One example of a graph that satisfies these properties is a cubic polynomial with the equation y=ax³+bx²+cx+d.
What is cubic polynomial?A cubic polynomial is a mathematical expression composed of terms that are raised to the third power. It is written as ax³ + bx² + cx + d, where a, b, c and d are constants and x is a variable. Cubic polynomials are used in many applications, such as approximating functions, solving equations, and finding the roots of polynomials. They can also be used to model physical phenomena, such as the motion of objects.
This graph will have a positive second derivative on the intervals (-infinity, -2) and (4, infinity). At the points -2, -1, 1, 2, and 3, the second derivative will be zero, the first derivative will be zero at -1, 1, and 3, and the function will be zero at 1.
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If 0 equal( Picture)
Answer:
[tex]\sin(\theta) = -\dfrac{\sqrt2}{2}[/tex]
[tex]\cos(\theta) = -\dfrac{\sqrt2}{2}[/tex]
Step-by-step explanation:
The sine of any given angle on the unit circle is the y-coordinate of the point on the circle at the given angle.
The cosine of any given angle on the unit circle is the x-coordinate of the point on the circle at the given angle.
See the attached image for a labeled unit circle.
The point on the unit circle that is at angle 5π/4 is:
[tex]\left(-\dfrac{\sqrt2}{2},-\dfrac{\sqrt2}{2}\right)[/tex]
This means that:
[tex]\sin\left(\dfrac{5\pi}{4}\right) = \cos\left(\dfrac{5\pi}{4}\right) = \boxed{-\dfrac{\sqrt2}{2}}[/tex]
PLEASE HELP QUICK 30 POINTS
What is the relationship between the radian measure of an angle and the length of the arc intercepted by that angle on the unit circle?
The radian measure of an angle is directly proportional to the length of the arc intercepted by that angle on the unit circle.
What is proportional?Proportional is a mathematical concept that describes the relationship between two or more values that have a constant ratio. It is commonly used to describe the relationship between two or more variables, such as the size of an object in relation to another or the amount of a certain item in relation to the total amount. In proportionality, the ratio of the amounts remains consistent, no matter what the size of the values.
This means that as the angle increases, so does the length of the arc. This is because the length of an arc is determined by the angle measure of the central angle created by the arc, and the radian measure of an angle is the ratio of the arc length to the radius of the circle. Therefore, if the angle measure increases, so does the arc length.
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For what values of c does the quadratic equation x^2-2x+c=0 have
1)no real roots
2)two roots of same sign
3)one root equal to zero and one neg root
4)two roots of opposite sign
The quadratic equation has no real roots for c > 1, two roots of the same sign for c ≥ 1, one root equal to zero & one negative root for 0 < c < 1, and two roots of opposite signs, c < 1.
What is a quadratic equation?
A quadratic equation is a polynomial equation of degree 2, which means that the highest exponent of the variable in the equation is 2. It has the general form:
[tex]ax^2 + bx + c = 0[/tex]
The quadratic equation [tex]x^2 - 2x + c = 0[/tex] has roots given by the quadratic formula:
x = (-b ±[tex]\sqrt{b^2 - 4ac}[/tex]) / (2a)
where a = 1, b = -2, and c is the unknown constant.
1) To have no real roots, the discriminant [tex]b^2 - 4ac[/tex] must be negative. So, we need:
[tex]b^2 - 4ac[/tex] < 0
[tex](-2)^2 - 4(1)(c)[/tex] < 0
4 - 4c < 0
4 < 4c
1 < c
Therefore, the quadratic equation has no real roots for c > 1.
2) To have two roots of the same sign, the discriminant [tex]b^2 - 4ac[/tex] must be negative or zero.
[tex]b^2 - 4ac[/tex] = [tex](-2)^2 - 4(1)(c)[/tex] = 4 - 4c
For two roots of the same sign, the discriminant must be negative or zero, so
4 - 4c ≤ 0
Simplifying the inequality, we get:
c ≥ 1
Therefore, for the quadratic equation, [tex]x^2 - 2x + c = 0[/tex] to have two roots of the same sign, c must be greater than or equal to 1.
3) To have one root equal to zero and one negative root, one of the roots must be zero, so we need:
x = 0 or x < 0
Setting x = 0 in the quadratic equation, we get:
c = 0
So, if c = 0, then x = 0 is the root of the quadratic equation. To find the negative root, we need:
[tex](-2)^2 - 4(1)(c)[/tex] > 0
4 - 4c > 0
1 > c
Therefore, the quadratic equation has one root equal to zero and one negative root for 0 < c < 1.
4) To have two roots of opposite signs, the discriminant [tex]b^2 - 4ac[/tex] must be positive.
So we need:
[tex]b^2 - 4ac[/tex] > 0
[tex](-2)^2 - 4(1)(c)[/tex] > 0
4 - 4c > 0
Simplifying the inequality, we get:
c < 1
Therefore, for the quadratic equation to have two roots of opposite signs, c must be less than 1.
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For c > 1, the quadratic equation has no real roots; for c ≥1, it has two roots of the same sign; for c<1, it has one root that is equal to zero and one root that is negative; and for 0 <c <1, it has two roots of the opposite signs.
Describe the quadratic equation?The largest exponent of the variable in a quadratic equation, which is a polynomial equation of degree 2, is 2. The formula is: ax² + bx + c.
The quadratic equation x² - 2x + c has roots given by the quadratic formula:
x = (-b ±√[b²-4ac]) / (2a)
where a = 1, b = -2, and c is the unknown constant.
1) To have no real roots, the discriminant b² - 4ac must be negative.
So, we need:
b² - 4ac < 0
(-2) ² - 4(1) < 0
4- 4c < 0
1 < c
Therefore, the quadratic equation has no real roots for c > 1.
2) To have two roots of the same sign, the discriminant b² - 4ac must be negative or zero.
b² - 4ac = (-2) ² - 4(1)c = 4 - 4c
For two roots of the same sign, the discriminant must be negative or zero, so
4 - 4c ≤ 0
Simplifying the inequality, we get:
c ≥ 1
Therefore, for the quadratic equation, x² - 2x + c to have two roots of the same sign, c must be greater than or equal to 1.
3) To have one root equal to zero and one negative root, one of the roots must be zero, so we need:
x = 0 or x < 0
Setting x = 0 in the quadratic equation, we get:
c = 0
So, if c = 0, then x = 0 is the root of the quadratic equation. To find the negative root, we need:
(-2) ² - 4(1)c > 0
4 - 4c > 0
1 > c
Therefore, the quadratic equation has one root equal to zero and one negative root for 0 < c < 1.
4) To have two roots of opposite signs, the discriminant b² - 4ac must be positive.
So, we need:
b² - 4ac > 0
(-2) ² - 4(1)c > 0
4 - 4c > 0
Simplifying the inequality, we get:
c < 1
Hence, c must be lower than 1 in order for the quadratic equation to have two roots with opposing signs.
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please help me i really need help
Answer:
B. (-3, 4)
Step-by-step explanation:
x=0-3=-3
y=0+4=4
(-3, 4)
Answer:
(-3, 4)
Second answer choice
Step-by-step explanation:
The coordinates of A(0, 0) are shifted to the left by 3 units. A shift to the left means the new x- coordinate = old x-coordinate -3 = 0 -3
A shift up means the new y-coordinate = old y-coordinate + 4 + 0 + 4 = 4
Therefore the new coordinates of A are (-3, 4)
Carter is a salesperson who sells computers at an electronics store. He makes a base pay amount each day and then is paid a commission for every computer sale he makes. Let P represent Carter's total pay on a day on which he sells x computers. The table below has select values showing the linear relationship between x and P. Determine the base pay Carter makes regardless of computer sales.
Carter is a salesperson who sells computers at an electronics store.
He gets paid a base pay amount each day and a commission for every computer sale he makes.
Carter's total pay on a day depends on the number of computers he sells, represented by x.
The relationship between x and Carter's total pay, represented by P, is linear.
linear means the graph is a straight line, not a curve
A table with select values of x and P is given.
The task is to determine Carter's base pay regardless of computer sales.
Table of select values of x and P:
x P
0 30
1 40
2 50
3 60
4 70
5 80
To determine Carter's base pay, we need to identify the amount he earns when he doesn't sell any computers, represented by x = 0. Looking at the table, we see that when x = 0, Carter's total pay is $30. Therefore, his base pay is $30.
ChatGPT
Sanjay attempts a 49-yard field goal in a football game. For his attempt to be a success, the football needs to pass through the uprights and over the crossbar that is 10 feet above the ground.
Sanjay kicks the ball from the ground with an initial velocity of 73 feet per second, at an angle of 34° with the horizontal.
What is true of Sanjay's attempt?
Responses
The kick is not successful. The ball is approximately 5 feet too low.
The kick is not successful. The ball is approximately 8 feet too low.
The kick is not successful. The ball is approximately 2 feet too low
The kick is good! The football clears the crossbar by approximately 5 feet.
In the above prompt involving a trajectory calculation, the correct option is: "The kick is not successful. The ball is approximately 5 feet too low." (Option A)
What is the rationale for the above response?x component of trajectory = 73 cos 34 f/s
Now how long will it take to travel 49 yards (= 147 feet) ?
147 / (73 cos 34) = 2.43 seconds
Initial y component of trajectory = 73 sin 34 f/s = 40.82 f/s
but this velocity is acted upon by gravity
y = y0 + vot - 1/2 a t^2
y0 = 0
Now we need to know the y value at 2.43 seconds to see if it will clear the uprights.
y = 40.82 (2.43) - 1/2 (32.174)(2.43)2
= 4.2 Feet
Thus, it is correct to state that the "The kick is not successful. The ball is approximately 5 feet too low."
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Use what you learned from analyzing the electricity bill to answer this question.
11. Using information from the electricity bill, explain the importance of budgeting electricity
into monthly finances. How would you create a plan to adjust your monthly budget as bills
fluctuate month by month?
Answer: Budgeting for electricity is important because it allows you to plan and allocate your financial resources in a way that ensures that you can pay your electricity bills on time and avoid late payment fees, disconnection, or debt accumulation. Electricity bills can fluctuate significantly from month to month, depending on factors such as the weather, the number of people living in your home, your electricity usage patterns, and changes in electricity rates.
To create a plan to adjust your monthly budget as bills fluctuate month by month, you can take the following steps:
- Review your past electricity bills to identify patterns and trends in your usage and costs. Look for any changes that may have occurred, such as the addition of new appliances, a change in occupancy, or a change in electricity rates.
- Use this information to estimate your average monthly electricity costs. This will be your baseline budget.
- Consider setting aside a buffer amount, such as 10-15%, to account for unexpected changes or fluctuations in your electricity bills.
- Monitor your electricity bills closely each month to compare your actual costs with your budgeted amount. If your bills are consistently higher or lower than your budgeted amount, adjust your budget accordingly for the following month.
- Look for ways to reduce your electricity usage and costs, such as turning off lights and appliances when not in use, using energy-efficient light bulbs and appliances, and adjusting your thermostat settings.
- Consider enrolling in a budget billing or level payment plan offered by your electricity provider, which allows you to pay the same amount each month based on your estimated annual usage.
By budgeting for electricity and adjusting your budget as bills fluctuate month by month, you can better manage your finances, avoid surprises, and ensure that you can pay your bills on time.
Step-by-step explanation:
-5/8 - -4/3 in simplest form
Answer:
To subtract two fractions, you need to have a common denominator. The common denominator for 8 and 3 is 24.
-5/8 = -15/24 (multiply both the numerator and denominator by 3)
-4/3 = -32/24 (multiply both the numerator and denominator by 8)
Now, we can subtract the two fractions by subtracting their numerators while keeping the common denominator.
-15/24 - (-32/24) = -15/24 + 32/24 = 17/24
Therefore, -5/8 - -4/3 = 17/24 in its simplest form.
solve the system of equations graphed on the coordinate axes below
The solution to the system of equations on the graph is (0, 0)
How to determine the solution to the systemFrom the question, we have the following parameters that can be used in our computation:
y = -2x and y = 4/3x represented on a graph
On the graph, we have two lines that intersect at a point
Using the above as a guide, we have the following:
The point of intersection of lines in a graph is the solution to the graph
In this case, they intersect at (0, 0)
So, the solution is (0. 0)
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Ron has an average of 83.5 on the first four mathematics tests this marking period. He needs an average of 85 to make the honor roll. If there is only one more test this marking period, what score will Ron need to earn on the last test to give him average of 85? Show your work and explain how you arrived at your answer.
Answer: 86.5
Step-by-step explanation:
(83.5 + x )/2= 85
2(85)= 83.5 + x
170-83.5 =x
x= 86.5
Solve the Following Inequality PLEASE
what is the largest possible median for the five number set (x,2x,3,2,5) if x can be any integer
The largest pοssible median fοr the five-number set (x, 2x, 3, 2, 5) is 8.5 (if x is οdd) οr 5.5 (if x is even)
What is Median?The median is the middle value in a set οf numbers arranged in οrder. It is the value that separates the higher half frοm the lοwer half.
Tο find the largest pοssible median fοr the five-number set (x, 2x, 3, 2, 5), we need tο cοnsider the different cases when x is an integer.
First, let's arrange the numbers in οrder:
{2, 3, 2x, 5, x}
Tο find the median, we need tο determine the middle number in the set. If the set has an οdd number οf elements, the median is the middle number. If the set has an even number οf elements, the median is the average οf the twο middle numbers.
Case 1: x is even
If x is even, then 2x is even and x < 2x. Therefοre, the middle numbers are 2x and 3, and the median is (2x + 3) / 2.
Case 2: x is οdd
If x is οdd, then 2x is even and 2 < 2x. Therefοre, the middle numbers are 2 and 2x, and the median is (2 + 2x) / 2.
Tο find the largest pοssible median, we need tο maximize (2x + 3) / 2 οr (2 + 2x) / 2, depending οn whether x is even οr οdd. This οccurs when x is the largest pοssible integer, which is:
x = 4 (if x is even)
x = 7 (if x is οdd)
Therefοre, the largest pοssible median fοr the five-number set (x, 2x, 3, 2, 5) is:
(2x + 3) / 2 = (2(7) + 3) / 2 = 8.5 (if x is οdd)
οr
(2x + 3) / 2 = (2(4) + 3) / 2 = 5.5 (if x is even)
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Which of the following products is most likely to be marketed using an undifferentiated approach?
O a. Seasoning salt
O b. Bicycle
O c. Oscillating fan
O d. Computer
Oe. Notebook
Please help me find the answer to this question pleaseeee
Help!!
A hiker is climbing a local peak. After 1.5 hours of hiking, he is at an altitude of 220 feet. After 4 hours, he is at an altitude of 410 feet.
What is the hiker's altitude after 4.5
hours?
The hiker's altitude after 4.5 hours is 448 feet.
What is arithmetic?
Arithmetic is an elementary part of mathematics that consists of the study of the properties of the traditional operations on numbers—addition, subtraction, multiplication, division, exponentiation, and extraction of roots.
Here, we have
Given: A hiker is climbing a local peak. After 1.5 hours of hiking, he is at an altitude of 220 feet. After 4 hours, he is at an altitude of 410 feet.
We have to find the hiker's altitude after 4.5 hours.
We have height as a function of time:
x = time, y = height
Our two points are (1.5, 220), (4, 410), and (4.5,x)
(4-1.5) = (410-220)
2.5 = 190
1 = 190/2.5
1 hours = 76 feet
0.5 hours = 38 feet
4.5 hours = 410 + 38 feet = 448 feet
Hence, the hiker's altitude after 4.5 hours is 448 feet.
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19. What is the total amount to be repaid on a 1-year term
loan of $800 with an interest rate of 14%?
A. $892
B. $902
C. $912
D. $922
Answer: the answer is C $912.
Step-by-step explanation: The interest on the loan is calculated as follows:
Interest = Principal x Rate x Time
where Principal is the amount borrowed, Rate is the interest rate as a decimal, and Time is the length of the loan in years. Substituting the given values, we get:
Interest = $800 x 0.14 x 1
Interest = $112
Therefore, the total amount to be repaid is the sum of the principal and the interest, which is:
Total amount = Principal + Interest
Total amount = $800 + $112
Total amount = $912
i don’t know how to do it
The total resistance of three resistors in parallel s 2 Ohms. Option A
What is resistance?Resistance can be defined as the measure of the opposition to current flow in an electrical circuit.
Resistance is measured in Ohms, using the Greek symbol for omega (Ω).
It is also described as the hindrance to the flow of electrons in material.
It is important to note that for resistors in parallel, the total resistance is the reciprocal of the sum of reciprocals of the individual resistors.
This is represented as;
1/Rt = 1/R₁ + 1/R₂ + 1/R₃ ...
Where the variables , 'R' represented the resistors
Now, substitute the values, we have;
1/Rt = 1/4 + 1/8 + 1/8
Find the lowest common multiple
1/Rt = 2 + 1 + 1/8
1/Rt = 4/8
Take the reciprocal of the values
Rt = 8/4 = 2 Ohms
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algebra 2 probability problem please help
The probabilities are given as follows:
a) All 10: 0.0163 = 1.63%.
b) Exactly eight: 0.3483 = 34.83%.
c) At least nine: 0.1518 = 15.18%.
What is the hypergeometric distribution formula?The mass probability formula, giving the probability of x successes, is presented as follows:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are listed as follows:
N is the size of the population from which the sample is taken.n is the size of the sample.k is the total number of desired outcomes in the population.The parameter values for this problem are given as follows:
N = 20, k = 15, n = 10.
Hence the probability of answering all 10 is given as follows:
[tex]P(X = 10) = h(10,20,10,15) = \frac{C_{15,10}C_{5,0}}{C_{20,10}} = 0.0163[/tex]
The probability of exactly 8 is given as follows:
[tex]P(X = 8) = h(8,20,10,15) = \frac{C_{15,8}C_{5,2}}{C_{20,10}} = 0.3483[/tex]
The probability of nine successes is of:
[tex]P(X = 9) = h(9,20,10,15) = \frac{C_{15,9}C_{5,1}}{C_{20,10}} = 0.1355[/tex]
Hence the probability of at least nine successes is of:
P(X >= 9) = P(X = 9) + P(X = 10) = 0.1355 + 0.0163 = 0.1518 = 15.18%.
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Nate made 8 loaves of bread on Monday and 10 more on Tuesday. He gave an equal number to each of his 9 neighbors. How many loaves of bread did each neighbor receive?
Enter your answer in the box.
Nate made 18 loaves of bread and gave an equal number to each of his 9 neighbors, resulting in each neighbor receiving 2 loaves of bread.
The problem provides us with some information about Nate's bread-making and bread-giving activities. We know that he made 8 loaves of bread on Monday and 10 more on Tuesday, for a total of 18 loaves. We also know that he gave an equal number of loaves to each of his 9 neighbors.
To find out how many loaves each neighbor received, we need to divide the total number of loaves (18) by the number of neighbors (9). This gives us:
18 loaves / 9 neighbors = 2 loaves per neighbor.
This means that each neighbor received 2 loaves of bread from Nate. We can check this by multiplying 2 (the number of loaves per neighbor) by 9 (the number of neighbors):
2 loaves/neighbor x 9 neighbors = 18 loaves
So, we can see that the math checks out and each neighbor received 2 loaves of bread from Nate.
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The annual rainfall in a certain region is approximately normally distributed with mean 40.9 inches
and standard deviation 5.3 inches. Round answers to the nearest tenth of a percent.
a) What percentage of years will have an annual rainfall of less than 44 inches?
%
%
b) What percentage of years will have an annual rainfall of more than 38 inches?
c) What percentage of years will have an annual rainfall of between 37 inches and 43 inches?
%
Answer:
a) To find the percentage of years with an annual rainfall of less than 44 inches, we need to find the area under the normal curve to the left of 44. Using a standard normal distribution table or a calculator, we find the z-score corresponding to 44 inches:
z = (44 - 40.9) / 5.3 = 0.585
The area to the left of z = 0.585 is approximately 0.7202. Therefore, about 72.0% of years will have an annual rainfall of less than 44 inches.
b) To find the percentage of years with an annual rainfall of more than 38 inches, we need to find the area under the normal curve to the right of 38. Using a standard normal distribution table or a calculator, we find the z-score corresponding to 38 inches:
z = (38 - 40.9) / 5.3 = -0.717
The area to the right of z = -0.717 is approximately 0.4713. Therefore, about 47.1% of years will have an annual rainfall of more than 38 inches.
c) To find the percentage of years with an annual rainfall between 37 inches and 43 inches, we need to find the area under the normal curve between the corresponding z-scores:
z1 = (37 - 40.9) / 5.3 = -0.736
z2 = (43 - 40.9) / 5.3 = 0.396
Using a standard normal distribution table or a calculator, we find the area between z = -0.736 and z = 0.396 is approximately 0.6181. Therefore, about 61.8% of years will have an annual rainfall between 37 inches and 43 inches.
Step-by-step explanation:
Step-by-step explanation:
a) To find the percentage of years with an annual rainfall of less than 44 inches, we need to find the area under the normal distribution curve to the left of 44 inches.
Using a standard normal distribution table or calculator, we can find the z-score:
z = (44 - 40.9) / 5.3 = 0.585
The area to the left of this z-score is approximately 0.72, or 72%.
Therefore, approximately 72% of years will have an annual rainfall of less than 44 inches.
b) To find the percentage of years with an annual rainfall of more than 38 inches, we need to find the area under the normal distribution curve to the right of 38 inches.
Using a standard normal distribution table or calculator, we can find the z-score:
z = (38 - 40.9) / 5.3 = -0.736
The area to the right of this z-score is approximately 0.77, or 77%.
Therefore, approximately 77% of years will have an annual rainfall of more than 38 inches.
c) To find the percentage of years with an annual rainfall between 37 inches and 43 inches, we need to find the area under the normal distribution curve between the z-scores for 37 inches and 43 inches.
Using a standard normal distribution table or calculator, we can find the z-scores:
z1 = (37 - 40.9) / 5.3 = -0.736
z2 = (43 - 40.9) / 5.3 = 0.394
The area between these z-scores is approximately 0.53, or 53%.
Therefore, approximately 53% of years will have an annual rainfall between 37 inches and 43 inches.
Write and solve an equation to answer the question.
What number a is 24% of 25?
Answer:6
Step-by-step explanation:
24------100%
x--------25%
100x=25*24
x=25*24/100=24/4=6
If A= B and AB= 3x-5 BC= 5x-6 and AC = 2x-9 find the value of X
Therefore, the value of x is -4 if A= B and AB= 3x-5 BC= 5x-6 and AC = 2x-9.
What is equation?An equation is a mathematical statement that shows the equality of two expressions. It is composed of two sides, separated by an equals sign (=), indicating that the two sides are equivalent in value. An equation may contain variables, which are unknown values represented by letters, as well as constants, which are known values. Equations are used in many areas of mathematics and science to model and solve problems. For example, the equation y = mx + b is a linear equation that describes the relationship between the variables x and y in a straight line, where m is the slope of the line and b is the y-intercept. Equations can be solved by manipulating the variables and using mathematical operations to isolate the unknown value.
Here,
Since A = B, we know that AB = B². So, we can rewrite the equation AB = 3x - 5 as B² = 3x - 5.
Similarly, we can rewrite BC = 5x - 6 as B² = 5x - 6, and AC = 2x - 9 as A² - B² = (2x - 9) - (B^2).
Since we know that A = B, we can substitute B for A in the last equation to get:
B² - B² = (2x - 9) - (B²)
Simplifying this equation, we get:
0 = 2x - 9 - B²
Now we can substitute the equation B² = 3x - 5 into the above equation to get:
0 = 2x - 9 - (3x - 5)
Simplifying this equation, we get:
0 = -x - 4
Solving for x, we get:
x = -4
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4. The equation h = -16t² + 20t + 19 gives the height h, in feet, of a ball as a function of time t, in seconds,
after it is kicked. What is the maximum height the ball reaches?
Answer:
The maximum height occurs at the vertex of the parabolic equation, which is given by the formula:
t = -b/2a
where a = -16 and b = 20. Substituting these values, we get:
t = -20 / (2 * -16) = 0.625 seconds
To find the maximum height, we can substitute this value of t back into the original equation:
h = -16(0.625)^2 + 20(0.625) + 19
h = -6.25 + 12.5 + 19
h = 25.25 feet
Therefore, the maximum height the ball reaches is 25.25 feet.
Answer:
h=16(t+5/8)^2+51/4
h=25.25
The identity (x + y)² is equal to x² +y².
True
False
Answer:
False
Step-by-step explanation:
[tex](x+y)^{2} = x^{2} +2xy +y^{2}[/tex]
This means that they are not equal. For this reason, the statement is false.
Ramona has saved $63. She has saved 3 times has much
money as Luke. How much money has Luke saved?
Answer:
Luke has saved $21
Step-by-step explanation:
Answer:
According to the problem, Ramona has saved 3 times as much money as Luke, so:
Ramona's savings = 3x
Luke's savings = x
The problem tells us that Ramona has saved $63, so we can write an equation:
3x = 63
To solve for x, we can divide both sides by 3:
x = 21
Therefore, Luke has saved $21.
The average yearly salary of a lawyer is $25 thousand less than twice that of an architect. Combined, an architect and a lawyer earn $209 thousand. Find the average yearly salary of an architect and a lawyer
Answer:
Step-by-step explanation:
Let's call the average yearly salary of an architect "A" and the average yearly salary of a lawyer "L".
From the first sentence, we know that:
L = 2A - 25
From the second sentence, we know that:
A + L = 209
We can substitute the first equation into the second equation:
A + (2A - 25) = 209
Simplifying:
3A - 25 = 209
Adding 25 to both sides:
3A = 234
Dividing both sides by 3:
A = 78
Now we can use the first equation to find L:
L = 2A - 25 = 2(78) - 25 = 131
Therefore, the average yearly salary of an architect is $78,000 and the average yearly salary of a lawyer is $131,000.
Which equation represents the vertex form of the equation y = x2 + 6x + 5?
The vertex form is:y(x-3)2-4
:) Good luck
Use the method of completing the square to express in vertex form.
Given
[tex]y = x^2 - 6x + 11[/tex]
To complete the square
add/subtract ( half the coefficient of the x- term )² to x² - 6x
[tex]y = x^2 + 2(- 3)x + 9 - 9 + 11[/tex], then
[tex]y = (x - 3)^2 + 2[/tex]
[tex]\bold{y= (x - 3)2 + 2}[/tex]How do I find the absolute deviation in simple words.
The average absolute deviation, which tells you how much the values in the data set vary from the mean on average.
What is deviation?Deviation is a statistical measure that indicates how much a set of data varies from its average or expected value. It is calculated by finding the difference between each data point and the mean value of the data set.
According to question:Absolute deviation is a measure of how far apart a set of numbers is from their average, or mean, value. It is calculated by finding the absolute value of the difference between each data point and the mean, and then taking the average of these absolute differences.
Here are the basic steps to find the absolute deviation:
1) Find the mean of the data set by adding up all the numbers and dividing by the total number of values.
2) For each value in the data set, subtract the mean from the value to find the difference.
3) Take the absolute value of each difference (ignore the positive or negative sign) by simply dropping the minus sign if there is one.
4) Add up all the absolute differences found in step 3.
5) Subtract the total number of values in the data set from the sum of the absolute differences.
The result is the average absolute deviation, which tells you how much the values in the data set vary from the mean on average.
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Solve the system
y=9x
x+y=1
Answer: (1/10, 9/10)
Step-by-step explanation:
-6..
6-
550
4
CN
4.
6
Ty
IS
6
X
Is this an odd function
The given function does not satisfy the condition for an odd function (f(-x) = -f(x)), we can conclude that -6.66 is not an odd function
Hi there! An odd function is a mathematical function that satisfies the condition f(-x) = -f(x) for all values of x in its domain. In simpler terms, an odd function exhibits symmetry with respect to the origin in a coordinate plane.
Now, let's analyze the given function: -6.66. This function represents a constant function since it has no variables (e.g., x or y). Constant functions have a graph that appears as a horizontal line on the coordinate plane.
For constant functions, f(-x) will always equal f(x) because the function's value doesn't change regardless of the input.
In this specific case, the function value is -6.66,
so f(-x) = f(x) = -6.66 for all x.
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