Answer:
[tex]T_n = \left \{ {{T_1=2} \atop {T_n =-5T_{n-1}}} n>1 \right.[/tex]
Step-by-step explanation:
Given
Geometric sequence: 2, -10, 50, -250
Required
Recursive formula of the sequence
We start by naming each sequence
[tex]T_1 = 2\\T_2 = -10\\T_3 = 50\\T_4 = -250[/tex]
Represent each term in relation to the previous term (except T1)
[tex]T_1 = 2\\T_2 =2 * -5\\T_3 = -10 * -5\\T_4 = 50 * -5[/tex]
Recall that
[tex]T_1 = 2\\T_2 = -10\\T_3 = 50\\T_4 = -250[/tex]
So, at this point; we have to make substitutions
[tex]T_1 = 2\\T_2 =T_1 * -5\\T_3 = T_2 * -5\\T_4 = T_3 * -5[/tex]
Subtract 1 from each term on the right hand side
[tex]T_1 = 2\\T_2 =T_{2-1} * -5\\T_3 = T_{3-1} * -5\\T_4 = T_{4-1} * -5[/tex]
Replace each term greater than 1 by n
[tex]T_1 = 2\\T_n =T_{n-1} * -5\\T_n = T_{n-1} * -5\\T_n = T_{n-1} * -5[/tex]
Remove repetition
[tex]T_1 = 2\\T_n =T_{n-1} * -5[/tex]
[tex]T_1 = 2\\T_n =-5T_{n-1}[/tex]
Hence, the recursive formula is
[tex]T_n = \left \{ {{T_1=2} \atop {T_n =-5T_{n-1}}} n>1 \right.[/tex]
0.2 ✕ -0.5 ✕ ( -0.9- -0.7)
Answer:
0.02
Step-by-step explanation:
[tex]0.2\times -0.5\times (-0.9 - -0.7)= \\\\0.2\times -0.5 \times (-0.2)= \\\\0.02[/tex]
Hope this helps!
0.02
[tex]solution \\ 0.2 \times \: - 0.5 \times ( - 0.9 - ( - 0.7)) \\ = 0.2 \times ( - 0.5) \times ( - 0.9 + 0.7) \\ = 0.2 \times( - 0.5) \times ( - 0.2) \\ = - 0.1 \times ( - 0.2) \\ = 0.02[/tex]
hope this helps..
Good luck on your assignment
What is the ratio of x to y? (Write it in simplest form)
Answer:
There is no explanation so I guess 1 to 1?
Step-by-step explanation:
Part A
Choose the inequality and solution to represent the number of cans, c, that Xander must still collect.
A. c + 64 ≤ 120; c ≤ 56
B. c + 120 ≤ 64; c ≤ –56
C. c + 64 ≥ 120; c ≥ 56
D. c + 120 ≥ 64; c ≥ –56
Part B
Choose the graph of the solution on the number line.
Answer:
Part A: A
Part B: A
Step-by-step explanation:
1)
the inequality should be less than or equal to, since we need to find how many are left
now, the answer B is wrong, since there can't be negative 56, since Xander collected some cans, though he still must collect a few
thus, the answer is A
2)
A again is correct, since it represents:c ≤ 56
B represents c ≥ 56
C represents c ≤ –56
D represents c ≥ -56
question in attachment
Answer:
it is C. An = 2(2)^n
Step-by-step explanation:
Answer:it is C. An = 2(2)^n
Step-by-step explanation:
To start a taco food truck service, a woman borrowed $7,500. If the loan was for 5 years and the amount of interest was $3187.50, what simple interest rate was she charged?
Answer:
The interest rate was 42.5%.
Step-by-step explanation:
20 cm
8 cm
8 cm
20 cm
15 cm
Find the area of the arrow above.
(?] square centimeters
Enter
Answer:
610 cm²
Step-by-step explanation:
This is an irregular figure. We can split it up by the triangle and the rectangle on the bottom.
To find the area of the triangle, we must determine the base length. As we can see, the bottom of the arrow has the measure 15 cm, and you can see that the missing section in the base of the triangle is the same measure. Now we find the measure of the base by adding 15 + 8 + 8, which equals 31 cm.
Now we multiply and divide by 2 to find the area of the triangle:
20*31 * 1/2
= 310 cm²
Now, we find the area of the rectangle. We can see that its dimensions are 15 by 20. We can plug these values into the rectangle formula:
A = 15*20
A = 300 cm²
Now we add these values to find the total area:
310 cm² + 300 cm²
= 610 cm²
The two cross sections shown are taken parallel to their respective bases. The cross sections have the same area. If the
heights of the two solids are equal, find the volume of the cylinder. Round your answer to the nearest hundredth.
A. 465.10 cm³
B. 480.08 cm³
C. 489.40 cm³
D. 498.04 cm³
Answer:
c
Step-by-step explanation:
Given that triangle PQR congruent triangle STU, , what is the measure of angle U ?
Answer: B or 52 degrees...
Step-by-step explanation:
Congruent means to have identical properties and because triangle PQR is congruent to triangle STU, their angles are also congruent.
In the theorem AAA, angle P is congruent to S, angle Q is congruent to T and angle R is congruent to U.
The sum of the angles in a triangle is 180 degrees and so you would do 180-86-42 which would get you to 52 degrees and that is the answer.
segment if a is a perpendicular bisector of segment BD if the measure of angle frd is represented by the expression 7x + 6 find the value of x
Answer:
x = 12
Step-by-step explanation:
If it is a perpendicular bisector, then the intercepting angles are always 90°.
If that is the case then we simply set the expression 7x + 6 equal to 90 and solve for x. We should get 12 as our answer.
Find the distance between two points (2,-3)and (2-,4). what is the answer?
Answer: 1 squealer apart if on a square grid
Step-by-step explanation:
Answer:
The distance is 1
Step-by-step explanation:
Since the x coordinates are the same, we only need to look at the y coordinates
-3 - -4
-3 +4
1
The multiplicative inverse of (-4)⁻² is (4)⁻². True False
Answer: false
Step-by-step explanation:
The exponents would have to have a different sign from each other (positive or negative), not the integer.
Four statistics professors and six chemistry professors are available to be advisors to a student organization. The student organization needs two of the professors to be advisors. If each professor has an equal chance of being selected, what is the probability that both professors are chemistry professors?
Step-by-step explanation:
Total professors = 10
Probability of chemistry professors = 2/6 = 1/3
Which graph represents the function f(x) = 4|x|? (please answer honestly I'm on a timed test rn)
Answer:
The graph that corresponds to the function is B.
Step-by-step explanation:
We want to see which one of the given graphs represents the function f(x) = 4*|x|
The correct option is the second graph.
How to find the correct graph?
Here we want to find the graph of the absolute value function:
f(x) = 4*|x|
To get it, we can evaluate the function in some values of x and then see which graph contains these points.
for example for x = 1 and x = -1 we have:
f(1) = 4*|1| = 4
f(-1) = 4*|-1| = 4
Then we need to see which graph contains the points (1, 4) and (-1, 4)
We can see that the only graph that contains these points is the second one, so the correct option is the second graph.
If you want to learn more about absolute value functions, you can read:
https://brainly.com/question/1782403
If the volume of the planter is 2,560 cubic inches,how tall is the planter
Answer:
Height of Planter = H = 20 in²
Step-by-step explanation:
As the planter is not given in the question, the question is incomplete.
First, lets complete the question by attaching the diagram related to this question.
(SEE THE ATTACHMENT)
Lets consider the right angled triangle that is formed at the top of the planter, as shown in the diagram attached.
The right angled triangle has a width of 16 inches and a heights of 16 inches as well.
We know that the Area of a triangle can be calculated by following formula:
[tex]A=\frac{1}{2}\cdot(width)\cdot(height)[/tex]
Substitute the values to find Area:
[tex]Area = \frac{1}{2}\cdot16\cdot16\\Area = 128 in^2[/tex]
We also know that the Volume of a triangular prism is given by:
[tex]Volume=(Area)\cdot(Height)[/tex]
Where
Area = Area of the face = 128 in²
Height = Height of the planter = H
Volume = 2560 in³
Substitute the values and solve for H:
[tex]2560=128\cdot{H}\\H=\frac{2560}{128}\\H=20in^2[/tex]
which is the discriminant of the quadratic equation 6x^2 + x -8=0?
Answer:
0?
Step-by-step explanation:
What is the rate of change in the table?
Answer:
3
Step-by-step explanation:
Answer:
1
From -2 to 0 there is 2, but from 1 to 3 there is also 2, so 2/2=1
What is the area of the garden in Plan A? (Type the numeric answer only
PLEASE HELP LOOK AT THE PHOTO I GAVE YOU PLEASE D:
Find the value of x and the measure of angle Y.
W
00
8
X< 62°
(4x - 2)°
Y
Value: 10
x is equal to
degrees.
Angle Y measures
degrees.
Answer:
x is equal to 16 degrees
Angle measures 62 degrees
Step-by-step explanation:
From Law of Sines:
XW/sin(∠Y) = WY/sin(∠X)
From the picture
XW = 8
WY = 8
∠X = 62°
Replacing into the equation:
8/sin(∠Y) = 8/sin(62°)
∠Y = 62°
Angle Y is also equal to:
∠Y = 4x - 2
62 = 4x - 2
62 + 2 = 4x
64/4 = x
16° = x
can you please help me! In a triangle, a segment is drawn joining the midpoint of two sides. What is true about this segment? a. Its length is equal to the 3 rd side. b. Its length is twice the 3 rd side. c. It is parallel to the 3 rd side. d. It is ⊥ to the 3 rd side.
Answer: The right answer for the question that is being asked and shown above is that: "Its length is twice the 3rd side." In a triangle, a segment is drawn joining the midpoint of two sides. The statement that is true about this segment is that Its length is twice the 3rd side
Step-by-step explanation:
Answer: Its length is twice the 3rd side.
Please helpppp what is the solution to the system of equations
Answer:
The third one
Step-by-step explanation:
Help would be much appreciated
Answer:
Given
Step-by-step explanation:
Question 1)
Answer is c) 12.94 units
Because,
The sides will be √20,√20 and 4 units, so you add them
You get √20 through Pythagorean theorem √(2^2 + 4^2)
= 4.47
Question 2)
Answer:
3x^2 + 4y^0 +x^-1
Substitute the values,
3*(4)^2 + 4*(5)^0 + (4)^-1
3*16 + 4*1 * 1/4
( Any number raised to 0 is 1
4^-1 = 1/4^1 )
= 49
Answer:
Option C
49
Step-by-step explanation:
sides of triangle:
4√2²+4²=√20=4.47√2²+4²=√20=4.47P=4+4.47*2=12.94
Option C is correct
================
x=4, y=5
3x²+4y⁰×x⁻¹=3×4²+4×5⁰×4⁻¹=48+1=49
There was 1/5 of a gallon of lemonade in the refrigerator. Kelly poured equal amounts into 4 cups . How much lemonade was in each cup ?
Answer:
1/20 gallon per cup
Step-by-step explanation:
Can someone help me solve this?
Answer:
x=3,y=-1 or (3,-1) The answer is D
Step-by-step explanation:
A fair,six sided dice is thrown once. Select the probability of a 3 showing on the dice.
A= 1/6
B=1/2
C=6%
D=1/3
E=1:7
Answer:
A
Step-by-step explanation:
cause it only has 3 in l side
The probability of a 3 showing on the dice would be equal to 1/6. the correct option is A.
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
The formula of probability is defined as the ratio of a number of favorable outcomes to the total number of outcomes.
P(E) = Number of favorable outcomes / total number of outcomes
We are given that A fair,six sided dice is thrown once.
There are 6 possibilities and 3 is one of them so, probability of 3 is 1 out of 6,
The probability of a 3 showing on a six-sided dice is;
P(E) = 1/6
Learn more about probability here;
https://brainly.com/question/9326835
#SPJ2
ASAP, pls I need help with these questions
Answer:
a) 2/5 x 900 = 360 hectares
b) 3/5th
c) 3/5 x 900 = 540
540 - 360 = 180
Farmer Richards needs to bring another 180 hectares under cultivation.
-5 5/8 + 3 1/2
A: -3 1/8 B: -2 1/2 C: -2 1/8 D: -7/8
ASAP
Answer:
C
Step-by-step explanation:
You take the fractions and turn them into mixed numbers. You do that by multiplying the whole number with the denominator and adding the numerator for the new numerator and the denominator stays the same. Now, you'd get -45/8 + 7/2. Change the denominator of the second one to 8 so you can add them, do this by multiplying the numerator and denominator by 4. Now you get -45/8 + 28/8. -45 +28 is -17 so your answer is -17/8. If you need it In mixed form, 8 goes into -17 2 times so you get -2 and the remainder 1/8 so -2 1/8.
A line is parallel to y = 4x – 2 and
intersects the point (5, -11).
What is the equation of this parallel line?
y = [?]x +
Hint: Use the Point-Slope Form: y - y1 = m(x - X1)
Then write the equation in slope-intercept form.
Answer:
y=4x-31
Step-by-step explanation:
Ignore the hint. Point slope form makes everything so much harder than it has to be.
Parallel lines always have the same slope, in this case 4.
So our equation is now: y = 4x + b
Let's solve for b by plugging in (5, -11), as it's the only point we know is on the parallel line.
-11 = 4(5) + b
-11-20 = b
b = -31
So plug in b: y = 4x - 31
--------------------
Also rate and tell me if I'm correct :)
Answer:
y = -4x + 15.
Step-by-step explanation:
To find the equation of a line perpendicular to y = -2 and passing through the point (4, -1), we can use the point-slope form of a linear equation.
The given line y = -2 has a constant slope of 0 since there is no variable term involving x. A line perpendicular to it will have an undefined slope.
Using the point-slope form, we have:
y - y₁ = m(x - x₁),
where (x₁, y₁) represents the coordinates of the given point (4, -1), and m represents the slope.
Since the slope is undefined, the equation becomes:
y - (-1) = undefined(x - 4).
Simplifying:
y + 1 = undefined(x - 4).
Now, we can write the equation in slope-intercept form by substituting the slope as -4 (the negative reciprocal of 0):
y + 1 = -4(x - 4).
Expanding the right side:
y + 1 = -4x + 16.
To isolate y, we can subtract 1 from both sides:
y = -4x + 16 - 1.
Combining the constants:
y = -4x + 15.
Therefore, the equation of the perpendicular line is:
y = -4x + 15.
Select the correct answer.
This pyramid has the same base as the prism, and its height is three times the height of the prism. What is the ratio of the volume of the
pyramid to the volume of the prism?
Answer:
b
Step-by-step explanation:
Find the value of x if A, B, and C are collinear points and B is between A and C. AB=2x,BC=x−2,AC=28
Answer:
x = 10
Step-by-step explanation:
Data
AB=2xBC=x−2AC=28Given that A, B, and C are collinear points and B is between A and C, then the addition of the measure of segments AB and BC must be equal to the measure of segment AC, that is:
AB + BC = AC
Replacing with data:
2x + (x - 2) = 28
3x - 2 = 28
3x = 28 + 2
x = 30/3
x = 10