Explicit formula is [tex]a_{n}[/tex] =a + (n-1)d
Here in the explicit formula of the sequence -2, 7, 16, 25....
Formula
[tex]a_{n}[/tex] = a +(n-1)d
In the formula, n is any term number and a(n) is the nth term.
This formula allows us to simply plug in the number of the term we are interested in, and we will get the value of that term.
To find the 5th term, for example, we need to plug n = 5 into the explicit formula.
common difference(d) = 7 - (-2) = 16- 7 = 9
[tex]a_{5}[/tex] = -2 + 9( 5-1)
= -2 + 36
= 34
To know more about the explicit formula for arithmetic sequence refer to the link given below:
https://brainly.com/question/11468530
#SPJ4
Determine the perimeter of a triangle with vertices defined by the given points to the nearest tenth. a(1,1),b(2,5),c(5,1)
A triangle with vertices located at A(1 , 1), B(2 , 5), and C(5 , 1) has a perimeter of 13.1 units.
A triangle is a two-dimensional shape that has three sides or edges and three vertices.
Perimeter refers to the distance around any two-dimensional shape. The perimeter of a triangle is the sum of the length of its sides.
To solve for the perimeter of triangle ABC with vertices located at A(1 , 1), B(2 , 5), and C(5 , 1), solve first for the length of each side, namely side AB, side BC, and side AC.
And to solve for the length of each side, use the distance formula given by:
d = √(x2 - x1)^2 + (y2-y1)^2
side AB : d = √(2 - 1)^2 + (5 - 1)^2 = √1 + 16 = √17 units
side BC : d = √(5 - 2)^2 + (1 - 5)^2 = √9 + 16 = √25 = 5 units
side AC : d = √(5 - 1)^2 + (1 - 1)^2 =√16 + 0 = √16 = 4 units
Solving for the perimeter of triangle ABC,
P = AB + BC + AC
P = √17 + 5 + 4
P = 4.123 + 9
P = 13.123 units
To learn more about perimeter of a triangle: https://brainly.com/question/323164
#SPJ4
3^4×2^3×3^7×2^2÷2^2×3^2×2^5×3^6
Answer:
the answer is
[tex] \frac{27}{4} [/tex]
If <3 measures 123°, what is the measure of <4?
The value of angle 4 is 57°
How to determine the angle
From the image shown, we can see that angle 3 and angle 4 are on a straight line.
It is important to note that angles on a straight line sum up to 180 degrees.
We have angles 1 and 2 are supplementary, that is, they sum up to 180 degrees
Angles 3 and 4 are also supplementary and sum up to 180 degrees
Angles 5 and 6 are also supplementary.
Then, if angle 3 = 123 , we have;
angle 3 + angles 4 = 180
123 + angle 4 = 180
Angle 4 = 180 - 123
Angle 4 = 57°
Thus, the value of angle 4 is 57°
Learn more about angles on a straight line here:
https://brainly.com/question/24024505
#SPJ1
1/5 (15b - 7) = 3b – 9
Answer: -7/5=-9
Step-by-step explanation:
I hope it helps
Answer: - 7/5 = -9
Step-by-step explanation: Combine like terms into single fraction, multiple by 1, subtract 3, simply.
(9.8)²-10² please help
Answer:
Step-by-step explanation:
-9
Collaborate
CSP Use Math Tools Work with a partner. If the measure of 21 in
the figure at the right is 40°, determine the measure of each given
angle without using a protractor. Then check your answers by
measuring with a protractor.
1. 22
3. 24
5. 26
7. 28
2. 23
4. 25
BeacO0CCO
6. 27
>
The measure of angles ∠1, ∠2, ∠3, ∠4, ∠5, ∠6, ∠7, and ∠8 will be 40°, 140°, 40°, 140°, 40°, 140°, 40°, and 140°, respectively.
What is an angle?The angle is the separation of the crossing surfaces or lines. Additionally, the angle is specified in degrees. One whole spin has an arc of 360 degrees.
If the total of two angles is 180 degrees, they are said to be supplementary angles.
In the third line, if two lines are parallel. Equal angles are formed by matching angles.
When two lines intersect, then their opposite angles are equal.
The measure of angle ∠1 is 40°.
Angle ∠1 and angle ∠2 are supplementary angles. Then the measure of angle ∠2 will be
∠1 + ∠2 = 180°
40° + ∠2 = 180°
∠2 = 140°
The vertical angles are given below.
∠1 = ∠3 = 40°
∠2 = ∠4 = 140°
The corresponding angles are given below.
∠1 = ∠5 = 40°
∠2 = ∠6 = 140°
∠3 = ∠7 = 40°
∠4 = ∠8 = 140°
Then the measure of angles ∠1, ∠2, ∠3, ∠4, ∠5, ∠6, ∠7, and ∠8 will be 40°, 140°, 40°, 140°, 40°, 140°, 40°, and 140°, respectively.
More about the angled link is given below.
https://brainly.com/question/15767203
#SPJ1
Read the question. Then fill in the correct answer on the answer document provided by your teacher or on a sheet of paper.
Suppose one base angle of an isosceles triangle has a measure of 44°. What is the measure of the vertex angle?
a. 108°
b. 92°
c. 56°
d. 44°
The measure of the vertex angle is 92°
Here,
The triangle is isosceles and one base angle of an isosceles triangle has a measure of 44°
We have to find the measure of the vertex angle.
What is Isosceles triangle?
A triangle is said to be isosceles if there is any two corresponding sides are equal and there angle are equal.
Now,
The triangle is isosceles triangle.
Hence, there corresponding sides and there angles are equal.
So, Both base angles of a triangle are equal.
And, Sum of angles of a triangle are 180°
Let the measure of the vertex angle is x°
Hence,
⇒ 44° + 44° + x° = 180°
⇒ x° = 180° - 88°
⇒ x° = 92°
Therefore, The measure of the vertex angle is 92°
Learn more about the isosceles triangle visit:
https://brainly.com/question/25812711
#SPJ4
I need help with this question please, my exam is tomorrow.
Answer:
Center: (2,2)
Radius: 2
Answers:
Center = (2,2)
Radius = 2
=================================================
Explanation:
Consider (A+B)^2 = A^2+2AB+B^2 after using the FOIL rule.
If A = x, then we have (x+B)^2 = x^2+2Bx+B^2
The coefficient of the x term is 2B. It divides in half to get B, and it squares to B^2 as the final term.
In short, if we want to complete the square on something like x^2-4x, then we do two things:
Divide the x coefficient in halfSquare the resultSo we go from -4 to -2 after dividing in half, and then from -2 to 4 after squaring. We'll add 4 to both sides to complete the square for the x terms.
[tex]x^2+y^2-4x-4y+4 = 0\\\\(x^2-4x)+(y^2-4y)+4 = 0\\\\(x^2-4x+4)+(y^2-4y)+4 = 4\\\\(x-2)^2+(y^2-4y)+4 = 4\\\\[/tex]
We'll do the same thing for the y terms. Though notice we already have a +4 on the left side. So we can have it absorb into the y terms parenthesis grouping like so
[tex](x-2)^2+(y^2-4y)+4 = 4\\\\(x-2)^2+(y^2-4y+4) = 4\\\\(x-2)^2+(y-2)^2 = 4\\\\[/tex]
Now compare that to the circle template
[tex](x-h)^2 + (y-k)^2 = r^2[/tex]
We see that
h = 2k = 2r = 2This circle has its center at (h,k) = (2,2)
The radius is r = 2
A conditional statement has the same truth value as:
Contrapositive
Converse
, ,
Inverse
A conditional statement has the same truth value as Contrapositive
How to complete the statement?From the question, we are to determine which type of conditional statement has the same truth value as the original statement
As a general rule, if the truth value of an original statement is True, the truth value of the contrapositive would also be true
Similarly;
If the truth value of an original statement is false, the truth value of the contrapositive would also be false
Hence, a conditional statement has the same truth value as contrapositive
Read more about conditional statement at:
https://brainly.com/question/11073037
#SPJ1
If DM = 35, what is the value of r? DG = r+2. GM = 2r-13.
Based on the given parameters, the value of r is 46/3
How to determine the value of r?
The given parameters are
DG = r + 2
GM = 2r - 13
DM = 35
This means that
DM = DG + GM
So, we have
r + 2 + 2r - 13 = 35
Evaluate the like terms
3r = 46
Divide both sides by 3
r = 46/3
Hence, the value of r is 46/3
Read more about line segments at:
https://brainly.com/question/2437195
#SPJ1
Please answer the question and help me pass
Answer:
10 *6= 60
60÷2=30
1÷2×b×h formula
answer- 30
Example 4 PH00F Write a two-column proof of Theorem 4.3 .
The proof of Theorem 4.3 with an example is shown.
What is theorem 4.3?Third Angles Theorem: If two angles of one triangle are congruent with two angles of another triangle, then the third angles must be congruent as well.To prove Theorem 4.3:
Let,s take two triangles, that is △ABC and △ADC.
In which AC⊥BD so ∠ACB ≅∠ACD.As, AC bisects ∠A so, ∠BAC ≅ ∠DAC.Since two pairs of angles are congruent, then the △ABC≅△ADC is under AA condition.
Then, ∠B≅∠D under CPCT condition (corresponding parts of congruent triangles).Therefore, the proof of Theorem 4.3 with an example is shown.
Know more about theorem 4.3 here:
https://brainly.com/question/2102943
#SPJ4
A diamond is purchased for $ 2500 . Suppose its value increases 5 % each year.
a. What is the value of diamond after 8 years?
Answer:
$3500
Step-by-step explanation:
x = value of diamond with an increase of 5% every year for 8 years
x= 2500(0.05)
x= 125(8)
x = 1000
2500 + 1000 = $3500
The value of the diamond after 8 years is the amount of $3693.63.
What is Compound interest?Compound interest is defined as interest paid on the original principal and the interest earned on the interest of the principal.
To find the value of the diamond after 8 years, we need to calculate the compound interest.
The formula for compound interest is:
A = P(1+r/100)ⁿ
here:
A = final amount
P = principal amount
r = annual interest rate (as a decimal)
t = time in years
Using this formula, we can calculate the value of the diamond after 8 years:
P = 2500
r = 5% = 0.05
t = 8
A = 2500 (1 + 0.05/1)¹ˣ⁸
A = 2500 (1.05)⁸
A = 2500 (1.4775)
A = $3693.63
Therefore, the value of the diamond after 8 years is $3693.63.
To learn more about Compound interest click here:
brainly.com/question/25857212
#SPJ2
-12x - 17 = -89
i neeeed help
Answer:
x = 6
Step-by-step explanation:
- 12x - 17 = - 89 ( add 17 to both sides )
- 12x = - 72 ( divide both sides by - 12 )
x = [tex]\frac{-72}{-12}[/tex] = 6
Given that →s is < 2,-6> and →t is <-10,7> , find the component form of →s + →t
The component form of →s + →t is <-8, 1>
We know that the component form of a vector is the ordered pair that describes the changes in the x- and y-values.
In this question, we have been given two vectors
vector s = < 2, -6>
and vector t = <-10, 7>
We need to find the component form of →s + →t
→s + →t
= < 2, -6> + <-10, 7>
= <2 + (-10), -6 + 7>
= <2 - 10, 1>
= <-8, 1>
Therefore, the component form of →s + →t is <-8, 1>
Learn more about the vectors here:
https://brainly.com/question/17607682
#SPJ4
A die is rolled. Find the probability of rolling a number greater than 4 .
F. 0.17
G. 0.33
H. 0.5
J. 0.67
The probability of getting a number that is greater than four is G. 0.33
Probability:
Probability defines the possible occurrence of the selected event across the total number of events.
Given,
A die is rolled.
And we need to find the probability of rolling a number greater than 4.
If you roll a single die there are 6 possible outcomes are
=> {1,2,3,4,5,6}
So, the numbers that are greater than 4 are,
=> 5 and 6.
So, there are 2 of which are greater than 4.
So in a single roll the probability of getting a number greater than 4 is
=> 2/6
=> 1/3.
For the decimal form it can be written as,
=> 0.33.
So, the correct option is G. 0.33.
Therefore, the probability of getting the number greater than 4 is 0.33.
To know more about Probability here.
https://brainly.com/question/27989637
#SPJ4
a is directly proportional to square of c.
w is inversely proportional to a³.
When c = 49, a = 35
When a = 2, w = 16.
Find the value of w when c = 4.
In the given question the value of w is 0.128.
What do we mean by directly proportional?When two quantities are directly proportional, it means that if one increases by a certain percentage, the other increases by the same percentage. For example, as the cost of gasoline rises, so do food prices.So, w when c = 4:
a∝√ca = k√c35 = k×7k = 5a = 5√cNow,
w ∝ 1/k³w = k/a³16 = k/8k = 128w = 128/a³Then,
c = 4a = 5×√4 = 10a = 10w = 128/10³w = 0.128Therefore, in the given question the value of w is 0.128.
Know more about directly proportional here:
https://brainly.com/question/24868934
#SPJ9
Sammie was looking for a dress to wear to the wedding. She found one that she liked for 20% off. To go along with it, she also purchased a necklace for $7.50. Which expression represents the amount Sammie spent?
The expression that represents the amount spent is 0.8x + 7.50
Which expression represents the amount Sammie spent?The given parameters are
Discount = 20%
Necklace = 7.50
Let the cost of the dress be x
So, the expression that represents the amount Sammie spent is
Expression = (1 - Discount) * x + Necklace
This gives
(1 - 20%) * x + 7.50
Evaluate
0.8x + 7.50
Hence, the expression that represents the amount spent is 0.8x + 7.50
Read more about discounts at:
https://brainly.com/question/7459025
#SPJ1
Find the simple interest paid on a 8 year loan
of $2764 at 12.25% interest
Answer: 1,585.12 is your interest. full is 4349.12
Step-by-step explanation: brainlist pls
Fill in the correct answer on the answer document provided by your teacher or on a sheet of paper.Kyle and his family are planning a vacation in Cancun, Mexico. Kyle wants to convert 200 US dollars to Mexican pesos for spending money. If 278 Mexican pesos are equivalent to 25 , how many pesos will Kyle get for 200?
F. 2178
G. 2224
H. 2396
J. 2504
Converting Mexican pesos to US dollars, Kyle will get 2224 Mexican pesos for 200 US dollars.
In mathematics, conversion is the process of changing the value of one form or unit to another. It can be changing ones unit of length, weight, volume or even currency to another.
A conversion factor is a number used to change one set of units to another, either by multiplying or dividing.
If 278 Mexican pesos is equivalent to 25 US dollars,
278 Mexican pesos = 25 US dollars
Dividing both sides by 25,
278/25 Mexican pesos = 25/25 US dollars
11.12 Mexican pesos = 1 US dollar
Therefore, 1 US dollar is equivalent to 11.12 Mexican pesos.
The conversion factor is 11.12 Mexican pesos/1 US dollar.
If Kyle wants to convert 200 US dollars to Mexican pesos for spending money, and 1 US dollar is equivalent to 11.12 Mexican pesos, multiply the amount by the conversion factor.
200 US dollars (11.12 Mexican pesos/1 US dollar)
= 2224 Mexican pesos
To learn more about conversion: https://brainly.com/question/97386
#SPJ4
A cell phone tower covers a circular area with a radius of 15 miles.
(a) If the tower is located at the origin, write an equation for this circular area of coverage.
If the tower is located at the origin, the equation of its circular area of coverage is [tex]x^{2} +y^{2} = 225[/tex]
A circle is a closed curve that is drawn from a fixed point. This point is called the center. All points on the curve are equidistant from this center point.
The equation of a circle with center at (h, k) and radius r is given by:
[tex](x - h)^{2} + (y-k)^{2} = r^{2}[/tex]
According to the given condition,
center is origin i.e., (h, k) is (0,0)
and r = 15.
Substituting these values in the equation above,
[tex](x - 0)^{2} + (y-0)^{2} = 15^{2}[/tex]
[tex]x^{2} + y^{2} = 225[/tex]
Thus, the equation of the tower located at origin and having coverage area of radius 15 miles is [tex]x^{2} + y^{2} = 225[/tex].
To learn more about circles, refer to this link:
brainly.com/question/23519482
#SPJ4
What is the slope of the line that passes through the given points?
d. Use the slope formula to show in part (a) that it does not matter which point you choose for (x₁, y₁) .
Lets consider an example to to show that it does not matter which point you choose for (x₁, y₁) .
Let the points be -
(2,1) and (4,7)
where x1 and x2 are 2, 4
y1 and y2 are 1,7.
So the formula for slope will be -
m = y2 - y1 / x2 - x1
⇒ 7 - 1 / 4 - 2
⇒ 6 / 2
⇒ 3 .......(1)
So, the slope of the equation is 3 for x1, x2 = 2, 4 and y1, y2 = 1,7
Now, let us consider,
x2 = 2 and x1 = 4 , y1 = 7 and y2 = 1
m = 1 - 7 / 2 - 4
m = -6 / -2
m = 3 ...........(2)
From (1) and (2), we can infer that it does not matter which point you choose for (x₁, y₁).
To learn more about slope of equations from given link
https://brainly.com/question/3493733
#SPJ4
Which equation has the variable, or missing number, in the correct place to match the given situation?
The Lerch family drove a total of 482 miles, starting on Friday and ending on Sunday. They drove 138 miles on Friday and 225 miles on Saturday. How many miles did they drive on Sunday?
From the total amount of miles driven, it is found the equation that matches the given situation is:
138 + 225 + x = 482.
Solving the equation, it is found that they drove 119 miles on Sunday.
How to find the total amount of miles driven?The total amount of miles driven is given by the addition of the number of miles driven on Friday, Saturday and Sunday.
The separate amounts are given as follows:
Friday: 138 miles.Saturday: 225 miles.Sunday: x miles.Total: 482 miles.Hence the equation that matches the given situation is:
138 + 225 + x = 482.
Solving the equation, we have that:
x = 482 - (138 + 225)
119.
They drove 119 miles on Sunday.
More can be learned about the addition of amounts at https://brainly.com/question/25734188
#SPJ1
Given p(x)=−3(x−4)2+14, what is the value of p(2)?
Answer:26
Step-by-step explanation:
-3(2-4)2+14= -3*-2*2+14=12+14=26
Ten students sit a test consisting of 20 questions. Two students get 8 questions correct and one student gets 9 questions correct. The remaining seven students all get at least 10 questions correct and the average number of questions answered correctly by these seven students is an integer. If the average number of questions answered correctly by all ten students is also an integer, then that integer is
(A) 10
(B) 11
(C) 12
(D) 13
(E) 14
Answer:
14
Step-by-step explanation:
That equation, with the given constraints, is easily solved using logical reasoning.10y is a multiple of 5, and 25 is a multiple of 5; that means 7x is a multiple of 5.And we know x is a number between 10 and 20. So x has to be 14
If m angle EFH = (5x+1), m angle HFG = 62 degrees, m angle EFG = (18x+11), find each measure
The measure of each angles are 21 and 83degrees
Addition postulateA line is defined as the distance between two points while an angle is the point where two lines intersect.
From the diagram shown, the expression below is true;
<EFH + <HFG = <EFG
Substitute the given parameters to have:
5x+1 + 62 = 18x + 11
Collect the like terms
5x - 18x = 11 - 63
-13x = -52
x = 52/13
x = 4
Find each measure
<EFH = 5(4) + 1
<EFH = 21
degrees
<EFG = 18(4) +11
<EFG = 72 + 11
<EFG = 83 degrees
Hence the measure of each angles are 21 and 83degrees
Learn more on addition postulate here: https://brainly.com/question/4208193
#SPJ1
If w = 22, what is the value of 4w − 12?
Answer:
76
Step-by-step explanation:
Well just substitute 22 in for w. Multiply 4 time 22 that equals 88. Then just subtract 12 from 88, and you end up with your final answer of 76
A bakery sells an average of 14 dozen cupcakes a day to about 50 customers. what is their average sale rate, in cupcakes per customer?
i also need the answer really quick!!!
The average sale rate is 3 cupcakes per customer.
What are mathematical operations?The principle of superposition denotes a mathematical operation (e.g., differentiation, multiplication by a constant) in which the action on the sum of two functions is the sum of the action on each function.So, in 1 dozen there are 12 pieces.
Then,
14 × 12 = 168168/50 = 3.36After rounding off: 3 pieces per customerTherefore, the average sale rate is 3 cupcakes per customer.
Know more about mathematical operations here:
brainly.com/question/28294142
#SPJ9
To determine the number of trout in a lake , a conservationist catches 171 trout,tags them and throws them back into the lake. Later 52 trout are caught; 13 of them are tagged. how many trout would the conservationist expect to be in the lake?
We can expect there to be 684 trout in the lake.
In the given statement is:
To determine the number of trout in a lake, a conservationist catches 171 trout, tags them and throws them back into the lake. Later 52 trout are caught; 13 of them are tagged.
Proportion:
A ratio gives us the measure of one quantity as compared to another quantity, and it is represented either as a fraction, decimal or a notation like a : b. When the same ratio is applicable to other quantities.
Now, According to the question:
Number of trout / number of trout = number of trout caught / caught that were tagged
Number of trout / 171 = 52/13
Number of trout = (171 x 52) / 13
Number of trout = 8,892 / 13 = 684
Hence, We can expect there to be 684 trout in the lake.
Learn more about Proportion at:
https://brainly.com/question/14147903
#SPJ1
A supermarket wants to find the percent of shoppers who use coupons. A manager interviews every shopper entering the greeting card aisle.
When the supermarket wants to find the percent of shoppers who use coupons. A manager interviews every shopper entering the greeting card aisle. This is a convenience sampling.
What is a convenience sampling?A non-probability sampling technique called convenience sampling includes taking a sample from the nearest area of the population. Pilot testing benefits the most from this kind of sample. The most popular kind of convenience sampling concentrates on gathering data from individuals (the sample) who are 'convenient' for the researcher to reach.
Convenience sampling techniques include inviting friends to take part in your study, gathering information from local sites, mailing surveys, and posting links on social media.
In conclusion, the correct option is A.
Learn more about sampling on;
https://brainly.com/question/24466382
#SPJ1
A supermarket wants to find the percent of shoppers who use coupons. A manager interviews every shopper entering the greeting card aisle.
convenience sample
Self-selected sample
systematic sample
random sample
