The inequalities that must be true if m is greater-than-or-equal-to n are given as:
Option 1: [tex]m \times 2.1 \geq n \times 2.1[/tex]Option 2: [tex]m - (-4) \geq n - (-4)[/tex]Option 4: [tex]16.5m \geq 16.5n[/tex]What operations are allowed in inequalities?Only those operations are allowed which are sure to not modify the inequality between the expressions in the statement.
Some operations that are sure not to modify the inequalities are:
Addition, Subtraction, multiplication by positive real numbers, division by positive real numbers etc.
Example, if 5 > 2, then you can do whatever which keeps the term on the side of 5 bigger than the terms formed on side of 2.
Thus, 5 + 1 > 2 + 1 is correct, (it was addition of 1, a real number).
For the considered case, we're given that:
[tex]m \geq n[/tex]
Checking all the options sequentially, we get:
Case 1: [tex]m \times 2.1 \geq n \times 2.1[/tex]It must be true, since the multiplication is done by 2.1, which is > 0
Case 2: [tex]m - (-4) \geq n - (-4)[/tex]It must be true since -4 is a real number, and addition or subtraction of any real number (if done on all the sides of the statement) doesn't change the inequality
Case 3: [tex]m - 3 \geq n + 3[/tex]From [tex]m \geq n[/tex], addition or subtraction is guaranteed to not change the inequality only if they are of same quantity on all the sides of the inequality. Thus, this inequality is not necessary to be true.
Example, if we take m = 5, n =3, then,
[tex]5 \geq 3[/tex] but [tex]5 - 3=0 \: \rm and \: 3 + 3= 6 \implies 5-3 < 3 + 3[/tex]
Case 4: [tex]16.5m \geq 16.5n[/tex]It must be true if given that [tex]m \geq n[/tex] since multiplication of equal positive real number on both the sides of [tex]m \geq n[/tex] was done.
Case 5: [tex]\dfrac{1}{2} 6m \geq 9m[/tex]one-half of 6 = 3, thus, this inequality means [tex]3m \geq 9m[/tex]
Dividing both the sides by 3, we get:
[tex]m \geq 3n[/tex]
It is not necessary to be true if [tex]m \geq n[/tex]. Example
[tex]3 \geq 2\\but\\ 3 < 3 \times 2 = 6[/tex]
Thus, the inequalities that must be true if m is greater-than-or-equal-to n are given as:
Option 1: [tex]m \times 2.1 \geq n \times 2.1[/tex]Option 2: [tex]m - (-4) \geq n - (-4)[/tex]Option 4: [tex]16.5m \geq 16.5n[/tex]Learn more about inequality here:
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To solve the equation below by completing the square, what is your first step?
3x2 + 18x = 21
Add 9 to each side of the equation.
Divide both sides of the equation by 3
Multiply both sides of the equation by 3
Add 81 to each side of the equation.
Step-by-step explanation:
well, for that I want the equation as simple a possible. especially do I want to have a pure "x²" term with "1" as the factor.
so, as I see that all terms in the equation are multiples of 3, my first step will be to divide both sides by 3.
leading to
x² + 6x = 7
Answer:
Answer:
The first step to solve the equation by completing the square 3x²+ 18x= 21 is multiply both sides of the equation by .
The factors of the equations 3x²+ 18x= 21 are 1 ,-7 .
Step-by-step explanation:
As given the equations
3x² + 18x = 21
Multiply both sides of the equation by .
Thus the equation becomes
Simplify the above
x² + 6x = 7
Adding 9 on both sides of the above equation
x² + 6x + 9 = 7 + 9
x² + 6x + 9 = 16
(As (a +b)² = a² + b² + 2ab
Thus (x+3)² = x² + 6x + 9 )
Put in the above
(x+3)² = 16
Taking square root on both side
√16 = ± 4
First take
(x + 3) = 4
x = 4 -3
x = 1
Second take
(x+ 3) = -4
x = - 4 -3
x = -7
Therefore the first step to solve the equation by completing the square 3x²+ 18x= 21 is multiply both sides of the equation by .
The factors of the equations 3x²+ 18x= 21 are 1 ,-7 .
Two times the sum of a number and four increased by three is at most six less than the number. Evaluate this problem situation for values of the number
Answer:
x=2
Step-by-step explanation:
interpreting the problem...
2x+5×3›6-x
2x+12›6-x
2x+x›6-12
3x›6
x›2
you can confirm if this is really the correct solution to the problem
A car gets 40 kilometers per gallon of gasoline. How many gallons of gasoline would the car need to travel 180 kilometers?
Answer:
4.5 gallons
Step-by-step explanation:
180/40=4.5
Lily began a plan for this proof.
Since ∠1 and ∠2 are supplementary and ∠1 and ∠3 are supplementary, then m∠1+m∠2=180° and m∠1+m∠3=180°. If she can get m∠2 and m∠3 to both equal the same expression, she can use the transitive property of equality to set them equal to each other.
How can Lily get m∠2 and m∠3 to both equal the same expression?
Answer:
Step-by-step explanation:
Answer:
she can subtract m < 1 from both sides of m < 1 + m < 2 = 180* and m < 1 + m < 3 = 180*
Step-by-step explanation:
IMAGINE MATH!1
9 + 4 to the third power x (20-8) / 2 + 6
1110.5 is the answer and your welcome
Three friends share some mangoes as follows;Fred receives 2 out of 5 the total, and the reminder is shared between yaw and kwame in the ratio 3:5. How many mangoes did kwame receive if yaw's share was 84 mangoes.
Given that the ratio between Yaw and Kwame is 3:5
So, [tex]\rm{\blue{Yaw:Kwame} = 3:5 = 84:n}[/tex]
[tex]\rm{\red{n = 84 \times 5 \div 3} = 140 \: mangoes }[/tex]
Hence, the answer is [tex]\rm{\blue{140} \: mangoes}[/tex]
Tanxcosx/ sinx =1
I need help to prove this trig function with steps.
Step-by-step explanation:
answer is provided in picture
Alex wants to pay off his credit card balance before he gets married. he decides to take the $2,300 out of his savings and apply it to his credit card debt of $5,390. the credit card has an apr of 16.5%. what will alex's minimum monthly credit card payment be in order to pay off his debt in 14 months? a. $109.40 b. $190.83 c. $244.15 d. $572.32
Answer:
I think C!
Step-by-step explanation:
I just took the test.
Alex's minimum monthly credit card payment will be $244.15.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Firstly calculate the remaining credit card balance after Alex applies his savings:
$5,390 - $2,300 = $3,090.
Calculate the monthly interest rate on the credit card: 16.5% / 12 = 0.01375.
Use the formula P = i / (1 - (1+r)⁻ⁿ) to calculate the minimum monthly payment.
i = the remaining balance = $3,090
r = the monthly interest rate = 0.01375
n = the number of months to pay off the balance = 14
Plugging in the values, we get:
P = 3090×(0.01375)/(1-(1+0.01375)⁻¹⁴)
= $244.15
Therefore, Alex's minimum monthly credit card payment will be $244.15.
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solve the equation 9r^2=108r
Answer:
r = 0, r = 12
Step-by-step explanation:
9[tex]r^{2}[/tex]=108r
Subtract 108r from both sides
9[tex]r^{2}[/tex] - 108r = 108r - 108r (simplify) -> 9[tex]r^{2}[/tex] - 108r = 0
Factor 9[tex]r^{2}[/tex] - 108r: 9[tex]r^{2}[/tex] (r - 12)
9[tex]r^{2}[/tex] (r - 12) = 0
r = 0, r = 12
∠A and ∠B are complimentary. The measure of ∠A is 42 more than 3 times the measure of ∠B. Find ∠A
Answer:
78 Degrees
Step-by-step explanation:
Complimentary Angles add up to 90 degrees so the equation below solves for x and then finds angle A.
3x+42+x=90
4x=48
x=12
3(12)+42=78
What expression represents the width of the rectangle
We are given a rectangle with one of its sides ( length ) equal to ( x - 7 ) Meters.
Also we are given the area of the rectangle as x² - 15x + 56 square meters .We have to find the expression for another side of the rectangle i.e it's width
We will use the formula of area of rectangle to find the expression :
Area = length × widthTherefore,
ㅤㅤ➝ A = l × w
ㅤㅤ➝ x² - 15x + 56 = ( x - 7 ) × w
ㅤㅤ➝ x² - 8x -7x + 56 = ( x - 7 ) × w
ㅤㅤ➝ (x² - 8x )( - 7x + 56 ) = ( x-7 ) w
ㅤㅤ➝ x( x - 8 )-7( x - 8 ) = ( x - 7 )w
ㅤㅤ➝ ( x - 8 )( x - 7 ) = ( x - 7 )
ㅤㅤ➝ ( x - 8 )w = ( x - 8 )( x - 7 )
ㅤㅤ➝ w = ( x - 8 )( x - 7 ) / ( x - 7 )
ㅤㅤ➝ w = ( x - 8 )
Find the average value of the function h(x, y) = x3y2 on the region bounded by f(x) = 2x 1, g(x) = −x2 − 2, x = 0, and x = 1
The average value of the function [tex]h(x,y) = x^{3}\cdot y^{2}[/tex] is approximately 3.1496.
How to find the average of a two-variable function
The average is defined by the following double integral equation:
[tex]\bar h = \frac{\int\limits^1_0 {\int\limits^{f(x)}_{g(x)} {x^{3}\cdot y^{2}} \, dy } \, dx }{(1-0)\cdot [y(1)-y(0)]}[/tex] (1)
If we know that [tex]g(x) = -x^{2}-2[/tex] and [tex]f(x) = 2\cdot x - 1[/tex], then the double average is:
[tex]h = \frac{\frac{1}{3} \int\limits^{1}_{0} {x^{3}\cdot [f(x)-g(x)]^{3}} \, dx }{(1-0)\cdot [f(1)-f(0)-g(1)+g(0)]}[/tex]
[tex]h = \frac{\frac{1}{3}\int\limits^{1}_{0} {x^{3}\cdot [2\cdot x-1+x^{2}+2]^{3}} \, dx }{1-1+3-2}[/tex]
[tex]h = \frac{1}{3}\int\limits^{1}_{0} {(2\cdot x^{2}-x+x^{3}+2\cdot x)^{3}} \, dx }[/tex]
The average value of the function [tex]h(x,y) = x^{3}\cdot y^{2}[/tex] is approximately 3.1496. [tex]\blacksquare[/tex]
Remarks
The statement presents mistakes and is poorly formatted:
Find the average value of the function [tex]h(x,y) = x^{3}\cdot y^{2}[/tex] on the region bounded by [tex]f(x) = 2\cdot x - 1[/tex], [tex]g(x) = -x^{2}-2[/tex], [tex]x = 0[/tex] and [tex]x = 1[/tex].
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what percent of 50 is 8
Answer:
8/50 × 100 = 16%
Answer:
Step-by-step explanation:
if i have 10,000 and spent some and only have 1567 left how much did i spent
Answer:
8433
Step-by-step explanation:
let x = money spent
1567 + x = 10 000
x = 10 000 - 1567
x = 8433
the price of a mountain bike ids decreased from 150$ to 120$. by what percent is trhe price decreased
Answer: Answer below
Step-by-step explanation:
We start off by subtracting 120 from 150, since we want to find the amount it decreased and not what percentage is left.
150 - 120 = 30
We now divide it by 150 to get our percentage.
30/150 = 1/5
1/5 = 0.2 or 20%
Our answer is 20%.
This is the 4th question
Answer:
a) There are 9 outcomes.
b) **i have attached the tree diagram**
c) 1/9
d) 1/9
Step-by-step explanation:
Both events (choosing a shirt and choosing pants) are not mutually exclusive (disjoint). Meaning that both events can occur at the same time.
a) For a sequence of two events in which the first event can occur m ways and the second event can occur n ways, the events together can occur a total of m • n ways. So for this problem, you would do 3 • 3 which equals 9.
b) **tree diagram is attached**
c) Because there are two different events occurring (choosing a shirt and choosing pants) you need to multiply using the Multiplication Rule for Independent Events : P(A and B) = P(A) * P(B)
The probability of event A occurring (choosing a red shirt) is 1/3 and the probability of event B occurring (choosing brown pants) is also 1/3.
1/3 * 1/3 = 1/9
d) You would do the same thing here as part c.
The probability of event A occurring (choosing a blue shirt) is 1/3 and the probability of event B occurring (choosing blue pants) is again 1/3.
1/3 * 1/3 = 1/9
I hope this was helpful!! :)
what is the difference between (1,2) and (-3,5)
Answer:
the difference is (1,2) is in quadrant first and (-3,5) is in quadrant second
The SUM of £1640 is invested in a banck the rate of intrest is 4. 5% annum. Claculate the simple intrest gained in 9 months
keeping in mind that a year has 12 months, thus 9 months are really 9/12 of a year, so
[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \pounds 1640\\ r=rate\to 4.5\%\to \frac{4.5}{100}\dotfill &0.045\\ t=years\to \frac{9}{12}\dotfill &\frac{3}{4} \end{cases} \\\\\\ I = (1640)(0.045)(\frac{3}{4})\implies I=55.35[/tex]
how do i do thissss..
4(5x3) + 2(4x3) = 60 + 24 = 84 square units
It is -12. 5°c outside when the temp starts increasing by 2. 5°c each hour. How long will it take for the temp to reach-5°c
Answer:
3 hours
Step-by-step explanation:
12.5/2.5 = 5
then convert it to negative
Find the area for number 5.
Answer:
The area of the pentagon is 249 square inches.
Step-by-step explanation:
Given, s = 12in; and a = 8.3, The formula to find the area of a pentagon with apothem is, Area of pentagon = 1/2 × perimeter × apothem. So, let us find the perimeter of the pentagon. Perimeter of the pentagon = 5 × side length.
perimeter = 5 x 12
= 60in.
Area = 1/2 × 60×8.3
= 249in².
Find the volume for the regular pyramid.
V=
Answer:
Step-by-step explanation:
First is to find area of base triangle:
It is an equilateral triangle with one side at 4
Height is given by 4*sin60degree = 2*sqrt(3)
Area = 1/2 * side * height
= 1/2*2*sqrt(3)*4
= 4*sqrt(3)
Height of pyramid is at centroid of the base equilateral triangle
Length of angle bisector of the base equilateral triangle
= sqrt(4^2 - 2^2)
= sqrt(16-4)
= sqrt(12)
Centroid is at sqrt(12)/3 from the nearest side.
Consider right-angle triangle formed by top of pyramid and centroid:
Height^2 + (sqrt(12)/3)^2 = 4^2 - 2^2
Height^2 = 16 - 12 - 12/9 = 24/9
Height = (2/3)*sqrt(6)
Volume of pyramid = 1/3*base area*height
= 1/3*4*sqrt(3)*(2/3)*sqrt(6)
= (8/3)*sqrt(2)
= 3.77
19,476 to the nearest ten thousand.
Answer:
19,000
Step-by-step explanation:
you don't round up because the next number is lower than 5
Rory is driving 584 miles to a family reunion she will drive half of the distance by herself the first day the second day Rory and her cousin will share the driving equally how many miles will her cousin drive?
Answer:
Her cousin will drive 142 miles
Paige had $80 to spend on clothes she bought two pair of pants that each cost $20 and one shirt that cost $15 which expression can be used to find how much money Paige had left after shopping 
Answer:
B 80-(2x23+15)
Step-by-step explanation:
first i did 80-46-15=19
so after shopping page had $19 dollars after shopping
Central Angles
Inscribed Angles
Vertex is in the center
of the circle
Vertex is on the circle
2 x Angle = Arc
Angle = 1/2 Arc
Angle = Arc
Answer:
here is the answer
Step-by-step explanation:
Central Angle: An angle whose vertex is the center of a circle. The measure of a central angle is equal to the measure of its intercepted arc. ... Inscribed Angle: An angle whose vertex is a point on a circle and whose sides contain chords.
help! HURRY! 20 points
Need help!
Find the exact volume of the cylinder.
Last one, for today!
Thanks! :)
[tex] \mathcal \pink{GIVEN:}[/tex]
Radius = 3 mHeight = 7 m[tex] \mathcal \purple{TO \: FIND:}[/tex]
Volume = ?[tex] \mathcal \blue{CALCULATION:}[/tex]
[tex] \qquad{ \sf \: volume = \pi{r}^{2}h }[/tex]
Where,
r is radiush is height[tex] \qquad{ \tt\nrightarrow \: \frac{22}{7} \times {3}^{2} \times 7}[/tex]
[tex] \qquad{ \tt\nrightarrow \: \frac{22}{ \cancel7} \times {3}^{2} \times \cancel7}[/tex]
[tex] \qquad{ \tt\nrightarrow \: 22 \times {3}^{2} }[/tex]
[tex] \qquad{ \tt\nrightarrow \: 22 \times 9 }[/tex]
[tex] \qquad{ \boxed{ \tt\Rrightarrow \: 198\: {m}^{3} }}[/tex]
➪ Henceforth, The volume of the cylinder is 198 m³...
The midpoint of a line can be found using either a compass and straightedge construction or a straightedge and tracing paper construction. True or false?
Answer:
The midpoint of a line can be found using either a compass and straightedge construction or a straightedge and tracing paper construction.True or false?TrueStep-by-step explanation:
#BrainliestBunchAnswer:
True is the answer.Step-by-step explanation:
#CarryonlearningPlease help!!
If one pound is equal to 453.592 grams, how many grams are there in one ounce?
1. 100
2. 10
3. 28.3495
4. 283.495