Five positive whole numbers add up to 47
One of the numbers is a multiple of 9
The other four numbers are equal.
Work out the result when the five numbers are multiplied.
Answers
Greetings from Brasil...
According to the statement
A + B + C + D + E = 47
making B the multiple of 9
A + 9B + C + D + E = 47
as the other 4 numbers are the same, let's call it A
A + 9B + A + A + A = 47
4A + 9B = 47 assigning values to B, we have
B = 1 ⇒ A ∉ ℤ
B = 2 ⇒ A ∉ ℤ
B = 3 ⇒ A = 5
B = 4 ⇒ A ∉ ℤ
B = 5 ⇒ A ∉ ℤ
B = 6 → from now on, A will be negative
Then
A = 5 and B = 3
Multiplying all numbers:
A·9B·A·A·A = 9A⁴B = 9·5⁴·3 = 16875
Related Questions
Determine if the conclusion follows logically from the premises. Is this a valid or invalid argument? Premise: No loving persons are thoughtless persons. Premise: No loving persons are aggressive people. Conclusion: No aggressive people are thoughtless persons.
Answers
"Premise: No loving persons are thoughtless persons. Premise: No loving persons are aggressive people. Conclusion: No aggressive people are thoughtless persons." This is a Valid Argument
This is further explained below.
What is a Valid Argument?Generally, In the context of deductive reasoning, an argument is considered to be sound if and only if it can be expressed in a way that makes it logically impossible for all of the premises to be true while still leading to an incorrect conclusion.
In conclusion, This is a Valid Argument
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What's the answer someone please help!
Answers
Step-by-step explanation:
Across
1.26
2.59
3.19
5.38
6.82
7.62
8.48
9.72
11.40
12.64
Down
1.24
2.59
3.18
4 42
5.32
6.88
7.65
8.42
9.70
10.34
"The unemployment rate has risen more than a percentage point to 8.9% in February from 7.1% last November." What is the relative change in the unemployment rate expressed as a percentage?
Answers
If the unemployment rate has risen more than a percentage point to 8.9% in February from 7.1% last November, then the relative change in the unemployment rate expressed as a percentage is 25.35%
Given,
The unemployment rate in February = 8.9%
The unemployment rate in November = 7.1%
The relative change in unemployment rate = [(unemployment rate in February - unemployment rate in November )÷ unemployment rate in November ] ×100
The relative change in unemployment rate= [tex](\frac{8.9-7.1}{7.1} )100[/tex]
=25.35%
Hence, If the unemployment rate has risen more than a percentage point to 8.9% in February from 7.1% last November, then the relative change in the unemployment rate expressed as a percentage is 25.35%
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1.
destions. Show your wor
For a recent Broadway musical, orchestra main floor seats cost $148 each, and
balcony seats cost $65 each. A theatre group purchased 30 tickets for an upcoming
show in June. If the total cost of the 30 tickets was $2,614, how many of each type
of ticket did the theatre group buy?
Number of orchestra tickets
Number of balcony tickets
Answers
Answer:
Number of orchestra tickets = 8
Number of balcony tickets = 22
Step-by-step explanation:
Let the number of orchestra tickets be x and number of balcony tickets be y.
So, cost of x orchestra tickets = $148 × x = $148x
Cost of y balcony tickets = $65 × x = $65y
Also given, total number of tickets = 30
Cost of 30 tickets = $2,614
So, the system of equations that can ne formed is :
x + y = 30 ....eq 1
148x + 65y = 2614 ....eq 2
Multiplying eq 1 by 148 and subtracting eq 2 by it,
148x + 148y - 148x - 65y = 4440 - 2614
83y = 1826
y = 1826/83 = 22
Substituting y = 22 in eq 1,
x + 22 = 30
So, x = 30 - 22 = 8
Thus,
Number of orchestra tickets = 8
Number of balcony tickets = 22
Decide whether the conditional statement is true or false:
It is noon when the clock strikes 12.
Answers
Answer:
True, When the clock transitions from 11:59am to 12:00pm, it is the first hour of noon.
Step-by-step explanation:
Please help
(100 Points)
Answers
Answer:
Equation: (14.71-4.48) [divided by] 3 =x
"Answer x": 3.41
Explanation:
14.71-4.48=10.23
10.23/3 = 3.41
3.41
If an employee at Tacos R US gets paid $11.50 per hour. Find his net pay if the
employee works 38 hours in that one week. Employee has a 10% federal tax rate. SS
tax is 6.2% and Medicare tax is 1.45%
Answers
the net pay (weekly) is $359.87
How to find the net pay?First, we know that the employee wins $11.50 per hour. The employee works 38 hours per week, then the weekly pay is:
38*$11.50 = $437
Now we need to discount the taxes:
There are 10% from federal tax, 6.2% from social services and 1.45% from medicare.
The total is:
10% + 6.2% + 1.45% = 17.65%
Then we need to discount a 17.65% of the weekly pay, we will get:
$437*(1 - 17.65%/100%) = $437*(1 - 0.1765) = $359.87
We conclude that the net pay (weekly) is $359.87
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Figurative language is different from literal language because _____.
A. it means exactly what it says
B.it is unclear
C.it contains meaning other than the actual word for word meaning
D.it is hard to define
Answers
Answer:
C i think
Step-by-step explanation:
Answer:
C.
Step-by-step explanation:
Answer A is the definition of literal language, while C is the definition of figurative. So, C is correct.
What is: 14 - (-20) + (-13)
Answers
Answer:
21
Step-by-step explanation:
14 - (-20) + (-13) =
= 14 + 20 - 13
= 34 - 13
= 21
30 points!!! But I need a 2 step problem with variables on both side and a fraction that equal 23
Answers
The equation of the two-step problem is 2x = x + 2/3
How to determine the two-step problem?The conditions are given as
Fraction = 2/3Variable on both sidesLet the variable in the equation be x
So, a possible equation is as follows
2x = x + 2/3
The solution to the equation is as follows
2x = x + 2/3
Subtract x from both sides
x = 2/3
Hence, the equation of the two-step problem is 2x = x + 2/3
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When time equals 0, why is the temperature in the oven not equal to 0? Why does the temperature eventually oscillate around 350°F?
Answers
The ambient temperature, aka the outside air temperature, isn't 0 degrees Fahrenheit. This is the reason why the oven isn't at 0 degrees Fahrenheit when the oven is off. For example, if it is 68 degrees Fahrenheit outside, then the oven's temperature is likely around this figure when it is off.
------------------------------
The way the oven works is that it heats the air using a gas or electric source. Once reaching 350 or slightly higher, the oven burner will turn off for a set period of time. This is so the temperature doesn't go too far over 350.
After the burner is turned off, the air inside the oven is still really hot and will stay around 350 for a while. But the temperature will slowly decrease. Once dipping slightly below 350, the oven will turn back on to heat back up to 350 again. This process repeats over and over.
This explains why you see the oscillating bouncing curve like this. It also explains why ovens seem to go on or off in the middle of a baking session.
If angle YXZ measures 90 degrees, which statement is true?
A. segment XZ is perpendicular to segment WY
B. WX =XY
C. segment XZ is a perpendicular bisector of segment WY
D. X is the midpoint of segment WY
Answers
Answer:
The 1st option is correct.
We are not clear that WX = XY.
3rd is is not correct.
4th option is also incorrect.
Find an equation for the line tangent to the circle
x2 + y2 = 100
at the point
(8, −6).
Answers
Second, plot the point (-6,8) on the circle.
Third, draw a radius from the origin to this point. You should be able to determine the SLOPE of this radius. Since slope is -8/6, this reduces to -4/3.
Fourth, use the point-slope form to find the equation:
y - y1 = m ( x - x1)
y - 8 = -4/3 ( x - -6 )
y - 8 = -4/3 ( x + 6 ) This is the Point-Slope form of the equation.
Fifth, sometimes the question specifies the Slope-Intercept form of the equation. If that is the case, then you only have 2 steps left. First, distribute the -4/3 on the right side of the equation.
y - 8 = -4/3(x) + 8 Now, we isolate the "y" by adding 8 to both sides of the equation.
+8 +8
_________________
y = -4/3(x) + 16
Hello! I'd really appreciate it if someone helped me solve this logarithm! It was my first class but the professor only showed the more simple versions :)
Answers
Answer:
(1/3)log(5) +(4/3)log(x) +log(y)
Step-by-step explanation:
You want the expanded form of the expression log(∛5·x^4·y^3).
Rules of logarithmsThe applicable rules of logarithms are ...
log(ab) = log(a) + log(b)
log(a^b) = b·log(a)
In addition to these, you need to know that a root is a fractional power: the cube root is the 1/3 power. Of course, the rules of powers tell you ...
(a^b)^c = a^(bc)
ApplicationYou can express the root as a fractional power before or after taking logs. Either way, you get the same result.
Before
[tex]\log\left(\sqrt[3]{5\cdot x^4y^3}\right)=\log\left(5^{\frac{1}{3}}\cdot x^{\frac{4}{3}}y^{\frac{3}{3}}\right)=\boxed{\dfrac{1}{3}\log(5)+\dfrac{4}{3}\log(x)+\log(y)}[/tex]
After
[tex]\log\left(\sqrt[3]{5\cdot x^4y^3}\right)=\dfrac{1}{3}\log\left(5}\cdot x^{4}y^{3}}\right)=\dfrac{1}{3}\left(\log(5)+4\log(x)+3\log(y)\right)\\\\=\boxed{\dfrac{1}{3}\log(5)+\dfrac{4}{3}\log(x)+\log(y)}[/tex]
__
Additional comment
Working a more complex problem is like working a simple problem, except it has more parts and may require the use of the rules more times. It may be tedious to keep track of all the parts, but it is not difficult.
if you know how to do this problem please let me know, thank you.
Answers
As per the question statement, we are given a mathematical expression [tex]|a+5| -1[/tex] is [tex]$\left[\begin{array}{cc}\text { Solution: } & -\infty < a < \infty \\ \text { Interval Notation: } & (-\infty, \infty)\end{array}\right]$[/tex]
As this question involves a modulus function therefore let us suppose that [tex]b=|a+5|-1[/tex]
Find the absolute value vertex. In this case, the vertex for [tex]b=|a+5|-1[/tex] is [tex](-5,-1)[/tex]
Function range definition
The set of values of the dependent variable for which a function is defined
Domain of [tex]$|a-5|-1: \quad-\infty < a < \infty$[/tex]
Extreme Points of [tex]$|a-5|-1: \quad$[/tex] Minimum [tex]$(5,-1)$[/tex]
Find the range for the interval [tex]$-\infty < a < \infty: \quad-1 \leq f(x) < \infty$[/tex]
Combine the ranges of all domain intervals to obtain the function range [tex]$f(x) \geq-1$[/tex]
Axis interception points of [tex]$|a-5|-1: \quad X$[/tex]Intercepts: [tex]$(4,0),(6,0), Y$[/tex]Intercepts:[tex]$(0,4)$[/tex]
x - axis interception points of[tex]$|a-5|-1: \quad(4,0),(6,0)$[/tex]
y - axis interception point of [tex]$|a-5|-1: \quad(0,4)$[/tex]
X Intercepts: [tex]$(4,0),(6,0), Y$[/tex] Intercepts: [tex]$(0,4)$[/tex]
Asymptotes of [tex]$|a-5|-1$[/tex] : None
Vertical asymptotes of [tex]$|a-5|-1$[/tex] : None
Horizontal Asymptotes of [tex]$|a-5|-1$[/tex] : None
Extreme Points of[tex]$|a-5|-1$[/tex] : Minimum [tex]$(5,-1)$[/tex]
First Derivative Test definition
Suppose that [tex]$x=c$[/tex] is a critical point of [tex]$f(x)$[/tex] then,
If [tex]$f^{\prime}(x) > 0$[/tex] to the left of [tex]$x=c$[/tex]and [tex]$f^{\prime}(x) < 0$[/tex] to the right of [tex]$x=c$[/tex] then $x=c$ is a local maximum.
If [tex]$f^{\prime}(x) < 0$[/tex] to the left of [tex]$x=c$[/tex] and [tex]$f^{\prime}(x) > 0$[/tex] to the right of[tex]$x=c$[/tex] then $x=c$ is a local minimum.
If [tex]$f^{\prime}(x)$[/tex] is the same sign on both sides of [tex]$x=c$[/tex] then [tex]$x=c$[/tex]
is neither a local maximum nor a local minimum.
[tex]f^{\prime}(a)=\frac{a-5}{a-5}$$[/tex]
Plug [tex]$a=5$[/tex] into [tex]$|a-5|-1: \quad-1$[/tex]
Minimum [tex]$(5,-1)$[/tex]
Absolute value vertex: The difference between two numbers; a number's positive value.Interval: A collection of values spanning two endpoints.To learn more about such Absolute value vertex:, click on the link given below:
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An average middle-income family will spend $242,020 to raise a child born in 2004
from birth to age 17. The graph shows the percents spent for various categories. To
the nearest dollar, how much will be spent to provide housing for the child? Use the
graph to answer.
graph numbers-- housing 34%, food 17%, miscellaneous 11%, child care 11%, health care 7%, clothing 6%, transportation 14%
Answers
Work Shown:
34% of $242,020 = 0.34*242020 = 82,286.80
This rounds to 82,287 when rounding to the nearest whole number.
Use equivalent ratios to answer
Answers
If out of 7 squares, 4 squares are in grey colour then if there are 15 white squares there will be 20 grey squares by solving through ratios.
Given that out of 7 squares, 4 squares are in grey colour.
We are required to find the number of grey colour squares if there are 15 white squares by using equivalent ratios.
Equivalent ratios are basically the ratios that are the same when we compare them. Two or more ratios can be compared with each other to find whether they are equivalent or not.
Ratio of white squares in 7 total squares=3:4
Total number of squares if there are 15 white squares=15*7/3=35
Number of grey squares=35-15=20
Hence if out of 7 squares, 4 squares are in grey colour then if there are 15 white squares there will be 20 grey squares by solving through ratios.
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Evaluate 13a+4b when a = 2 and b = 5
Answers
Answer:
46
Step-by-step explanation:
13a+4b
Substitute
13(2)+4(5)
Multiply
26+20
Add
46
A square rug has an area of 35 square ft. What is the exact side length of the rug?
Answers
The exact side length of the rug is √35.
What is the area of parallelogram
Let take the area of length as =a
As per the given question
A square rug has an area=35 sq ft
Area is the quantity that measures the number of unit square
As we know
area of square= a^2
Square area formula: A = a²
As already given a^2=35
So a=√35
The exact side length of the rug is √35.
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Kenny and his family went on a backpacking trip. They started hiking at 3:48 P.M. It took 2 hours and 59 minutes to reach their campsite. After they arrived, it took 1 hour and 35 minutes to set up the campsite. What time was it when Kenny and his family finished setting up their campsite?
Answers
Based on the time that it took Kenny and his family to reach the campsite and set it up, the time when they finished setting up the campsite was 8:22 pm
How to find the time taken to set up?First, find the time that Kenny and his family reached their campsite:
= 3:48 pm + 2 hours 59 minutes
= 6:47 pm
After getting to the campsite at 6:47 pm, Kenny and his family took 1 hour 35 minutes to finish setting up their campsite:
= 6:47 pm + 1 hour 35 minutes
= 8:22 pm
In conclusion, Kenny and his family finished setting up at 8:22 pm.
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helpnsisiisisisisiwiwiwi
Answers
Answer:
For Ai - P = 4 , Q = 4 , R = 4
For Aii - P = 3 , Q = 4 , R = 5
For Aiii - b^13 × b^-2 / b^1 = b^10
Step-by-step explanation:
I hope this is correct answer.
In the diagram m∠ACB=25° and CE bisects ∠DCF. explain how to find m∠DCE
Answers
The measure of ∠ DCE is equal to 57.5° by using the property of bisectors and vertically opposite angles.
We are given a ray diagram.
In the diagram, the measure of angles are given as:
∠ ACB = 25°
∠ ACG = 90°
We need to find the measure of angle ∠ DCE when CE bisects ∠ DCEF.
Now, we know that:
∠ BCG = ∠ DCF ( Vertically opposite angles.) … (1)
Now,
∠ BCG = ∠ ACB + ∠ ACG
∠ BCG = 25° + 90°
∠ BCG = 115° … (2)
∠ DCF = ∠ DCE + ∠ CEF
∠ DCF = ∠ DCE + ∠DCE ( as ∠ DCE = ∠ CEF since CE bisects them)
∠ DCF = 2 ∠ DCE … (3)
Now, put (2) and (3) in (1), we get that:
115° = 2 ∠ DCE
∠ DCE = 115 / 2°
∠ DCE = 57.5°
Therefore, we get that, the measure of ∠ DCE is equal to 57.5° by using the property of bisectors and vertically opposite angles.
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what is the value of x?!?
please help!
Answers
Answer:
x = 25
Step-by-step explanation:
The given angles, x° and (6x+5)° form a linear pair. You want the value of x.
Linear pairTwo angles that together form a straight line are called a linear pair. A linear pair of angles has a total measure of 180°.
x° +(6x +5)° = 180°
7x +5 = 180 . . . . . . . . . divide by °, collect terms
7x = 175 . . . . . . . . . . subtract 5
x = 25 . . . . . . . . . . divide by 7
The value of x is 25.
Find rules for the tables below. State your rules in two different ways: (1) as a sentence; and (2) as a rule, using x for the input and y for the output. a. X 6 0 2 -3 1 Process y -3 9 -21 3 33 Rule: (1) X and Topic 3: Foundations of Y are Linear (2) relationship Y = 6x=3
Answers
Answer:6x+3
Step-by-step explanation:
the midpoint of AB is M (2,0). if the coordinates of A are (-3,3), what are the coordinates of B?
Answers
Hence , the coordinate of point B is (7 , -3) .
Midpoint refers to some extent that's within the middle of the road connexion 2 points. A centre could be a purpose lying between 2 points and is within the middle of the road connexion the 2 points. If a line is drawn connexion the 2 points, then the centre could be a purpose at the center of the road and is equal from the 2 points.The centre formula is outlined for the points within the coordinate axes. Let (x₁), (y₁) and (x₂), (y₂) be the endpoints of a line section is given by M = (x₁ + x₂ /2 , y₁ + y₂ /2 ).We have given two coordinate A (-3,3) and M (2,0) .
Let the coordinate of B (x, y) .
Using midpoint formula , we get
[tex](2,0) = ( \frac{-3+x}{2} ,\frac{3+y}{2} )[/tex]
On comparing , we get
[tex]\frac{-3+x}{2} =2\\\ \\-3+x = 4\\x = 7[/tex]
[tex]\frac{3+y}{2} =0\\3+y=0\\y=-3[/tex]
We get coordinate (7 , -3) .
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A 14 yo client with type 1 diabetes
Heighing 110 pounds has on attack of
hypoglycemia. He has been prescribed
0.5g/kg of 50%. dextrose. The 50%
dextrose is supplied in 0.5mg/ml
Prefilled syringes. Calculate the dosage for
the client by converting the weight into Kilograms and the amount of
dextrose in syringe into grams.
Answers
Answer:
Step-by-step explanation: it will be having 10 kg each
If the third of three consecutive integers is subtracted from 132, the result is the sum of the first and second. What are the integers?
Answers
Answer:
gg
Step-by-step explanation:
Answer:
Three consecutive integers are 43, 44, 45
Step-by-step explanation:
Let three consecutive integers be x, (x + 1), (x + 2)
According to the question, if the third of three consecutive integers is subtracted from 132, the result is the sum of the first and second.
[tex] \therefore [/tex]
[tex] \implies \rm 132 - (x + 2) = x + (x + 1) \\ \\ \implies \rm 132 - x - 2 = x + x + 1 \\ \\ \implies \rm 130 - x = 2x + 1 \\ \\ \implies \rm 130 - 1 = 2x + x \\ \\ \implies \rm 129 = 3x \\ \\ \implies \rm 3x = 129 \\ \\ \implies \rm x = \frac{129}{3} \\ \\ \implies \rm x = 43[/tex]
So,
The integers are as follows:
x = 43
x + 1 = 44
x + 2 = 45
what is the vertex of f(x)=x^2+10x+1
Answers
The vertex of f(x)=x²+10x+1 is found to be (-5,-24).
The Vertex of the quadratic equation f(x)=ax²+bx+c is (h,k) where
h=-b/2a and k=f(h).
In the given question
f(x)=x²+10x+1
On comparing with ax²+bx+c
we get a=1 , b=10 , c=1
So , h=-b/2a
h=-10/2(1)
h=-5 ...(i)
k=f(h)
Substituting the value of x=h in f(x) we get
k=(-5)²+10(-5)+1
k=25-50+1
k=-25+1
k=-24
Therefore , the vertex of f(x)=x²+10x+1 is (-5,-24).
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What is the equation of a line through the points (0, 9) and (3, 0)?
0-9
3-0 y=-3x + 9
Obecause m=
Obecause m=
Obecause m=
O because m=
0-9
3-0 y=-3x + 3
3-0
0-9;y=-
y=-x+9
3-0
1
0-9; X=-3x+3
Answers
[tex](\stackrel{x_1}{0}~,~\stackrel{y_1}{9})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{0}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{0}-\stackrel{y1}{9}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{0}}} \implies \cfrac{ -9 }{ 3 }\implies -3 \\\\\\ \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}{9}=\stackrel{m}{-3}(x-\stackrel{x_1}{0}) \\\\\\ y-9=-3x\implies y=-3x+9[/tex]
need answer asap:
Shelby made a list of her test scores: 88,100,92,80,85,94,90. What is the lowest score she can get on her next test to have a mean score of 90?
ty pls answer quickk
Answers
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