35.124, so rounded it is just 35.124
The sum of two numbers is $30$. the difference of twice the larger number and three times the smaller number is $5$. what is the positive difference between the two numbers?
The positive difference between the two numbers is 8, which is found by setting up a system of linear equations based on the sum of the numbers and the difference of twice the larger number and three times the smaller number.
To solve the system of equations given by the problem, we can set up two equations based on the information provided. Let x be the larger number and y be the smaller number. We are given:
The sum of two numbers is $30: x + y = 30.The difference of twice the larger number and three times the smaller number is $5: 2x - 3y = 5.Solving this system of equations will allow us to find the values for x and y. From the first equation, we can express y in terms of x as y = 30 - x.
Substituting this into the second equation gives us 2x - 3(30 - x) = 5, which simplifies to 2x - 90 + 3x = 5 and further to 5x = 95.
Dividing both sides by 5, we find x = 19. Now we can determine y by plugging x back into the first equation, resulting in y = 30 - 19, so y = 11.
The positive difference between the larger and smaller number is 19 - 11 = 8.
Hisham is saving to buy a video game system. every month he spends $30 of what he earns. after four months, he has saved $300. how much money does hisham earn every month?
Huilan is 15 years older than thomas. the sum of their ages is 55 . what is thomas's age?
Which of the following is the inverse of the statement, "If it is an orange, then it is a citrus fruit"? A.If it is a citrus fruit, then it is not an orange. B.If it is a citrus fruit, then it is an orange. C.If it is not an orange, then it is not a citrus fruit. D.If it is not a citrus fruit, then it is not an orange.
By graphing the system of constraints, find the values of x and y that maximize the objective function.
2<_x<_6
1<_y<_5
x+y<_8
Maximum for p=3x+2y
Answers:
A. (2,1)
B. (6,2)
C. (2,5)
D. (3,5)
Answer: (6,2)
Step-by-step explanation:
What is the least common denominator (LCD) of 1/2 and 3/5 ?
he equation for the line of best fit is y = 0.39x + 15.89. Which of the following statements is true for the above graph?
Hank's pickup can travel 64 miles on 4 gallons of gas. How many gallons will Hank's pickup need to travel 32 miles?
Find the height of the pole if the shadow of a boy 6 ft. tall is 3 ft. and the shadow of the pole is 2 1/3 yards. 1 yards 4 feet 14 feet
Answer:
14 feet
Step-by-step explanation:
Given ONL=MLN, O and M are right angles prove LM=NO
Using the properties of Isosceles triangles and right-angled triangles, it can be deduced that LM = NO given that angles ONL = MLN and O and M are right angles.
Explanation:The given question is about proving equivalency of lines in a geometric figure. Given the figure has the angles ONL and MLN that are equal and O and M are right angles. Given these conditions, using the properties of triangles especially the Isosceles Triangle (where two sides are equal), we can conclude that LM = NO.
To prove this assumption, we incorporate the following facts: In an isosceles triangle, the angles opposite to equal sides are equal. Hence, if ONL = MLN, it implies that NO = LM. Additionally, if angles O and M are right angles, it signifies that the triangles formed are right angled triangles. Therefore, using the property of isosceles right angled triangles, the sides opposite to equal angles are equal.
Based on these facts and the properties of geometric concepts [Isosceles Triangle, Pythagorean theorem and right angled triangles], we can confidently conclude that LM = NO. This proves that given the conditions in the problem, the lines LM and NO are equal in length.
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Given that ONL=MLN and O and M are right angles, we can say that triangles ONL and MLN are congruent right-angled triangles. Therefore, according to the property of congruent triangles, the sides opposite the equal angles in these triangles (i.e., LM and NO) should also be equal to each other.
Explanation:The question involves proving the equivalence of two lines in a geometric configuration, LM and NO, where two angles, ONL and MLN, are given as equal and O and M are right angles. This is quite a typical problem in Geometric Proof, an important topic in High School Mathematics.
To solve this, we need to apply the properties of triangles and the concept of congruent triangles. Since ONL and MLN are given as equal angles and O and M are right angles, we know that triangle ONL and MLN are right-angled triangles. In a right-angled triangle, if one angle is equal, then the other angles will be equal because the summing of angles in a triangle is 180 degrees.
Because we have now two right-angled triangles with their respective angles equal (ONL = MLN and NOM = LNM), they must be congruent triangles by the Angle-Angle (AA) criterion for congruency. This implies that the sides opposite the equal angles in these two triangles should also be equal. So, LM = NO in these triangles.
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Find the indicated real nth root(s) of a.
n=2, a=100
1. ∠E and ∠F are vertical angles with m∠E=9x+12 and m∠F=3x+24
What is the value of x?
2. What is m∠KNL?
Becky created a graph to represent her distance away from home one afternoon. She left home and ran to the park, met some friends and stayed at the park, and then walked back home using the same route. Which graph could Becky have created?
Answer: The first graph is the right graph according to the given situation.
Step-by-step explanation:
Given: Becky created a graph to represent her distance away from home one afternoon.
She left home and ran to the park⇒ She started running from zero distance from the home .⇒the second and fourth graphs are wrong .
After that she met some friends and stayed at the park, then walked back home using the same route.⇒ The first one is correct because there we can see the graph is parallel to time axis for a interval but in the third one it shows that she she hasn't took rest .
In order to be elected to student council, Jeremy must have at least 50% of the current council members vote in his favor. If x represents the percent of favorable votes received, which inequality represents the percent of favorable votes that Jeremy needs for election to student council?
a baby elephant weighs 250 lb.
What is the elephants weight in TONS AND KILOGRAMS
(1kg=2.2lb)? round to the nearest thousandths place
Answer:
250 lb⋅1 ton2000 lb=2502000 tons = 18 ton = 0.125 tons
250 lb⋅1 kg2.2 lb≈2502.2 kg ≈ 113.636 kg
If parallelogram rstu has all sides the same length then it would be true that rs = st
Drag a statement or reason to each box to complete this proof.
If 3x−4=14, then x=6.
1. 3x−4=14 >>>> Given
2. 3x−4+4=14+4 >>>>?
3. Simplifying >>>>?
4. 3x3=183 >>>>?
5. >>>?
A. Simplifying
B. Division property of equality
C. Addition property of equality
D. x=6
E. 3x=18
Final answer:
In this proof, we use the Addition and Simplifying properties of equality to show that if 3x-4 equals 14, then x equals 6.
Explanation:
Given: 3x-4=14
3x-4=14 >> Given
3x-4+4=14+4 >> Addition property of equality
Simplifying >> Simplifying
3x=18 >> x=6
Answer: x=6
According to a survey, 75% of adults in the united states think the u. s. government system is broken. of these 75%, about 7 out of 10 think that the government can be fixed.
a.find the probability that a randomly selected adult thinks the u. s. government system is broken and thinks the government can be fixed.
b.given that a randomly selected adult thinks the u. s. government system is broken, find the probability that he or she thinks the government cannot be fixed.
1. Probability that a randomly selected adult thinks the U.S. government system is broken and can be fixed:
P (A and B) = P (A) * P (B|A) = .75 * .7 = 0.525
2. Probability that given that a randomly selected adult thinks the U.S. government system, he or she thinks the government cannot be fixed.
P (B|A) = (1 – P (B|A) = 3/10 = 0.3
To calculate the probability that an adult thinks the U.S. government is broken and can be fixed, multiply 75% by 70%, resulting in 52.5%. The probability that an adult thinks the government is broken but can't be fixed is found by subtracting 70% from 100%, yielding 30%.
The subject in question pertains to probability and statistics, which involves calculating the likelihood of certain outcomes based on given data and constructing confidence intervals to understand the population parameters.
Part A:
To find the probability that a randomly selected adult thinks the U.S. government system is broken and thinks the government can be fixed, we multiply the two given probabilities: 75% of adults think the system is broken and, of these, 70% think it can be fixed. Therefore:
0.75 (probability of thinking the system is broken) × 0.70 (probability of thinking it can be fixed given the system is broken) = 0.525 or 52.5%.
Part B:
Given that an adult thinks the government system is broken, to find the probability that they think it cannot be fixed, we subtract the probability that they think it can be fixed from 1:
1 - 0.70 = 0.30 or 30%.
50 pts.
Solve this algebraic equation.
-6x + 5 + 12x -6
What is 3x-9-5x=-7 if you solve for x
3x-9-5x = -7
combine like terms -9-2x = -7
add 9 to both sides
-2x = 2
divide both sides by -2
x - 2/-2 = -1
x = -1
Answer+explanation plz and thank you! :) these are quadratic equations.
I need work shown please
Q:
x^2+3x-28
________
x^2-7x+12
A:
x+7
___
x-3
I just need work shown
CAN ANYONE HELP ME WITH THIS QUESTION!!!!!??? The length of a string in yards is a function f(n) of the length n in inches. Write a function rule for this situation.
A. f(n)=36n
B. f(n)=1/36 n
C. f(n)=12n
D. f(n)=n/12
What is the capacity of the cube in liters? Cube with length, width, and height labeled as 9 centimeters. 0.81 L 0.729 L 81 L 729 L
Jim has a membership to a comic book club. He pays $9.00 per month for membership and $2.50 for each comic book he purchases. What are the parameters in this scenario?
A.) The parameters are not defined.
B.) The slope is 9 and the y-intercept is 2.5
C.) The slope is 2.5 and the y-intercept is 9.
D.) x and f(x)
How do you simplify -3.3+5.5
The product of two prime numbers is one less than 12 squared. What are they two prime numbers?
Find the mean of this data: 37, 36, 40, 36, 40, 36, 38. If necessary, round to the nearest tenth.
Please help me thank you!
Two fair dice are rolled. find the probability of a "double" given that the sum is 11.
There are 0 (zero) probability of a "double" given that the sum is 11.
What is mean by Probability?
The term probability refers to the likelihood of an event occurring.
Given that;
Two fair dice are rolled.
And, The probability of a "double" given that the sum is 11.
Now,
Since, The the probability of a "double" means;
''Two fair dice after rolled gives the same numbers.''
Since, The sum of two same number is always gives the even number.
So, We cannot get the sum 11.
Hence, There are 0 (zero) probability of a "double" given that the sum is 11.
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