Answer:
405
Step-by-step explanation:
This is a geometric sequence, so we need the common ratio and the first term
To find the common ratio, we take the second term and divide by the first term
15/5 =3
The common ratio is 3
We are multiplying by 3 each time
The first term is 5
The formula is
an = a1 * (r) ^ (n-1) where n is the term number
We want the 5th term
a5 = 5 * (3) ^ (5-1)
a5 = 5 *3^4
= 5 *81
= 405
The fifth term is 405.
[tex]a_{n}[/tex] = [tex]a_{1}[/tex]* [tex]r^{n-1}[/tex]
In this formula,[tex]a_{1}[/tex] is the first term,
r is the common ratio, and
n is the term number.
From the given sequence 5, 15, 45,..., we can identify the following:
[tex]a_{1}[/tex] = 5
r = 15 / 5 = 3 (common ratio)
Now, we need to find the fifth term (n = 5):
[tex]a_{5}[/tex] = 5 * [tex]3^{5-1}[/tex]
= 5 * [tex]3^{4}[/tex]
= 5 * 81
= 405
So, the fifth term of the geometric sequence is 405.
Carl plans to prepare for the upcoming track season by running 160 miles. So far he has ran 28 miles. How many more miles does he have to run?
Answer:
132 miles
Step-by-step explanation:
miles ran + miles to run = total miles
28 + miles to run = 160
Subtract 28 from each side
28-28 + miles to run = 160-28
miles to run = 132
He still need to run 132 miles
Answer:
132 mi
Step-by-step explanation:
since he ran 28 miles but he has to run 160 miles, he still has to run some miles. if we make the amount he still has to run x, we can do 28+x=160. now we can solve this by subtracting 28 on both sides to getx=132
28+x=160
-28 -28
-------------------------
x=132
wich of the following is a graph of the equation y=√x +5-2
The value of graph of equation y =√(x+5) - 2 is shown in figure.
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
We have to given that;
Equation is,
⇒ y = √(x + 5) - 2
Now, We can draw graph of equation y =√(x+5) - 2 is shown in figure.
Hence, The figure is shown in image.
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Fabian is decorating a triangular pennant for a football game. The pennant has a base of 10 inches and a height of 24 inches. What is the total area of the pennant?
Please help!!!!
Answer: [tex]120in^2[/tex]
Step-by-step explanation:
The formula that is used to calculate the area of a triangle is:
[tex]A_{(triangle)}=\frac{b*h}{2}[/tex]
Where the base of the triangle is b and the height of triangle is h.
If the pennant has a base of 10 inches and a height of 24 inches, you know that:
[tex]b=10in\\h=24in[/tex]
As it is a triangular pennant, you can substitute the values of the base and the value of the height into the formula used to calculate the area of a triangle.
Then, total area of the pennant is:
[tex]A_{(pennant)}=\frac{(10in)(24in)}{2}\\\\A_{(pennant)}=120in^2[/tex]
Yolanda tossed a coin 15 times. The results were 9 heads and 6 tails. Determine the experimental probability of tossing tails.
The experimental probability of tossing tails in the given scenario is 0.4 or 40%, which is determined by dividing the number of tails (6) by the total number of tosses (15).
Explanation:The student is asking to determine the experimental probability of tossing tails when a coin was tossed 15 times and resulted in 9 heads and 6 tails. Experimental probability is calculated by dividing the number of times an event occurs by the total number of trials. In this case, the coin landed as tails 6 times out of 15 tosses.
To find the experimental probability of tossing tails, use the formula:
Experimental Probability of Tails = Number of Tails / Total Number of Tosses
So, it would be:
Experimental Probability of Tails = 6 / 15
Experimental Probability of Tails = 0.4 or 40%
Graph the ellipse with equation x squared divided by 16 plus y squared divided by 4 = 1.
Answer:
See attached image.
Step-by-step explanation:
To easily solve this question, we use a graphing tool, or a calculator to plot the graph of the ellipse.
(1/16)*x^2 + (1/4)*y^2 = 1
Please see image below
Answer:
Step-by-step explanation:
Please help with this ASAP! Please give an actual answer and show your work, I want to be able to understand how the problem is done, 35 points thank you very much.
Answer:
The answer would be 60cm.
Step-by-step explanation:
If triangle ABC has a side length of 4 cm and the area is equal to 40, the triangle PQR with a side length of 6 cm would have an area of 60.
05.05)The coordinates below are the three vertices of a rectangle. Identify the fourth coordinate and the area of the rectangle. A coordinate plane with the following points A at negative 2, 2; B at negative 2, negative 4; and C at 2, negative 4.
Answer:
the other one is (2, 2)
the area is 24
Step-by-step explanation:
A = (2+2)(2+4) = 24
What is the decimal representation of seven hundredths
Answer:
0.07
.7 is 7 tenths or 70 hundredths
.07 is 7 hundredths
please tell me a answer please and thank you and please show steps =^)
Answer: $105.25
Step-by-step explanation: The first step is to calculate the total of the purchases that she made, which is done by this formula:
(2x$16) + 40 +25=
$32 + 40 + 25 =
$97 is the total of the clothing
Tax is 8.5%, so to calculate the tax by multiplying .085 x 97 = $8.25 Sales Tax
In order to determine the total, add $97 + 8.25 = $105.25
What is the median of these numbers: 14, 20, 24, 16, 20, and 18
♫ - - - - - - - - - - - - - - - ~Hello There!~ - - - - - - - - - - - - - - - ♫
➷ To find the median of the numbers, you have to order them:
14, 16, 18, 20, 20, 24
Then, you find the average of the middle two numbers if the amount of numbers is even.
18+20/2
18+20=38
38/2=19
Final answer:
The median of those numbers is 19
✽
➶ Hope This Helps You!
➶ Good Luck (:
➶ Have A Great Day ^-^
TROLLER
♫ - - - - - - - - - - - - - - - ~Hello There!~ - - - - - - - - - - - - - - - ♫
➷ To find the median, you need to order your numbers first.
14, 16, 18, 20, 20, 24
There is an even amount of numbers, so you find the mean of the middle two numbers.
18+20=38/2=19
Median=19
✽
➶ Hope This Helps You!
➶ Good Luck (:
➶ Have A Great Day ^-^
DOGE
Determine the solution to the system of equations given below y=x^2-5x+15
Answer:
x=(5+i*sqrt(35))/2, (5-i*sqrt(35))/2
Step-by-step explanation:
Use the quadratic formula with the following values.
a = 1
b = -5
c = 15
Substitute and simplify.
(5+-sqrt((-5)^2-4*(1*15)))/2*1
x = (5+-i*sqrt(35))/2
When you get a negative number inside the square root, remember that you can pull out i to make the number inside positive.
You and three friends are comparing the amount of money you have in your bank accounts. You have a balance of -$50, and your friends have balances of $20,
-$10, and $5. Which balance is the least?
Answer:
Step-by-step explanation:
Your balance or -50$
what is the y- value of the intersection y=2x and y=x^2-3
Answer:
y = - 2 or y = 6
Step-by-step explanation:
Given the 2 equations
y = 2x → (1)
y = x² - 3 → (2)
Substitute y = x² - 3 into (1)
x² - 3 = 2x ( subtract 2x from both sides )
x² - 2x - 3 = 0 ← in standard form
(x - 3)(x + 1) = 0 ← in factored form
Equate each factor to zero and solve for x
x - 3 = 0 ⇒ x = 3
x + 1 = 0 ⇒ x = - 1
Substitute these values into (1) for corresponding values of y
x = 3 : y = 2 × 3 = 6
x = - 1 : y = 2 × - 1 = - 2
Before a renovation, a movie theater had 138 seats. After the renovation, the theater has 186 seats. What is the approximate percentage increase of the number of seats in the theater? If necessary, round to the nearest tenth of a percent.
The approximate percentage increase of the number of seats in the movie theater after the renovation is 34.8% when rounded to the nearest tenth of a percent.
To calculate the approximate percentage increase of the number of seats in the movie theater, we start by finding the difference in the number of seats before and after the renovation. We then divide this difference by the original number of seats and multiply by 100 to get the percentage increase.
Original number of seats = 138
New number of seats = 186
Increase in seats = New number of seats - Original number of seats
Increase in seats = 186 - 138 = 48
Next, we calculate the percentage increase:
Percentage increase = (Increase in seats \/ Original numbe of seats) x 100
Percentage increase = (48 \/ 138) x 100
Percentage increase \/= 34.7826...
When rounded to the nearest tenth of a percent, the percentage increase is approximately 34.8%.
The product of (4z^2 + 7z - 8) and (-z + 3) is -4z^3 + xz^2 + yz - 24. What is the value of x? What is the value of y?
Answer:
[tex]x=5+\frac{29}{z}-\frac{y}{z}[/tex]
[tex]y=5z+29-xz[/tex]
Step-by-step explanation:
Given: [tex](4z^2+7z-8)(-z+3)=-4z^3+xz^2+yz-24[/tex]; find x and y.
Let's start with finding x first. Let's distribute the left side of the equation.
[tex]-4z^3+5z^2+29z-24=-4z^3+xz^2+yz-24[/tex]
Let's move everything we can to the left side of the equation. Some things will cancel out.
[tex]5z^2+29z=xz^2+yz[/tex]
Now, let's move the term that includes [tex]x[/tex] to the left side of the equation. Everything else should be moved to the right.
[tex]-xz^2=-5z^2-29z+yz[/tex]
Let's get rid of the negative sign in front of [tex]x[/tex] by dividing both sides by -1.
[tex]xz^2=5z^2+29z-yz[/tex]
To get [tex]x[/tex] completely isolated, divide both sides by [tex]z^2[/tex].
[tex]\frac{xz^2}{z^2}=\frac{5z^2}{z^2}+\frac{29z}{z^2}-\frac{yz}{z^2}[/tex]
Simplify.
[tex]x=5+\frac{29}{z}-\frac{y}{z}[/tex]
Let's solve for y. We will start with the distributed and simplified equation to make it easier.
[tex]5z^2+29z=xz^2+yz[/tex]
Now, let's move the term that includes [tex]y[/tex] to the left side of the equation. Everything else should be moved to the right.
[tex]-yz=-5z^2-29z+xz^2[/tex]
Again, let's get rid of the negative sign in front of the [tex]y[/tex] by dividing both sides by -1.
[tex]yz=5z^2+29z-xz^2[/tex]
To isolate y, divide both sides by z.
[tex]\frac{yz}{z}=\frac{5z^2}{z}+\frac{29z}{z}-\frac{xz^2}{z}[/tex]
Simplify.
[tex]y=5z+29-xz[/tex]
Answer:
x = 5
y = 29
Step-by-step explanation:
Edge Answer
How do you find the circumference or a circle with only a diameter?
To find the circumference of a circle that lists only as a diameter, you would do pi*d so lets say the diameter is 6, you would do pi*6 which would end up giving you 18.84. I hope this helps a bit! (:
Answer:
pi * d
Step-by-step explanation:
Multiply 3.14 by the Diameter.
Find the sum of the first 20 terms
Answer:20.5
Step-by-step explanation:
1.5+1.45+1.40+1.35+1.30+1.25+1.20+1.15+1.10+1.05+1.00+0.95+0.90+0.85+0.80+0.75+0.70+0.65+0.60+0.55=20.5
anyone please help me? tysm!
Answer:
6 ft
Step-by-step explanation:
The surface area of a cube is given by
SA = 6s^2
216 = 6s^2
Divide each side by 6
216/6 = 6s^2/6
36 = s^2
Take the square root of each side
sqrt(36) = sqrt(s^2)
6 =s
Each side is 6ft
what is 365885325790986666*89625895187465785 56 points for answer.
Answer: This was HARD! 3.279279986x10^34
Step-by-step explanation:
I HOPE TO GOD THAT HELPED! phew!
What is the place value of the 9 in the number 31,985?
Answer:
Hundreds
Step-by-step explanation:
If x and y satisfy both 9x+2y=8 and 7x+2y=4, then y=?
Answer:
The value of y is -5
Step-by-step explanation:
we have
[tex]9x+2y=8[/tex] ------> equation A
[tex]7x+2y=4[/tex] ------> equation B
we know that
If x and y satisfy both equations, then (x,y) is the solution of the system of equations
Using a graphing tool
Remember that
The solution of the systems of equations is the intersection point both graphs
The intersection point is (2,-5)
therefore
The solution of the system of equations is the point (2,-5)
The value of y is -5
To find the value of y in the given system of equations, we can use the method of substitution.
Explanation:To find the value of y in the system of equations 9x + 2y = 8 and 7x + 2y = 4, we can use the method of substitution. First, we solve one equation for one variable and substitute the expression into the other equation. In this case, we can solve the second equation for y: 7x + 2y = 4, y = (4 - 7x)/2. Now substitute this expression for y in the first equation: 9x + 2((4 - 7x)/2) = 8. Simplify and solve for x. Once we have the value of x, we can substitute it back into the second equation to find y.
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How to solve this problem ?
Answer:
By using math skills, lol.
Step-by-step explanation:
Thats easily how you solve the problem..
While shopping for clothes Tracy spent $38 less than three times what Daniel spent right and solve an equation to find how much Daniel spent where X represents how much Daniel spent
Answer:
y=3x-38
Step-by-step explanation:
We know that Tracy spent $38 in less than 3 times than what Daniel spent. Given this information we can put our eqaution together.
Y=3x-38
Hope this helps! :)
Evaluate 3x2+x-2 when x=-2
Answer:
8
Step-by-step explanation:
Evaluate 3x^2+x-2 when x=-2
Just plug in x = - 2 into the expression
= 3(-2)^2 + (-2) -2
= 3(4) -2 - 2
= 12 - 4
= 8
The value of the expression [tex]3x^2+x^{-2}[/tex] at x=2 will be equal to 8.
What are mathematical expressions?
Expressions are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.
Evaluate [tex]3x^2+x^{-2 }[/tex]when x=-2
Just plug in x = - 2 into the expression
[tex]= 3(-2)^2 + (-2) -2[/tex]
[tex]= 3(4) -2 - 2[/tex]
[tex]= 12 - 4[/tex]
[tex]= 8[/tex]
Hence value of the expression [tex]3x^2+x^{-2}[/tex] at x=2 will be equal to 8.
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(8c+5)(-2c-3) simplify
(8c+5)(-2c-3)
Multiply each term together, then combine like terms:
8c * -2c = -16c^2
8c *-3 = -24c
5 * -2c = -10c
5 *-3 = -15
Now combine:
-16c^2 - 24c -10c -15
Simplify:
-16c^2 -34c -15
Answer:
-16c^2 - 24c -10c -15
Step-by-step explanation:
The base of a cone has a radius of 4 millimeters and the height of the cone is 24 millimeters. What is the volume of the cone?
Question 6 options:
A. 32π mm3
B. 96π mm3
C. 128π mm3
D. 384π mm3
Answer:
The volume of the cone is 128π mm³ ⇒ answer (C)
Step-by-step explanation:
* Lets study the cone
- Its base is a circle
- Its height the perpendicular distance from its vertex to
the center of the base
- The length of its slant height = √(h² + r²)
- The volume of the con is 1/3 the volume of the cylinder
∵ The volume of the cylinder = πr²h
∴ The volume of the cone = (1/3) πr²h
* In our problem:
- r = 4 mm
- h = 24 mm
∴ Its volume = (1/3) × π × (4)² × 24 = 128π mm³
* The volume of the cone is 128π mm³
The courtyard behind Jennie’s house is shaped like a trapezoid the bases measures 8 meters and 11 meters the height of the trapezoid is 12 meters what is the area of the courtyard
Answer:
A = 114 m²
Step-by-step explanation:
The formula for area of a trapezoid is
A = (1/2)(B + b)h where B is the bottom base, b is the top base, and h is the height.
We are given B = 11, b = 8, and h = 12, plug those values in and simplify
A = (1/2)(11 + 8)(12)
A = (1/2)(19)(12)
A = (19)(6) (half of 12 is 6)
A = 114 m²
AC is tangent to the circle with center at B. The measure of angle ACB is 58 degrees.
What is the measure of ABC?
Answer: ABC = 32 degrees
Step-by-step explanation:
We are already given the measurement of angle ACB, which is 58. And given AC is tangent to circle B we also know that BAC is 90 degrees.
So,
ABC = 180 - (BAC + ACB)
ABC = 180 - (90 + 58)
ABC = 180 - (148)
ABC = 32 degrees
Hope I could help :)
Answer:
ABC is equal to 32 degrees
what is the correct inverse function for f(x)=In(3x)
Answer:
[tex]f^{-1}(x)=\dfrac{e^x}{3},\ x\in(-\infty,\infty),\ y>0[/tex]
Step-by-step explanation:
Consider the function [tex]f(x)=\ln 3x.[/tex] the domain of this function is x>0 and the range of this function is all real numbers. The inverse function has the domain all real numbers and the range y>0.
If
[tex]y=\ln 3x,[/tex]
then
[tex]3x=e^y,\\ \\x=\dfrac{e^{y}}{3}.[/tex]
Change x into y and y into x:
[tex]y=\dfrac{e^x}{3}.[/tex]
Thus, the inverse function is
[tex]f^{-1}(x)=\dfrac{e^x}{3}.[/tex]
ANSWER
[tex]{f}^{ - 1} (x) = \frac{ {e}^{x} }{3} [/tex]
EXPLANATION
The given logarithmic function is
[tex]f(x) = ln(3x) [/tex]
Let
[tex]y = ln(3x) [/tex]
Interchange x and y.
[tex]x = ln(3y) [/tex]
Solve for y.
[tex] {e}^{x} = {e}^{ ln(3y) } [/tex]
[tex] {e}^{x} = 3y[/tex]
Divide both sides by 3.
[tex] \frac{ {e}^{x} }{3} = y[/tex]
Therefore
[tex] {f}^{ - 1} (x) = \frac{ {e}^{x} }{3} [/tex]
What is a car loan ?
Answer:
A loan that you usually have to get from a bank to use specifically for paying for a car,which you later have to pay back
Step-by-step explanation:
A car loan is a type of secured loan, where we can say that the car we buy is collateral for the loan.
In case of failure of payment of loan, the lender can repossess the car and sell it to pay off the loan.
In other words, we can say the lender or banks purchase the car for us and gives us few years time to pay back that loan.
The loan is granted with interest rates, that one has to pay above the principle amount during the tenure of the loan.