The equation is now in the standard shape of a hyperbola, as per the provided assertion. [(x - h)² / a²] - [(y - k)² / b²] = 1
What, in plain words, is a hyperbola?A curve formed by the junction of a double right-angled cone and a plane that slices one half of the cone. a plane curve produced by a point so mobile that the difference between its distance from two fixed locations is a constant.
To complete the square for the given equation, we will group the x and y terms and complete the square separately for each.
4x² + 24x - 9y² + 18y - 9 = 0
4(x² + 6x) - 9(y² - 2y) = 9
4(x² + 6x + 9 - 9) - 9(y² - 2y + 1 - 1) = 9
4(x + 3)² - 9(y - 1)² = 36
Dividing by 36, we get:
(x + 3)² / 9 - (y - 1)² / 4 = 1
So, the equation is now in the standard form of a hyperbola:
[(x - h)² / a²] - [(y - k)² / b²] = 1
where h and k are the coordinates of the center, a is the distance from the center to the vertices along the x-axis, b is the distance from the center to the vertices along the y-axis, and the slope of the asymptotes is b/a.
Comparing with the standard form, we can see that:
h = -3, k = 1, a = 3, b = 2, and the slope of the asymptotes is b/a = 2/3.
The center is (-3, 1). The hyperbola opens horizontally, and its vertices are located at (-3 + a, 1) and (-3 - a, 1). So, the vertices are (-6, 1) and (0, 1).
The asymptotes are two straight lines passing through the center with a slope of ±(b/a) = ±2/3. So, the equations of the asymptotes are y - 1 = (2/3)(x + 3) and y - 1 = -(2/3)(x + 3), which simplify to y = (2/3)x + 5/3 and y = -(2/3)x + 1/3.
The distance between the center and the foci is c = sqrt(a² + b²) = √(13). The foci are located at (-3 + c, 1) and (-3 - c, 1). So, the foci are approximately (-0.16, 1) and (-5.84, 1).
The graph of the hyperbola looks like two mirrored U-shaped curves, with the vertices being the endpoints of the transverse axis.
The asymptotes intersect at the center and divide the hyperbola into four parts, called branches. The foci are located on the transverse axis, inside the branches.
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The sum of twice a number,n, and 14 is 30. Write an equation that models this statement.Then explain how you might use reasoning to find the value of n.
Answer:
2n + 14 = 30
Step-by-step explanation:
Since you know that 2n + 14 = 30, we can determine the values by first subtracting 14 from 30. Our equation would then be 2n = 16. Divide 2 from both sides and n = 8.
This model represents the total on the top and the 2 parts on the bottom.
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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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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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
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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Simplificacion de 18/25
Answer:
Step-by-step explanation:
Ici, nous allons réduire la fraction 18/25 aux termes les plus bas et la convertir en un nombre fractionnaire, si nécessaire.
Dans la fraction 18/25, 18 est le numérateur et 25 est le dénominateur.
On commence par trouver le plus grand diviseur commun de 18 et 25, qui est 1. Ensuite, on divise 18 et 25 par le plus grand diviseur commun pour obtenir la plus petite expression, écrite comme suit :
(18 ÷ 1) / (25 ÷ 1)
= 18/25
Find the surface area of the composite figure shown below that
consists of a right cone sitting atop a right cylinder. Use 3.14 form and
give the answer in square meters.
1-20 m
r 13 m
h=13m
Using the right cone formula we know that the surface area is 1281.77638m³ respectively.
An axis that is perpendicular to the base plane defines a right circular cone. By rotating a right triangle around one of its legs, we may create a right cone.
The right circular cone in the illustration has an axis that is perpendicular to the base and a circular base with a radius r.
So, the formula for the surface area of the right cone is as follows:
πr(r+√h²+r²)
We have the values: r = 13m and h = 13m
Now, insert values as follows:
= πr(r+√h²+r²)
= π13(r+√13²+13²)
= 1281.77638
Therefore, using the right cone formula we know that the surface area is 1281.77638m³ respectively.
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*PLEASE HELP ME!*
Explore
Here is a number pyramid puzzle. Fill in the blanks so that each number is the product of the two numbers directly beneath it.
The blanks of the number pyramid puzzle can be filled with numbers calculated below.
How fill in the blanks of the number pyramid puzzle?
A number pyramid puzzle is a type of mathematical puzzle where a pyramid-shaped grid of numbers is given, with some of the numbers missing.
Check the attached image for labeling. Since each number is the product of the two numbers directly beneath it. We can say:
m = -4 * 0.5 = -2
k = 0.5 * 1/8 = 1/16
x * (-1/8) = 8
x = 8/(-1/8)
x = -64
y = x * 1/8
y = -64 * 1/8
y = -8
j = m * k
j = -2 * 1/16 = -1/8
p = -48 * m
p = -48 * (-2) = 96
n = y * 8
n = -8 * 8 = -64
t = p * j
t = 96 * (-1/8) = -12
w = -1/2 * n
w = -1/2 * (-64) = 32
c = t * 1/16
c = -12 * 1/16 = -3/4
u = 1/16 * w
u = 1/16 * 32 = 2
d = c * u
d = -3/4 * 2 = -3/2
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A shipping container is in the form of a right rectangular prism, with dimensions of
30 ft by 8 ft by 8 ft 9 inches. How many cubic feet of shipped goods would it hold
when it is full? Round your answer to the nearest tenth if necessary.
Answer:2,160ft
Step-by-step explanation: Volume=length * width * height
30x8x9=2160
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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A company estimates that 0.8% of their products will fail after the original warranty period but within 2 years of the purchase, with a replacement cost of $200.
If they offer a 2 year extended warranty for $22, what is the company's expected value of each warranty sold?
$
Therefore , the solution of the given problem of percentage comes out to be the firm expects that each warranty it sells will be worth $1.41.
What is percentage?In statistics, "a%" is used to refer to a figure or number that is expressed as a percentage of 100. Additionally rare are the forms that "pct," "pct," or "pc". It is typically represented by the symbol "%," though. Additionally, there are not any indicators and the proportion of each item to the overall amount is flat. Since percentages typically add up to 100, they are essentially integers. Either the expression "fraction" or the symbol for percentage (%) .
Here,
The price to substitute each item is $200. The anticipated price for each component is thus:
Expected cost per product equals Replacement cost x Failure Probability
=> Cost per product anticipated = 0.008 x $200
=> Expected price per item is $1.60.
So, the following is the anticipated value of each warranty sold:
Expected worth of the warranty = Failure rate x (Replacement cost - Cost of warranty)
=> Expected guarantee value = 0.008 * ($200 - $22 - $1.60).
=> Expected guarantee value = 0.008 * $176.40
=> Expected warranty worth is $1.41
As a result, the firm expects that each warranty it sells will be worth $1.41.
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21 students in the class like chocolate ice cream. this is 75% of the class. how many students are in the class?
Answer:
28 people
Step-by-step explanation:
21 / 3 = 25
7 = 25%
25 x 4 = 100%
so
7 x 4 = 28
28 people are in the class
Elena wants to tile the top of a circular table. The diameter of the tabletop is 28 inches. What is the perimeter?
Answer:
86.96 inches.
Step-by-step explanation:
C = 2πr
d = 2r
Solving for C
C = πd = π · 28 ≈ 87.96459 inches
PLEASE HELP! Find missing side lengths of B and C. Explain
Answer:
b=7 & c=7√2
Step-by-step explanation:
b=7 as it is an isosceles triangle
now using Pythagoras theorem,
(c)^2= (7)^2+(7)^2
⇒(c)^2= 49+49
⇒(c)^2= 98
⇒c= √98
⇒c=7√2
Answer:
b = 7c = 7√2Step-by-step explanation:
You want the missing side lengths in an isosceles right triangle with one side given as 7.
Isosceles right triangleThe two congruent acute angles tell you this right triangle is isosceles. That means sides 7 and b are the same length:
b = 7
The hypotenuse of an isosceles right triangle is √2 times the side length:
c = 7√2
__
Additional comment
You can figure the hypotenuse using the Pythagorean theorem if you haven't memorized the side relations of this "special" right triangle.
c² = 7² + b²
c² = 7² +7² = 2·7²
c = √(2·7²) = 7√2
The side length ratios for an isosceles right triangle (angles 45°-45°-90°) are 1 : 1 : √2.
The other "special" right triangle is the 30°-60°-90° triangle, which has side length ratios 1 : √3 : 2.
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.
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?
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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can someone please solve????!! thanks
Answer:
(a) Figure 3
(b) 66.2 meters per second
Step-by-step explanation:
You want to know the figure that shows the best fit of a curve to the data, and you want to know the value of the curve when x = 8 seconds.
Best fitThe fit is best when the difference between the data points and the curve is minimized. Often the sum of the squared differences is the metric that is minimized when the fit is best.
The gaps between the data points and the curve shown are greatest in Figures 1 and 2, so Figure 3 has the best fit.
Estimated valueThe speed is estimated by the equation of the curve of best fit as ...
y = 0.6x² +2.1x +11
A slight rearrangement can make this easier to evaluate:
y = (0.6x +2.1)x +11
For x=8, the value of y is ...
y = (0.6·8 +2.1)·8 +11 = 6.9·8 +11 = 66.2
The predicted speed at 8 seconds is 66.2 meters per second.
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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prove this question in the image please
The parallelogram ABCD's congruency can be proven using Side-Angle-Side (SAS) congruence theorem.
How to prove congruency?Prove that ΔABC ≅ ΔDCB using the Side-Angle-Side (SAS) congruence theorem.
Given that ABCD is a parallelogram, AB || CD and BC || AD. Therefore, ∠ABC ≅ ∠DCB and ∠ACB ≅ ∠DCA because they are corresponding angles.
AB ≅ CD and BC ≅ AD because opposite sides of a parallelogram are congruent.
Lastly, AC ≅ AC because it is a shared side between the two triangles.
Therefore, the following congruent parts:
∠ABC ≅ ∠DCB (by corresponding angles)
AB ≅ CD (by opposite sides)
BC ≅ AD (by opposite sides)
AC ≅ AC (shared side)
The SAS congruence theorem concludes that ΔABC ≅ ΔDCB.
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Image transcribed:
Prove ΔABC ≅ ΔDCB
70% of 140 is what value? 20 70 84 98
Answer:
Step-by-step explanation:
70% of 140 is equal to 0.7 x 140 = 98. Therefore, the answer is 98.
Answer:
98
Step-by-step explanation:
70% can also be written as 0.7, therefore, we can multiply 140 by 0.7.
140 x 0.7 = 98.
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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Is ∆PQR a right triangle? Explain
Answer:
Yes, ∆PQR is a right triangle.
Step-by-step explanation:
A right triangle has one right angle, which is 90°. This triangle has one right angle, so it is a right triangle.
What is the image of the point (7, 0) when the translation rule (x, y)→(x+1, y−2) is used?
(1, −2)
(8, −2)
(6, 2)
(5, 1)
Answer:
To find the image of the point (7, 0) under the given translation, we apply the translation rule:
(x, y) → (x + 1, y - 2)
Substituting (7, 0) for (x, y), we get:
(7, 0) → (7 + 1, 0 - 2)
= (8, -2)
Therefore, the image of the point (7, 0) under the given translation is (8, -2).
So, the correct answer is (8, −2).
Step-by-step explanation:
hope its help <:
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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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 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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The radius of a circle is 11 meters. What is the circle's circumference?
Use 3.14 for л.
r=11 m
Answer:
The formula for the circumference of a circle is C = 2πr, where r is the radius of the circle and π (pi) is a mathematical constant approximately equal to 3.14.
Substituting the given value of r=11 m and using π = 3.14, we get:
C = 2πr
C = 2 x 3.14 x 11 m
C = 69.08 m
Therefore, the circumference of the circle is 69.08 meters
(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)]
HELP ME!!! Find the percent equivalent to 14 over 35. 21% 40% 42% 50%
Answer:
The answer is 40% :) Hope this helps!