Answer:
a₄ = - [tex]\frac{27}{2}[/tex]
Step-by-step explanation:
In a geometric sequence, the common ratio r is calculated as
r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{a_{3} }{a_{2} }[/tex] , substitute values
[tex]\frac{2x+2}{x}[/tex] = [tex]\frac{3x+3}{2x+2}[/tex] ( cross- multiply )
(2x + 2)² = x(3x + 3) ← expand both sides
4x² + 8x + 4 = 3x² + 3x ( subtract 3x² + 3x from both sides )
x² + 5x + 4 = 0 ← in standard form
(x + 1)(x + 4) = 0 ← in factored form
Equate each factor to zero and solve for x
x + 1 = 0 ⇒ x = - 1
x + 4 = 0 ⇒ x = - 4
However x ≠ - 1 as this would make the denominator of the second term equal to zero and therefore undefined.
Thus x = - 4 and
r = [tex]\frac{2(-4)+2}{-4}[/tex] = [tex]\frac{-8+2}{-4}[/tex] = [tex]\frac{-6}{-4}[/tex] = [tex]\frac{3}{2}[/tex]
Then
a₁ = - 4
a₂ = - 4 × [tex]\frac{3}{2}[/tex] = - 6
a₃ = - 6 × [tex]\frac{3}{2}[/tex] = - 9
a₄ = - 9 × [tex]\frac{3}{2}[/tex] = - [tex]\frac{27}{2}[/tex]
Determine the value of x.
29°
(11r - 65)
Answer:
122
Step-by-step explanation:
11x-65+58=180. The 58 comes from adding 29+29=58. You do this because there are two 29 due to it being an isosceles triangle meaning there are two sides equal.
Add your a like terms
11x-7=180
11x=180+7
11x=187
x=17
Plug the 17 in for 11x-65
11*17-65=122
You can change yourself by adding 29+29+122=180. You know this right because all triangles add to 180. '
If you have any question let me know (:
Money off coupons have been circulated to 300 households.Only⅖ of these were redeemed (used) in the local supermarket to get a free shampoo. What fraction of coupons were unused
Answer:
3/5
Step-by-step explanation:
From the above question,
Fraction of used coupons = 2/5
Let us assume the total number of coupons sent = 1
The Fraction of unused coupons =
1 - 2/5
= 3/5
Therefore, the fraction of unused coupons = 3/5
F(x) =5x^2-20x+3 how to find minimum
Answer:
(2,-17) should be the minimum.
Step-by-step explanation:
The minimum of a quadratic function occurs at [tex]x=-\frac{b}{2a}[/tex] . If a is positive, the minimum value of the function is [tex]f(-\frac{b}{2a})[/tex]
[tex]f_{min}x=ax^2+bx+c[/tex] occurs at [tex]x=-\frac{b}{2a}[/tex]
Find the value of [tex]x=-\frac{b}{2a}[/tex]
x = 2
evaluate f(2).
replace the variable x with 2 in the expression.
[tex]f(2)=5(2)^2-20(2)+3[/tex]
simplify the result.
[tex]f(2)=5(4)-20(2)+3[/tex]
[tex]f(2)=20-40+3[/tex]
[tex]f(2)=-17[/tex]
The final answer is -17
Use the x and y values to find where the minimum occurs.
HOPE THIS HELPS!
Hey guys what's 25 divided by 7 plus 10??
The value of (-15)
A. 0
B. 1
C. -15
D. -1
Answer:
-15
Step-by-step explanation:
(-15) remove brackets
-15
Answer:
C. -15
Step-by-step explanation:
P.S Can I have brainliest?
Solve y=f(x) for x. Then find the input when the output is -3.
f(x) = (x-5)^3 -1
x = __
The input is __ when the output is -3.
Answer:
Please check the explanation
Step-by-step explanation:
Given the function
[tex]f\left(x\right)\:=\:\left(x-5\right)^3-1[/tex]
Given that the output = -3
i.e. y = -3
now substituting the value y=-3 and solve for x to determine the input 'x'
[tex]\:\:y=\:\left(x-5\right)^3-1[/tex]
[tex]-3\:=\:\left(x-5\right)^3-1\:\:\:[/tex]
switch sides
[tex]\left(x-5\right)^3-1=-3[/tex]
Add 1 to both sides
[tex]\left(x-5\right)^3-1+1=-3+1[/tex]
[tex]\left(x-5\right)^3=-2[/tex]
[tex]\mathrm{For\:}g^3\left(x\right)=f\left(a\right)\mathrm{\:the\:solutions\:are\:}g\left(x\right)=\sqrt[3]{f\left(a\right)},\:\sqrt[3]{f\left(a\right)}\frac{-1-\sqrt{3}i}{2},\:\sqrt[3]{f\left(a\right)}\frac{-1+\sqrt{3}i}{2}[/tex]
Thus, the input values are:
[tex]x=-\sqrt[3]{2}+5,\:x=\frac{\sqrt[3]{2}\left(1+5\cdot \:2^{\frac{2}{3}}\right)}{2}-i\frac{\sqrt[3]{2}\sqrt{3}}{2},\:x=\frac{\sqrt[3]{2}\left(1+5\cdot \:2^{\frac{2}{3}}\right)}{2}+i\frac{\sqrt[3]{2}\sqrt{3}}{2}[/tex]
And the real input is:
[tex]x=-\sqrt[3]{2}+5[/tex]
[tex]x=3.74[/tex]Jeanne makes hair bows to sell at the craft fair. Each bow requires 1.5 feet of ribbon. At the fabric store, ribbon is sold by the foot. If Jeanne wants to make 84 bows, how many feet of ribbon must she buy
Answer:
126
Step-by-step explanation:
That might be the answer sorry if im wrong
Which expression is equivelant to -28x2 +35x?
A, -7x (4x + 5)
B, 7x (4x - 5)
C, 7x (4x + 5)
D, -7x (4x - 5)
Answer:
I think its A'
Step-by-step explanation:
If the graphs of a system of linear equations are the same line, how many solutions does the system have?
Answer:
If the graphs of the equations do not intersect (for example, if they are parallel), then there are no solutions that are true for both equations. If the graphs of the equations are the same, then there are an infinite number of solutions that are true for both equations.
Step-by-step explanation:
Answer:
1) no, because a solution must be an ordered triple pair (x,y,z)
2) { x+y+z=5
{ 2x-3y+z=7
{ x+2y-4z=2
3) infinity many solutions
4) use equations (1) and (2) to eliminate y
5) solve one equation for one of its variables
Step-by-step explanation:
should be 100% on the quick check if you put those answers
please help!! I’ll give brainliest!!!
Michelle biked 21 miles in 4 hours.
Part A: What is Michelle's average speed in miles per hour?
Michelle’s average speed it __ miles per hour.
Part B: At the same rate, how many hours will it take Michelle to bike 42 miles?
It will take Michelle __ hours to bike 42 miles
Every week, Fred deposits $84 into his savings account, which is 20% of his weekly income. How much income does Fred make each week?
Answer:
420 dollars.
Step-by-step explanation:
The sale price is $6.85 less than the regular price. The sale price is
$42.50. What is the regular price?
Answer:
49.35$
Step-by-step explanation:
just add the two together
Answer:
49.35
Step-by-step explanation:
A telescope is on sale for $126. This represents a 30% discount. What was the original price of the telescope? (not $163.80)
Answer:
163.8
Step-by-step explanation:
During unusually cold weather, the temperature in Miami Beach was 10°C. This was 12 degrees more than in Tallahassee. What is the temperature in Tallahassee?
Answer:
-2°
Step-by-step explanation:
10 - 12 = -2
What are the solutions of the equation (x - 3)2 + 2(x – 3) – 8 = 0? Use u substitution to solve.
A)x= -5 and x = 1
B)x= -1 and x = 5
C)x= -1 and x = -7
D)x= 1 and x = 7
Answer:
b on edge
Step-by-step explanation:
The solution to the equation (x - 3)² + 2(x - 3) - 8 = 0 is,
B) x= - 1 and x = 5.
What is a quadratic equaton?A quadratic equation is an algebraic expression in the form of variables and constants.
A quadratic equation has two roots as its degree is two.
Given, A quadratic equation of the form (x - 3)² + 2(x - 3) - 8 = 0.
Substituting, U = (x - 3).
(U)² + 2(U) - 8 = 0.
U² + 4U - 2U - 8 = 0.
U(U + 4) - 2(U + 4) = 0.
(U + 4)(U - 2) = 0.
U = - 4, 2.
x - 3 = - 4, 2.
x = - 4 + 3, 2 + 3.
x = - 1, 5.
So, The solution to the equation is - 1, 5.
learn more about quadratic equations here :
https://brainly.com/question/22364785
#SPJ5
Lyla grew 16 flowers with 2 seed packets.
How many seed packets does Lyla need to have
a total of 40 flowers in her garden?
Answer:
Lyla needs 640 seed packets.
Step-by-step explanation:
16 x 40 = 640
What is the solution to the system of equations shown??
Answer:
-5, 3
Step-by-step explanation:
Answer:
Thr answer is option 4.
Step-by-step explanation:
To find the solutions, you have to find the coordinates where both lines intersect each other. In the graph above, both lines intersect at (-5,3).
Do you have any equal/opposite terms or variables?
x+3y=7 and 2x-4y=-6
yes
no
Answer:no
Step-by-step explanation:
Solve for x.
3(x + 2) = 12
2
X = 4
3
1
x = 3
3
O
x = 2
x = 6
Answer:
1.3(x + 2) = 12
2.3x + 6 = 12
3.3x = 6
4.x=2
Step-by-step explanation:
Please help me with this review sheet
Step-by-step explanation:
-2y = 6x + 6
y = -3x - 3.
Since (1/3)(-3) = -1, the 2 lines are perpendicular to each other
Answer:
B
Step-by-step explanation:
When you simplify the second equation
-2y = 6x + 6
you divide both sides by -2
y = -3x - 3
notice equation 1's slope is 1/3 and equation 2's slope is -3, for the second, it is negative and a reciprocal of the first, that suggests they are perpendicular to one another.
What is the length of the missing leg
Answer:
a= 12
Step-by-step explanation:
Use pythagorean theorem
a^2 + b^2 = c^2 where c is the hypotenuse
so 9^2 + a^2 = 15^2
81 + a^2 = 225
a^2 = 144
square root both sides to get a = 12
I really need help asap
Step-by-step explanation:
there isn't enough information to answer z sorry
pls help asap! brainliest!!
Answer:
11. Linear Equation: C = 10L + 12.
12. Cost for 4 lessons: $52.
Step-by-step explanation:
There are 28 female performers in a dance recital. The ratio of men to women is 3:7. How many men are in the dance recital?
ANSWER
There are 21 men in the dance recital.
Irrational numbers are
a. Non-Recurring and Terminating
b. Non-Recurring and Non-Terminating
c. Recurring and Terminating
d. Recurring and Non-Terminating
(-3x+4)+(8x-5)
A.) 5x - 1
B.) 5x - 9
C.) 11x - 1
D.) 11x - 9
E.) none of these
Using the SMART goal-writing criteria, which refers to a goal being practical?
Specific
Measurable
Realistic
Timely
Answer:
I would say timely is the answer
Answer: Realistic
Step-by-step explanation: In my assignment it said "Realistic - the goal needs to be practical."
Hope this helps! o(^U^)o
Factorise:
(x - 2y)2 - 12(x - 2y) + 32
Hi there.
The answer is (x-2y-8)(x-2y-4)
Explanation:
[tex](x - 2y)^{2} - 12(x - 2y) + 32[/tex]
Let (x-2y) = x
[tex] {x}^{2} - 12x + 32[/tex]
Then factor the quadratic polynomial by 2 brackets factoring.
[tex](x - 8)(x - 4)[/tex]
Then convert x to (x-2y)
[tex](x - 2y - 8)(x - 2y - 4)[/tex]
Factor Quadratics
(10 Point)
x² + 3x – 18
(x - 3) (x + 6)
(x - 2) (x + 7)
(x - 2) (x + 3)
(x - 5) (x + 7)
Answer:
Let's factor x2+3x−18
x2+3x−18
The middle number is 3 and the last number is -18.
Factoring means we want something like
(x+_)(x+_)
Which numbers go in the blanks?
We need two numbers that...
Add together to get 3
Multiply together to get -18
Can you think of the two numbers?
Try -3 and 6:
-3+6 = 3
-3*6 = -18
Fill in the blanks in
(x+_)(x+_)
with -3 and 6 to get...
(x-3)(x+6)
Answer:
(x−3)(x+6)
Step-by-step explanation:
