Final answer:
The equations y = 5x + 9 and y - 5x = 3 have the same slope of 5, indicating that their graphs are parallel lines. The difference lies in their y-intercepts; the first line crosses the y-axis at 9 and the second at 3, meaning they are parallel but at different vertical positions.
Explanation:
To compare and contrast the graphs of y = 5x + 9 and y - 5x = 3, we first need to rewrite the equations in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. The first equation is already in this form, with a slope of 5 and a y-intercept of 9. We can rearrange the second equation by adding 5x to both sides to get y = 5x + 3, which has a slope of 5 and a y-intercept of 3.
Both lines have the same slope of 5, which means they are parallel and will never intersect. The difference between them is their y-intercepts; the first line intersects the y-axis at 9, whereas the second line intersects the y-axis at 3. This difference in y-intercepts means that while they have the same steepness and direction, they are located at different vertical positions on the coordinate plane.
What is the sum of the first five terms of the geometric series 3 − 6 + 12 − . . . ?
Hint: r ≠ 1, where a1 is the first term and r is the common ratio.
Hint: image attached
OPTIONS:
A) S5 = −136
B) S5 = −33
C) S5 = 12
D) S5 = 33
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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Find f(-3) if f(x) = x^2.
-9
-6
6
9
It's not -6!!
Answer:
f(-3) = (-3)²
= -3 * -3
= 9
Step-by-step explanation:
The isotope calcium-41 decays into potassium-41, with a half-life of 1.03 × 10^5 years. There is a sample of calcium-41 containing 5 × 10^9 atoms. How many atoms of calcium-41 and potassium-41 will there be after 4.12 × 10^5 years?
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)
One positive number exceeds another by 4, and their product is 60. Find the numbers.
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
Robert bought his car 4 years ago.
Each year the value of the car has depreciated by 15%.
The car is now $6264
Calculate how much the car was worth when he bought it.
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.
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.
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
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.
How to solve on a road map of pennsylvania, the disatance from philadelphia to washington,
d.c. is 6.8 centimeters. the map scale is 2 cm;40 mi. what is the actual distance between the cities?
Write the word sentence as an equation. Then solve. A number x multiplied by 2/5 is 3/20 .
The given word sentence translates into the algebraic equation 2/5 * x = 3/20. Solving this equation returns x = 3/8 as the solution.
Explanation:The word sentence 'A number x multiplied by 2/5 is 3/20' is translated into an algebraic equation as: 2/5 * x = 3/20. To solve for x, you could do cross multiplication or simply divide both sides of the equation by 2/5, which gives: x = (3/20) / (2/5). Simplifying this equation leads to: x = 3/20 * 5/2 = 15/40 = 3/8. Therefore, the solution to the equation is x = 3/8.
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Find the value of xx that makes m ∥ n.
Which expression is equal to (−12−2i)+(2+2i)?
10−4i
−10−4i
−10
10
Answer:
-10!
Step-by-step explanation:
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.
Roy realized that some other conditions or constraints apply. Write an inequality for each constraint described below.
the pattern below follows the rule "starting with a value of 3, every consecutive row has a value that is 2 less than twice the value of the previous row" what is the fifth value? a. 18 b. 12 c. 34 d. 66
Answer: a. 18
Step-by-step explanation:
Given phrase : "starting with a value of 3, every consecutive row has a value that is 2 less than twice the value of the previous row"
The recursive formula for the given phrase :-
[tex]a_n=2a_{n-1}-2[/tex]
The first term : [tex]a_1=3[/tex]
The second term : [tex]a_2=2(3)-2=4[/tex]
The third term : [tex]a_3=2(4)-2=6[/tex]
The fourth term : [tex]a_4=2(6)-2=10[/tex]
The fifth term : [tex]a_5=2(10)-2=18[/tex]
Hence, the fifth value of the pattern = 18
Answer:18
Step-by-step explanation:
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
Given: Angle 2 and Angle 3 are a linear pair. Angle 3 and Angle 4 are a linear pair. Prove Angle 2 is congruent to Angle 4.
1. Angle 2 and Angle 3 are a linear pair. Angle 3 and Angle 4 are a linear pair. Reason: Given
2. Angle 2 and Angle 3 are supplementary. Angle 3 and Angle 4 are Supplementary.
Reason: ?
3. Angle 2 is congruent to Angle 4.
Reason: ?
Angle 2 and Angle 4 are congruent because they form a linear pair and their sum is 180 degrees.
Explanation:Given that Angle 2 and Angle 3 are a linear pair and Angle 3 and Angle 4 are a linear pair, we can prove that Angle 2 is congruent to Angle 4.
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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.
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
HELP PLEASE!
What is the value of f(−1) when f(x)=2x+2 ?
Enter your answer in the box.
f(−1)= ?
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.
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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point P coordinates (-6,6) and P' is it's reflection across the x axis
Choose the correct slope of the line that passes through the points (−4, 8) and (−3, −6). (1 point)
7
−14
0
14
Answer:
-14
Step-by-step explanation:
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?