The sum of the 112th term of the geometric series is 256 and the common ratio is 3/4. Find the first term of the first geometric series.
Answers
Answer:
First term = 64
Step-by-step explanation:
We are given the formula for the nth term of a geometric series to be;
S_n = (a1(1 - rⁿ))/(1 - r)
Where:
S_n is the sum of n terms
A1 is first term
r is common ratio
We are given;
S_112 = 256
r = ¾
Thus;
256 = a1(1 - ¾^(112))/(1 - ¾)
256 = a1(4)
a1 = 256/4
a1 = 64
Related Questions
Help with trigonometry homework
Answers
By definition of tangent,
tan(A - π/4) = sin(A - π/4) / cos(A - π/4)
Expand the numerator and denominator using the angle sum identities for sin and cos:
tan(A - π/4) = (sin(A) cos(π/4) - cos(A) sin(π/4)) / (cos(A) cos(π/4) + sin(A) sin(π/4))
Divide through everything on the right by cos(A) cos(π/4):
tan(A - π/4) = (sin(A) / cos(A) - sin(π/4) / cos(π/4)) / (1 + (sin(A) sin(π/4)) / (cos(A) cos(π/4)))
Simplify the sin/cos terms to tan:
tan(A - π/4) = (tan(A) - tan(π/4)) / (1 + tan(A) tan(π/4))
tan(π/4) = 1, so we're left with
tan(A - π/4) = (tan(A) - 1) / (1 + tan(A))
Replace tan(A) with -√15:
tan(A - π/4) = (-√15 - 1) / (1 - √15)
Then the last option is the correct one.
Due within next 5 minutes! Please help!
Mrs. B budgeted $175 per month for gasoline, $100 per month for
maintenance, and $150 per month for insurance. What is her weekly,
monthly, and yearly budget for owning her car?
Answers
Answer:
Weekly: $106.25
Monthly: $425
Yearly: $5,100
Step-by-step explanation:
Answer:
Step-by-step explanation:
WEEKS:
$175 divided by 4= 43.75
100 divided by 4= $25
150 divided by 4: $37.5
TOTAL: 106.25
YEARLY:
$175 times 12: $2,100
$100 times 12: $1,200
$150 times 12: $1,800
TOTAL: 5,100
MONTHLY: $425
Evaluate 2/g + 2h + 5 when g=3 and h=6
Answers
Answer:
17 2/3
Step-by-step explanation:
2/g + 2h + 5 when g = 3 and h = 6
~Substitute
2/3 + 2(6) + 5
~Simplify
2/3 + 12 + 5
~Add
12 2/3 + 5
~Add
17 2/3
Best of Luck!
Find the remainder when f(x) = 2x3 − 12x2 + 11x + 2 is divided by x − 5.
Answers
Answer: I couldn’t find your answer to this mathematics question, try a different question to this mathematics answer so I can get it.
Step-by-step explanation:
Answer:
Its 7 pls brainliest
Step-by-step explanation:
Evaluate the expression on top helllp pls
Answers
Answer:
159
Step-by-step explanation:
Answer:
the answer is 59
Step-by-step explanation:
apply
Parentheses
Exponents
Multiplication
Division
Addition
Subtraction
First, add inside the parentheses. Your equation is now 8^2-5.
8 squared is sixty four, and subtract five to get 59. Hope this helped!
Disney held a breakfast for parents and their children to eat with Mickey and Minnie Mouse (and
the rest of the gang, too!) Adult tickets cost $17.95 and children's tickets cost $12.95. Disney
made $7355 from ticket sales from a total of 500 people that attended. How many adults and
how many children were at the breakfast?
Answers
176 adults 324 children
i will give lots of points and brainly please help asap What is the equation of the quadratic of the quadratic graph with a focus of (1,3) and a directex of y= 1 show your work please
Answers
check the picture below.
now, we know the directrix is at y = 1, and the focus point is at 1,3, well, notice the picture, the distance between those fellows is just 2 units.
the vertex is half-way between those fellows, therefore, the vertex will be at 1,2.
the distance "p", from the vertex to either the directrix or focus, is really just 1 unit. Since the focus point is above the directrix, is a vertical parabola, and it opens upwards, like in the picture, and since it opens up, the "p" value is positive, or +1.
PLEASE HELP ME!!! ASAP!! ITS ALMOST DUE!!
Answers
Answer:
I'm pretty sure it's the first one. If i'm wrong i am terribly sorry
Step-by-step explanation:
Answer:
Y-intercept is -6 and the slope is 1
Step-by-step explanation:
You can use Y2-Y1/X2-X1 to find the slope. Then, you can use y=mx+b to find the y-intercept.
2)
Mike went to the doctor and was found to be 20 pounds overweight.
The doctor discovered that Mike ate an average of 2000 calories per
day. He said for Mike to lose weight and meet his goal, the maximum
amount of calories he could eat per day was 1750. How many calories
will Mike be cutting out each week (7 days)?
Answers
Answer:
1750 Calories
Step-by-step explanation:
2000-1750=250
250x7=1750
Determine if the lines are parallel, perpendicular, or neither. y + 3 = 7/4x and -4/7x + y = 9. Do I still have to solve y + 3 = 7/4x?
Answers
Answer:
No you dont have to solve it. And I believe it is perpendicular.
Step-by-step explanation:
Answer:
Perpendicular
Step-by-step explanation:
you have to solve both. If you make the lines in a graph it will turn out to be perpendicular because they are going to intersect.
The following measurements were added: 5.45 + 6.1 + 2.84. what should
the answer be reported as *
1)14.39
2)14.3
3)14.4
4)14
Answers
Explanation:
5.45+2.84= 8.29
Then for 6.1 you add a zero to the end and make it 6.10 which is the same thing
Now 8.29+6.10= 14.39
Which division problem would have an estimated quotient of 15 if the divisor and dividend were rounded to the nearest whole number?
90.24 divided by 6.3
79.85 divided by 3.99
85.01 divided by 16.77
59.87 divided by 10.21
Answers
Answer:
A. 90.24 divided by 6.3
Step-by-step explanation:
We take each option one by one and solve for it
A. 90.24 divided by 6.3
Divisor = 90.24
Dividend = 6.3
if the divisor and dividend were rounded to the nearest whole number?
= 90÷ 6
= 15
Answer:
A, I got it right on edge.
Step-by-step explanation:
a cook has 6 1/2 cups of sliced carrots
how many 3/4 cup servings of carrots is this
Answers
8 2/3 cup servings of carrot.
Explanation
Divide 61/2 by 3/4
Answer:8 2/3
Step-by-step explanation:
At noon, a tank contained 8 in. of water. After several hours, it contained 2 in. of water. What is the
percent decrease of water in the tank?
Answers
Answer:
75%
Step-by-step explanation:
To find the percent decrease, use the percent change formula:
(difference / original) x 100
8 - 2 = 6, so the difference is 6.
Plug in the difference and original:
(6 / 8) x 100
= 75
So, the percent decrease is 75%
A class of 32 students has 12 girls. What is the ratio of girls to boys?
A. 3:5
B. 5:3
C. 3:8
D. 8:3
Answers
Answer:
d is the answer
in think
Step-by-step explanation:
try it
Answer:
A
Step-by-step explanation:
Number of student=32
Number of girls=12
Number of boys=32-12
=20
Ratio of girls to boys=12:20
=6:10
=3:5
Which ordered pair is a solution to the system
Answers
9514 1404 393
Answer:
(3, 1)
Step-by-step explanation:
The lines on the graph cross at the point (x, y) = (3, 1). That is the solution to the system of equations.
Solve 2x +2>10 quickly please
Answers
Answer:
x > 4
Step-by-step explanation:
2x+2>10 Subtract by 2 on both sides
2x>8 Divide by 2 on both sides
x>4
Jimmy bought a pair of jeans for $50 and a shirt for $25. He has a coupon to save 1/10 of the total on his purchase. How much does Jimmy pay for the jeans and shirt after the discount?
Answers
Answer:
$67.5
Step-by-step explanation:
50+25=75. Then, it's 1/10 of 75 which is $7.5. Then, 75-7.5 which is $67.5
Hope this helps :D Please mark brainliest
5d divided by c+2;let d=10,c=5
Answers
Answer:
here is the answer in photo form
Answer:
Step-by-step explanation:
Simple and best practice solution for (c-5)d=2 equation. ... If it's not what You are looking for type in the equation solver your own equation and let us solve it. ... 2 + 5d cd = 2 + 5d Divide each side by 'd'. c = 2d-1 + 5 Simplifying c = 2d-1 + 5 Reorder ... 11/4-t8 | | (3x^2+5x+2)+(4x^2+3x+2)= | | 4Y+7-Y=4+2Y-8 | | 10x+190=360 ...
For example, let's say with have the equation x+5 ... If we evaluate the same expression when x=10 , we get: 3(10)+7=30+7=37 . Here's a variable expression with two variables : 3x−2y ... How do you express the phrase "a number z divided by 19" as an algebraic expression? ... How do you simplify 11c+5d−9c−9d?Let the number of cows be x and their legs be 4x. ... or, x = 7 [dividing by 2 on both sides]. ... The roots of the equation ax2 + bx + c = 0 will be reciprocal if: ... A circle of radius 10 inches has its center at the vertex C of an equilateral triangle ABC ... (a) 15, (b) 30, (c) 60, (d) 90, (e) 120. Circle Problem Answers. Answer: (b) 5.
Solve the equation below for x.
1/2(x+2)=7/5
Answers
Answer:
x = 4/5
Step-by-step explanation:
What is the slope and y-intercept of the equation 3(y-2) + 6(x+1)-2 = 02
Answers
Answer:
i think its b
Step-by-step explanation:
just quessing though
Would someone please help me with this pre final practice?
Answers
Answer:
i think 5 so i say pick 5 because 19no 12no10 no so it 5
How are rates ratios and proportions used in careers in the medical field
Answers
Answer:
Ratios and Proportions
Nurses do not prescribe medicine, but they administer medication to their patients. When doing so, they use ratios and proportions to help them. ... The ratios and proportions also allow the nurse to know how long the medication will stay in the body of the patient before needing another dosage.
Step-by-step explanation:
Answer:
they are used for comparing data
Step-by-step explanation:
even im the medical feild, mathematics is an impeccable way to explain phenomenons... by using mathematical formulas ratios and fraction, data can be communicated easier and help it to be easier to understand
Factor the common factor out of this expression.
25u^2+20v^2+5v
Answers
Answer:
Hi Answer Is 5(5u^2+4v^2+v)
System of Equations in Three Variables Word Problem
Answers
Answer:
i think the answer is a number or multiple number and maybe a decimal.
Step-by-step explanation:
go to Tiger Algebra Solver
m(p + q); use m = 2, p = 6, and q = 1
Answers
m(p+q)
2(6+1)
2(7)
14
Answer: 14
Step-by-step explanation:
If they say that m(p+q) = 2(6+1) then we take what is in the parenthasis first (6+1) then we get (7). After that take m=2 times 7= 14
You want to buy carpet for your living room. The room is rectangular and the dimensions are 10 feet by 6 feet. How many square feet of carpet do you need to buy?
Answers
Answer:
60 ft^2
Step-by-step explanation:
This is a problem where you calculate the area of a rectangle A=bh. b=10 and h=6 so A=6*10 or 60 ft^2
How do you get from one number to the next using multiplication or division?
From 100 to 106
From 100 to 90
From 90 to 100
From 106 to 100
Answers
Answer:
You use decimal values. Like for the first one, multiply 100 by 0.01.
Step-by-step explanation:
The multiplication or division is 10^6/10^4
How to interpret integral multiplication?Suppose that there are two positive integer numbers( numbers like 1,2,3,.. ) as a and b
Then, their multiplication can be interpreted as:
[tex]a \times b = a + a + ... + a \: \text{(b times)}\\\\a \times b = b + b +... + b \: \text{(a times)}[/tex]
For example,
[tex]5 \times 2 = 10 = 2 + 2 + 2 + 2 + 2 \: \text{(Added 2 five times)}\\or\\5 \times 2 = 10 = 5 + 5 \: \text{(Added 5 two times)}[/tex]
Given;
From 100 to 10^6;
100 * 10^4 = 10^6
From 100 to 90;
100/10*9=90
From 90 to 100
90/9*10=100
From 10^6 to 100
10^6/10^4=100
Therefore, by multiplication or division will be 10^6/10^4
Learn more about multiplication here:
https://brainly.com/question/26816519
#SPJ2
Which is a graph for the inequality m greater than or equal to 2?
Answers
Answer:
The third one is the answer. if you ever need help hit me up.
Step-by-step explanation:
what is the volume
Answers
Answer:
The volume is 227.5
Step-by-step explanation:
The volume for a triangular prism, such as this is, (lxwxh)/2. Because in all shapes volume equals the area multiplied by the height or depth. And an area of a triangle is l or base multiplied by the altitude or w, divided by 2. So the area would be 5x7/2, 35/2, 17.5. And the volume would be 17.5x13, 227.5