Answer:
[tex] \huge A (n) = 5 ({2})^{n - 1} \\ [/tex]
Step-by-step explanation:
The nth term of a geometric sequence is given by
[tex]A(n) = a _ 1( {r})^{n - 1} [/tex]
a1 is the first term
r is the common ratio
From the question we have the final answer as
[tex]A (n) = 5 ({2})^{n - 1} [/tex]
Hope this helps you
The length of a rectangle is twice the width if the perimeter of the rectangle 60 units find the area of the rectangle
Answer:
200
Step-by-step explanation:
Length = 2w
2w + 2l = 60
substitute l out with 2w
2w + 2(2w) = 60
2w + 4w = 60
w = 10
l = 20
Area = w • l
= 10 • 20
= 200
State the number of complex roots and the possible number of real and imaginary roots for each equation. The find all roots? If possible.
Answer:
x =2
x = -2
Step-by-step explanation:
(x - 2)(x + 2)(x^2 + 4) = 0
(x - 2) = 0
x = 0 + 2
x = 2
(x + 2) = 0
x = - 2
x = - 2
(x^2 + 4) = 0
x^2 = 4
x = [tex]\sqrt{4}[/tex]
x = 2
Petra jogs 3 miles in 30 minutes at this rate how long would it take a jog 10 miles
Answer:
100 minutes or 1 hour and 40 minutes
Step-by-step explanation:
3 miles in 30 minutes means 1 mile in 10 minutes
10 miles takes 100 minutes or 1 hour and 40 minutes.
1 hour and 40 minutes
help me please somone
Answer:
Iscoccecles
Sorry if i spelled it wrong.
Step-by-step explanation:
can somone help me pls ?
[tex]\huge\mathtt{Hello!}[/tex]
[tex](6x - 23) = (4x + 9)[/tex]
[tex]6x -4x = 9 + 23[/tex]
[tex]2x = 32[/tex]
[tex]x = 16[/tex]
It is because the sides are equal, so the angles opposite to them also are equal.
Have a nice day!
indicate in standard form the equation of the line passing through the given points, in the equation box below. X(0, 6), Y(5, 6)
Answer:
0x + y = 6
Step-by-step explanation:
Equation of the Line
The equation of a line passing through points (x1,y1) and (x2,y2) can be written as follows:
[tex]\displaystyle y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
It can be later converted to any other form of the line. For example, the standard form is:
[tex]Ax + By = C[/tex]
Let's find the equation by using the given points (0,6) (5,6):
[tex]\displaystyle y-6=\frac{6-6}{5-0}(x-0)[/tex]
Operating:
[tex]\displaystyle y-6=\frac{0}{5-0}(x-0)[/tex]
y - 6 = 0
Or, equivalently:
0x + y = 6
This corresponds to a horizontal line
A taxi cab charges a flat fee of $1.75 plus $0.30 for each half-mile or fraction of a half-mile.
a) Fill in the chart.
b)write and equation for the function.
Answer:
a) there is no chart but we can elaborate one:
taxi fee half-miles driven
$1.75 0
$2.05 1
$2.35 2
$2.65 3
$2.95 4
$3.25 5
$3.55 6
b) y = 0.3x + 1.75
where:
y = taxi fee
x = half miles driven
2+4 i need help right now
Answer:
6?
Step-by-step explanation:
Answer:
6
Step-by-step explanation:
2 + 4 =6
just add 2 by 4 than ans 6
find area of triangle formed by (1,1) (2,3) (4 ,5) using heron's formula
Answer:
The area of a triangle is:
A = 1 unit²Step-by-step explanation:
Given the points of a triangle
A(1, 1)
B(2, 3)
C(4, 5)
[tex]\mathrm{Compute\:the\:distance\:between\:}\left(x_1,\:y_1\right),\:\left(x_2,\:y_2\right):\quad \sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}[/tex]
Distance between AB:
[tex]AB=\sqrt{\left(2-1\right)^2+\left(3-1\right)^2}[/tex]
[tex]=\sqrt{1+4}[/tex]
[tex]=\sqrt{5}[/tex]
so
[tex]a=\sqrt{5}[/tex]Distance between BC:
[tex]BC=\sqrt{\left(4-2\right)^2+\left(5-3\right)^2}[/tex]
[tex]=\sqrt{2^2+2^2}[/tex]
[tex]=\sqrt{2^3}[/tex]
[tex]=2\sqrt{2}[/tex]
so
[tex]b=2\sqrt{2}[/tex]Distance between AC:
[tex]AC=\sqrt{\left(4-1\right)^2+\left(5-1\right)^2}[/tex]
[tex]=\sqrt{3^2+4^2}[/tex]
[tex]=\sqrt{5^2}[/tex]
[tex]=5[/tex]
so
[tex]c=5[/tex]Semiperimeter = sum of sides ÷ 2
[tex]s=\frac{\sqrt{5}+2\sqrt{2}+5}{2}=5.03224[/tex]
Area of the triangle:
[tex]A=\sqrt{s\left(s-a\right)\left(s-b\right)\left(s-c\right)}[/tex]
[tex]a=\sqrt{5}[/tex][tex]b=2\sqrt{2}[/tex][tex]c=5[/tex][tex]A=\sqrt{s\left(s-\sqrt{5}\right)\left(s-2\sqrt{2}\right)\left(s-5\right)}[/tex]
[tex]A=\sqrt{5.03224\dots \left(5.03224\dots -\sqrt{5}\right)\left(5.03224\dots -2\sqrt{2}\right)\left(5.03224\dots -5\right)}[/tex]
[tex]A=1[/tex]
Therefore, the area of a triangle is:
A = 1 unit²yler's brother earns $12 per hour. The store offers him a raise— a 5% increase per hour. after the raise,how much will tyler make per hour
Answer:
$12.60
Step-by-step explanation:
12/100 × 12 = 0.60
12 + 0.60 = 12.60
A person on a moving sidewalk travels 56 feet in 8 seconds. The moving sidewalk has a length of 210 feet. How long will it take to move from one end to the other?
PLEASE HELP ME WILL REPORT IF TROLL
Answer:
The answer is 1470 seconds.
Step-by-step explanation:
4x + 16y = -19
-2x - 8y = 10
Answer:
No solution.
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDASEquality PropertiesAlgebra I
Solving systems of equations using substitution/eliminationSolving systems of equations by graphingStep-by-step explanation:
Step 1: Define systems
4x + 16y = -19
-2x - 8y = 10
Step 2: Rewrite systems
-2x - 8y = 10
Add 8y to both sides: -2x = 8y + 10Divide -2 on both sides: x = -4y - 5Step 3: Redefine systems
4x + 16y = -19
x = -4y - 5
Step 4: Solve for y
Substitution
Substitute in x: 4(-4y - 5) + 16y = -19Distribute 4: -16y - 20 + 16y = -19Combine like terms: -20 ≠ -19Here we see that -20 does not equal -19.
∴ This systems of equations has no solution
Step 5: Graph
Check the systems.
Hard to see, but they are parallel lines.
Mrs. Conley asks her class what kind of party they want to have to celebrate their excellent behavior. Out of all the students in the class, 5 want a ice cream party, 7 want a movie, 10 want a costume party, and the rest want are undecided. If 20% want a ice cream party, how many students are in class?
Answer:
25
Step-by-step explanation:
Find the values of a and b such that x² - 2x + 2 = ( x - a )² + b
Answer:
a = b = 1
Step-by-step explanation:
x² - 2x + 2 = ( x - a )² + b
x² - 2x + 2 = ( x² - 2x + 1) - 1 + 2 = (x - 1)² + 1
a = b = 1
Can someone please help, ty!!
(Will mark brainliest)
Answer:
Yellow is correct.
You can add the valued and divide by how many values there are to find the mean
The score of 20 is an outlier and brings the mean score down by almost 10%
Step-by-step explanation:
Answer:
3: The low score causes the mean to decrease.
Step-by-step explanation:
If you add a significantly lower number, it will bring down the overall average.
Hope this helps!
PLSSSS HELPPP I WILLL GIVEEE BRAINLIESTTTT!!!!!!!!!!!!!!!!!
PLSSSS HELPPP I WILLL GIVEEE BRAINLIESTTTT!!!!!!!!!!!!!!!!!
PLSSSS HELPPP I WILLL GIVEEE BRAINLIESTTTT!!!!!!!!!!!!!!!!!
PLSSSS HELPPP I WILLL GIVEEE BRAINLIESTTTT!!!!!!!!!!!!!!!!!
If f(x) = -3x + 4, find f(-4)
Answer:
Step-by-step explanation:
-3x+4
-3(-4)+4
12+4
16
Answer:
3x+4
3(-4)+4
12+4
16
Step-by-step explanation:
A tree is 72 feet (ft) tall. How many inches (in) is this? First fill in the blank on the left side of the equation using one of the ratios. Then write your answer on the right side of the equation.
1 foot = 12 inches:
1/72 = 12/x
Cross multiply:
1x = 72 * 12
x = 864 inches
the is factoring quadratics with a leading coefficient: 5x to the 2 power - 14x + 8
Answer:
The factorization of [tex]5x^2-14x+8[/tex] is (5x-4)(x-2)
Step-by-step explanation:
Given quadratic polynomial is:
[tex]5x^2-14x+8[/tex]
To factor a quadratic polynomial with leading co-efficient has to be factorized, the leading co-efficient and the constant are multiplied and pairs(a,b) of the product are made so that their sum or subtraction is equal to the co-efficient of x
We get 40 by multiplying 8 and 5
And the pair we get are: 10 and 4
[tex]=5x^2-10x-4x+8\\=5x(x-2)-4(x-2)\\=(5x-4)(x-2)[/tex]
Hence,
The factorization of [tex]5x^2-14x+8[/tex] is (5x-4)(x-2)
13. The population of a city is currently 45,000 and is declining at a rate of 2% each year. Estimate the population after a period of 5 years. Use the formula ƒ(t) = aert.
Given:
Initial population = 45,000
Decreasing rate = 2%
Time = 5 year
To find:
The population after a period of 5 years.
Solution:
Formula used:
[tex]f(t)=ae^{rt}[/tex]
where, a is initial population, r is rate and t is time.
[tex]r=\dfrac{2}{100}=0.02[/tex]
Decreasing rate represented by -0.02.
Substitute a=45000, r=-0.02 and t=5 in the above formula.
[tex]f(5)=45000e^{-0.02(5)}[/tex]
[tex]f(5)=45000e^{-0.1}[/tex]
[tex]f(5)=45000(0.904837418)[/tex]
[tex]f(5)=40717.68381 [/tex]
Approximate the value to the previous integer.
[tex]f(5)\approx 40717 [/tex]
Therefore, the population after 5 years is 40717.
Answer:
40,718
Step-by-step ex
The population of a city is currently 45,000 and is declining at a rate of 2% each year. Estimate the population after a period of 5 years. Use the formula ƒ(t) = aert. planation:
Rhombus ABCD has the following vertices:
A(-8,11)
B(-1, -13)
C(14,7)
D(7,31)
Is rhombus ABCD a square, and why?
Answer: No because BC is not perpendicular to AB.
Step-by-step explanation:
Yes, rhombus ABCD is a square as all four angles of the rhombus are right angles.
A square is a special type of rhombus where all four sides have the same length and all four angles are right angles.
In this case, we can see that all four sides of the rhombus have the same length by calculating the distance between each pair of vertices. For example, the distance between A and B is:
distance = [tex]\sqrt{[/tex] [tex]((-8 - (-1))^2[/tex] + [tex](11 - (-13))^2[/tex])
distance = [tex]\sqrt{[/tex] ([tex]7^2[/tex] + [tex]24^2[/tex])
distance = [tex]\sqrt{[/tex] (625) = 25
The distance between each other pair of vertices is also 25, so all four sides of the rhombus have the same length.
We can also see that all four angles of the rhombus are right angles by calculating the angles between each pair of adjacent sides. For example, the angle between sides AB and BC is:
angle = arctan((13 - (-13))/(-8 - (-1)))
angle = arctan(26/7)
angle = 78.6°
The angle between each other pair of adjacent sides is also 78.6°, so all four angles of the rhombus are right angles.
Therefore, rhombus ABCD is a square.
To learn more about rhombus here:
https://brainly.com/question/12665650
#SPJ2
Which of the following is not a reason used in this proof?
A) Definition of perpendicular
B) Vertical angles are equal
C) Reflexive
Answer:
Reflexive
Step-by-step explanation:
Because C and D are right angles. That’s def of perpendicular. I’m not sure about the vertical angles but it’s shown in the proof
Answer:
Reflexive
Step-by-step explanation:
Q14.
Solve the simultaneous equations
2x - 3y = 24
6x + 2y = -5
landimorament
Michael’s father bought him a 16-foot board to cut into shelves for his bedroom. michael plans to cut the board into 11 equal size lengths for his shelves.the saw blade that michael will use to cut the board will change the length of the board by -0.125 inches for each cut. how will this affect the total length of the board?
Step-by-step explanation:
you have to know how many inches make a foot or vice versa the you do simple proportion by equating the inches to the foot to get the answer. simple as abc
A sequence of steps for solving the equation 3(x - 2) = 4 is shown. Match a property to each blank box to show the reason for each step. Question 6 options: 3(x - 2) = 4 3x - 6 = 4 3x = 10 x = 103 1. Given 2. Distributive Property 3. Addition property of equality 4. Division property of equality
Step-by-step explanation:
Given the equation;
3(x-2) = 4
A sequence of steps for solving the equation is as shown;
Step 1: Open the parenthesis by applying distributive law to distribute 3 over x and 2 as shown;
3(x-2) = 4
3(x)- 3(2) = 4
3x - 6 = 4
Step 2: Add 6 to both sides of the equation (Addition property)
3x-6+6 = 4+6
3x = 10
Step 3: Division property of equality. Divide both sides by 3;
3x = 10
3x/3 = 10/3
x = 10/3
PLZ Help Urgent. 15 POINTS, BRAINLY Guaranteed.
Plz Answer honestly or you will be reported.
Evaluate.
(2/7)^3
A: 8/343
B: 8/7
C: 3/343
D: 6/7
Answer:
8/343
so A
Step-by-step explanation:
Question 5 of 8
Put these substances in order of density with the most dense first and the
least dense last.
1 iron
Trubber
cotton ball
Ti helium
Answer:
cf
cf
centru. toc htc. toc cf. activ. cfc fgfvxv. chvv
Last year, the cost of a family-sized dinner at a picnic was $8.50. This year, the cost is $11.56. What is the percent of increase of the price? ( I need a step-by-step explanation not just the answer) ill give brainliest
#12: Kara is deciding between The Lyme Point Inn and Ever After Farms for 1 point
her wedding reception. The Lyme Point Inn charges $3,000 for the venue
and $100 for each meal. Ever After Farm charges $5,400 for the venue and
$70 for each meal. Write and solve an equation to find the number of
meals at which the total cost charged by the two venues would be the
same. *
Your answer
ooo
Answer:
80 meals
Step-by-step explanation:
Set up an equation where x is the number of meals:
100x + 3000 = 70x + 5400
Solve for x:
100x + 3000 = 70x + 5400
30x + 3000 = 5400
30x = 2400
x = 80
So, at 80 meals, the cost of the 2 venues will be the same
Answer:
80 metals
Step-by-step explanation:
100x + 3000 = 70x + 5400
How to Solve for x:
100x + 3000 = 70x + 5400
30x + 3000 = 5400
30x = 2400
x = 80
So, at 80 meals, the cost of the 2 venues will be the exact same
Mia has 12 boxes of cookies. Each box contains 36 cookies. she has another 258 cookies in the pantry. How many cookies does she have in all?
690
12×36 + 258 = 690 For extending to 20 characters
Harry wants a fence around his garden.
Height: 16.7m
Length: 16.3m
What is the perimeter of the whole garden?
Answer:
66m
Step-by-step explanation:
perimeter is the distance all round a figure
perimeter(p)= 2( length(l) + width(w)) or perimeter= 2 length + 2 width
p= 2(l + w) or p = 2l + 2w
p= 2(16.3 +16.7) or p= 2(16.3) + 2(16.7)
p=2(33) or p= 32.6 + 33.4
p=66m or p= 66m