Hence option (B) is a correct choice and rest all other options are incorrect
1/b^2 ∑ (-1)^k(t^2/b^2)^k
Step-by-step explanation:
Remember that the sum of infinite GP is given by the formula blow:
First term=a
Common ratio=r
S=a/1 - r
Wherever the common ratio r falls within the interval (-1,1)
When the given series is compared to the infinite sum:
First term=a
Common ratio=r
S= a/1-r = 1/b^2+t^2
Now given: |t| < |b|=0<t^2/b^2<1
S=1/B^2.1/1-(-T^2/B^2)
=A=1
R=-T^2/B^2
Writing the general form:
Hence option (B) is a correct choice.
What are real numbers simple definition?
Real numbers can be defined as the union of both rational and irrational numbers. They can be both positive or negative and are denoted by the symbol “R”. All the natural numbers, decimals and fractions come under this category.
INCOMPLETE QUESTION: if b and t are real numbers such that 0<|t|<|b|, which of the following infinite series has sum 1b2 t2
A) 1/b^2 ∑(t^2/b^2)^k.
B) 1/b^2 ∑(-1)^K(t^2/b^2)^k.
C)B^2∑(T^2/B^2)^K
D)b^2∑(-1)(t^2/b^2)^k
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BRAINLIEST FOR THIS QUESTION
A shop sells orange juice in the following ways: 500 ml bottle for £1.40 2 litre carton for £2.50 each or 2 cartons for £4.50 3 litre carton for £3.50 What's the cheapest way of buying exactly 7 litres with no extra? Find the amount of each type of bottle or carton you need and the total cost of buying 7 litres.
The cheapest way of buying exactly 7 litres with no extra is buying 500 ml bottle for £1.40
The amount of buying 7 litres of orange juice at the cheapest buy is £2.52
What is the cheapest buy?500 ml bottle for £1.40
Convert ml to liters:
500 ml = 0.5 liters
Unit rate = 0.5/1.40
= £0.36 per liter
2 litre carton for £2.50
Unit rate = 2/2.50
= £0.8 per liter
2 cartons for £4.50
Unit rate = 2/4.50
= $0.44 per carton
3 litre carton for £3.50
Unit rate = 3 / 3.50
= £0.86 per liter
The cheapest buy per liter of the orange juice is buying 500 ml bottle for £1.40.
Therefore, the cost of 7 liters at the cheapest buy
= £0.36 per liter × 7
= £2.52
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How to do log2 in Excel?
The syntax for using BASE in Excel is "=LN(number,base)" where "number" is the number for which you want to calculate the logarithm and "base" is the base to which the logarithm should be calculated.
For example, if you want to calculate the logarithm of 10 to the base 2, you would use the formula "=LN(10,2)".
The idea is to express the given integer (20) in terms of either the base or the values given (3 and 5).
Next, since we have the multiplication sign, we use the addition law:
The power of the number becomes the product of the log, so we have:
When you have the same base and number, the result is always 1.
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-2y - 10 = x -10x
- y = −14
Answer:
Step-by-step explanation:
-2y-10=x-10x
-2(-14) - 10= x - 10x
28 - 10 = x - 10x
18= x-10x
18= -9x
/-9 /-9
-2=x
Each side when you plug in (-2) for x and (-14) for y you get 18.
If, when you plug in the number, you get different numbers for each side, then that means there's a mistake and the answer is wrong.
Hope this helps!
PLEASE PLEASE HELP I WILL MARK THE BRAINIEST (the little crown thingy)
Answer: A
Step-by-step explanation: They both go up but they have diffrent patterns
hopes this helps any
Answer:
A.
Step-by-step explanation:
the 'x' slot is going up two and the 'y' slot is going up one every change.
The rectangular floor of a classroom is 36 feet in length and 27 feet in width.A scale drawing of the floor has a length of 12 inches.What is the area, in square inches, of the floor in the scale drawing?
The area of the scale drawing is 108 square inches.
I know this because I divided 36 by 13 to get 3. Then I took 27/3 and got 9. So I knew that the scale drawing was 9 by 12 and so then I just multiplied 9 by 12 and got 108
Boxes A and B contain some counters.
6y + 2
counters
Box A
Clip A19b
4y + 6
counters
Box B
The number of counters in each box is the same.
Work out the value of y
Find a Clip
106
Please give me the answer it’s really hard no one will help
By simple algebra, The number of counters in each box is 2.
What is Algebra?Algebra is the study of mathematical symbols and the methods for incorporating them into formulas.
Why is algebra so difficult?Since algebra is the first math subject most students take where they must deal with variables, complex concepts, and problem-solving abilities, many find it scary.
Given,
counter in Box A = 6y+2
counter in Box b=4y+6
Since there are the same amount of counters in both boxes.
hence
6y+2=4y+6
6y-4y=6-2
2y=4
y=2
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y-int coordinates of y=x^2-5x+6, please explain
The y intercepts of the quadratic equation y = x² - 5x + 6 is given by (0 , 6)
and the x intercepts are ( 3 , 0 ) and ( 2, 0 )
What is Quadratic Equation?A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.
The roots of the quadratic equations are
x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )
where ( b² - 4ac ) is the discriminant
when ( b² - 4ac ) is positive, we get two real solutions
when discriminant is zero we get just one real solution (both answers are the same)
when discriminant is negative we get a pair of complex solutions
Given data ,
Let the quadratic equation be represented as A
Now , the value of A is
y = x² - 5x + 6 be equation (1)
On simplifying the equation , we get
y = x² - 2x - 3x + 6
Taking the common factors of the equation , we get
y = x ( x - 2 ) - 3 ( x - 2 )
On factorizing the equation , we get
y = ( x - 3 ) ( x - 2 )
To find the y intercepts , substitute the value of x = 0 , we get
y = ( 0 - 3 ) ( 0 - 2 )
y = ( -3 ) ( -2 )
So , y = 6
Hence , the y intercepts of the equation is ( 0 , 6 )
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Which simplified ratio correctly compares 5 meters to 100 centimeters?
A. 5:1
B. 20:1
C. 1:5
D. 1:20
The simplified ratio that compares 5 meters to 100 centimeters is 5: 1 .Option A
How to determine the ratioRatio is simply described as the non equal comparison of two numbers, variables, or events.
It shows how many times a number or variable contains another.
The comparison is also based on size.
From the information given, we have;
5 meter to 100 centimeters
It is important to note that;
100 centimeters = 1 meters
Also, 1 meter= 100 centimeters
5 meters = x centimeters
cross multiply
x = 100(5)
Multiply the values
x = 500 centimeters
Then,
5 meters = 1 meter
Hence, the ratio is 5:1
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Selena has 9 homemade bracelets for $12 each then 14 bracelets for $8 each. How much did she make in sales?
(Use the correct operation or combination of operations to solve the problem)
She will make a total profit of $220. Profits are amounts of money paid to a person with the right of immediate occupation for using the land when no permission has been granted for that use.
What are the different types of profit?Profit is the term used to describe the monetary gain experienced when the revenue from a commercial activity outpaces the costs, costs, and taxes incurred to support the activity in question. There are three primary ways to measure profit. These include operating profit, net profit, and gross profit. Gross profit and operating profit are indicators of how efficiently your company uses its resources to produce its goods and run day-to-day operations.
number of bracelets sold for $12 each=9
number of bracelets sold for $8 each=14
Total profit=9x12+8*14=$220
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A box contains six cards. Three of the cards are black on both sides, one card is black on one side and red on the other, and two of the cards are red on both sides. You pick a card uniformly at random from the box and look at a random side. Given that the side you see is red, what is the probability that the other side is red? Express your answer as a common fraction.
The probability that the other side of the card is red is [tex]\frac{4}{5}[/tex].
What is conditional probability?The possibility of an event or outcome happening contingent on the occurrence of a prior event or outcome is known as conditional probability. The probability of the prior event is multiplied by the current likelihood conditional, occurrence to determine the conditional probability.
Suppose you choose a red/black card:
The probability of choosing a red and black card is [tex]\frac{1}{6}[/tex].
Now, since this card has one side as red the probability of seeing a red side in this card is [tex]\frac{1}{2}[/tex].
Suppose you choose a red/red card:
The probability of choosing red and red card is 2/6.
Now, since the card has two red sides the probability of seeing red side in this card is [tex]\frac{2}{2}[/tex] .
Considering we see a single side of the card we have the following probability:
[tex]\frac{2}{6} * \frac{2}{2} = \frac{1}{3}[/tex]
The total probability of seeing a red side is [tex]\frac{1}{12} + \frac{1}{3} = \frac{5}{12}[/tex].
The probability that you pick red-red card and see a red side is [tex]\frac{1}{3}[/tex].
So, the conditional probability of both red sides is given as:
[tex]\frac{\frac{1}{3} }{\frac{5}{12} } = \frac{4}{5}[/tex]
Hence, the probability that the other side of the card is red is [tex]\frac{4}{5}[/tex].
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Please help me!
Will give you brainlist!!!!
The augmented matrix of a linear system has been reduced by row operations to the form shown. Continue the appropriate row operations and describe the solution set of the original system.
[1 7 3 -5]
[0 0 0 3]
[0 0 1 2]
[0 1 -1 4]
Select the correct choice below and; if necessary; fill in the answer boxes to complete your choice A: The solution set has exactly one element; (Type integers or simplified fractions B. The solution set has infintely many elements C. The solution set is empty:
For the given Augmented Matrix ,the correct option is :
A) The solution set has exactly one element.
The exact solution is x = -25 , y = 2 and z = 2.
Augmented Matrix:
An augmented matrix is a means of solving simple linear equations. Coefficients and constant values of linear equations are represented as matrices called augmented matrices. Simply put, an augmented matrix is a combination of two simple matrices along columns. If the first matrix has m columns and the second matrix has n columns, then the augmented matrix has m + n columns.
Now, as given the Augmented matrix:
[1 7 3 -5]
[0 0 0 3]
[0 0 1 2]
[0 1 -1 4]
From this system we get:
y - z = 4 --------------------------- (1)
z = 2
and, z = 3
and, x + 7y + 3z =-5 ---------------- (2)
Now, Solving the equation with z = 2,
y - 2 = 4
⇒ y = 6
and, putting y = 6 and z = 2
x + 7× 6 + 3×2 = -5
⇒ x + 42 + 6 = -5
⇒ x +48 = -5
⇒ x = -53
Therefore, x = -53, y=6 and z =2
Now, for z = 3 in equation (1)
y - 3= 4
⇒ y = 7
Putting y =7 and z =3, we get:
x + 7 × 7 + 3×3 = -5
⇒ x + 49 + 9 =-5
⇒ x + 58 = -5
⇒ x = -63
Therefore, x = -63, y =7 and z =3
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what must be true for (m+p) so that the value of the expression below is negative? Explain.
-2 + (m + p)
For the expression to be negative (m + p) < 2.
What is an expression?An expression is a group of terms and mathematical symbols which can be evaluated to a given value.
How to determine what must be true for (m+p)?Since we have the expression -2 + (m + p), we need to determine the value of (m + p) for which the value of the expression is negative.
This implies that the value of the expression is less than zero.
So, we proceed as follows.
Since the expression is -2 + (m + p), for it to be negative, it must be less than zero.
So, -2 + (m + p) < 0
⇒ -2 < -(m + p)
Dividing both sides by -1, we have that
-2/-1 < -(m + p)/-1
2 > (m + p)
(m + p) < 2
So, for the expression to be negative (m + p) < 2.
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Molly and Liza are exercising. Molly does
10 push-ups at the same time
as Liza
does 15 push-ups. When Molly does
40 push-ups, how many push-ups does
Liza do?
Answer:
25
Step-by-step explanation:
so molly and liza are exercising right?.so 10 push-ups at the same time wich means they do 10 push-ups together and liza push-ups 15 and molly does 40 pushups so. its addition so 10+15=25 so thats the answer.
What is 2 point midpoint?
The 2-point midpoint formula is a method for finding the equation of a line that passes through the midpoint of two given points.
The formula for the 2-point midpoint is:
y - y1 = m(x - x1)Where (x1, y1) and (x2, y2) are the two given points, and m is the slope of the line.
The slope of line is calculated by (y2-y1)/(x2-x1)
By using the midpoint of two given points, the 2-point midpoint formula eliminates the need for calculating the y-intercept of the line, which can save time and effort. It is particularly useful when working with geometric figures or real-world applications that involve moving objects or changing data. It also helps in predicting the values of future point when we know the past point.
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8. Given DF bisects LEDF, find n and then find FG. The diagram is not drawn to scale.
2 points
Show your work to find FG
Show your work to find n
GIVING 20 POINTS!!
The measure of length of FG is 105 units.
What is bisection?
To determine the roots of a polynomial problem, utilise the bisection method. It splits and separates the interval in which the equation's root is located. The continuous functions intermediate theorem serves as the method's guiding premise.
From the given diagram, since Line DF bisects angle EDG, then -
EF = FG
Given the following parameters -
EF = 9n - 3
FG = 8n + 9
Equating both expressions -
9n - 3 = 8n + 9
9n - 8n = 9 + 3
n = 12
Get the measure of FG -
FG = 8n + 9
FG = 8(12) + 9
FG = 96 + 9
FG = 105
Hence, the line FG measures as 105 units.
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How do you solve a 3 variable 2 equation?
The process of solving the 3 variable with 2 equation is explained below.
The term equation is defined as a relationship between two terms on either side of an equal sign.
Here we have the following steps to solve the 3 variable for two equation is solved accordingly.
First of all we have to take any two equations and solve it for one variable.
And then again we have to take another two pair of equations and solve for the same variable.
Now, we have a system of two equations with two unknown variables.
Then we have to solve the equation by using the appropriate arithmetic operations.
and then substitute it accordingly until all the value of the variable are solved.
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How do you graph the equation y = 1x / 2 + (-5)
To graph the equation y = 1x / 2 + (-5), you will need to plot several points that satisfy the equation and then connect them with a line.
To do this, you can pick a few values of x, substitute them into the equation to find the corresponding values of y, and then plot these points on the coordinate plane.
For example, if you choose x = -2, the corresponding value of y is (-2) * (1 / 2) + (-5) = -5.5. If you choose x = 0, the corresponding value of y is (0) * (1 / 2) + (-5) = -5. And if you choose x = 2, the corresponding value of y is (2) * (1 / 2) + (-5) = -4.
You can then plot these points on the coordinate plane and connect them with a line to graph the equation.
Im really sorry that I was unable to provide a picture. I hope this helped!
Answer:
Graph the line using the slope and y-intercept, or two points.
Slope:
1/2
y-intercept: (0,−5)
x y
0 −5
2 −4
Step-by-step explanation:
3: 5 and 2:10 is are equivalent . explain
The ratios are not equivalent.
1. What is the measure of angle ABE?
M Sesergab,
916 108 algns bris
risq
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2. Select all true statements about the figura
E
A
B
129
lellisisa
40°
gros
20 Wov
C
saq bebundenda
10 bos kasnil 62 anil
The solution is 40°
The measure of the angle ∠ABE = 40°
What are Parallel Lines Cut by Transversal?Straight, equally spaced lines that never cross each other and are on the same plane are called parallel lines. The angles that are created when any two parallel lines are intersected by a line (referred to as the transversal) have a relationship. Corresponding angles, Alternate Interior Angles, Alternate Exterior Angles, and Consecutive Interior Angles are some of the several pairs of angles that are created at this intersection.
Corresponding angles
When two parallel lines are intersected by a transversal, the corresponding angles have the same relative position
Alternate Interior Angles
Alternate interior angles are formed on the inside of two parallel lines which are intersected by a transversal.
Alternate Exterior Angles
The pairs of angles formed on either side of a transversal that divides two parallel lines are known as alternate exterior angles.
Consecutive Interior Angles
When two parallel lines are cut by a transversal, the pairs of angles formed on the inside of one side of the transversal are called consecutive interior angles or co-interior angles.
Given data ,
Let the angle be represented as ∠ABE
Now , let the line be EBC and the total angle of a straight line = 180°
And , the measure of ∠CBD = 40°
Since , ∠ABE and ∠CBD are vertically opposite angles ,
The measure of ∠ABE = measure of ∠CBD
Therefore , the value of ∠ABE = 40°
Hence , the measure of vertically opposite angle ∠ABE = 40°
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What is the discriminant of 3x^2 2x 1 0?
The discriminant of quadratic equation 3x^2 + 2x + 1 =0 is -8
We know that the standard form of quadratic equation is ax^2 + bx + c = 0, with a ≠ 0
The discriminant of quadratic equation ax^2 + bx + c = 0 is:
D = b^2 - 4ac
Comparing given quadratic equation 3x^2 + 2x + 1 =0 with ax^2 +bx + c = 0 we get,
a = 3, b = 2 and c = 1
So, the discriminant of given equation would be,
D = b^2 - 4ac
D = 2^2 - 4(3)(1)
D = 4 - 12
D = -8
Therefore, the discriminant is D = -8
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I really need help on this one too
The solution is Option C and Option D.
The exponential function is given by f ( x ) = 2 ( 3 )ˣ
The exponential function is given by f ( x ) = 800 / 4ˣ
What are the laws of exponents?
When you raise a quotient to a power you raise both the numerator and the denominator to the power. When you raise a number to a zero power you'll always get 1. Negative exponents are the reciprocals of the positive exponents.
The different Laws of exponents are:
mᵃ×mᵇ = mᵃ⁺ᵇ
mᵃ / mᵇ = mᵃ⁻ᵇ
( mᵃ )ᵇ = mᵃᵇ
mᵃ / nᵃ = ( m / n )ᵃ
m⁰ = 1
m⁻ᵃ = ( 1 / mᵃ )
Given data ,
Let the equation be represented as A
Now , the value of A is
a)
Let the x values be x = { 0 , 1 , 2 , 3 }
Let the y values be y = { 7 , 19 , 31 , 43 }
The equation of line is y = 12x + 7
This is a linear equation
b)
Let the x values be x = { 0 , 1 , 2 , 3 }
Let the y values be y = { 5 , 10 , 15 , 30 }
The equation is a quadratic equation
c)
Let the x values be x = { 0 , 1 , 2 , 3 }
Let the y values be y = { 2 , 6 , 18 , 54 }
The equation is y = 2 ( 3 )ˣ
This is an exponential function
d)
Let the x values be x = { 0 , 1 , 2 , 3 }
Let the y values be y = { 800 , 200 , 50 , 12.5 }
The equation is f ( x ) = ( 800 / 4ˣ )
This is an exponential function
Hence , the exponential equations are solved
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The two smaller angles of a right triangle have equal measures. find the measure of all three angles.
Answer:
Step-by-step explanation: Because all three angles of the triangle must equal to 180 degrees, the two smaller angles of the right triangle must be 45 degrees. This is because a right angle always is 90 degrees and because you know that the other two angles are the same, and it must all equal to 180, the angles must be 45 degrees, 45 degrees, and 90 degrees.
Angle 1: (right angle) 90 degrees
Angle 2: 45 degrees
Angle 3: 45 degrees
Can someone help me solve this?
The value of x is 15 units and the value of y is 12 units from the given figure.
What are similar triangles?Two triangles are similar if the angles are the same size or the corresponding sides are in the same ratio. Either of these conditions will prove two triangles are similar.
From the figure, AB is parallel to CD.
∠AOB=∠COD (Vertically opposite angles)
∠OAB=∠ODC (Alternate angles)
By AA similarity ΔAOB similar to ΔCOD
Now, 9/x =y/20 =3/5
9/x=3/5
x=15 units
y/20=3/5
y/4=3/1
y=12 units
Therefore, the value of x is 15 units and the value of y is 12 units from the given figure.
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HIJK is a square and KI = 6√2. Find HI
The length of HI will be;
⇒ 6 units.
What is Pythagoras theorem?The Pythagoras theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the square of the other two sides.
Given that;
HIJK is a square.
The length of KI = 6√2
Now,
Since, HIJK is a square.
Hence, There are all sides are equal.
Let the side of square = x
So, By Pythagoras theorem, we get;
⇒ KI² = HI² + HK²
Substitute the given values, we get;
⇒ (6√2)² = x² + x²
⇒ 72 = 2x²
⇒ x² = 36
⇒ x = √ 36
⇒ x = 6
Thus, The length of HI = 6 units
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Ben's mom is 22 years older than ben. In 5 years she will be 3 times as old as he will be. How old are they now?
In linear equation, Ben is 9 years old currently.
What in mathematics is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables. Equations with variables of power 1 are referred to as linear equations. One example with only one variable is where ax+b = 0, where a and b are real values and x is the variable.
Ben's mom = 22 years
Ben is 9 years old currently.
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Suppose that $a$ is a multiple of $3$ and $b$ is a multiple of $6$. Which of the following statements must be true? A. $b$ is a multiple of $3$. B. $a-b$ is a multiple of $3$. C. $a-b$ is a multiple of $6$. D. $a-b$ is a multiple of $2$. List the choices in your answer separated by commas. For example, if you think they are all true, then answer "A,B,C,D".
The statements that are true, based on the multiples of 3 and 6 are:
A. $b$ is a multiple of $3$. B. $a-b$ is a multiple of $3$. How do multiples relate ?When a number is a multiple of a smaller number, then all the multiples of that larger number, will be the multiples of the smaller number.
This means that all the multiples of 6 ( including b ) will be multiples of 3 as well because 6 is a multiple of 3.
It is also interesting to note that the difference between the multiples of 3 are also multiples of 3. This means that a - b will result in a number that is a multiple of 3.
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One computer in a lab is programmed to back up data at the turn of the minute every five minutes. Another computer is programmed to back up data at the turn of the minute every two minutes. Find the number of times in twenty-four hours that the two computers back up data at the same time.
(Assume that the computers do not back up at the start of the 24-hour period.)
The number of times which the two computers back up at the same time in twenty four hours as required is; 144.
How many times does the computers back up at the same time in 24 hours?It follows from the task content that the first computer backs up after every five minutes and the second computer backs up every two minutes.
On this note, the least common multiple of both backup times represents when the two computers back up at the same time.
Hence, since the LCM of 5 and 2 is; 10.
It follows that the two computers back up at the same time after every ten minutes.
Ultimately, the number of times for which they backup at the same time in 24 hours; since 60 minutes = 1 hour is;
= ( 24 × 60 ) / 10
= 24 × 6
= 144 times.
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Patel is solving 8x2 + 16x + 3 = 0. Which steps could he use to solve the quadratic equation? Select three options. 8(x2 + 2x + 1) = –3 + 8 x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot x = –1 Plus or minus StartRoot StartFraction 4 Over 8 EndFraction EndRoot 8(x2 + 2x + 1) = 3 + 1 8(x2 + 2x) = –3
The three steps which Patel could use to solve the quadratic equation include the following:
A. 8(x² + 2x + (2/2)²) = -3 + 8.
B. x = -1 ±√5/8
E. 8(x² + 2x) = -3.
How to solve the quadratic equation?In order to solve the given quadratic equation, we would use the completing the square method as follows;
Separating the variables in the quadratic equation from constant, we have the following;
8x² + 16x + 3 = 0
8x² + 16x = -3
By factorizing the common variables in the quadratic equation from constant, we have the following;
8(x² + 2x) = -3 (step 1).
By completing the squares in the brackets and then balancing the expression on the right-hand side, we have the following;
8(x² + 2x + (2/2)²) = -3 + 8 (step 2).
8(x² + 2x + 1) = -3 + 8
8(x + 1)² = 5
Dividing both sides of the quadratic equation by 8, we have the following;
(x + 1)² = 5
Taking the square root of both sides of the quadratic equation, we have the following;
(x + 1) = ±√5/8
x = -1 ±√5/8 (step 3).
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A school wants to buy a chalkboard that measures 1 meter by 2 meters. The chalkboard costs $31.00 per square meter. How much will the chalkboard cost?
Answer:
62$
Step-by-step explanation:
Board in square meters = 2×1 = 2 m²
Cost per square meter = $31.00
Total cost = 31×2 = $62.00
Answer:
The cost of the chalkboard is $27.74
Step-by-step explanation:
right!!