Consider we need to find the first five terms of the given AP and the explicit formula.
Given:
[tex]a_n=a_{n-1}-3[/tex] when [tex]a_1=5[/tex]
To find:
First five terms of the given AP and the explicit formula.
Solution:
We have,
[tex]a_n=a_{n-1}-3[/tex] ...(i)
[tex]a_1=5[/tex], it means first term is 5.
Putting n=2 in (i), we get
[tex]a_2=a_{2-1}-3[/tex]
[tex]a_2=a_{1}-3[/tex]
[tex]a_2=5-3[/tex]
[tex]a_2=2[/tex]
Second term is 2. So, common difference is
[tex]d=a_2-a_1[/tex]
[tex]d=2-5[/tex]
[tex]d=-3[/tex]
First terms is 5 and common difference is -3. So, the first five terms of the AP are 5, 2, -1, -4, -7.
The explicit formula of an AP is
[tex]a_n=a_1+(n-1)d[/tex]
[tex]a_n=5+(n-1)(-3)[/tex]
[tex]a_n=5-3n+3[/tex]
[tex]a_n=8-3n[/tex]
Therefore, the explicit formula of AP is [tex]a_n=8-3n[/tex].
Which point represents the center of the circle shown below?
R
A
A. Point T
B. Points
C. Point A
D. Point o
Answer:
C.
Step-by-step explanation:
Which statement best explains if the graph correctly represents the proportional relationship y = 0.5x? (4 points)
A coordinate plane is shown. Points are graphed at 1 and 0.5 and 4 and 2. The points are joined by a line.
It does, the points shown on the line would be part of y = 0.5x.
It does, all proportions can be shown on a graph of this line.
It does not, the points shown would not be part of y = 0.5x.
It does not, proportions cannot be represented on a graph.
Answer:
I believe the answer is
Yes, the points shown on the line would be part of y = 0.5x
Answer:
A
Step-by-step explanation:
I’ll give 20 points.
Answer:
m∠AYB = 85°
m∠C = 50°
Step-by-step explanation:
By is the angle bisector of ∠ABC,
Therefore, m∠1 = m∠2 = 30°
m∠3 = 35°
m∠AYB + m∠YAB + m∠ABY = 180°
m∠AYB = 180° - [(m∠1 + m∠2) + m∠3]
= 180° - [(30° + 30°) + 35°]
= 180° - 95°
= 85°
m∠A + m∠B + m∠C = 180°
2(30°) + 2(35)° + m∠C = 180°
60° + 70° + m∠C = 180°
m∠C = 180° - 130°
m∠C= 50°
Answer:
Step-by-step explanation:
Three triangles have the side lengths given below:
Triangle X: 8cm, 13cm, 5cm
Triangle Y: 14cm, 30cm, 17cm
Triangle Z: 26cm, 10cm, 24cm
Which of the triangles could not be right triangles?
Answer:
Triangle Z
Step-by-step explanation:
If a triangle is a right angle triangle, it will follow the Pythagoras theorem.
By Pythagoras theorem,
(Hypotenuse)² = (Leg 1)² + (Leg 2)²
Options (1)
Side lengths of the triangle X: 8 cm, 13 cm, 5 cm
By Pythagoras theorem,
(13)² = 8² + 5²
169 = 64 + 25
169 = 69
False.
Option (2)
Side lengths of triangle Y: 14 cm, 30 cm, 17 cm
By Pythagoras theorem,
(30)² = (14)² + (13)²
900 = 196 + 169
900 = 365
False.
Option (3)
Side lengths of triangle Z: 26 cm, 10 cm, 24 cm
By Pythagoras theorem,
(26)² = (10)² + (24)²
676 = 100 + 576
676 = 676
True.
Therefore, triangle Z represents a right triangle.
b) The cost price of an article was Rs 4000.Find the marked price of the
article so that there will be a profit of 20% after allowing a discount of
20%. show process
Answer:
Market price = Rs. 6,000
Step-by-step explanation:
Given:
Cost price = R.s 4,000
Profit after discount = 20%
Discount = 20%
Find:
Market price
Computation:
Sales price = Cost price[1+Profit after discount]
Sales price = 4,000[1+20%]
Sales price = 4,800
Market price = Sales price[100/(100 - Discount)]
Market price = 4,800[100/(100 - 20%)]
Market price = Rs. 6,000
Do you think it’s possible to have an excess of friends Explain
Answer:
yes
Step-by-step explanation:
vvttgvggf
please help ASAP!!!!!
Answer:
a=16
Step-by-step explanation:
I believe this is right if it is wrong please tell me.
Answer:
16km
Step-by-step explanation:
Since its a right angle triangle we can use the pythogorean theorem, which is a^2 + b^2 = c^2
So if we apply it to this situation we get,
12^2 + b^2 = 20^2
144 + b^2 = 400
b^2= 400 - 144
b^2= 256
b= 16
So the answer is 16km
Hope this helped :)
A jeweler is making a triangular pendant. He has two sides of length 23 mm and 31 mm. What are the
possible lengths (in whole mm) for the third side?
Answer:
38.60mm
Step-by-step explanation:
Step one:
Given data
We are given that the dimension of the triangles are length 23 mm and 31 mm
Let us assume that the triangle is a right angle triangle
Step two:
Applying the Pythagoras theorem we can find the third as
[tex]z^2= x^2+y^2\\\\z^2= 31^2+23^2\\\\z^2= 961+529\\\\z^2= 1490\\\\[/tex]
square both sides
z= √ 1490
z= 38.60mm
Hence a possible dimension of the third side is 38.60mm
Solve the equation 8 sin x = 2.5 for
the interval 0° to 720°
Answer:
18.2°, 161.8° and 378.2°
Step-by-step explanation:
Given the expression:
8 sin x = 2.5
Divide both sides by 8
sinx = 2.5/8
Sinx = 0.3125
x = arcsin(0.3125)
x1 = 18.2
Since sin theta is positive in the second quadrant, x2 = 180 - 18.2 = 161.8°
Since our angle must lie in between 0° and 720°,then;
x3 = 360 + 18.2 = 378.2°
Hence the required angles are 18.2°, 161.8° and 378.2°
linear or non linear
b Identify the coefficient and the number of terms in the
following expression.
15x2 + 8
A.) Coefficient: x, number of terms: 1
B.) Coefficient: 2, number of terms: 2
C.) Coefficient: 8, number of terms: 1
D.) Coefficient: 15, number of terms: 2
write a quadratic polynomial, sum of whose zeroes is 2 and product is -8
Answer:
x^2 +2x-8
Step-by-step explanation:
Here, we want to write the quadratic polynomial given the sum of the root and the product
mathematically, we can have the factors as -2 And +4
So we have the equation as;
(x-2)(x + 4)
= x^2+ 2x - 8
Express in simplest form (5a^2-3a+8)+ ( -4a^2-1)+(15a +11)
Answer:
[tex]a^{2} + 12a + 18[/tex]
Step-by-step explanation:
Help if you’re good at math I’ll give brainliest
Answer:
(4,2)
Step-by-step explanation:
Just by looking at the graph, you can see that they intersect at (4,2). But just to check:
x - 2 = -0.5x + 4
1.5x = 6
x = 4
y = 4 - 2 = 2
(4,2)
As an estimation we are told 5 miles is 8 km.
Convert 20 km to miles.
Answer:
12.4 miles
Step by Step Explanation:
You have to multiply 20 by 0.6213 then you get your answer. You can round it if you want.
Answer:
12.5
Step-by-step explanation:
I got the answer on Hegarty maths
hope its helpfully
An original oil painting measures 55" x 55". The artist wants to produce prints that are 2.5 times smaller than the original painting. What will be the side length, in inches, of the prints?
Answer:
The side length of the prints is approximately 34.785 inches.
Step-by-step explanation:
First, we have to calculate the area of the original oil painting ([tex]A[/tex]), measured in square inches, by the following formula:
[tex]A = l^{2}[/tex] (1)
Where [tex]l[/tex] is the length of the side, measured in inches.
And the length of the miniature is determine by means of reduction factor ([tex]k[/tex]), with no unit:
[tex]\frac{A}{k} = l'^{2}[/tex] (2)
If we know that [tex]l = 55\,in[/tex] and [tex]k = 2.5[/tex], then the side length of the miniatures is:
[tex]l' = \sqrt{\frac{l^{2}}{k} }[/tex]
[tex]l' = \frac{l}{\sqrt{k}}[/tex]
[tex]l' = \frac{55\,in}{\sqrt{2.5}}[/tex]
[tex]l' \approx 34.785\,in[/tex]
The side length of the prints is approximately 34.785 inches.
2x-8+3x+2=4x+10+3x-6
Step by step
Answer:
2x-8+3x+2=4x+10+3x-6
We move all terms to the left:
2x-8+3x+2-(4x+10+3x-6)=0
We add all the numbers together, and all the variables
2x+3x-(7x+4)-8+2=0
We add all the numbers together, and all the variables
5x-(7x+4)-6=0
We get rid of parentheses
5x-7x-4-6=0
We add all the numbers together, and all the variables
-2x-10=0
We move all terms containing x to the left, all other terms to the right
-2x=10
x=10/-2
x=-5
Step-by-step explanation:
12.You spend $12 for a movie ticket. The theater charges 8% sales tax for each ticket sold. What is the sales tax you pay for your ticket?
What is the total cost you end up paying for your movie ticket in question #12?
Answer:
You end up paying $12.96 for the movies tickets
Step-by-step explanation:
Before Tax Price: $12.00
Sale Tax: 8.00% or $0.96
After Tax Price: $12.96
Janelle flies her kite several feet in the air. She then reels the kite in at a constant number of feet per minute. The equation y=-18+ 240 represents this situation, where x is the number of minutes and y is the height of the kite in the air. What does the number -18 in the equation represent?
A. The kite is 18 feet above the ground before Janelle starts reeling it in.
B. The kite ascends 18 feet per minute.
C.The kite descends 18 feet per minute.
D.The kite is 18 feet above the ground after Janelle is done reeling it in.
Examine these points on line u and line v. Line u: (9, –8), (5, 4) Line v: (4, 2), (7, –7) How many points of intersection are there between line u and line v?
Answer:
The line u and line v have no point of intersection because they are parallel lines
Step-by-step explanation:
The slope of a straight line is given as follows;
[tex]Slope, \, m =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
The slope of line u is (4 - (-8))/(5 - 9) = -3
The equation for line u is y - 4 = -3*(x - 5)
y = -3·x + 15 + 4 = 19 - 3·x
The slope for line v is (-7 - 2)/(7 - 4) = -3
The equation for the line v is y - 2 = -3*(x - 4)
∴ y = -3x + 12 + 2 = -3x + 14
y = 14 - 3·x
Therefore. line u and line v have the same slope and are therefore parallel and they do not intersect
Answer:
The correct answer is A: Zero
Step-by-step explanation:
Consider the graph of the linear equation 2x - 5y = 10.
A tour director collected AED 258 for 13 tour packages. Tour packages A cost AED 18 and tour package B costs AED 22. How many of each tour package were sold?
Answer:
6 packages B
7 packages A
Step-by-step explanation:
let the number of packages A be a and the number of packages B be b
Total number of packages is 13;
Thus;
a + b = 13 •••••(i)
Total package a cost is 18(a) = 18a
Total package b cost is 22(b) = 22b
Total of both is 258
18a + 22b = 258 •••••••(ii)
From i, a = 13-b
Put this in equation ii
18(13-b) + 22b = 258
234-18b + 22b = 258
4b = 258-234
4b = 24
b = 24/4 = 6
since;
a + b = 13
a + 6 = 13
a = 13-6
a = 7
Please help asap, thank you!
Answer:
x ≈ 2.1
y ≈ 5.4
w = 5
Step-by-step explanation:
The given parameters are;
Segment AC = 13
Segment BC = y
Segment AD = 12
Segment CD = w
Segment BD = x
By Pythagoras's theorem, for the right triangle ΔACD, we have;
[tex]\overline {AC}[/tex]² = [tex]\overline {AD}[/tex]² + [tex]\overline {CD}[/tex]²
∴ 13² = 12² + w²
w² = 13² - 12² = 25
w = √(25) = 5
w = 5
By, Pythagoras's theorem similarly, in the right triangle ΔBCD we have;
y² = x² + w²
∴ y² = x² + 5² = x² + 25
y² = x² + 25
In the right triangle ΔABC we have;
[tex]\overline {AB}[/tex]² = [tex]\overline {AC}[/tex]² + [tex]\overline {CB}[/tex]²
∴ (12 + x)² = 13² + y² = 13² + (x² + 25)
(12 + x)² = 13² + (x² + 25)
144 + 24·x + x² = 13² + x² + 25
24·x = 13² + 25 - 144 = 50
x = 50/24 ≈ 2.1
x ≈ 2.1
y² = x² + 25
∴ y = √(x² + 25) = √((50/24)² + 25) = 65/12 ≈ 5.4
y ≈ 5.4
Write the next three terms of the geometric sequence.
Answer:
5, 1, 0.2
Step-by-step explanation:
Divide the number by 5 to get the next one.
Please help with this acellus question!
Find the value of x.
2x-3
14
х
10
x = [?]
Enter
Answer:
The value of x is 5
Step-by-step explanation:
In the given triangle
∵ A segment joining two points lie on the two side
∵ This segment is parallel to the third side
∴ This segment divides the two sides into parts that have the same ratio
→ That means x over 2x - 3 equal to 10 over 14
∵ [tex]\frac{x}{2x-3}[/tex] = [tex]\frac{10}{14}[/tex]
→ By using cross multiplication
∴ 10 × (2x - 3) = x × 14
∴ 10(2x) - 10(3) = 14x
∴ 20x - 30 = 14x
→ Add 30 to both sides
∵ 20x - 30 + 30 = 14x + 30
∴ 20x = 14x + 30
→ Subtract 14x from both sides
∵ 20x - 14x = 14x - 14x + 30
∴ 6x = 30
→ Divide both sides by 6
∴ x = 5
∴ The value of x is 5
Answer:
x = 5
Hope This Helps Mate!
What is a benefit of health insurance? A. It covers outpatient surgery expenses for your family and friends. B. It guarantees a certain sum of money to your family after your death. C. It ensures that you get paid despite being absent from work because of poor health. D. It reduces the cost of your health services and treatments.
Answer: D. It reduces the cost of your health services and treatments.
Step-by-step explanation:
Health insurance is a form of insurance that is applicable when someone is sick and has medical expenses to pay.
The benefit of health insurance is that it reduces the cost of your health services and treatments.
Health insurance protects an individual from paying huge amount on medical costs. Once a person is insured, the expense paid by six person is typically low as the insurance company covers the expenses.
David is making patterns using these rules. Rule for Pattern A: start with 20 and subtract 2 Rule for Pattern B: start with 10 and subtract 1 Which patterns did David make?
Answer:
20,18,16,14,12,10,8,6,4,2
10,9,8,7,6,5,4,3,2,1
Step-by-step explanation:
Pattern A:
Rule : start with 20 and subtract 2
Pattern B:
Rule : Start with 10 and subtract 1
Pattern 1:
20 - 2 = 18
18 - 2 = 16
16 - 2 = 14
14 - 2 = 12
12 - 2 = 10
10 - 2 = 8
8 - 2 = 6
6 - 2 = 4
4 - 2 = 2
20,18,16,14,12,10,8,6,4,2
Pattern 2:
10 - 1 = 9
9 - 1 = 8
8 - 1 = 7
7 - 1 = 6
6 - 1 = 5
5 - 1 = 4
4 - 1 = 3
3 - 1 = 2
2 - 1 = 1
10,9,8,7,6,5,4,3,2,1
Explain why the quotient of two integers with different signs is negative PLEASE.
Answer:
Ok, so we have the fact that plus +minus=minus
Thats the fact. It always works that way that same signs means positive and different means negative, as explained with logic.
4+(-5)
So we know that 4 is positive and -5 is negative
if you look at it through a number line, substracting 5 from 4 you have
3--->2---->1---->0---->-1
Under zero, the negatives start, so its proved by maths and logic as well.
Step-by-step explanation:
The quotient of two integers with different signs is negative because if a number is divided by the negative number it always gives a negative value.
What is the quotient?The number being divided is referred to as the dividend, and the number being divided by it is referred to as the divisor. The quotient is the outcome of the division.
Due to the following causes, it is discovered that the two quotients with the two different signs give a negative quotient.
Divide the absolute values of the integers to divide the two numbers with a different sign. The ratio is adverse. Note from this rule that 12/–3 and −12/3 are equal to – 4.
The product of two negative integers has a positive quotient. If the indicators differ, the response is unfavorable. The answer is yes if the signals are consistent.
Thus, the quotient of two integers with different signs is negative because if a number is divided by the negative number it always gives a negative value.
Learn more about the quotient here,
https://brainly.com/question/16134410
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pls help and show ur work pls
i will give brainiest to whom is correct
What is the equation of the function shown in the table?
Input x -2 -1 0 1 2
Output y -3 -1 1 3 5
y = - 1/2 x - 1
y = 2x + 1
y = 2x - 2
y = -2x + 1
Answer:
y = 2x + 1
Step-by-step explanation:
According to the table:
+1 +1 +1 +1
[x] -2 -1 0 1 2
[y] -3 -1 1 3 5
+2 +2 +2 +2
y = mx + b
b is y when x = 0
m is the change in y divided by the change in m = ∆y/∆x or slope.
+2/+1 = 2 = m
y = 1 when x = 0 so b = 1
therefore y = 2x + 1