The two numbers are 10 and 6.
Now, let's take the larger number to be x and the smaller number to be y.
According to the question,
We have the following details:
The difference between two numbers = 4
So, we have the following expression:
(x-y) = 4 .... (1)
The sum of the smaller number and three times the larger number = 36
So, we have the following expression:
(3x+y) = 36 ....(2)
Now, we will use the elimination method to solve these equations. So, we will add equation 1 and 2.
(Please note that the left hand side is added to the left hand side and the right hand side numbers are added to the right hand side numbers.)
(x-y+3x+y) = (4+36)
4x = 40
x = 40/4 (4 is in multiplication on the left hand side. So, it is in the division on the right hand side.)
x = 10
Now, putting the value of x in equation 1,
(x-y) = 4 .... (1)
(10-y) = 4
-y = 4-10
-y = -6
y = 6
Hence, the larger number is 10 and the smaller number is 6.
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you repeatedly roll a fair six-sided die until you roll a 1 (and then you stop). every time you roll a 3, you win a points, and every time you roll a 6, you lose b points. you do not win or lose any points if you roll a 2, 4 or a 5. what is the expected number of points (as a function of a and b) you will have when you stop?
The expected number of points as a function of a and b is C = b+a.
In this questions what we are been asked is for the expected value C, to solve the problem we need to recognize the random variables and their respective probability.
x1 = roll a 1 -> P1 = 1/6
x2 = roll a 2 -> P2 = 1/6
x3 = roll a 6 -> P3 = 1/6
x4 = roll a 1, 4 or 5 -> P4 = 1/2
E = P1*x1 + P2*x2 + P3*x2 + P4*x4
x1 is equal to zero (no points and the game stop), x2 is equal to C+b (win a points, affecting the expected value), x3 is equal to C-a (win b points, affecting the expected value) and x4 is equal B (no points are lost and the game continues, therefore the expected value is not affected)
C = 1/6*0 + 1/6*(C+b) + 1/6*(C-a) + 1/2*(C)
1/6*C = 1/6*b + 1/6a
Solving for C
C = b+a
Conclusion: If you get a "2, 4 or 5, this means the game will be unaffected (in terms of points), you need to pay special attention to x1 and x2 (all with the same probability) that are the results that are going to affect your game.
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Which equation is y = –3x2 – 12x – 2 rewritten in vertex form?
y = –3(x + 2)2 + 10
y = –3(x – 2)2 + 10
y = –3(x + 2)2 – 14
y = –3(x – 2)2 – 2
Answer:
y = -3(x + 2)^2 + 10.
Step-by-step explanation:
y = –3x2 – 12x – 2
Divide first 2 terms by -3:
y = -3(x^2 + 4x) - 2 Now complete the square on x^2 + 4x:-
y = -3(x^2 + 4x + 4 - 4) - 2
y = -3[(x + 2)^2 - 4] - 2
y = -3(x + 2)^2 + 12 - 2
y = -3(x + 2)^2 + 10.
Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options.
x < 5
–6x – 5 < 10 – x
–6x + 15 < 10 – 5x
A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right.
A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
The value of the inequality expression given as –3(2x – 5) < 5(2 – x) are x < 5 and number line (4)
What are inequality expressions?Inequality expressions are mathematical statements that are represented by variables, coefficients and operators where the opposite sides are not equal
How to solve the inequality expression?The inequality expression is given as
–3(2x – 5) < 5(2 – x)
Open the brackets
So, we have
-6x + 15 > 10 - 5x
Collect the like terms
So, we have
5x -6x > 10- 15
Evaluate the like terms
So, we have
-x > -5
This gives
x < 5
When represented on a number line, it can be represented as the number line in option (4)
Hence, the equivalents of the inequality are x < 5 and number line (4)
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HELPPPPPP
You are selling concessions at a local swim meet. Hot dogs are being sold for $1.00 and soda is being sold for $0.50. At the end of the day you made $150. Let x represent the number of hotdogs sold and y represent the number of sodas sold. Write an equation that can be used to find the number of hotdogs and sodas sold at the swim meet.
a. Standard Form:
b. Slope-Intercept Form:
c. If you sold 40 hot dogs how many sodas did you sell?
d. Using the Standard Form, identify the x - intercept of the graph and explain
how the x-intercept relates to the number of hot dogs and sodas sold.
e. Using the Standard Form, identify the y-intercept of the graph and explain how the y-intercept relates to the number of hot dogs and sodas sold.
d. Using the Standard Form, identify the x - intercept of the graph and explain
how the x-intercept relates to the number of hot dogs and sodas sol
Maybe sorry if i got it wrong
. (4, 9) and (1, 6) the slope between the two points
Answer: the slope is 1
Step-by-step explanation:
Explain how you can represent a proportional relationship using an equation.
The proportional relationship can be represented by using an equation y = kx
Proportional relationship defined as the relationships between two variables where their ratios are equivalent. We can say that , in a proportional relationship, one variable is always a constant value times the other. That constant is called as the "constant of proportionality"
Consider y and x are in direct proportional relationship
y ∝ x
We can write this proportional relationship as
y = kx
Where y and x are the two variables
K is the constant of proportionality
In this equation we can see that the variable y is a constant value times the other variable x
Hence, the proportional relationship can be represented by using an equation y = kx
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F = G(m1m2/d2)
Solve for m1
Answer:
[tex]m_1=\frac{Fd^2}{Gm_2}[/tex]
Step-by-step explanation:
[tex]F=G \left(\frac{m_1 m_2}{d^2} \right) \\ \\ \frac{F}{G}=\frac{m_1 m_2}{d^2} \\ \\ \frac{Fd^2}{G}=m_1 m_2 \\ \\ m_1=\frac{Fd^2}{Gm_2}[/tex]
Solve for x (6x+5) 86
Answer:
x = -5/6
Step-by-step explanation:
First, set the equation (6x + 5) * 86 equal to 0. The equation is now (6x + 5) * 86 = 0. Next, simplify (6x + 5) * 86 by multplying 86 to 6x and 5. This will turn the equation into 516x + 430 = 0. Next, subtract 430 from both sides, cancelling out the 430 on the left side. After that, get the x value by itself by dividing 516 on both sides, cancelling out the 516 on the left side. Now, x = -430/516. From here, find the common factor of both the numerator and denominator; this turns out to be 86. Since 86 is the common factor, divide the numerator and denominator by 86 and you get x = -5/6.
ANSWER QUICK PLEASE ILL GIVE BRAINLY AND POINTS
Answer:
x = -11
Step-by-step explanation:
JL + LM = JK + KM
x + 2 + 2x + 27 = 9 + 7
x + 2x + 22 + 27 = 9 + 7
Combine like terms,
3x + 49 = 16
Subtract 49 from both sides,
3x = 16 - 49
3x = -33
Divide both sides by 3,
x = -33/3
x = -11
HELPPPPPPPPPPPPPPPP PLEASE
Answer:
use v for the value
Step-by-step explanation:
27 ÷ 9 = 3, therefore 27 ÷ 0.9 = 30.
True
False
Answer: True
Step-by-step explanation:
Answer:
True
Step-by-step explanation:
Please answer the question in the photo
Answer: 40
Step-by-step explanation:
There are 9 cogs on the outside, and the circumference of a circle is 360 degrees. Dividing 360 by 9 yields 40 degrees.
7x-15= where x=3
[tex]222[/tex]
The Marianas Trench in the Pacific Ocean is the deepest part of the ocean. It's depth is 6.85 miles. Sound
travels 4700 feet in one second under water. Find the time, to the nearest tenth of a second, it takes sound to
travel from the surface of the ocean to the bottom of the Marianas Trench and back.
6.85 miles is how deep it is. Under water, sound may travel 4700 feet in a second. The Time takes to travel the sound is 7.69.
Given that,
The deepest area in the ocean is the Marianas Trench in the Pacific Ocean. 6.85 miles is how deep it is. Under water, sound may travel 4700 feet in a second.
We have to calculate the time it takes for sound to travel from the ocean's surface to the Marianas Trench's depths and back, to the nearest tenth of a second.
We know the Distance formula is
Distance =rate×times
Time=Distance/rate
We convert 4700 feet to miles
We get,
4700 feet =0.89 miles
Now,
Time=6.85/0.89
Time=7.69
Therefore, the Time takes to travel the sound is 7.69.
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During the 2021 winter storm in texas, snow fell at a constant rate. in 3 hours, 19.5 centimeters of snow fell. how many centimeters of snow fell per hour?
Answer:
19.5/3=6.5 centimeters
Step-by-step explanation:
Solve for that value of x which makes like m and n parallel
Answer:
x = 300°
Step-by-step explanation:
If m and n are parallel, then m∠4x is equal to 120, since they are congruent angles.
Solve for x:
4x = 1200
Divide both sides by four
x = 300
Determine whether the table represents a linear or nonlinear function.
Answer:
Linear Function
Step-by-step explanation:
A linear function has constant slope
That means the ratio of y differences to x differences must be the same throughout the function. In other words the rate of change of the function y value is the same throughout the function
IF we look at the table we see that as x increases by 1, y decreases by 15
For example at x = 0, y = 20 and at x = 1, y = 5
So change in y/change in x = 0 = (5-20)/(1-0) = -15/1 = -15
If we look at another pair of points, say x = 1, y=5 and x = 2, y = -10
we get the rate of change = (-10 - 5)/(2-1) = -15/1 = -15
This is the same for any two x, y pair of values
So it is a linear function
There are 25 students competing in a volleyball tournament.
They are all wearing school colors. There are 4 students with blue shirts, 11 students with white shirts, and 10 students with yellow shirts.
A student is selected at random to be the captain. Match each probability to an outcome.
The captain has a blue shirt
The captain has a red shirt
The captain has a blue or white shirt.
impossible unlikely
neither unlikely nor likely
likely certain
Probability when a student is selected at random to be the captain. Probability the captain has a blue shirt is unlikely. Probability the captain has a red shirt is impossible. Probability the captain has a blue or white shirt is likely certain.
The total number of students is 15.
4 students are wearing blue shirt.
11 students are wearing white shirt.
10 students are wearing yellow shirt.
Only any one student can be captain.
The total outcomes are 25.
Probability that the student has blue shirt B is,
Total favorable outcomes = 4
P(B) = 1/25.
Probability that the student has red shirt R is,
Total favorable outcomes = 0
P(B) = 0/25.
P(B) = 0
Probability that the student has blue or white shirt B and W is,
Total favorable outcomes = 15
P(B&W) = 15/25.
P(B&W) = 3/5.
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If I bought a scooter and it dropped by 24% in the FIRST year and after every year it drops by 13% for 7 years. I payed £850. How much is it worth now
Step-by-step explanation:
850÷100=17/2=8.5
8.5×24=204
850-204=646
646÷100=6.46
6.46×13=83.98 1st
646-83.98=562.02
562.02÷100=5.6202 2nd
5.6202×13=73.0626
562.02-73.0626=488.9574
488.9574÷100=4.889574 3rd
4.889574×13=63.564462
4.889574×13=63.564462
488.9574-63.564462=425.392938
425.392938÷100=4.25392938 4th
4.25392938×13=55.30108194
425.392938-55.30108194=370.0918561
370.0918561÷100=3.700918561 5th
3.700918561×13=48.11194129
370.0918561-48.11194129=321.9799148
321.9799148÷100=3.219799148 6th
3.219799148×13=41.85738893
321.9799148-41.85738893=280.1225259
280.1225259÷100=2.801225259 7th
2.801225259×13=36.41592836
280.1225259-36.41592836=243.7065975
I spent waaaaay to much time typing this
answer out I swear if it is incorrect I am done
£243.71
URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
Answer:
D
Step-by-step explanation:
What is the rate of change for this table?
Prime Factorization *Student A stated that the PRIME FACTORIZATION of 96 is 2x3x5x5. *Student B said that the PRIME FACTORIZATION of 96 is 2x2x2x2x2x3. Mr. Hrenko asks three students to find the PRIME FACTORIZATION of 96. *Student C stated that the PRIME FACTORIZATION of 96 is 2x2x3x3x5. Which student is correct? Prove your answer by making a factor tree. O Student B Studnet C O None of the students are correct O Student A
The student that is correct with regards to the prime factorization of 956 is student B.
Which student is correct?A factor is a number that divides another number without leaving any remainder. For example, 10 is a factor of 100. A prime number is a number that is perfectly divisible by 1 and that number only.
For example, a prime number is 7. A prime factor is the factor of a number that is a prime number. For example, a prime factor of 28 is 2.
In order to determine the prime factorization of a number, express the number as its prime factors.
Prime factors of 92 = 2 x 2 x 2 x 2 x 2 x 3
Thus, it is only student B that is correct. 5 is not a factor of 96.
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Is the relation represented in this table a function?
Is the relation in this set of points a function?
Answer:
the relation in the table is a function
the relation in the set of points is not a function
Step-by-step explanation:
the definition of a function is that one input (x) can only have one output (y). In the set of points, the input 4 appears twice, which means it is not a function.
Last year you mowed grass and shoveled snow for 12 houses. You earned $225 for each lawn you mowed
and $200 for each house you shoveled for a total of $2600. How many lawns did you mow? How many
driveways did you shovel?
1800 lawns were mowed. 800 driveways were shoveled.
What is equation?A formula that expresses the connection between two expressions on each side of a sign. Typically, it has a single variable and an equal sign. Like this: 2x - 4 Equals 2. In the above example, the variable x exists. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.
Given Data
Let mowed grass be x
Let shoveled snow be y
Last year you mowed grass and shoveled snow for 12 houses
x + y = 12
y = 12 -x
You earned $225 for each lawn you mowed and $200 for each house you shoveled for a total of $2600.
225x + 200y = 2600
Equating value of y
225x + 200(12-x) = 2600
225x + 2400 - 200x = 2600
225x - 200x = 2600 - 2400
25x = 200
x = 8
For value of y,
y= 12 -x
y = 12 - 8
y = 4
Lawn mowed = 225(8)
Lawn mowed = 1800
Shoveled snow = 200(4)
Shoveled snow = 800
1800 lawns were mowed. 800 driveways were shoveled.
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una tuberia tiene 7 tramos iguales de 0.75 m. ¿cual es la longitud de la tuberia?
Answer: la respuesta es 5.25
Step-by-step explanation: 0.75 x 7 = 5.25
please help me fasttt need to find the equation
The equation of the linear graph is expressed in slope intercept form as; y = 20x
What is the equation of the Linear Graph?The equation of a line in slope intercept form is;
y = mx + c
where;
m is slope
c is y-intercept (which is the point where the line crosses the y-axis)
From the graph given we can see that the line crosses the y-axis at 0. Thus; c = 0
Now, we can pick two coordinates to find the slope;
Slope = (y2 - y1)/(x2 - x1)
Slope = (40 - 20)/(2 - 1)
Slope = 20
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The ratio of Ed's toy cars to Pete's toy cars was initially 5:2. After Ed gave 30 toys car to Pete, they each owned an equal number of toy cars. How many toy cars did they have altogether?
Answer:
5:2
5x-30 = 2x+30
3x = 60
x = 20
total cars:
5(20)+2(20)
=100+40
=140cars
Write a directed number suggested by the following :
A 14 degrees below zero
B altitude 200 metres
The directed number suggested by the following will be:
A 14 degrees below zero = -14°
B altitude 200 metres = +200
How to illustrate the information?It should be noted that the directed number simply means the numbers that had both size and direction. It should be noted that the direction can either be positive or negative.
A measurement of altitude or height is the distance between a location or item and a reference datum, typically in the vertical or "up" direction. Although the term "altitude" is frequently used to refer to a location's height above sea level, the term "elevation" is frequently preferred in the context of geography. The term "depth" often refers to vertical distance measurements taken in the "down" direction. Globally, the research team discovered that the pace of temperature change frequently quickens as altitude increases.
Therefore, the directed number suggested by 14 degrees below zero will be negative 14 and this will be -14°
Also, altitude 200 metres will be positive 200 and this will be +200
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A bag contains 3 green, 4 blue, 2 red, 1 black, 6 yellow and 4 brown marbles. Suppose you randomly select a marble, replace it in the bag, and randomly pick a second
marble. What is the probability you pick a blue marble and then another blue marble?
i need help! please is expression equivalent
No the value of functions are not same .
What is function in math?
A quantitative expression, rule, or law that describes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions occur widespread, and they are essential for defining physical links in the sciences.A function is a type of rule that generates one output for a single output. This is represented by the equation y=x2. Any inputs for x result in an output for y. Given that x is the input value, we would state that y is a result of x.- 5 × ( -5)⁻⁹ = -5 × 1/-5⁹ ⇒ 1/5⁸ = 1/390625
[ -5 × (-5)]⁻⁹ = [25]⁻⁹ = 1/25⁹ = 1/3814697265625
No the value of functions are not same .
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