Answer: Please see explanation column for answer
Step-by-step explanation:
According to sequence 2, 6, 18, 54, 162
--we can see that it is a geometric sequence since to go from one term to the next requires us to multiply by 3 which is called the common ratio which is gotten by dividing the next by the previous.
ie term 2/ term 1= 6/2 = 3
term 3/ term 2= 18/6= 3
term 4/ term 3= 54/28= 3
term 5 / term 4= 162/54=3
term 6 will therefore be 162 x3 = 486
and term 7 = 486 x 3=1,458 and so on
Recall that nth term of GP is
Tn = ar^n-1
Where a= first term
r= common ratio
n= term
such that to easily find particular term, we plug in the values and calculate
for example the 10th term of the above sequence
Tn = ar^n-1
= 2 X 3 ^(10-1)
2 X 3^9
T10 =39,366
A certain brand of shampoo contains 12 ounces in a bottle. The company
decides to redesign the shape of the shampoo bottle. The new type of
bottle contains 15 ounces of shampoo. What is the percent of increase in
the amount of shampoo the new bottle contains?
Answer: 15% I think
Step-by-step explanation:
The percent of increase in the amount of shampoo the new bottle contains is 25%.
Given that, a certain brand of shampoo contains 12 ounces in a bottle and the new type of bottle contains 15 ounces of shampoo.
What is the percentage of increase?Percentage increase is the difference between the final value and the initial value, expressed in the form of a percentage.
Percentage increase = (Final value - Initial value) / Initial value × 100
Now, initial value = 12 and final value = 15
Percentage increase = (15-12)/12 × 100
= 3/12 × 100
= 1/4 × 100
=25%
Therefore, the percent of increase in the amount of shampoo the new bottle contains is 25%.
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Please help will give brainliestw
Answer:
6 square units
Step-by-step explanation:
In oder to do this, you need graph paper to make it easier and then mark your graph paper with the quadrants.
I got 3 unites for the height and 4 units for the base
4 x 3 = 12 square units
however the formula for a triangle is Ab/2
so divide 12/2 = 6
So its 6 square units
Joe ordered some books online and spent a total of $75 . Each book cost $6 and he paid a total of $3 for shipping . How many books did he buy ?
NEED HELP ASAP GIVING BRAINLEST:
Write a real world situation that could be represented using the following equation:
x - 100 = 40
Answer: if Lisa has ? sheets of paper and she uses 100 sheets and has 40 sheets left how many sheets of paper did she start with
I will give BRAINLIEST:)
Answer:
A'C'=AC=3
Step-by-step explanation:
Answer:
C: 3 units
Step-by-step explanation:
Just think about it... 180 degrees rotated is exactly opposite rotation degree.
If you rotate 90 degrees, the triangle will end up on quadrant 4.
Rotate 360 degrees, the triangle will stay in the same quadrant.
In conclusion, C is the best option
Select the correct answer.
Answer:
a
Step-by-step explanation:
i did this test and question beforer si know what it iso
Mr. Brown purchased tires for his car. The tires were $75 each, including tax, plus $10 for installation. Mr. Brown paid $160 for the tires and installation. Which equation can be used to find the number of tires, t, that Mr. Brown purchased?
A. t = 160 + 75(10)
B. 75 + t(10) = 160
C. 75t + 10 =160
D. 160t - 75 = 10
Could you show your work? Thanks!
Answer:
Step-by-step explanation:
The answer is C because t = 2 so 75x2=150 and 150 + 10= 160.
A petting zoo has 7 lambs, 12 rabbits, 6 goats, and 3 piglets. Find the
ratio of rabbits to the total number of animals. Write the ratio in
simplest form.
Answer:
3:7
Step-by-step explanation:
The number of rabbits is 12 while the total number of animals
7 + 12 + 6 + 3 = 28
So the ratio of rabbits to animals is 12:28 = 3:7
The track team is trying to reduce their time for a relay race. First they reduce their time by 1.2 minutes. Then they are able to reduce that time by 1/10. If their final time is 3.60 minutes, what was their beginning time?
Answer:
5.2 Minutes, or 5 minutes and 12 seconds
Step-by-step explanation:
You can solve this problem by working backward. Since our number gets smaller by a 1/10 or 0.1, in order to work backward we must multiply 3.60 by 10/9, since one tenth has been taken away already. When we do this, we get 4.0. When we add 1.2 minutes to that, we get a final answer of 5.2 minutes, or 5 minutes and 12 seconds.
Here are sketches of four triangles in each triangle the longest side is exactly 1cm the other length is given to 2 decimal places work out the value of x give your answer to 1 decimal place 4 cm 57°
If the hypotenuse is 4 cm and an angle is 57°. Then the measure of the length of the side x will be 3.36 cm.
What is a right-angle triangle?It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function. The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.
The right triangle is given with a hypotenuse of 4 cm and an angle of 57°.
Then the value of x will be
The value of x will be given by the sine rule.
sin θ = x/h
WE have
θ = 57°
h = 4 cm
Then we have
sin 57° = x/4
x = 3.3546
x ≅ 3.36
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Grapes are priced at $2.25 per pound. Which of the following equations best represents the cost, c, of buying g, pounds of grapes?
A. c=2.25g
B. c=g+2.25
C. g=c+2.25
D.g=2.25c
Pleaseeee help meeeee
Answer:
x=-8
Step-by-step explanation:
1) remove the constant(number without variable) to do this, we must use the opposite operation(in our case, subtraction)
so
4x+1=-31
a) 4x+1-1=-31-1
4x=-32
b) remove the coefficient by doing the opposite operation(division in our case)
x=-8
Convert to %
1) 1/2
2) 1/4
3) 1/3
4) 3/10
5) 6.5/10
Answer:
1) 50%
2) 25%
3) 33.33 %
4) 30%
5) 65%
help please I'll mark brainiest xx
Josh and his family are taking a family vacation. They travel 340 miles in 5 hours before stopping at a rest stop.
How far did the family get in 3 1/2 hours?
Answer:
238 miles
Step-by-step explanation:
340 miles = 5 hours
So get 1 hour by dividing by 5 on both sides
5/5 = 1 hr
340/5 = 68
So in 1 hour they travel 68 miles
You want to find 3 1/2 hours
Do 68 x 3 to get 3 hours
So it would be 68 x 3 =204
Plus the half an hour - which you get by doing 68/2 = 34
68 = 1 hour, so half of that must be half an hour
So to get the final distance you do 204 (3 hours) +34 (half an hour)
204 + 34 =238
A baker made 20 muffins for a cafe. By noon, 15% of the muffins were sold. How many muffins were sold by noon?
Answer:
15% of 20 is 3, so 3 muffins were sold.
Step-by-step explanation:
To get this answer, multiply the percent by the total (15 x 20 = 300) and then divide the answer by 100. (300 / 100 = 3). Hope this helps :)
Answer:3
Step-by-step explanation:
0.15x20=3
0.15 is the percent of muffins, to find out a percentage over a number, you do the percentage dived by 100. Than, you multiply it by the number.
hi could you please tell me the answer to this?
Answer:
5
Step-by-step explanation:
5
A polynomial equation with rational coefficients has roots +5 plus 12 i and −−negative 9 minus 7 i. List two more roots of the equation.
Answer:
The additional roots are: [tex]5 - 12i[/tex] and [tex]-9 + 7i[/tex]
Step-by-step explanation:
Given
Roots: [tex]5 + 12i[/tex] and [tex]-9 -7i[/tex]
Required
Determine two additional roots
For a polynomial with two rational roots, the additional roots are the conjugates of the roots.
Take for instance, the following expression:
[tex]a + \sqrt b[/tex]
The conjugate of [tex]a + \sqrt b[/tex] is: [tex]a - \sqrt b[/tex].
Having established how to determine the additional roots, we proceed to determine the roots.
The conjugate of [tex]5 + 12i[/tex] is [tex]5 - 12i[/tex] and the conjugate of [tex]-9 -7i[/tex] is [tex]-9 + 7i[/tex]
Hence, the additional roots are: [tex]5 - 12i[/tex] and [tex]-9 + 7i[/tex]
please help! it would be much appreciated
Answer:
20
Step-by-step explanation:
$2,400 with a sales tax of 8%
How much is the total cost for the TV?
What inverse operation should be used to isolate the variable in the equation
k - 9 = 10?
Answer:
k-9=10
k=10+9
k=19
take care of yourself
have a nice day
Does the point (2, 5) satisfy the equation y = 5x − 5?
Answer:
yes
Step-by-step explanation:
so x=2 and y=5
5 = 5 x 2 - 5
0=0
equation is right
please help omg ♀️ !!
Answer:
first blank: 50-10=40
second blank: 50-20=30
third blank: 50-25=25
Step-by-step explanation:
hope this helps!
Answer:
Step-by-step explanation:
40 30 25
10 20 25
40 30 25
solve the following simultaneous equations using an algebraic method.
5x + 3y = 11
2x - 7y = 29
will be grateful!
A side of the triangle below has been extended to form an exterior angle of 68º. Find
the value of x.
Answer:
112°
Step-by-step explanation:
The width of a rectangle is x. Its length is 3x. How long is the diagonal of the rectangle? Express your answer in simplified radical form.
Answer:
The length of the diagonal is x√10
Step-by-step explanation:
Here, we want to find the length of the diagonal
The diagonal will represent the hypotenuse of a triangle formed with the width and length of the triangle being the measure of the other sides
Mathematically, we then apply Pythagoras’ theorem to get this
we have this as that the square of the diagonal equals the sum of the squares of the two other sides
d^2 = x^2 + (3x)^2
d^2 = x^2 + 9x^2
d^2 = 10x^2
d = √(10x^2)
d = x√10
A volleyball camp charges $150 per camper for 10 campers. When a team brings 15 campers, the rate is reduced to $125 per camper.
What is the rate of change in cost per camper?
Answer:
the answer is eight dollars and thirty four cents $8.34
solve each equation below showing every step checking your solution is optional
Answer:
x=4
Step-by-step explanation:
Answer:
for question d, 58.3 repeated
Step-by-step explanation:
cross multiply 3x=175
175/3= 58.3 repeated or 58 and one third.
please helpppp and explain
Answer:
angle BAC=50-2x
Step-by-step explanation:
angle ACD=115+x
then, angle ACB=180-(115+x) because it is a supplementary angle
angle ABC=angle ACB because it is an isosceles triangle
angle BAC=180-2[180-(115+x)]
angle BAC=180-360+230-2x
angle BAC=50-2x
For what value of k is the expression x^4 + kx^2 + 49 a perfect square?
Answer:
[tex]k=14[/tex]
Step-by-step explanation:
Completing the square gives
[tex]x^4 + kx^2 + 49\\= (x^2+7)^2 - 14x^2 + kx^2[/tex]
So we have to cancel the latter two terms out for the expression to always become a square (otherwise we are dealing with a square plus something else, which doesn't always result in a square), giving us our answer directly.
Answer:
k=± 14
Step-by-step explanation:
[tex]x^4+kx^2+49\\Disc.=b^2-4ac=k^2-4*1*49\\it ~ is ~a ~ perfect ~ square.\\k^2-196=0\\k^2=196\\k= \pm 14[/tex]
410 is what percent of 65?
Answer:
15.85%
Step-by-step explanation:
you know you have 65 and you have 410 so you just multiply and try and figure out the ratio and how much percentage is out of it.