The sum of two numbers is twenty-five. One number is five less than the other.
Answers
Answer: x=15, y=10
*Note: x and y are only variables used to solve this problem, but know that the two numbers are 15 and 10.
Step-by-step explanation:
For this problem, we can use system of equations. Let's use x for one number and y for the other.
First Equation:
x+y=25
We get this equation because it states that the sum of the two numbers is 25.
Second Equation:
y=x-5
We get this equation because it says one number (y) is 5 less than the other (x).
Since we have two equations, we can use substitution method to solve.
[tex]x+(x-5)=25[/tex] [distribute 1 to (x-5)]
[tex]x+x-5=25[/tex] [combine like terms]
[tex]2x-5=25[/tex] [add both sides by 5]
[tex]2x=30[/tex] [divide both sides by 2]
[tex]x=15[/tex]
Now that we have x, we can plug it into any of the equations to find y.
[tex]x+y=25[/tex] [plug in x=15]
[tex]15+y=25[/tex] [subtract both sides by 15]
[tex]y=10[/tex]
Finally, we have our answer, x=15 and y=10.
Answer:25,-5
Step-by-step explanation:
Related Questions
For each relation, indicate whether it is reflexive or anti-reflexive, symmetric or anti-symmetric, transitive or not transitive.
a. The domain of the relation L is the set of all real numbers. For x, y ∈ R, xLy if x < y.
b. The domain for the relation D is the set of all integers. For any two integers, x and y, xDy if x evenly divides y. An integer x evenly divides y if there is another integer n such that y = xn. (Note that the domain is the set of all integers, not just positive integers.)
Answers
Answer:
(a)
L is not reflexive, L is anti-reflexive
L is not symmetric.
L is not anti-symmetric
L is transitive.
(b)
D is reflexive
D is not symmetric.
D is anti-symmetric
D is transitive.
Step-by-step explanation:
a)
Given that;
domain of the given relation L is the set of all real numbers
For x , y ∈ R , xLy if x less than y.
relation L, where xLy if x less than y, For x, y ∈ R
so For every x ∈ R, it is then false that x less than x.
That is (x, x) does not belongs to L.
∴ L is not reflexive, L is anti-reflexive.
For every x,y ∈ R, if (x,y) ∈ L (i.e. x < y), then (y, x) does not belongs to L, since it is false that y < x.
∴ L is not symmetric.
For every x ∈ R, we can say its false that x less than x. That is (x, x) does not belongs to L.
∴ L is not anti-symmetric.
For every x,y,z ∈ R, if (x, y) ∈ L(i.e. x < y) and (y, z) ∈ L(i.e. y < z), then (x, z) ∈ L, since it is true that x<z when x<y and y<z.
∴ L is transitive.
b)
Also lets consider a relation D, where xDy if there is an integer n such that y = xn, For x, y ∈ Z.
Now
For every x ∈ Z, it is true that x = x × 1. That is (x, x) belongs to D.
∴ D is reflexive,
For every x,y ∈ Z, if (x,y) ∈ P (i.e. y=x × n), then (y, x).
if (x,y) ∈ D, then there exist an integer n such that y=x × n.
Then x = y × (1/n).
Thus, (y,x) does not belongs to D, since 1/n is not an integer, but it is a real number.
∴ D is not symmetric.
For every x,y ∈ Z, if (x,y) ∈ D (i.e. y=x × n), then (y, x) also belongs to D only when x=y. where n=1.
∴ D is anti-symmetric.
For every x,y,z ∈ Z, if (x,y) ∈ D (i.e. x × n1= y), and (y,z) ∈ D (i.e. y × n2 = z), then (x,z)∈ D.
if (x,y) ∈ D, then there exist an integer n1 such that y=x × n1.
if (y,z) ∈ D, then there exist an integer n2 such that z=y × n2.
Thenz = (x × n1) × n2 ⇒ z=x × (n1 × n2).
where (n1 × n2) is an integer. Thus (x,z) ∈ Z
∴ D is transitive.
Which is one of the transformations applied to the graph of f(x) = x2 to change it into the graph of g(x) = –3x2 – 36x – 60?
Answers
Hey There!! ☄️ The general vertex to The general vertex form is this:
v(x) = a (x-h)2 + k
where (h,k) is the coordinates of the of vertex.
and a indicates the widening or shrinking of the function compared to another parabolic function. If a become bigger, the graph becomes narrower. If a becomes negative, the graph is reflected over the x-axis.
Comparing f(x) = x2 with g(x) = -3(x+6)2 + 48, we have the following transformations:
The graph is reflected over the x-axis
The graph is made narrower.
The graph is shifted 6 units to the left.
The graph is shifted 48 units up.
From the choices we only have:
The graph of f(x) = x2 is made narrower
The graph of f(x) = x2 is made narrower.
It is given that f(x) = x2 and g(x) = –3x2 – 36x – 60.
To find the transformations applied to the graph.
What is graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
The general vertex to The general vertex form is this:
v(x) = a (x-h)2 + k
where (h,k) is the coordinates of the of vertex.
Indicates the widening or shrinking of the function compared to another parabolic function. If a become bigger, the graph becomes narrower. If a becomes negative, the graph is reflected over the x-axis.
Comparing f(x) = x2 with g(x) = -3(x+6)2 + 48, we have the following transformations:
The graph is reflected over the x-axis.
The graph is shifted 6 units to the left.
The graph is shifted 48 units up.
From the choices we only have:
So, the graph of f(x) = x2 is made narrower.
Learn more about graph here:
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What are the critical points for the plane curve defined by the equations x(t)=t 33−t22−2t−4y(t)=t32−2t+2
Answers
Answer:
The points are
[tex]t_1 = 0.7433[/tex]
[tex]t_2 = -0.299[/tex]
Step-by-step explanation:
From the question we are told that
The first equation is [tex]x(t) = 3t^3 -2t^2-2t -4[/tex]
The second equation is [tex]y(t) = 3t^2 -2t -2[/tex]
Now differentiating the first and second equation
[tex]\frac{dx(t)}{dt} = 9t^2 -4t-2[/tex]
and
[tex]\frac{dy(t)}{dt} = 6t-2[/tex]
Now
[tex]\frac{dy(t)}{dx(t)} = \frac{\frac{dy(t)}{dt} }{\frac{dx(t)}{dt} } = \frac{9t^2 -4t-2}{6t-2}[/tex]
at critical point
[tex]\frac{dy(t)}{dx(t)} = 0[/tex]
=> \frac{9t^2 -4t-2}{6t-2}=0[/tex]
=> [tex]9t^2 - 4t-2 = 0[/tex]
solving using quadratic formula we have that
[tex]t_1 = 0.7433[/tex]
and [tex]t_2 = -0.299[/tex]
Samuel was riding in the back seat of the station wagon on the way home after a long and tiring day at the
beach. He fell asleep halfway home. He didn't wake up until he still had half as far to go as he had already
gone while asleep. How much of the entire trip home was Samuel asleep?
Answers
Answer: One fourth of the entire trip.
Step-by-step explanation:
The initial distance is D.
" He fell asleep halfway home."
Then he fells asleep when the distance between his actual position and his house was half of D, or:
D/2.
"He didn't wake up until he still had half as far to go as he had already
gone while asleep."
So he wakes up when his actual position is a fourth of the initial distance:
(D/2)/2 = D/4.
Then if the entire trip has a distance D, and he was sleeping between:
D/2 - D/4 = 2D/4 - D/4 = D/4.
in a trip of a distance D, he was asleep a distance of D/4.
Then, returning to the question:
How much of the entire trip home was Samuel asleep?
This is equal to the quotient between the distance that he travels asleep and the total distance:
r = (D/4)/D = 1/4.
Then he was asleep in 1/4 of the entire trip.
A hot air balloon starts at a height of 6 feet above the ground and then rises at a rate of 20 feet each minute. Which equation gives the height h in feet as a function of time t in minutes? Oh=6t Oh = 20$ Oh=20t + 6 Oh=6+ 20
Answers
Answer:
The height h it will travel in t minutes
Height h = 6 + 20(t)
Oh=20t + 6
Step-by-step explanation:
A hot air balloon starts at a height of 6 feet above the ground and then rises at a rate of 20 feet each minute.
Initial height h0 = 6 feet
Then it travel 29 feet each minute
Rate = 20 feet/ minute
The height h it will travel in t minutes
Height h = 6 + 20(t)
The water level as a river recedes after a flood is measured at regular intervals, and its height relative to normal, in inches, follows the sequence below. If the sequence continues, what do you expect the 7th measurement to be? 16, 9, 2, –5, ...,
Answers
Answer:
7th measurement = -26
Step-by-step explanation:
The sequence is 16, 9, 2, –5, ...,
First term( a)= 16
Second term=9
Common difference (d) = 9-16
Common difference= -7
The sequence is a arithmetic progression
For AP's ,the terms formula is
Term(n) = a + (n-1)d
Where n represent the term to be found
In this case,we Are looking for the 7th term , so n= 7
Term(7) = 16+ (7-1)-7
Term(7)= 16 +6(-7).
Term (7) = 16-42
Term(7) = -26
7th term =-26
Plz help with this questio!
Thanks!♡︎
Answers
Answer:
Week 3.
Step-by-step explanation:
Add up the hours for each week.
Week 3 is the highest at 36 hours.
Answer:
week 3
Step-by-step explanation:
week 3. it totals for 36 hours in this week
Antonio purchased adult and child tickets for the fair. Tickets cost $29.35 for each adult and $17.45 for each child. Let x represent the number of adult tickets purchased and y represent the number of child tickets purchased. Write an expression to represent the total cost of the tickets Antonio purchased
Answers
Answer:
The answer is B: $29.35x + $17.45y
The value, V(m), of a comic book m must be months after publication has an average rate of change of -0.04 between m=36 and m=60. Which statement must be true?
A) The value of the comic book decreased by a total of $0.04 between m=36 and m=60
B) The value of the comic book increased by a total of $0.04 between m=36 and m=60
C) The value of the comic book decreased by an average of $0.04 each month between m=36 and m=60
D) The value of the comic book increased by an average of $0.04 each month between m=36 and m=60
Answers
Answer:
A
Step-by-step explanation:
The average is over the months not added each month
Write 927 as a mathematical expression in expanded form.
Answers
Answer:
900 + 20 + 7
Answer:
[tex]900+20+7[/tex]
Step-by-step explanation:
Write 927 as a mathematical expression in expanded form.
So we see the number 927. It has hundreds, tens, ones. So the only thing we have to do it separate the number by hundreds, tens, ones. So now, let's start!
Hundreds: [tex]900[/tex]
Tens: [tex]20[/tex]
Ones: [tex]7[/tex]
We have 900, 20, and 7. Let's try adding them up to make 927.
[tex]900+20+7[/tex]
[tex]=927[/tex]
This is how we do 927 in expanded form.
Hope this Helps!
Show all work to identify the asymptotes and zero of the function f(x)= 5x/x^2-25. Please answer ASAP!!!
Answers
Answers:
root: x = 0Vertical asymptotes: x = 5 and x = -5Horizontal asymptote: y = 0The term "root" is another way of saying "zero of a function"
============================================
Explanation:
To find the roots, we need to solve f(x) = 0 for x
f(x) = 0
5x/(x^2 - 25) = 0
5x = 0*(x^2-25)
5x = 0
x = 0/5
x = 0
Plugging x = 0 into f(x) leads to f(x) = 0.
The root is x = 0 meaning the x intercept is at 0 on the x axis number line. This is the origin (0,0).
---------------
To find the vertical asymptotes, set the denominator equal to 0 and solve for x
x^2 - 25 = 0
x^2 - 5^2 = 0
(x-5)(x+5) = 0 ... difference of squares rule
x-5 = 0 or x+5 = 0
x = 5 or x = -5
If either x = 5 or x = -5, then then the denominator x^2-25 is zero
We cannot divide by zero, so these values are excluded from the domain, and this produces the vertical asymptotes.
--------------
The horizontal asymptote is y = 0 because the degree of the numerator is 1, while the degree of the denominator is 2. The denominator's degree is larger, which leads to y = 0. The rules for finding the horizontal asymptote are
If m < n, then the horizontal asymptote is y = 0If m = n, then the horizontal asymptote is y = a/bIf m > n, then there is no horizontal asymptote (use polynomial long division to find the oblique asymptote)For those rules above, m and n are the degrees of the numerator and denominator respectively. The a,b refers to the leading coefficients of the numerator and denominator.
The asymptotes and zero of the function are ±5 and 0 respectively
Given the function below;
[tex]f(x)=\frac{5x}{x^2-25}[/tex]The vertical asymptotes occur at the point where the function goes large that is the denominator is zero.
If the denominator is zero, hence;
x^2 - 25 = 0
x^2 = 25
x = ±√25
x = ±5
Hence the asymptotes of the function is ±5
For the zero of the function;
[tex]\frac{5x}{x^2-25}=0\\5x = 0\\x = 0\\[/tex]
Hence the zero of the function is 0
Learn more on asymptotes here: https://brainly.com/question/25827382
The sum of a number and three is six less than twice that number
Answers
Answer:
Algebraic expression = x+3=2x-6
Step-by-step explanation:
Let the unknown number be x ;
[tex]x+3 =2x-6[/tex]
Further explanation
[tex]x+3=2x-6\\\\\mathrm{Subtract\:}3\mathrm{\:from\:both\:sides}x+3-3=2x-6-3\\\\Simplify\\x=2x-9\\\\Collect\:like\:terms\\x-2x =-9\\\\Simplify\\-x =-9\\\\\mathrm{Divide\:both\:sides\:by\:}-1\\\frac{-x}{-1}=\frac{-9}{-1}\\\\x =9[/tex]
PLEASE SOMEONE HELP
I WILL GIVE 25 POINTS JUST PLEASE HELP
Answers
Answer:
50) 8, 16, 24, 32, 40, 48 (count by 8’s)
12, 24, 36, 48, 60, 72 (Count by 12’s)
Common Multiples: 24, 48
Least Common Multiple: 24
51) 7: 7, 14, 21, 28, 35, 42
11: 11, 22, 33, 44, 55, 66
Common Multiples: none
Least Common Multiple: none
52) 25: 25, 50, 75, 100, 125, 150
10: 10, 20, 30, 40, 50, 60
Common Multiples: 50
Least Common Multiple: 50
53) 24: 24, 48, 72, 96, 120, 144
36: 36, 72, 108, 144, 180, 216
Common Multiples: 72, 144
Least Common Multiple: 72
Step-by-step explanation:
50) 8, 16, 24, 32, 40, 48 (count by 8’s)
12, 24, 36, 48, 60, 72 (Count by 12’s)
Common Multiples: 24, 48
Least Common Multiple: 24
51) 7: 7, 14, 21, 28, 35, 42
11: 11, 22, 33, 44, 55, 66
Common Multiples: none
Least Common Multiple: none
52) 25: 25, 50, 75, 100, 125, 150
10: 10, 20, 30, 40, 50, 60
Common Multiples: 50
Least Common Multiple: 50
53) 24: 24, 48, 72, 96, 120, 144
36: 36, 72, 108, 144, 180, 216
Common Multiples: 72, 144
Least Common Multiple: 72
Round the following number to the nearest hundred
123,456
Answers
Answer:
Hey!
Your answer is 123,500!
Step-by-step explanation:
TO ROUND TO THE NEAREST HUNDRED we need to look at the TENS column...
IN THIS CASE WE LOOK AT '5'...
If its bigger than 4 INCREASE THE DIGIT IN THE HUNDREDS PLACE BY ONE
If its smaller than 5 DECREASE THE DIGIT IN THE HUNDREDS PLACE BY ONE!
So as 5 is a digit that makes us ROUND UP...we change 4 to a 5 to have 123,500 as our answer!
HOPE THIS HELPS!
3 Question
Simplify this expression:
4(1 - 25) + 70 - 10.
Type the correct answer in the box
Answers
Explanation:
4(1 - 25) + 70 - 10
= 4 - 100 + 60
= -100 + 64
= -36
Answer:
-36
Step-by-step explanation:
4(1 - 25) + 70 - 10
PEMDAS
Parentheses first
4( -24) + 70 -10
Then multiply and divide
-96 + 70-10
Then add and subtract
-36
Which property is illustrated by the equation –8 + 8 = 0?
additive inverse
additive identity
commutative property
distributive property
Answers
31, -32, 33, -11, 5 least to greatest
Answers
Answer: -32, -11, 5, 31, 33
Answer:
-32, -11, 5, 31, 33
Step-by-step explanation:
The smallest one is -32. I know this because it's:
A negativeIs the farthest back on a number lineThe next one is -11. -11 is the next smallest because it's:
A negativeIs larger than -32 (it's closer to 0 and the positives on a number line)The third one is 5. It's the third greatest because it's:
A positiveIs the closest positive option to 0.The fourth one is 31. It's the fourth greatest because it's:
A positiveIt's larger than 5, but smaller than 33The last one is 33. It's the greatest because it's:
A positiveIt's larger than all the other numbersHmm can you help me solve god bless you
Answers
Answer:
(3/2)x - 14
Step-by-step explanation:
If two lines are perpendicular, their slopes are mathematically negative reciprocals of one another.
Here the given line is y = (-2/3)x; the slope is -2/3, and the negative reciprocal of that is 3/2. The desired line will have this slope 3/2.
Using the slope-intercept form of the equation of a straight line, y = mx + b, we write out
-8 = (3/2)(4) + b, obtaining -8 = 6 + b, or b = -14.
The desired equation is (3/2)x - 14.
2. Richie solved the equation 24x + 18(x - 2) = 216 for x.
Some of his steps are shown below.
Step 1: 24x + 18(x - 2) = 216
Step 2: 24x + 18x - 36 = 216
Step 3: 42x - 36 = 216
Step 4: 42x = 252
List the steps Richie took to solve the equation.
the answer is 6 he nned to divide 42 and
252
Answers
Step-by-step explanation:
42x=252
x=252/4
x=6
well hope that helps
Answer: Answer is the steps
Step-by-step explanation:
Step 1: Richie rewrite the equation as 24x + 18(x-2) =216
Step 2: Richie applied the distributive property to eliminate the parentheses and got the equation 24x + 18x - 32 = 216
Step 3: Richie combine like terms to get the equation 42x -36 =216
Step 4: Richie added 36 to both sides to get the new equation 42x = 252
Richie was not done solving for x so in
Step 5: Richie should have divided both sides by 42 to get the final answer
x = 6.
The first significant digit in any number must be 1, 2, 3, 4,5, 6, 7, 8, or 9. It was discovered that first digits do not occur with equal frequency. Probabilities of occurrence to the first digit in a number are shown in the accompanying table. The probability distribution is now known as Benford's Law. Forexample, the following distribution represents the first digits in 187 allegedly fraudulent checks written to a bogus company by an employee attempting to embezzle funds from his employer.
a.) Using the level of significance alpha 0.10, test whether the first digits in the allegedly fraudulent checks obeyBenford's Law. What is the null hypothesis?
b.) What is the alternative hypothesis?
c.) What is the test statistic?
d.) What is the p-value?
e.) Using the P-value approach, compare the P-value with the given alpha = 0.10, level of significance. Based on theresults, do the first digits obey the Benford's Law?
f.) (b) Based on the results of part (a),could one think that the employee is guilty of embezzlement?
Digit Probability Frequency
1 0.301 36
2 0.176 25
3 0.125 28
4 0.097 26
5 0.079 23
6 0.067 17
7 0.058 9
8 0.051 16
9 0.046 7
Answers
Answer:
We fail to reject the null hypothesis
Step-by-step explanation:
See the attachment for detailed calculations
How can you prove that a conjecture is false?
Answers
Answer:
In mathematics, counterexamples are often used to prove the boundaries of possible theorems. By using counterexamples to show that certain conjectures are false, mathematical researchers avoid going down blind alleys and learn how to modify conjectures to produce provable theorems.
Step-by-step explanation:
-170=5(8n+6)
Help please !!
Answers
Answer:
Step-by-step explanation:
40n + 30 = -170
40n + 30 = -170
40n = -200
n = -5
What is another way to name plane T?
Answers
Answer:
plane EHV
Step-by-step explanation:
To find the other name of plane T, we have to find any three non-collinear points on the plane T.
It means we have to find any three points which lie on the plane T but in a single straight line.
From the given figure it is clear that points E, H and V lie on plane T and they are not collinear.
Therefore, the other name of plane T is plane EHV.
Note: There are many other possible names of plane T, EHV is one of them.
Which of the following graphs represent a function?
Graph A
Graph B
Graph
Graph
a. Graph A and Graph C
b. Graph A
C. Graph D
D. graph b and d
Answers
The graphs that represent functions are given as follows:
a. Graph A and Graph C.
When does a graph represents a function?A graph represents a function if it has no vertically aligned points, that is, each value of x is mapped to only one value of y.
For this problem, we have that:
Graph B has one vertically aligned point, hence it is not a function.Graph D has multiple vertically aligned points, hence it is also not a function.Hence the graphs that represent functions are given as follows:
a. Graph A and Graph C.
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Answer: The only graphs that classify as function are Graph A and Graph C, so the answer is C. It's not possible for B and D to be functions.
(5x10) plus (2x1/100)
Answers
Answer:
2501/50
Decimal:50.02
Step-by-step explanation:
5 × 10 + 2× 1/100
5 × 10 = 50
2 × 1/100 = 1/50
50 + 1/50
50×50. 1
_____ + ___
50. 50
50 × 50 + 1 = 2501 meaning 2501 over 50 is your answer
Answer:
100
Step-by-step explanation:
Hope this helped! ;)
Caleb bought stock in a company two years ago that was worth xx dollars. During the first year that he owned the stock, it increased by 38%. During the second year the value of the stock decreased by 12%. Write an expression in terms of xx that represents the value of the stock after the two years have passed.
Answers
Answer:
1.2144xx
Step-by-step explanation:
The multiplier of value for the first year was (1 +38%) = 1.38.
The multiplier of value for the second year was (1 -12%) = 0.88.
Then the multiplier of value for the two years was ...
1.38×0.88 = 1.2144
The value of the stock after 2 years was ...
1.2144xx
_____
Comment on the variable
We have used the variable given in the problem statement (xx). If you intend something different, replace xx with the variable you intend.
Show how 10-6 helps solve 50-6
Answers
Answer:
The digit in the ones spot will come out to be 4.
Step-by-step explanation:
Since the are both an even number of ten, and you're subtracting 6, their both gonna come out to have a 4 in the ones spot in the number answer.
Well 50 is just 10 x 5 so...
if you solve 10 + 6 = 16 then you can do 50 + 6 = 56
What is the sum of 637,391+372,088
Answers
Answer:
1009479
Step-by-step explanation:
637,391 + 372,088 = 1009479
Answer:
the answers 1009479
Step-by-step explanation:
Rosanne makes 1 1 2 liters of strawberry lemonade. She pours 1 4 of a liter of lemonade into a thermos to take to the park. Her brother drinks 2 5 of the remaining lemonade. How much lemonade does Rosanne's brother drink?
Answers
Answer:
1/2 liter
Step-by-step explanation:
If she starts with 1 1/2 liters and removes 1/4 liter, the remaining amount is ...
(1 1/2) -(1/4) = 1 2/4 -1/4 = 1 1/4 . . . liters.
The brother drinks 2/5 of that, so drinks ...
(2/5)(1 1/4 L) = (2/5)(5/4 L) = 2/4 L = 1/2 L
Rosanne's brother drinks 1/2 L of the lemonade.
Write the phrase as an algebraic expression. Use the variable x to represent the unknown number. Seven times a number.
Answers
Answer:
7x.
Step-by-step explanation:
Seven times a number = 7x.
An algebraic expression for the given statement is 7x.
The given statement is seven times a number.
We need to write an algebraic expression for the given statement.
What is an algebraic expression?An algebraic expression (or) a variable expression is a combination of terms by the operations such as addition, subtraction, multiplication, division, etc.
Given that, use the variable x to represent the unknown number.
Now, seven times a number=7x
Therefore, an algebraic expression for the given statement is 7x.
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