Answer:
steps below
Step-by-step explanation:
aₙ = a₁ * rⁿ⁻¹
a₁ * r²⁻¹ = 6
a₁ * r = 6 ... (1)
a₁ * r⁵ = 1458 ... (2)
(2)/(1) : r⁴ = 243 r = ±3 [tex]\sqrt[4]{3\\}[/tex]
if r = 3 [tex]\sqrt[4]{3\\}[/tex]
[tex]a_{1} = 6 / 3\sqrt[4]{3} \\a_{1} = \frac{2}{3} \sqrt[4]{27}[/tex]
if r = -3 [tex]\sqrt[4]{3\\}[/tex]
[tex]a_{1} = -\frac{2}{3} \sqrt[4]{27}[/tex]
The first term of the geometric progression is 256.
What is a geometric sequence?A geometric sequence is a sequence of numbers in which the ratio between consecutive terms is constant.
We have,
Let the first term of the geometric progression be denoted by 'a', and let the common ratio be denoted by 'r'.
According to the problem, the second term is 6, so we have:
ar = 6 ...(1)
Similarly, the seventh term is 1458, so we have:
[tex]ar^6[/tex] = 1458 ...(2)
We can use equation (1) to solve for 'r', and then substitute the value of 'r' into equation (2) to solve for 'a'.
From equation (1), we have:
r = 6/a
Substituting this into equation (2), we get:
[tex]a(6/a)^6[/tex] = 1458
Simplifying the right side of the equation, we have:
[tex]6^6[/tex] = 1458a
Solving for 'a', we get:
a = [tex]6^6[/tex]/1458 = 256
Therefore,
The first term of the geometric progression is 256.
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Write
17/3
as a mixed number.
O A. 3
O-B. 3
© C.53
O D. 53
Answer:
5 2/3
Step-by-step explanation:
15 ÷ 3 = 5.
with 2 leftover, you will have 2/3
5 + 2/3 = 5 2/3
Good Luck!
-kiniwih426
Answer:
I am not really sure about the answer choices, but the answer is 5 2/3
Step-by-step explanation:
17/3 - 3/3 = 1 14/3
14/3 - 3/3 = 2 11/3
11/3 - 3/3 = 3 8/3
8/3 - 3/3 = 4 5/3
5/3 - 3/3 = 5 2/3
Hopefully this helped!
Brainliest please?
12 + 4x > 24 or 10 - 12x > 22
Answer:
10 - 12 × > 22 Yan Yong sagot
Help this is due today
Answer:
The answer is 19/12
Step-by-step explanation:
Hope this helped
In triangle, ABC, sin A = 1/2b =20,and m
Answer:
here your answer
good luck
A speaker is in the shape of a cube with an edge length of 3.5 inches. The speaker is sold in a package in the shape of a square prism with a base area of 16 in2 and a height of 4.25 inches. What is the surface area of the package
Step-by-step explanation:
A square prism is a three-dimensional cuboid where the base and top are equal squares and the remaining 4 faces are rectangles.
to get the surface area of the package (that square prism) the size of the content inside is irrelevant and only there to confuse us.
the package has a base area of 16 in².
that means it also has a top (or cover) area of the same size : 16 in².
as top and bottom are squares, that means their areas are the square of their side lengths.
therefore, the side length of such a square is
s = sqrt(16) = 4 in
now we know also the dimensions of the 4 rectangles that are the side areas (faces) : 4 in × 4.25 in
the area of such a rectangle is
4 × 4.25 = 17 in²
so, the total surface area is (top and bottom + 4 side areas)
2×16 + 4×17 = 32 + 68 = 100 in²
Shamika's grandmother opens an account with a deposit of $5,000 for Shamika as a
college savings account. The account pays 5 percent annual interest. How much
money will be in the account after 10 years?
A. 8,954.24
B. 8,144.47
C. 8,052.55
D. 7,401.22
9514 1404 393
Answer:
B. $8,144.47
Step-by-step explanation:
The compound interest formula is ...
A = P(1 +r)^t
where r is the annual rate compounded annually for t years, applied to principal P.
A = $5000(1 +0.05)^10 = $8144.47
After 10 years, there will be $8,144.47 in the account.
There are 20% more goblins than wizards in magic club. There are 220 goblins and wizards together in magic club. How many goblins are in magic club ?
Answer:
120
Step-by-step explanation:
w = wizards
1.2w = goblins
_________
w + 1.2w = 220
2.2w = 220
w = 100
This means there are 100 wizards. To find the number of goblins just plug the number of wizards in the goblins = 1.2w.
1.2 (100) = 120.
There are 120 goblins in the magic club.
PLEASE HELPPP!
assume the random variable X has a by normal distribution with the given probability of obtaining a success.  find the following probabilities, given the number of trials in the probability of obtaining a success. P(X < 5), n = 6, p = 0.7
Answer:
-7
Step-by-step explanation:
PLS HELP ME 100 POINTS AND FIRST TO ANSWER GETS BRAINLIEST
Which arrangement shows −512 , −5 , −6.4 , and −264 in order from least to greatest? −264, −6.4, −5, −512 −512 , −6.4 , −264 , −5 −512 , −5 , −264 , −6.4 −264, −6.4, −512, −5
Answer:
-512, -264, -6.4, -5
Step-by-step explanation:
Since we need to go from least to largest, you would use the order above.
The order from least to greatest is -512, -264, -6.4, -5.
The given integers are −512, −5, −6.4 and −264.
What is ascending order of negative integers?Ascending order of negative numbers means to arrange the given negative numbers from smallest to largest values.
It is very important to learn as in the case of negative numbers the absolute values of smaller numbers are greater than the absolute values of larger numbers, which makes it confusing.
Now, ascending order of given negative integers is as follows:
-512 < -264 < -6.4 < -5
So, the order from least to greatest is -512, -264, -6.4, -5.
Therefore, the order from least to greatest is -512, -264, -6.4, -5.
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Question is attached.
Step by step explanation only!
Answer:
Attached is your answer.
Step-by-step explanation:
hence Proved.Hope it helps you!!
LHS
[tex]\\ \sf\longmapsto \dfrac{cos(90-\Theta)}{sin\Theta}+\dfrac{sin\Theta}{cos(90-\Theta)}[/tex]
[tex]\boxed{\sf cos(90-A)=sinA}[/tex]
[tex]\\ \sf\longmapsto \dfrac{sin\Theta}{sin\Theta}+\dfrac{sin\Theta}{sin\Theta}[/tex]
[tex]\\ \sf\longmapsto 1+1[/tex]
[tex]\\ \sf\longmapsto 2[/tex]
Hence proved
Roman numerals for 29 is
hello!
Answer:
XXIX
Step-by-step explanation:
Hope this helps! :)
Use the given property to complete the statement.
Distributive Property
3(x-1)= 3x - ?
A) -1
B) -3
C) 1
D) 3
Answer:
B) -3
Step-by-step explanation:
Use distributive property.
3(x-1)(3*x) - (3*1)3x - 3∴ 3(x-1) = 3x - 3
Hence, it is verified that choice B) -3 is the correct answer.
18,234.9+516.1 show your work
Answer:
18,751
Step-by-step explanation:
18 234 . 9
516 . 1
----------------
18 751 . 0
----------------
Answer:
18,751
Step-by-step explanation:
18,234.9+516.1=18,751
A theater group made appearances in two cities. The hotel charge before tax in the second city was $500 higher than in the first. The tax in the first city was
3.5%, and the tax in the second city was 5%. The total hotel tax paid for the two cities was $386.25. How much was the hotel charge in each city before tax?
First city:
Х
SLU
Second city: 0
5
?.
3) At a school several teachers were holding a contest to see which class could earn the most trivia points. Mrs. Clawson's class scored 94 points. Mr. Grant's class earned 82 points. Mrs. Jones's class earned 94 and Mrs.Price's class earned 86. Determine the mean (rounded to the nearest tenth), median, mode and range of the number of points scored. Mean: Median: Mode: Range:
Answer:
Mean: 89
Median: 90
Mode: 94
Range: 12
Simplity -4/3 ➗2/-6
-4
-2
2
4
I
Answer:
-4
Step-by-step explanation:
-4/3÷2/-6
⇒ -4/3×-6/2
⇒ -24/6
⇒ -4
Find the value of x that makes m ∥ n.
Geometry: CC 2015 > Chapter 3: Proofs with Parallel Lines > Section Exercises 3.3
Answer:
X = 23∘
Step-by-step explanation:
(
7
x
−
11
)
=
(
4
x
+
58
)
corresponding angles are always equal.
3
x= 69
x = 69
3 = 23
Adding Unlike denominators 1/11 + 1/4
Answer: 15/44
Step-by-step explanation:
You have to make the denominators match so:
1/11(4) + 1/4(11)=
4/44 + 11/44=
15/44
HELLOOO HELPPPPPPPPPP
Answer:
the answer to this question is 2/5
the quotient of a number less than 8 and 5
Answer:
8/5
Step-by-step explanation:
1. One species of bamboo can grow at an average rate
of 60 centimeters per day. Assuming that the
bamboo plant maintains the average rate of
growth per day, how tall will the bamboo plant be
if it grows for:
a. 10 days?
b. 30 days?
c. one-half day?
Show step by step please
Un empresario compró 1000 tabletas a $1500 cada una. Vendió 450 de ellas obteniendo una
ganancia del 25%.
¿ A qué precio deberá vender las otras 550 restantes si la utilidad promedio del lote completodebe ser del 40%?
Answer:
Step-by-step explanation:
1000($1500(0.40)) = $600 000
450($1500(0.25)) = $168,750
600,000 - 168,750 = $431,250
$431,250 / 550 = 784.0909090... $784.09
$1500 + $784.09 = $2,284.09
Highest common factor of 42,72,and 56
Answer:
the HCF is 2
Step-by-step explanation:
Select the two roots of (3x+7)(2x-5)=0
A= -7/3
B= 5/2
C= -5/2
D= 7/3
Thank you
Given
(3x + 7)(2x - 5) = 0
Equate each factor to zero and solve for x
3x + 7 = 0 ⇒ 3x = - 7 ⇒ x = - \frac{7}{3}
3\7
→ A
2x - 5 = 0 ⇒ 2x = 5 ⇒ x = \frac{5}{2}
2\5
→ B
What is the answer please
Answer:
-2 < x < 4.5
Step-by-step explanation:
Step 1: Add 1 to all parts/sections.
[tex]-5+1<2x-1+1<8+1[/tex] [tex]-4<2x<9[/tex]Step 2: Divide all parts/sections by 2.
[tex]\frac{-4}{2}<\frac{2x}{2} <\frac{9}{2}[/tex] [tex]-2 < x < 4.5[/tex]Therefore, the range of possible values of x is -2 < x < 4.5.
A pair of parallel lines cut by a transversal as shown. Which of the following best represents the relationship between angles p and q?
A. p = 180 degrees - q
B. q = 180 degrees - p
C. p = 2q
D. p = q
Answer:
p=q is the right answer...
David is making a model of a regular triangular prism.
Calculate the surface area of the prism.
__ inches squared
Please answer the question in the picture
Answer:
f(x)=2x+1
Step-by-step explanation:
gradient =(y2-y1)/(x2-x1)
(3-1)/(1-0)
=2
y=1
Write the equation for the function graphed below.
The equation of the function graphed below is f(x) = a(x - 2)² - 3 since the vertex is at (2, -3).
We have,
From the graph given,
The vertex is at (2, -3).
Now,
The vertex form of a quadratic function is given by:
f(x) = a(x - h)² + k
Where (h, k) is the vertex of the parabola.
Given the vertex (2, -3), we can plug in the values of h and k into the vertex form:
f(x) = a(x - 2)² - 3
Thus,
The equation of the function graphed below is f(x) = a(x - 2)² - 3
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Test: Chapter 1-4 Test
Is 9 a solution to the equation x+2=x+2?
Yes
No
Answer:
Yes..............
....
.