Answer:
a₁ = - 16 , a₂₁ = 24
Step-by-step explanation:
The nth term of an AP is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Given a₂ = - 14 , then
a₁ + d = - 14 → (1)
The sum to n terms of an AP is
[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ]
Given S₂₁ = 84 , then
[tex]\frac{21}{2}[/tex] [ 2a₁ + (n - 1)d ] = 84 ( multiply both sides by 2 )
21(2a₁ + 20d) = 168 ( divide both sides by 21 )
2a₁ + 20d = 8 → (2)
From (1) d = - 14 - a₁ ← substitute into (2)
2a₁ + 20(- 14 - a₁) = 8 , that is
2a₁ - 280 - 20a₁ = 8
- 18a₁ - 280 = 8 ( add 280 to both sides )
- 18a₁ = 288 ( divide both sides by -18 )
a₁ = - 16
Substitute a₁ = - 16 into (1)
- 16 + d = - 14 ( add 16 to both sides )
d = 2
Then
a₂₁ = - 16 + 20(2) = - 16 + 40 = 24
Multiply (x + 1)(x + 3)
Answer:
x² + 4x + 3
Step-by-step explanation:
(x + 1)(x + 3)
Each term in the second factor is multiplied by each term in the first factor, that is
x(x + 3) + 1 (x + 3) ← distribute parenthesis
= x² + 3x + x + 3 ← collect like terms
= x² + 4x + 3
Answer:
it's the answer ...
hope your day will be happy
and the last add 3x+x = 4x
HELP ME PLEASE! IM IN SEARCH OF ANSWERS AND I DONT GET ANY UNDER MY POST SO IF YOU COULD, PLEASE ANSWER THIS QUESTION AND EXPLAIN IF YOU WANT.
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Answer:
3 a) 8x +8 in
3 b) 24 in
3 c) 4x +4 in
3 d) 16x + 16 in
Step-by-step explanation:
3 b) You have to put 2 in place of x and calculate the perimeter:
8•2 +8
16 +8
24 in
Need help ASAP pls !!!!
7. Dean has a checking account at City Center Bank. During the month of April, he made deposits
totaling $2,458.52 and wrote checks otaling $789.23. He paid a maintenance fee of $25 and
earned $3.24 in interest. His balance at the end of the month was $4,492.76. What was the
balance at the beginning of April
Answer:
2848.47
Step-by-step explanation:
Need help understanding! please and thank you.
Answer:
I only know 5 and 6. 7 stumped me
5) even
6) odd
Step-by-step explanation:
At 4:00 a.m., the temperature was -9°F. At noon, the temperature was 18°F. What
was the change in temperature??
help me pls :\
What number doubled and added to 12 gives 20?
Answer:
8
Step-by-step explanation:
4 doubled and added to 12 gives 20.
What is algebraic expression?A number, a variable, or a mix of numbers, variables, and operation symbols make up an expression. Two expressions joined by an equal sign form an equation. Word illustration: The product of 8 and 3. Word illustration: The product of 8 and 3 is 11
Given
Let number be x
2x + 12 = 20
2x = 20-12 = 8
2x = 8
x = 8/2 = 4
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Which theorem can be used to show that AABC = ADEC?
solve for variable (image attached)
Answer:
x = 2
Step-by-step explanation:
Given
[tex]\frac{3(6x+8)}{4}[/tex] = 15 ( multiply both sides by 4 to clear the fraction )
3(6x + 8) = 60 ( divide both sides by 3 )
6x + 8 = 20 ( subtract 8 from both sides )
6x = 12 ( divide both sides by 6 )
x = 2
The value of x in the equation is 2
The equation given :
3(6x + 8) / 4 = 15
Multiply both sides by 4
3(6x + 8) = 15 × 4
3(6x + 8) = 60
Open the bracket
18x + 24 = 60
18x = 60 - 24
18x = 36
x = 36/18
x = 2
The value of x in the equation is 2
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How many different ways can you use the digits 3 and 5 to write
expressions in exponential form? What are the expressions?
Answer:
Therefore , Total no of ways to fill the 3-digits number is = 3*3*3 =27 . So, we can make 27 different 3-digits number using these numbers 1 ,5 ,7 by arranging them in 27 different waysStep-by-step explanation:
Tom bought $81 worth of milk. The price of a bottle of Brand A milk was $1.50 and of Brand B milk was $2.10. He bought 40 bottles of Brand A milk. How many bottles of Brand B milk did he buy?
Will Mark Brainliest
A couple is getting married. The event venue for their reception costs $3000 plus $20 per guest for catering. Decorations will cost $750. If the couple wants to keep the total cost of their reception under $6,000, what is the maximum number of guests that they can invite? Define a variable, write an inequality and solve.
Answer:
112.5 guests
Step-by-step explanation:
3,000 + 750 = 3,750. 6,000 - 3,750 = 2,250. 2,250/20 = 112.5 hope this helps
A total of 388 tickets were sold for the school play. They were either adult tickets or student tickets. The number of student tickets sold was three times the number of adult tickets sold. How many adult tickets were sold?
Answer:
97
Step-by-step explanation:
388 (number of tickets) / 4 (number of groups (adults, and the 3 times as many kids))
If the number of student tickets sold was three times the number of adult tickets sold, 97 adult tickets were sold.
Let's assume the number of adult tickets sold is 'x.'
According to the information given, the number of student tickets sold was three times the number of adult tickets sold. So, the number of student tickets sold is 3x.
The total number of tickets sold is the sum of the adult and student tickets, which is 388:
x + 3x = 388
Now, combine like terms:
4x = 388
To find the value of 'x,' divide both sides of the equation by 4:
x = 388 / 4
x = 97
To verify the result, let's find the number of student tickets:
Number of student tickets = 3 * 97 = 291
Now, let's add the adult and student tickets:
97 (adult) + 291 (student) = 388
The result checks out, and we have 97 adult tickets and 291 student tickets, which together sum up to the total of 388 tickets sold for the school play.
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f(x) 2x+6; vertical shrink by a factor of 1/2
Prove that the bisector of the vertical angle of isosceles triangle is the perpendicular bisector of the base
Answer:
We will take two angles and name them 'x'
And their sum must equal 180
So,
x + x = 180
2x = 180
x = 180/90
x = 90
Hence, it is proved that the bisector of the vertical angle of isosceles triangle is the perpendicular bisector of the base.
Explain what are all of the properties of real numbers and use an example for each.
Answer:
mark me as a brainlist answer
Step-by-step explanation:
Give examples to explain the properties of real numbers
Property (a, b and c are real numbers, variables or algebraic expressions)Examples8.Additive Inverse Property a + (-a) = 04 + (-4) = 09.Multiplicative Inverse Property10.Zero Property of Multiplication a • 0 = 04 • 0 = 011.Closure Property of Addition a + b is a real number10 + 5 = 15 (a real number)
What is the equation of the line that passes through the point (4,-8)(4,−8) and has a slope of -1/2
9514 1404 393
Answer:
y +8 = -1/2(x -4)
Step-by-step explanation:
The point-slope form of the equation of a line is ...
y -k = m(x -h) . . . . . . . line with slope m through point (h, k)
Your line has a slope of -1/2 and goes through point (4, -8). Its equation is ...
y +8 = -1/2(x -4)
_____
In slope-intercept form, this is ...
y = -1/2x -6
In standard form, it is ...
x +2y = -12
express tan J as a fraction in simplest terms
Answer:
tan j = 15/9
Step-by-step explanation:
tan(theta) is equal to perpendicular by base
Please help simplify with work. Will give brainliest.
Answer:
[tex]162 {x}^{10} {y}^{4} {z}^{12} [/tex]
Step-by-step explanation:
[tex]2 {x}^{4} (9 {x}^{3} y^{2} {z}^{6} {)}^{2} [/tex]
➡️[tex] {9}^{2} \times ( {x}^{3} {)}^{2} \times ( {y}^{2} {)}^{2} \times ( {z}^{6} {)}^{2} [/tex]
➡️ [tex]81 \times ( {x}^{3} {)}^{2} \times ( {y}^{2} {)}^{2} \times ( {z}^{6} {)}^{2} [/tex]➡️ [tex]81 {x}^{6} \times ( {y}^{2} {)}^{2} \times ( {z}^{6} {)}^{2} [/tex]➡️ [tex]81 {x}^{6} {y}^{4} \times ( {z}^{6} {)}^{2} [/tex]➡️ [tex]81 {x}^{6} {y}^{4} {z}^{12} [/tex]➡️ [tex]2 {x}^{4} \times 81 {x}^{6} {y}^{4} {z}^{12} [/tex]➡️[tex]162 {x}^{4} \times {x}^{6} {y}^{4} {z}^{12} [/tex]
➡️[tex]162 {x}^{4 + 6} {y}^{4} {z}^{12} [/tex]
➡️[tex]162 {x}^{10} {y}^{4} {z}^{12} [/tex] ✅
Only some of the students in the Level 1 swim lessons move up to Level 2 at the end of the session. The table shows what fraction of each swim instructor's students move up to Level 2. Which list orders the fractions from least to greatest?
Answer:
7/12 ,2/3, 17/24, 3/4
Point W is on line segment V X. Given VX = 18 and VW = 14 determine the length W X
Answer: WX = 4
Concept:
Here, we need to know the idea of segment addition postulate.
The Segment Addition Postulate states that given 2 points A and C, a third point B lies on the line segment AC if and only if the distances between the points satisfy the equation AB + BC = AC.
Solve:
Given information
VX = 18
VW = 14
Given expression deducted from the segment addition postulate
WX = VX - VW
Substitute values into the expression
WX = 18 - 14
Simplify by subtraction
WX = 4
Hope this helps!! :)
Please let me know if you have any questions
Simplify: (14^6*15^5)/(35^6*6^5)
Answer:
2/5
Step-by-step explanation:
=(2*7)^6 * (3*5)^5/ (7*5)^6 * (2*3)^5
=(2^6 * 7^6) * ( 3^5 * 5^5) / (7^6 * 5^6) * ( 2^5* 3^5)
=2^5 * 2^1 * 5^5/ 5^5 * 5^1 *2^5
=2/5
The simplified expression of (14^6*15^5)/(35^6*6^5) is 2/5
How to simplify the expression?The expression is given as:
(14^6*15^5)/(35^6*6^5)
Express 14 as 2 * 7, 15 as 3 * 5 and 35 as 5 * 7
[tex]\frac{(2 * 7)^6 * (3 * 5)^5}{(5 * 7)^6 * (2 * 3)^5}[/tex]
Expand the expression
[tex]\frac{2^6 * 7^6 * 3^5 * 5^5}{5^6 * 7^6 * 2^5 * 3^5}[/tex]
Divide the common factors
[tex]\frac{2}{5 }[/tex]
Rewrite as:
2/5
Hence, the simplified expression of (14^6*15^5)/(35^6*6^5) is 2/5
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Terry has 14 coins. She has some quarters, 5 nickels and one dime more than she has nickels. How many of
each coin does she have? How much money does she have all together?
Answer:
1.60 ............................
2. Using what you learned in Question 1, try to write
each of these quadratic expressions as a product of
two linear expressions. That is, try to write each
expression in factored form.
a. x^2 + 5x + 6
b. x^2 + 2x - 15
C. X^2 - 3x + 10
d. x^2 - 9x+8
e. x^2 - 16
f. X^2 - 10x + 6
Answer:
Ans
Step-by-step explanation:
In Q. No. F, 1st page last step there is /2.
OK
I NEEDDD HELPPPP!! Order the numbers from least to greatest. 1=least and 4=greatest
Answer:
✓9/4,5/3,✓5,2.5
Step-by-step explanation:
✓9/4=3/2=1.5
✓5=2.2
5/3=1.6
What are the dimensions of this rectangle?
Answer:
F:53cm by 102cm
Step-by-step explanation:
The perimeter of a rectangle can be seen as 2l + 2w, with the length being l, and the width being d. If the ratio is 3:2, then 3+2= 5 parts would be the sum of the length and the width, This is half of the perimeter 2(l+w), so 510÷2 = 255. One part would be 255÷5=51.
If you put it into the ratio, effectively it is:
Length:Width
3×51:2×51
153 :102
Therefore the dimensions are 153cm by 102cm, which is F.
If 2x minus 4 equals negative 18 what is x with shown work
Answer:
-7
Step-by-step explanation:
Equation: 2x - 4 = -18
First, add 4 to both sides:
2x = -14
Finally, divide both sides by 2:
x = -7
Check (optional):
2(-7) - 4 = -18
-14 - 4 = -18
-18 = -18 so this is correct
If you're confused about any of these steps, just let me know and I'll try to clear it up for you! :)
Its line segment please help
Step-by-step explanation:
[tex]here \: c \: is \: the \: mid \: point \\ so \: bc = cd \\ 6x - 16 = 4x + 10 \\ x \: terms \: to \: gather \\ 6x - 4x = 10 + 16 \\ 2x = 26 \\ x = \frac{26}{2} = 13 \\ \\ thank \: you[/tex]
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Add dress and shoes together:
30 + 25 = 55
1/5 off means the total after discount would be 4/5 ( 1 - 1/5 = 4/5)
Multiply total price by 4/5:
55 x 4/5 = (55 x4)/5 = 220/5 = 44
Total after discount is 44
Now add shipping:
44 + 8 = 52
Total paid = £52
Answer:
She will pay $52
Step-by-step explanation:
So she buys them both, which equals 55 dollars. But the website has a deal that is if you buy both of them it's 1/5 of the price off. And 1/5 of 55 is $11, so 55-11=44. You might think you're done but your not. At the end it says they add $8 for the shipping/handling, which is 44+8. This equals 52 dollars. By the way substitute this money sign $ for the one on your page
Randy and Trey take turns cleaning offices on the weekends. It takes Randy at most 4 hours to clean the offices. It takes Trey at most 6 hours to clean the offices. What is the greatest amount of time it would take them to clean the offices together?
2.4 hours
2.5 hours
3.0 hours
4.0 hours
The answer is supposedly 2.4 hours, but how ?? Please explain. Thanks!
In one hour Randy cleans at least 1/4 of the offices and in one hour Trey cleans at least 1/6 of the offices.
Working together they would clean at least 1/4 + 1/6 = 5/12 of the offices.
Let x be the greatest amount of time it would take them to clean the offices together. Then we can write the following equation:
5x/12=1