(x³ + kx² - 34x +56) ÷ (x + 7)
Answer:
Step-by-step explanation:
Because this problem is not easily solvable through factoring, we must use long division to find the answer.
_______________ x+7 | x3 + kx2 - 34x + 56
When performing long division on polynomials, we should try to cancel out the term with the greatest power first. So, we must figure out how many x's go into x3, because x is the first term of the first polynomial and x3 is the first term of the second polynomial. x*x2 = x3, so:
x2
_______________ x+7 | x3 + kx2 - 34x + 56
(-) x3 + 14x2
(k-14)x2 - 34x
Then, we see how many x's go into (k-14)x2. x*(k-14)x = (k-14)x2, so:
x2 + (k-14)x
_______________ x+7 | x3 + kx2 - 34x + 56
(-) x3 + 14x2
(k-14)x2 - 34x
(-) (k-14)x2 - 7kx - 98x
-7kx - 132x + 56= (-7k-132)x + 56
x*(-7k-132) = (-7k-132)x, so:
x2 + (k-14)x + (-7k-132)
_______________ x+7 | x3 + kx2 - 34x + 56
(-) x3 + 14x2
(k-14)x2 - 34x
(-) (k-14)x2 - 7kx - 98x
(-7k-132)x + 56
(-) (-7k-132)x - 7k - 924
-7k - 868
The answer is x2 + (k-14)x + (-7k-132) - [(7k-868)/(x+7)]
OFFERING 70 POINTS AND BRAINLEST
Which number line shows the solution to the inequality? y minus 2 less-than negative 5 A number line going from negative 8 to positive 2. An open circle is at negative 3. Everything to the left of the circle is shaded. A number line going from negative 8 to positive 2. A closed circle is at negative 3. Everything to the left of the circle is shaded. A number line going from negative 8 to positive 2. An open circle is at negative 3. Everything to the right of the circle is shaded. A number line going from negative 8 to positive 2. An open circle is at negative 7. Everything to the left of the circle is shaded.
The correct number line is: A number line going from negative 8 to positive 2. An open circle is at negative 3. Everything to the left of the circle is shaded.
What is inequality?The mathematical expression of a connection between two values, stating that one value is larger than, less than, or not equal to another value, is called an inequality. Common symbols for inequality include (less than), > (greater than), (less than or equal to), and (greater than or equal to). For instance, the inequality 2x + 3 > 7 denotes that the value of 2x + 3 is larger than 7. Depending on the circumstance, inequalities can be resolved algebraically or visually. A collection of values that meet the connection implied by the inequality is the answer to an inequality.
Here, the inequality is y - 2 < -5, which can be rewritten as y < -3.
Hence, the correct option is: A number line going from negative 8 to positive 2. An open circle is at negative 3. Everything to the left of the circle is shaded.
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Jason studied how quickly ants consume things. He counted the number of ants on a banana peel at the end of each minute for five minutes. His results formed the pattern below.
12, 19, 26, 33, 40
Let n represent the number of minutes since Jason began his study. Which expression could be used to predict the number of ants on the banana peel after n minutes?
5+7n
7+5n
12n
7n
The expression that could be used to predict the number of ants on the banana peel after n minutes is given as follows:
5 + 7n.
What is an arithmetic sequence?An arithmetic sequence is a sequence of values in which the difference between consecutive terms is constant, being called common difference d.
The nth term of an arithmetic sequence is given by the explicit formula presented as follows:
[tex]a_n = a_1 + (n - 1)d[/tex]
In this problem, the difference between consecutive terms is of 7, meaning that it represents an arithmetic sequence with a common difference of 7.
The first term is of 12, hence we obtained the explicit formula as follows:
12 + 7(n - 1) = 12 + 7n - 7 = 5 + 7n.
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What is an equation for the linear relationship in slope-intercept form?
A. y=2x+3
B. y=12x+3
C. y=12x−3
D. y=−12x−3
A: y=2x+3. This is an equation for the linear relationship in slope-intercept form. The equation states that the value of y is equal to the slope of the line, 2, multiplied by the value of x, plus 3.
What is slope?Slope is a measure of the steepness of a line. It is the ratio between the vertical change in a line (change in y-values) over the horizontal change in the same line (change in x-values). It is also referred to as the rate of change, as it is a measure of how quickly the value of y changes with respect to the x-value.
This equation is used to describe a straight line that has a constant rate of change between two variables. This equation can be used to determine the slope, y-intercept, and x-intercept of a line.
The slope, which is the coefficient of x in the equation (2 in this case), is the rate at which y changes with respect to x. It is the rise over run, or the change in y over the change in x. The y-intercept is the value of y when x is equal to 0 (in this case, it is 3). The x-intercept is the value of x when y is equal to 0 (in this case, it is -3/2).
This equation is often used to represent a linear relationship between two variables, such as the amount of money a person earns in relation to the number of hours they work.
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CAN SOMEONE HELP WITH THIS QUESTION?
The rate of change of the area outside the circle but inside the square is 1 m² per minute.
What is area?Area is the measure of the size of a two-dimensional (2D) shape or planar region. It is expressed in terms of square units, such as square metres (m2) and square feet (ft2). The area of a shape is the total space contained within its boundaries.
To answer this question, we need to find out the area outside the circle but inside the square. This can be done by subtracting the area of the circle from the area of the square.
The area of the circle is equal to πr², where r is the radius of the circle. In this case, the radius is 3 meters, so the area of the circle is π×32 = 28.27 m².
The rate of change of the area outside the circle but inside the square is 1 m²per minute.
The area of the square is equal to side², where side is the length of one side of the square. In this case, the side is 16 meters, so the area of the square is 162 = 256 m².
Subtracting the area of the circle from the area of the square gives us the area outside the circle but inside the square. This is 256 - 28.27 = 227.73 m².
Now, we know the area outside the circle but inside the square, and we know that the radius of the circle is increasing at a rate of 1 meter per minute and the sides of the square are increasing at a rate of 2 meters per minute. This means that the area outside the circle but inside the square is increasing at a rate of (2 - 1) = 1 m²per minute.
Therefore, the rate of change of the area outside the circle but inside the square is 1 m² per minute.
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Part B: create your own cube root function.
Come up with the equation of 2 different cube root functions. None of these can be the parent function y=^3 squared root of x. For each, find the domain, range, x- and y-intercepts, and describe any transformation for each. Also, give the coordinates of 3 points that you known are on the function (coordinates must be exact values).
Three points on the graph: (4, 0), (13, 5), (28, 8)
What is function ?
Function can be defined in which it relates an input to output.
Function 1: y = [tex](x+2) ^{1/3}[/tex] - 1
Domain: x ≥ -2
Range: y ≥ -1
x-intercept: There is no x-intercept.
y-intercept: (0, -1)
Transformation: The cube root function is shifted 2 units to the left and 1 unit down.
Three points on the graph: (-2, -1), (-1, 0), (6, 1)
Function 2: y = 3[tex](x - 4)^{1/3}[/tex] + 2
Domain: x ≥ 4
Range: y ≥ 2
x-intercept: (4, 0)
y-intercept: There is no y-intercept.
Transformation: The cube root function is shifted 4 units to the right, vertically stretched by a factor of 3, and shifted 2 units up.
Therefore, Three points on the graph: (4, 0), (13, 5), (28, 8)
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Please I need help
The area of the shaded region is
The area of the shaded region in the standard normal distribution can be found to be 0.3510.
How to find the area in the standard normal distribution curve ?To find the area of the shaded region between -2.25 and -0.35 in a standard normal distribution, you would use a Z-table or a calculator with a built-in Z-table function.
Area between -2.25 and -0.35 = Area to the left of -0.35 - Area to the left of -2.25
Area to the left of -0.35 = 0.3632
Area to the left of -2.25 = 0.0122
find the difference between these two areas:
Area between -2.25 and -0.35 = 0.3632 - 0.0122 = 0.3510
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HELP ME!!! Find the percent equivalent to 14 over 35. 21% 40% 42% 50%
Answer:
The answer is 40% :) Hope this helps!
Amiya jogged 1/3 of a mile, and stopped to rest. Then, she jogged another 1/3 of a mile. How far did Amiya jog? Draw to solve.
Answer:
To solve the problem, we can draw a number line and mark off the distances that Amiya jogged.
We start at 0 and mark off 1/3 of a mile to represent the distance Amiya jogged initially. Then we mark off another 1/3 of a mile to represent the distance she jogged after resting.
The total distance Amiya jogged is the distance from the starting point (0) to the end point (2/3), which is 2/3 of a mile.
Therefore, Amiya jogged a total of 2/3 of a mile.
Taking it further, to convert miles to meters, we need to know that 1 mile is equal to 1609.34 meters (approximately).
So to find out what 2/3 of a mile is in meters, we can multiply 2/3 by the conversion factor:
2/3 mile x 1609.34 meters/mile = 1072.89 meters
Therefore, 2/3 of a mile is approximately equal to 1072.89 meters.
Select the correct answer.
What is the simplified form of this expression?
(2x + 9) + (11x − 4)
A.
13x + 5
B.
13x + 13
C.
18x
D.
-9x + 5
Answer:
13x+5
Step-by-step explanation:
Here's why
2x+9+11x-4
subtract 4 from 9
2x+5+11x
combine like terms
13x+5
If the median is 3.5, we can assume the mean is ____________than 3.5
We cannot make a general assumption about whether the mean is greater or less than 3.5 based solely on the fact that the median is 3.5.
What is mean?The mean is a measure of central tendency that represents the average value of a set of numbers. It is also called the arithmetic mean or simply the average.
According to question:We cannot make a general assumption about whether the mean is greater or less than 3.5 based solely on the fact that the median is 3.5.
The mean and the median are two different measures of central tendency, and they can have different values depending on the distribution of the data. In general, if a data set is symmetric and bell-shaped, the mean and the median are close to each other. However, if the data set is skewed, the mean and the median may be different.
For example, consider the following two data sets:
Set 1 data: 1, 2, 3, 4, and 5.
The median is 3.
The mean is (1 + 2 + 3 + 4 + 5) / 5 = 15 / 5 = 3.
Data set 2: 1, 2, 3, 4, 10
The median is 3.
The mean is (1 + 2 + 3 + 4 + 10) / 5 = 20 / 5 = 4.
In data set 1, the mean is the same as the median. In data set 2, the mean is greater than the median because the value 10 is an outlier that pulls the mean up.
Therefore, without additional information about the distribution of the data, we cannot make a general assumption about whether the mean is greater or less than 3.5 based solely on the fact that the median is 3.5.
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(-8)-(-2) porfa lo necesito
Answer:
-6
Step-by-step explanation:
A college professor claims that students who major in engineering in college score higher on standardized test then students who major in ancient history. He randomly selected 50 students from each subject and gave them this assignment the results of which are shown here.
See chart and answer choices in photo!
Please answer quickly, tysm!
The option that describes the null and alternative hypothesis, test statistic and conclusion will be B. test statistic = -1.5625 and the conclusion is to reject the null hypothesis.
What is the hypothesis about?In statistical hypothesis testing, the null hypothesis (H0) is a statement that assumes no significant difference or relationship between two or more variables. It represents the default position that there is no effect or change, or that any observed effect is due to chance.
The alternative hypothesis (H1), on the other hand, represents the opposite of the null hypothesis. It states that there is a significant difference or relationship between the variables being tested. The alternative hypothesis is typically what the researcher is trying to prove or support with their study.
The test statistic will be:
= (116 - 121) / 16(✓1/50 + 1/50)
= -1.5625
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Describe the possible values of x if the area of the rectangle is at least 40 square inches
The value of x is 32.
Describe Rectangle?A rectangle is a quadrilateral (a four-sided polygon) with four right angles (90-degree angles) and opposite sides that are parallel and congruent (the same length). The opposite sides of a rectangle are also perpendicular to each other, meaning they intersect at a 90-degree angle.
The rectangle is a special case of a parallelogram, where all the angles are right angles. A square is also a special type of rectangle, where all the sides are congruent.
We can use the formula for the area of a rectangle, which is:
Area = Length x Width
Substituting the given values, we get:
40 = (5/8)x + 5 x 4
Simplifying, we get:
40 = (5/8)x + 20
Subtracting 20 from both sides, we get:
20 = (5/8)x
Multiplying both sides by 8/5, we get:
x = 32
Therefore, the value of x is 32.
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I have five people that can move 12 crates in an hour, how many people do I need to move 60to create in an hour, assuming that the rate of work is the same?
Answer:
Below
Step-by-step explanation:
You need to move 5 times as many crates in the same amount of time....so you will need 5 times as many people = 25 people
Can anyone solve the following two maths?
In conclusion the team took 50 strokes to complete the final 500 meters of the race and at the end of the season, the team's mean split time should be 99 seconds.
How to find?
To find the answer to question 37, we know that the team rowed the final 500 meters in 108 seconds. We also know that they rowed at a rate of 28 strokes per minute during this split. To find out how many strokes they took to complete the final 500 meters, we need to convert the split time to minutes and then multiply by the stroke rate.
First, we convert the split time to minutes:
108 seconds ÷ 60 seconds per minute = 1.8 minutes
Then, we multiply by the stroke rate to find the total number of strokes:
1.8 minutes x 28 strokes per minute ≈ 50 strokes
Therefore, to the nearest whole number, the team took 50 strokes to complete the final 500 meters of the race.
To find the answer to question 38, we need to find the team's mean split time and then reduce it by 10%. The mean split time is found by taking the total race time and dividing by 4, since there are 4 splits in the race.
Total race time = 440 seconds
Mean split time = Total race time ÷ 4 = 110 seconds
To reduce the mean split time by 10%, we multiply it by 0.9:
New mean split time = 110 seconds x 0.9 = 99 seconds
Therefore, at the end of the season, the team's mean split time should be 99 seconds.
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PLS HELP MEEEEEEEEEEEEEEEEEE I CAN'T ANSWER
A. Tell whether distance, speed, or time is asked in each given situation.
_____1. How long will it take Zihann to arrive at school if she walks a constants 2 kilometers per hour?
_____2. How far do you need to travel at an average speed for 5 hours?
_____3. How fast should you travel to arrive at your destination that is 2.5 hours away?
_____4. If Carla travels a distance of 150 kilometers and arrive after 3 hours, how fast did she drive?
_____5. If Alwyn drove at an average speed to travel a certain distance, how long did it take him to travel?
Kevin drove 18 1/2 miles in 2/3 hours. If he drove at a constant rate, how far did he travel in one hour
Answer:
27.75 miles
Step-by-step explanation:
(18 1/2 miles) / (2/3 hours) = (37/2 miles) × (3/(2 hours)) = 111/4 miles/hour
111/4 miles/hour = 27.75 miles/hour
Answer: 27.75 miles
3. Assume that there are only 2 commodities and that the utility function is multiplication of the form U = 1÷4qxqy.Find the demand function of the commodity x and y and explain the relationship between price and income in relation to the demand.
Answer:
Step-by-step explanation:
Sophia and morgan are interested in recycling they each weight their families daily recycling for 2 weeks the dot plots show their data Without calculating Sophia says that the Mad for Morgan's data is Sophia correct? Iready check
No, Sophia is not correct. While we can see that Morgan had more total weight overall in their two week recycling data, we can't say for sure that Morgan's data is greater without calculating the exact numbers.
What is recycling data?Recycling data is information collected from the recycling process that is used to measure and analyze the effectiveness of the process. This data can include the type and amount of materials collected, the location of collection, the method of collection, and the end-use of recycled materials. Recycling data can be used to help identify areas for improvement, develop innovative recycling solutions, and evaluate the impact of current programs. It can also be used to understand consumer behavior and inform decisions on waste management. By collecting and analyzing recycling data, governments, businesses, and organizations can better understand how to reduce waste and increase the reuse and recycling of materials.
We need to calculate the means of the data to determine which one is larger.
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Samir and Kylie are making fruit salads for a picnic. Samir mixes 1 cup of melon and 3 cups of apple and Kylie mixes 2 cups of melon and 9 cups of apple. Use Samir and Kylie’s percent of melon to determine whose fruit salad will taste more melony.
Samir's fruit salad has a higher percentage of melon and will taste more melony than Kylie's fruit salad.
What is percentage?Percentage is a way of expressing a proportion or a fraction as a number out of 100. It is represented by the symbol % (percent).
In the given question,
To determine whose fruit salad will taste more melony, we need to calculate the percentage of melon in each fruit salad.
For Samir's fruit salad:
The total amount of fruit is 1 + 3 = 4 cups
The amount of melon is 1 cup
The percentage of melon is (1/4) x 100% = 25%
For Kylie's fruit salad:
The total amount of fruit is 2 + 9 = 11 cups
The amount of melon is 2 cups
The percentage of melon is (2/11) x 100% = 18.18% (rounded to two decimal places)
Therefore, Samir's fruit salad has a higher percentage of melon and will taste more melony than Kylie's fruit salad.
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The latus rectum of the parabola with the equation 2y^2 - 15x - 4y - 28 = 0 is
15
15/2
15/4
Answer: 15/2
Step-by-step explanation: Im doing this lesson right now and I looked up the answer on a math calculator online its called emathhelp.net and it gave me 15/2
Factor.
f(x) = 6x^2 - 7x+2
Answer: f(x)=(2x−1)(3x−2)
Step-by-step explanation:
Answer:
Step-by-step explanation:
(2x−1)(3x−2)
Find the length indicated.
7) Find FG
E
2x+1
F
16
2x+3
G
Find the volume of a cone with a radius of 4 ½ m. and a height of 10 m.
The volume of the cone is approximately 211.06 cubic meters.
Why is that?
Well, the formula for the volume of a cone is:
V = (1/3)πr^2h
where:
Substituting the given values, we get:V = (1/3)π(4.5m)^2(10m)
V = (1/3)π(20.25m^2)(10m)
V = (1/3)π(202.5m^3)
V = 67.5π
Using a calculator, we get:
V ≈ 211.06 cubic meters
Therefore, the volume of the cone is approximately 211.06 cubic meters.
A fizzy drink comes in a rigid can (its volume remains constant). If the can is left in a hot car, what will happen to the pressure of the gas inside the can as the temperature increases? Explain what is happening to the gas particles. Which gas law does this follow?
its for chemistry class not for math
Therefore , the solution of the given problem of unitary method comes out to be the gas particles inside the can will acquire kinetic energy and collide with its walls more frequently, increasing pressure.
A unitary technique is what ?The objective can be accomplished by variable use of what has been clearly learned thus far, implementing advantage of this worldwide convenience, and incorporating all essential components from prior flexible research that used a specific approach. If the anticipated claim outcome actually occurs, it will be feasible to get in connection with the entity once more; if not, both crucial systems will undoubtedly miss the statement.
Here,
The pressure of the gas inside the can will rise as the temperature rises. This is due to the fact that the gas particles inside the can will accelerate and acquire kinetic energy, causing them to collide with the can's walls more frequently and more violently.
The pressure rises as a result of these collisions' greater power per unit area.
The Ideal Gas Law, which says that PV = nRT, where P is tension, V is volume, n is the number of moles of gas,
R is the optimal gas constant, and T is temperature in Kelvin, describes this relationship between pressure and temperature.
In conclusion, the Ideal Gas Law predicts that as the temperature inside the vehicle rises, the gas particles inside the can will acquire kinetic energy and collide with its walls more frequently, increasing pressure.
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A cylinder has the net shown.
net of a cylinder with diameter of each circle labeled 3.8 inches and a rectangle with a height labeled 3 inches
What is the surface area of the cylinder in terms of π?
40.28π in2
22.80π in2
18.62π in2
15.01π in2
Answer: It is 18.62 or c
Step-by-step explanation:
A superintendent of a school district awarded a total of $5000 in bonuses to the most productive teachers that helped impact student achievement this pat year. The bonuses were awarded in the amount of $500 or $1000. If at least one $500 bonus and at least one $1000 bonus were awarded, what is a total possible number of $500 bonuses awarded?
A total possible number of bonuses awarded is given as follows:
6 bonuses.
How to obtain the total number of bonuses awarded?The total number of bonuses awarded is obtained applying the proportions in the context of the problem.
The total amount of bonuses is of $5,000, and at least one $500 bonus and at least one $1000 bonus were awarded, hence the remaining amount to be awarded is of:
5000 - (500 + 1000) = $3,500.
For an amount of $3,500, a possible division of the bonuses is given as follows:
One bonus of $500.Three bonuses of $1000.Hence a possible number of bonuses is given as follows:
2 + 1 + 3 = 6 bonuses.
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I need help finding the regression equation pls!
Answer:
i did this in 8th grade. (I'm homeschooled)
Step-by-step explanation:
Heres the best i got
Who knows this? I need help
#16
Answer:
Step-by-step explanation:
adjacent: [tex]\angle BOC, \angle EOD[/tex] (both are adjacent)
complementary: [tex]\angle BOC[/tex]
supplementary: [tex]\angle EOD[/tex]
vertical angles: [tex]\angle AOE[/tex]