x+y=20 3x-3y=30 Which values of x and y satisfy this system of equations?
x +y = 20 ( rewrite as x = 20-y)
3x - 3y =30
3(20-y) - 3y = 30
60-3y - 3y = 30
60-6y = 30
-6y = -30
y = -30 / -6 = 5
x=20-5 = 15
x = 15, y = 5
Consider the equation below. f(x) = 4x3 + 6x2 − 24x + 3 (a) find the intervals on which f is increasing. (enter your answer using interval notation.)
The function f(x) = 4x^3 + 6x^2 - 24x + 3 is increasing on the interval (-2/3, 1.5), where the derivative of the function is positive.
Explanation:To find the intervals on which the function f(x) = 4x^3 + 6x^2 − 24x + 3 is increasing, we first need to calculate its derivative, which will give us the slope of the tangent line to the function at any point x. The function is increasing wherever its derivative is positive.
The derivative of f with respect to x is:
f'(x) = 12x^2 + 12x - 24.
To find where the function is increasing, set the derivative greater than zero:
12x^2 + 12x - 24 > 0
Solve this inequality to find the intervals for x. Factoring the quadratic, we get:
(2x - 3)(6x + 4) > 0
The zeros of this equation are x = 1.5 and x = -2/3. These values divide the real number line into intervals. Test a value from each interval to see where the function is increasing:
If x < -2/3, for example x = -1, the derivative becomes negative, indicating the function is decreasing.If -2/3 < x < 1.5, for example x = 0, the derivative is positive, indicating the function is increasing.If x > 1.5, for example x = 2, the derivative is again negative, indicating the function is decreasing.Thus, the function f(x) is increasing in the interval (-2/3, 1.5).
the steps to solve it
Three friends were born in consecutive years. The some of their birth years is 5982.find the year in which each person was born
Answer:
The birth years of first person is 1993.
The birth years of second person is 1994.
The birth years of third person is 1995.
Step-by-step explanation:
Three friends were born in consecutive years
Let the birth years of first person be x,
Let the birth years of second person be (x+1)
Let the birth years of third person be(x+2)
The sum of their birth years is 5982.
[tex]x+(x+1)=(x+2)=5982[/tex]
Solving the given equation for x:
[tex]3x+3=5982[/tex]
[tex]x=\frac{5982-3}{3}=1993[/tex]
The birth years of first person = x = 1993
The birth years of second person = (x+1) = 1993+ 1 = 1994
The birth years of third person = (x+2) = 1993+2 = 1995
Farmer Tom raises ducks and horses on his farm. All of his horses need new horseshoes. He calls the farrier (a person who puts shoes on horses) but has a difficult time remembering how many of each animal he owns. He knows that there are a total of 24 animals. The animals have a total of 62 legs (all animals have either two or four legs). How many horses does Tom own?
h+d=24
h = 24-d
4h +2d = 62
4(24-d) +2d = 62
96 -4d +2d =62
96-2d =62
-2d =-34
d =-34/ -2 = 17
17 ducks
24-17 = 7 horses
IS Δ ABC WITH VERTICES A(-2, -5), B(-3, 2) AND C(1, -2) A RIGHT TRIANGLE?
A.) Δ ABC IS NOT A RIGHT TRIANGLE.
B.) Δ ABC IS A RIGHT TRIANGLE BECAUSE AB ⊥ AC
C.) Δ ABC IS A RIGHT TRIANGLE BECAUSE BC ⊥ AC
D.) Δ ABC IS A RIGHT TRIANGLE BECAUSE AB ⊥ BC
Answer:20
Step-by-step explanation:
Haven't seen this question before
Select the type of equations
A.) Consistent
B.) Equivalent
C.) Inconsistent
Answer:
A). Consistent.
Step-by-step explanation:
We have been given a graph of a system of equations. We are asked to determine the type of the given system.
Upon looking at our given graph, we can see that both lines intersect exactly at one place, so it will have exactly one solution.
We know that a system of equations exactly with one solution is known as consistent system.
Therefore, option A is the correct choice.
To buy a truck you can pay $14,000 cash or put down $5000 and make 24 monthly payments of $551.09. how much would you save by paying cash (to the nearest hundredth)?
Final answer:
By paying $14,000 in cash for the truck instead of making a $5,000 down payment and 24 monthly payments of $551.09, you would save $4,226.16.
Explanation:
To determine how much you would save by paying cash for the truck versus making a down payment and monthly payments, we need to calculate the total cost for each option.
Down payment: $5,000
Monthly payments: 24 payments of $551.09 each
The total cost when financing the truck would be:
$$5,000 + (24 × $551.09) = $5,000 + $13,226.16 = $18,226.16$
The cash payment option is $14,000. Therefore, the savings when paying cash would be:
$$18,226.16 - $14,000 = $4,226.16$
By paying cash, you would save $4,226.16, to the nearest hundredth.
Name a pair of adjacent complementary angles
In geometry, complementary angles are two angles whose measures add up to 90 degrees. A pair of adjacent complementary angles could be 30 degrees and 60 degrees.
Explanation:In geometry, complementary angles are two angles whose measures add up to 90 degrees. For example, if one angle measures 30 degrees, the other angle measures 60 degrees because 30 + 60 = 90. So, a pair of adjacent complementary angles could be 30 degrees and 60 degrees.
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What is the area of a rectangle with vertices at (−3, −1) , (1, 3) , (3, 1) , and (−1, −3) ? Enter your answer in the box. Do not round any side lengths. ___units²
The area of the rectangle is 8 units².
Explanation:To find the area of a rectangle, we can use the formula A = length * width. In this case, we can use the coordinates of the vertices to determine the length and width of the rectangle.
Using the distance formula, we can find the length between the points (-3, -1) and (1, 3) to be 4 units, and the width between the points (1, 3) and (3, 1) to be 2 units.
Therefore, the area of the rectangle is 4 * 2 = 8 units².
A car travels 416 miles in 8 hours and at this rate how many miles will the car travel in 22 hours
To find out how many miles the car will travel in 22 hours, we calculate the unit rate by dividing 416 miles by 8 hours to get 52 miles per hour and then multiply this unit rate by 22 hours to get 1144 miles
The question involves calculating the distance a car will travel at a given rate over a different period of time. This is a basic rate problem in math, often approached by finding the unit rate and then scaling it to the desired time.
Step 1: Identify the rate of travel. The car travels 416 miles in 8 hours.
Step 2: Find the unit rate by dividing the distance by the time. Unit rate = 416 miles / 8 hours = 52 miles per hour.
Step 3: Calculate the distance the car will travel in 22 hours using the unit rate. Distance = 52 miles/hour * 22 hours = 1144 miles.
So, at this rate, the car will travel 1144 miles in 22 hours
The pitch of the roof is the number of feet the roof rises for each 12 feet horizontally. If a roof has a pitch of 8. What is its slope expressed as a positive number? What does the slope mean in this story?
The slope of the roof, expressed as a positive number, is 0.67. This represents the steepness of a roof, with a higher number indicating a steeper roof. The figure is calculated using the rise over run ratio.
Explanation:The pitch of a roof is a number that expresses how much the roof's height changes for every 12 feet you move along horizontally. If a roof has a pitch of 8, it means that for every 12 feet you move horizontally, the height of the roof increases by 8 feet. This gives us a rise/run ratio, which is how slope is defined in mathematical terms.
In this case, the rise is 8 feet, and the run is 12 feet. So, the slope would be 8/12, or 0.67 when expressed as a positive decimal number.
The slope here represents the steepness of the roof. A higher slope means a steeper roof and vice versa. By expressing the slope as a number, we can get an idea of how steep the roof is without having to see it in person.
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Write the ratio as a fraction in simplest form a/b. What is the ratio of baseballs to basketballs?
Answer: 5/8 im pretty sure i hope it helps :) i took it on freckle so i know but i think this is right
You are the human resources manager for a new local bank. Create a customer service code of behavior for the bank’s employees. In the code, identify the top five areas that bank employees should focus on to meet the needs of their customers. For each area, list three behaviors or practices employees should demonstrate to keep the bank’s customers satisfied.
The top five areas that bank employees should focus on for customer satisfaction include professionalism, focus and productivity, commitment to service, respect for authority, and continuous learning and improvement. For each area, employees are expected to adhere to specific behaviors and practices.
Explanation:As a human resources manager for a banking institution, creating a customer service code of behavior is an essential task. Notably, there are five areas employees should focus on to meet their customers' needs. They include:
Professionalism: Employees should demonstrate punctuality, maintain a professional appearance, and treat everyone with respect. Focus and Productivity: Avoid personal distractions, complete tasks on time, and demonstrate support for the company's goals. Commitment to Service: Display a positive attitude, express enthusiasm, and be committed to providing excellent customer service. Respect for Authority: Employees should respect from their supervisors and managers. Continuous Learning and Improvement: Employees should actively seek to understand their roles and their manager's expectations, adopt effective time management and conflict resolution strategies, identify and respect their rights and responsibilities, and continuously strive for growth and improvement.
These practices and behaviors are expected to provide satisfactory services to the bank's customers and help maintain a productive work environment.
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Can someone give me the steps to solving this equation? 3^x = 81
Which pairs of quadrilaterals can be shown to be congruent using rigid motions?
Select Congruent or Not Congruent for each pair of quadrilaterals.
Congruent Not Congruent
quadrilateral 1 and quadrilateral 2
quadrilateral 1 and quadrilateral 3
quadrilateral 1 and quadrilateral 4
quadrilateral 2 and quadrilateral 3
quadrilateral 2 and quadrilateral 4
quadrilateral 3 and quadrilateral 4
Answer:
quadrilateral 1 and quadrilateral 2 NOT CONGRUENT
quadrilateral 1 and quadrilateral 3 CONGRUENT
quadrilateral 1 and quadrilateral 4 CONGRUENT
quadrilateral 2 and quadrilateral 3 NOT CONGRUENT
quadrilateral 2 and quadrilateral 4 NOT CONGRUENT
quadrilateral 3 and quadrilateral 4 CONGRUENT
Step-by-step explanation:
quadrilateral 1 and quadrilateral 2 NOT CONGRUENT
quadrilateral 1 and quadrilateral 3 CONGRUENT:
rigid motion: reflection
axis of reflection: y=x
quadrilateral 1 and quadrilateral 4 CONGRUENT:
rigid motions: translation and reflection
axis of reflection y=0
quadrilateral 2 and quadrilateral 3 NOT CONGRUENT
quadrilateral 2 and quadrilateral 4 NOT CONGRUENT
quadrilateral 3 and quadrilateral 4 CONGRUENT:
rigid motions: translation and reflection
axis of reflection: x=0
The corresponding parts of congruent quadrilateral are congruent.
The true statements are:
Quadrilateral 1 and quadrilateral 2 Not Congruent Quadrilateral 1 and quadrilateral 3 Congruent Quadrilateral 1 and quadrilateral 4 Congruent Quadrilateral 2 and quadrilateral 3 Not Congruent Quadrilateral 2 and quadrilateral 4 Not Congruent Quadrilateral 3 and quadrilateral 4 Congruent
From the attached figure:
Quadrilaterals 1, 3 and 4 are congruentQuadrilateral 2 is not congruent to any of the other quadrilaterals.The above highlights mean that:
Statements 1, 4 and 5 are Not CongruentStatements 2, 3 and 6 are CongruentRead more about congruent quadrilaterals at:
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There is a sales tax of $6 on an item that costs $93 before tax. A second item costs $294.50 before tax. What is the sales tax on the second item?
Answer:
its 19
Step-by-step explanation:
If a second item costs $294.50 before tax. The sales tax on the second item will be $19.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.
It is given that, there is a sales tax of $6 on an item that costs $93 before tax. A second item costs $294.50 before tax.
We have to apply the ratio as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.
$6/$93 = t/$294.5
t = 6 × 294.5 / 93
t = $ 19
Thus, if a second item costs $294.50 before tax. The sales tax on the second item will be $19.
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Express 3/4th in seconds.
30"
45"
50"
Answer:
45''
Step-by-step explanation:
Consider the function represented by the graph. What is the domain of this function
Answer: The answer is [tex]\{x:x\geq 0\}.[/tex]
Step-by-step explanation: We are given a graph that represents a function. We are to find the domain of the graphed function.
Domain and Range: If y=f(x) is a function, then the domain is the set of all first elements of ordered pairs (x-coordinates) and the range is the set of all second elements of ordered pairs (y-coordinates).
In the given graph, 'x' takes the values from 0 to infinity and 'y' takes the values from negative infinity to 9.
Therefore, domain of the function is [0, ∞) and the range is (-∞, 9).
Thus, the domain is given by the set [tex]\{x:x\geq 0\}.[/tex]
BRAINLIESTTTT , FIVE STAR RATING, AND THANKS ASAPPP
the class median is lower than the exam median ( the dark blue lines in the middle of the rectangles)
m + 2m - 6 = -12 + 2m
solve for m
The solution of m is -6 for the equation m + 2m - 6 = -12 + 2m
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The given equation is m + 2m - 6 = -12 + 2m
m plus two times of m minus six equal to minus twelve plus two mines of m.
Plus and minus are the operators of the equation.
Take all the variables on one side and constants on other side.
3m-2m=-12+6
Add the like terms
m=-6
Hence, the solution of m is -6 for the equation m + 2m - 6 = -12 + 2m
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y is 5 less than the product of 4 and x
Answer: heres all the answers for the practice
1.A c=8+n/2
2.C y=4x-5
3.D 3/5 b-7=a
4.C w=2.5 + h/3
5.B e=8.7n
6.B a=8- 1/6 b
7.C h=40+21t
8.D 99 square cm
9.A 8 square ft
10.A -435.5m
hope i helped
Step-by-step explanation:
if three times x is equal to x decreased by 2, then x is
If a polygon POLYG is oriented clockwise, what is the orientation of a reflection image P’O’L’Y’G’?
How would I solve -5 over -6 divided by -2 over 4
Describe which of the two points lies on the graph of the line
X-y=2
A. 6,4
B, 5,7
Ten seconds after a plane in an air-show dives, it is 200 feet from where it began. After 30 seconds, it is 600 feet from where it began. At what rate is the plane diving?
I NEED HELPPPPPP WILL GIVE A BRAINLIEST TO BEST ANSWER THAT INCLUDES ALL WORK SHOWN, CORRECT ANSWER, AND EVERYTHING MAKES SENSE.
(Variables on both sides of an equation)
Solve: 18x-5=3(6x-2)
If an exterior angle of a regular polygon is 21.2° how many sides does the polygon have?
LINEAR INEQUALITIES ! Jason needs to rent a hall to host a party. A particular rental hall charges a flat fee, with an additional charge per person, excluding the host. The cost per person to rent the hall is listed in the table below.
Number of People Total Cost
(in $)
( 1 50)
(2 55)
(3 60)
(4 65)
Which of the following inequalities can be used to determine how many friends Jason can invite to the party if he wants to spend less than $100?
The correct answer is shown below