If we evaluate the ∫(2to1)(v^6+v^5)/4 dv the answer would be 7.16
An integral gives numerical values to functions to represent concepts like volume, area, and displacement that result from combining infinite small amounts of data. Integration is the action of locating integrals.
The signed area of the region in the plane that is circumscribed by the graph of a specific function between two points on the real line can be used to represent definitive integrals.
Traditionally, portions above the plane's horizontal axis are positive, and those below it are negative.
First, calculate the corresponding indefinite integral.
∫(v^6+v^5)/4 dv= v^6(6v+7)/168
According to the Fundamental Theorem of Calculus, ∫(b to a) F(x)dx=f(b)−f(a), so just evaluate the integral at the endpoints
(v^6(6v+7)/168)at (v=2)=152/21.
(v^6(6v+7)/168)at (v=1)=13/168
∫(2to1)(v^6+v^5)/4 dv= (v^6(6v+7)/168)at (v=2) - (v^6(6v+7)/168)at (v=1) = 401/56 = 7.16
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Is it possible to draw a triangle the length of whose sides are 2.5 cm 4.2 cm 8 cm?
No, it is not possible to draw a triangle with side lengths of 2.5 cm, 4.2 cm, and 8 cm.
The triangle inequality theorem states that for any triangle, the sum of the lengths of the two shorter sides must be greater than the length of the longest side.
In other words, for a triangle with sides of lengths a, b, and c, where c is the longest side, the following must be true: a + b > c, b + c > a, and a + c > b.
In the case of the triangle with side lengths of 2.5 cm, 4.2 cm, and 8 cm, the sum of the lengths of the two shorter sides (2.5 cm + 4.2 cm) is 6.7 cm, which is less than the length of the longest side (8 cm).
Therefore, it is not possible to form a triangle with these side lengths, as the triangle inequality theorem is not satisfied.
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please help i need this assigment done today!!
Answer:
Step-by-step explanation: Bro honestly math is some bull
What is the equation of the line which passes through the points 2 3 and (- 4 1?
The equation of the line which passes through points (2 3) and (-4 1) is 3y - x = 7.
What is the equation of the line?
The formula for a straight line is y=mx+c where c is the height at which the line intersects the y-axis, often known as the y-intercept, and m is the gradient.
Here, we have
Given: points (2 3) and (-4 1)
We have to find the equation of a line.
we need to determine the slope of the line. The slope can be found by using the formula
m = (y₂ - y₁) /(x₂ - x₁)
Now, we put the given points and get the value of m.
m = (1 - 3) /(-4 - 2)
m = 1/3
Now, we can use the point-slope formula to find an equation for the line. The point-slope formula states:
(y - y₁) = m(x - x₁)
(y - 3) = 1/3 (x-2)
3y - 9 = x - 2
3y - x = 7
Hence, the equation of the line which passes through points (2 3) and (-4 1) is 3y - x = 7.
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What are the 4 types of factorization?
Answer:
The four main types of factoring are the Greatest common factor (GCF), the Grouping method, the difference in two squares, and the sum or difference in cubes.
Step-by-step explanation:
Hope it helps!
Enter the total area of kite LMNP in quare meter
6. 4 meter
5 meter
12. 4 meter
6. 4 meter
The total area of kite LMNP with diagonal length of 6.4 m and 12.4m in square meters is 39.68 square meters.
Therefore the answer is 39.68 square meter.
To find the area of a kite, you need to know the lengths of its diagonals. The formula for finding the area of a kite is
(d1 × d2) / 2
where d1 and d2 are the lengths of the diagonals.
Here diagonals d1 = 6.4m and d2 = 12.4m, so
area = (d1 × d2) / 2
area = (6.4 × 12.4) / 2
area = 39.68 square meters
So area of the kite LMNP is 39.68 square meters.
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You have been asked to find the value of f(-5) for the function:
f(x)=3[tex]x^{2}[/tex] -2x+5
Which of the following options is NOT a possible way to evaluate that function and find the correct answer?
Answer 1: See what x is when y=-5
Answer 2: Graph the equation and look at the table to find the y-value when x=-5
Answer 3: Substitute (-5) wherever there is an x and solver using a calculator
Answer 4: Graph the equation and find the y-value of the ordered pair when x=-5
The option that is not a possible way to evaluate that function and find the correct answer is given as follows:
Answer 1: See what x is when y=-5.
How to find the numeric value of a function or of an expression?To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.
The function for this problem is defined as follows:
f(x) = 3x² - 2x + 5.
At x = -5, the numeric value is obtained replacing the two instances of x by -5, hence:
f(-5) = 3(-5)² - 2(-5) + 5 = 90.
Meaning that only answer 1 is incorrect.
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17 exceeds one-eighth of a number by 9. what is the number?
The number that satisfies the given condition is x= 64.
What are equations?Equation: A declaration that two expressions with variables or integers are equal. In essence, equations are questions, and attempts to systematically identify the solutions to these questions have been the driving forces behind the creation of mathematics.
Let the number be x.
Then one eight of the number can be represented as follows: [tex]\frac{1}{8}x[/tex]
The number 17 exceeds by 9, this is written as [tex]\frac{1}{8}x + 9 =17[/tex]
Using the equation, we find the value of x by isolating the variable:
[tex]\frac{1}{8}x + 9 =17\\\\x+ (8)(9) = (17)(8) \\\\x = 136 - 72\\\\x=64[/tex]
Hence the number x that satisfies the given condition is 64.
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A candle's height is modeled by the equation y=-5x+30, where x is the hours spent burning, and y is the height of the candle in centimeters. Interpret the slope, using a complete sentence. Please explain how you got the answer. I will mark you brainliest!!
The number -5 represents the rate of decreasing 5 centimeters per hour.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
A candle's height is modeled by the equation y = -5x + 30, where x is the hours spent burning, and y is the height of the candle in centimeters.
The number -5 represents the rate of decreasing 5 centimeters per hour and 30 represents the initial length of the candle.
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-5/7÷ 2/4. solve this complex equation
Answer:
-10/7 or -1.429
Step-by-step explanation:
-5/7 ÷ 2/4
Fractions can't be divided, so you reciprocate and replace the division sign with a multiplication sign.
-5/7 × 4/2
-20/14
= -10/7 or -1.429
Gerardo changed a $100 at the bank. He received $20 bills and $10 bills.
$20 bills was 2 more than the number of $10 bills. How many bills of each kind did he
receive?
Write using LESCA
Answer:
• Two $10 bills
• Four $20 bills
Step-by-step explanation:
We are told that Gerardo received a number of $20 and $10 bills upon changing a $100 bill at the bank. We are also told that he received 2 more $20 bills than $10. Then we are asked to find the number of each kind of bill.
To solve this problem, let's consider the number of $10 bills he received was [tex]x[/tex]. Since he received 2 more $20 bills, he got [tex](2 + x)[/tex] $20 bills. Therefore, in total he received:
[tex]10 \times x + 20 \times (x +2)[/tex]
This should add up to $100 since that is the amount he changed. Solving the resulting equation for [tex]x[/tex] will give us the number of $10 bills he received.
[tex]10 \times x + 20 \times (x +2) = 100[/tex]
⇒ [tex]10x + 20x + 40 = 100[/tex]
⇒ [tex]30x +40 = 100[/tex]
⇒ [tex]30x + 40 - 40 = 100 - 40[/tex] [Subtracting 40 from both sides of equation]
⇒ [tex]30x = 60[/tex]
⇒ [tex]\frac{30}{30}x = \frac{60}{30}[/tex] [Dividing both sides of the equation by 30]
⇒ [tex]x = \bf 2[/tex]
Therefore, he received 2 $10 bills.
Since the number of $20 bills is 2 more than the number of $10 bills,
no. of $20 bills = 2 + 2
= 4
write a cosine function that has a midline of 4, an amplitude or 3 and a period of 7/3
The cosine function will be equal to f(x) = 3cos(π(6/7)x) + 4
What is a function?A function is defined as the expression that set up the relationship between the dependent variable and independent variable.
A generic cosine function is written as:
f(x) = Acos(wx + p) + M
where:
A = amplitude
w = angular frequency
p = phase
M = midline.
We know that:
The midline is 4, then M = 4
The amplitude is 3, then A = 3
There is no information about the phase, so p = 0.
And we know that the period is 7/3.
The period is written as T, and the relation between the period and the angular frequency is:
T = 2π/w
Then we have:
7/3 = 2π/w
w = (2π)*(3/7) = π x (6/7)
where π= 3.14
Then we have:
w = π x (6/7)
A = 3
M = 4
p = 0
Hence, the cosine function is: f(x) = 3cos(π(6/7)x) + 4
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Use the Exterior Angle Theorem to find the measure of each angle.
Answer: <C = 32, <D = 80, <DEC = 68
Step-by-step explanation:
First, the exterior angle DEF equals the sum of the two other interior angles that are not adjacent to it, meaning that the angle DEF equals the sum of angles DCE and EDC.
Therefore, you get the equation
2y+8+6y+8=112
8y+16=112
8y = 96
y = 12
Since y is 12, let's use this to find the measure of the other angles.
DCE = 2y+8 = 32
EDC = 6y+8 = 80
Angle DEC equals 180 - 112 = 68
Rhode Island Red chicks cost $3.20 each and Buckeye chicks cost $3.44 each. A farmer buys 4 Rhode Island Red chicks for every 3 Buckeye chicks.
He buys 70 chicks in all. What is the total cost of the farmer’s chicks?
Answer:$231.2
Step-by-step explanation:
An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
The total cost of farmers' chicks is $231.2
What is an equation?
An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x = 5 is an equation.
We have,
Total chicks = 70
4 Rhode Island Red chicks = 3 Buckeye chicks.
Multiply 10 on both sides.
40 Rhode Island Red chicks = 30 Buckeye chicks.
We see that,
40 + 30 = 70
Now,
Rhode Island Red chicks cost = $3.20
Buckeye chicks cost = $3.44
Now,
= 40 x 3.20 + 30 x 3.44
= 128 + 103.2
= $231.2
Thus,
The total cost of farmers' chicks is $231.2
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____the transformation is an example of a translation because the figure slides in one direction, but does not flip, turn, or change size.
The transformation is an example of a translation because the figure slides in one direction, but does not flip, turn, or change size.
Now, According to the question:
Type of Transformation:
There are four types of transformation in geometry, namely translation, reflection, rotation, and dilation. In translation, it slides the figure in any direction while in reflection, it flips the figure over a point or a line. Also, in rotation the figure turns, while in dilation the figure is either enlarged or reduced.
The type of transformation can be defined as moving a figure to a new location, without any change in the figure's size or shape being called translation. In translation, the figure merely slides or moves in the same direction and distance.
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The nth term of sequence S is 2n+5
The nth term of sequence T is 3n - 6
(a) Show that 91 is a term in sequence S.
b) Show that 91 is not a term in sequence T
The term 91 is present in sequence S at n = 43, and the term is not a part of the sequence T.
What is sequence?A sequence is an enumerated group of items in mathematics where repetitions are permitted, and order is important. Similar to a set, it has members.
Given that:
a = 91
Substitute the value of a in the given sequence.
Sequence S:
a = 2n+5
91 = 2n + 5
91 - 5 = 2n
n = 43
Sequence T:
a = 3n - 6
91 + 6 = 3n
n = 97/3
As the terms present in a sequence cannot be a fraction we figure that 91 is not present in sequence T.
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ian measures the mass of his cat and his kittens. the mass of the kitten is 6 and 1/5 lb. the kitten is 3 and 7/8 lb lighter than the cat. what is the total mass of cat and the kitten?
Number of jelly beans in a scoop:
47, 28, 38, 47, 58, 34, 76, 35, 32, 45, 53, 43, 35, 27
Which numbers would be used for the stems in a stem-and-leaf plot of the data set?
Answer:
4
2
3
4
5
3
7
3
4
5
4
3
2
Step-by-step explanation:
What will be the area of triangle whose sides are 9 cm 12 cm and 15 cm?
The area of triangle whose sides are 9 cm 12 cm and 15 cm is 54 cm².
The formula to be used for calculating of the area of triangle is -
A = ✓s(s-a) (s-b) (s-c), where a, b and c are sides of triangle. S is (a+b+c)/2.
Let us assume side a to be 9 cm, side b to be 12 cm and side c to be 15 cm. Calculating the value of s.
s = 9 + 12 + 15/2
Adding values on Right Hand Side of the equation
S = 36/2
Performing division
S = 18
Keep the values in formula of area -
A = ✓18 × (18 - 9) × (18 - 12) × (18 - 15)
Performing subtraction
A = ✓18 × 9 × 6 × 3
Performing multiplication
A = ✓2916
Taking square root
A = 54 cm²
Thus, the area of triangle is 54 cm².
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What is 4 1/3 x 6 Need a little help thanks
The result of the given multiplication of the mixed fraction is found as 78/3.
Define the term mixed fractions?A number that combines an integer as well as a legal fraction is referred to as a mixed fraction.
Mixed number is another name for mixed fraction.It is possible to change an improper fraction into the a mixed fraction and the other way around.When converting a mixed fraction to the an improper fraction, both denominator and the overall number are multiplied, the product is added to the numerator, and the sum is written as the numerator and denominator.The given expression:
= 4 1/3 x 6
Solving the mixed fraction.
= (4*3 + 1)/3 x 6
= (12 + 1)/3 x 6
= 13/3 x 6
= 78/3
Thus, the result of the given multiplication of the mixed fraction is found as 78/3.
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Classifying Triangles
According to the lengths of their sides, triangles can be classified into three types which are: Scalene, Isosceles. Equilateral.
What is the Classification of Triangles in Geometry?Triangles come in six different types and are divided into two groups, namely sides and angles. The three triangles are categorised as equilateral triangles, isosceles triangles, and scalene triangles based on their sides. Triangles can be classified as acute, obtuse, or right-angled depending on the angle at which they are formed.
Triangles are divided into three sorts based on their sides.
Equilateral triangle: A triangle is deemed to be an equilateral triangle if its three sides are all the same length.
Isosceles triangle: An isosceles triangle is one in which each of its sides are equal.
A triangle is said to be a scalene triangle if each of its three sides is a different length.
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Which of the following is not an expression? A. 6x-3=5 B. 3x+4 C. 1 = x/4 D. X-5
Option C is correct. 1 = x/4 is not an expression. It is an equation. An expression is a combination of numbers, variables, and operators (such as +, -, *, /) that can be simplified or evaluated to a single value, while an equation is a statement that asserts the equality of two expressions.
What is the difference between expressions and equation?Expression: In order to indicate the value of something, an expression is defined as a grouping of integers (constant), letters (variables), or their combination connected by operators (+, -, *, /). A mathematical, algebraic, polynomial, or analytical expression can be used.
It does not demonstrate any relationship because it lacks the equals (=) sign. As a result, it lacks left and right sides. An expression can be made simpler by grouping related terms together, or it can be evaluated by replacing the variables with values to get a numerical value.
Equation: Equation refers to a claim of equivalence. In this statement, two expressions are positioned on either side of one another. The value of the relevant variable must be known in order for an equation to be satisfied; this is referred to as the solution or root of the equation.
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Plot the whole number benchmarks on the open number line then plot the number you are subtracting from label the distance of each jump 6.57 - 3.86
Answer:
109 it is the answer
Step-by-step explanation:
02947 029377393
One tennis club charges $ 34 per session to play tennis. Another tennis club charges an annual fee of $ plus $ 22 per session. After how many sessions is the cost at the two clubs the same?
The cost of the two clubs will be the same after 4 sessions
How to determine the number of sessions at which the cost at the two clubs the same?A word problem is a mathematical exercise where significant background information on the problem is presented in ordinary language rather than in mathematical notation
Let x represent the number of session
Since One tennis club charges $ 34 per session to play tennis. We can write the cost as:
cost = 34x
And another tennis club charges an annual fee of $ plus $ 22 per session. We can write the cost as:
cost = 48 + 22x
At the same cost, we have:
34x = 48 + 22x
34x - 22x = 48
12x = 48
x = 48/12
x = 4
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Complete Question
One tennis club charges $30 per session to play tennis. Another tennis club charges an annual fee of $48 plus $22 per session. After how many sessions is the cost at the two clubs the same?
Use the given form of the expression to write the equivalent form.
Answer:
Step-by-step explanation:
remember,
x^(a/b) corresponds to
bth root of x^
7.
x^(2/3) × y^(5/3)
= 3rd root of (x²y⁵)
8.
(a³b⁷/(a²b^-3))
= a¹×b¹⁰
so, the whole expression is
a^(1/5) × b^(10/5) = a^(1/5) × b²
9.
(2^(1/2) × 3^(5/2))^(1/3)
= (2^(1/6) × 3^(5/6))
the whole expression is
6th root of (2 × 3⁵)
what is 4/9 divided by 8/15 as a simplified fraction.
Answer:0.3
Step-by-step explanation:
What is inequality statements in math?
In mathematics, an inequality is a statement that compares two expressions or values.
The expressions or values being compared are separated by an inequality symbol, such as; > (greater than), < (less than), ≥ (greater than or equal to), ≤ (less than or equal to), or ≠ (not equal to).
For example, the inequality statement "3 < 5" means that 3 is less than 5. The symbol "<" is the inequality symbol, and it shows the relationship between the two values 3 and 5. Another example would be "x + 2 > 5", this inequality states that the value of x + 2 is greater than 5, where x can be any value.
Inequality statements can also be represented graphically on a number line. For example, the inequality x > 3 would be represented by a line on the number line with an open circle at 3, with all the numbers to the right of 3 being included in the solution set.
Inequality statements can also be combined to form a system of inequalities, which can then be solved graphically by finding the common solution set of all the inequalities in the system.
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solve for x
u = 1/2x - 1
2x²+4x+5=ax²+(2b-6)x+c find the constant a,b,c
Please help me if you can thanks
[tex]26 sin 58°[/tex] is the expression that represents the length of segment PR.
What is Length?The word "length" is used to describe an object's size or the separation between two points. The length of an object or the separation between two points is measured by its length. It is employed to determine an object's size or the separation between two points.
Since triangle JKL and triangle PQR are similar, we can use the similarity ratios to find the length of PR.
We know that the ratio of PR to JK is the same as the ratio of PQ to JL. We know that [tex]PQ = 26 and JL = 26 + 13 = 39[/tex], so the ratio is [tex]26/39[/tex].
So, [tex]PR = (26/39) * 13 = 26sin( JL/2) = 26sin58°[/tex]
So the answer is [tex]26 sin 58°[/tex]
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The Algebra 2 test grades are posted, and all students taking the test scored over 75. Unfortunately, 5 students were absent from the test, so the teacher listed their scores as 0 until the test is taken. Assuming that no score repeated more times than the 0's, what measure of central tendency would most likely give the best representation of this data? Explain.
The measure of central tendency that would most likely give the best representation for the data would be Median.
Why would the median give the best representation ?The mean (average) would be greatly skewed by the presence of 0's and would not accurately represent the scores of the students who took the test. Since the scores were all above 75, the mean would be much lower than the actual scores due to the presence of 0's.
The mode (most common value) would be 0 and it would not be a good representation of the scores of the students who took the test.
The median can be calculated by ordering the scores and finding the middle value. Since 5 students were absent and their scores were listed as 0, it would be the middle value of the test scores that were above 75. This is therefore the best measure of central tendency.
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