The solution is [tex]x = 2 \text{ and } y = \frac{1}{2}[/tex]
Solution:
Let us assume,
[tex]a = \frac{1}{x}\\\\b = \frac{1}{y}[/tex]
Given system of equations are:
[tex]\frac{2}{x} - \frac{3}{y} = -5[/tex]
[tex]\frac{4}{x} + \frac{6}{y} = 14[/tex]
Rewrite the equation using "a" and "b"
2a - 3b = -5 ------------ eqn 1
4a + 6b = 14 -------------- eqn 2
Let us solve eqn 1 and eqn 2
Multiply eqn 1 by 2
2(2a - 3b = -5)
4a - 6b = -10 ------------- eqn 3
Add eqn 2 and eqn 3
4a + 6b = 14
4a - 6b = -10
( - ) --------------------
8a = 4
[tex]a = \frac{4}{8}\\\\a = \frac{1}{2}[/tex]
Substitute a = 1/2 in eqn 1
[tex]2(\frac{1}{2}) -3b = -5\\\\1 - 3b = -5\\\\3b = 6\\\\b = 2[/tex]
Now let us go back to our assumed values
Substitute a = 1/2 in assumed values
[tex]a = \frac{1}{x}\\\\\frac{1}{2} = \frac{1}{x}\\\\x = 2[/tex]
Substitute b = 2 in assumed value
[tex]b = \frac{1}{y}\\\\2 = \frac{1}{y}\\\\y = \frac{1}{2}[/tex]
Thus the solution is [tex]x = 2 \text{ and } y = \frac{1}{2}[/tex]
There are 3 consecutive integers with a sum of 18. Which integers are they?
Answer:
5, 6, 7
Step-by-step explanation:
5+6+7=18
Answer:
5+6+7
Step-by-step explanation:
Intergers: Three consecutive integers)
18 = (X-1) + (X) + (X+1)
18 = 3X
X = 6
SUbstitute =
(6-1) + (6) + (6+1)
5+6+7
= 18
Fraction equivalents
7/15 = ?/45
Answer:
21/45
Step-by-step explanation:
please give me brainliest i just need 4 more
11/3 divided by what equals 11 it has to be a fraction
Answer:
1/3
Step-by-step explanation:
We can solve using algebra: let x be the unknown number.
so 11/3 ÷ x = 11.
Solving:
11/3 = 11x.
x = 11/3 ÷11 = 1/3
You can also check the answer by going:
11/3 ÷ 1/3 = 11/3 x 3/1 = 33/3 = 11 (using fraction rules for multiplying and dividing ie. to divide by a fraction we multiple by it's reciprocal, and to multiply by a fraction, we multiple the numerators and the denominators).
11/3 divided by 1/3 so that it will be equals to 11.
When facing a division problem like 11/3 divided by what equals 11, we need to find a number which, when 11/3 is divided by it, gives us the result of 11. To solve this, let's set up an equation where the unknown number is represented by a variable, such as 'x':
11/3 ÷ x = 11
To find 'x', we need to isolate it. This can be done by multiplying both sides of the equation by 'x', and then dividing both sides by 11 to solve for 'x'.
(11/3) ÷ x = 11
(11/3) ÷ x × x = 11 × x
11/3 = 11x
Now we divide both sides by 11 to get:
x = (11/3) ÷ 11
x = 1/3
So, the fraction that you must divide 11/3 by to get 11 is 1/3.
What is the slope of the line that passes through the points (4,8) and (2,12)?
Answer: m = -2
Step-by-step explanation: Using our slope formula, we take the second y minus the first y which in this case is 12 - 8 over our second x minus our first x which in this case is 2 - 4.
So 12 - 8 is 4 and 2 - 4 is -2. So we have 4/-2 which can be simplified to -2.
The variable that's used to represent slope is m.
So we would say m = -2.
Work is provided in the image attached.
While traveling to his grandma for his George fell asleep a fifth of the way through the journey when he awoke he still had to travel a quarter of the distance that he had traveled while sleeping. For what part of the journey had he been asleep
Answer:
George fell asleep when he had traveled 1/5 of the total distance, slept 3/5 of the distance and he awoke up when he's still 1/5 away from his grandma
Step-by-step explanation:
1. Let's review the information given to us to answer the question correctly:
George fell asleep a fifth of the way
He awoke up when he still had to travel a quarter of the distance that he had traveled while sleeping
2. For what part of the journey had he been asleep?
George fell asleep a fifth of the way: 1/5 of the total distance traveled and 4/5 of the distance away from his grandma
When he awoke up = 1/4 * 4/5 = 1/5
He had been asleep = 5/5 - 1/5 -1/5 = 3/5
It means George fell asleep when he had traveled 1/5 of the total distance, slept 3/5 of the distance and he awoke up when he's still 1/5 away from his grandma
If 13 is added to a number and the sum is doubled the result is -10 less than the number
Equation for solving: (13+x)2= -10-x
Step one: 26+2x=-10-x
step two: 26+3x=-10
step three: 3x=-36
answer: -12
The area of triangle with a base of 4 meters and a height of 5 meters
Answer:10
Step-by-step explanation:
4 x 5 = 20
20/2 or 20 x 1/2
= 10
Answer: 10 meters squared
Step-by-step explanation:
You find the area of a triangle by doing base x height ÷2 therefore 4x5=20÷2=10
How many solutions does this system of equations have?
y = –2x + 3
y = –2x – 1
Answer:
Step-by-step explanation:
in y = mx + b form, the slope is in the m position and the y int is in the b position
y = -2x + 3.....slope is -2 and y int is 3
y = -2x - 1...slope is -2 and y int is - 1
same slope, different y int's....means parallel lines...NO SOLUTION
learn this...it helps
same slope, different y int's = no solution
different slopes, different y int's = 1 solution
same slope, same y int's = infinite solutions
Final answer:
The given system of equations represents two parallel lines with the same slope and different y-intercepts, implying there are no solutions where the lines intersect.
Explanation:
The system of equations provided is:
y = –2x + 3
y = –2x – 1
These two equations represent two separate lines. To determine the number of solutions to the system, we observe the slopes of the two lines. Both equations have the same slope of –2. Because they have the same slope but different y-intercepts, these two lines are parallel and will never intersect. Therefore, the system has no solutions.
My age is the difference between twice my age in 5 years and twice my age 5 years ago
Answer:
10
Step-by-step explanation:
If you are solving for x in the diagram shown, which fact would help you to set up the problem? A) Tangents touch a circle in exactly one point. B) Chords that intercept congruent arcs are congruent to each other. C) Tangent segments from the same point outside the circle are congruent. D) The product of the segments formed by intersecting chords are congruent.
Answer:
Tangent segments from the same point outside the circle are congruent. This Geometric Theorem allows you to set up the problem and solve for x.
Step-by-step explanation:
Answer:Tangent segments from the same point outside the circle are congruent. (c) i got it right on USATESTPREP
A circus charges $2.50 for kids tickets and $6 for adult’s tickets. Last weekend, twice as many kids attended the circus than adults. If the ticket sales totaled $7,150, how many kids attended the circus?
The number of kids attending the circus is 1300.
Let's denote:
- ( K ) as the number of kids attending the circus.
- ( A ) as the number of adults attending the circus.
Given:
- The price of a kid's ticket is $2.50.
- The price of an adult's ticket is $6.
- The total ticket sales is $7,150.
- The number of kids attending the circus is twice the number of adults.
We can set up a system of equations based on the given information:
1. The total ticket sales:
[tex]\[ 2.50K + 6A = 7150 \][/tex]
2. The number of kids attending the circus is twice the number of adults:
[tex]\[ K = 2A \][/tex]
Now, we can solve this system of equations.
We can substitute the expression for ( K ) from equation 2 into equation 1:
[tex]\[ 2.50(2A) + 6A = 7150 \][/tex]
[tex]\[ 5A + 6A = 7150 \][/tex]
[tex]\[ 11A = 7150 \][/tex]
Now, solve for ( A ):
[tex]\[ A = \frac{7150}{11} \][/tex]
[tex]\[ A \approx 650 \][/tex]
So, the number of adults attending the circus is approximately 650.
Now, we can find the number of kids attending the circus using the expression we found for ( A ) in terms of ( K ):
[tex]\[ K = 2A \][/tex]
[tex]\[ K = 2 \times 650 \][/tex]
[tex]\[ K = 1300 \][/tex]
So, the number of kids attending the circus is 1300.
A TUB USES 20 GALLONS. a shower uses 15 gallons. if 40 people take a bath instead of a shower, how much extra water is used?
Answer:
200 additional gallons of water are used when 40 people take a bath instead of a shower
Step-by-step explanation:
1. Let's review the information given to us to answer the question correctly:
Amount of water used when we take a bath = 20 gallons
Amount of water used when we take a shower = 15 gallons
Number of people who wants to take a bath = 40
2. How much extra water is used?
Extra water is used = Number of people * (Amount of water used when we take a bath - Amount of water used when we take a shower)
Replacing with the real values, we have:
Extra water is used = 40 * (20 - 15)
Extra water is used = 40 * 5 = 200 gallons
What is the LCM of 2 and 5?
Answer:
Step-by-step explanation:
10
Answer:
10Step-by-step explanation:
Since 2 and 5 are co-prime then
LCM(2 , 5) = 2×5 = 10
:)
What property is it when Segment AB is Congruent to AB
Answer:
Therefore,
[tex]Segment\ AB \cong Segment\ AB[/tex] ....Reflexive Property.
Step-by-step explanation:
Reflexive Property :
The reflexive property of equality means that anything is equal to itself. The formula for this property is a = a. This property tells us that any number is equal to itself. For example, 3 is equal to 3.Here it is given When
[tex]Segment\ AB \cong Segment\ AB[/tex]
AB is Equal to itself, Hence it is the Reflexive Property.
Therefore,
[tex]Segment\ AB \cong Segment\ AB[/tex] ....Reflexive Property.
Lindsey went to the teacher supply store. She bought 10 white boards for a total of $35 and some posters for $5.40 each. If she spent $51.20 total, how many posters did lindsey buy
Answer:3
Step-by-step explanation:
Answer:
Lindsey bought 3 posters.
Step-by-step explanation:
$51.20 - $35 = $16.20
$16.20 ÷ $5.40 = 3 Posters
Water leaves a spigot at a rate of 462 cubic inches per minute. How many cubic feet of water in this per hour?
What is the least amount of wrapping paper needed to wrap a gift box that measures 8 inches by 8 inches by 10 inches. Explain
448 square inches.
The surface area of the box is 448 square inches so that is the least amount of paper needed to cover the box.
Answer:204
Step-by-step explanation: Just that good.
last week, the price, in dollars, of a gallon of gasoline was g. This week the price of gasoline per gallon increased by 5%. Which expressions represent this weeks price, in dollars, of a gallon of gasoline?
A. g+0.05
B. g+0.05g
C. 1.05g
D. 0.05g
E. (1+0.05)g
The price of gasoline in this week is 1.05g. Option C
Step-by-step explanation:
Given,
The price of a gallon of gasoline = g in last week.
The price of gasoline increased by 5% this week.
To find the price of gasoline this week.
Formula
If an original price of an object a increased by b% the final price will be = a×[tex]\frac{100+b}{100}[/tex]
So,
The price of gasoline in this week = g×1.05 = 1.05g
[ Please note: Here option C and E have same value. So, both are correct].
The expressions represent this week's price, in dollars, of a gallon of gasoline, is 1.05g.
Given that,
Last week the price, in dollars, of a gallon of gasoline was g.
This week the price of gasoline per gallon increased by 5%.
We have to determine,
Which expressions represent this week's price, in dollars, of a gallon of gasoline?
According to the question,
The price of a gallon of gasoline = g in last week.
The price of gasoline increased = 5% = 0.05
The expressions represent this week's price, in dollars, of a gallon of gasoline is,
= Price of gallon last week + Price of gallon increased this week
= g + 0.05g
= (1 + 0.05)g
= 1.05g
Hence, The expressions represent this week's price, in dollars, of a gallon of gasoline, is 1.05g.
For more details refer to the link given below.
https://brainly.com/question/16553745
In a vial containing 5/6 parts, you withdraw 1/12. How many parts remain?
F(7) if f(x)=5x
Answer_______
Answer:
35
Step-by-step explanation:
put 7 instead x and it will be 5*7 that is 35
Gorillas and chimpanzees can learn language to communicate with humans. By 2017 , a gorilla named Koko had learned 700 words. This was 50 fewer than 5 times as many as a chimp named Washoe knew a decade earlier. How many words did Washoe know?
Answer:
130
Step-by-step explanation:
700 - 50 = 650
650/5 = 130
Answer:
150 words
Step-by-step explanation:
k = 700....koko knows 70 words
k = 5c - 50....this is 50 fewer then 5 times the chimps(c)
5c - 50 = 700
5c = 700 + 50
5c = 750
c = 750/5
c = 150 <=== the chimp, Washoe, knew 150 words
What is the slope of the line represented by the equation y =
x - 3?
Answer:
The slope of the line is: 1
The y-intercept is: -3
You can graph the line using the slope and y-intercept, or two points.
Answer:
1.
Step-by-step explanation:
The general form of a line is y = mx + c where m = the slope.
y = x - 3
or we can write it as y = 1x - 3
- so the slope is 1.
The sum of the first 46 postive and odd numbers is
The sum of first 46 positive and odd numbers is 2116
Solution:
Given that we have to find the sum of first 46 positive and odd numbers
The sum of first "n" natural odd numbers which are positive is given as:
[tex]Sum = n^2[/tex]
Here, n = 46
Therefore,
sum of first 46 positive and odd numbers = [tex]46^2[/tex]
sum of first 46 positive and odd numbers = [tex]46 \times 46 = 2116[/tex]
Thus the sum of first 46 positive and odd numbers is 2116
Twyla puts $1000 in a saving account that pays 4% interest, compounded monthly. How much money will in the account 11 years later if she makes no more deposits?
Answer:
$1551.57
Step-by-step explanation:
Each month, the account balance is multiplied by 1+.04/12, so after 132 months, it will be ...
$1000×(1 +.04/12)^132 ≈ $1551.57
There are 6 buses going on a field trip. There are 30 students on each bus. When they get to the park 42 students when to the slides. 28 students went to the swings. 39 students went to the grassy area to eat lunch. How many students are left?
Answer:
There are 71 students that are left
Step-by-step explanation:
Let's calculate the number of students left this way:
Total students = 30 * 6 = 180
Students that went to the the slides = 42
Students that went to the the swings = 28
Students that went to the the swings = 39
Students left = Total students - Students that went to the the slides - Students that went to the the swings - Students that went to the the swings
Replacing with the real values, we have:
Students left = 180 - 42 - 28 - 39
Students left = 180 - 109
Students left = 71
A and B are two events.
Given that P(A)=0.25 , P(B)=0.3 and P(AandB)=0.05 .
Drag and drop the answers into the boxes.
Events A and B are not independent because [tex]P(A / B) \neq P(A)[/tex]
Step-by-step explanation:
Given that [tex]P(A)=0.25[/tex], [tex]P(B)=0.3[/tex] and [tex]P(A \text { and } B)=0.05[/tex]
Two events are said to be independent events, if it satisfies any one of the following conditions,
[tex]P(A / B) = P(A)[/tex] or [tex]P(B / A) = P(B)[/tex] or [tex]P(AB)=P(A)P(B)[/tex]
First, let us substitute the values in the equation [tex]P(A / B) = P(A)[/tex]
The formula to find [tex]P(A / B)[/tex] is [tex]P(A / B)=\frac{P(A \cap B)}{P(B)}[/tex]
Substituting the values, we get,
[tex]P(A / B)=\frac{0.05}{0.3} =0.1667[/tex]
But [tex]P(A)=0.25[/tex]
Hence, [tex]P(A / B) \neq P(A)[/tex]
Thus, A and B are not independent events.
After 2 weeks of training Amanda learned a total of 5 appetizer recipes after 6 weeks of training how much appetizers will she learn?
Amanda learns 2.5 recipes per week, so over 6 weeks of training, she would be expected to learn 15 appetizer recipes.
Explanation:To establish the rate of Amanda learning new appetizer recipes, we need to determine the relationship between time (in weeks) and the number of recipes she learned. After 2 weeks of training, she learned 5 recipes, so we can assume that she learns at a rate of 5 recipes per 2 weeks, or 2.5 recipes per week.
Consequently, to estimate how many recipes she will learn after 6 weeks, we multiply the rate by the amount of weeks, which is: 2.5 recipes per week * 6 weeks = 15 recipes. Therefore, Amanda would be expected to learn 15 appetizer recipes after 6 weeks of training.
Learn more about Rate Calculation here:https://brainly.com/question/16549128
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$650 is invested in an account at 3%
simple interest per year. Write the
first 5 terms of the sequence that
shows the value of the account at
yearly intervals.
Answer:
Step-by-step explanation:
Simple interest = [tex]650*\frac{3}{100}=$19.5[/tex]
End of first year = 650+19.5 = $669.50
End of second year = 669.50+19.5 = $ 689
End of third year = 689+19.5 = $708.50
End of fourth year = 708.50 +19.5 = $ 728
End of fifth year = 728 +19.5 = $747.50
WHAT IS (50-2*5)+16/16
If 7 notepads cost $3.15, what is the unit price of the notepads?
Answer:
$0.45
Step-by-step explanation:
Unit price is basically the same as unit rate. Unit rate is the cost of one item.
So $3.15 divided by seven is point fourty-five.
Answer: 45 cents
Step-by-step explanation: Unit price means the cost per unit. In this case, the cost per notepad.
Since we know that it costs $3.15 for 7 notepads, to find the cost for 1 notepad, we need to divide 7 into $3.15 or 7 into 3.15.
I used long division wish I have shown in the image attached and ended up with .45 which means that each notepad costs 45 cents.
So the unit price for 7 notepads is 45 cents.