Answer:
Proof:
Using the given information, we know that PQ is approximately equal to QS and QS is exactly equal to ST.
Since a value that is approximately equal to another value can be treated as equal in many cases, we can say that PQ is roughly equal to ST.
To prove that PQ is exactly equal to ST, we must use the transitive property of equality.
Transitive Property of Equality: If a = b and b = c, then a = c.
Using the transitive property, we can say:
PQ ≈ QS and QS = ST → PQ ≈ ST
Since PQ is approximately equal to ST and they have the same units of measurement, we can round the values to the same number of decimal places and say:
PQ ≈ ST ≈ rounded value
Therefore, PQ is exactly equal to ST because they have the same rounded value.
Destiny Rubio Definite Integrals of Rational Functions Feb 23, 11:55:41 AM Find the average value of the function f(x)=(12)/(x-10) from x=1 to x=7. Express your answer as a constant times ln3. Answer: ln3 Submit Answer
The Average value of the function f(x)=(12)/(x-10) from x=1 to x=7 -2 ln3.
The average value of a function f(x) over the interval [a,b] is given by the formula:
Average value = (1/(b-a)) ∫[a,b] f(x) dx
In this case, the function is f(x) = (12)/(x-10), the interval is [1,7], and we need to find the average value. Plugging in the values into the formula, we get:
Average value = (1/(7-1)) ∫[1,7] (12)/(x-10) dx
Average value = (1/6) ∫[1,7] (12)/(x-10) dx
Next, we need to find the integral of the function. We can use the formula for the integral of a rational function:
∫ (a)/(x-b) dx = a ln|x-b| + C
In this case, a = 12 and b = 10, so the integral of the function is:
∫ (12)/(x-10) dx = 12 ln|x-10| + C
Plugging this back into the formula for the average value, we get:
Average value = (1/6) (12 ln|7-10| - 12 ln|1-10|)
Average value = (1/6) (12 ln|-3| - 12 ln|-9|)
Average value = (1/6) (12 ln|3| - 12 ln|3^2|)
Average value = (1/6) (12 ln|3| - 12 (2 ln|3|))
Average value = (1/6) (12 ln|3| - 24 ln|3|)
Average value = (1/6) (-12 ln|3|)
Average value = -2 ln|3|
Therefore, the average value of the function f(x) = (12)/(x-10) from x = 1 to x = 7 is -2 ln|3|. We can express this as a constant times ln3 by factoring out the ln3:
Average value = -2 ln|3| = -2 ln3
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Evaluate the following by the Change-of-Base Formula:
log13 (297)
- approximately 2.4728
- approximately 2.2198
- approximately 1.1139
- approximately 0.4505
The answer is approximately 2.2198, which is option (b).
How did we get the value?To evaluate log13(297) using the change-of-base formula, we can express it in terms of a logarithm with a base that we can easily calculate, such as the common logarithm (base 10) or the natural logarithm (base e).
Let's use the common logarithm:
log13(297) = log10(297) / log10(13)
We can use a calculator to find the decimal approximations of log10(297) and log10(13), and then divide them to get the final answer:
log13(297) ≈ 2.2198 (rounded to 4 decimal places)
Therefore, the answer is approximately 2.2198, which is option (b).
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Find the value of x 10,26
The value of x for the given equation is 16.
What is the value of x?
To find the value of x in the equation x + 10 = 26, we need to isolate x on one side of the equation by performing the same operation to both sides of the equation.
We can start by subtracting 10 from both sides of the equation:
x + 10 - 10 = 26 - 10
Simplifying the left-hand side gives:
x = 16
Therefore, the value of x is 16, as this is the solution that satisfies the equation x + 10 = 26.
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The complete question is below:
Find the value of x: for x +10 = 26
Tyee goes out to lunch. The bill, before tax and tip, was $14.20. A sales tax of 6% was added on. Tyee tipped 18% on the amount after the sales tax was added. How much tip did he leave? Round to the nearest cent.
Answer:
$4.09
Step-by-step explanation:
14.20+6% of 14.20 = 15.05
118% of 15.05= 18.29
18.29-14.20=4.09
Leslie is a biologist. She is going to randomly select one animal from her lab to study. There are
5
55 salamanders,
3
33 crayfish, and
12
1212 minnows in her lab.
What is
P(salamander
)
P(salamander)start text, P, left parenthesis, s, a, l, a, m, a, n, d, e, r, end text, right parenthesis?
Answer:
The probability that Leslie randomly selects a salamander is
1
4
4
1
Step-by-step explanation:
In general, when we are interested in finding the probability of a event, we just need to divide the number of possibilities the event we are interested in can happens by the number of all possible results.
In this case, we have
20
20 differents animals to be chosen and we are interested in when one of the five salamanders is chosen. That is, P(salamander) =
5
20
=
1
4
20
5
=
4
1
Kingston weighed 9 pounds, 2 ounces at birth. His baby brother, Karmichael, weighed 7 pounds, 11 ounces a birth. How much bigger was Kingston's birth weight compared to Karmichael's?
Answer: 1lb 7oz
Step-by-step explanation:
All you have to do is subtract 9lbs and 2oz by 7lbs and 11oz, which is 1lb and 7oz
(16 oz in a pound)
If the artist charges $280
for a painting that takes 7
hours to create, which equation represents the total amount, t
, the artist charges for a painting that takes h
hours to create?
Answer:
Step-by-step explanation:
idrk
Round all answers to 3 decimal places. The vertex of g is (-5,2)
The function g has a local _____ of ___ that occurs at u= ____
What is the domain of g in interval notation? What is the range of g in interval notation? The u-intercept(s) of g are ?
The g(u)-intercept is?
On what interval is g increasing? On what interval is g decreasinq?
The first derivative of a function equals zero on an interval, the function has a relative extremum on that interval.
Answer: The interval on which the function g(x) increases and decreases.The g function's vertex is at (-5, 2), and we need to figure out where the function increases and decreases. When a function has a vertex, it always opens up or down. As a result, the vertex serves as the function's minimum or maximum point.Given the above, we can assume that g(x) decreases to the left of x = -5 and increases to the right of x = -5. If we want to be more precise about the intervals, we can use the first derivative test. The first derivative of g(x) is as follows:g'(x) = 3x + 15The first derivative test states that if the first derivative of a function is greater than zero on an interval, the function is increasing on that interval. If the first derivative of a function is less than zero on an interval, the function is decreasing on that interval. Finally, if the first derivative of a function equals zero on an interval, the function has a relative extremum on that interval. We now need to find where g'(x) > 0 and where g'(x) < 0.3x + 15 > 0 => x > -5g(x) is increasing on the interval (-5, ∞)3x + 15 < 0 => x < -5g(x) is decreasing on the interval (-∞, -5)
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Students were asked to prove the identity (sec x)(csc x) = cot x + tan x. Two students' work is given.
Part A: Did either student verify the identity properly? Explain why or why not. (10 points)
Part B: Name two identities that were used in Student A's verification and the steps they appear in. (5 points)
The expression is proved by the following steps.
What is Trigonometric Functions?Trigonometry uses six fundamental trigonometric operations. Trigonometric ratios describe these operations. The sine function, cosine function, secant function, co-secant function, tangent function, and co-tangent function are the six fundamental trigonometric functions.
The ratio of sides of a right-angled triangle is the basis for trigonometric functions and identities. Using trigonometric formulas, the sine, cosine, tangent, secant, and cotangent values are calculated for the perpendicular side, hypotenuse, and base of a right triangle.
Part A:
student A verified the identity properly Reason student A applied the trigonometric identities
Part B:
The identities used in student A verification are
step 1: sec x = 1/cosx
cosecx= 1 /sin x
(sec x)(csc x) = cot x + tan x
Hence this above equation is proved.
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What is the shortest distance from the point (6,5) to the line 2x+3y=1 ? (A) √13 (B) 2√13 (C) 4√13 (D) 6√13 (E) None of these
The shortest distance from a point to a line can be found by using the formula:
d = |Ax + By + C| / √(A² + B²)
where A, B, and C are the coefficients of the line equation and x and y are the coordinates of the point.
In this case, A = 2, B = 3, C = -1, x = 6, and y = 5.
Plugging these values into the formula, we get:
d = |(2)(6) + (3)(5) - 1| / √(2² + 3²)
d = |17| / √(13)
d = 17 / √(13)
d = √(13) * 17 / 13
d = √(13) * √(13) / √(13)
d = √(13)
Therefore, the shortest distance from the point (6,5) to the line 2x+3y=1 is √(13).
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Classify the polygon. Be as specific as possible.
Quadrilateral JKLM with JK = 10, KL = 7, ML = 10, and JM = 7
We can say that JKLM is an isosceles trapezoid, since the non-parallel sides (JK and ML) are congruent.
What is Polygon?A polygon is a closed plane figure with three or more straight sides that meet at the vertices. It is formed by connecting line segments endpoint-to-endpoint with each segment intersecting exactly two others.
The given quadrilateral JKLM has four sides, and its opposite sides are parallel.
Furthermore, since all four sides have different lengths, it is not a parallelogram.
Also, since no angles or sides are congruent, it is not a kite or a rhombus.
Therefore, the most specific classification for this quadrilateral would be a trapezoid, which is a quadrilateral with one pair of parallel sides.
To be more specific, we can say that JKLM is an isosceles trapezoid, since the non-parallel sides (JK and ML) are congruent.
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PLEASE HELP
Tanner is spray painting an arrow on the side of a building to point to the entrance of his store. The can of gold spray paint he wants to use covers up to 12 square feet. Does Tanner have enough spray paint for his arrow?
Using the area formula, it is obtained that Tanner has enough spray paint to cover the arrow with one can of spray paint.
What is area?
An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure.
To determine if Tanner has enough spray paint for his arrow, we need to find the total area of the arrow and compare it to the coverage of one can of spray paint.
The arrow consists of a rectangle and a triangle.
The rectangle has a length of 2 feet and a width of 5 1/3 feet, so its area is -
Area of rectangle = length × width
= 2 ft × 5 1/3 ft
= 10 2/3 sq. ft.
The triangle has a base of 3 feet and a height of the difference between the width of the rectangle (5 1/3 feet) and the width of the arrow (6 feet):
Height of triangle = 6 ft - 5 1/3 ft = 2/3 ft
Area of triangle = 1/2 x base x height = 1/2 x 3 ft x 2/3 ft = 1 sq. ft.
The total area of the arrow is the sum of the area of the rectangle and the area of the triangle -
Total area of arrow = Area of rectangle + Area of triangle
Total area of arrow = 10 2/3 sq. ft. + 1 sq. ft.
Total area of arrow = 32/3 sq. ft. + 1 sq. ft.
Total area of arrow = 11 2/3 sq. ft.
Therefore, since one can of spray paint covers up to 12 square feet, Tanner has enough spray paint to cover the arrow with one can of spray paint.
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a culture of a certain bacteria is known to dpuble in number every 4 hr. if the culture has an initial count of 25, what will be the population of the culture at the end of the 24 hr?
The population of the culture at the end of 24 hours will be 1600.
To find this answer, we can use the formula for exponential growth:
P = P₀ * 2^(t/h)
Where P is the final population, P₀ is the initial population, t is the total time in hours, and h is the time it takes for the population to double.
Plugging in the given values, we get:
P = 25 * 2^(24/4)
Simplifying the exponent:
P = 25 * 2^6
Solving for P:
P = 25 * 64
P = 1600
So the population of the culture at the end of 24 hours will be 1600.
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Which function is undefined when Theta = StartFraction pi Over 2 EndFraction radians?
cos Theta
cot Theta
csc Theta
tan Theta
Answer:
Option 4 [tex]tan[/tex]θ is undefined.
Step-by-step explanation:
Given : θ [tex]\\=\frac{\pi }{2}[/tex] radians
To find : Which function is undefined
Solution : Put θ [tex]\\=\frac{\pi }{2}[/tex] in all the given options to check which are undefined
[tex]Cos[/tex]θ [tex]=cos\frac{\pi }{2} =0[/tex]
[tex]Cot[/tex]θ [tex]=cot\frac{\pi }{2}=\frac{cos\frac{\pi }{2} }{sin\frac{\pi }{2} } =\frac{0}{1} =0[/tex]
[tex]Csc[/tex]θ [tex]=cosec\frac{\pi }{2} =\frac{1}{sin\frac{\pi }{2} } =\frac{1}{1}=1[/tex]
[tex]tan[/tex]θ [tex]=tan\frac{\pi }{2} =\frac{sin\frac{\pi }{2} }{cos\frac{\pi }{2} } =\frac{1}{0} =infinity[/tex]
Therefore, we get that [tex]tan[/tex]θ is not defined or undefined.
Please help me I don’t want to fail
The measure of line KR is 8 inches
How to determine the measure of the length
It is important that we know the properties of an isosceles trapezoid.
Only one pair of sides are parallelNon-parallel sides are equal in measureThe diagonals are equal in measureThe opposite angles are supplementary, that is, their sum is equal to 180 degreesFrom the information given, we have that;
KR = 1/2x + 5
DH = 2x - 4
Since the non- parallel sides of an isosceles trapezoid are equal, then, we have;
KR = DH
1/2x + 5 = 2x - 4
collect the like terns, we have
1/2x - 2x = -4 - 5
x - 4x /2 = - 9
cross multiply
-3x = -18
x = 6
KR = 1/2(6) + 5 = 8 inches
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#6
The frequency table shows the results of a survey that asked 175 high schoolers how they learn about news stories.
Rounded to the nearest hundredth, the relative frequency of a student being a twelfth grader that gets their news from the internet is 0.25.
What is relative frequency?The proportion of times a particular value or event occurs within a set of data is termed as Relative frequency.
It is calculated by dividing the frequency of the event by the total number of observations. It is often expressed as a percentage or decimal value between 0 and 1.
The relative frequency of a student being a twelfth grader that gets their news from the internet can be calculated by dividing the number of twelfth graders who get their news from the internet by the total number of students surveyed:
Relative frequency = (number of twelfth graders who get news from the internet) / (total number of students surveyed)
Relative frequency = 43 / 175
Relative frequency = 0.2457 (rounded to four decimal places)
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Complete the equation of the line whose yyy-intercept is (0,-1)(0,−1)left parenthesis, 0, comma, minus, 1, right parenthesis and slope is 444.what is y=
Answer:
The equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.
In this case, the y-intercept is (0, -1) and the slope is 4. So we have:
y = 4x - 1
Therefore, the equation of the line with y-intercept (0, -1) and slope 4 is y = 4x - 1.
Can someone please solve this?
3(2x+5)+2x=x+50
x=5
Hint: x+50
-x
Answer: x=5
Step-by-step explanation:
Is the algebraic expression a polynomial? If it is, write the polynomial in standard form. 3x^(2)+3x^(-3)-2
Yes, the algebraic expression [tex]3x^(2)+3x^(-3)-2[/tex] is a polynomial.
A polynomial is an algebraic expression consisting of variables and coefficients that involves only the operations of addition, subtraction, and multiplication, as well as non-negative integer exponents. The given algebraic expression satisfies these conditions, so it is a polynomial.
To write the polynomial in standard form, we need to rearrange the terms in descending order of exponents. In this case, the term with the highest exponent is [tex]3x^(2)[/tex], followed by the term with the lowest exponent, [tex]3x^(-3)[/tex], and finally the constant term, -2.
Therefore, the polynomial in standard form is:[tex]3x^(2)+3x^(-3)-2 = 3x^(2)-2+3x^(-3)[/tex] So, the polynomial in standard form is [tex]3x^(2)-2+3x^(-3)[/tex].
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Which graph can be used?
A graph that can be used to find the real solution(s) to 3 - 4x = -3 - x² - 4x is shown in the image attached below.
What is a quadratic function?In Mathematics, a quadratic function can be defined as a mathematical expression which defines and represent the relationship that exists between two (2) or more variable on a graph, with a maximum exponent of two.
Next, we would use an online graphing calculator to plot the given quadratic function 3 - 4x = -3 - x² - 4x as shown in the graph attached below.
By splitting the quadratic function, we have:
y = -3 - x² - 4x
y = 3 - 4x
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I need to solve and shade
Answer:
Step-by-step explanation:
2). y > - x - 2
y < - 5x + 2
3). y ≤ [tex]\frac{1}{2}[/tex] x + 2
y < - 2x - 3
A sample is taken from the 15th and 50th items from 100
production lines. Which is this sampling method?
Answer options:
Systematic sampling
Cluster sampling
Convenient sampling
Stratified sampling
A sample is taken from the 15th and 50th items from 100 production lines. The sampling method used in this scenario is Systematic sampling.
Systematic sampling is a method in which a sample is taken at regular intervals from a larger population. In this case, the sample is taken from the 15th and 50th items from 100 production lines, meaning that the sample is taken at regular intervals from the larger population of 100 production lines.
This method is different from cluster sampling, which involves dividing the population into groups and then selecting a sample from each group. It is also different from convenient sampling, which involves selecting a sample based on convenience or accessibility.
Finally, it is different from stratified sampling, which involves dividing the population into strata and then selecting a sample from each stratum. Therefore, the correct answer is Systematic sampling.
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What is the answer to the question 3 times 3
Answer: 9
Step-by-step explanation:
Answer:
Step-by-step explanation:
9
Describe the graph of y=1/2x-10 compared to the graph of y=1/x
The equation y=1/2x-10 is in the slope-intercept form while the other equation y=1/x is a hyperbola.
What is the hyperbola?A circular cone and a plane that passes through both of the cone's nappes (see cone) connect to form a hyperbola, a two-branched open curve with a conic section.
A hyperbola is made up of two mirror images of one another that resemble two infinite bows.
These two sections are known as connected components or branches.
the hyperbola's equation denoted as (xh)2a2(yk)2b2=1).
So, the equation y=1/2x-10 is in the slope-intercept form and we know the slope which is 1/2, and b which is -10 by just observing the equation.
On the other hand, y=1/x is the hyperbola.
Therefore, the equation y=1/2x-10 is in the slope-intercept form while the other equation y=1/x is a hyperbola.
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7÷8-7÷10 in its lowest terms
Let k be a field. Show that I = {p(x) ∈ k[x] : p(0) =
0} is an ideal of k[x] and
that it is a principle ideal.
I is both an ideal of k[x] and a principle ideal.
Let k be a field. The ideal of k, I = {p(x) ∈ k[x] : p(0) = 0}, is an ideal of k[x] because it satisfies the following properties:
1) Closure under addition: If p(x) and q(x) are both in I, then p(x) + q(x) is also in I. This is because p(0) + q(0) = 0 + 0 = 0, so (p + q)(0) = 0.
2) Closure under multiplication by elements of k[x]: If p(x) is in I and r(x) is any polynomial in k[x], then r(x)p(x) is also in I. This is because r(0)p(0) = 0, so (rp)(0) = 0.
Additionally, I is a principle ideal because it can be generated by a single element. In this case, the principle idea is the polynomial x, since any polynomial in I can be written as a multiple of x. For example, if p(x) = x^2 + 2x, then p(x) = x(x + 2), so p(x) is a multiple of x and is therefore in the ideal generated by x.
Therefore, I is both an ideal of k[x] and a principle ideal.
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Math part 2 question 3
The value of (g times f)(x) is 6x² + x - 2. So correct is C.
Describe Function?The input values of a function are called the domain, and the output values are called the range. The domain can be any set of values, but each input value must have a unique corresponding output value. If there are multiple input values that produce the same output value, the function is not considered to be well-defined. Functions are used to model a wide range of phenomena in many different fields, including science, engineering, and economics. They are also used in calculus to study rates of change and slopes of curves.
Overall, functions are a fundamental concept in mathematics, and have many practical applications in the real world.
To find g(x) times f(x), we need to multiply the two functions together.
(g times f)(x) = g(x) * f(x)
First, we need to find g(f(x)):
g(f(x)) = g(3x+2) = 2(3x+2) - 1 = 6x + 3
Now we can substitute this into the expression for (g times f)(x):
(g times f)(x) = g(x) * f(x) = (2x-1) * (3x+2)
Using the distributive property, we get:
(g times f)(x) = 6x² + 4x - 3x - 2 = 6x² + x - 2
Therefore, (g times f)(x) = 6x² + x - 2.
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Find two posible langths of the basses of a trapizodes with a hight of 1 foot and an area of 9 square feet
Two possible lengths of the bases of a trapezoid with a height of 1 foot and an area of 9 square feet are 6 feet and 12 feet, or 4 feet and 14 feet.
Let's denote the lengths of the two bases of the trapezoid as b1 and b2 (where b1 is the longer base), and the height as h = 1 foot. The formula for the area of a trapezoid is,
A = (b1 + b2) / 2 × h
Given that the area is 9 square feet, we can plug in the values and solve for one of the bases,
9 = (b1 + b2) / 2 × 1
9 = (b1 + b2) / 2
18 = b1 + b2
b2 = 18 - b1
We can substitute b2 in terms of b1 in the formula for the area to get:
9 = (b1 + (18 - b1)) / 2 × 1
9 = 18 / 2
9 = 9
This equation is true for any value of b1, which means that there are infinitely many possible trapezoids with a height of 1 foot and an area of 9 square feet. However, we can find two specific values of b1 that correspond to different trapezoids:
If we let b1 = 6 feet, then b2 = 18 - b1 = 12 feet. This trapezoid has bases of length 6 feet and 12 feet, and a height of 1 foot.
If we let b1 = 4 feet, then b2 = 18 - b1 = 14 feet. This trapezoid has bases of length 4 feet and 14 feet, and a height of 1 foot.
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Which is the graph
F(x)=4(1/2)x
Answer:
Step-by-step explanation:
Need help asap! Step by step please, greatly appreciated!
The value of x from the given exponential function is -8.159.
What is the exponent?Exponent is defined as the method of expressing large numbers in terms of powers. That means, exponent refers to how many times a number multiplied by itself.
The given equation is [tex]9^{3x}=4^{5x+2}[/tex].
Take the logarithm of both sides of the equation to remove the variable from the exponent.
Here, [tex]ln(9^{3x})=ln(4^{5x+2})[/tex]
x=2ln(4)/3ln(9)-5ln(4)
x= -8.159
Therefore, the value of x is -8.159.
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