard form?

Answers

24 x 10^5
Hope this helps

(20 Pts) What is the value of h when the function is converted to vertex form? Note: Vertex form is p(x)=a(x−h)^2+k . p(x)=x^2−14x+29

Answers

a=1 and the x-coefficient is -14. The value of h is -(-14)/(2*1) = 7.

A regular decagon is mapped onto itsslf everytime it is rotated by how many degrees

Answers

Answer:

36° is correct.

Step-by-step explanation:

The degree of rotational symmetry is equal to 360° divided by the number of sides of a regular polygon

360° ÷ 10 = 36°

Answer:

A regular decagon is mapped onto itself every time it is rotated by 36°

Step-by-step explanation:

A regular decagon means a polygon with 10 sides and all sides are equal.

Refer the given figure, if we rotate by 36° we will get same decagon.

So a regular decagon is mapped onto itself every time it is rotated by 36°

Given: ΔABC ≅ ΔFDE. . What is the length of segment DE rounded to the nearest tenth?. . 3.2. . 4.2. . 2.2. . 3.6. .

Answers

[tex]d= \sqrt{(3-2)^2 + (1-4)^2 } [/tex]
[tex]d= \sqrt{( x_{2}- x_{1})^2 + ( y_{2}- y_{1})^2 } [/tex]
[tex]d= \sqrt{(1)^2 + (-3)^2 } [/tex]
[tex]d= \sqrt{1+9 } [/tex]
[tex]d= \sqrt{10 } [/tex]
[tex]d= 3.2[/tex]
The length of segment DE is 3.2 

Answer:

The length of segment DE is 3.2  (A)

Step-by-step explanation:

A tour group charges a flat price for a tour of up to 20 people. The cost per person varies inversely with the number of people. If five people pay 135 each, what must 15 people pay per person.

Answers

Answer:
15 people must pay 45 unit currency each

Explanation:
Assume that the number of people is x and that the price per person is y.
We are given that the cost per person varies inversely with the number of people.
This means that as the number of people (x) increases, the cost per person (y) decreases and vice versa

This can be translated into the following equation:
y = k / x
where k is the constant of proportionality.

Now, we need to get k.
We are given that:
for number of people (x) = 5, the charge per person (y) is 135.
Substitute with this in the above equation to get k as follows:
y = k / x
135 = k / 5
k = 135 * 5 = 675

The equation now became:
y = 675 / x

Finally, we want to get the cost per person (y) when the number of people (x) is 15.
All we have to do is substitute in the above equation to get the y as follows:
y = 675 / x
y = 675 / 15
y = 45

This means that, for a group of 15 people, each one will pay 45 unit currency

Hope this helps :)
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