Answers
x < 18 is the solution to the inequality -13 < 5 - x.
What is the solution to the given inequality?Given the inequality in the question;
-13 < 5 - xx = ?To solve the inequality, move all terms containing variable to the left side and the constant to the right side of inequality.
-13 < 5 - x
Add 13 to both sides
-13 + 13 < 5 + 13 - x
0 < 5 + 13 - x
Add 5 and 13
0 < 18 - x
Now, add x to both sides
0 + x < 18 - x + x
-x and x cancel out
0 + x < 18
x < 18
Therefore, the solution is x < 18.
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Related Questions
(-17.2 x 2.5) x 4 Write your answer as a decimal
Answers
Answer as a decimal is -172.
Given :
= (-17.2 x 2.5) x 4
= (-43) x 4
= -172
Therefore the answer as a decimal is -172.
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can anybody tell me what 11.8 x 5 is step by step ?
Answers
Step-by-step explanation:
hope this helps!! the explanation is in my working. bring the "4" from the "40" (8 x 5) to the top of "1"
Answer:
59
Step-by-step explanation:
To mutlipy a decimal by a whole number, just multiply it like normal
118 x 5 = 590
11.8 has one decimal place so your answer will have one too
59.0 which is the same as 59
Which expression is equivalent to k4⋅m9⋅−(k5m4)0?
Answers
Answer: eighty-eight thousand
Step-by-step explanation:
The expression equivalent to [tex]k^4m^9 - (k^5m^4)[/tex] would be; [tex]k^{-1}m^5[/tex]
What are equivalent expressions?Those expressions that might look different but their simplified forms are the same expressions are called equivalent expressions.
To find equivalent expressions of some expressions, we can either make it look more complex or simple. Usually, we simplify it.
We need find the expression into an equivalent form [tex]k^4m^9 - (k^5m^4)[/tex]
This expression could also be given by;
[tex]k^4m^9 - (k^5m^4)[/tex]
Now subtract the like terms to get the values then we get;
[tex]k^4m^9 - (k^5m^4)[/tex] = [tex]k^{-1}m^5[/tex]
Hence, the expression equivalent to form [tex]k^4m^9 - (k^5m^4)[/tex] would be; [tex]k^{-1}m^5[/tex]
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Solving Systems of Equations by Substitution
-2x-y=-9
5x-2y=18
explain please.
Answers
Answer:
(4,1)Step-by-step explanation:
Systems of equations may be solved in one of two manners: substitution and graphing. This requaests they be solved by substitution, but I'll add the graphing solution, also.
Substitution:
We want to eliminate one of the two variables to result in an expression that only has one of the two remaining. We can do that by manipluating one of the equations such that, when it is combined with the other, results in the elimination of one of the variables.
Given:
-2x-y=-9
5x-2y=18
we can multiply or divide one of the equations so that one of the terms has equal, but opposite, values. We could multiply the first equation by 2.5 so that it becomes -5x -2.5y = 9*(2.5). Then it could be added to the second to eliminate the x term.
My preference is to find a way to avoid fracticious fractions, so I will multiply the first equation by -2 so that we can eliminate y:
-2*(-2x-y =-9)
4x+2y = 18
No add this to the second equation:
4x+2y = 18
5x-2y = 18
9x = 36
x = 4
Since x = 4:
-2x-y=-9
-2*(4)-y=-9
-8 - y = -9
y = 1
The solution is (4,1). It is the point the satisfies both equations.
-2x-y=-9
-2(4)-(1)=-9
-8-1=-9 YES
----
5x-2y=18
5(4)-2(1)=18
20 - 2 = 18 YES
Graphing:
The solution to these equations is the point at which the lines intersect. See the attached graph. The lines intersect at (4,1).
Find the monthly interest payment in the situation described below. Assume that the monthly interest rate is 1/12 of the annual interest rate. You maintain an average balance of $500 on your credit card, which carries an 18% annual interest rate. WHat is the monthly interest payment?
Answers
Using an average credit card amount of $500 and an annual percentage rate of 18%, the monthly interest payment is $7.5.
It is possible to calculate the monthly interest payment as follows:
I = [tex]\frac{PNR}{100}[/tex]
Given P = 500, N = 1, R = 18%
[tex]I = \frac{500*1*18}{100}[/tex]
[tex]I = \frac{9000}{100}[/tex]
[tex]I = 90[/tex]
Yearly Interest is $[tex]90[/tex]
Monthly interest :
[tex]M.I = \frac{18}{12}[/tex]
[tex]M.I = 1.5%[/tex]
Monthly interest payment = $[tex]500*1.5[/tex]= $[tex]7.5[/tex]
Monthly interest payment:
The percentage of the monthly payment earmarked for paying off the loan charge is referred to as the monthly interest payment.
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pls help me is due in 30 min
Answers
1540 / 2200 = 0.7
0.7 x 100 = 70%
Final answer - 70%
Find the volume of the cylinder
Answers
Answer: 150.72 in^3
Step-by-step explanation:
the radius (r) is 2 because the diameter of the cylinder is 4.
the height (h) is 12 (obviously because that's provided in the picture.)
the formula to find the volume of the cylinder is:
[tex]3.14(2^2)\times 12[/tex]
therefore, it is 150.72 in^3
i hope this helps :)
Problem: Mickey Mouse has an account balance of $250 and is withdrawing $15 per
week. Minnie Mouse has $100 in her bank account and deposits $10 each week. At what
week will they have the same amount in their accounts? What will that amount be?
What are you trying to find out:
Workspace:
Solution:
Answers
If you’re depositing money to an account, you are adding more money. So, you’ll use addition.
What are you trying to find out: At what week will both Minnie And Mickey Mouse have an equal account balance? How much money will they both have in their account at that week?
So we can find the answer by using the equation, 250 - 15x = 100 + 10x where the variable x represents the amount of weeks.
Workspace:
You can either replace the x with multiple numbers until you get your answer or solve the problem a quicker way.
1. Move all terms containing x to the left
250 - 15x = 100 + 10x
Use inverse operations, so instead of + 10 you’ll - 10. You can only add, subtract, multiply, and divide alike terms.
250 - 15x - 10x = 100
250 - 25x = 100
2. Move all terms that do NOT contain x to the right
To do this you must do inverse operations, so - 250, remember that you can only preform operations on alike terms.
-25x = 100 - 250
-25x = - 150
3. Divide each term by -25
A variable next to a number means multiplication, and division is the opposite of multiplication.
-25x/-25 = -150/-25
Cancel out both -25s on the left but leave the x
x = -150/-25
x = 6
So, at week 6 both will have the same amount of money in their account. We still have to answer the second question, what will the amount be? But, all we have left to do is replace the x with 6, and figure out the rest, which should be easy.
250 - 15(6) = 100 + 10(6)
250 - 90 = 100 + 60
160 = 160
Solution: At week 6, both Mickey and Minnie Mouse will have an equal amount of money in their account, which would be $160.
you have $1 and you are going to buy some pencils and 7 patties let X represent the number of pencils you can buy and let y represent the number of peppermint patties you can buy if pencils cause 0.10 each and Peppermint Patties cost 0.05 each write a linear equation in standard form that represents this situation what does the x intercept represent? what does the Y intercept represent
Answers
Let:
x = Number of pencils you can buy
y = Number of peppermint patties you can buy
a = cost of each pencil
b = cost of each peppermint patty
The standard form of a linear equation is given by:
[tex]\begin{gathered} Ax+By=C \\ \\ \end{gathered}[/tex]So:
[tex]0.1x+0.05y=1[/tex]The graph of this equation is:
The x-intercept represents the maximum number of pencils you can buy
The y-intercept represents the maximum number of peppermint patties you can buy
3. Solve the following equations.
a. 33.5 ÷ 10 = b. 412 ÷ 10 =
c. 73.6 ÷ 10 = d. 6,132 ÷ 10 =
4. Explain the placement of the decimal point when dividing by a power of 10.
Answers
The corresponding solutions of equations a, b, c and d are 3.35. 41.2, 7.36 and 613.2
How to solve an equation with powers of 10?a. 33.5 ÷ 10 = 3.35
b. 412 ÷ 10 = 41.2
c. 73.6 ÷ 10 = 73.6
d. 6,132 ÷ 10 = 613.2
When a number is divided by powers of 10, the decimal point moves to the left side by the number of places the power has e.g
345 ÷ 10 = 34.5 (It moves one place to the left because the power of 10 is 1 i.e. 10 = 10²)
3456 ÷ 100 = 34.56 (It moves two places to the left because the power of 100 is 2 i.e. 10 = 10²)
Therefore, the solution of a, b, c and d are 3.35. 41.2, 7.36 and 613.2 respectively.
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please help me and show work
Answers
Answer:
C
Step-by-step explanation:
find the gradient of the 2 points (2,6) &(-3,2)
y2-y1/x2-x1...use the gradient formula
-2-6/-3-2
=-8/-5
=8/5
therefore the line parallel to this line will have the same answer
Therefore C is correct
The area of the triangle below is 60 in2. What is the perimeter?
Answers
Answer:
P = 63 inches
Step-by-step explanation:
the area (A) of a triangle is calculated as
A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the height )
here b = 2x - 6 , h = 4 and A = 60 , then
[tex]\frac{1}{2}[/tex] × 4 ×(2x - 6) = 60
2(2x - 6) = 60 ( divide both sides by 2 )
2x - 6 = 30 ( add 6 to both sides )
2x = 36 ( divide both sides by 2 )
x = 18
2x - 6 = 2(18) - 6 = 36 - 6 = 30
perimeter (P) is the sum of the 3 sides , so
P = 18 + 30 + 15 = 63 inches
Select the correct constant rate of change for each table of data.
Answers
The constant rate of change for the tables are:
First table: 10
Second table: 12.
Third table: 1/12.
Last table: 1/10.
How to Find the Constant Rate of Change of a Table?To find the constant rate of change (k) of a table of x and y variables, the formula that can be used is:
k = y/x.
Any pair of values, (x, y), from the given table can be used in finding the constant rate of change between the two given variables in each of the tables.
a. The constant rate of change of the first table = 110/11 = 70/7 = 30/3 = 10.
b. The constant rate of change of the second table = 108/9 = 12.
c. The constant rate of change of the third table = 10/120 = 1/12.
d. Constant rate of change for the last table = 10/100 = 1/10.
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The length of the hypotenuse of a right triangle is 13cm. The length of one leg is 5cm. Find the length of the other leg.
Answers
5^2 = 25
x^2 + 25 = 169
169 - 25 = 144
Square root of 144 = 12
12cm
2) The graph represents the cost of a medical treatment, in dollars, as a function of time, d, in decades since 1978.
It is said that the expression 150(1.8225) ଷrepresents the cost of medical treatment sometime after
1978.
a) Which year does it represent?
b) What would be the medical cost in 1998?
c) If this trend continues, what are the medical costs in 2022?
Answers
Since 1978, the graph shows the dollar cost of a medical procedure as a function of time, d. In 1993 year does it represent.
The cost of treatment when d = 1 is $273
Given that,
Since 1978, the graph shows the dollar cost of a medical procedure as a function of time, d.
We have to find in which year does it represent.
Let the equation be
y=150×[tex]e^{at}[/tex]
Where t is the time for year
According to the figure,
y pass (0.5,202.50)
We get,
202.5=150×[tex]e^{0.5a}[/tex]
[tex]e^{0.5a}[/tex]=1.35
Now,
150×(1.35)³=150×[tex](e^{0.5a})^{3}[/tex]
150×(1.35)³=150×[tex]e^{1.5a}[/tex]
1.5 is for 15 years.
1978+15=1993.
Therefore, in 1993 year does it represent.
The graph represents an exponential function:
[tex]$$y=a b^x$$[/tex]
When (x, y)=(0,150), the equation becomes
[tex]$$\begin{aligned}&150=a b^0 \\&a=150\end{aligned}$$[/tex]
When (x, y)=(0.5,202.5), the equation becomes [tex]$202.5=a b^{0.5}$[/tex]
Substitute 150 for a
[tex]$$202.5=150 b^{0.5}$$[/tex]
Divide both sides by 150
[tex]$$1.35=b^{0.5}$$[/tex]
Square both sides
b=1.82
So, the equation of the graph is:
y=150 * 1.82^x
When x=1, we have:
[tex]$$\begin{aligned}&y=150 * 1.82^1 \\&y=273\end{aligned}$$[/tex]
Hence, the cost of treatment when d=1 is [tex]$\$ 273$[/tex].
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What table represents a function?
Answers
Table A represents a function.
Define functions.A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.
Functions are crucial instruments in the creation of mathematical models because we continually develop beliefs about connections between variables in nature and society. Typically, functions in school mathematics contain numerical inputs and outputs and are frequently specified by algebraic expressions.
Given,
Table A represents a function,
A visual table with columns and rows that shows the function in relation to the input and output is called a function table. Function tables are frequently referred to as function machines by younger students. Each function has a rule that governs how the input and output are related to one another.
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If 672,342= 6.72342x 10n what is the value of n
Answers
An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
The value of n in the equation 672,342 = 6.72342 x 10n is 10,000
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x = 9 is an equation.
6x+ 2 = 9 is ana equation.
We have,
672,342 = 6.72342 x 10n
Divide both sides by 6.72342
672,342 / 6.72342 = 10n
We get,
100000 = 10n
Divide both sides by 10.
100000 / 10 = n
n = 10,000
Thus,
The value of n in the equation 672,342 = 6.72342 x 10n is 10,000
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write 3/4 in lowest terms
Answers
Answer:
that is the lowest term I think
rectangular paperboard measuring 28 long and 18 wide has a semicircle cut out of it, as shown below. Find the area of the paperboard that remains. Use the value for , and do not round your answer. Be sure to include the correct unit in your answer.
Answers
Perimeter that remains after the semicircle is removed = 377.77
How to find area of the paperboard ?
Length of paper board = 28
Width of paper board = 18
Now, the area of the board = 28 * 18 = 505
Radius of the semi circle = Half of the width of the paperboard = 9
Area of semicircle is = 1/2πr² = 127.23so the area of paperboard is 505 and semicircle is 127.23 .
TO find area of paper board after the cutting semi circle = 505 - 127.23
= 377.77
The remaining area of rectangle is 377.77
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What is r, -3(1+6r)=14-r
Answers
Step-by-step explanation:
-3(1+6r) = -3-18r =14-r
17r = -17 Therefore, r = -1
|x| + 4> 8 .............
Answers
Answer:
x>4, x<-4
Step-by-step explanation:
|x| + 4 > 8
|x| > 4
x>4, x<-4
Write three numbers that are divisible by 2, 4, 8, and 10
Answers
Answer:
40, 80, 120
Step-by-step explanation:
-they’re common multiples of 2, 4, 8, and 10
A medical company tested a new drug for possible side effects. The table shows the relative frequency that a study participant experienced the side effect.
Does this data suggest an association between age and experiencing side effects?
Answers
Solve for X please help I do not understand !
Answers
Answer:
x=45
Step-by-step explanation:
Melissa's average daily balance for the last month was $560. The finance charge was $8.12.
What was the monthly percentage rate? Round to the nearest hundredth of a percent.
Answers
Answer:
1.45%
Step-by-step explanation:
[tex] \frac{8.12}{560} (100) = .0145(100) = 1.45\%[/tex]
Simplify as far as possible without a calculator.
(
3
−
√
7
)
(
3
−
√
7
)
Answers
Answer:
- 26
Step-by-step explanation:
(3−√7)(3−√7)
9 - 3√7 -3√7 + √7√7
9 - 6√49 + √49
9 - 6*7 + 7
9 - 42 + 7
= -26
Find the area of a square tile which has a width of 3x - 5
Answers
Answer:
[tex]9x^2 - 30x + 25[/tex]
Step-by-step explanation:
To solve for area, multiply the width times the height. In this case, since the shape is a square, the width is the same as the height. So, multiplying 3x - 5 times 3x - 5 should give us the area.
[tex](3x-5)(3x-5)\\(3x)(3x) + (3x)(-5) + (-5)(3x) + (-5)(-5)\\9x^2 - 15x - 15x + 25\\9x^2 - 30x + 25[/tex]
If you don't understand the algebra there, use an area model, and please let me know if you're not sure how to do that. I'll help you out as much as I can! :)
5 girls decide to only spend $40 between them. on average, how much money can each girl spend? Write an inequality. Each sister has 10 dollars
Answers
40 = 5X
X = 10 dollars
Now divide 40/5 = 8
On average, each girl spends $8 dollars
Now write an inequality ,for this situation
5X ≤ 40
(a + b + c + d + e)/5 = 40
For the function g, g(3)= -11 and g(7)= 5. What is the function rule for g(x)?
Answers
Answer:
g(x) = 4x - 23
Step-by-step explanation:
We will assume a linear function for g(x)
This will be of the form g(x) = ax + b where a and b are constants
Given the info,
g(3) = a(3) + b = -11
g(7) = a(7) + b = 5
Thus we have two equations in a and b
3a + b = -11 [1]
7a + b = 5 [2]
Subtract [1] from [2]:
7a + b - (3a + b) = 5 - (-11)
7a + b - 3a - b = 5 + 11
4a = 16
a = 4
Substitute for a in equation [2]:
4(7) + b = 5
28 + b = 5
b = 5-28 = -23
So equation of g(x) is
g(x) = 4x - 23
10. Higher Order Thinking Winston compares the heights of two plants
to see which plant grows more per day. The table shows the height
of Plant 1, in centimeters, over 5 days. The graph shows the height
of Plant 2, in centimeters, over 10 days. Winston says that since
Plant 1 grows 6 cm per day and Plant 2 grows 4 cm per day,
Plant 1 grows more per day.
Plant 1
Days
2
Height (cm) 6
a. Do you agree with Winston? Explain your response.
3 4 5
9 12 15
b. What error might Winston have made?
Answers
Answers to both subparts are shown:
Although Plant 2 clearly grew 2 cm per day as per the graph, Plant 1 still outgrew Plant 2 by 4 cm.Winston's claim that Plant 2 grows 4 cm per day is false, as shown by the graph, which contradicts Winston's claim, and Plant 2 actually grows 2 cm per day.What is a graph?The relationship between lines and points is described by a graph, which is a mathematical representation of a network. A graph is made up of some points and connecting lines. It doesn't matter how long the lines are or where the points are located. A node is a name for each element in a graph.So, (A) The given statement of Winston is partially correct.
In the graph, we can clearly see that Plant 2 grew 2 cm per day, but still, Plant 1 grows more than plant 2 by 4 cm.(B) Error in Winston's statement:
From the above part, we know that the error is Winston's statement that Plant 2 grows 2 cm per day, but according to the graph Plant, 2 grows by 2 cm per day.Therefore, answers to both subparts are shown:
Although Plant 2 clearly grew 2 cm per day as per the graph, Plant 1 still outgrew Plant 2 by 4 cm.Winston's claim that Plant 2 grows 4 cm per day is false, as shown by the graph, which contradicts Winston's claim, and Plant 2 actually grows 2 cm per day.Know more about graphs here:
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