Answer:
a₄₅ = 13
Step-by-step explanation:
The n-th term of an arithmetic sequence with first term a₁ and common difference d is given by the formula ...
aₙ = a₁ +d(n -1)
SetupYou want the 45th term where a₁ = 2 and d = 1/4. Putting these values into the formula gives ...
a₄₅ = a₁ +d(n -1) = 2 +(1/4)(45 -1)
SolutionEvaluating this expression, we have ...
a₄₅ = 2 +44/4 = 2 +11
a₄₅ = 13
The 45th term of the sequence is 13.
The forty-fifth term of the sequence whose initial term a = [tex]2[/tex] and common difference d = [tex]\frac{1}{4}[/tex] is [tex]13[/tex]
How to find the nth term of the Arithmetic series?
The nth term of the arithmetic series is find by [tex]Tn = a+(n-1)d[/tex] where Tn is the nth term of the series a is called the initial number and is the common difference between two number. n is the number of term of that arithmetic series.
In the given series initial term a = [tex]2[/tex] and common difference d = [tex]\frac{1}{4}[/tex]
We have the find the forty-fifth term of the given series.
= [tex]Tn=a+(n-1)d[/tex]
= [tex]Tn = 2+(45-1)\frac{1}{4}[/tex]
= [tex]Tn=2+44\cdot\frac{1}{4}[/tex]
= [tex]Tn = 2+11[/tex]
= [tex]Tn = 13[/tex]
So, the forty-fifth term of the sequence whose initial term a = [tex]2[/tex] and common difference d = [tex]\frac{1}{4}[/tex] is [tex]13[/tex]
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Sierra ha a bottle with 2 cup of orange juice left. I thi enough to make 6 frozen juice bar? Explain
No, it depends upon the size of the bottle but it's not enough for a normal bottle to make 6 frozen juice bars.
No, 2 cups of orange juice is not enough to make 6 frozen juice bars. Each frozen juice bar typically requires a certain amount of juice, and it is likely that 6 bars would require more than 2 cups of juice. To be sure, you would need to check the recipe or packaging for the frozen juice bars to determine the exact amount of juice required per bar.
It is also important to note that even if the juice is enough to make 6 bars, it might not yield the same taste as desired because of the lack of enough juice, also the freezing process might not work as well as it should because of the small quantity of juice.
Therefore, It is not enough as it depends upon the size of the bottle but it's not enough for a normal bottle to make 6 frozen juice bars.
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Mr. Walker used proportions and the following example to teach students how to calculate speeds: An F-15 Eagle travels at a speed of 1,875 miles per hour for 3.5 hours. Which distance solves the proportion he used?
Answer:
6,562.5 miles
Step-by-step explanation:
The proportion is 1,875 miles/1 hour.
At that speed, the distance can be calculated when the time is known, which is 3.5 hours in this case:
(1,875 miles/hr)*(3.5 hr) = 6562.5 miles
How many prime triplets exist?
Answer:
A prime triplet is a set of three prime numbers that are consecutive and differ by 2 (e.g. 3, 5, 7). The first prime triplet is (3, 5, 7), and it is well known that there are no other prime triplets. There is only one prime triplet that exist.
It is important to note that the concept of prime triplet is not commonly used in number theory and there are not many studies that focus on counting the number of prime triplets. Also, it is not known if there are an infinite number of prime triplets or not.
Step-by-step explanation:
What do you first need to do to the problem 8 - 11?
Step-by-step explanation:
8-11= -3
which means it negative number
A baker is making cookies and number of cookies is represented by the function y = 5x + 9
where x is the time in hours and y is the total number of cookles in the bakery (in dozens). Select the rate of change for this situation.
The rate of change of the system will be equal to 5.
What is the rate of change?An indicator of how one quantity changes in proportion to another is called a rate of change. Consequently, if y is the dependent variable and x is the independent variable.
Rate of change = Slope of the line
Given that a baker is making cookies and the number of cookies is represented by the function y = 5x + 9 where x is the time in hours and y is the total number of cookies in the bakery.
For the given equation the slope is,
y = 5x + 9
Rate of change = slope
Rate of change = 5
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What is the formula of substitution reaction?
Let's assume that the reaction is taking place between alkyl bromide and the nucleophile is OH- , then the formula for substitution reaction will be , R-Br + OH− => R-OH + Br− .
Nucleophiles are known as organisms that are strongly linked to an area of positive charge in the form of an ion or a molecule. These are believed to be fully charged or to have negative ions on a molecule. Cyanide ions, water, hydroxide ions, and ammonia are common examples of nucleophiles.
Electrophiles are compounds which are involved in the electrophilic substitution process. They are the molecules that transfer a pair of electrons during the creation of a covalent bond.
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Which system has no solution y=-3x+8 6c+2y=-4.5i
Answer:6c+2y=4.5i
Step-by-step explanation:
i am pretty sure it that answer is because you cant add 2 variables in a problem well 2 different variable
hope its right
Is movie a real image?
A movie is not a real image, it is a series of still images or frames that are played back in rapid succession to create the illusion of motion.
Real images are those that are formed by light that has been refracted or reflected by an object or lens. These images are located on the same side of the lens as the object and can be projected onto a screen or viewed directly.
In movie, the images are typically captured on film or digitally and then played back on a screen at a high frame rate (usually 24 or 30 frames per second) to create the illusion of motion.
This is known as the persistence of vision effect. The images are not actually moving, but the human eye and brain perceive them as moving because of the rapid succession of still images.
In conclusion, a movie is not a real image, it is a series of still images played back in rapid succession to create the illusion of motion.
Real images are formed by light that has been refracted or reflected by an object or lens, whereas in movie the images are captured on film or digitally and then played back on a screen at a high frame rate to create the illusion of motion.
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What is the image of point 3 4?
The image of the point (3, 4) with respect to the line x = y is the point that results from reflecting (3, 4) across the line x = y.
To understand this, we first need to understand what it means for a point to be reflected across a line.
Reflection is a transformation that flips a figure across a mirror line or line of reflection. In this case, the line of reflection is x = y. When a point is reflected across a line, the image point is located on the opposite side of the line from the original point, and it is the same distance from the line as the original point.
To find the image of points (3, 4) with respect to x = y, we need to first draw a line x = y in the coordinate plane. Then, we can visualize points (3, 4) on one side of the line and their image on the other side.
When we reflect points (3, 4) across the line x = y, the coordinates of the point will be flipped. The new coordinates will be (4, 3) instead of (3, 4). So the image of the point (3, 4) with respect to x=y is (4,3)
In summary, the image of the point (3, 4) with respect to the line x = y is (4, 3), which is the point that results from reflecting (3, 4) across the line x = y by flipping the coordinates of the point.
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Can I get some help please and thank you!!
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
Write a list of steps that are needed to find the measure of ∠B
Solve the compound inequality n+2≤−5 and n+6≥−6
The solution of the inequality are n ≤ -7 and n ≥ -12.
How to solve compound inequality?A compound inequality is an inequality that combines two simple inequalities.
Therefore, let's solve the compound inequality individually.
n + 2 ≤ −5 and n + 6 ≥ −6
Hence,
n + 2 ≤ − 5
subtract 2 from both sides of the inequality
n + 2 - 2 ≤ − 5 - 2
n ≤ -7
n + 6 ≥ −6
subtract 6 from both sides of the inequality
n + 6 ≥ −6
n + 6 - 6 ≥ −6 - 6
n ≥ -12
Therefore, n ≤ -7 and n ≥ -12
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Which equation has the solutions x = startfraction negative 3 plus-or-minus startroot 3 endroot i over 2 endfraction? 2x2 + 6x + 9 = 0 x2 + 3x + 12 = 0 x2 + 3x + 3 = 0 2x2 + 6x + 3 = 0.
The equation that has the solutions [tex]\frac{-3 \pm \sqrt{3}i }{2}[/tex] will be a) 2x² + 6x + 9
Here we have to find the equation which has roots
[tex]\frac{-3 \pm \sqrt{3}i }{2}[/tex]
This means that the factors of the roots will be
[tex]x+\frac{3 + \sqrt{3}i }{2}[/tex] and [tex]x+\frac{3 - \sqrt{3}i }{2}[/tex]
Now since all our options are quadratic equations, they have to be a product of these 2 factors and ONLY an additional numerical co-efficient
Hence we get
[tex][x+\frac{3 + \sqrt{3}i }{2}][x+\frac{3 - \sqrt{3}i }{2}][/tex]
rearranging this will give us
[tex][x+\frac{3}{2} + \frac{ \sqrt{3}i }{2}][x+\frac{3}{2} - \frac{ \sqrt{3}i }{2}][/tex]
using the formula
a² - b² = (a + b)(a - b) we get
(x + 3/2)² - (√3i/2)²
= x² + 9/4 + 3x + 9/4 [since i² = -1]
Hence we get x² + 3x + 9/2
= a) 2x² + 6x + 9
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Correct Question
Which equation has the roots
[tex]\frac{3 \pm \sqrt{3}i }{2}[/tex]
a) 2x² + 6x + 9 = 0
b) x² + 3x + 12 = 0
c) x² + 3x + 3 = 0
d) 2x² + 6x + 3 = 0.
Which equation shows the value of -1.5 - 2.75
The value of the given expression is -4.25
What is an expression?
Expression in math is a sentence with a minimum of two numbers or variables and at least one math operation. This math operation can be addition, subtraction, multiplication, or division.
Given that, an expression, -1.5 - 2.75
= -1.5 - 2.75
= -1.5 + (-2.75)
= -4.25
Hence, the correct expression is -1.5 + (-2.75) = -4.25
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Roger received $200 for his birthday. He wants to use the money to buy new clothes for
work. He can buy pants for $30 and shirts for $20. He wants at least 6 new items. Which
combinations of shirts and pants can he buy?
Answer:
Step-by-step explanation: He can get 150 worth of clothes
He can buy 3 new shirts and 3 pairs of new pants!
Given: PR bisects ZQPS, PQ = 12 units, and PS= 12 units
Prove: QR
SR
P
S
How could you show QR SR?
OA.
OB.
O C.
R
OD.
Use AAS to show triangle PRQ is congruent to triangle PRS
Use SAS to show triangle PRQ is congruent to triangle SRP
Use SAS to show triangle PRQ is congruent to triangle PRS
Use ASA to show triangle PRQ is congruent to triangle PRS
Every matching portion of one triangle is congruent to the other if two triangles are congruent.
what is triangle ?A triangle, which is a polygon, has three sides and three vertices. One of geometry's basic shapes is it. A triangle with the vertices A, B, and C is referred to as Triangle ABC. A unique plane and triangle are discovered in Euclidean geometry when the three points are not collinear. Having three sides and three corners, a triangle is a polygon. The triangle's corners are defined as where the three sides meet one another end to end. 180 degrees is the result of adding the three triangle angles.
given
PQ = 12 units, and PS = 12 units, with PR dividing ZQPS.
OA validates AAS's triangular display. Triangle is consistent with PRQ. Triangle is shown by SAS thanks to PRS OC. Triangle is consistent with PRQ. SRP
Every matching portion of one triangle is congruent to the other if two triangles are congruent.
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Solve: 2.5x-3=18
be sure to show your work
One angle of an isosceles triangle measures 56°. What measures are possible for the other two angles? Choose all that apply.
The possible measures of the other two angles would be -
56° and 68° respectively.
What are triangles?A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane
Given is that one angle of an isosceles triangle measures 56°.
Angles opposite to equal sides are equal. In a isosceles triangle, two sides are equal. So, we can write -
∠1 = ∠2 = 56° {Angles opposite to equal sides are equal}
∠3 + ∠1 + ∠2 = 180
∠3 = 180 - 2 x 56
∠3 = 180 - 112
∠3 = 68°
Therefore, the possible measures of the other two angles would be -
56° and 68° respectively.
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NASA's InSight is a robotic lander designed to study the deep interior of Mars. The solar panels on InSight are shaped like regular decagons. Find the measure of each interior angle of the solar panels. Then find the measure of each exterior angle.
Interior angle: ?
Exterior angle: ?
An interior angle of a regular decagon is given by the formula (n-2) * 180 / n, where n is the number of sides. Since a decagon has 10 sides, the measure of each interior angle is (10-2) * 180 / 10 = 160 degrees.
The measure of each exterior angle of a regular polygon is given by the formula 360 / n, where n is the number of sides. So in the case of a decagon, each exterior angle measures 360 / 10 = 36 degrees.
Here's a box plot that summarizes the number of pencils in each student's desk.
H+++
0 2 4
+++
6
6
8
Number of pencils
Find the range of the data.
+++H
pencils
10 12 14
The range of the data on the boxplot is 12
How to determine teh rangeFrom the question, we have the following parameters that can be used in our computation:
The box plot
The range is calcilated as
Range = Maximum - Minimum
From the plot, we have
Maximum = 12
Minimum = 0
Substitute the known values in the above equation, so, we have the following representation
Range = 12 - 0
Evaluate
Range = 12
Hence, the range is 12
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What is the image of (-3,-4) after a dilation be a scale factor of 4 centered at the origin?
The image of the point (-3,-4) after a dilation with a scale factor of 4 centered at the origin is (12,-16).
What is triangle dilation?Generally, Dilation is a method for producing figures with a similar appearance.
By multiplying the distances between each point with the scale factor, each point is extended outwards from the center point D.
(Towards the outside in the event that the scale factor is greater than 1) To alter the profile of the triangle, move the points A, B, and C respectively.
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Answer:(-12, -16)
Step-by-step explanation:
I took the test
Three vehicles recorded the following information about their trips.
Van:500 miles in 7.5 hours
Truck:300 miles in 5 hours
Car:400 miles in 5.5 hours
Find the unit rate miles/hour for the van.
The unit rate of miles/hour taken by the van is 66.67 miles/hr.
What is unit rate?A unit rate is a price for one unit of something. This is written as a ratio with a denominator of one. A unit rate compares one amount to one unit of another amount. Unit rates include miles per hour, cost per item, and calories per serving.Here given that,
The records of the trip of three vehicles are:
Van:500 miles in 7.5 hours
Truck:300 miles in 5 hours
Car:400 miles in 5.5 hours
We have to find unit rate miles/hour of the van.
So ,
Van covers 500 miles in 7.5hrs.
To find the unit rate,
Unit rate = total distance covered / total time taken
By substituting the values,
unit rate = 500/7.5
= 66.67 miles/hr
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In AABC, a = 11, b = 20, and c = 28. Find m/A.
Measure of angle A is m∠A = 18.358
please help!! will give brainliest! only help if you know how to do this! (statistics and two-way tables)
A representative sample is one that is drawn at random from the population and is large enough to provide accurate data.
What is sample?A population refers to the entire population about which you want to draw conclusions. A sample is the specific group from which you will collect data. The sample size is always less than the total population size.A sample is a subset of the population that is representative of the whole. A sample is sometimes required because accessing the entire population is not always feasible or cost effective.For instance, suppose a researcher is investigating the impact of inflation on US families. It is not possible to reach all of the families in the United States. As a result, the researcher would use a representative sample of US families. This is referred to as a sample.To learn more about sample refer to :
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What is the relationship between squaring and getting the square root?
Finding a number's square root is the equivalent as squaring it, or the opposite process. When you multiply the square root of a given integer by itself, you get the original number. Since 8 x 8 equals 64, as fact, 8 is the square root of 64.
What is square roots?It is possible to multiply an integer by its square root in order to obtain the original value. Square root of, end square root is the symbol for this mathematical concept. Contrary to squaring, finding a number's square root is the reverse. For instance, 3 is squared at 9, 32, and its square root at 9, which is 9, is equal to 3. It is simple to multiply by 9 since it is a perfect square.
Thus, there is a reverse relationship between squaring and getting the square root.
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Can someone help me please Assap?
Step-by-step explanation:
[tex]\frac12(8k+12k^2+6k^3)\\=4k+6k^2+3k^3\\[/tex]
Rearrange into descending order:
[tex]\boxed{3k^3+6k^2+4k}[/tex]
EXPRESS 7 + 12x -3x^2 in the form a+b(x+c)^2
Answer:
19 - 3(x - 2)²
Step-by-step explanation:
7 + 12x - 3x² ( rearrange terms in x )
7 - 3x² + 12x ( factor out - 3 from each of the x- terms )
= 7 - 3(x² - 4x)
using the method of completing the square on x² - 4x
add/subtract ( half the coefficient of the x- term )² to x² - 4x
= 7 - 3(x² + 2(- 2)x + 4 - 4)
= 7 - 3(x - 2)² - 3(- 4)
= 7 - 3(x - 2)² + 12
= 19 - 3(x - 2)² ← in the form a + b(x + c)²
with a = 19 , b = - 3 , c = - 2
How do you find the image of a point across a line?
The point's x and y coordinates may be switched to create the point's image around the line y=x. As an illustration, consider the picture of the point (a,b) about the line y=x: (b,a).
What is image coordinate system?A main image's spatial reference is specified by an image coordinate system. No distortions appear when a main picture is presented in its own image coordinate system, and secondary images and features can be projected onto the primary image using its image coordinate system.
The point B(l,m) is the point that corresponds to the point P in the line mirror ax+by+c=0 such that PB is perpendicular to ax+by+c=0 and the midpoint L of PB falls on the line ax+by+c=0.
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Burger Mania ell 10 chicken nugget for $1. 50,At thi rate how much hould a family pack of 45 chicken nugget
The cost of a family pack of 45 chicken nuggets = 6.75 dollars
Given that Burger Mania sells 10 chicken nuggets for $1. 50
First we find the cost of one chicken nugget.
10 chicken nuggets = 1. 50 dollars
So, 1 chicken nugget = (1.50) / 10 dollars
= 0.15 dollars
= 15 cents
We need to find the cost of 45 chicken nuggets.
Using Unitary method the cost of 45 chicken nuggets would be,
45 × 0.15 = 6.75 dollars
Therefore, at given rate a family pack of 45 chicken nuggets must be 6.75 dollars
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How many images will be formed if 2 mirrors are kept at an angle of 72?
The number of images formed by two mirrors kept at an angle of 72° are;
5 images, If the object is positioned symmetrically between the mirrors
4 images if the object is placed asymmetrically between the mirrors
How can the number of images formed by two mirrors placed at an angle be found?The formula that can be used to find the number of images formed, n, when two mirrors are placed at a specified angle, θ, to each other is presented as follows;
If [tex]\dfrac{360^{\circ}}{\theta}[/tex] is an even number, the number of images formed is obtained using the formula;
[tex]n = \dfrac{360^{\circ}}{\theta} -1[/tex]If [tex]\dfrac{360^{\circ}}{\theta}[/tex] is an odd number, the number of images formed is obtained using the formula;
[tex]n = \dfrac{360^{\circ}}{\theta} -1[/tex]If [tex]\dfrac{360^{\circ}}{\theta}[/tex] is an odd number, and the position of the object is asymmetric, the number of images formed is obtained using the formula;
[tex]n = \dfrac{360^{\circ}}{\theta}[/tex]When θ = 72°, we get;
[tex]n = \dfrac{360^{\circ}}{72^{\circ}} = 5[/tex], which is an odd number, therefore;
If the object is placed symmetrically between the two mirrors, the number of images formed is therefore;
[tex]n = \dfrac{360^{\circ}}{72^{\circ}}-1 = 4[/tex]
If the object is placed asymmetrically between the two mirrors, the number of images formed is [tex]n = \dfrac{360^{\circ}}{72^{\circ}} = 5[/tex]
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A water tank ha the hape of an inverted right circular cone, with radiu at the top 15 meter and the depth 1 meter. Water i flowing into the tank at the rate of 2 cubic meter per minute. How fat i the depth of water in the tank increaing at the intant when the depth i 8 meter
The depth of water in the tank is increasing at the rate of approximately 0.0135 meters per minute when the depth is 8 meters.
A cone is a three-dimensional geometric structure with a smooth transition from a flat base—often but not always circular—to the point at the top, also known as the apex or vertex.
To find the rate at which the depth of water in the tank is increasing, we can use the formula for the volume of a cone:
V = (1/3) * π * r^2 * h
Where V is the volume, π is pi, r is the radius, and h is the height (depth) of the cone.
We know that the radius at the top of the tank is 15 meters, the depth of the tank is 8 meters, and the rate of water flow is 2 cubic meters per minute.
So we can use the above formula to find the rate at which the depth is increasing.
Let's call the rate at which the depth is increasing "dh/dt"
V = (1/3) * π * 15^2 * 8
dV/dt = (1/3) * π * 15^2 * dh/dt
Now we know that the rate at which the water is flowing is 2 cubic meters per minute, so we can substitute it for dV/dt
2 = (1/3) * π * 15^2 * dh/dt
Solving for dh/dt
dh/dt = 2/( (1/3) * π * 15^2 )
Therefore, the depth of water in the tank is increasing at the rate of approximately 0.0135 meters per minute when the depth is 8 meters.
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