Therefore , the solution of the given problem of expressions comes out to be (x+y) is the LCM of (x+y, x-y).
What is an expression?Utilizing shifting integers that may prove rising, minimizing, or blocking is preferable to using approximations generated at random. Sharing resources, knowledge, or answers to problems was the only way they could assist one another. An equation for a declaration of truth may contain the justifications, components, and mathematical comments for methods like additional disagreement, manufacture, and mixture.
Here,
We must factor each polynomial into its irreducible factors and then take the sum of the highest powers of each irreducible factor to determine the LCM of two polynomials.
Here are the facts:
=> x+y = (x+y)
=> x-y = -(y-x)
We don't need to include the second component separately in the LCM because it is simply the negation of the first factor.
The LCM is just (x+y) because x+y is already indivisible.
Consequently, (x+y) is the LCM of (x+y, x-y).
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PLS HELP!!
Will give brainliest!!
The length of the side AC or the height of the smaller equilateral triangle is 3√2 inches.
What is the length AC?The length of the side AC is equal to the height of the smaller equilateral triangle.
We know that in an equilateral triangle, all sides are equal, and all angles are 60 degrees.
Let's call the height of the smaller equilateral triangle h, and the length of one side of the smaller triangle x.
We can use the Pythagorean theorem to find the value of h:
(1/2)x^2 + h^2 = x^2
h^2 = x^2 - (1/2)x^2
h^2 = (1/2)x^2
h = sqrt((1/2)x^2)
Now, we also know that the side of the large equilateral triangle is 6 inches, so x = 6 inches.
Substituting this value into the equation for h, we get:
h = √((1/2)(6^2))
h = √(18)
h = 3√2 inches.
Therefore, the height of the smaller equilateral triangle is 3√2 inches.
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2. The length of a rectangular floor is 4 feet longer than its width w. The area of the floor is 165 ft2.
(a) Write a quadratic equation in terms of w that represents the situation. Show how you created it.
(b) Solve the quadratic equation using one of the methods covered in Unit 4 and then clearly state the dimensions of the floor in a sentence.
Show your work.
Answer:
(a)
[tex]W^2+4W-165=0[/tex]
(b)
Width: 11 feet
Length: 15 feet
Step-by-step explanation:
Given:
Width (W) = W ft
Length (L) = (4 + W) ft
Area (A) = 165 ft^2
(a)
The area of a rectangle is equal to the product of its length and width, therefore:
[tex]A=L\times W[/tex]
[tex]\text{We replacing}[/tex]
[tex]165=(4+W)\times(W)[/tex]
[tex]4W+W^2=165[/tex]
[tex]W^2+4W-165=0[/tex]
(b)
We solve the equation by factoring:
[tex]W^2+4W-165=0[/tex]
[tex]4W=-11W+15W[/tex]
[tex]W^2-11W+15W-165=0[/tex]
[tex]W(W-11)+15(W-11)=0[/tex]
[tex](W-11)(W-15)=0[/tex]
[tex]W-11=0\rightarrow W=11[/tex]
[tex]W+15=0\rightarrow W=-15[/tex]
The width of the rectangle is equal to 11 feet and the length of the rectangle is equal to 15 feet.
Which is the BEST system to measure the likelihood of an event occurring? A between 0 and 12 B between 0 and 1 C between 0 and 10
D between 0 and 100
D) Between 0 and 100.
The best system to measure the likelihood of an event occurring would be option D between 0 and 100. This system allows for a greater level of granularity and precision in the measurement of probability, as it provides a wider range of possible values to represent different levels of likelihood. The other options may not provide enough resolution to accurately capture and distinguish between different probabilities.
below is a sorted stem-and-leaf diagram for the measured speeds (miles per hour) of 49 randomly chosen vehicles on highway i-80 in nebraska. what is the highest observed speed? stem unit
The highest observed speed is 85 miles per hour.
Below is a sorted stem-and-leaf diagram for the measured speeds (miles per hour) of 49 randomly chosen vehicles on
highway I-80 in Nebraska.
The stem unit is 5. So, the data range is from 50 to 85.
In the stem-and-leaf diagram below, each stem has ten leaves.
The stem-and-leaf diagram for the speeds of the 49 randomly selected vehicles on highway I-80 in Nebraska is as
follows: Stem | Leaf 5 | 08 6 | 013578 7 | 02346678 8 | 0123
The highest observed speed is 85 miles per hour.
The leaf corresponding to the stem 8 is 3, and it is in the last column of the stem-and-leaf diagram.
So, the highest observed speed is 85 miles per hour.
Therefore, the correct option is the one that reads "85."
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Suppose that P(x) represents the percentage of income spent on health care in year x and I(x) represents income in year x. Determine a function H that represents total health care expenditures in year x.
The function H that represents total health care expenditures in year x is _______
The total health care expenditures in year x would be equal to the product of the percentage of income spent on health care (P(x)) and the income (I(x)) in year x. Therefore, the function H can be expressed as:
H(x) = P(x) * I(x)
This function takes into account both the amount spent on health care as well as the income level, providing a comprehensive representation of health care expenditures.
Step-by-step explanation:
that depends on the result dimension of P(x).
if P(x) delivers the percentage in the form xx.xx%, then
H(x) = I(x) × P(x) / 100
if P(x) delivers the percentage in the form 0.xxxx, then
H(x) = I(x) × P(x)
very basically, the absolute amount of a percentage of a whole is the product between both (and divided by 100).
e.g.
let's say, the whole amount is $64,000.
and we need to know 10% of that.
10% of 64,000 is then
64,000 × 10 / 100 = 6,400
or
64,000 × 0.10 = 6,400
can you see the connection, and why both versions do the same ?
A Rectangle has a base of 5 and a height of 9. What is the area of the rectangle ?
Answer:
45
Step-by-step explanation:
Answer:
45
Step-by-step explanation:
Find all solutions to the equation in the interval [0, 2pi] Enter the solutions in increasing order. cosine of 2x = cosine of x
The solutions in the interval [0, 2) are:
x = 0 and x = 2π/3.
What is the trigonometric ratio?
The trigonometric functions are real functions that relate an angle of a right-angled triangle to ratios of two side lengths. They are widely used in all sciences that are related to geometry, such as navigation, solid mechanics, celestial mechanics, geodesy, and many others.
Using the identity cos2θ = cos²θ - sin²θ, we can rewrite the equation as:
cos²x - sin²x = cos x
We can then use the Pythagorean identity sin² x + cos² x = 1 to substitute for sin² x:
cos²x - (1 - cos²x) = cos x
Simplifying this equation gives:
2cos² x - cos x - 1 = 0
We can solve for cos x using the quadratic formula:
cos x = [1 ± √(1 + 8)] / 4
cos x = [1 ± √9] / 4
cos x = (1 ± 3) / 4
cos x = 1 or cos x = -1/2
If cos x = 1, then x = 0.
If cos x = -1/2, then x = 2π/3 or x = 4π/3.
However, we need to check that these solutions are in the interval [0, 2). The solution x = 4π/3 is outside this interval, so we discard it.
Therefore, the solutions in the interval [0, 2) are:
x = 0 and x = 2π/3.
In increasing order, the solutions are:
x = 0 and x = 2π/3.
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Need help with the first 4 problems
Answer:
1) ABE is NOT SIMILAR to DBC
2) FPG is SIMILAR to FGH (AAA)
3) CAN is SIMILAR to HLV (SAS)
4) QRP is SIMILAR to XYP (SSS)
Step-by-step explanation:
1) ABE is NOT SIMILAR to DBC
Since DC and AE are not parallel
2) FPG is SIMILAR to FGH (AAA)
QPF = 180 - 93
QPF = 87
PQF = 180 - 63 - 87
PQF = 30
PQF = GHF
FGH = 180 - 63 - 30
FGH = 87
FGH = QPF
GFH = PFQ
3) CAN is SIMILAR to HLV (SAS)
63 = [tex]x[/tex] x 42
[tex]x[/tex] = 1.5
51 = [tex]x[/tex] x 34
51 = 1.5 x 34
51 = 51
Hypotenuse of CAN = 1.5 x Hypotenuse of HLV
4) QRP is SIMILAR to XYP (SSS)
10 = [tex]x[/tex] x 8
[tex]x[/tex] = 1.25
(20 + 5) = 1.25 x XY
XY = 20
(24 + 6) = 1.25 x XP
XP = 24
which point is the vertex of the quadratic function f(x)=x^2-6x+8
Answer:
(3, -1).
Step-by-step explanation:
f(x)=x^2-6x+8
Convert to vertex form by completing the square:
f(x) = (x - 3)^2 - 9 + 8
= (x - 3)^2 -1
So the vertex is at (3, -1).
graph the inequality on a number line.
Answer:
you would put a solid circle on the 3 and go to the left, for example:
Step-by-step explanation:
You would want the variable to be on the left, so you would need to see that the 3 is bigger or equal to a.
I need Helpppp my teacher sucks at teaching
Answer: 10
Step-by-step explanation:
Adjacent angles in a parallelogram are supplementary (add up to 180), so we know that the unknown angle equals 100°, since the adjacent angle equals 80°.
So, we can set up an equation:
[tex]11x-10=100\\11x=110\\x=10[/tex]
how can i do (56 4/5+1 1/6) +1 1/3
Answer:
1789/30
Step-by-step explanation:
To solve the expression
You have to convert the mixed fraction => improper:
(284/5 + 7/6) + 4/3
After that add:
1749/30 + 4/3
Add:
1789/30
A rectangular house is 43 yards wide and 127 yards long. What is its perimeter?
Examine the following typical corporate bond listing: A 5-column table with 1 row. Column 1 is labeled Bonds with entry N Y Tel 7 and one-fourth 33. Column 2 is labeled current yield with entry 6.9. Column 3 is labeled Volume with entry 18. Column 4 is labeled Close with entry 101 and three-fourths. Column 5 is labeled net change with entry negative startFraction 1 Over 8 EndFraction. In the name column, NYTel is the abbreviated name of the company (New York Telephone) issuing the bond. What was the closing price of the bond? What was the dollar amount? a. 101Three-fourths; $101,750 b. 7One-fourth; $7250 c. 101Three-fourths; $1017.50 d. 107One-fourth; $1072.50
This bond has a Current yield of 6.9 percent, a volume of 18, and a net change of negative one-eighth. The correct answer is (a) 101Three-fourths; $101,750.
The bond listing provided is a typical example of how Corporate bonds are displayed. The table consists of 5 columns with 1 row, where each column provides specific information about the bond.
The first column displays the name of the bond, which in this case is NYTel 7 and one-fourth 33, indicating that it is a bond issued by New York Telephone.
The second column shows the current yield of the bond, which is 6.9 percent.
The third column displays the volume of the bond, which is 18.
The fourth column provides the closing price of the bond, which is 101 and three-fourths.
Finally, the fifth column shows the net change of the bond, which is negative one-eighth.
To answer the question, we need to determine the closing price and dollar amount of the bond. According to the bond listing, the closing price of the bond is 101 and three-fourths. To calculate the dollar amount, we need to multiply the closing price by the face value of the bond. Assuming that the face value of the bond is $1,000, the dollar amount of the bond would be $101,750 (101.75 x 1000).
Therefore, the correct answer is (a) 101Three-fourths; $101,750. This bond has a current yield of 6.9 percent, a volume of 18, and a net change of negative one-eighth. Understanding how to read and interpret bond listings is crucial for investors who want to make informed investment decisions.
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Fifteen students purchase lunch at the restaurant for $1.75 each. Another 15 purchase the same snack at the restaurant, but the cost is unknown. Together, the cost of all the food is $35.55.
Write an equation that can be used to find the price of each snack, x. Solve for x.
After answering the presented question, we can conclude that equation Therefore, the price of each snack is $0.62.
What is equation?An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x Plus 3" equals the value "9." The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. The variable x is raised to the second power in the equation "x2 + 2x - 3 = 0." Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.
price of each snack x.
15 × $1.75 = $26.25
cost of snacks for the other fifteen students
$26.25 + 15x = $35.55
15x = $35.55 - $26.25
15x = $9.30
x = $0.62
Therefore, the price of each snack is $0.62.
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data was collected for 300 fish from the north atlantic. the length of the fish (in mm) is summarized in the gfdt below. what is the lower class boundary for the first class? class boundary of a frequency table
The lower class boundary for the first class is 122.5.
Data was collected for 300 fish from the North Atlantic.
The length of the fish (in mm) is summarized in the GFDT below.
| Length (mm) | Frequency | 123 - 145 | 34 | 146 - 168 | 89 | 169 - 191 | 107 | 192 - 214 | 44 |
The class boundaries for a frequency table are calculated by taking the lower limit of one class and subtracting 0.5
from it to find the lower class boundary, and taking the upper limit of the previous class and adding 0.5 to it to find the
upper class boundary.
For the first class, the lower limit is 123 and the upper limit is 145. So the lower class boundary is:123 - 0.5 = 122.5
Therefore, the lower class boundary for the first class is 122.5.
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HELP PLEASE!!!
A bakery makes cylindrical mini muffins that measure 2 inches in diameter and one and one fourth inches in height. If each mini muffin is completely wrapped in paper, then at least how much paper is needed to wrap 6 mini muffins? Approximate using pi equals 22 over 7.
A- 14 and 1 over 7 in2
B -23 and 4 over 7 in2
C -47 and 1 over 7 in2
D - 84 and 6 over 7 in2
A,B,C,D which one
Hence, it takes 23 and 4 over 7 in² of paper's surface area to wrap six cylindrical mini muffins.
Describe the cylinder's shape:A cylinder is only a three-dimensional shape in geometry. A cylinder has a cylinder-like form and a top and bottom that are shaped like circles. Both the top and bottom are flat and of the same size. I think the simplest way to visualise a cylinder's shape is to think of a soup can.
Given data:
Height of mini muffins 1 ¹/₄ = 5/4 in = 1.25 inDiameter d = 2 inRadius r = 2/2 = 1 in.surface area of total 6 number of cylindrical mini muffins:
S = 6*(π*r²*h)
S = 6* (22/7 * 1² * 1.25)
S = 23.55 in²
S = 23 ⁴/₇ in²
Hence, it takes 23 and 4 over 7 in² of paper's surface area to wrap six cylindrical mini muffins.
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This data gives the average number of hours different students spend on the computer each day.
Average time (h): 1.6, 2.0, 2.0, 2.0, 1.8, 1.8, 1.5, 2.0, 1.9, 1.6, 1.9, 1.7, 1.6, 1.6, 2.0, 1.8, 1.5, 2.0
Create a line plot to display this data.
To create a line plot, hover over each number on the number line. Then click and drag up to plot the data.
Students Weekly Computer Time
To display this data on a line plot, we need to create a number line with a range of values from 1.4 to 2.0 with intervals of 0.1.
Then, we can plot each data point by hovering over the corresponding number on the number line and clicking and dragging up to the corresponding value.
The line plot will show a visual representation of the data, with each point representing the average time spent on the computer each day by a different student.
The line connecting the points will show the trend of the data and can be used to make inferences about the overall behavior of the students in terms of their computer usage.
In conclusion, the line plot for the given data on the average number of hours different students spend on the computer each day will show the student's weekly computer time and provide insight into their computer usage patterns.
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GEOMETRY PLS HELP ASAP
Answer:
C) 56
Step-by-step explanation:
2(AE) = BD
AC = BD
2(2x + 6) = 6x - 10
4x + 12 = 6x - 10
-2x = -22
x = -22/-2 = 11
AC = 6(11) - 10 = 56
I need help i DONT understand
Can someone HELPPPP ME PLEASEEEE
Answer:find the root of 6
Step-by-step explanation:
if the sample results show that 36 of the workers belonged to unions, what is the p-value for your hypothesis test? find the value of the test statistic. (round your answer to two decimal places.)
The test statistic is z = 0.68, and the p-value is approximately 0.2486.
This problem involves testing the hypothesis that the proportion of union workers in the population has increased from 11.5%.
Let p be the true proportion of union workers in the population.
The null hypothesis is H0: p = 0.115, and the alternative hypothesis is Ha: p > 0.115 (one-tailed test, since we are testing for an increase in union membership).
To find the test statistic, we use the formula for a z-test for proportions:
z = ([tex]\bar p[/tex] - p) / [tex]\sqrt{(p(1-p)/n) }[/tex]
where, [tex]\bar p[/tex] is the sample proportion, n is the sample size, and sqrt denotes the square root function.
In this case, [tex]\bar p[/tex] = 36/300 = 0.12, n = 300, and p = 0.115.
Substituting these values into the formula, we get:
z = (0.12 - 0.115) / [tex]\sqrt{(0.115(1-0.115)/300) }[/tex]≈ 0.68
To find the p-value, we need to find the probability of getting a test statistic as extreme or more extreme than 0.68, assuming that the null hypothesis is true (i.e., assuming that p = 0.115).
Since this is a one-tailed test, we need to find the area under the standard normal curve to the right of 0.68:
p-value = P(Z > 0.68) ≈ 0.2486
Using a standard normal distribution table or a calculator, we find that the area to the right of 0.68 is approximately 0.2486.
Therefore, the p-value for the test is approximately 0.2486.
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Question: You may need to use the appropriate appendix table or technology to answer this question. An agency reports that historically 11.5% of workers in a particular country belong to unions. Suppose a sample of 300 workers is collected to determine whether union efforts to organize have increased union membership. If the sample results show that 36 of the workers belonged to unions, what is the p-value for your hypothesis test? Find the value of the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to four decimal places.) p-value = ?
A summary of two stocks is shown.
52W high 52W low Name of Stock Symbol High Low Close
37.18 29.39 Zycodec ZYO 39.06 32.73 34.95
11.76 7.89 Unix Co UNX 16.12 12.11 15.78
Last year, a stockholder purchased 40 shares of Zycodec at its lowest price of the year and purchased 95 shares of Unix at its highest price of the year. If the stockholder sold all shares of both stocks at their respective closing price, what was the overall gain or loss?
Answer:
The gain is 139.
Step-by-step explanation:
34.95x25= 873.75
29.39x25= 734.75
873.75- 734.75= 139
MANY POINTS, PLEASE HELP ME
Given: ABCD is a trapezoid
Segments BA & CO are congruent
Prove: segment BD is congruent CA
Assemble the proof by dragging tiles to
the Statements and Reasons
Please send full proof chart, or picture of completed proof chart. The assignment is found on edguinty or other school platforms and is a multiple step answer. Will mark brianlist and give points
Angles:
Triangles:
BAD
CDA
Statements:
ABCD is a trapezoid
ABCD is an isosceles trapezoid
Reasons:
Given
Base angles theorem
Reflective property
def. if isosceles trapezoid
Therefore, segment BD is congruent to segment CA, as required.
What is trapezoid?A trapezoid is a quadrilateral with at least one pair of parallel sides. In this case, we are given that AB is parallel to CD. The base angles theorem states that the base angles of an isosceles trapezoid are congruent. Since AB and CD are congruent (as given by the reflective property of congruence), the opposite angles formed by the intersecting lines BA and CD (i.e., ∠BAD and ∠CDA) are congruent as well. This establishes that ABCD is an isosceles trapezoid. An isosceles trapezoid has two pairs of congruent sides: AB = CD and AC = BD. Since BA and CO are congruent (as given), we can conclude that AC and BD are congruent as well (by the isosceles trapezoid definition). Finally, the symmetric property of congruence allows us to state that BD is congruent to CA.
Here,
given that ABCD is a trapezoid and segments BA and CO are congruent:
Statements | Reasons
ABCD is a trapezoid | Given
AB || CD | Definition of a trapezoid
∠BAD ≅ ∠CDA | Base angles theorem
AB ≅ CD | Reflective property of congruence
BA ≅ CO | Given
AC ≅ BD | Isosceles trapezoid definition
BD ≅ CA | Symmetric property of congruence
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Write an inequality for the graph below.
In Mathematics, the relationship between two values which are not equal is expressed by inequalities. The equation of inequality for the given graph is y ≥ -1/2x + 2.
Define inequalities.In mathematics, an inequality is a relationship in which two numbers or other mathematical expressions compare unequal. Most commonly used to compare two numbers on the number line based on size. There are different notations used to represent different types of inequalities.
The notation a < b means that b is greater than a.The notation a > b means that a is greater than b.In both the cases a is not equal to b and such relationships are known as strict inequalities. This means that a is either strictly less than or greater than b. Equivalents are excluded whereas in inexact inequalities.
The notation a ≤ b or a ⩽ b means that a is less than or equal to b (or equivalently at most b or less than or equal to b).The notation a ≥ b or a ⩾ b means that a is greater than or equal to b (or equivalently at least greater than or equal to b or b).For the given graph:
take run = 1 and rise = -1/2
Thus, the slope will be,
Slope = (⁻¹/₂)/1
Slope = -1/2
Since, the y intercept is 2. Then the equation is y = -1/2x + 2
Take point (1,2) on the graph and apply in the equation:
y = -1/2x + 2
2 = -1/2 (1) + 2
2 = -1/2 + 2
2 = 3/2
As, 2 > 3/2. We can replace the = sign into ≥.
So, the eq inequality equation is y ≥ -1/2x + 2.
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3 √5 + 3 √5
I need help adding this please
The answer is 6√5
In 3√5 and 3√5, √5 is multiplied with 3 in both terms,
∴ 3 is the common factor
∴ 3√5+3√5= 3(√5+√5)
= 3×2√5
= 6√5
Hence the answer is 6√5
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consider the following: which statement is true? question 1 options: this is not a function because some of the elements in the range are not associated with any element in the domain. this is a function. this is not a function because some of the elements in the domain are mapped onto the same element in the range. this is not a function because some elements in the domain have multiple elements in the range associated with it.
The true statement is B. This is a function.
In order to be considered a function, each element in the domain must be associated with exactly one element in the range. As long as every element in the domain is mapped to one and only one element in the range, it is a function. Option A is incorrect because a function does not require every element in the range to be associated with an element in the domain. There can be unused elements in the range without affecting the status of a function.
Option C is also incorrect because having elements in the domain mapped onto the same element in the range does not disqualify it from being a function. Multiple elements in the domain can share a single element in the range, and it will still be a function as long as each domain element is paired with only one range element. Finally, option D is incorrect because if an element in the domain has multiple elements in the range associated with it, then it would not be a function. However, the correct statement, option B, already indicates that this is a function, so option D is not true for the given question.
In conclusion, the statement "this is a function" is true, as long as each element in the domain has exactly one associated element in the range. Therefore, the correct option is B.
The question was incomplete, Find the full content below:
consider the following: which statement is true? question 1 options:
A. this is not a function because some of the elements in the range are not associated with any element in the domain.
B. this is a function.
C. this is not a function because some of the elements in the domain are mapped onto the same element in the range.
D. this is not a function because some elements in the domain have multiple elements in the range associated with it.
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The box plots display measures from data collected when 20 people were asked about their wait time at a drive-thru restaurant window.
A horizontal line starting at 0, with tick marks every one-half unit up to 32. The line is labeled Wait Time In Minutes. The box extends from 10 to 14.5 on the number line. A line in the box is at 12.5. The lines outside the box end at 5 and 20. The graph is titled Fast Chicken.
A horizontal line starting at 0, with tick marks every one-half unit up to 32. The line is labeled Wait Time In Minutes. The box extends from 8.5 to 15.5 on the number line. A line in the box is at 12. The lines outside the box end at 3 and 27. The graph is titled Super Fast Food
Which drive-thru typically has more wait time, and why?
Fast Chicken, because it has a large
r median
Fast Chicken, because it has a larger mean
Super Fast Food, because it has a larger median
Super Fast Food, because it has a larger mean
Super Fast Food typically has more wait time because its box plot shows a larger range, with the minimum at 3 and the maximum at 27, compared to the Fast Chicken box plot with a minimum at 5 and a maximum at 20. Additionally, the median of Super Fast Food is 12, compared to the median of Fast Chicken at 12.5. This suggests that the middle value of the data for Super Fast Food is lower than that of Fast Chicken, indicating that Super Fast Food typically has shorter wait times. Therefore, the correct answer is "Super Fast Food, because it has a larger median."
#1) A scuba diver ascended at a rate of 8ft per second for one minute. What was the elevation over that period of time
#2) A gopher dug a burrow 6ft below ground. He came up 2ft to find food, then dug back down another 8ft. How many feet below ground is he?
Answer:
1. 480ft
2. 12ft below the ground
Step-by-step explanation:
1. 80 × 60 = 480
2. 0 - 6 + 2 - 8 = -12
In how many places does the graph of f(x) = x4 + 10x3 + 24x2 cross or touch the horizontal axis?
Answer: 3 times
Step-by-step explanation:
Setting up the equation
If the function touches the horizontal axis, that means y=0, or f(x)=0 at that point(s).
So, we set our equation equal to 0
[tex]0=x^4+10x^3+24x^2\\[/tex]
Factor out x^2
[tex]0=x^2(x^2+10x+24)[/tex]
So, either [tex]x^2[/tex] or [tex](x^2+10x+24)[/tex] must equal zero
Factoring
[tex]x^2+10x+24=0\\(x+6)(x+4)=0\\[/tex]
x=-6 or x=-4
from before, [tex]x^2 = 0\\x=0[/tex]
So, f(x) equals zero at 3 places, when x=0, when x=-6, and when x=-4