The sum of the sequence [tex](-1)^{-10} +(-1)^{-9} +(-1)^{-8} +\cdots+ (-1)^9+ (-1)^{10}[/tex] is 1
Consider given sequence [tex](-1)^{-10} +(-1)^{-9} +(-1)^{-8} +\cdots+ (-1)^9+ (-1)^{10}[/tex]
here, the dots . . . means that there are 21 numbers being added, one for each integer from −10 to 10.
We need to find the sum.
We can observe that the above sequence is a geometric sequence with the common ratio r = -1 and the first term a1 = [tex](-1)^{-10}[/tex] i.e., a1 = 1
We know that the formula of the sum of n-terms of a geometric sequence is:
[tex]S_n= a_1 \times (\frac{1-r^n}{1 -r} )[/tex]
For n = 21, r = -1 and a1 = 1
[tex]S_{21}=1 \times (\frac{1-(-1)^{21}}{1-(-1)} )\\\\S_{21 }= 1\times (\frac{1-(-1)}{1 +1} )\\\\S_{21 }=\frac{1+1}{2} \\\\S_{21 }= \frac{2}{2} \\\\S_{21 }= 1[/tex]
Therefore, [tex](-1)^{-10} +(-1)^{-9} +(-1)^{-8} +\cdots+ (-1)^9+ (-1)^{10}[/tex] = 1
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Jackson used all the butter to make the brownies. If each brownie is 19 1 9 of a batch, how many brownies did he make? Enter your answer in the box.
Answer:
9 brownies
Step-by-step explanation:
Since we are not given the total number of batches. Let us assume the total batches is 81
If each brownie is 1/9 of a batch, number of brownie made will be equivalent to:
Amount of brownie made = 1/9 × 81
Amount of brownie made = 81/9 = 9 brownies
Hence he made 9 brownies
Equivalent expression
The ladder touches the building at 4.53 meters right angle triangle vertical distance from the ground.
What is right-angled triangle?The triangle that has one 90 degrees angle is called right-angled triangle. The Pythagorean theorem is applicable for right-angled triangle.
What is the height of the point where the ladder touches the building A ladder leans up against a building at an angle of 65 degrees with the ground. the length of ladder = 5 meters
we understand that the ladder, building and ground together formed a right-angled triangle. The right angle is in between the building and ground. The length of ladder acts as a hypotenuse of this triangle. If we consider the angle 65 degrees,
then sin 65° = opposite side length / hypotenuse here, opposite side length = the required length we need to determine sin 65° × hypotenuse = opposite side opposite side = 0.9063 × 5 =4.53 meters
the ladder touches the build at 4.53 meters vertical distance from the ground.
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(52 − 3 − 8)− (− 82 − 9 + 12)
Type the correct answer in each box. Use numerals instead of words. Find the missing side and angle measures in triangle ABC. Round your answers to the nearest tenth. Scalene triangle ABC with side AC labeled 23 and side BC labeled 15. Angle A measures 40 degrees. The measure of angle B is approximately . The measure of angle C is approximately . The length of side AB is approximately
The measures of the angles of the triangles are
The measure of ∠B = 80.3°
The measure of ∠C = 59.7°
The length of side AB = 20.2 units
What is a Triangle?A triangle is a plane figure or polygon with three sides and three angles.
A Triangle has three vertices and the sum of the interior angles add up to 180°
Let the Triangle be ΔABC , such that
∠A + ∠B + ∠C = 180°
The area of the triangle = ( 1/2 ) x Length x Base
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
if a² + b² = c² , it is a right triangle
if a² + b² < c² , it is an obtuse triangle
if a² + b² > c² , it is an acute triangle
Given data ,
Let the triangle be represented as ΔABC
Now , the measure of side AC = 23
The measure of side BC = 15
The measure of ∠A = 40°
From the law of sines , we get
( sin A ) / a = ( sin B ) / b = ( sin C ) / c
Substitute the value of A and a in the equation , we get
sin ( 40 )° / 15 = sin B / 23
On simplifying the equation , we get
sin B = ( 23/15 ) x sin ( 40 )°
Now , m∠B = 80.27°
So , the measure of angle ∠B = 80.3°
And ,
The interior angles of a triangle is 180°
So , The measure of angle ∠C = 180° - ( 80.3° + 40° )
On simplifying the equation , we get
The measure of angle ∠C = 59.7°
Now ,
From the law of cosines , c² = a² + b² - 2ab ( cos C )
Substitute the value of a , b and cos C in the equation , we get
c² = 15² + 23² - 2 ( 15 ) ( 23 ) cos ( 59.7 )°
On simplifying the equation , we get
c² = 225 + 529 - 348.12363
c² = 405.87
Taking square roots on both sides of the equation , we get
c = 20.156
c = 20.2 units
Therefore, the measure of side AB = 20.2 units
Hence , the measures angles of triangle is solved
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Decide whether the rates are equivalent.
$16 for 4 pounds
$1 for 4 ounces
O Equivalent
O Not equivalent
HELP DUE IN 10 MINS!
Find the value of x and y in the kite below.
x=?? degrees
y=?? degrees
Answer:
Diagonals of a kite are perpendicular.
x = 90° - 58° = 32°y = 90° - 22° = 68°helppp plzzzzzzzz i will give brainlist
Rudy says that the sum of the measures of the exterior angles of a regular hexagon is 720°. Is Rudy correct? Why or why not?
Answer:
Yes, Rudy is correct
Explanation:
Number of sides of a hexagon = 6
The sum of all interior angles of a polygon with n sides = (n-2)*180
Here, since a regular hexagon has 6 sides, n = 6
= (6 - 2)*180
= 4*180
= 720 degrees
Hope it helps :)
Have a great day!
Find the volume of each solid. Round to the nearest tenth if necessary. Use 3.14 for or
22/7
A : 14.7 m3
B : 3.7 m3
C : 4.7 m
D : 6.7 m3
Answer:
1.1^2 = 1.21
1.21 x 3.14 = 3.7994
3.7994 x 2.9 = 11.01826
11.01826 divided by 3 = 3.67275333333 rounded = 3.7 m3
Which statement correctly describes this picture?
__________ are designed so that the objective of the test is not apparent to the test taker. A. Projective tests B. Source errors C. MMPI tests D. 16PF tests Please select the best answer from the choices provided A B C D
Projective tests are created so that the test taker cannot tell what they are testing for.
What is Projective tests?Projective tests are created so that the test taker cannot tell what they are testing for.A personality test used in psychology is called a projective test. This kind of test provides answers to confusing situations, phrases, or visuals. Unconscious motivations or attitudes are disclosed by asking the person a question or giving them a stimulus that is unclear. Projective exams are designed to enlighten individuals about sentiments, wants, and conflicts that are not readily apparent to them. Psychoanalysts try to find unconscious feelings that might be behind a person's troubles in life by evaluating responses to ambiguous stimuli. Projective testing is mostly used to evaluate personality functioning.To learn more about Projective tests refer to:
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Use the distributive property to simplify the expression
6(8x+5)
Step-by-step explanation:
6(8x+5)
Use the distributive property to multiply 6 by 8x+5.
48x+30
Hope it Helps!
find three fifth of Ghana cedis 200
Answer:
Hi.
three fifth of 200 is 120.
*HELP PLEASE*
In circle J with HJK = 146", find the HLK.
A) 214°
B) 73°
C) 292°
D) 46.5°
Answer:
B. 73°
Step-by-step explanation:
How do you solve this?.....Katherine has a loyalty card good for a 3% discount at her local grocery store. What number should she multiply the prices on the tags by to find the price she would have to pay, before tax, in one step?
Answer:
Step-by-step explanation:
To find the number Katherine should multiply the prices on the tags by to find the price she would have to pay before tax, we need to calculate the inverse of the discount percentage, which is 1 - (discount percentage / 100).
Given that the discount is 3% and we want to find the price after the discount, that means:
1 - (3/100) = 1 - 0.03 = 0.97
So, the number Katherine should multiply the prices on the tags by to find the price she would have to pay, before tax, in one step, is 0.97. Multiplying the price of an item by 0.97 is equivalent to subtracting 3% from the original price, which is the same as finding the final price after the discount.
For example, if an item is priced at $10, Katherine can multiply this by 0.97 to find that the final price she would have to pay before tax is $9.7
10*0.97 = 9.7
The annual gym subscription for a single member is Rs.1000, while an annual family membership is Rs.1500. The gym is considering increasing all membership fees by the same amount. If this is done then a single membership would cost 5/7 of a family membership. Determine the amount of the proposed increase.
The amount of the proposed increase is, Rs 1071.4
What is Division method?Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
The annual gym subscription for a single member is Rs.1000,
And, An annual family membership is Rs.1500.
Here, A single membership increased cost 5/7 of a family membership.
Hence, The increased cost = 5/7 of 1500
= 1071.4 Rupees
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How do you describe a logarithmic function?
A logarithmic function is a type of inverse function.
A logarithmic function is a type of inverse function that is commonly used in mathematics and science. It is typically written in the form of y = log base b (x), where b is the base of the logarithm, and x is the input value. The most common bases for logarithms are 10 (common logarithm) and e (natural logarithm).
The logarithmic function is the inverse of the exponential function with base b. This means that if y = log base b (x) then x = b^y
One way to describe a logarithmic function is to say that it represents the exponent to which the base number must be raised in order to produce the input value x. For example, log base 10 of 100 is 2, because 10^2 = 100.
Another way to describe a logarithmic function is to say that it is a way of expressing very large or small numbers in a more manageable form. For example, instead of expressing a number like 10^9 as 1 billion, it can be expressed as 9 using a logarithm to base 10.
It is also important to note that logarithmic function have some key characteristics such as:
The domain of a logarithmic function is x>0, since the logarithm of a non-positive number is undefined.
The range of a logarithmic function is all real numbers.
The graph of a logarithmic function has a vertical asymptote at x=0, since the logarithm of a non-positive number is undefined.
A logarithmic function is increasing over its domain and concave down.
The x-intercept of the graph is (1,0), since the logarithm of 1 is always 0.
Overall, logarithmic functions are mathematical tools that allow us to simplify the representation and manipulation of very large and small numbers, and are used in many areas of science and engineering.
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Kim paid $33 for 2 shirts and $48 for 3 shirts including a fixed shipping fee assuming the same function applies to any numbers of shirts bought how much in dollars would 1 shirt cost before the shipping fee
Answer:
33=2x+y, 48=3x+y
Step-by-step explanation:
Sorry my internet isn't working well. Go to math-way and put that in and it will give you the answer :)
Fill in the blank: If a number is located to the left
of another number on the number line, that
number is ____ the other number
Answer:
smaller/ less than
Answer:
less than
Step-by-step explanation:
On a number line, the values go from least to greatest, left to right. So if you go towards the left, the number is decreasing.
What are m∠1 and m∠2?
A. ∠1 = 30°, m∠2 = 35°
B. ∠1 = 35°, m∠2 = 30°
C. ∠1 = 65°, m∠2 = 60°
D. ∠1 = 85°, m∠2 = 80°
The measure of m∠1 = 85 degrees and m∠2 = 15 degrees.
The correct answer is option D: ∠1 = 85°, m∠2 = 15°.
What is the right triangle?
A right-angle triangle is a triangle that has one of its angles 90 degrees. The sum of angles in a right triangle is 180 degrees.
To find the measures of angles 1 and 2, we can use the fact that the sum of the angles in a triangle is 180 degrees.
We know that angles 1, 2, and 3 form a triangle, so we can write:
m∠1 + m∠2 + m∠3 = 180
Substituting the given values, we get:
m∠1 + m∠2 + 80 = 180
Simplifying, we get:
m∠1 + m∠2 = 100
We also know that angles 2, 3, and 4 form a triangle, so we can write:
m∠2 + m∠3 + m∠4 = 180
Substituting the given values, we get:
m∠2 + 80 + 85 = 180
Simplifying, we get:
m∠2 = 15
Substituting this value in the first equation, we get:
m∠1 + 15 = 100
Simplifying, we get:
m∠1 = 85
Therefore, the measure of m∠1 = 85 degrees and m∠2 = 15 degrees.
The correct answer is option D: ∠1 = 85°, m∠2 = 15°.
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Answer:
Step-by-step explanation:
The measure of m∠1 = 85 degrees and m∠2 = 15 degrees.
The correct answer is option D: ∠1 = 85°, m∠2 = 15°.
What is the right triangle?
A right-angle triangle is a triangle that has one of its angles 90 degrees. The sum of angles in a right triangle is 180 degrees.
To find the measures of angles 1 and 2, we can use the fact that the sum of the angles in a triangle is 180 degrees.
We know that angles 1, 2, and 3 form a triangle, so we can write:
m∠1 + m∠2 + m∠3 = 180
Substituting the given values, we get:
m∠1 + m∠2 + 80 = 180
Simplifying, we get:
m∠1 + m∠2 = 100
We also know that angles 2, 3, and 4 form a triangle, so we can write:
m∠2 + m∠3 + m∠4 = 180
Substituting the given values, we get:
m∠2 + 80 + 85 = 180
Simplifying, we get:
m∠2 = 15
Substituting this value in the first equation, we get:
m∠1 + 15 = 100
Simplifying, we get:
m∠1 = 85
Therefore, the measure of m∠1 = 85 degrees and m∠2 = 15 degrees.
The correct answer is option D: ∠1 = 85°, m∠2 = 15°.
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value of the 7 in the number 8765?
PLEASE HELP!
Answer:
the answer would be seven hundred
8,000
700
60
5
hope this helps :)
The value of 7 in the number represents 100th place.
What is a place value system?The mathematical expression is the combination of numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
The precise position of a number within a series is assigned a value by a place-value system.
The given number is 8765 in the number 7 is representing 100th place. The expanded form of the number can be written as:-
8765 = 8000 + 700 + 60 + 5
Here in the expanded form, it is observed that 7 is the 100th place of the number.
Therefore, the value of 7 in the number represents the 100th place.
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Which equation is the slope intercept form of this equation?
y - 4 = -2 (x – 5)
a- x = - 2y + 3
b- 2x + y = 6
c- y = -2x + 14
d- y – 4 = -2x + 10
Answer:
C
Step-by-step explanation:
Y - 4 = -2x + 10 Multiply -2 to the inside the brackets
Y = -2x + 14 Add the 4 over
Anyone know this? I’m a wee bit brain dead any help is appreciated
Answer:
I believe this is the only answer I got from you bro.
hope it helps.
Choose the type of variation that relates the variables in the table.
Answer:
Multiply the x by 5 to get the y
Which line L has a slope of zero?
Answer:
D
Step-by-step explanation:
GradientA Gradient is also called a slope of a line, which represents how steep a line is.
Formula of slope: Vertical difference ÷ Horizontal difference
For a slope to be zero, the line must be horizontal.
SolutionBased on the question given, we can deduce that D is a horizontal line and therefore the slope is zero.
help please thanks :))))))))))))))))
how to solve x-y+x/2 (if x=10, y=1)
solve for x.
please help with this problem i am really bad at geometry!! will give thanks
Answer:
[tex]x = 11[/tex]
Step-by-step explanation:
[tex] \frac{12x + 8 - 4x + 4}{2} = 50[/tex]
[tex] \frac{8x + 12}{2} = 50[/tex]
[tex]8x + 12 = 100[/tex]
[tex]8x = 88[/tex]
[tex]x = 11[/tex]
If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a Question 18 options: A) kite. B) trapezoid. C) hexagon. D) parallelogram.
If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
Option (d) is the correct choice.
A parallelogram is a straightforward quadrilateral with two sets of parallel sides in Euclidean geometry. A parallelogram's facing or opposing sides are of equal length, and its opposing angles are of similar size.
A parallelogram has the following qualities:
The opposing sides are equally spaced and parallel.
Angles on either side are equal.
The following or neighboring angles are supplemental.
All of the angles will be at right angles if any one of them is a right angle.
The two diagonals cut across one another.
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Pleaseeeee answer ASAP ✌
Answer:
h=10
Step-by-step explanation:
Answer:
7
Step-by-step explanation:
3/7 = h/14- 2/7
3/7=h/14 - 4/14
7/14 - 4/14 = 3/7
(4/14 is the same as 2/7)