The given linear equation will have only one possible solution
What is function?A function is a relation between a dependent and independent variable. We can write the examples of functions as -
y = f(x) = ax + b
y = f(x, y, z) = ax + by + cz
Given is to find the total number of solutions for the linear equation -
10(x + 6) 2 - 9 = (15x + 1) 3 - 8
A linear equation is a equation of degree one. The number of solutions of a equation are equal to its degree. So, the given linear equation will have only one solution.
Therefore, the given linear equation will have only one possible solution.
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One positive number exceeds another by 4, and their product is 60. Find the numbers.
Find the value of xx that makes m ∥ n.
1. Solve the system by substitution- 2x+y=-11, 3x-4y=11.
Answers are:
C
B
B
C
A
Thank you so much T-T
which would not be a step in solving 5x + 15 + 2x = 24 + 4x?
A. Isolate the variable.
B. Collect variable terms on one side.
C. Collect like terms.
D. Use the distributive property.
The step that would not be necessary in solving 5x + 15 + 2x = 24 + 4x is D. Use the distributive property.
What is an equation?An equation is a pair of algebraic equations with the equal sign (=) in the middle and the same value.
To solve the equation 5x + 15 + 2x = 24 + 4x, we need to simplify and manipulate the equation to isolate the variable on one side.
First, we can combine like terms:
5x + 2x - 4x = 24 - 15
3x = 9
Then, we can isolate x by dividing both sides by 3:
x = 3
Therefore, the correct steps to solve this equation are:
B. Collect variable terms on one side.
C. Collect like terms.
A. Isolate the variable.
We do not need to use the distributive property in this problem.
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Suppose we build a sequence of numbers using the method of adding the previous two numbers to build the next one. this time, however, suppose our first two numbers are 2 and 1. generate the first 15 terms. this sequence is called the lucas sequence and is written as l1, l2, l3 , …. compute the quotients of consecutive terms of the lucas sequence as we did with the fibonacci numbers. what number do these quotients approach? what role do the initial values play in determining what number the quotients approach? try two other first terms and generate a sequence. what do the quotients approach?
The sequence is given below:
What is sequence?A sequence is an enumerated collection of objects in which repetitions are allowed and order matters.
Given:
The table showing the sequence of the first 15 terms is:
Sequence Term Quotient
1 2 2
2 1 2 (2 / 1)
3 3 (2 + 1) 0.333 (1 / 3)
4 4 (1 + 3) 0.750 (3 / 4)
5 7 (3 + 4) 0.571 (4 / 7)
6 11 (4 + 7) 0.633 (7 / 11)
7 18 (7 + 11) 0.611 (11 / 18)
8 29 (11 + 18) 0.621 (18 / 29)
9 47 (18 + 29) 0.617 (29 / 47)
10 76 (29 + 47) 0.618 (47 / 76)
11 123 (47 + 76) 0.618 (76 / 123)
12 199 (76 + 123) 0.618 (123 / 199)
13 322 (123 + 199) 0.618 (199 / 322)
14 521 (199 + 322) 0.618 (322 / 521)
15 843 (322 + 521) 0.618 (521 / 843)
The quotient converges around the value of 0.618, as shown in the above table.
The preceding sequence is a Lucas adaptation of the so-called Fibonacci sequence, where the initial two numbers serve as seeds and result in the quotient known as the "Golden Ratio," which is created by adding the previous two consecutive terms in each term.
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What is x-intercept of the line with the equation 4×+2y=12?
if the discriminant of an equation is positive, which of the following is true of the equation?
A. it has one complex solution
B. it has two real solutions
C. it has one real solution
D. it has two complex solutions
point P coordinates (-6,6) and P' is it's reflection across the x axis
Each small square on the grid is 1 ft².
Which estimate best describes the area of this figure?
25 ft²
35 ft²
50 ft²
65 ft²
see the attached figure to better understand the problem
we know that
the area of the figure is the area of the square minus the areas marked with x
area of the square is equal to
[tex]A1=8*8=64\ ft^{2}[/tex]
the areas marked with x is equal to
[tex]A2=15\ ft^{2}[/tex]
so
the area of the figure is
[tex]A=A1-A2 \\ A=64-15=49\ ft^{2}[/tex]
therefore
the answer is
[tex]50\ ft^{2}[/tex]
Answer: here is the k12 test answer
Step-by-step explanation:
Roy realized that some other conditions or constraints apply. Write an inequality for each constraint described below.
The sophomore class sold a total of 700 adult and student tickets to the school play. adult tickets sold for $4.50 each, and student tickets cost $2.00 each. if they took in a total of $1,200, which system of equations can be used to find x, the number of student tickets sold, and y, the number of adult tickets sold
Answer:
Step-by-step explanation:
Given that the sophomore class sold a total of 700 adult and student tickets to the school play. adult tickets sold for $4.50 each, and student tickets cost $2.00 each.
Total = 1200
x, the number of student tickets sold, and y, the number of adult tickets sold
Then we have
[tex]x+y =700\\4.5x+2y = 1200[/tex]
These are the system to solve for x
In right triangle ABC, B = 51° and AB = 14.
BC = _____
8.8
10.8
11.3
Given: the triangle is a right triangle, find a.
(The side opposite angle A.)
Answer:
a = 8.8104 ≈ 8.8
Step-by-step explanation:
∠A = ?, ∠B = 51°, ∠C = 90°
∠A = 180° - ( ∠B + ∠C )
∠A = 180° - ( 51° + 90° ) = 180° - 39°
∠A = 39°
[tex]\frac{a}{sin A}=\frac{b}{sin B} =\frac{c}{sin C}\\\\\frac{a}{sin39degrees}=\frac{14}{sin90degrees}\\\\\frac{14}{sin90degrees}*sin39degrees\\\\= 14 * 0.629\\= 8.8104[/tex]
So side a or BC = 8.8
Find the area of the polygon with the given vertices. w(0, 0), x(0, 3), y(−3, 3), z(−3, 0)w(0, 0), x(0, 3), y(−3, 3), z(−3, 0)
Management theories of leadership focus on which of the following?
A. Situations <--- My Answer
B. The leader's style
C. Rewards and punishments
D. Relationships
2. In which conflict style do people often have a firm idea of what they want to see happen and they will fight to make that happen?
A. Collaborative
B. Competitive
C. Compromising
D. Accomodating
3. With a de-emphasizing approach to conflict, the focus is put on which of the following?
A. Areas of agreement
B. Differences in personality
C. Points of contention
D. All of the above
4. Behavioral theories of leadership argue that leaders are born, not made.
True
False
The total area or NC is 53,800 square miles. Land accounts for 48800 square miles. What percent of North Carolina is covered in water?
9.3% of North Carolina is covered in water.
What is Area?The area is the entire amount of space occupied by a flat (2-D) surface or an object's form. On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a form on paper is the area that it occupies.
To find the percent of North Carolina covered in water, we need to subtract the land area from the total area, and then express the result as a percentage.
The water area is:
53,800 - 48,800 = 5,000 square miles
To express this as a percentage, we need to divide the water area by the total area and then multiply by 100:
(5,000 / 53,800) x 100 = 9.3%
Therefore, 9.3% of North Carolina is covered in water.
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How do you find the answer for 7x-(3x+8)
Kyle has 125 marbles. Fifty of these marbles are red and the rest are other colors. What is the ratio of the number of red marbles to the total number of marbles expressed in simplest terms?
Answer:
2/5
Step-by-step explanation:
its asking in "simplest terms" so you would divide the number of marbles Kyle has by the 50 red marbles. 125 divide by 50 is 2.5 which equals to 2/5.
So 2/5 will be your answer. Hope this helps <3
A bus traveled 472 miles at a constant rate in 16 hours. What was the speed of the bus?
miles per hour
Answer:
29.5 miles per hour.
Step-by-step explanation:
We have been given that a bus traveled 472 miles at a constant rate in 16 hours. We are asked to find the speed of the bus.
We will use speed formula to solve our given problem.
[tex]\text{Speed}=\frac{\text{Distance}}{\text{Time}}[/tex]
Upon substituting our given values in above formula, we will get:
[tex]\text{Speed}=\frac{472\text{ Miles}}{16\text{ hours}}[/tex]
[tex]\text{Speed}=\frac{29.5\text{ Miles}}{\text{ hour}}[/tex]
Therefore, the speed of the bus is 29.5 miles per hour.
Which of the following best represents the average speed of a fast runner? (1 point) 10 meters per second 10 miles per minute 10 centimeters per hour 10 kilometers per second
Answer:
10 meters per second
Step-by-step explanation:
Great question, it is always good to ask away and get rid of any doubts that you may be having.
The best representation would be 10 meters per second. Usain Bolt, The fastest person person alive runs at approximately 12.5 meters per second.
10 miles per minute would be insanely fast. That is equivalent to 600 miles per hour, no human can run at that speed. Cars do not even reach that speed. Same goes for 10 kilometers per second.
10 centimeters per hour is incredibly slow. Although 470 times faster than a snail it is incredibly slow for a human.
I hope this answered your question. If you have any more questions feel free to ask away at Brainly.
5. A gym membership costs $30 to join and $12 each month. Write and use an algebraic expression to find the cost of the gym membership for 6 months.
Math problem...
375
x 6
------
The mathematics question asks to multiply the numbers 375 and 6. By following the multiplication process, we find the answer to be 2250, which is a basic arithmetic operation in middle school mathematics.
The student has presented a multiplication problem, which is a basic arithmetic operation in mathematics. The problem can be solved by multiplying the two numbers given, 375 and 6. The calculation goes as follows:
Multiply the digit in the one's place of the bottom number (6) by each digit of the top number (375), starting from the one's place of the top number.
Write down the result of each multiplication and carry over any tens if necessary.
After you complete the multiplication process, add any carried-over numbers to the resultant product.
The completed multiplication should give you the final answer to the problem.
Example Calculation:
375
x 6
------
2250
Here, the answer to the multiplication problem is 2250.
What is the mathematical sentence for 7 is subtracted from a number y. then the result is multiplied by 3. the final answer is less than or equal to 12?
Ken and roberta each sold fifty tickets for the school play. the cost of a student ticket was three fourths the cost of an adult ticket. roberta sold ten more student tickets that adult tickets and collected a total of $212.50.
a. how many tickets did roberta sell?
b. what was the cost of a student ticket?
c. if ken collected $200 in all, how many student tickets did he sell?
Roberta sold 30 tickets in total, with 10 adult tickets and 20 student tickets. The cost of a student ticket was $3. Ken collected $200 in total and sold 20 student tickets.
Explanation:To solve this problem, we can set up two equations based on the given information. Let's use variables to represent the unknown quantities.
Let's say the cost of an adult ticket is A dollars. Then the cost of a student ticket would be 3/4 of A dollars, or (3/4)A dollars.
Based on the information given, we can set up the following equations:
Robera sold 10 more student tickets than adult tickets, so let's say she sold X adult tickets and X + 10 student tickets.
The total collected by Roberta was $212.50, so we have the equation:
(A * X) + ((3/4)A * (X + 10)) = $212.50
Ken sold 50 tickets in total, so he sold 50 - (X + 10) student tickets. The total collected by Ken was $200, so we have the equation:
((3/4)A * (50 - (X + 10))) + (A * X) = $200
Now we can solve these equations to find the values of X and A.
Plugging in A = 4, we get X = 10. Therefore, Roberta sold 10 adult tickets and 20 student tickets. The cost of a student ticket was (3/4) * 4 = $3.
In conclusion, Roberta sold 30 tickets in total, with 10 adult tickets and 20 student tickets. The cost of a student ticket was $3. Ken collected $200 in total and sold 20 student tickets.
Ollie is catering a dinner party for more than 26 guests. Each guest has a choice between a vegetarian dinner or a steak dinner. The vegetarian dinner is $20 per plate and the steak dinner is $30 per plate. Ollie can spend no more than $690 on the entire party. If Ollie wants to purchase the most amount of food and still stay within budget, which combination of vegetarian and steak dinners is optimal?
The earnings of two employees are given below: Employee A: 6% commission on all sales Employee B: 4% commission on the first $80,000 and 8% on anything over $80,000 How much more does a straight commission employee make than the graduated commission employee for sales of $100,000?
Employee A makes $1,200 more than Employee B for sales of $100,000.
The earnings of Employee A are:
= Commission rate x Sales
= 6% x 100,000
= $6,000
The earnings of employee B are:
= Commission on first $80,000 + Commission on anything above $80,000
= (4% x 80,000) + (8% x (100,000 - 80,000)
= 3,200 + (8% x 20,000)
= $4,800
The difference is:
= Employee A commission - Employee B commission
= 6,000 - 4,800
= $1,200
In conclusion, Employee A makes $1,200 more than Employee B for sales of $100,000.
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Which expression is equal to (x+2)(−3x2+3x+1)?
−3x2−3x+2
−3x2+5x+3
−3x3−3x2+7x+2
−3x3+9x2−5x+2
Option C is correct. The required product of the functions is -3x³ - 3x² + 7x + 2
Given the functions (x+2) and (-3x² + 3x + 1)
Taking the product of the functions:
= (x+2)(-3x² + 3x + 1)
Expand the bracket
= x(-3x²) + x(3x) + x(1) + 2(-3x²) + 2(3x) + 2(1)
= -3x³ + 3x² + x - 6x² + 6x + 2
Collect the like terms;
= -3x³ + 3x² - 6x²+ x + 6x + 2
= -3x³ - 3x² + 7x + 2
Hence the required product of the functions is -3x³ - 3x² + 7x + 2
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What is the runner’s average rate of change between the hours: 0.5 and 2? mph 1.5 and 2.5? mph Average Rate of Change
Answer:
4mph
5mph
slower
Step-by-step explanation:
i did it
To calculate the average rate of change, divide the total change in distance by the total change in time. Without the specific distance covered in the given durations, it's impossible to provide absolute answers, but an example calculation has been given using an average speed of 9.5 mph.
Explanation:In your question, the average rate of change refers to the change in distance with respect to time, also known as velocity or speed. Since there are no concrete values mentioned in your question for the distances covered by a runner between time 0.5 and 2 hours, and 1.5 to 2.5 hours, it would be impossible to provide an accurate answer without such data.
However, allow me to explain how you could calculate these values. If you assume that a runner has the marathon runner's average speed of 9.5 miles per hour, then the average rate of change, or average speed, over a certain time period is just the total change in distance divided by the total change in time. For instance, if the runner covered 9.5 miles between 0.5 and 2 hours, then the average rate of change would be 9.5 miles per 1.5 hours, or approximately 6.33 mph. This same method would apply to calculations between 1.5 and 2.5 hours.
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Four consecutive integers that total -86
The longer base of isosceles trapezoid is 12 cm. the side is 5 cm. the acute angle is 37º. find the shorter base.
The shorter base of the isosceles trapezoid is approximately 6 cm.
Explanation:To find the shorter base of the isosceles trapezoid, we need to use the properties of the trapezoid. Firstly, let's draw the isosceles trapezoid and label the given information.
The longer base is 12 cm, the side is 5 cm, and the acute angle is 37º. We can see that the trapezoid has two congruent triangles, and we can find the height of the triangle using trigonometry.
Step 1: Find the height of the triangle using the sine of the acute angle.
sine(37º) = opposite / hypotenuse
sin(37º) = h / 5
h = 5 * sin(37º) ≈ 3 cm
Step 2: Use the height to find the shorter base of the trapezoid.
The shorter base can be found by subtracting twice the height from the longer base.
shorter base = longer base - 2 * height
shorter base = 12 cm - 2 * 3 cm
shorter base = 12 cm - 6 cm
shorter base ≈ 6 cm
Therefore, the shorter base of the isosceles trapezoid is approximately 6 cm.
things you cant assume from a diagram