We can use the points (12, 5) and (9, 8) to solve.
Slope formula: y2-y1/x2-x1
= 8-5/9-12
= 3/-3
= -1
______
Best Regards,
Wolfyy :)
Need help with geometric sequences
30 points
Answer:
[tex]a_{n}[/tex] = 6[tex](5)^{n-1}[/tex]
Step-by-step explanation:
The n th term of a geometric sequence is
[tex]a_{n}[/tex] = a[tex](r)^{n-1}[/tex]
where a is the first term and r the common ratio
Here a = 6 and r = 30 ÷ 6 = 5, thus
[tex]a_{n}[/tex] = 6[tex](5)^{n-1}[/tex]
Molly is having her birthday party at Pizza Party Palace. The costs involved are listed below. Pizza Party Palace requires a 10% deposit prior to the date of the event. If the deposit has been paid, how much is still owed for Molly's party?
The right answer is Option D.
Step-by-step explanation:
Given,
Food and Drinks = $200
Game tokens = $100
Other = $60
Total amount = 200+100+60 = 360
Deposit = 10%
Deposit amount = 10% of total amount
[tex]Deposit\ amount=\frac{10}{100}*360\\Deposit\ amount=\frac{3600}{100}\\Deposit\ amount= \$36[/tex]
Amount left to be paid = Total amount - deposit amount
Amount left to be paid = [tex]360-36=\$324[/tex]
$324 is still owed for Molly's party.
The right answer is Option D.
Keywords: Percentage, subtraction
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A student in Greece discovers a pottery bowl
that contains 21% of its original amount of C-
14.
N = Noe-kt
No = inital amount of C-14 (at time t = 0)
N = amount of C-14 at timet
t = time, in years
k = 0.0001
age of the pottery bowl to the nearest year??
Answer:
The age of the pottery bowl to the nearest year is 15606 years.
Step-by-step explanation:
Let the initial amount of C-14 in the bowl i.e. [tex]N_{0} = 100[/tex] and today (say after t years) the amount of C-14 in the bowl i.e. N = 21.
Therefore, from the given equation we can write
[tex]21 = 100 e^{- 0.0001t}[/tex] {Since, k is give to be 0.0001}
⇒ [tex]0.21 = e^{- 0.0001t}[/tex]
Now, taking ln on both sides we get
ln 0.21 = - 0.0001t (ln e) {Since, [tex]\ln a^{b} = b \ln a[/tex]}
⇒ - 1.560647 = - 0.0001t {We have ln e = 1}
⇒ t = 15606.47 years ≈ 15606 years
Therefore, the age of the pottery bowl to the nearest year is 15606 years.(Answer)
3. Evaluate a + b for a = -46 and b= 34.
A:-12
B:80
C:-80
D:12
Answer:
A: -12Step-by-step explanation:
Put the values of a = -46 and b = 34 to the expression a + b:
-46 + 34 use the commutative property a + b = b + a
= 34 + (-46) = 34 - 46 = -12
The question is asking to evaluate the expression a + b, with a being -46 and b being 34. Evaluating the expression, we substitute the given values in to get -12. Therefore, the correct answer is A: -12.
Explanation:In algebra, when a question asks us to evaluate an expression, that simply means we need to substitute the given values into the equation and perform the operations to simplify it. In this problem, the expression is a + b, and the values given are a = -46 and b = 34.
To evaluate this, we substitute the given values in: (-46) + 34. When you add -46 and 34 together, you get a result of -12. Therefore, the correct answer is A: -12.
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What does x equal if x-10 divided by x-4 equals 50 divided by -6
Answer:
x=65/14
Step-by-step explanation:
(x-10)/(x-4)=50/-6
-50/6=-25/3
(x-10)/(x-4)=-25/3
x-10=-25/3(x-4)
x-10=-25/3x+100/3
x-(-25/3x)=100/3+10
x+25/3x=130/3
28/3x=130/3
x=(130/3)/(28/3)
x=(130/3)(3/28)
x=130/28
x=65/14
Elsa is taking physical fitness tests in her strength training class. Each day, her results are compared to her results from previous days. The first day she completes a test is considered the baseline and is represented by 0. For instance, on the first day she did the flexibility test, her result was calculated as 0. On the second day, in comparison to her first day's result, she was able to reach 1/16inches less than the first day, which was recorded as - 1/16. Then, on the third day, Elsa recorded a result of -5/8.
A. On which day did Elsa reach farther: the second or third day?
B. By how much?
HELP ME D:
Answer:
A) The second day
B) 9/16 inches
Step-by-step explanation:
A) Elsa reached farther on the second day because -1/16 > -5/8
B) To calculate this we must first put both fractions above the same denominator. We can then subtract the smaller one from the bigger one:
-1/16 - (-10/16) = 9/16
Elsa reached 9/16 inches farther on the second day then she did on the first.
Final answer:
Elsa reached farther on the second day than the third day during her flexibility tests. She reached 9/16 inches farther on the second day compared to the third day.
Explanation:
Elsa is taking physical fitness tests in her strength training class where she tracks her progress by comparing her flexibility results to the baseline (first day). A negative value indicates she did not reach as far as the baseline.
A. On the second day, Elsa's flexibility test result was recorded as - 1/16 inches, and on the third day, it was -5/8 inches. Since -1/16 is greater than -5/8 (closer to zero), it means Elsa reached farther on the second day than the third day.
B. To find out by how much Elsa reached farther on the second day compared to the third day, we calculate the difference between the two measurements: (-1/16) - (-5/8) = 5/8 - 1/16. We must find a common denominator to subtract these fractions, which is 16. So we have (10/16) - (1/16) = 9/16 inches. Therefore, Elsa reached 9/16 inches farther on the second day compared to the third day.
A 2-column table has 4 rows. The first column is labeled x with entries negative 2, negative 1, 0, 1. The second column is labeled f (x) with entries 0.004, 0.02, 0.1, 0.5.
What is the growth factor of the exponential function represented by the table?
0.2
0.1
5
20
Answer:
5
Step-by-step explanation:
take 0.5 divided by 5 and it gives you your next number on the chart:)
Answer: 5
Step-by-step explanation:
The growth factor of the exponential function is the ratio of the two consecutive terms (y-values).
i.e. Growth factor = [tex]b=\dfrac{y(x_2)}{y(x_1)}[/tex]
As per given , we have table
x y
-2 0.004
-1 0.02
0 0.1
1 0.5
Then, for [tex]x_1=-2[/tex] and [tex]x_2=-1[/tex] the growth factor of the exponential function represented by the table would be :
[tex]b=\dfrac{y(-1)}{y(-2)}=\dfrac{0.02}{0.004} =5[/tex]
Hence, the growth factor of the exponential function represented by the table is 5 .
Solve the system of equations: 2x + 3y = 13 x = 2 + 3y
PLEASE HELP ME I don’t know the answer
Answer:
7 and 8 would work
Step-by-step explanation:
just insert them as w and they have to be greater than 20. I hope this helps.
Answer:
7 and 8
Step-by-step explanation:
Solving the inequality
5w - 10 > 20 ( add 10 to both sides )
5w > 30 ( divide both sides by 5 )
w > 6
The only values from the solution set greater than 6 are
7 and 8
What is the factored form of the quadratic expression x^2+36
Answer:
(x − 6i) (x + 6i)
Step-by-step explanation:
Using real numbers, x² + 36 is already simplified.
Using imaginary numbers:
x² + 36
x² − 36i²
(x − 6i) (x + 6i)
ts Graph the line whose x-intercept is 5 and whose y-intercept is 3
Answer:
The equation of line whose x-intercept is 5 and whose y-intercept is 3
is given as 5 y + 3x = 15.
Step-by-step explanation:
Here, the given x - intercept = 5.
⇒ The point on the given equation is (x,0) = (5,0)
And, the y- intercept is given as 3
⇒ The point on the given equation is (0,y) = (0,3)
So, the two points given on the equation of line is A(5,0) and B(0,3)
Now, the slope of the line equation [tex]m = \frac{y_2 - y_2}{x_2-x_1}[/tex]
So, here the slope of line AB is [tex]m = \frac{3- 0}{0-5} = -\frac{3}{5}[/tex]
Now by POINT SLOPE FORMULA:
The equation of a line with point (x0,y0) and slope m is given as:
(y- y0) = m (x-x0)
⇒The equation of line AB is given as
[tex]( y - 0) = -\frac{3}{5} (x -5)\\\implies 5 y = -3x + 15\\\implies 5 y + 3x = 15[/tex]
Hence, the equation of line AB is given as 5 y + 3x = 15.
2.3 is 46% of what number
Answer:
46% × 2.3 =
(46 ÷ 100) × 2.3 =
(46 × 2.3) ÷ 100 =
105.8 ÷ 100 =
1.058 ≈
1.06;
find the solution of this system of equations. -x - 5y= 30, 10x + 5y= -75
Answer:
x=-5, y=-5. (-5, -5).
Step-by-step explanation:
-x-5y=30
10x+5y=-75
-----------------
9x=-45
x=-45/9
x=-5
-(-5)-5y=30
5-5y=30
5y=5-30
5y=-25
y=-25/5
y=-5
13 + 2k = 3k + 4(k - 3)
Answer:
k=5
Step-by-step explanation:
7
k
−
12
=
13
+
2
k
Move all terms containing
k
to the left side of the equation.
PLEASE HELP!!!!!!!! y+1=1/3(x−3) how do i graph this? what are the points?
Step-by-step explanation:
You have the equation of a line in the point-slope form:
[tex]y-y_1=m(x-x_1)[/tex]
m - slope
(x₁, y₁) - point on a line
Convert the given equation to the slope-intercept form:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept (0, b)
[tex]y+1=\dfrac{1}{3}(x-3)[/tex] use the distributive property
[tex]y+1=\dfrac{1}{3}x-1[/tex] subtract 1 from both sides
[tex]y=\dfrac{1}{3}x-2[/tex]
We only need two points to draw the line.
Choose two different x values. Put them in the line equation and calculate the y values:
for x = 0:
[tex]y=\dfrac{1}{3}(0)-2=0-2=-2\to(0,\ -2)[/tex]
for x = 3:
[tex]y=\dfrac{1}{3}(3)-2=1-2=-1\to(3,\ -1)[/tex]
6 identical sunglasses cost $420. What is the cost of one pair of sunglasses?
Answer:
One pair of sunglasses is $70
Step-by-step explanation:
Which value satisfies the inequality 5x + 7 ≤ 8x - 3 + 2x?
A) -2
Eliminate
B) -1
C) 0
D) 2
Answer:
D) 2
Step-by-step explanation:
5x + 7 [tex]\leq[/tex] 8x -3 +2x
5x + 7 [tex]\leq[/tex] 10x - 3
7 + 3 [tex]\leq[/tex] 10x - 5x
10 [tex]\leq[/tex] 5x
2[tex]\leq[/tex] x
x[tex]\geq[/tex]2
Find a quadratic function that includes the set of values below.
(0,9). (2,15) (3,12)
Answer:
[tex]f(x) = -2x^2 + 7x + 9[/tex]
Step-by-step explanation:
[tex]f(x) = ax^2 + bx + c\\f(0) = 9 => c = 9;\\f(2) = 15 = 4a + 2b + 9 <=> 2a + b = 3\\f(3) = 9a + 3b + 9 = 12 <=> 3a + b = 1\\Subtract the second equation from the first:\\-a = 2 => a = -2; b = 7; c = 9\\f(x) = -2x^2 + 7x + 9[/tex]
To find a quadratic function, substitute each given coordinate into the equation and solve the resulting system of equations.
Explanation:To find a quadratic function, we need to use the form y = ax^2 + bx + c. From the given set of values, we can substitute each coordinate (x, y) into the equation to get three different equations. So:
When x = 0, y = 9, we get: 9 = a(0)^2 + b(0) + c, which simplifies to c = 9.When x = 2, y = 15, we get: 15 = a(2)^2 + b(2) + 9, which simplifies to 4a + 2b = 6.When x = 3, y = 12, we get: 12 = a(3)^2 + b(3) + 9, which simplifies to 9a + 3b = 3.Now we have a system of equations that we can solve simultaneously. Solving the second and third equations using any appropriate method, we find that a = -1 and b = 5.
Therefore, the quadratic function that includes the given set of values is y = -x^2 + 5x + 9.
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The first term in this sequence is -1. Write the function that represents the sequence
Answer:
[tex]a_{n}[/tex] = 2n - 3
Step-by-step explanation:
Note the difference in consecutive terms is constant, that is
1 - (- 1) = 3 - 1 = 5 - 3 = 7 - 5 = 2
This indicates that the terms are an arithmetic sequence with
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here a₁ = - 1 and d = 2, thus
[tex]a_{n}[/tex] = - 1 + 2(n - 1) = - 1 + 2n - 2 = 2n - 3
help will rate you 5 stars!!!!!!!!!
Answer:
first proof should be cpctc, second proof is the triangle sum theorem
7 2/15+52/3+9 13/15 a. 20 2/3 B.21 10/15 C.21 2/3 D.22 2/3 pls do i will mark brainlessness
Answer:
101/3 or 33 2/3
Step-by-step explanation:
7 2/15=107/15
9 13/15=138/15
107/15+52/3+138/15
107/15+138/15+52/3
245/15+52/3
245/15+260/15
505/15
simplify,
101/3
Tomas buys a bag of 5 peaches for $3.55. Write and solve an equation to find how much money, m, Tomas paid for each peach
Answer:
Step-by-step explanation:
$3.55 ÷ 5 = .71 each peach
To find out how much Tomas paid for each fruit, we set up the equation m = $3.55 / 5, which when solved gives m = $0.71. This means that Tomas paid $0.71 for each peach.
Explanation:To find out how much Tomas paid for each peach, you can set up an equation. Because Tomas buys 5 peaches for $3.55 in total, you can express this as a simple division. To solve the equation, divide $3.55 (total cost) by 5 (total number of peaches).
So, the equation would be m = $3.55 / 5.
Solving this equation gives: m = $0.71. Therefore, Tomas paid $0.71 for each peach.
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If 4 + 6 = 10, does (4 + 6) X 3 = 10 x 3? Why
or why not?
Answer:
yes.
Step-by-step explanation:
because I did the work and 10 times 3 equals 30 and 4 plus 6 times 3 equals 30.
Answer:
Yes because L.H.S = R.H.S
Step-by-step explanation:
4 + 6 = 10
(4 + 6) X 3
=> 10 X 3
=> 30
Passes through (-1,4) and has a slope of 4
Answer:
y-4=4(x+1)
Step-by-step explanation:
y-y1=m(x-x1)
m=4
y-4=4(x-(-1))
y-4=4(x+1)
Answer: equation = y=4x+8
Step-by-step explanation:
y=mx+b
4=4(-1)+b
b=8
equation = y=4x+8
PLEASE HELP ASAP:))))))))!!!!!!!!!!!!
Which of the following purchases shows the LEAST expensive unit price?
Group of answer choices
A 4 pack of t-shirts for $2.24
A 3 pack of t-shirts for $3.00
An 8 pack of t-shirts for $4.24
A 6-pack of t-shirts for $3.12
Answer:
6-pack for 3.12
Step-by-step explanation:
Find unit price
2.24/4=0.56
3.00/3=1
4.24/8=0.53
3.12/6=0.52
Kenny had 35 baseball cards in his collection last year. This year he has 20% more baseball cards. Kenny sold 8 of his baseball cards for extra money. How many baseball cards does Kenny have after he sold 8 for extra money? Show Work!
(A) 7 baseball cards left
(B) 34 baseball cards left
(C) 35 baseball cards left
(D) 42 baseball cards left
The right answer is Option B.
Step-by-step explanation:
No. of baseball cards = 35
Increase = 20%
Number of increased cards = 20% of 35
[tex]Increased\ cards = \frac{20}{100}*35\\Increased\ cards=\frac{700}{100}\\Increased\ cards=7[/tex]
Total cards = 35+7 = 42
No. of cards sold = 8
Cards left = Total cards - No. of cards sold
[tex]Cards\ left=42-8\\Cards\ left=34[/tex]
The right answer is Option B.
Keywords: Addition, subtraction
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Please help me with this math problem I don’t know it I need to pass this class !!!!!!
The correct option is Option 4: [tex]2a^2b^3 + 10ab^4[/tex]
Step-by-step explanation:
Given
Length of box = l = ab
Width of box = w = a+5b
Height of box = h = 2b^2
The volume of a box is given by:
[tex]V = Length*Width*Height\\V = l*w*h[/tex]
Putting the values
[tex]V = (ab)(a+5b)(2b^2)\\ = (ab)(2b^2)(a+5b)\\=(2ab^3)(a+5b)\\Distributive property\\=(2ab^3*a) + (2ab^3*5b)\\=2a^2b^3 + 10ab^4[/tex]
Hence,
The correct option is Option 4: [tex]2a^2b^3 + 10ab^4[/tex]
Keywords: Volume, Polynomials
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Jose's banquet hall charges a one time fee of $100 plus $50 per guest for weddings. Another wedding venue, Palace of Aaron, Charges a one-time fee of $200 in addition to $45 per guest. Letting "g" represent the number of wedding guests, Write an algebraic expression to represent the cost of renting each of the banquet halls.
(First part)
(Second part)
At how many wedding guests is the cost the same for both venues? Show your work.
Answer:
Part 1:
Jose's Banquet Hall: 50g+100
Palace of Aaron: 45g+200
Part 2:
20 guests
Step-by-step explanation:
Part 1:
$50 per guest plus $100 fee
50g+100
$45 per guest plus $200 fee
45+200
Part 2:
$50(20)+$100=$1100
$45(20)+$200=$1100
Answer:
II. [tex]\displaystyle 20\:wedding\:guests[/tex]
I. [tex]\displaystyle 100 + 50g = 200 + 45g[/tex]
Step-by-step explanation:
100 + 50g = 200 + 45g
- 200 - 50g - 200 - 50g
___________________
[tex]\displaystyle \frac{-100}{-5} = \frac{-5g}{-5} \\ \\ 20 = g[/tex]
So, at twenty wedding guests, the cost will balance for both venues.
I am joyous to assist you anytime.
The highest mountains in the world are the Himalayas, at the border between the Indian and Eurasian plates. The Himalayas formed in a ________________.
A. subduction zone
B. divergent boundary
C. collision zone
D. transform boundary
Answer: collision zone
Step-by-step explanation:As a result of this collision, the sedimentary rocks which were settled in the large-scale depression in the Earth's crust called Tethys were folded and formed the Himalayas.
C collision zone
The Himalayas are the world's highest mountains, straddling the Indian and Eurasian plates. The Himalayas were formed by a collision zone.
What is meant by collision zone?A collision zone occurs when two tectonic plates with continental lithosphere collide at a convergent boundary. A collision zone occurs when two tectonic plates with continental lithosphere collide at a convergent boundary. Because continental lithosphere is rarely subducted due to its low density, the result is a complex orogeny involving folding and thrust faulting as blocks of continental crust pile up above the subduction zone. This includes the collision zone in Eastern Anatolia. Tropical Asia is a hotspot for plate collisions between the northward-drifting Australian plate and plates from the Pacific and the Asian mainland. As a result, the area is mountainous and shaped by shear zones and volcanism. as well as the Banda Arc-Australian collision zoneTo learn more about collision zone, refer to:
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If y varies inversely as the square of x and y=2 when x=4.Find x when y=4/5
Answer:
hnjmmm
Step-by-step explanation:
m,,\
l;'
Answer:
x = 2[tex]\sqrt{10}[/tex]
Step-by-step explanation:
Given that y varies inversely as the square of x then the equation relating them is
y = [tex]\frac{k}{x^2}[/tex] ← k is the constant of variation
To find k use the condition y = 2 when x = 4
k = yx² = 2 × 4² = 2 × 16 = 32
y = [tex]\frac{32}{x^2}[/tex] ← equation of variation
When y = [tex]\frac{4}{5}[/tex], then
[tex]\frac{4}{5}[/tex] = [tex]\frac{32}{x^2}[/tex] ( cross- multiply )
4x² = 160 ( divide both sides by 4 )
x² = 40 ( take the square root of both sides )
x = [tex]\sqrt{40}[/tex] = [tex]\sqrt{4(10)}[/tex] = 2[tex]\sqrt{10}[/tex]