Answers
Answer: D) square root 49
Step-by-step explanation: a rational number is a number that eventually ends. Square root 49 is the answer, because it terminates.
Related Questions
How do you write an equation in standard form for a line that passes through (-5, 2) and (1, -2)?
Answers
In response to the query, we can state that Hence, 2x + 3y = -4 is the equation equation of the line in standard form.
What is equation?An equation is a mathematical statement that proves the equality of two expressions connected by an equal sign '='. For instance, 2x – 5 = 13. Expressions include 2x-5 and 13. '=' is the character that links the two expressions. A mathematical formula that has two algebraic expressions on either side of an equal sign (=) is known as an equation. It depicts the equivalency relationship between the left and right formulas. L.H.S. = R.H.S. (left side = right side) in any formula.
y - y1 = m(x - x1) (x - x1)
where m is the slope of the line and (x1, y1) is one of the line's points.
With the two provided locations, we can first determine the slope of the line:
m = (y2 - y1)/(x2 - x1) = (-2 - 2)/(1 - (-5)) = -4/6 = -2/3
Let's utilise the point-slope form with one of the given points, (-5, 2):
y - 2 = (-2/3)(x - (-5))
y - 2 = (-2/3)x - 10/3
When we multiply both sides by 3, we obtain:
3y - 6 = -2x - 10
2x + 3y = -4
Hence, 2x + 3y = -4 is the equation of the line in standard form.
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How to multiply a exponent with diferent bases
Answers
you can multiply the two bases together and then raise the product to the sum of the exponents.
When you have two exponential expressions with different bases and want to multiply them together, you cannot directly multiply the bases together.
An exponent is a mathematical notation that indicates the number of times a number, variable, or expression is multiplied by itself. It is usually written as a superscript to the right of the base number, as in "[tex]a^b[/tex]", where "a" is the base and "b" is the exponent.
The exponent "b" tells us how many times the base "a" should be multiplied by itself. For example, in the expression 2c, the base is 2, and the exponent is 3. This means that we need to multiply 2 by itself three times, resulting in 2 × 2 × 2 = 8.
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can yall help me again im sorry!!!
Answers
Answer:
30%
Step-by-step explanation:
156/120 =1.3 =130%-100
1) You are at (-4, 3). You move 2 units up and 6 units right. Where do you land?
Answers
Given a starting point of (-4, 3), if move 2 units up and 6 units right, you will end up at the point (2,5).
You are at (-4, 3). You move 2 units up and 6 units right. Where do you land?A point in a coordinate system has two coordinates - an x-coordinate and a y-coordinate.
The x-coordinate tells you how far to move horizontally from the origin (0,0), and the y-coordinate tells you how far to move vertically from the origin.
Given the point (-4,3) means that you start at the point that is 4 units to the left of the origin and 3 units above the origin.
Now, moving 2 units up from (-4,3), you will end up at the point that is 2 units higher on the y-axis.
So, your new y-coordinate will be 3 + 2 = 5.
When you move 6 units right from (-4,3), you will end up at the point that is 6 units to the right on the x-axis.
So, your new x-coordinate will be -4 + 6 = 2.
Therefore, you end up at the point (2,5).
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Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options. x2 + (y – 3)2 = 36 x2 + (y – 5)2 = 6 (x – 4)² + y² = 36 (x + 6)² + y² = 144 x2 + (y + 8)2 = 36
Answers
The correct options are:
x² + (y-6)² = 36
x² + (y+8)² = 36
How does diameter work?
the distance that a straight line must travel in order to connect two points on opposite edges of a circular object or shape The diameter is twice as large as the radius. The pond's circumference is six feet.
Since the circle's centre is on the y-axis, its x-coordinate is zero. Moreover, the circle's radius is 6 units because its diameter is 12 units.
As a result, the equations that depict circles with a centre on the y-axis and a diameter of 12 units are as follows:
(x-0)² + (y-h)² = r², where h is the y-coordinate of the center and r is the radius of the circle.
(x-0)² + (y-k)² = r², where k is the y-coordinate of the center and r is the radius of the circle.
2 = r2, where k is the circle's center's y-coordinate and r is its radius.
We can see from these equations that circles with a diameter of 12 units and a centre on the y-axis are represented by the following equations:
x² + (y-6)² = 36 (center at (0,6))
x² + (y+6)² = 36 (center at (0,-6))
As a result, the following choices depict circles that satisfy these requirements:
x² + (y-6)² = 36
x² + (y+8)² = 36
The appropriate choices are thus:
x² + (y-6)² = 36
x² + (y+8)² = 36
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Four times a number is greater than -48. Define a variable, write an inequality, and solve the problem.
Answers
Answer:
n is greater than negative 12
Step-by-step explanation:
I put the answer on the attached please see it
can you guys and girls help me
Answers
Alex does not have enough strawberries to make fruit salad and jam.
What are mixed fractions?A mixed fraction is a fraction that is created by fusing a fraction with a whole number.
An improper fraction is a fraction that cannot be further simplified and has a numerator higher than or equal to the denominator. For instance, 13/5 is a bad fraction. Let's find the mixed fraction equivalent of this incorrect fraction. Divide the denominator by the numerator in step 1. Step 2: Track down the rest. In step 3, arrange the numbers as follows: quotient, followed by a portion of the remainder or divisor.
Given that, Alex wants to use 1 3/4 and 3 1/2 cups of strawberries.
Thus the total strawberries are:
1 3/4 + 3 1/2
= 7/4 + 7/2
Taking LCM we have:
= 21/4 = 5.2 cups
Hence, Alex does not have enough strawberries to make fruit salad and jam.
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Please Help
In this unit, you’re factoring a variety of polynomials. But not all polynomials can be factored! Here are some examples: x squared minus 6 x minus 5 x squared plus 4 3 x squared plus 2 x plus 1 x cubed plus 2 x squared plus 2 x plus 3 We might say that these polynomials cannot be factored further, or that they are completely factored. This means the expressions cannot be rewritten as the product of two or more quantities that divide them exactly. In this discussion, you’ll work with your classmates to examine some more examples of this. In your first post, write a polynomial that cannot be factored further. Explain in detail how you know it can’t be factored further. Describe the factoring techniques that might work with this polynomial, and show why they don’t work. Please follow these guidelines for your discussion posts: Write at least 150–300 words. Make sure your posts are grammatically and mechanically correct. Address all parts of the prompt. Provide at least one example to support your response. (Example choices include an anecdote, statistic, and/or textual evidence.)
Answers
x = (-b ± sqrt(b^2 - 4ac)) / 2a
where a, b, and c are the coefficients of the quadratic polynomial (ax^2 + bx + c). In this case, a = 1, b = 0, and c = 2. Substituting these values into the formula, we get:
x = (-0 ± sqrt(0^2 - 4(1)(2))) / 2(1)
x = ±sqrt(-8)/2
Since the square root of a negative number is not a real number, we can conclude that x^2 + 2 cannot be factored further using real numbers. This is because the solutions to the quadratic equation are imaginary.
As for factoring techniques that might work with this polynomial, we can try factoring by grouping or factoring using the difference of squares formula. However, both of these techniques do not work for this polynomial since it cannot be expressed as the product of two or more quantities that divide it exactly.
In conclusion, x^2 + 2 is a polynomial that cannot be factored further using real numbers, and this is because the solutions to the quadratic equation are imaginary. Factoring by grouping and factoring using the difference of squares formula do not work for this polynomial since it cannot be expressed as the product of two or more quantities that divide it exactly.
One group of 40 students has a mean score 75in exam.A second group of 50 students has a mean score of 60.A third group of 30 students has a mean score of 85.Find the mean of all 120 stidents
Answers
Answer:73
Step-by-step explanation:
add 75 + 60 + 85 = 220
then divide to divide you need to find how much times you added then divide by 220 so 75 + 60 + 85 which is 3 times so you divide 220 by 3 and you get 73.33333333333333 or 73
Need help with this question please
Answers
Answer: 22
Step-by-step explanation:
perimeter = a+b+c+d
84 = 4x+4x+(4x+2)+(4x+2)
84 = 16x + 4
80 = 16x
5 = x
length:
=4x+2
=4(5)+2
=22
Find the sum of the geometric series 3 + (-6) + ... + 768
Answers
The sum of the geometric series is 513.
EquationsTo find the sum of a geometric series, we use the formula:
S_n = a[tex](1-r^{n})[/tex] / (1 - r)
where S is the sum of the first n terms, a is the first term, r is the common ratio, and n is the number of terms.
In this case, we know that the first term is 3, and the common ratio is -2. To find the number of terms, we need to determine what value of n satisfies the equation:
768 = 3 x [tex](-2^{n-1} )[/tex]
We can simplify this equation by dividing both sides by 3:
256 = [tex](-2^{n-1} )[/tex]
Taking the logarithm of both sides (to base 2), we get:
n - 1 = [tex]log_{2}[/tex](256)
n - 1 = 8
n = 9
Therefore, there are 9 terms in the series for this question.
Using the formula for the sum of a geometric series, we have:
S = 3(1 - [tex](-2^{9} )[/tex] / (1 - (-2))
S = 3(1 - (-512)) / 3
S = 3(513) / 3
S = 513
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Wyatt bought stock in a company two years ago that was worth x dollars. During the
first year that he owned the stock, it increased by 37%. During the second year the
value of the stock increased by 29%. Write an expression in terms of a that
represents the value of the stock after the two years have passed.
x
A
Answer:
Answers
Therefore, the expression that represents the value of the stock after the two years have passed in terms of x is:
A = 1.7673x
How precisely are stocks chosen?By dividing the number of shares they possess by the total number of outstanding shares and multiplying the result by 100, stockholders can calculate their ownership stake in a corporation.
After the first year, the value of the stock increased to:
x + 0.37x = 1.37x
After the second year, the value of the stock increased to:
1.37x + 0.29(1.37x) = 1.37x + 0.3973x = 1.7673x
Therefore, the expression that represents the value of the stock after the two years have passed in terms of x is:
A = 1.7673x
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Marques wants to use a sheet of fiberboard 36 inches long to create a skateboard ramp with a 30^{\circ}
∘
angle of elevation from the ground. How high will the ramp rise from the ground at its highest end? Round your answer to the nearest tenth of an inch if necessary.
Answers
The ramp will rise 20.79 inches from the ground at its highest end.
What is Algebraic expression ?
Algebraic expression can be defined as combination of variables and constants.
Let's assume that the ramp will be in the shape of a right triangle, where the length of the base (the horizontal distance from the ground to the highest end of the ramp) is 36 inches and the angle between the base and the hypotenuse (the ramp itself) is 30 degrees.
We can use trigonometry to find the height of the ramp (the vertical distance from the ground to the highest end of the ramp).
First, we need to find the length of the hypotenuse. We can use the formula:
hypotenuse = base / cosine(angle)
In this case, the base is 36 inches and the angle is 30 degrees, so:
hypotenuse = 36 / cosine(30) = 41.57 inches (rounded to the nearest hundredth)
Next, we can use the formula for the sine of an angle:
sine(angle) = opposite / hypotenuse
In this case, the opposite side (the height of the ramp) is what we want to find. So we can rearrange the formula to solve for the height:
height = sine(angle) x hypotenuse
Plugging in the values we know, we get:
height = sine(30) x 41.57 = 20.79 inches (rounded to the nearest hundredth)
Therefore, the ramp will rise 20.79 inches from the ground at its highest end.
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ion using long division or synthetic division. ks on the back to complete the story. (x^(4)+x^(3)-8x^(2)-13x-7)-:(x+2)
Answers
Using synthetic division, you can solve the following equation: (x^(4)+x^(3)-8x^(2)-13x-7)-:(x+2).
Step 1: Write down the coefficients of the polynomial in the top row of the synthetic division table.
x^(4) x^(3) -8x^(2) -13x -7
Step 2: Write the divisor in the left-most column.
x+2
Step 3: Bring down the first coefficient of the dividend and write it in the second row of the table.
x^(4) x^(3) -8x^(2) -13x -7 | x+2
x^(3) -8x^(2) -13x -7
Step 4: Multiply the divisor by the number in the second row and write it in the third row.
x^(4) x^(3) -8x^(2) -13x -7 | x+2
x^(3) -8x^(2) -13x -7 | x+2
x^(2) -15x -19
Step 5: Subtract the third row from the second row and write it in the fourth row.
x^(4) x^(3) -8x^(2) -13x -7 | x+2
x^(3) -8x^(2) -13x -7 | x+2
x^(2) -15x -19 | x+2
-7x -26
Step 6: Bring down the next coefficient in the first row and repeat steps 4 and 5.
x^(4) x^(3) -8x^(2) -13x -7 | x+2
x^(3) -8x^(2) -13x -7 | x+2
x^(2) -15x -19 | x+2
-7x -26 | -7
-22
Step 7: Multiply the divisor by the number in the fourth row and write it in the fifth row.
x^(4) x^(3) -8x^(2) -13x -7 | x+2
x^(3) -8x^(2) -13x -7 | x+2
x^(2) -15x -19 | x+2
-7x -26 | -7
-22 | -14
Step 8: Subtract the fifth row from the fourth row and write it in the sixth row.
x^(4) x^(3) -8x^(2) -13x -7 | x+2
x^(3) -8x^(2) -13x -7 | x+2
x^(2) -15x -19 | x+2
-7x -26 | -7
-22 | -14
8
Step 9: The final answer is: (x^(4)+x^(3)-8x^(2)-13x-7)/(x+2) = x^3-7x^2-15x-26 + 8/(x+2).
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Can u work out Q1 & Q2 out?
I need an answer as quick as possible.
Answers
A. (√6)^2×(√2)^2=
{(6)^1/2×2}×{2^1/2×2}=
6^1×2^1=
6×2=12
B. (3√3^3)×(√12^2)=
(3√27)×(√144)=
3×12=36
for a tetrahedron abcd a plane p is called a middle plane if all four distances from the vertices a, b, c and d to the plane p are the same. how many middle planes are there for a given tetrahedron?
Answers
There are no middle planes for a given tetrahedron. This is because a tetrahedron is a three-dimensional figure with four faces, each of which is a triangle. Each of the four vertices of a tetrahedron is equidistant from one of the faces, but not from any of the other three faces. Therefore, there are no planes that are equidistant from all four vertices of a tetrahedron.
To further explain, let's consider the four distances from the vertices A, B, C, and D to a plane P. If all four distances are the same, then the plane P must be equidistant from all four vertices. However, this is not possible in a tetrahedron because each vertex is closer to one face than it is to the other three faces. Therefore, there are no middle planes in a tetrahedron.
In conclusion, there are no middle planes for a given tetrahedron because each vertex is closer to one face than it is to the other three faces.
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mp of a book is rs. 250 if the shopkeeper allows 14% discount to his customers and gains 25% . find the cp.
Answers
The cost price that was used to get the book is: R.S 172
How to find the cost price?The parameters given are:
Marked Price: M.P = RS. 250
Discount allowed = 10%
The formula to find the selling price here will be:
S.P = M.P * (100 - Discount)/100
Thus:
S.P = 250 * (100 - 14)/100
S.P = 250 * 0.86
S.P = R.S 215
Since the profit is 25%, then we have:
Cost Price = (S.P * 100)/(100 + Gain%)
Cost price = (215 * 100)/(100 + 25)
Cost Price = 21500/125
Cost price = R.S 172
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i need help asap please
Answers
Answer:
no question is there for me to answer
Step-by-step explanation:
(6×100+33)/100
=633/100
=6.33
Using Pythagoras' theorem, calculate the length of the hypotenuse in this right- angled triangle. Give your answer in centimetres (cm) to 1 d.p. 2 cm 1.5 cm
Answers
Answer:
2.5 cm
Step-by-step explanation:
In any right triangle, the formula [tex]a^2+b^2=c^2[/tex] can be used to find its side lengths.
Given the side lengths,
[tex]a = 2 \\b = 1.5\\\\2^2+1.5^2=c^2\\4+2.25=c^2\\6.25=c^2\\c=\sqrt{6.25}\\c=2.5[/tex]
Compare the functions f(x) and g(x) and choose the correct statement.
f(x)=3x-2
1. They are the same function.
2. f(x) has a greater y-intercept than g(x).
3. g(x) has a steeper slope than f(x).
4. f(x) has a steeper slope than g(x).
Answers
Answering the question, we may state that incorrect. In conclusion, none of the claims are true based function on the facts provided.
what is function?Mathematicians investigate the relationships between numbers, equations, and related structures, as well as the locations of forms and possible placements for these items. A set of inputs and their corresponding outputs are referred to as a "function" in this context. If each input results in a single, unique output, the relationship between the inputs and outputs is known as a function. Each function has its own domain, codomain, or scope. A common way to denote functions is with the letter f. (x). is an x for entry. One-to-one capabilities, so multiple capabilities, in capabilities, and on functions are the four main categories of accessible functions.
It is difficult to compare g(x) with f(x) and establish whether they are the same function or not since g(x) is not provided. Option 1 is thus incorrect.
Setting x = 0 and figuring out y will reveal the y-intercept of f(x). Hence, f(0) = 3(0) - 2 = -2. This indicates that f(xy-intercept )'s is -2. No details are provided on the y-intercept of g. (x).
It is impossible to tell if f(x) has a sharper slope than g because f(x) has a slope of 3 and g(xslope )'s is unknown (x). As a result, choice 4 is also incorrect.
In conclusion, none of the claims are true based on the facts provided.
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I need some help please
Answers
The solution to the inequality is [tex]$x\in\left(-\infty,\frac{4}{3}\right]\cup\left[\frac{4}{3},\infty\right)$.[/tex]
What is inequality?
In mathematics, an inequality is a statement that one value or expression is greater than, less than, greater than or equal to, or less than or equal to another value.
The given inequality is
[tex]|\frac{1}{4}x-\frac{1}{3}|\leq \frac{1}{3}[/tex]
To solve the inequality
[tex]$|\frac{1}{4}x-\frac{1}{3}|\leq \frac{1}{3}$,[/tex]
we need to consider two cases:
Case 1:
[tex]\frac{1}{4}x-\frac{1}{3}\geq 0$[/tex],
which gives
[tex]$\frac{1}{4}x\geq\frac{1}{3}$[/tex] or
[tex]$x\geq\frac{4}{3}$.[/tex]
Substituting this value of x in the inequality, we get:
[tex]$$\left|\frac{1}{4}\cdot\frac{4}{3}-\frac{1}{3}\right|\leq\frac{1}{3}$$[/tex]
Simplifying, we get [tex]$\frac{1}{3}\leq\frac{1}{3}$[/tex], which is true.
Case 2: [tex]$\frac{1}{4}x-\frac{1}{3} < 0$[/tex], which gives [tex]$\frac{1}{4}x < \frac{1}{3}$[/tex] or [tex]$x < \frac{4}{3}$[/tex].
Substituting this value of x in the inequality, we get:
[tex]$$\left|\frac{1}{4}\cdot\frac{4}{3}-\frac{1}{3}\right|\leq\frac{1}{3}$$[/tex]
Simplifying, we get [tex]$\frac{1}{3}\leq\frac{1}{3}$[/tex], which is true.
Therefore, the solution to the inequality is [tex]$x\in\left(-\infty,\frac{4}{3}\right]\cup\left[\frac{4}{3},\infty\right)$.[/tex]
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Add 450 to 348, and then multiply by 7. 450 + 348 × 7
(450 + 348) × 7
450 × 7 + 348
450 × (7 + 348)
Answers
The correct expression for the mathematical statement "Add 450 to 348, and then multiply by 7." is (450 + 348) × 7 , the correct option is (b).
An Algebraic Expression is defined as a mathematical phrase which contains one or more variables, numbers, and are joined by mathematical operators such as addition, subtraction, multiplication, and division.
The expression for the mathematical statement "Add 450 to 348, and then multiply by 7" is represented in ,option (b) (450 + 348) × 7 ;
Let the statement be read in two parts,
First "Add 450 to 348", which means we add 450 and 348 together, which is represented as "450+348";
In second part ,we "Multiply by 7", which means we multiply result in first part by 7.
Putting it all together, we get:
⇒ (450 + 348) × 7
Therefore , the correct Algebraic Expression is (b) (450 + 348) × 7.
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The given question is incomplete, the complete question is
Select the correct expression for the given mathematical statement. "Add 450 to 348, and then multiply by 7."
(a) 450 + 348 × 7
(b) (450 + 348) × 7
(c) 450 × 7 + 348
(d) 450 × (7 + 348)
What is the longest flagpole (in whole feet) that could be shipped in a box that measures 3 ft by 3 ft by 14 ft?
Answers
Answer: 14 feet
Step-by-step explanation:
Answer: 12 feet
Step-by-step explanation: The longest flagpole that could be shipped in a box is approximately 12 ft .
The tire on Levi's bike moves 6.25 feet in one rotation. How far will the tire move in 10.5 rotations?
Answers
Answer:
A bicycle with 26 inch diameter wheels travels a distance of 200 feet. Find the number of revolutions. I am not sure
Step-by-step explanation:
Find the gradient of the line passing through (-2, 5) and (5, -5)
Answers
Answer:
slope = - [tex]\frac{10}{7}[/tex]
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 2, 5 ) and (x₂, y₂ ) = (5, - 5 )
m = [tex]\frac{-5-5}{5-(-2)}[/tex] = [tex]\frac{-10}{5+2}[/tex] = - [tex]\frac{10}{7}[/tex]
If the length of the minor arc in the small tree ring is equal to 3 inches, what is the length of the minor are in the large tree ring?
Answers
Answer: There is not enough information to answer the question accurately.
The length of the minor arc in a tree ring depends on the circumference of the tree ring and the angle that the arc subtends at the center of the ring. Without additional information about the sizes and shapes of the two tree rings, we cannot determine the length of the minor arc in the large tree ring based solely on the length of the minor arc in the small tree ring.
Step-by-step explanation:
a medical diagnosis app lets users track their symptoms. whenever a user reports a symptom, the app adds a row to a database table. each row contains: the user id the date of the report the time of the report a description of how they're feeling the severity of the feeling (1-10) here are a few rows from the table: user id date time description severity 62038 11/19/2018 07:52 skin rash on arms 4 20394 09/24/2018 03:45 pounding headache 9 36917 04/11/2018 23:22 leg cramps 2 the app marketing team wants to understand their users better and asks the data analyst for various statistics. which statistic can not be calculated from the table of reports? choose 1 answer: choose 1 answer: (choice a) the average duration of the feeling. a the average duration of the feeling. (choice b) the user id with the most number of reports. b the user id with the most number of reports. (choice c) the total number of reports from all users. c the total number of reports from all users. (choice d) the distribution of severity ratings across reports. d the distribution of severity ratings across reports.
Answers
Option d is correct.
The distribution of severity ratings across reports can also be calculated by counting the number of reports with each severity rating.
The statistic that cannot be calculated from the table of reports is the average duration of the feeling.
This is because the table only provides information about the date, time, description, and severity of the feeling, but not the duration.
To calculate the average duration, one would need to take the difference between the time of the first report and the time of the last report for each user.
This information is not provided in the table.
However, other statistics can be calculated from the table of reports.
For example, the user id with the most number of reports can be calculated by counting the number of reports for each user and identifying the user with the highest count.
Similarly, the total number of reports from all users can be calculated by simply adding up the total number of rows in the table.
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5x+4y=ー7 -5x-2y =1 elimination
Answers
Answer:
To eliminate x, add the two equations together:
5x + 4y = -7
(-5x - 2y = 1)
2y = -6
Solve for y:
2y = -6
y = -3
Substitute y = -3 into one of the original equations, say -5x - 2y = 1, and solve for x:
-5x - 2y = 1
-5x - 2(-3) = 1
-5x + 6 = 1
-5x = -5
x = 1
Therefore, the solution is (x, y) = (1, -3).
Step-by-step explanation:
The guitar francisca wants is on sale at two different stores. The original price of the guitar at both stores is $160. At which store is the guitar less expensive? How much less expensive? A. Store a offers 75% B.Store B offers 50% off + additional 30% off in all discounted prices. Its two questions so please answer correctly.
Answers
Using the given information, the guitar is less expensive at Store A
It is less expensive by $16
Determining the store which the guitar is less expensiveFrom the question, we are to determine where the guitar is less expensive.
A. Store A offers a discount of 75%. Therefore, the price of the guitar at Store A after the discount is:
Price at Store A = Original price * (1 - Discount percentage)
Price at Store A = $160 * (1 - 0.75)
Price at Store A = $40
Thus, the guitar is $40 at Store A after the discount.
B. Store B offers a discount of 50% off the original price, followed by an additional 30% off in all discounted prices. This means that the price of the guitar at Store B after the two discounts is:
Price at Store B = Original price * (1 - First discount percentage) * (1 - Second discount percentage)
Price at Store B = $160 * (1 - 0.5) * (1 - 0.3)
Price at Store B = $160 * 0.5 * 0.7
Price at Store B = $56
Thus, the guitar is $56 at Store B after the two discounts.
Hence, the guitar is less expensive at Store A
$56 - $40 = $16
It is less expensive by $16
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Use the Intermediate Value Theorem to show that the polynomial P(x) has a real zero in the interval [1,2]. Approximate this zero to two decimal places. P(x)=x5−2x2−12 The approximate zero of P(x) is (Round to two decimal places as needed.) The polynomial is (Type an expression using x as the variable.)
Answers
The approximate zero of P(x) is 1.87, and the polynomial is P(x) = x5 − 2x2 − 12.
When finding the real zero in the interval [1,2] using the Intermediate Value Theorem and polynomial P(x) = x5 − 2x2 − 12, there are several steps to follow. We will outline them below. Step 1: State the Intermediate Value Theorem (IVT)The Intermediate Value Theorem (IVT) states that if a function is continuous on an interval [a,b], then it takes on every value between f(a) and f(b) at least once. This means that if f(a) and f(b) have opposite signs, the function has at least one real zero between them. This is useful when the function cannot be solved explicitly. Step 2: Determine the values of f(1) and f(2)Plugging in 1 and 2 to the polynomial P(x) = x5 − 2x2 − 12, we get: f(1) = (1)5 − 2(1)2 − 12 = −13f(2) = (2)5 − 2(2)2 − 12 = 8Hence, f(1) and f(2) have opposite signs, so by the Intermediate Value Theorem, the polynomial P(x) = x5 − 2x2 − 12 has at least one real zero in the interval [1,2]. Step 3: Approximate the real zero to two decimal placesTo approximate the real zero of P(x), we can use a graphing calculator or an iterative method such as Newton's method. Using a graphing calculator, we find that the real zero of P(x) in the interval [1,2] is approximately 1.87 (rounded to two decimal places).Therefore, the approximate zero of P(x) is 1.87, and the polynomial is P(x) = x5 − 2x2 − 12.
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