Answer:
see explanation
Step-by-step explanation:
Note the common ratio r between consecutive terms of the sequence
r = 6 ÷ 3 = 12 ÷ 6 = 24 ÷ 12 = 48 ÷ 24 = 2
The explicit rule for a geometric sequence is
[tex]a_{n}[/tex] = a₁[tex](r)^{n-1}[/tex]
where a₁ is the first term and r the common ratio
Here a₁ = 3 and r = 2, thus
[tex]a_{n}[/tex] = 3[tex](2)^{n-1}[/tex] ← explicit rule
what is 2940 divided by 8
367.5, there are 367.5 8's in 2,940.
Hope this helps, if not, comment below please!!!!
Answer:
365.7
Step by step solving:
Jacob has purchased a $129,000 home with a 30-year mortgage at 5.15%. He can make a monthly payment of $1000. If he were to make this
payment each month, how many months will it take him to pay off his mortgage? Round you answer to a whole number.
Answer: 188 months
Step-by-step explanation:
Principal = $129 000
Payment = $1000
Mortgage % = 5.15
Since,
Number of Months = log (1+[rate/(Payment/Principal)-rate] / log (1 + rate)
Also,
rate = 5.15/1,200 = 0.004292
Number of Months = log (1 + [0.004292/(1,000/129000) -0.004292] / log(1+0.004292)
Number of Months = log ( 1 + 0.004292/ ((0.007752 -0.004292) / log (1.004292)
Number of Months = log ( 1 + (0.004292/0.00346))/ log (1.004292)
Number of Months = log (1 + 1.240) / log (1.004292)
Number of Months = log (2.240) / log (1.004292)
Number of Months = 0.3502 / 0.001860
Number of Months = 188.28 months
Approximation to whole month,
Number of months = 188 Months.
2. Choose all the expressions that are equal
to 2/3
1/6 + 1/2 yes or no
2/9 + 17/18 yes or no
5/12 + 1/4 yes or no
1 1/6-1/3 yes or no. 2 - 1 1/3 yes or no
Answer:
Yes, No, Yes, No, No
Step-by-step explanation:
⭐ Please consider brainliest! ⭐
✉️ If any further questions, inbox me! ✉️
Write the general equation for the circle that passes through the points (-1,2)(4,2)(-3,4)
Answer:
x² + y² - 3x - 13y + 18 = 0
Step-by-step explanation:
Recall that the general equation of a circle looks something like this:
x² + y² + Ax + By + C = 0
substituting each of the points into the equation we get:
for (-1,2)
(-1)² + (2)² + A(-1) + B(2) + C = 0
1 + 4 -A+2B + C = 0
-A + 2B + C + 5 = 0 ------------ eq 1
for (4,2)
(4)² + (2)² + A(4) + B(2) + C = 0
16 + 4 + 4A + 2B + C = 0
4A + 2B + C + 20 = 0 ------------- eq 2
for (-3,4)
(-3)² + (4)² + A(-3) + B(4) + C = 0
9 + 16 -3A + 4B + C = 0
-3A + 4B + C + 25= 0 ----- eq 3
Now we have a system of equations with 3 equations and 3 unknowns.
Solving for A, B and C, we eventually get:
A = -3, B = -13, C = 18
Substituting these into the general equation:
x² + y² + Ax + By + C = 0
x² + y² - 3x - 13y + 18 = 0
Find x in the given figure.
Answer:
Step-by-step explanation:
7x + 95+2x + x+25 + 90 = 360
10x + 210 = 360
10x = 360 -210
10x = 150
x = 150/10
x = 15
For the equations given below, which statement is true?
-3x-8=19
-3x-2=25
A. The equations have the same solution because the second equation can be obtained by subtracting 6 from both sides of the first equation.
B. The equations have the same solution because the second equation can be obtained by adding 6 to both sides of the first equation.
C. The equations have the same solution because the second equation can be obtained by subtracting 19 from both sides of the first equation.
OD. The equations do not have the same solution because the second equation can be obtained by adding 6 to both sides of the first equation.
Answer:
B
Step-by-step explanation:
If you add 6 to both sides, you get -3x-8+6=19+6 which is then -3x-2=25
an airplane travels at a rate of 250 miles/he with the wind and at a rate of 150 miles against the wind. what is the rate of the wind?
50 miles per hour is the rate (speed) of the wind.
Step-by-step explanation:
Let consider the variable ‘x’ for speed of wind.
Below we write two values of the speed of the airplane in the air in terms of ‘x’:
1. Subtract wind speed from airplane speed: 250 - x.
2. Add wind speed to the airplane speed against the wind: 150 + x.
And now, set these above two expressions equal to each other to find x (wind speed),
250 – x = 150 + x
2x = 100
x = 50 miles per hour
The cost of a company picnic varies directly as the number of employees attending the picnic. If a company picnic costs $487.50 for 30 employees, how much does a company picnic cost for 80 employees? ANSWER ASAP PLEASEEE
The company picnic cost $ 1300 for 80 employees
Solution:
Given that cost of a company picnic varies directly as the number of employees attending the picnic
Let "c" be the company picnic cost
Let "n" be the number of employees attending the picnic
Therefore,
[tex]cost \propto \text{ number of employees attending picnic }[/tex]
[tex]c \propto n\\\\c = kn[/tex]
Where "k" is the constant of proportionality
c = kn ---------- eqn 1
Given that company picnic costs $487.50 for 30 employees
Therefore substitute c = 487.50 and n = 30
[tex]487.50 = k(30)\\\\k = \frac{487.50}{30} = 16.25[/tex]
How much does a company picnic cost for 80 employees?
Substitute n = 80 and k = 16.25 in eqn 1
[tex]c = 16.25(80) = 1300[/tex]
Thus $ 1300 is the cost for 80 employees
Answer:
$1,300.00
Step-by-step explanation:
Which pairs of triangles are similar? Check all that
apply.
AABC - ADEF
ADEF - AGHI
Ο ΔGHI - ΔABC
O AGHI - AJKL
AJKL - AABC
Answer:
JKL and ABC
DEF and GHI
Step-by-step explanation:
we know that
If two triangles are similar, then the ratio of its corresponding angles is proportional and its corresponding angles are congruent
so
In this problem
1) triangles JKL and ABC are similar
because
[tex]\frac{KL}{BC} =\frac{JL}{AC}[/tex]
substitute the given values
[tex]\frac{10}{20} =\frac{7}{14}[/tex]
Simplify
[tex]\frac{1}{2} =\frac{1}{2}[/tex] ---> is true
therefore
The ratio of the corresponding sides is proportional
That means----> The triangles are similar
2) triangles DEF and GHI are similar
because
[tex]\frac{HI}{EF} =\frac{GI}{DF}[/tex]
substitute the given values
[tex]\frac{15}{10} =\frac{12}{8}[/tex]
Simplify
[tex]1.5=1.5[/tex] ---> is true
therefore
The ratio of the corresponding sides is proportional
That means----> The triangles are similar
The pairs of triangles that are similar to each other are:
B. ΔDEF ~ ΔGHI
E. ΔJKL ~ ΔABC
Similar TrianglesCorresponding angles of two triangles that are similar are always congruent, however, their corresponding sides are proportional to each other. This means, their ratio is equal.
Thus, triangles KJL and ABC are similar triangles because:
BC/KL = AC/JL = 2
Also, triangles DEF and GHI are similar triangles because:
GI/DF = HI/EF = 1.5
Therefore, the pairs of triangles that are similar to each other are:
B. ΔDEF ~ ΔGHI
E. ΔJKL ~ ΔABC
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LeBron has 6 yards of cable.he needs 15 feet of cable to install a stereo.does he have enough cable to install the stereo?explain your answer
PLEASE MARK BRAINLIEST!
Answer:
Yes!Step-by-step explanation:
This is because 6 yards equals 18 feet. If there is 15 feet needed to install a stereo, and we have 18 feet of cable, we have MORE THAN ENOUGH cable to install the stereo. So yes, there is enough cable to install the stereo.
I hope this helps!
- sincerelynini
Answer:
Yes.
Step-by-step explanation:
There is 3 feet in every yard. So LeBron has 18ft of cable.
I will mark brainliest for answering this question.
On a trip to visit relatives you drive 1,115.625 miles over the course of 21
hours and 15 minutes. What was the unit rate of the speed of your vehicle in miles
per hour? Round to the nearest tenth of a mile.
The unit rate of speed is 52.5 miles per hour
Solution:
Given that On a trip to visit relatives you drive 1,115.625 miles over the course of 21 hours and 15 minutes
We know that, 1 hour = 60 minutes
21 hours and 15 minutes = 21 hours + (15/60) hours = 21 + 0.25 = 21.25 hours
So they drive 1115.625 miles in 21.25 hours
To find the unit rate of speed of your vehicle in miles per hour, divide the total miles by time taken
unit rate of speed means miles driven in 1 hour
[tex]\rightarrow \frac{1115.625}{21.25} = 52.5[/tex]
So the unit rate of speed is 52.5 miles per hour
The amount of money in an account can be determined by the formula A re where is the
initial investment, r is the annual interest rate, and tis the number of years the money was
invested. What is the value of a $5000 investment after 18 years, if it was invested at 4% interest
compounded continuously?
Answer: $10272.17
Step-by-step explanation: Please see attachment for explanation
Answer:
[tex]\$10272.17[/tex]
Step-by-step explanation:
Since it is compounded continuously, we will use:
[tex]A=A_0 \cdot e^{k t}[/tex]
[tex]A_0[/tex] is the amount invested.
[tex]k[/tex] is the rate.
[tex]t[/tex] is the number of years you let the money sit.
[tex]A[/tex] is the future amount after the [tex]t[/tex] years that has been accumulated.
(Note:
I'm going to write [tex]r=4%[/tex] as a decimal. [tex]r=\frac{4}{100}=0.04[/tex].)
[tex]A=5000 \cdot e^{0.04 \cdot 18}[/tex]
[tex]A=5000 \cdot e^{0.72}[/tex]
[tex]A=5000 \cdot 2.0544332[/tex] (approximated)
[tex]A=10272.16605[/tex] (approximated)
To the nearest cent this is [tex]\$10272.17[/tex].
The axis of symmetry for the function f(x) = –2x2 + 4x + 1 is the line x = 1. Where is the vertex of the function located? (0, 1) (1, 3) (1, 7) (2, 1)
Answer:
Step-by-step explanation:
If the axis of symmetry is located at x = 1, that is the h value of our vertex (h, k). If we know h, all we have to do to find k is sub the value for h into the quadratic and evaluate.
[tex]f(1)=-2(1)^2+4(1)+1[/tex]
so f(1) = 3. Your choice is (1, 3)
The solution is (1, 3) where the vertex of the function located.
What is function?Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.
here, we have
given that,
The axis of symmetry for the function f(x) = –2x2 + 4x + 1 is the line x = 1.
now, we have to find the vertex of the function.
If the axis of symmetry is located at x = 1, that is the h value of our vertex (h, k).
If we know h, all we have to do to find k is sub the value for h into the quadratic and evaluate.
now, putting the value of x as 1 ,
so, we get,
f(1) = –2(1)^2 + 4*1+ 1
=-2 + 4 +1
=3
so f(1) = 3.
The solution is (1, 3).
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10. Alex is writing a number in scientific
notation. The number is greater than one
million and less than ten million. Which
number will Alex use as the exponent
of 10?
A 8
B 7
C 6
D 5
Answer:
C. 6
Step-by-step explanation:
Since the number is greater than one million and less than ten million, the number is seven digit which ranges from two million to nine million
Therefore, Alex will use 6 as the exponent
Linear system word problem
Answer:
1 year
Step-by-step explanation:
Create two equations to represent each tree. Linear equations are written in the form y = mx + b. "m" is the slope or rate. "b" is the constant or starting value.
In this problem, "m" is the rate of growth in inches per year.
"b" is the starting height.
let "x" be the number of years
let "y" be the height in inches
Tree A: y = 8x + 3
Tree B: y = 9x + 2
Solve the system of equations. Since both are equal to "y", you can equate them to each other and solve for "x". Isolate by doing reverse operations.
8x + 3 = 9x + 2
8x + 3 - 3 = 9x + 2 - 3 Subtract 3 from both sides
8x = 9x - 1
8x - 9x = 9x - 9x - 1 Subract 9x form both sides
-x = -1 Divide both sides by -1 to isolate
x = 1 Number of years for the trees to be the same height
Therefore it will take 1 year for the trees to be the same height.
If you wanted to know how tall the trees will be at the same height, find y. You can substitute x=1 in one of the equations.
y = 8x + 3
y = 8(1) + 3
y = 11 Number of inches when trees are the same height
Solve the system of equations algebraically. Verify your
answer using the graph.
y = 4x - 5
y=-3
What is the solution to the system of equations?
(1, -3)
in
Answer:
The solution is the point (0.5,-3)
Step-by-step explanation:
we have
[tex]y=4x-5[/tex] ----> equation A
[tex]y=-3[/tex] ----> equation B
Solve the system by substitution
Substitute equation B in equation A
[tex]-3=4x-5[/tex]
Solve for x
Adds 5 both sides
[tex]-3+5=4x[/tex]
[tex]2=4x[/tex]
Divide by 4 both sides
[tex]x=0.5[/tex]
therefore
The solution is the point (0.5,-3)
Verify your answer using the graph
using a graphing tool
Remember that the solution of the system of equations is the intersection point both graphs
The intersection point is (0.5,-3)
therefore
The solution is the point (0.5,-3)
see the attached figure
Answer:
Since y= -3, just put that in the equation.
-3 = 4x - 5
+5 +5
2 = 4x
/4 /4
x=1/2
if the sales tax rate is 7.25% in california, then how much would u pay in los angeles for a coat that cost $120.00
Answer:
The amount to be pay for coat is $128.70.
Step-by-step explanation:
Given:
The sales tax rate is 7.25% in California.
The cost for a coat in Los angeles is $120.00.
Now, to find amount to be paid.
Sales tax = 7.25%.
Cost = $120.00.
So, amount to be paid = $120 + 7.25% of $120.00.
[tex]=120+\frac{7.25}{100} \times 120.[/tex]
[tex]=120+\frac{870}{100}.[/tex]
[tex]=120+8.70[/tex]
[tex]=\$128.70[/tex]
Therefore, the amount to be pay for coat is $128.70.
PLEASE HELP!!! 15 POINTS AND WILL GIVE BRAINLIEST!!!
Two functions are represented in different formats.
Function 1:
x y
−2 −1
0 1
2 3
5 6
Function 2:
Graph of a line passing through the origin and the point begin ordered pair 1 comma 3 end ordered pair.
Which statements are true?
Select each correct answer.
Function 1 has a greater rate of change than function 2.
Function 2 has a greater rate of change than function 1.
Function 1 has a greater y-intercept than function 2.
Function 2 has a greater y-intercept than function 1.
Function 1 has a greater y-intercept than function 2
Step-by-step explanation:
solve for x:3x=5x -8
Answer:
4
Step-by-step explanation:
3x = 5x - 8 is your equation. To solve for x, you want to get all the x's on the same side. You first subtract 5x from each side to get -2x = -8, and multiply both by 1- to get 2x = 8, and then divide both sides by 2 to find x = 4.
Answer:
Step-by-step explanation:
3x=5x -8
3x - 5x = - 8
-2x = -8
x = -8/-2
x = 4
Molly has 9 cups of flour. If this is -
of the number she needs to make bread, how many cups does she need?
struct the tape diagram by reading it backward. Draw a tape diagram and label the unknown.
Answer:
9 pounds of flour
Step-by-step explanation:
mix together
The function f(x) = −x2 + 44x − 384 models the hourly profit, in dollars, a shop makes for selling coffee, where x is the number of cups of coffee sold, and f(x) is the amount of profit. Part A: Determine the vertex. What does this calculation mean in the context of the problem? (4 points) Part B: Determine the x-intercepts. What do these values mean in the context of the problem? (4 points) Part C: Determine the y-intercept. What does this value mean in the context of the problem? (2 points) (10 points)
Answer:
Part A) The vertex is the point (22,100) see the explanation
Part B) The x-intercepts are the points (12,0) and (32,0 see the explanation
Part C) The y-intercept is the point (0,-384) see the explanation
Step-by-step explanation:
Let
x ----> the number of cups of coffee sold
f(x) ---> the amount of profit
we have
[tex]f(x)=-x^{2} +44x-384[/tex]
This is a vertical parabola open downward (the leading coefficient is negative)
The vertex represent a maximum
Part A) Determine the vertex. What does this calculation mean in the context of the problem?
Convert the quadratic equation in vertex form
Factor -1
[tex]f(x)=-(x^{2}-44x)-384[/tex]
Complete the square
[tex]f(x)=-(x^{2}-44x+22^2)-384+22^2[/tex]
[tex]f(x)=-(x^{2}-44x+484)+100[/tex]
Rewrite as perfect squares
[tex]f(x)=-(x-22)^{2}+100[/tex]
The vertex is the point (22,100)
That means ----> The maximum profit of $100 is when the number of cups of coffee sold is 22
Part B) Determine the x-intercepts. What do these values mean in the context of the problem?
we know that
The x-intercepts are the values of x when the value of the function is equal to zero
so
we have
[tex]f(x)=-(x-22)^{2}+100[/tex]
For f(x)=0
[tex]0=-(x-22)^{2}+100[/tex]
solve for x
[tex](x-22)^{2}=100[/tex]
take square root both sides
[tex](x-22)=\pm10[/tex]
[tex]x=22\pm10[/tex]
so
[tex]x=22+10=32[/tex]
[tex]x=22-10=12[/tex]
The x-intercepts are the points (12,0) and (32,0)
That means -----> When the number of cups of coffee sold is 12 or 32 the profit is equal to zero
Part C) Determine the y-intercept. What does this value mean in the context of the problem?
we know that
The y-intercept is the value of the function when the value of x is equal to zero
so
For x=0
[tex]f(x)=-x^{2} +44x-384[/tex]
substitute the value of x
[tex]f(x)=-(0)^{2} +44(0)-384[/tex]
[tex]f(x)=-384[/tex]
The y-intercept is the point (0,-384)
That means ----> When the number of cups of coffee sold is zero the profit is negative -$384 (the cost is greater than the revenue)
I need help getting the answer to 1484 divided by 28
Answer:
53
Step-by-step explanation:
What is the sum or difference 2/3(7w+4) - 1/3(2w-1)
Answer:
4w+3
Step-by-step explanation:
2/3(7w+4)-1/3(2w-1)
14/3w+8/3-2/3w+1/3
14/3w-2/3w+8/3+1/3
12/3w+9/3
4w+3
A coin toss is based on what type of probability?
Answer:
50/50 chance
Step-by-step explanation:
Answer: Classical Probability (also know as priori or theoretical probability)
Step-by-step explanation:
Round 639.13787717 to 2 decimal places.
Answer: 639.14
Step-by-step explanation:
Find the midpoint of the line segment (-5,-8), (-7,3)
Answer:
Step-by-step explanation:
(-5,-8), (-7,3)
midpoint = (x₁+x₂/2, y₁+y₂/2)
= ( -5+-7/2 , -8+3/2) = (-5-7/2,-8+3/2)
= (-12/2, -5/2) = (-6,-5/2)
A new energy drink advertises 106 calories for 8oz. How many calories are in 12oz of the drink?
12oz of the drink contains 159oz of calories.
To Calculate How many calories are in 12oz of the drinkA new energy drink advertises 106 calories for 8oz.
Based on the given conditions, formulate: 12*(106/8)
=12*(13.25)=159
Calories are in 12oz of the drink is 159oz
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What is the slope of a line that is parallel to the line containing (-11, 5) and (-6, 1)?
Answer:
(5-1)/-11-(-6) = -4/5
Step-by-step explanation:
since the lines are parallel they have same slope/gradient
Answer:
-4/5
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(1-5)/(-6-(-11))
m=-4/(-6+11)
m=-4/5
4(x + 7) = 90(2+x)
4x + 28 = 180 + 90x
208 = 94x
What is the next step I have to do in solving this please help
Answer: 2.12
Step-by-step explanation: Divide by 94 on both sides to get X by itself
A circle with area 25pi has a sector with a central angle of 9/10pi radians. What is the area of a sector? Either enter an exact answer in terms of pi or use 3.14 for pi and enter your answer as a decimal rounded to the nearest hundredth.
Answer:
11.25 pi
Step-by-step explanation:
Pi is 180 degrees, a circle is 360 degrees, 9/10's of 180 is 162, and divide that by the full 360 which is .45. Then, multiply that by 25 and you have 11.25 pi is the area of that sector.