Why do we reverse the direction of the inequality symbol when multiplying or dividing by a negative number?

Answers

Answer 1
When you multiplied both sides by a NEGATIVE number, what WAS negative became positive, and what WAS positive became negative! Everything that was larger became small, and what was smaller became large. Everything REVERSED


Related Questions

Which statements are true regarding the diagram

Answers

Always remember:
Complementary means equal to 90 degrees.
Supplementary means equal to 180 degrees. 

Choice #1 is correct because the angles have to be equal to 90 degrees, and in the picture you can see that those two together are a right angle, which is 90 degrees.  

Choice #2 is incorrect because on the picture it is obviously less than 180 degrees. 

Choice #3 is correct (same reason #1 is correct)

Choice #4 is correct because we can see that HNL is a straight line, which is equal to 180, and the angles add up toe the line HNL. 

Choice #5 is incorrect because MNG was already a 90 degree angle, so adding another angle would not make it a right angle again. 

I hope this helps!! 

Answer:

A. AngleGNH and AngleHNJ are complementary.

C.AngleKNL and AngleLNM are complementary.

D.mAngleHNK + mAngleKNL = 180°

Step-by-step explanation:

Find f(x) and g(x) so the function can be expressed as y = f(g(x)). There may be more than one possible decomposition.

y = (x^3 + 1)^2

Answers

g(x)  could be x^3

and f(x) would be (x + 1)^2

Find the value of tan θ given cot θ=5/7.

Answers

[tex]\bf cot(\theta )=\cfrac{1}{tan(\theta )}\\\\ -------------------------------\\\\ cot(\theta )=\cfrac{5}{7}\implies \cfrac{1}{tan(\theta )}=\cfrac{5}{7}\implies \cfrac{7}{5}=tan(\theta )[/tex]

If i was born in 2002 how old will i be in 2130

Answers

To find that, we have to find the difference of 2130 and 2002, which is
2130-2002=128. We use subtraction due to that we start in 2002 but end in 2130, and therefore find the difference

24 divided by 2 find the qoutient

Answers

24/2 = 12

 the quotient is 12

Answer: So your answer is 12 for 24 divided by 2 which gives you 12 I hope this helps

Step-by-step explanation:

24 divided by 2 = 12

12 times 2= 24

Or 2 times 12 = 24

Keiko runs 10 miles in 75 minutes. at the same rate, how many miles would she run in 69 minutes?

Answers

She would be running at a rate of 1 mile every 7.5 minutes. 75/10=7.5 minutes a mile. I figured the distance she would travel at 69 minutes is 9.2 miles. I guessed at the numbers when trying to figure it out. I don't know if you need it to be worked out to explain how you got that answer!

Solve the triangle. A = 46°, a = 31, b = 27

Answers

Final answer:

To solve the given triangle with A = 46°, a = 31, and b = 27, we use the Law of Sines to first find angle B, then use the sum of angles to find angle C, and finally, use the Law of Sines again to find side c.

Explanation:

To solve the triangle with the given information A = 46°, a = 31, and b = 27, we need to use the Law of Sines or the Law of Cosines. Since we have one angle and the side opposite to it (a = 31), as well as another side (b = 27), we first need to find angle B using the Law of Sines:

\frac{\sin(A)}{a} = \frac{\sin(B)}{b}
\frac{\sin(46°)}{31} = \frac{\sin(B)}{27}

By solving for sin(B), we get:

\sin(B) = \frac{\sin(46°) * 27}{31}

Next, we calculate the value of sin(B) and then angle B. After that, we can find angle C by using the fact that the sum of angles in a triangle is 180°:

A + B + C = 180°
C = 180° - A - B

Once we have angle C, we can use the Law of Sines again to find side c:

\frac{\sin(C)}{c} = \frac{\sin(A)}{a}

By rearranging and solving for c, we get:

c = \frac{\sin(C) * a}{\sin(A)}

This process will give us the lengths of all sides and the measurements of all angles, thus solving the triangle.

Triangle PQR has vertices P(–2, 6), Q(–8, 4), and R(1, –2). It is translated according to the rule (x, y) → (x – 2, y – 16).

What is the y-value of P'?

Answers

Since you subtract 16 from the y value, P is (-2, 6), and the y value comes second (meaning that it's 6), we get 6-16=-10

Answer:

The answer is -10

Step-by-step explanation:


Point M is the midpoint of LN. LM = 7x - 12 and MN = 3x + 16. Find LM.

Answers

Since point M is the midpoint of LN, LM and MN are equivalent in length.

7x - 12 = 3x + 16 (LM=MN)

7x = 3x + 28

4x = 28

x = 7

Now that we know the value of x, we can find the value of LM by plugging the value in the equation.

LM = 7(7) - 12

LM = 49 - 12

LM = 37

If P is the midpoint of ST, SP = x + 4, and ST = 4x, determine the length of ST

Answers

If P is the midpoint of ST then ST = 2SP

4x = 2(x + 4)
4x = 2x + 8
4x - 2x = 8
2x = 8
x = 8/2
x = 4

ST = 4x = 4*4 = 16 units

Answer:

ST = 16.

Step-by-step explanation:

Given  : P is the midpoint of ST, SP = x + 4, and ST = 4x,

To find :  Determine the length of ST.

Solution : We have given P is mid point of ST.

It mean P divide the ST in to two equal parts .

So, SP = PT .

We can say

ST  = 2 SP .

Plug the given values SP = x + 4, and ST = 4x,

4x = 2 ( x +4).

4x = 2x + 8.

On subtracting both sides by 2x

4x -2x = 8.

2x = 8

On dividing both sides by 2

x = 4.

ST = 4 * 4 = 16.

Therefore, ST = 16.

In buffalo, New York, the temperature was -14F in the morning. If the temperature dropped 7F, what is the temperature now?

Answers

Final answer:

The initial temperature in Buffalo was -14°F. After a drop of 7°F, the new temperature would be -21°F.

Explanation:

The student asked: In Buffalo, New York, the temperature was -14°F in the morning. If the temperature dropped 7°F, what is the temperature now? To solve this, we need to perform a simple subtraction operation. We begin with the initial temperature of -14°F and subtract the temperature drop of 7°F.

The calculation is as follows:

Initial temperature: -14°F
Temperature drop: -7°F
New temperature: -14°F - 7°F = -21°F

Therefore, after the temperature drop, the new temperature in Buffalo would be -21°F.

Final answer:

After the temperature in Buffalo dropped by 7°F from an initial -14°F, the current temperature is now -21°F.

Explanation:

In Buffalo, New York, the temperature was -14°F in the morning. If the temperature dropped 7°F, to find the current temperature, you subtract 7 from -14. This calculation is as follows:

Starting temperature: -14°FTemperature drop: 7°FCurrent temperature: -14 - 7 = -21°F

Therefore, the temperature now in Buffalo is -21°F.

How many even numbers can be formed from the digits 1,2,3,4,5?

Answers

120 even numbers that can be made out of those numbers.

Which function grows at the fastest rate for increasing values of x?
p(x)=5x3+3
f(x)=8x2−3x
h(x)=2x
g(x)=19x

Answers

Calculate the derivative of each function
And btw answer is p(x)
Answer:

The function which has the  fastest rate for increasing values of x are:

                     [tex]p(x)=5x^3+3[/tex]

Step-by-step explanation:

We are given four polynomial functions as:

[tex]p(x)=5x^3+3\\\\\\ f(x)=8x^2-3x\\\\\\h(x)=2x\\\\\\g(x)=19x[/tex]

Now as we know that if the degree of the polynomial increases the function becomes more extreme i.e. it increases very quickly with the increasing value of x.

Hence, among the given options the function which has the fastest rate of increase is:

                            [tex]p(x)=5x^3+3[/tex]

( Since, it's degree is 3 which is highest as compared to the other polynomials (one of degree 2 and 2 of degree 1) )

Felipe has a job transporting soft drinks by truck. his truck is filled with cans that weigh 14 ounces each and bottles that weigh 70 ounces each. there is a combined total of 800 cans and bottles in his truck. let x be the number of 14 -ounce cans in his truck. write an expression for the combined total weight (in ounces) of the cans and bottles in his truck.

Answers

Hello,

Let x be the number of 14-ounce cans

800-x be the number of bottles

Total weight=14*x+70*(800-x)=14x+56000-70x=56000-56x=56(1000-x)

A rectangle has area 64 m2. Express the perimeter of the rectangle as a function of the length L of one of its sides. State the domain of P

Answers

A rectangle is a two-dimensional shape with two sets of equal, parallel sides. These dimensions are the length (L) and the width (W). The formula for the rectangle's area is the product of the two dimensions. The formula for perimeter is

P = 2L + 2W

Since
A = LW = 64
W = 64/L
Substituting to the formula for perimeter would be,

P = 2L + 2(64/L)
P = 2L + 128/L

The admission fee at a small fair is $1.50 for children and $4.00 for adults. on a certain day, 2200 people enter the fair and $5050 is collected. how many children and how many adults attended that day?

Answers

I would write systems of equations for this problem.

1.5x + 4y = 5050

x + y = 2200

From there solve the system of equations where x represents the number of children and y represent the number of adults.

x + y = 2200

x = 2200 - y

Plug "x" into the other system of equation.

1.5(2200-y) + 4y = 5050

3300 - 1.5y + 4y = 5050

2.5y = 1750

y = 700

Since you have the value for y, solve for x.

x + y = 2200

x + 700 = 2200

x = 1500

So, the solution is: 1500 children and 700 adults attended.

Just to check our answers:

1.5x + 4y = 5050

1.5(1500) + 4(700) = 5050

2250 + 2800 = 5050

5050 = 5050


In the expression 12 + 7, the values on the right and left of the + symbol are called _____ .

Answers

I believe the answer is addends.

In the expression 12 + 7, the values on the right and left of the + symbol are called operands.

What are operands?

A mathematical object upon which an operator acts.

Given that, an expression 12+7,

In maths, the values that an operator acts on are called operands. In this case, 12+7 are the operands.

Hence, the asked statement is operands.

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Math Help Please!!!
On a team’s opening day, fans in a baseball stadium were asked how many home games they plan to attend this season. The histogram shows the results. How many fans plan on attending fewer than 20 games?

Answers

fewer then 20.....thats gonna be ur first 2 bars added....so it will be (17 + 8) = 25 <==

Answer: 25

Step-by-step explanation:

Given : On a team’s opening day, fans in a baseball stadium were asked how many home games they plan to attend this season.

In the given histogram , it can be seen that the number of fans attending fewer than 10 = 8

And the number of fans attending between 10-20=17

Then, the number of fans attending fewer than 20 games =[tex]8+17=25[/tex]

Therefore, 25 fans plan on attending fewer than 20 games

Simplify -4/7 + (-4/3)

Answers

-4/7 - 4/3 

- 12/21 - 28/21 = -40/21

your answer is -1 19/21

hope this helps

D: Region D help please .....

Answers

The inequality y <= (-1/3)x + 3 will be the shaded region composed of regions C and D. These regions are below the line with negative slope.

The inequality y >= 3x+2 is the shaded region composed of regions A and D which are above the positive sloped line. 

The overlapping region is region D. This region is found in BOTH shaded solution sets of the two inequalities.

This is why region D is the final answer.

The equation h(t)=−16t2+78t+45 gives the height of a firework, in feet, t seconds after it is launched from a platform. What is the height of the platform? Enter your answer in the box.

Answers

The height of the platform should be 45 feet. Hope this helps

The height of the platform is 45 feet.

What is Equation?

Two or more expressions with an Equal sign is called as Equation.

The equation h(t)=−16t² +78t+45 gives the height of a firework

When a firework is launched from a platform, its height at time t=0 seconds is equal to the height of the platform.

To find the height of the platform, we can substitute t=0 into the equation:

h(0) = -16(0)² + 78(0) + 45

h(0) = 0 + 0 + 45

h(0) = 45

Therefore, the height of the platform is 45 feet.

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what number fills in the blank to complete the factorization of 3x+24?

Answers

you sure it's not 3x=24? or is it actually 3x+24?

Answer:

Complete factorization of 3x+24 is:

3(x+8)

Step-by-step explanation:

we have to completely factorize:

3x+24

Taking 3 common in the above expression

3(x+8)

This cannot be factorized further

Hence, complete factorization of 3x+24 is:

3(x+8)

The sum of two even numbers is even. the sum of 6 and another number is even. what conjecture can you make about the other number?

Answers

Answer: We can say that the other number is even since the sum of two even numbers is even.

The required conjecture is given as the other number must be an even number.

What is an even number?

An even number is defined as a number that is a multiple of 2 is called even number, such as 2, 4, 6, 12, and so on.

What is arithmetic?

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,

here,
The sum of two even numbers is even. Following the statement,
If the sum of 6 and another number is even, that another number must be even to get the sum of 6 and another number to be even, while 6 it self is an even number.

Thus, the required conjecture is given as the other number must be an even number.

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A basketball player scored 29 points in a game. The number of three-point field goals the player made was 29 less than three times the number of free throws (each worth 1 point). Twice the number of two-point field goals the player made was 15 more than the number of three-point field goals made. Find the number of free-throws, two-point field goals, and three-point field goals that the player made in the game.

A-10 free throws; 1 two-point field goals; 8 three-point field goals

B-11 free throws; 8 two-point field goals; 4 three-point field goals

C-10 free throws; 9 two-point field goals; 3 three-point field goals

D-10 free throws; 8 two-point field goals; 1 three-point field goals

Answers

If you let x represent the number of free throws.         
let y represent the number of two-point field goal.         
let z represent the number of three-point shots made.

Then the correct system of linear equations is as follows: 

x + 2y + 3z = 29 (The total number of points scored is 29.)
z = 3x - 29 (The number of 3-pointers was 29 less than 3 times the number of free throws.)
2y = z + 15 (Twice the number of 2-point shots made was 15 more than the number of 3-pointers.) 

Solution:
This basketball player scored 10 points via free throws (10 at 1 point each), 16 points via 8 two-point shots made, and 3 points via 1 three-point shots made. So, in the choice its letter D.

Answer:

,

Step-by-step explanation:

The answer is D)

Please answer me this equation

Answers

Hello,

Perimeter is a function of the number of hexagons.

[tex]p_1=6\\ p_2=2*6-1\\ p_3=3*6-2\\ p_4=4*6-3\\\\ \boxed{p_n=n*6-(n-1)}\ =6n-n+1=\boxed{5n+1}\\ [/tex]

What is the surface area of this cone ?

Answers

The answer is C) 678.24 :)

A pet-sitting company charges $25 to board a pet for one day. It also charges all customers an extra $7.50 to trim the pet's nails once per stay.
How much will it cost to board a dog for two weeks?

A.
$57.50

B.
$65.00

C.
$357.50

D.
$455.00

Answers

2 weeks = 14 days

14 * 25 = 350

350 + 7.50 = 357.50

 Answer is C

How many, and what type of, solutions does 6x2−2x+7=0 have?

A.) 2 nonreal solutions
B.) 2 irrational solutions
C.)2 rational solutions
D.) 1 rational solution

Answers

Answer:

Nope! The answer is 2 Nonreal Solutions i took the test! :)

Step-by-step explanation:

The given quadratic equation will have 2 nonreal solutions. The correct option is A.


What is a quadratic equation?

A quadratic equation is a polynomial with a degree of 2 or the maximum power of the variable is 2 in quadratic equations. It has two solutions as its maximum power is 2.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication and division.

Given that the quadratic equation is 6x²−2x+7=0. The equation can be solved as below;-

6x²−2x + 7 = 0

The equation will have two non-real values for x. The correct option is A.

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an angle's measure is twice the measure of its complement. the larger angle is how many degrees greater than the smaller angle.

Answers

Two angles are complementary when they add up to 90 degrees

smaller angle = x
larger angle = 2x

x + 2x = 90
3x = 90
x = 90/3
x = 30°  ←  smaller angle 
larger angle = 2x = 2 * 30 = 60°

larger angle - smaller angle = 60° - 30° = 30°

The larger angle is 30 degrees greater than the smaller angle.

A machine manufactures wheels with a diameter of 70 cm. It is acceptable for the diameter of a wheel to be within 0.02 cm of this value. Write and solve an absolute-value equation to find the minimum and maximum acceptable diameters.

Answers

The expected diameter is 70 cm.

It is acceptable for the diameter to be within 0.02 cm of the expected value.
Therefore the acceptable values for the diameter, d, are
[tex]d \pm 0.02 = 70[/tex]

The minimum acceptable value of d is obtained from
d + 0.02 = 70
d = 69.98 cm

The maximum acceptable value of d is obtained from
d - 0.02 = 70
d = 70.02 cm

Answer:
Minimum acceptable diameter = 69.98 cm
Maximum acceptable diameter = 70.02 cm

To find the minimum and maximum acceptable diameters for wheels manufactured by a machine with a 70 cm diameter tolerance set within 0.02 cm, an absolute-value equation is used to determine the range of acceptable values.

The question is: A machine manufactures wheels with a diameter of 70 cm, and it can be within 0.02 cm of this value. To find the minimum and maximum acceptable diameters, we need to set up an absolute-value equation.

Let x be the diameter of the wheel.The absolute-value equation is |x - 70| ≤ 0.02.Solving this equation, the minimum acceptable diameter is 69.98 cm, and the maximum acceptable diameter is 70.02 cm.
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