Without any more information, the first term can be any number.
Let a be the first term in the geometric progression, and let r be the common ratio between consecutive terms. Then
a + ar + ar ² + ar ³ + ar ⁴ + ar ⁵ = 9 (a + ar + ar ²)
ar ³ + ar ⁴ + ar ⁵ = 8 (a + ar + ar ²)
r ³ + r ⁴ + r ⁵ = 8 (1 + r + r ²)
r ³ (1 + r + r ²) = 8 (1 + r + r ²)
r ³ = 8
r = 2
Now with this ratio, the sum of the first six terms is
a (1 + r + r ² + r ³ + r ⁴ + r ⁵) = a (1 - r ⁶)/(1 - r) = 63a
while the sum of the first three terms is
a (1 + r + r ²) = a (1 - r ³)/(1 - r) = 7a
and of course 63a = 9 • 7a, and this is true for any a.
given f(x)=2x-5, find x when f(x)=9
Answer:
x = 7
Step-by-step explanation:
9 = 2x - 5
add 5 to both sides
14 = 2x
divide by 2 to get x by itself
x = 7
What is the least common multiple of the two denominators 6/8, 4/32
Answer:
32
Step-by-step explanation:
what is the value of d+3
Answer:
you need to explain
Step-by-step explanation:
Solve (10b+7b^2-6b^3)-(12b^2-3b^3)
Answer:
-3b³ - 5b² + 10b
General Formulas and Concepts:
Pre-Algebra
Distributive PropertyAlgebra I
Combining Like TermsStep-by-step explanation:
Step 1: Define Expression
(10b + 7b² - 6b³) - (12b² - 3b³)
Step 2: Simplify
Distribute negative: 10b + 7b² - 6b³ - 12b² + 3b³Combine like terms (b³): -3b³ + 10b + 7b² - 12b²Combine like terms (b²): -3b³ - 5b² + 10bFind the 61st term of -12, -28, -44,
Answer:
[tex]a_{61}=-972[/tex]
Step-by-step explanation:
Arithmetic Sequences
The arithmetic sequences are identified because any term n is obtained by adding or subtracting a fixed number to the previous term. That number is called the common difference.
The equation to calculate the nth term of an arithmetic sequence is:
[tex]a_n=a_1+(n-1)r[/tex]
Where
an = nth term
a1 = first term
r = common difference
n = number of the term
We are given the first terms of a sequence:
-12, -28, -44,...
Find the common difference by subtracting consecutive terms:
r = -28 - (-12) = -16
r = -44 - (-28) = -16
The first term is a1 = -12. Now we calculate the term n=61:
[tex]a_{61}=-12+(61-1)(-16)[/tex]
[tex]a_{61}=-12-60*16=-12-960[/tex]
[tex]\mathbf{a_{61}=-972}[/tex]
hey im dum dum what's 45*23455/76?
Answer:
13887.8289474
Step-by-step explanation:
i used a calculator cuz im dum too lol
Answer:
45*23455/76 = 133887.82894736
Help me find the radius please
Answer:
The radius is 2.46686837338 or simplified: 2.5.
Step-by-step explanation:
A = 60 so it would be √60/3.14 =2.46686837338
I hope this helps and if it did I would appreciate it if you marked me Brainliest. Thank you and have a nice day!
please help I need the answer!!! thanks in advance!
Answer:
0.903
Step-by-step explanation:
[tex] log_{a}8 \\ \\ = log_{a} {2}^{3} \\ \\ = 3log_{a} {2} \\ \\ = 3 \times 0.301 \\ \\ log_{a}8 = 0.903[/tex]
To walk to her friend's house, Cristal normally walks 63 yards north and 16 yards east as shown. How many
yards shorter would it be if Julie took the diagonal shortcut, x?
16 yd
63 yd
х
A
(10
Answer:
65 yd
Step-by-step explanation:
The image of this walking path of Cristal is missing, so i have attached it.
From the image attached, we can see that the path "x" is the hypotenuse path a the triangle.
Thus, we can use pythagoras theorem to find the area. Thus;
x² = 16² + 63²
x = √(16² + 63²)
x = √4225
x = 65 yd
human activities have drastic effects on biomes match the human activities with the biomes they primarily
Find the area of the triangle.
7 yd
24 yd
The area is
square yards.
Answer:
84 yd^2
Step-by-step explanation:
Answer:
½ × 7yd × 24yd = 84yd² <<<<< the answer
I just want ppl to check, extra points too!
Answer:
thats correct
Step-by-step explanation:
i had that on my test and i ot it right
A university organization shows that 108 of the university's 253 assistant professors were women, along with 97 of the 301 associate professors and 78 of the 350 full professors. (a) What is the probability that a randomly chosen university professor (of any rank) is a woman
Answer:
[tex]Probability = 0.3131[/tex]
Step-by-step explanation:
Required
Determine the probability of selecting a woman
The given data can be represented to show women distribution as:
-------------------------------------- Women ------------------- Total
Assistant Professors ----------- 108 ----------------------253
Associate Professors ---------97 -------------------------301
Full Professors -----------------78---------------------------350
First, we calculate the number of women
[tex]Women = 108 + 97 + 78[/tex]
[tex]Women = 283[/tex]
Next, we calculate the total number of professors
[tex]Professors = 253 + 301 + 350[/tex]
[tex]Professors = 904[/tex]
Probability of selecting women is then calculated as:
[tex]Probability = \frac{Women}{Professors}[/tex]
[tex]Probability = \frac{283}{904}[/tex]
[tex]Probability = 0.31305309734[/tex]
[tex]Probability = 0.3131[/tex] -- (approximated)
1
A. (f = g)(x) = 2 - 4
.
true or false
Answer:
=-2
Step-by-step explanation:
x=-(4-2)
Answer:
false
hope this helps
Find the value of x. Will give brainliest
Answer:
x = 11
Step-by-step explanation:
Angle CAB = 33 degrees (Z-figure)
Angle ACE = 180 degrees (line), therefore angle ACB = 180 - 5x.
Sum of all angles in the triangle should equate to 180 degrees.
Now the sum is of all angles in triangle ABC is:
CAB + ABC + ACB = 33 + (180 - 5x) + 2x = 213 - 3x
So 213 - 3x should equal 180.
213 - 3x = 180 <=> -3x = -33 <=> x = 11
put the numbers in order from least to greatest.
5 * 10^6
4000000
5 * 10^5
0.6 * 10^7
75 * 10^5
Write an equation of the line below
Answer:
ok.
Step-by-step explanation:
y=-1/1x+4. hope this helped :))
Answer: y= -8/8x + 4
or y=-x+4
Step-by-step explanation:
While President, Obama received an average of 60, 000 letters per week at the White House.
Approximately how many letters does he receive in a day?
Answer:
8571 letters per day
Step-by-step explanation:
60,000/1 week is the same as 60,000/7 days so
60,000/7 = 8571.428571
is aproximately 8571 letters per day
Ramon earns $1,785 each month and pays $53.80 on electricity. To the nearest tenth of a percent, what percent of Ramon's earnings are spent on electricity each month?
Answer:
3.0%
Step-by-step explanation:
[tex](\frac{53.80}{1785}) * 100 = 3.01[/tex]
A school club wants to collect at least 500 canned goods for a school food drive. The club has already collected 30 canned goods.
Part A
If 10 club members each collect the same number of canned goods, which inequality represents the minimum number of canned goods, n, each
club member must collect for the club to meet the goal?
10n +30<500
10n + 30 500
30n + 10 < 500
30n + 10 > 500
find the area of each trapezoid 32 ft x 16 ft 18 ft
Answer:
A = 432 ft^2
Step-by-step explanation:
[tex]A=\frac{a+b}{2} *h[/tex]
A = (32+16)/2 * 18
A = 48/2 * 18
A = 24*18
A = 432 ft^2
help please, I need help
Answer:
1. <
2. <
3. >
Step-by-step explanation:
-8 is smaller than 8
the absolute value of -4 is 4, but there is another minus, so it becomes -4. -4 is smaller than -2
-7 is bigger than -9
Answer:
Step-by-step explanation:
-8 < |8|
-|-4| < -2
-7 > -9
absolute value has the || sign around the number. If you see that, and there's a "minus" sign, then reverse it to a PLUS sign. Because absolute value is just how far away the number is to 0. So -8 is "8" to 0.
now if we have for example, -|-4| then it'd be -4 because |-4| is 4, but then -4 again cause there's a minus sign.
Refer to - KLMN
2x
M
101
-3
2y
P
y + 3 cm
60°
К.
N
x + 4 cm
mZ1 + m22 =
Answer:
[tex]m∠1 + m∠2 = 180[/tex]
Step-by-step explanation:
[tex]m∠1 = m∠3 \\ m∠2 = m∠4[/tex]
[tex]m∠ 1 = m∠3 \\ 60 = 60[/tex]
[tex]360 - m∠1 + m∠3 = m∠2 + m∠4[/tex]
[tex]360 - 60 + 60 = m∠2 + m∠4[/tex]
[tex]360 - 2(60) = m∠2 + m∠4[/tex]
[tex]360 - 120 = m∠2 + m∠4[/tex]
[tex]240 = m∠2 + m∠4[/tex]
[tex] \frac{240}{2} = m∠2 = m∠4[/tex]
[tex]120 = m∠2 = m∠4[/tex]
[tex]m∠2 = 120 \\ m∠4 = 120[/tex]
[tex]m∠1 = 60 \\ m∠3 = 60[/tex]
[tex]m∠2 = 120 \\ m∠4 = 120[/tex]
[tex]m∠1 + m∠2 + m∠3 + m∠4 { = }^{?} 360[/tex]
[tex]60 + 120 + 60 + 120 { = }^{?} 360[/tex]
[tex]2(60) + 2(120) { = }^{?} 360[/tex]
[tex]120 + 240 { = }^{?} 360[/tex]
[tex]360 = 360[/tex]
[tex]m∠1 + m∠2 [/tex]
[tex]60 + 120 = 180[/tex]
[tex]m∠1 + m∠2 = 180[/tex]
Help plz 13. Mildred is flying a kite on a 30 m string. The angle of elevation of the kite measures 40 degrees,
and Mildred's hand is 2 m above the ground. About how high is the kite off the ground?
a. 21.3 m
c. 19.3 m
b. 25 m
d. 23 m
Answer: 21.3m
Step-by-step explanation:
The height of the kite of the ground would be calculated as:
We have to calculate the question using a right angled triangle that has angle ACB as 90° while angle CAB will be 40°.
Therefore, the height of the kite would be:
= 30 sin 40 + 2
= 30 (0.6428 ) + 2
= 19.284 + 2
= 21.284 m
= 21.3 m
Evaluate 15 squared show work
Answer:
225
Step-by-step explanation:
15x15=225
There is a cool trick you can do. Lets take 28 and square it.
First you round the number up. 28 rounded is 30. You rounded up by 2 (30-28=2) so you minus 2 from 28.
You are left with these two numbers, 26 and 30. Add a zero to the 26.
You now have 260 and 3 (you remove 0 on the 30 since you added it to the 26)
Then you multiply by 3.
260x3=780
Then you add the square of the number you rounded up too, which is 2.
You are left with this equation.
(2^2)+780= 784
28x28=784.
This works for numbers below 100 and integers
The diagram represents the enlargement of a rectangle by using a scale factor of 6.
A rectangle has a length of 30 feet and width of 6 feet.
What are the dimensions of the original rectangle?
Answer:
lenght of 5 feet and width of 1 feet
Step-by-step explanation:
30/6=5
6/6=1
Answer:
lenght of 5 feet and width of 1 feet
Step-by-step explanation:
30/6=5
6/6=1
Step-by-step explanation: like what that peson said! way to go and good luck on your test!
-3(1)+(-3)(-1) =
+()]
-3(1) + (-3)(-1)=-3[0]
-3(1)+(-3)(-1) =
_
+(-3)(-1) =
+
Answer:
³⅜
Step-by-step explanation:
⁴⁵⅖
+⁷⅝×⅖i
I HOPE IT HELP TYSM
Answer:
i dunno
Step-by-step explanation:
Jill would like an increase in the hourly wage she receives from the Mathematics Research Center, where she works in the mail room. Her boss gives her an equation to solve, telling her that her raise is the solution to the equation, but only if she can solve it. The equation is x 2- 6x + 9 = 0. What was the amount of her raise per hour? Answer:
Answer:
Jill will receive an increase of $3 per hour
Step-by-step explanation:
The Quadratic Equation
The quadratic equation can be represented in the standard form as:
[tex]ax^2+bx+c=0[/tex]
being a,b, and c are constants.
It can be solved by using the quadratic formula:
[tex]\displaystyle x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
Jill would like an increase in her hourly wage. The increase will come as the solution for a maths equation.
She must solve the equation:
[tex]x^2-6x+9=0[/tex]
The solution to the equation, or value of x, is the increase in her hourly wage.
Comparing with the general form, we have a=1, b=-6, c=9. Thus, the solutions are:
[tex]\displaystyle x=\frac{-(-6)\pm \sqrt{(-6)^2-4(1)(9)}}{2(1)}[/tex]
[tex]\displaystyle x=\frac{6\pm \sqrt{36-36}}{2}[/tex]
[tex]\displaystyle x=\frac{6\pm \sqrt{0}}{2}[/tex]
The square root is 0, therefore is only one solution:
[tex]\displaystyle x=\frac{6}{2}=3[/tex]
x = 3
Thus, her raise per hour is $3.
Find the x and y intercepts of the following equation. 3x - 8y = 24
Amit’s school bus travelsat 36km/hr and Sushma’s school bus travels at 11 m/s. Whose school bus is faster ?
Answer:
This answer is not originally mine so Don give me credit
Step-by-step explanation:
Amit's school bus in m/s will be
36×1000/3600
36 × 10/36
= 10 m/s
While sushma's school bus has speed of 11 m/s
so sushma's school bus is faster than Amit's school bus
Answer:
Amit's: 10 m/s
Sushma's 11 m/s
Step-by-step explanation:
Amit's:
36 x 1000/3600
36 x 10/36
Sushma's:
11 m/s
Sushma's school bus is faster than Amit