Two numbers are such that twice the greater number exceeds thrice the smaller one by 15 and 1/5 of the smaller and 1/9 of the greater number are together 10. Find the numbers.
Answer: The two numbers are $x = 5$ and $y = 7.5$.
Step-by-step explanation:
Let the two numbers be $x$ and $y$, where $x < y$. We can write the two given statements as the following two equations:
$$2y = 3x + 15$$
$$\frac{1}{5}x + \frac{1}{9}y = 10$$
We can solve this system of equations using elimination. Multiplying the first equation by 5 and the second equation by 9, we get
$$10y = 15x + 75$$
$$9x + y = 90$$
Subtracting these equations, we get
$$8y - 9x = 15$$
Multiplying this equation by 8, we get
$$64y - 72x = 120$$
Adding this equation to 5 times the first equation, we get
$$69y - 72x = 120 + 75$$
$$69y - 72x = 195$$
Dividing both sides by 3, we get
$$23y - 24x = 65$$
Subtracting this equation from 4 times the second equation, we get
$$96y - 36x = 360 - 260$$
$$96y - 36x = 100$$
Dividing both sides by 60, we get
$$\frac{16}{3}y - \frac{6}{5}x = \frac{5}{3}$$
Substituting the expression for $y$ from the first equation, we get
$$\frac{16}{3}(3x + 15) - \frac{6}{5}x = \frac{5}{3}$$
This simplifies to
$$\frac{16}{5}x + \frac{64}{5} = \frac{5}{3}$$
Solving for $x$, we find that $x = 5$. Substituting this value into the first equation, we find that $y = 15/2 = 7.5$. Therefore, the two numbers are $x = 5$ and $y = 7.5$.
Which of the following statements must be true based on the diagram below?
Select all that apply. (Diagram is not to scale.)
UV is a segment Bisector.
What is a segment Bisector?A segment bisector is a line, ray, or segment that splits another line segment in half evenly at its center. The midpoint of the line segment is always bisected by the line, which divides it into two equally sized parts.
What is the bisector rule?The angle bisector theorem states that a triangle's opposite side is divided into two parts by an angle bisector that is proportional to the triangle's other two sides.
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HELP PLEASE show work if possible I WILL MARK BRAINLIEST TO BEST ANSWER
The Value for x and y as follow:
A) x=2 and y=-8
B) x = -2 and y = 5
C) x = -9/4 and y= -5/2
What is Elimination Method?The elimination approach involves taking one variable out of the system of linear equations by utilising addition or subtraction together with multiplication or division of the variable coefficients.
Given:
A) 9x- 2y = 34...............(1)
5x+ 2y = -6..............(2)
Adding equation (1) and (2) we get
9x -2y = 34
5x + 2y = -6
_____________
14x = 28
x= 28/14
x= 2
and, 5x +2y= -6
5(2) + 2y= -6
2y = -6 -10
y = -8
B) x+ 6y = 28.....................(3)
2x -3y = -19................(4)
Multiply equation (2) by 2 we get
4x - 6y = -38.......................(5)
Adding equation (3) and (5), we get
x + 6y = 28
4x- 6y = -38
___________
5x = -10
x= -2
and, x+ 6y= 28
-2 +6y= 28
6y= 30
y=5
C) 8x -6y = -3................(6)
6x -5y = -1......................(7)
Multiply equation (6) by 5 and equation by (6), we get
40x - 30 y = -15
36 x - 30y = -6
- + +
____________
4x = -9
x= -9/4
and, 8x - 6y = -3
8(-9/4) - 6y = -3
-18 - 6y= -3
-6y = 15
y = -5/2
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Which graph is defined by the function given below?
y=(x + 2)(x+7)
10-
A.
-10
OA. Graph A
OB. Graph B
C. Graph C
OD. Graph D
10+
B.
10-
10
10-
D.
Graph A is defined by the function y=(x + 2)(x+7) as the graph at y=0 where the function crosses those two points .
what is function ?The study of mathematics comprises the study of quantities and their variations, equations and associated structures, shapes and their positions, and locations where they can be found. A combination of inputs and corresponding outputs are referred to as a "function," which describes the relationship between them. The term "function" refers to an association between inputs and outputs where each input produces a single, unique result. There are two domains, or scopes, assigned to each function. Usually, the symbol f is used to signify functions (x). input is an x. There are four basic categories of functions that are available: on functions, one-to-one functions, many-to-one functions, within functions, and on functions.
given
The function's zeros are
0=x+2 x=-2
and
0=x+7 x=-7
Consequently, the graph at y=0 where the function crosses those two points .
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to solve 2/5 x = 14, you multiply both sides of the equation by 5/2. your friend divides both sides of the equation by 2/5. who is right? explain.
Both of you are correct because using either way can solve the equation for the value of x.
How to solve for x ?In the case of solving for x in 2/5 x = 14, the goal is to get rid of the fraction that is multiplying x on the left side. This can be done by either multiplying both sides of the equation by the inverse of 2 / 5 ( which is 5 / 2 ) or by dividing both sides by 2 / 5.
Doing either of these things would get rid of the 2 / 5 and give an answer to x as shown below :
Multiplying :
2/5 x = 14
5 / 2 x 2 / 5 x = 14 x 5 / 2
x = 35
Dividing :
2/5 x = 14
2 / 5 x / 2 / 5 = 14 / 2 / 5
x = 35
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A bus rental company charges $60 for booking a bus and $120 for each hour the bus is rented. A tour group pays $780 to rent a bus. HELP WANTED TY!!
Select the equation that represents the given situation and find the number of hours the tour group rented the bus.
A. 60x + 120 = 780 ; 11 hours
B. 60x + 120 = 780 ; 6 hours
C. 120x + 60 = 780 ; 11 hours
D. 120x + 60 = 780 ; 6 hours
Answer:d. 120x+60=780
Step-by-step explanation:
120 cost per x hours
Flat Rental cost 60
120x+60=780
-60 as the flat rate which won’t change based on time.
120x=720
Divided by a rate of 120 per hour
x=6 hours
A pet shelter has 5 cats and 9 dogs.
Enter the ratios in the boxes.
ratio of cats to all animals:
ratio of dogs to cats:
The ratio of cats to all animals is 5:14
the ratio of dogs to cats is 9:5
Given-
Cats = 5
Dogs = 9
Total animals = cats+ Dogs
5+9=14
so the ratio of cats to all animals = 5: 14
and dogs to the cats= 9:5
Ratio give the relation between quantities of to identies.
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what is the quotient of g and 25
Answer:
the quotient of g and 25 is g/15.
‐3 + 4(a – 3b + 2) – 5(2 – a + 3b)
Answer: 15a – 12b – 5.
Step-by-step explanation: To solve this equation, we need to distribute the constants in front of the parentheses. Doing so, we get:
-3 + 4(a – 3b + 2) – 5(2 – a + 3b)
= -3 + 4a – 12b + 8 – 10 + 15a – 15b
= (15a – 12b) + (-10 + 8) – 3
= 15a – 12b + -2 – 3
= 15a – 12b – 5
Thus, the solution to the equation is 15a – 12b – 5.
Simplify x+2+3x++5+x+3+2x
Answer: 7x+10
Step-by-step explanation:
combine like terms
x+3x+x+2x+2+5+3
7x+10
Answer:
Step-by-step explanation:
Simplification of : x + 2 + 3x + 5 + x + 3 + 2x = 7x + 10
First: find the (x) and collect them, put them in the bracket (to ensure the + or -)
(x + 3x + x + 2x) + 2 + 5 + 3
= 7x + 2 + 5 + 3
Then we add up the numbers
= 7x + 10
This is the end result.
x + 2 + 3x + 5 + x + 3 + 2x = 7x + 10
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Lesson 17
Using the info given, solve for the missing value of the right triangle. Round each angle to the nearest degree, each length to the nearest tenth, & each trigonometric value to four decimal places, if necessary.
Hypotenuse = 14.5 meters
Opposite side = 6.3 meters
θ = ?
The measure for θ is 25.747121°.
What is Trigonometry?The area of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and acronyms (csc).
Given:
Hypotenuse = 14.5 meters
Opposite side = 6.3 meters
Now, using Trigonometry
sin θ = Opposite side / Hypotenuse
by putting the given values we get
sin θ = 6.3 / 14.5
sin θ = 63/145
sin θ = 0.4344
θ =25.747121°
Hence, the angle is 25.747121°.
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a letter is chosen at random from the word FOOTBALL, the probability that the letter chosen is not an L is:
Answer:
7/8
Step-by-step explanation:
Step 1: Count the total number of letters in the word FOOTBALL
There are 8 letters in the word FOOTBALL.
Step 2: Count the number of letters that are not L
There are 7 letters that are not L.
Step 3: Calculate the probability
The probability that the letter chosen is not an L is 7/8.
Solve the equation 5(4x-1.5x) + 12 = 4x- 124 for X
[tex] \sf \: 5(4x -1.5x) + 12 = 4x - 124 \\ \sf \: 5 \times 2.5x + 12 = 4x - 124 \\ \sf \: 12.5x + 12 = 4x - 124 \\ \sf \: 12.5x - 4x = - 124 - 12 \\ \sf \: 8.5x = - 136 \\ \sf \: x = - 16[/tex]
A paint store makes lime green paint by mixing 3 parts yellow paint to 1 part blue paint. A clerk mixès 5 parts yellow paint to 2 parts blue paint. did the clerk use the correct ratio of yellow paint to blue paint? Explain.
Answer:
No
Step-by-step explanation:
The ratio used should have been 6 parts yellow paint to 2 parts blue paint
hope this helps
Write an equation and solve for b using the diagram
below. YOU MUST WRITE THE EQUATION IN
ORDER TO GET CREDIT.
(3b + 18)°
93°
Step-by-step explanation:
hope this is right hehe.....
Assuming these rates continue, how many likes does Dagogo get, on average, for each minute of video he uploads?
The average like for each minute of the video that he uploads will be 2,000 likes.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The total number of likes is calculated as,
Like / View = 1 / 5
Like / 9,000,000 = 1 / 5
Like = 1,800,000
The total number of minutes is calculated as,
Time length = (9,000,000 / 150,000) x 15
Time length = 60 x 15
Time length = 900 minutes
The average like for each minute of the video that he uploads will be given as,
⇒ 1,800,000 / 900
⇒ 2,000
The average like for each minute of the video that he uploads will be 2,000 likes.
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The complete question is given below.
Dagogo uploads 3 videos on his channel every month. Each video averages 15 minutes in length and gets an average of 150,000 new views. The average ratio of likes-to-views of Dagogo's videos is 1: 5. Dagogo wants to reach a total of 9,000,000 views on his channel.
Assuming these rates continue, how many likes does Dagogo get, on average, for each minute of the video he uploads?
PLIS HELP
The total cost in dollars, y, that a t-shirt company charges can be modeled by the toes per day by the equation y = 5x + 62, where x represents the number of t-shirts sold. If they sell 74 shirts, what will the total cost be?
The total cost of the 74 shirts will be;
⇒ $432
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The total cost in dollars, y, that a t-shirt company charges can be modeled by the toes per day by the equation is,
⇒ y = 5x + 62
Where, x represents the number of t-shirts sold.
Now,
Since, The equation is,
⇒ y = 5x + 62
Where, x represents the number of t-shirts sold.
Hence, For 74 shirts, the cost is fund by substitute x = 74 in above equation,
⇒ y = 5x + 62
⇒ y = 5 × 74 + 62
⇒ y = $432
Thus, The total cost of the 74 shirts = $432
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Six families went to the food festival. Each family has 2 adults and 4 children. The entry fee for each child ticket costs $4, and an adult ticket costs $8. What would be the total cost of the festival tickets?
By solving an expression we will see that the total cost for the tickets is $192.
What would be the total cost of the festival tickets?We know that six families went to the food festival, each family has 2 adults and 4 children, then there are:
6*2 = 12 adults in total.
6*4 = 24 children in total.
We know that each child ticket costs $4, and an adult ticket costs $8, then the total cost of all the tickets is what we get when we solve the expression below:
12*$8 + 24*$4
That is, the number of adults times the cost of an adult ticket plus the number of children times the cost of a children ticket.
The total cost is then:
12*$8 + 24*$4 = $192
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PLEASE HELP ME DUE TODAY NOW ASAP THANKS
The rate of change of the end points of the line is 32/10
What is slope?
Slope is defined as the rate of change of y with respect to x. Also it is defined as increase in y over increase in x or decrease in y over decrease in x
slope is denoted by the formula = Δy/Δx
Where Δy = change in y
Δx= change in x
The given points are (-9, -2) and (5, 119/5)
The slope of the end points (119/5 + 21)/(5+9)
The slope is (119+105)/5
M= 44.8/14
The slope is 3.2 = 32/10
Therefore the rate of change is given as 32/10
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In the construction of bridges, engineers use a formula to help
determine the allowable stress on a bridge rocker, a component of the
bridge that handles the stress and weight placed on the pavement of the
bridge. The engineers use the formula F =11/300d (F − 13), where F is the
strength of the steel in kilopound per square inch and d is the diameter
of the rocker in millimeters.
Solve the formula F =11/300d (F − 13) for d.
From the engineers formula given, making d the subject of the formula gives us; d = 300F/(11(F - 13))
How to change the subject of the formula?
We are given the engineers formula as;
F = (¹¹/₃₀₀)d(F - 13)
Where;
F is the strength of the steel in kilopound per square inch.
d is the diameter of the rocker in millimeters.
From the given formula, we can start by;
Multiply both sides by 300 to get;
300F = 11d(F - 13)
Divide both sides by 11(F - 13) to get;
d = 300F/(11(F - 13))
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Help if you know how to do this! I’d really appreciate it!
The value of x is 20 and the value of y is 8 from the given quadrilaterals.
What is a Congruent Polygon?The definition of a congruent polygon is a polygon that is the same shape, has the same length of sides, and has the same interior angles as the polygon it is being compared to. Congruent shapes must all be the same type of shape in order to fulfill the requirement.
Given that, ABCD≅EFGH
We know that, corresponding parts of congruent polygon are equal.
Now, (4y-4)°=28°
4y=32
y=8
(10x-65)°=135°
10x=200
x=20
Therefore, the value of x is 20 and the value of y is 8 from the given quadrilaterals.
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WILL GIVE BRAINLIEST
There are 6.02 × 10^23 atoms in 1 gram of hydrogen. How many atoms are there in 400 grams of hydrogen? Write your answer in scientific notation. If necessary, round your answer to two decimal places.
If possible PLEASE write the answer in the form of 54x10^3
Answer: 2.403 × 10^3 atoms
Step-by-step explanation:
10^13 x 6.02 = 6.02^23 and 6.02^23 x 4 = 2,403 turned into 2.403 x 10^3 atoms.
A(n)___ is a convex in which both pairs of opposite side are parallel
4th option: parallelogram
The midpoint M of the line segment AB is (1,3). If the coordinate of B is (-5,7), what is the coordinate of the point A
Answer:
( 7,-1 )
Step-by-step explanation:
Draw a number line to show 2/8 and 4/16 are equivalent.
Step-by-step explanation:
think of it as a ruler the small dashes represents the 16ths and the big dashes represents the 4ths. They are on the same line therefore they are equal.
Shaikha types at a rate of 34 words per minute. How many words does she type in 2 minutes?
Answer:
68 words
Step-by-step explanation:
If 34 words are typed in a minute what about two minutes hence take 34×2
Answer:
68
Step-by-step explanation:
What is a rate?A rate can be a quantity, or frequency, measured against a different quantity or amount.
If we know that Shaikha can type at a rate of 34 words per minute, and we need to figure out how many words she can type in 2 minutes, we can use an equation that looks like this:
Let m = minutes, w = words per minute and t = total words
m × w = t
Simply just insert your numbers into the equation.
2 × 34 = 68
Therefore, the number of words, or rate, that Shaikha types in 2 minutes is 68.
a particular dress requires 3 1/4 yards of fabric for manufacturing. if the matching jacket requires 1/6 yards less fabric, how much fabric is needed for both pieces?
Answer: The matching jacket requires 1/6 yards less fabric than the dress, which is 3 1/4 - 1/6 = 3 1/4 - 2/12 = 3 1/4 - 1/6 = 3 1/4 - 1/6 = 3 1/4 - 1/6 = 3 3/12 yards of fabric.
To add these two amounts of fabric together, you need to add the yards and the inches separately.
For the dress: 3 1/4 yards = 3 + 1/4 = 3 + 0.25 = 3.25
For the jacket: 3 3/12 yards = 3 + 3/12 = 3 + 0.25 = 3.25
So, for both pieces, the required fabric is 3.25 + 3.25 = 6.5 yards
Step-by-step explanation:
If a house has decreased 35% since it was purchased and it currently values 117,000 what was purchase value
Step-by-step explanation:
that means the current value of $117,000 is 100 - 35 = 65% of the original price.
65% = $117,000
1% = 65%/65 = 117000/65 = $1,800
100% = 1%×100 = 1800×100 = $180,000
the original (100%) purchase value was $180,000.
Ashanti cashed her paycheck at Cash-n-Go. The fee at Cash-n-Go is 7.5% of the amount of the check. Her paycheck was $670. How much was the fee for Ashanti to cash her paycheck?
Answer:
$50.25
Step-by-step explanation:
7.5% as a decimal is 0.075.
So, the fee is [tex](0.075)(670)=\$50.25[/tex].
A construction crew is lengthening a road. Let y represent the total length of the road (in miles). Let x represent the number of days the crew has worked.
Suppose that x and y are related by the equation y = 53+2x.
Answer the questions below.
Note that a change can be an increase or a decrease.
For an increase, use a positive number. For a decrease, use a negative number.
What is the change per day in the road's length?
miles
What was the road's length when the crew started working?
Answer: The equation y = 53+2x relates the variables x and y, where x represents the number of days the crew has worked and y represents the total length of the road.
The change per day in the road's length is given by the coefficient of x in the equation, which is 2. Thus, the change per day in the road's length is 2 miles.
The road's length when the crew started working is given by the constant term in the equation, which is 53. Thus, the road's length when the crew started working was 53 miles.
Step-by-step explanation: