[tex]\bf{9x > -36 }[/tex]
Divide both sides by 9.
[tex]\bf{\dfrac{9x}{9} > \dfrac{-36}{9} }[/tex]
[tex]\bf{x > -4 \ \ \to \ \ \ Answer}[/tex]
{ Pisces04 }Answer:
{x | x > -4}
Step-by-step explanation:
{a few basic reminders: > means greater than; < means less than; ≥ means greater than or equal to; ≤ means less than or equal to
for example: 4 < 7
4 ≤ 4
4 ≥ 3
4 > 3}
When we see an inequality, such as 9x > -36, we are trying to figure out what possible numbers x can be to make this statement true.
We can either use logic / words (see below), or in a much more efficient manner, we can solve this algebraically [as though it were an equation]
So, like when working with any other variable, we want to isolate x:
9x > -36
÷9 ÷9
x > -4
just in case none of this makes sense (it can be quite confusing at first),
here's how we can think about it logically
we know that whatever multiplies with 9 must be more than -36, and because -4 multiples with 9 to be exactly -36, any number greater than -4 also will be greater than -36
meaning that x must be more than -4, which we express as: x > -4
So, the solution set (solution set means set of possible solutions) is
{x | x > -4}
hope this helps!! have a lovely day :)
What is the reciprocal of 2x/y? Please help.
The reciprocal is determined by interchanging y with 2x to have y/2x. Hence the reciprocal of 2x/y is y/2x
Reciprocal of a functionThe reciprocal is determined by changing the numerator for denominator
Given the expression
f(x, y) = 2x/y
The reciprocal is determined by interchanging y with 2x to have y/2x. Hence the reciprocal of 2x/y is y/2x
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The reciprocal of 2x / y is equals to y / 2x
How to find reciprocal of a number?Reciprocal is simply defined as the inverse of a value or a number.
For example If x is a real number, then its reciprocal will be 1/x.
Therefore, the reciprocal of 2x / y can be calculated as follows:
Reciprocal of 2x / y =
Hence,
[tex]\frac{1}{\frac{2x}{y} } = 1 X \frac{y}{2x}[/tex]
Therefore, the reciprocal of 2x / y = y / 2x
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Find the exact value of x.
Answer:
x is 8√2.
Step-by-step explanation:
Answer:
8√2
Step-by-step explanation:
Idea 1 : (Pythagorean theorem)
2x² = 16²
then
2x² = 256
then
x² = 256/2 = 128
then
x = √128
then
x = √(64×2)
then
x = √64 × √2
then
x = 8√2
………………………………………………………
Idea 2 : (diagonal of a square)
16 is the diagonal of a square with side square of lengths x
Then
x√2 = 16
Then
[tex]x = \frac{16}{\sqrt{2} } =\frac{8\times2}{\sqrt{2} } =\frac{8\times\sqrt{2} \times \sqrt{2} }{\sqrt{2} } =8\sqrt{2}[/tex]
Which is the graph of the cube root function f(x) = RootIndex 3 StartRoot x EndRoot?
The graph of a function f(x) = ∛x is shown in the picture, and the domain of the function will be all real numbers.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
We have a function:
f(x) = ∛x
The domain of the function will be all real numbers.
x ∈(-∞, ∞)
The graph will be curved.
Plug x = 0, y = 0
x = 1, y = 1
The graph is shown in the attached picture.
Thus, the graph of a function f(x) = ∛x is shown in the picture, and the domain of the function will be all real numbers.
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Volume= m3
What is the volume? Help me please. Thanks
Answer: 5.22
Step-by-step explanation:
The apothem = 87 cm = 0.87 m.
Using the formula [tex]A=\frac{1}{2}ap[/tex] to find the area of the base, where a is the apothem and p is the perimeter, we get [tex]A=\frac{1}{2}(0.87)(6)=2.61[/tex]
So, using the formula [tex]V=Bh[/tex], we get the volume to be [tex]2.61(2)=5.22 \text{ m}^{3}[/tex]
The population of a small town is decreasing exponentially at a rate of 14.3% each year. The current population is 9,400 people. The town's tax status will change once the population is below 6,000 people.
Create an inequality that can be used to determine after how many years, t, the town's tax status will change, and use it to answer the question below.
Will the town's tax status change within the next 3 years?
Using an exponential function, the inequality is given as follows:
[tex]9400(0.857)^t < 6000[/tex]
The solution is t > 2.9, hence the tax status will change within the next 3 years.
What is an exponential function?A decaying exponential function is modeled by:
[tex]A(t) = A(0)(1 - r)^t[/tex]
In which:
A(0) is the initial value.r is the decay rate, as a decimal.For this problem, the parameters are given as follows:
A(0) = 9400, r = 0.143.
The population after t years is modeled by:
[tex]A(t) = A(0)(1 - r)^t[/tex]
[tex]A(t) = 9400(1 - 0.143)^t[/tex]
[tex]A(t) = 9400(0.857)^t[/tex]
The tax status will change when:
[tex]A(t) < 6000[/tex]
Hence the inequality is:
[tex]9400(0.857)^t < 6000[/tex]
Then:
[tex](0.857)^t < \frac{6000}{9400}[/tex]
[tex]\log{(0.857)^t} < \log{\left(\frac{6000}{9400}\right)}[/tex]
[tex]t\log{0.857} < \log{\left(\frac{6000}{9400}\right)}[/tex]
Since both logs are negative:
[tex]t > \frac{\log{\left(\frac{6000}{9400}\right)}}{\log{0.857}}[/tex]
t > 2.9.
The solution is t > 2.9, hence the tax status will change within the next 3 years.
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Please include what axioms and theorems were used as well.
Part (i)
1. ABCD is a quadrilateral in which AD=BC and ∠DAB=∠CBA (given)
2. AB = AB (reflexive property)
3. Triangles ABD and BAC are congruent (SAS)
Part (ii)
4. BD=AC (corresponding sides of congruent triangles are equal)
Part (iii)
5. ∠ABD = ∠BAC (corresponding angles of congruent triangles are equal)
Answer:
Hey!
In △ABD and△BAC,
AD = BC (it's given)
∠DAB = ∠CBA (it's given)
AB = BA (Common)
By SAS congruence rule,
∴△ABD≅△BAC
=> BD = AC (By C.P.C.T) (ii)
And, ∠ABD = ∠BAC (By C.P.C.T) (iii)
Hope it helps, any confusions you may ask.
A cyclist traveled kilometers per hour faster than an in-line skater. In the time it took the cyclist to travel kilometers, the skater had gone kilometers. Find the speed of the skater.
The speed of skaters was 10 km per hr.
How to solve?
Mathematically, the speed of an object is directly proportional to the distance traveled and inversely proportional to the time taken. In simple words, the more the speed, the distance traveled is more in a short period and vice-versa.
Let the speed of the skater be x
We know, speed = [tex]\frac{Distance}{Time}[/tex]
According to the question:
[tex]\frac{20}{x} = \frac{40}{x + 10}[/tex]
Cross multiplying both sides,
20(x+10) = 40x
20x + 200 = 40x
20x = 200
x = 10
Thus, the speed of skaters was 10 km per hr.
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Sadie earned $21.25 more than in week .
Her earnings vary directly with her number of hours worked
How to determine the variation?The hourly rate is given as:
Rate = $21.25 per hour
This means that:
She earns $21.25 each hour
This in other words means that, her earning increases as the number of hours increase.
The above is an illustration of a direct variation.
Hence, her earnings vary directly with her number of hours worked
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Complete questionSadie earns $21.25 per hour. Do her earnings vary inversely or directly with her number of hours worked?
Use the equation k = x÷ y to find the constant of proportionality for the set of values
below. Then, complete the table with three more values. Graph the points on the
coordinate plane, draw a line through the points, and answer the question.
How does the graph show that the change of rate is constant
The constant of proportionality is 1/3
and three more values are
x 1 2 3 4 5
y 3 6 9 12 15
VariationFrom the question, we are to determine the constant of proportionality
The given equation is
k = x ÷ y
From the given information,
When x = 1, y = 3
∴ k = 1 ÷ 3
k = 1/3
Thus, the constant of proportionality is 1/3
Now, we will determine the values of y for the values x = 3, x = 4, and x = 5
Since
k = x ÷ y
Then,
y = x ÷ k
When x = 3
y = 3 ÷ 1/3
y = 3 × 3
y = 9
When x = 4
y = 4 ÷ 1/3
y = 4 × 3
y = 12
When x = 5
y = 5 ÷ 1/3
y = 5 × 3
y = 15
Hence, the constant of proportionality is 1/3
and three more values are
x 1 2 3 4 5
y 3 6 9 12 15
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The manager of a cafeteria that caters only to the workers at a hospital wants to conduct a survey to determine which drink served at the cafeteria is most popular during lunch. What is the population that the manager is studying?
A. Hospital workers who go out for lunch.
B. Hospital workers who bring lunch from home.
C. Hospital workers who eat in the cafeteria.
D. Hospital workers’ families.
Answer:
Hello!
The manager of a cafeteria that caters only to the workers at a hospital wants to conduct a survey to determine which drink served at the cafeteria is most popular during lunch. What is the population that the manager is studying?
The correct answer would be:
C. Hospital workers who eat in the cafeteria
Hope this helps.
Scientists are preparing two satellites to be launched. The equation y=400x represents the number of miles, y, that the satellite, Space Explorer B, flies in x hours. The satellite, Space Explorer A, flies 36400 miles in 13 hours. How many fewer miles does Space Explorer B travel in one hour than Space Explorer A?
Answer:
2400 miles
Step-by-step explanation:
So the first equation is pretty straight forwards, it's in the slope-intercept form y=mx+b where m is the slope, and b is y-intercept, since as x increases by 1, the value y increases by m, which by definition is what the slope is, so m is the slope. In this context the slope is how many miles in x hours. So Space Explorer B flies 400 miles per hour. The amount of miles that Space Explorer A flies per mile can be calculated by dividing the 36400 by the 13 hours it had to travel. This gives you 2800 miles. So to find how many fewer miles Space Explorer B travels than Space Explorer A you subtract the 2 slopes. 2800 - 400 = 2400. So Space Explorer B travels 2400 fewer miles than Space Explorer A
Please explain urgent! Brainly to anyone who can answer!
Answer:
JK ≈ 6.86 units
Step-by-step explanation:
According to the diagram MK is the angle bisector of ∠LMJ in the triangle LMJ.
Use angle bisector theorem, which states:
an angle bisector of an angle of a triangle divides the opposite side into two parts that are proportional to the other two sides of the triangle.Applied to the given triangle, the ratios are:
LK/JK = LM/JMUse segment addition postulate and substitute known values to get:
(LJ - JK)/JK = LM/JM(14 - JK)/JK = 50/4850JK = 48(14 - JK)50JK = 672 - 48JK50JK + 48JK = 67298JK = 672JK = 672/98JK = 6.86 (rounded)Is anyone able to solve this?
The value of ? and X are 24 and 32 respectively
Similarity theorem of a triangleA triangles is 2D shape with three sides and angles.
From the given diagram, the ratio of similar sides is equal to a constant as shown;
15/20 = 9+15/20+x
Cross multiply
15/9+15 = 20/20+x
15/24 = 20/20+x
Comparing with the given ratio
? = 24
X = 20+x
Find x
15(20+x) = 480
300 + 15x = 480
15x = 180
x =12
X = 20 +x
X= 32
Hence the value of ? and X are 24 and 32 respectively
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the sum of perimeter of two similar polygons is 24cm,and the ratio of their corresponding sides is 1:3, find the perimeter of the larger polygon
Answer:
18
Step-by-step explanation:
Polygon A : Polygon B = x : 3x
4A = 24
A = 6
B = 18
B is the larger polygon so the perimeter is 18.
Two different numbers are selected simultaneously and at random from the set {1,2,3,4,5,6,7,8,9,10}. What is the probability that the positive difference between the two numbers is 3 or greater
The probability of getting positive difference between the numbers 3 or greater between 1,2,3,4,5,6,7,8,9,10 if two numbers are selected is 28/45.
Given Numbers:{ 1,2,3,4,5,6,7,8,9,10}
We have to find the probability that the positive difference between the numbers selected is 3 or greater.
Probability is the likelihood of happening an event among all the events possible.
Total number of combinations when two numbers are selected from 10 numbers is 10 C 2=10!/2!(10-2)!
=10*9*8!/2*1(8!)
=10*9/2
=45 combinations
Combinations of numbers whose difference will be 3 or more are: (10,7),(10,6),(10,5),(10,4)(10,3)(10,2)(10,1)(9,6)(9,5)(9,4)(9,3)(9,2)(9,1)(8,5)(8,4)(8,3)(8,2)(8,1)(7,4)(7,3)(7,2)(7,1)(6,3)(6,2)(6,1)(5,2)(5,1)(4,1)
Total numbers =28
Probability=numbers/total combinations
=28/45
Hence the probability that two numbers selected gives difference of 3 or more is 28/45.
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Which irrational number can be multiplied by –StartRoot 41 EndRoot to get a product that equals 1?
StartRoot StartFraction 1 Over 41 EndFraction EndRoot
Negative StartRoot 41 EndRoot
Negative StartRoot StartFraction 1 Over 41 EndFraction EndRoot
StartRoot 41 EndRoot
The irrational number that can be multiplied to produce 1 is - √41/41
Irrational numbersLet the following expression
-√41 x = 1
We are to find the value of x that will make the expression true
√41 x = -1
Divide both sides by √41
√41 x/ √41 = -1/ √41
x = - √41/41
Hence the irrational number that can be multiplied to produce 1 is - √41/41
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I need help with both geometry questions.
Answer:
5) x = 5
6) x = 8
Step-by-step explanation:
5) Since RT is 40 and RS is 15, ST = RT- RS=25
Since ST also equals 5x, 5x = 25 and x = 5.
6) Since ∠CBD and ∠DBA are supplementary, they add up to [tex]180^\circ[/tex], and because ∠CBD = [tex]90^\circ[/tex], ∠DBA = [tex]90^\circ[/tex].
Since ∠DBA - ∠DBE = ∠EBA, ∠EBA = [tex]90^\circ-40^\circ=50^\circ[/tex].
Also ∠EBA = 6x + 2, so 6x + 2 = [tex]50^\circ[/tex].
6x = 48, and x = 8.
To graph the inequality y> 5x - 4, you would draw a solid line.
A. True
B. False
Answer:
The answer is B
Step-by-step explanation:
Answer:
False
Step-by-step explanation:
y > 5x-4
This inequality is greater than, so it would be a dotted line
You would have a solid line when it is greater than or equal to ≥ or less than or equal to ≤
Determine whether the ordered pair (1, 1) is a solution of the inequality. y ≤ -3x+1
-------------------------------------------------------------------------------------------------------------
Answer: [tex]\textsf{(1, 1) is NOT a solution of the inequality}[/tex]
-------------------------------------------------------------------------------------------------------------
Given: [tex]y \le-3x + 1[/tex]
Find: [tex]\textsf{Determine if (1, 1) is a solution of the inequality}[/tex]
Solution: In order to determine if (1, 1) is a solution we need to plug in 1 for the x values and 1 for the y values and see if the equation evaluated to true.
Plug in the values
[tex]y \le-3x + 1[/tex][tex]1 \le-3(1) + 1[/tex]Simplify
[tex]1 \le-3 + 1[/tex][tex]1 \le-2[/tex]As we can see the expression states that 1 is less than or equal to -2 which is false therefore (1, 1) is NOT a solution of the inequality.
Hey there!
Keywords and Concepts:Algebra I
Inequality
Ordered pair
How do we determine whether an ordered pair is a solution of a given inequality?Step 1: Define.y ≤ -3x+1
Step 2: Plug in the given values.1 ≤ -3(1) + 1
Step 3: Multiply (Identity Property of 1).1 ≤ -3 + 1
Step 4: Add.1 ≤ -2
Step 5: Validate. Is the statement true?The statement is NOT true as 1 is not less than or equal to -2.
Therefore, the ordered pair is not a solution of the inequality.
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a number is chosen ar random from 1 to 50. find the probaility of selecting multiplies of 3
Answer:
16/50 or 32% chance of getting a multiple of 3
Step-by-step explanation:
Starting at 0 and going to 50, there are 16 numbers in the range that are multiples of 3.
3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, and 48
Attached is a chart for reference!
So, 16 of the 50 numbers are multiples of 3, making your odds 16/50 (divide that to get .32 which = 32%!)
step by step explanation:
(multiples of 3)= 3 , 6 ,9, 12 ,15, 18 ,21 ,24, 27, 30, 33, 36 ,39 ,42, 45 and 48
probability (multiples of 3)= nó of required outcome/ nó of possible outcome
16 /50 = 8/25 ( you get this after dividing 16/50)
in percentage 8/ 25 would give you 32%
For the equation y = 3×2¹ +4 what is the value of y when x = 1?
Answer:
See below.
Step-by-step explanation:
Is the equation written correctly?
y = 3×2¹ +4 has no variable, unless the "3×2" is supposed to be "3x*2^1"
If so,
y = 3x*2¹ +4 for x = 1 would be
y = 3(1)2¹ +4
y = 3*2 +4
y = 10
⊰________________________________________________________⊱
Answer:
See Below.
Step-by-step explanation:
[tex]\large\begin{gathered} \sf{Start \ by \ plugging \ in \ the \ number \ that \ x \ is: 1} \\ \sf{Now, \ evaluate: y=3*1*2^1+4} \\ \sf{y=3*2+4} \\ \sf{Multiply \ 3 \times 2 \ first: y=6+4} \\ \sf{Now, \ just \ add: y=10}{ \end{gathered}[/tex]
Done!!
⊱________________________________________________________⊰
[tex]\bf{\overbrace{C}\underbrace{A}\overbrace{LL}\underbrace{I}\overbrace{G}\underbrace{R}\overbrace{A}\underbrace{P}\overbrace{H}\underbrace{Y}}[/tex]
Will give brainliest and about 50-100 points if done right!
Answer:
1st = [tex]A. \sf \ y = 1[/tex]
2nd = [tex]D. \ \sf y - 5 = 3(x + 2)[/tex]
PART A
Given: y = -2
This equation has a slope of 0
Equation that pass (-1, 1)
y - 1 = 0(x -(-1))
y = 1
PART B
[tex]\sf Given : y = -\dfrac{1}{3} x + 2[/tex]
Here slope is -1/3 and y-intercept is 2
Perpendicular lines has negatively inverse slope.
→ per. slope = -(slope)⁻¹ = -(-1/3)⁻¹ = 3
Equation in point slope form:
[tex]\sf y - y_1 = m(x - x_1)[/tex]
[tex]\sf y - 5 = 3(x - (-2))[/tex]
[tex]\sf y - 5 = 3(x + 2)[/tex]
Answer:
[tex]y = 1[/tex]
[tex]y-5=3(x+2)[/tex]
Step-by-step explanation:
The line [tex]y = -2[/tex] is a horizontal line.
Therefore, a line that is parallel to the given line and passes through point (-1, 1) is another horizontal line with the y-value of the point.
Therefore, the line is [tex]y = 1[/tex]
----------------------------------------------------------------------------------
Slope-intercept form of a linear equation:
[tex]y=mx+b[/tex]
where:
m is the slopeb is the y-interceptGiven linear equation:
[tex]y=-\dfrac{1}{3}x+2[/tex]
Therefore, the slope of this equation is -1/3.
If two lines are perpendicular to each other, the product of their slopes will be -1. Therefore, the slope (m) of the line perpendicular to the given line is:
[tex]\implies m \cdot -\dfrac{1}{3}=-1[/tex]
[tex]\implies m=3[/tex]
Use the point-slope form of a linear equation, with the found slope and the point (-2, 5) to create the equation:
[tex]\implies y-y_1=m(x-x_1)[/tex]
[tex]\implies y-5=3(x-(-2))[/tex]
[tex]\implies y-5=3(x+2)[/tex]
Help me please would help me a lot
Answer:
Step-by-step explanation:
Argument
One of the ways to recognize the domain is that it should be on the x axis of a graph. That lets out A and D. They are both describing the y axis. t = 0 has no meaning with this question.
Answer B
Find the probability that a single randomly selected value is greater than 204.3. Round your answer to four decimal places.
The answer is P(>204.3) = 0.5000
There are an infinite number of real numbers > 204.3, but an equally infinite number of real numbers < 204.3
The chance of randomly selecting a number >204.3 is 1/2 or 50%
or for 4 decimals: 50.0000%
The probability of an event can be calculated via chance formula with the aid of truly dividing the favorable range of effects by means of the whole number of feasible effects.
Opportunity = the wide variety of ways of achieving fulfillment. The whole range of viable effects. As instance, the possibility of flipping a coin and it being head is ½, because there is 1 way of having a head and the whole range of viable effects is two (a head or tail).
Chance is the department of mathematics that research the possible outcomes of given occasions together with the outcomes' relative likelihoods and distributions.
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If the mass of the empty container is 250 grams and the final mass of the container with liquid is 1,300 grams, calculate the mass of the liquid by itself.
Hello!
To find the mass of the liquid by itself, subtract the mass of the container from the mass of the liquid and container.
⇒ 1,300 - 250
⇒ 1,050 grams
∴ The mass of the liquid by itself is 1,050 grams.
Find the expression that is equivalent to 3(x2 + 2x + 5).
7x2 - 18 - 4x2 – 3 + 6x
7x2 +18 - 4x2 – 3 + 8x
7x2 +18 - 4x2 – 3 + 6x
7x2 +18 - 3x2 – 3 + 6x
Answer:
c. 7x2 +18 - 4x2 – 3 + 6x
Step-by-step explanation:
3(x^2 + 2x + 5)
3x^2 + 6x + 15
a.) 7x^2 - 18 - 4x^2 – 3 + 6x
= 3x^2 - 21 + 6x
b.) 7x^2 +18 - 4x^2 – 3 + 8x
= 3x^2 + 15 + 8x
c.) 7x2 +18 - 4x2 – 3 + 6x
= 3x^2 + 15 + 6x
d.) 7x2 +18 - 3x2 – 3 + 6x
= 4x^2 + 15 + 6x
Sumin bought a pen and a book for $x. the pen cost $5. (a) express the cost of the book in terms of x. (b) if x = 11, find the cost of the book. (c) if x = 15, find the cost of the book.
Answer:
a. x = total - $5
b. x = $6
c. x = $10
Step-by-step explanation:
a. pen + book = total
Let x = book
$5 + x = total
x = total - $5
b. pen + book = total
Total = 411
$5 + x = $11
x = $11 - $5
x = $6
c. pen + book = total
Total = $15
$5 + x = $15
x = $15 - $5
x = $10
A mini-golf course is determining the par score for each of its holes. the dot plot shows the number of strokes required to place a ball in the ninth hole for a sample of 31 players. a number line going from 1 to 9. 2 dots are above 1. 3 dots are above 2. 4 dots are above 3. 5 dots are above 4. 5 dots are above 5. 3 dots are above 6. 2 dots are above 7. 0 dots are above 8. 1 dot is above 9. which measure of center is best to use to determine the expected number of strokes required for the ninth hole?
The mean is the best central tendency to measure the expected number of strokes required for the ninth hole.
What is mean?
In statistics, in addition to the mode and median, the mean is one of the measures of central tendency. Simply put, the mean is the average of the values in the given set. It indicates that values in a particular data set are distributed equally.
The three most frequently employed measures of central tendency are the mean, median, and mode. The total values provided in a datasheet must be added, and the sum must be divided by the total number of values in order to determine the mean.
Why mean is the best choice in this case?
Since it considers all of the data in relation to one another, the mean is an effective indicator of central tendency. When there are outliers (extreme values) in the data, for example, the mean is a poor measurement; in this situation, the median is preferable.
The data set is roughly symmetrical in the scenario described in the question, so the mean is the most-suited central tendency measure to employ here.
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Answer:
The mean is the best choice because the data is nearly symmetrical.
anybody can help me?
The proportional relationship is correctly graphed by graph vs.
What is a proportional relationship?A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:
y = kx
In which k is the constant of proportionality.
In this problem, the relationship that gives the montant M considering the number of items sold n is:
M = 3n.
Considering that the montant is the vertical axis, the graph is composed by points (n, 3n), that is, points (100, 300), (200, 600) and so on, hence the graph is graph vs.
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Select the correct answer
Answer:
option b is the answer
Step-by-step explanation: