Question : Why do we reverse the direction of the inequality symbol when multiplying or dividing by a negative number ??
please write a thought out good answer ! T-T
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Answers
Answer:
Down Here ↓↓↓↓
Step-by-step explanation:
Hello!
Let's take an example: x > y
The rule that we currently have would state that -x < -y.
Now, let's substitute values for x and y. Say x is 5 and y is -3.
5 is greater than -3 (x > y), but -5 would be less than -3. (-x < -y). Hence the inequality would be true.
We can also take a look at this graphically on a number line. Turning a number negative is simply reflecting it over value 0.
As you can see, flipping the signs would change the values. To keep the inequality accurate, we reverse the inequality sign as well.
Related Questions
john thinks of a number,he adds 3 to a number and multiplies the number by 4 and then gets an answer of 10.find the number john was thinking of?
Answers
The number john was thinking of is -0.5
As in the given problem let john thinks of a number x.
He adds 3 to a number i.e x+3
Then he multiplies the number by 4 i.e. 4*(x+3)
The answer he gets is 10.
Thus we an write
4*(x+3)=10
or x+3=5/2
or x=(5/2)-3
=-0.5
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Write a variable expression that represents the following word phrase:
Four less than half the difference of 3 and x
Answers
Answer:
Answer: -4
Step-by-step explanation:
(3-x)/2 -4=-4
Step-by-step explanation:
Difference of 3 and x : 3-x
Half of it : (3-x)/2
And then four less : (3-x)/2 - 4
please help i do not understand
Answers
Answer: a. 17
b. an=-2.5n+24.5
Step-by-step explanation:
Term number: 3, 4, 5
Terms: 17, 14.5, 12
Term 3 is 17, term 4 is 14.5, and term 5 is 12.
a. The corresponding value to term 3 is 17.
b. Slope formula: m=(y2-y1)/(x2-x1) where x=term number and y=term.
m=(17-14.5)/(3-4)
m=2.5/(-1)
m=-2.5
y=mx+b ==> Linear equation with slope
12=-2.5(5)+b ==> substitute a term number and it's corresponding term
12=-12.5+b
b=12+12.5
b=24.5
y=-2.5x+24.5
an=-2.5n+24.5 ==> convert linear equation back to an form.
Dwayne wants to redecorate his bedroom and decides to purchase new furniture. The following graph could be used to represent the value of the new bedroom furniture, f(x), after x years.
a graph of an exponential function which decreases through the points 0 comma 1100 and 2 comma 704
Which of the following statements is/are true based on the graph and the context of the problem?
The function is positive on its entire domain.
The domain is x ≥ 0 to represent the number of years after the bedroom furniture was purchased.
The x-intercept (0, 1100) represents the initial cost of the bedroom furniture.
I only
I and II only
I and III only
I, II, and III
Answers
The correct statements regarding the function are:
I and II only.
What are the correct statements regarding the function?The functions models the value of the furniture after x years, showing exponential decrease. We have that:
Time is never negative, hence the domain is x ≥ 0, representing the number of years since the furniture was purchases.The value of a product will never be negative, and a exponential function that is not shifted never touches 0, hence the function is positive on the entire domain.(0,1100) is the y-intercept, not the x-intercept, and represents the initial cost of the bedroom furniture.Hence statements I and II are correct.
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Answer:
l and lll only
Step-by-step explanation:
just did it
The table shows the proportional relationship between a hedgehog's
weight loss and the number of days of hibernation. How much weight does
the hedgehog lose during 120 days of hibernation?
Explain how you know that the relationship between the hedgehog's weight
loss and the number of days of hibernation is proportional.
The hedgehog’s total change in weight over 120 days is ____ ounces.
Answers
Answer:
-3.6
Step-by-step explanation:
proportional means the amount on the right is amount on the left multiplied by some coefficient - proportion. The proportion is calculated by dividing one side by another. Since you need to calculate weight based on days, you need the proportion of weight/days, so divide -0.27/9 or -0.78/26, in all cases you'll receive -0.03. This means for each day in hibernation hedgehog loses 0.03 pounds. 120 days will be 120*-0.03 which gives you -3.6
If James' total marks for the four terms was 256,and he represented his marks by a pie chart, what would be the size of the angle representing term 2
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A possible name for this type of chart is Scatter Chart. James scored the most at first glance.
James tried to make his results look impressive in his first graph by drawing the graph from right to left instead of left to right.
This is a schematic of a data set showing the relationships between variable quantities. So if you look closely at the chart from left to right, you can see that Jane is the clear winner. Because James' results are not good and continue to decline.
Pie charts can be used to display percentages of the whole, representing percentages at a particular point in time.
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Simplify 6+√-80-
O 6+4/√5
O 6+16/51
O 6+4√5/
O 6+16/ √5
Answers
Answer:
what are u simplifying for?
Step-by-step explanation:
What is the equation of the line that passes through the point (8,6)
and has a slope of frac{1}{4}
Answers
[tex](\stackrel{x_1}{8}~,~\stackrel{y_1}{6})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{1}{4} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{6}=\stackrel{m}{ \cfrac{1}{4}}(x-\stackrel{x_1}{8}) \\\\\\ y-6=\cfrac{1}{4}x-2\implies y=\cfrac{1}{4}x+4[/tex]
christina has $22 more than 3 times as much money as melissas has. together they have $122. How much money does each girl have
Answers
Then amount Christina has is "3n+22"
EQUATION:
Melissas + Christina's = $122
n + 3n+22 = 122
4n=100
n=$25 (amount Melissa has)
3n+22= 75+22= #97 (amount Christina has)
-4x + 15 + -49
please show work
Answers
Answer:
12
Step-by-step explanation:
that is my answer and I don't need your
Does the figure above appear to have rotational symmetry? Is yes select the angles of rotation less than 360
Answers
Answer:
the answer should be 180
With explanation! Need it asap
Second Question: Name the polygon.
Answers
Answer:
Decagon or 10
Step-by-step explanation:
Well to find the angle of B, you would have to do 180=2(18) which is 36 + x
x=180-36 x is 144 this is a decagon with ten sides due to the equation: 180(n-2)=144n where the answer is n=10
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please help
A triangle with vertices at (-6, 5), (-5, 1), and (-8, 2) is reflected over the y-axis What are the coordinates of the vertices of the reflected image? Enter the correct answers in the boxes. Show Hints Preimage coordinates Image coordinates (-6,5) (-5,1) (-8,2) 03
Answers
Answers:
(6, 5)
(5, 1)
(8, 2)
==================================================
Explanation:
The rule we use is [tex](\text{x}, \text{y}) \to (-\text{x}, \text{y})[/tex] when reflecting over the vertical y axis.
The x coordinate flips from positive to negative, or vice versa. The y coordinate stays the same. So a point like (-6, 5) reflects over to (6, 5). The x coordinate -6 flipped to +6 or simply 6. The y coordinate stayed at 5.
Use this idea to reflect the other points.
help with this math questions
Answers
Answer: the answer is A because A for apple!
Step-by-step explanation:
123+ 1223e = 1200 e -5
Answers
Answer: I worked the equation out and it came as false
Step-by-step explanation:
Ellason wants to solve the following system using the elimination method:
5x + 2y = 30
x + y = 8
What number should the equation x + y = 8 be multiplied by to eliminate y? (4 points)
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14.7 kilograms is how many pounds?
Answers
The given kilograms in pounds is 32.407952541177 pounds.
Given that there are 14.7 kilograms.
The SI unit of mass is the kilogram (kg). It is equal to the mass of the international prototype of the kilogram and One kg is approximately equal to 2.20462262184878 pounds.
One pound, the international peso, is legally defined as exactly 0. 5359237 kilograms.
To calculate the kilogram value with its corresponding value in pounds, simply multiply the quantity in kilograms by 2.20462262184878.
Pounds = kilograms × 2.20462262184878
Now, substitute kilograms=14 kilograms, we get
Pounds = 14.7× 2.20462262184878
Pounds=32.407952541177
Hence, in 14.7 kilograms there are 32.407952541177 pounds.
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Find the point-slope equation for
the line that passes through the
points (-2, -20) and (9, 79). Use
the first point in your equation.
y - [?] = [](x-[])
Answers
The point slope equation for the line that passes through the points (-2, -20) and (9, 79) is 9 x - y - 2 = 0.
We are given the points as:
(- 2 , - 20) and ( 9 , 79)
We will first find the slope:
Slope = m = y₂ - y₁ / x₂ - x₁
m = 79 + 20 / 9 + 2
m = 99 / 11
m = 9
Now, we have to find the point-slope equation for the line that passes through the points (- 2, - 20) and (9, 79).
The point slope equation is:
y - [y₁] = [m](x-[x₁])
Substituting the values, we get that:
y + 20 = 9 ( x + 2 )
y + 20 = 9 x + 18
9 x - y + 18 - 20 = 0
9 x - y - 2 = 0
Therefore, the point slope equation for the line that passes through the points (-2, -20) and (9, 79) is 9 x - y - 2 = 0.
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A given rectangle has an area of 20 square feet. What is the length for various widths??
Answers
Answer:
The area of a rectangle is the length multiplied by the width, so the width can be any factor of 20.
1, 2, 4, 5, 10 or 20
The ratio of the measures of three sides of a triangle is 2: 5: 4 , and its perimeter is 165 units. Find the measure of each side of the triangle.
Answers
Answer:
30 units, 75 units and 60 units respectively
Step-by-step explanation:
Determine the solutions of the equation:
x = −11 and x = 5
x = −81 and x = 45
x = −99 and x = 45
x = −99 and x = 99
Answers
The solutions of the absolute value equation are x = −99 and x = 45.
How to determine the solutions of the absolute value equation?Here we have the absolute value equation:
| (1/3)*x + 9| - 3 = 21
First, we can add 3 in both sides so we get:
| (1/3)*x + 9| = 21 + 3 = 24
This can be decomposed into two equations, we will get:
(1/3)*x + 9 = 24
(1/3)*x + 9 = -24
Solving these two we can get the two solutions.
The first one gives.
(1/3)*x = 24 - 9 = 15
x = 3*15 = 45
The second one gives:
(1/3)*x = -24 - 9 = -33
x = 3*-33 = -99
The solutions are x = −99 and x = 45.
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What is the value of the exponential expression below?
16²
OA. 6
OB. 2
OC. 4
D. 8
Answers
The value of the exponential expression is 4 which is option (C).
Exponential equations, as the name suggests, involve exponents. The exponent (radix) of a number indicates how many times the number (radix) is multiplied.A number's exponent indicates how many times the number has been multiplied by itself. For example, 2×2×2×2 can be written as 24 because 2 is multiplied by 4. Here 4 is called the "exponent" or "power". In general, xn means multiply x by n times. Power law is given by[tex](a^m)^n=a^{m\times n}[/tex]We can write 16 as [tex]4^2[/tex] .
Using exponent property ,we get
[tex]16^\frac{1}{2}=((4)^2)^\frac{1}{2} \\\\16^\frac{1}{2}=4[/tex]
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The complete question below :
What is the value of the exponential expression below?
[tex]16^\frac{1}{2}[/tex]
A. 6
B. 2
C. 4
D. 8
How to express ABC in terms of x?
Answers
Check out the attached photo
Answer:
∠ ABC = 180 - 2x
Step-by-step explanation:
AB and BC are congruent , so the triangle is isosceles with base angles congruent , that is
∠ A = ∠ C = x
the sum of the 3 angles in the triangle = 180° , then
∠ ABC + x + x = 180
∠ ABC + 2x = 180 ( subtract 2x from both sides )
∠ ABC = 180 - 2x
Solve the following quadratic equation for all values of x in simplest form.
(x + 2)^2 – 46 = 24
Answers
Answer:
x = - 2 ± [tex]\sqrt{70}[/tex]
Step-by-step explanation:
(x + 2)² - 46 = 24 ( add 46 to both sides )
(x + 2)² = 70 ( take square root of both sides )
x + 2 = ± [tex]\sqrt{70}[/tex] ( subtract 2 from both sides )
x = - 2 ± [tex]\sqrt{70}[/tex]
then solutions are
x = - 2 - [tex]\sqrt{70}[/tex] , x = - 2 + [tex]\sqrt{70}[/tex]
find the volume of the parallelepiped with adjacent edges pq, pr, and ps. p(−2, 1, 0), q(4, 4, 4), r(1, 4, −1), s(3, 6, 1)
Answers
The volume of the parallelepiped with adjacent edges PQ, PR, and PS is 24 cubic units.
What is parallelepiped?Six parallelograms come together to form a three-dimensional shape called a parallelepiped (the term rhomboid is also sometimes used with this meaning). It is comparable to a parallelogram in the same way that a cube is comparable to a square. In Euclidean geometry, the four concepts—parallelepiped and cube in three dimensions, parallelogram, and square in two dimensions—are specified; however, only parallelograms and parallelepipeds exist in the setting of a more generic affine geometry, where angles are not discriminated.
There are three similar descriptions of a parallelepiped:
A polyhedron called a hexahedron, which has six parallelogram-shaped facesThree pairs of parallel faces on a hexahedron, andA prism with a parallelogram as its base.We have been that p(−2, 1, 0), q(4, 4, 4), r(1, 4, −1), and s(3, 6, 1) are the adjacent edges of parallelepiped
PQ = Q-P = <6,3,4>
PR = R-P = <3,3.-1>
PS= S-P = <5,5,1>
[ PQ PR PS] = [tex]\begin{vmatrix}6& 3 & 4 \\ 3& 3 &-1 \\ 5 & 5 & 1 \\ \end{vmatrix}\\ \notag&& \\[/tex]
= 6(3+5)-3(3+5)+4(15-15)
= 6×8-3×8+0
=48-24
=24
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The price of a train ticket consists of an initial fee of \$5$5dollar sign, 5 plus a fee of \$2.75$2.75dollar sign, 2, point, 75 per stop. julia has \$21$21dollar sign, 21 and would like to travel 505050 kilometers. she wants to know the largest number of stops she can afford to buy on a ticket. let sss represent the number of stops that julia buys. 1) which inequality describes this scenario?
Answers
An inequality that represents given scenario is 5 + 2.75x ≤ 21
For given question,
The $21 means that there is a limit to the number of stops she can take using the train.
From given information, we have the following parameters:
Initial Fee = $5
Rate per stop = $2.75
Amount = $21
The inequality that represents the scenario is calculated using:
Initial Fee + Rate × Number of stops ≤ Amount
We use ≤ because the total charges must not exceed the amount.
Let the number of stops be x.
The above formula becomes
5 + 2.75x ≤ 21
Therefore, an inequality that represents given scenario is 5 + 2.75x ≤ 21
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Please help! I don’t exactly understand how to do this
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Answer:
-6 -3
Step-by-step explanation:
How much principal must be deposited to earn $1,000 simple interest in 250 days at a rate of 5.05%?
Answers
The principal must be deposited to earn $1,000 simple interest in 250 days at a rate of 5.05% is $28,514.85
How is simple interest determined?
The simple interest on deposit is determined as the principal multiplied by the simple interest rate and the time of the deposit as shown below:
I=PRT
I=simple interest earned=$1,000
P=principal deposited=unknown
R=simple interest rate =5.05%
T=number of days that deposit lasted as a fraction of number of days in a year=250/360
$1000=P*5.05%*250/360
$1000=P*0.0350694444444444
P=$1000/0.0350694444444444
P=$28,514.85
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ASAP. Please help me.
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Passing through (3,3) and parallel to the line whose equation is 2x+y-2=0; slope intercept form.
Answers
Answer:
Step-by-step explanation:
y = -2x +2
y - 3 = -2(x -3)
y - 3 = -2x + 6
y = -2x + 9