Answer:
Step-by-step explanation:
The formula for fundung the nth term of t geometeric series is expressed as;
Tn = ar^(n-1)
a is the first term
n is the number of term
r is the common ratio
Given
a = 3
r = 21/3 = 48/12 = 4
Substitute
Tn = 3(4)^(n-1)
Tn = 3(4^n/4)
Tn = 3/4(4^n)
Tn = 0.75(4^n)
Hence the nth term of the geometric series is Tn = 0.75(4^n)
To get any term, simply substitute the value of into the equation
Factor this expression completely.
6x^2- 13x - 28
Answer:
this is the solution
(2−7)(3+4)
Step-by-step explanation:
Answer:
(X+1)(6x-21)
Step-by-step explanation:
6x^2- 13x - 28
6x^2-(21-6)x-28
6x^2-21x+6x-28
X(6x-21)+1(6x-21)
(X+1)(6x-21)
Help with substitution
Answer:
x=5
y=1
Step-by-step explanation:
First, put x=2y+3 inside 2x, which is the top equation. This will come out as 2(2y+3)-3y=7.
If you distribute, it would become 4y-6-3y=7. Then you have to combine like terms to get y+6=7
Add 6 on both sides to get y=1.
Put the value of y, which is 1 into the top or bottom equation. I would prefer the bottom equation because it is simpler. The equation would come out as
x=2(1)+3
x=2+3
x=5
Answer:
The answer will be listed below.
Step-by-step explanation:
Since there is an x= 2y+3, you can plug that equation into x in the equation 2x-3y=7. You must find y first.
2(2y+3)-3y=7
Now distribute 2 and you will get 4y+6-3y=7.
Combine 4y and -3y and have an equation of y+6=7.
Subtract 6 to both sides and you will have an answer of y=1
Now since you found y, now find x. To find x, substitue y=1 into any equation listed (you'll get the same answer anyways). Let's use x=2y+3 as an example. Substitute the 1 for y.
x=2(1)+3
Now you have x=2+3, which is 5.
x=5 and y=1.
To make sure this is correct, plug both the numbers into an equation, let's use the first one now.
2(5)-3(1)=7
7=7
In the end, the euqtaion equals 7, which means the answer is correct.
PROBABILITY! PLEASE HELP!
Samuel wants to create a password containing one, two, or three lowercase vowels followed by two digits. How many different passwords are possible? (Note: assume the letters "a", "e", "i", "o", and "u" are the ONLY vowels of the English alphabet.)
Using the fundamental counting principle, it is found that 15500 different passwords are possible.
----------------------------
The fundamental counting principle states that if there are p ways to do one things, and q ways to do other thing, and they are independent, there are p*q ways to do both things.
----------------------------
For each digit, there are 10 ways.For each vowel, there are 5 ways.The digits and the vowels are independent, thus, the fundamental counting principle is applied.----------------------------
With one vowel followed by two digits, there are [tex]5 \times 10^2 = 5 \times 100 = 500[/tex] passwords.With two vowels followed by two digits, there are [tex]5^2 \times 10^2 = 25 \times 100 = 2500[/tex] passwords.With three vowels followed by three digits, there are [tex]5^3 \times 10^2 = 125 \times 100 = 12500[/tex] passwords.In total, there are [tex]500 + 2500 + 12500 = 15500[/tex] passwords.A similar problem is given at https://brainly.com/question/23855405
Given: -4 - (-7), use this expression and the idea of a balloon model to describe what happens to the hot air balloon.
a. Where does the balloon start?
b. Do you add or subtract something from the balloon?
c. What do you add or subtract from the balloon?
d. Where does the balloon end up?
Answer:
Step-by-step explanation:
-4 - (-7) = -4+7=3
For a. the balloon starts at -4
for B. your adding something to the balloon
For c. your adding 7 to -4
for D. the balloon ends up and 3
Find an equation of the tangent line to the of the function at the given point.
f(x) = 3x2 – In x (1,3)
The answer is 5x-y-2=0 but I don’t know how to get to it.
Step-by-step explanation:
The slope of the tangent line is equal to the derivative.
f(x) = 3x² − ln x
f'(x) = 6x − 1/x
f'(1) = 6(1) − 1/1
f'(1) = 5
Use point-slope form:
y − 3 = 5 (x − 1)
Simplify:
y − 3 = 5x − 5
0 = 5x − y − 2
Find x. Round to the nearest tenth if needed.
Answer:
x = 16
Step-by-step explanation:
Use that the addition of all internal angles of a triangle must add up to 180, and the fact that the two given triangles are similar:
51 + 65 + 4 x = 180
combine and solve for "x"
116 + 4 x = 180
4 x = 180 - 116
4 x = 64
x = 64 / 4
x = 16
Answer:
x = 16
Step-by-step explanation:
A triangle is 180 degrees. Since two of the angles are congruent to each other, the third angle must be congruent as well. This means that the third measure for both triangles is 4x. Knowing all of this, we can solve for x:
65 + 51 + 4x = 180
116 + 4x = 180
4x = 64
x = 16
A meal at a restaurant cost $34.50, before tip. You decide to leave the server an 18% tip. What is your total bill?
The number line shows four points. Which point represents the approximate location of V12?
A) point A
B). point B
C) point C
D) point D
Answer:
point A
Step-by-step explanation:
Answer:c
Step-by-step explanation:
a car travels 304 miles on 16 gallons of gas how far can a car travel on 5 gallons
Answer: 95
304/16=19
19X5=95
solve write a linear equation in slope-intercept form for the graph shown the y-intercept of the line is 2 the slope is
Answer:
this is the answer.
Step-by-step explanation:
Find the Equation of a Line Given That You Know Its Slope and Y-Intercept. The equation of a line is typically written as y=mx+b where m is the slope and b is the y-intercept.
Which of the following is NOT a benefit of swimming?
A.
joints supported in water
B.
full-body exercise
C.
good exercise for cross-training
D.
burn less than 400 calories per hour
Answer:
d on edge
Step-by-step explanation:
Answer:
d
Step-by-step explanation:
What value of a, b, and c make this equation true?
Answer:
I think you need to know the value of X to get this answer.
Step-by-step explanation:
what is 576 - 354 + 7 = ?
Please help. -----------------------------------------
Answer:
D
Step-by-step explanation:
the equation tells you that 1 yard is 3 feet
so when you move one unit to the right on the x-axis, you should move three units up on the y-axis
The points A (0,4), B (6, 4) and C (6, -2) are 3 corners of a square ABCD.
What are the coordinates of D, the 4th corner?
Answer: It would be (0,-2)
Step-by-step explanation:
what is 205÷5 please help!
Answer:
41
Step-by-step explanation:
Just used the calculator :D
A person can burn
8 Calories per minute of running.
Determine whether the number of
Calories is proportional to the number
of minutes
Answer:
absolutely
Step-by-step explanation:
if you run for one min., you burn 8 calories right?
so if you run for example 10 mins., you would burn 80 calories
80>8
so yes
Seven more than a number, x, is at most 20
Answer:
x+7 ≤ 20
Just take it step by step:
seven more than a number is a number plus 7 (x+7)- keep in mind we dont know what the number is so we use x to represent the number.
it then says it's equal to at most 20.
This means that it cant equal anything above 20 since 20 is the max. Therefore, it must be 20 and below that x+7 equals
x+7≤ 20
≤ -this symbol means less than or equal to
Step-by-step explanation:
What molecules does a plant need to make glucose in the process of photosynthesis? Choose all correct answers. oxygen water carbon dioxide light
Answer: water, carbon dioxide , light
Step-by-step explanation:
Answer:
water and carbon dioxide
Step-by-step explanation:
i gut finched the quiz for k12 and this is the right answer
light is wrong
divide 3÷2/5
answer choses
A. 7
B. 7 1/5
C.7 1/2
D. 8
Answer:
7 1/2
Step-by-step explanation:
When you divide by fractions, the first number stays the same, but the second number is flipped(recipricol) and then multiplied.
3 divided by 2/5
3 * 5/2 = 15/2 = 7 1/2
7 1/2
5 plus1000 equal what
Help pleaseeeeeeeeeeeeeeeeeeeeee
Answer:
A) 2 1/12
Step-by-step explanation:
I just added all the fractions and subtracted from 10 1/12 :)
CLOTHING A online retailer is running a special on jeans. All pairs of jeans are $39. The function f(x) = 39x models the total cost of buying x pairs of jeans. The retailer also charges $6 flat rate shipping fee. a. Write a function g(x) that represents the cost of purchasing jeans and having them shipped. b. Find the cost of purchasing 3 pairs of jeans before and after shipping
Answer:
a. g(x) = 39x + 6
b. The price before shipping is $117 and the price after shipping is $123
Step-by-step explanation:
To represent the cost of purchasing jeans and shipping them, add 6 to the function, since it is a flat rate.
So, the function will be g(x) = 39x + 6.
Then, use this function to find the cost of 3 pairs of jeans after shipping:
g(x) = 39x + 6
g(3) = 39(3) + 6
g(3) = 117 + 6
= $123
Then, use the original function, f(x) = 39x, to find the price before shipping:
f(x) = 39x
f(3) = 39(3)
= $117
So, the price before shipping is $117 and the price after shipping is $123
{ colours in the rainbow}
Answer:
The colours of the rainbow are Red, Orange, Yellow, Green, Blue, Indigo and Violet.
Use the digits 5, 3 and 2 two only once in each number how many different three digit numbers can you make
Eric wants to attend a public four-year university. He estimates that the average cost of one year at this university is $19,500. He can save at most $325 a month. Without factoring in interest, grants, or scholarships, what is the minimum number of months he needs to save in order to be able to pay for one year of college?
60
62
65
67
Answer:
A 60
Step-by-step explanation:
While playing pool, you try to shoot the eight ball into the corner pocket.
Imagine that the coordinate plane is placed over the pool table. The eight ball is at ( 4, 3⁄4) and the pocket you are aiming for is at (10,4). You are going to make a bank shot at (6, 0).
a.) Write an equation for the path of the ball. b.) Do you make your shot? Why or why not?
Answer:
Step-by-step explanation:
to go from (4, 3/4 ) to (6, 0) you need
a line with slope m= (y2-y1)/(x2-x1) = [tex]\frac{3}{4}[/tex] -0 / 4-6 = [tex]\frac{3}{4} /\frac{-2}{1} =\frac{3}{4} *\frac{-1}{2} =\frac{-3}{8}[/tex]
use the quation of a line point-slope
(y-y1)=m(x-x1)
substitute m= -3/8 and (x1,y1) with (6,0)
[tex]y=\frac{-3}{8} (x-6)[/tex]
Now does point (10,4) where is the aim is verified by this equation?
substitute x=10, y=4 in the equation to check
4= -3(10-6)/8
4= -3*4/8
4=-3/2 this is never true so you do NOT make the shot
a.) The equation for the path of the ball is:[tex]\(y = -\frac{3}{8}x + \frac{9}{4}\).[/tex]
b.) The equation is not true because 4 is not equal to -3/2. Therefore, the ball does not make it into the pocket. The bank shot is not successful.The reason the shot fails is that the path of the ball (as represented by the linear equation) does not intersect the pocket point (10, 4), so the ball does not reach the desired target.
a.) To find the equation for the path of the ball, we can use the concept of a linear equation, which represents a straight line on the coordinate plane. The general form of a linear equation is:
[tex]\(y = mx + b\)[/tex]
where:
- y is the y-coordinate of a point on the line.
- x is the x-coordinate of the same point.
- m is the slope of the line (change in y divided by change in x).
- b is the y-intercept, which is the point where the line intersects the y-axis (x = 0).
a.) Equation for the path of the ball:
We can find the slope m of the line passing through (4, 3/4) and (6, 0) as follows:
[tex]\(m = \frac{{y_2 - y_1}}{{x_2 - x_1}} \\= \frac{{0 - \frac{3}{4}}}{{6 - 4}} \\= \frac{{-\frac{3}{4}}}{{2}} \\= -\frac{3}{8}\)[/tex]
Now, let's find the y-intercept b by substituting the values of (x, y) from one of the given points (let's use (4, 3/4)) and the calculated slope m :
[tex]\(y = mx + b\)\\\(\frac{3}{4} = -\frac{3}{8} \times 4 + b\)\\\(\frac{3}{4} = -\frac{3}{2} + b\)[/tex]
Now, solve for
[tex]\(b\): \(b = \frac{3}{4} + \frac{3}{2}\\ = \frac{3}{4} + \frac{6}{4} \\= \frac{9}{4}\).[/tex]
b.) To determine if the ball makes it into the pocket at (10, 4), we need to check if the y-coordinate (4) of the pocket point lies on the path of the ball. Substitute [tex]\(x = 10\) and \(y = 4\)[/tex] into the equation for the path of the ball:
[tex]\(4 = -\frac{3}{8} \times 10 + \frac{9}{4}\)\\\(4 = -\frac{30}{8} + \frac{9}{4}\)[/tex]
Now, let's find a common denominator and simplify:
[tex]\(4 = -\frac{30}{8} + \frac{18}{8}\)\\\(4 = -\frac{12}{8}\).[/tex]
To know more about linear equation:
https://brainly.com/question/34495857
#SPJ2
Determine whether the ordered pair (10, 4) is a solution to the equation 3x – 5y = 10
Yes, (10,4) is a solution.
No, (10,4) is not a solution.
Answer:
Yes, (10,4) is a solution.
Step-by-step explanation:
3x - 5y = 10
Substitute x and y to see if you get 10;
x = 10
y = 4
3(10) - 5(4) = 10
30 - 20 = 10
10 = 10
True!!!
11. A recipe calls for 1/2
tsp of vanilla extract and
2 1 / 2
cups of sugar. Jack used 10 cups of
sugar for his recipe. How much vanilla extract does he need for the recipe to taste
right?
Answer:
if jack uses 10 cups of sugar he will need to use 6 tsp of vanilla extract
Step-by-step explanation:
10 devided by 2 1/2= 4
and 1/2 multiplied by 4 is 6
Answer:
2 tsp
Step-by-step explanation:
This is a ratio/ proportionality problem. The recipe calls for 2 1/2 cups of sugar, Jack uses 10 cups. Then 10/(2[tex]\frac{1}{2}[/tex]) = 4, meaning he used 4 times the amount of sugar than in the original. Using that, just multiply [tex]\frac{1}{2}[/tex] by 4 to get 4 times the vanilla of the og recipe, which equals 2 tsp.
Can you use the properties of exponents you discovered to simplify 5^2 · 2^5 ?
5² × 2⁵ = 25 × 32 =. 800
Hope this helps
