If the sum of first four terms in a G.P. is 30 and that of the last four terms is 960, then the sum of the first 8 terms is 990
We also know that a = 2
sum of first 4 terms
= 2(r^4 - 1)(r-1) = 30
r^4 - 1 = 15r - 15
r^4 - 15r + 14 = 0
r = 1 works for the equation , but r = 1 would make all the terms of the
GP the same, so clearly not a solution
r^4 - 15r + 14 = 0 , a bit of trial and error ....
(r-1)(r - 2)(r^2 + 3r + 7) = 0
so r = 2 or r = not real
check: sum(4) = 2(2^4 - 1)/(2-1) = 30 , as needed
so r = 2 , BUT it does not work for sum(8)
sum(8) = 2(2^8 - 1)(2-1) = 510 , not 990 as necessary according to your second part of the question.
check your question.
What is the area of a semicircle with a diameter of 8 feet? Estimate using 3.14 for TT
A) 25.12 ft ²
B) 50.24 ft²
C)200.96 ft ²
D) 100.48 Ft²
Step-by-step explanation:
So r = D ÷ 2
Since the area of a circle = πr²
then the area of a semi-circle = (¹/₂π (¹/₂D)²)
Area of a semicircle given the diameter = (¹/₂π (¹/₂D)²)
= (¹/₂(3.14) (¹/₂ 8ft)²)
= 25.12 ft²
Help me with this question.
Answer:
The equation for the nth term of the arithmetic sequence is:
[tex]a_{n} = a + (n-1)d\\[/tex]
The [tex]a_{30}[/tex] is 140
Step-by-step explanation:
"a" represents the first term which is -5.
"d" represents the common difference which is 5.
To find the common difference, just subtract the 2nd and 1st term.
0 - (-5) = 5
Now put the values in the equation:
[tex]a_{n} = a + (n - 1)d\\a_{n} = (-5) + (n - 1)5[/tex]
We are finding the 30th term so just put 30 to the "n" to help us find the 30th term of the sequence.
[tex]a_{30} = -5 + (30-1)5\\a_{30} = -5 + (29)5\\a_{30} = -5 + 145\\a_{30} = 140[/tex]
So the 30th term is 140
14a + 2 =
Please help
Answer: ( 2 x 7 ) a + 2
Step-by-step explanation:
1 + tan^2 (π/6) = _______.
A. csc^2 (π/6)
B. sec^2 (π/6)
C. cot^2 (π/6)
D. 1 - tan^2 (π/6)
Answer: B??
Step-by-step explanation:
Correc me if i wrong ovo
Determine if the table represents a linear function, quadratic function, or exponential function.
Answer:
please no of one is not function so sorry
find the measure indicated angle that makes lines u and v parallel
Answer:
91°
Step-by-step explanation:
The answer is 91°. What you do is you name the angle next to 89° with x, and you know that an angle whose arms are horizontal makes 180°. So, you go:
180°=x+89°
x=180°-89°
x=91°.
Now, there is this rule that says that when two angles are on sides like x and ? are, then they are equal. Therefore, the angle marked with ? is 91°.
Determine whether the following ratios are equivalent. (9:12 and 24:18)
0111100109090909099999999999999999
Not sure how to do this. Help is much appreciated. :D
Answer:
m = √n/3 -k
Step-by-step explanation:
√n = 3(k + m)
=> √n/3 = k + m
∴ m = √n/3 -k
Hope this helps!!
I forgot how to do this stuff so please help
Answer:
116 in
Step-by-step explanation:
A unit cube could be 6 units long by 6 units wide by 6 units tall. True or false?
Answer:
True
Step-by-step explanation:
Evaluate the Expression for x=5 and y =3 and z = 1/4
Answer:
4
Step-by-step explanation:
We start with this:
[tex]\frac{5x-6y +20z}{4yz}[/tex]
Then we insert the vales of the variables like this:
[tex]\frac{5(5)-6(3) +20(\frac{1}{4} )}{4(3)(\frac{1}{4}) }[/tex]
Next, Simplify:
[tex]\frac{25-18 +5}{3 }[/tex]
[tex]\frac{12}{3 }[/tex]
Simplify further, and we get our answer: 4
Which equation represents the sentence?
Six less than a number is half the number.
n−6=n2
n2−6=n
6−n=n2
6−n2=n
Answer:
It is n-6=n/2.
Step-by-step explanation:
I took the quiz.
I need to know the answer to 2 1/3 x 4/5
Answer:
Simplify the expression.
Exact Form:
28/15
Decimal Form:
1.8¯6
Mixed Number Form:
1 13/15
Step-by-step explanation:
Answer:
Step-by-step explanation:
Convert 2 1/3 to improper fraction
[tex]2\dfrac{1}{3}*\dfrac{4}{5}=\dfrac{7}{3}*\dfrac{4}{5}\\\\\\=\dfrac{7*4}{3*5}\\\\\\=\dfrac{28}{15}\\\\= 1\dfrac{13}{15}[/tex]
Stossel is listening to an audiobook that at normal speed will last 10 hours. Stossel decides listen the audiobook at 2.5 faster. How long will the book be?
Answer:
4 hoursStep-by-step explanation:
Speed and time are inverse functions.
At normal speed the time is 10 hours.
If the speed is 2.5 times faster, then time is 2.5 times less:
10 hours / 2.5 = 4 hoursSpeed is 2.5
Distance is 10
Time
10/2.510/(25/10)100/254hrsPlease help with algebra question on empirical rule!!
Answer:
Step-by-step explanation:
The Empirical Rule states that 99.7% of data observed following a normal distribution lies within 3 standard deviations of the mean. Under this rule, 68% of the data falls within one standard deviation, 95% percent within two standard deviations, and 99.7% within three standard deviations from the mean.
what is the answer need help
Answer:
2
Step-by-step explanation:
x + 2y = 14
2y = -x + 14
y = -1/2 x + 7
m = -1/2
product of slopes is -1
so perpendicular slope is 2
a square has a shaded part with 7cm and 4cm and 40 cm. workout the percentage of the are inside the square that is shaded
Answer:
68
Step-by-step explanation:
You multipliy 7x4 and you get 28 now you add the 40+28=68.
A study investigated the job satisfaction of teachers allowed to choose supplementary curriculum for their classes versus teachers who were assigned all curricular resources for use in their classes. On average, when surveyed regarding job satisfaction, teachers give a score of 3. 3 out of 5 with a standard deviation of 0. 6. When the authors of the study interviewed 40 teachers who supplemented with their own materials, they found 3. 5 to be the mean. The authors wanted to know if the group of teachers that could choose supplementary curriculum had a higher level of job satisfaction. They used a significance level of 1%. Which of the following statements is valid based on the results of the test? The data shows that teachers allowed to choose supplementary curriculum for classes are more satisfied with their jobs. The data shows that teachers who were assigned all curricular resources for classes are more satisfied with their jobs. The data shows that there is no difference in job satisfaction between the two groups of teachers. The data shows that the authors cannot make a determination either way with this data.
Answer:the data shows that the authors cannot make a determination either way with this data
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
on edge
the sum of 2 numbers is 99 and their quotient is 8What are the 2 numbers
Answer:
11 and 88
Step-by-step explanation:
I just set up a system of equations:
x + y = 99,
x/y = 8
I decided to use the method of substitution which is expressing one variable in terms of the other and substituting it into the other equation.
To use substitution, I changed the second equation to:
x = 8y
And then, I substituted that value for x into the first equation:
8y + y = 99
And that means:
9y = 99
Hence, y = 11. To find the second number, just substitute 11 for y in the first equation to get:
x + 11 = 99
And that means x = 88.
simpify 5 cubed to the power of 6
[tex]5 cubed to the power of 6[/tex]
[tex]\displaystyle (5^3)^6 = 5^{(3 \times 6)} = 5^{18}[/tex]
P is the point of intersection of the lines with equations 5x — y = 1 and x + 2y = 9
Write down the coordinates of P.
Answer:
P = (1,4)
Step-by-step explanation:
First turn both equations to slope intercept form (y=mx+b).
5x - y = 1
Subtract 5x on both sides to get -y = -5x + 1, and since we want the y to be positive simply flip all the signs to get
y = 5x - 1.
x + 2y = 9
Subtract x on both sides to get 2y = -x + 9, then divide both sides by 2 to get
y = -1/2x + 9/2.
Now you can graph the two lines and see where they intercept each other. (I graphed them above for you⤴⤴⤴).
Hope this helps :)
The chess team wants to have practice two different days next week from money through friday. How many schedules can be made?
Answer:
2 schedule
I I think you can go for Tuesday and Friday because Tuesday totally good and Friday is stress-free because the day after is Saturday
I also try to gather the chess team in figure out a way suitable for your practice, maybe some are going to be busy
The price of oranges is proportional to the number of oranges if
One orange costs 1200 Rs. Find:
A. The price of 12 oranges.
B. The amount of oranges that cost 32,000 Rs.
#1
Cost of 1orange=1200
Cost of 12 oranges:-
[tex]\\ \sf\longmapsto 1200(12)=14400[/tex]
#2
Total cost=32000Cost of one orange=1200Total oranges
[tex]\\ \sf\longmapsto 32000\div 1200[/tex]
[tex]\\ \sf\longmapsto 2666.6[/tex]
[tex]\\ \sf\longmapsto 2667[/tex]
. Add the following. Answer in feet and inches. a) (3 ft. 8 in) + (4 ft. 9 in)
Answer:
8 ft. 5 in.
Step-by-step explanation:
First, let's change everything to inches
[] 3 ft. 8 in -> 3 * 12 = 36, 36 + 8 = 44 inches
[] 4 ft. 9 in -> 4 * 12 = 48, 48 + 9 = 57 inches
Now, we can add
44 + 57 = 101 inches
Last, we will simplify
101 -> 8 feet and 5 inches
Have a nice day!
I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)
- Heather
Which of the following sets of lengths could form the sides of a triangle? Choose all that
apply.
А
7, 9, 17
B
7, 2,8
C
3, 1,5
D
6, 3,5
E
12, 12, 13
F
3,11,8
Answer:
B, D and E
Step-by-step explanation:
The first triangle inequality theorem states:
the lengths of any two sides of a triangle must add up to more than the length of the third side.
So as long as the sum of the two shortest is greater than the longest side a triangle is possible
А
7 + 9 < 17 NO
B
2 + 7 > 8 YES
C
1 + 3 < 5 NO
D
3 + 5 > 6 YES
E
12 + 12 > 13 YES
F
3 + 8 = 11 NO
I thought of a 2 digit number. The digits of my number are different. The unit digit of my number is the tens digit raised theird power. What is my number?
Answer:
Step-by-step explanation:
I thought of a 2 digit number. The digits of my number are different: [XY]
Then I'm lost. Does "The unit digit of my number is the tens digit raised third power" mean that the X is raised to the third power?:
X^3
But then we need more information. X could be 1, 2,3, or 4. At 5 it becomes a three digit number. All of the other option result in a two digit number with different digits, so all seem possible. I don't know how to answer this without more information.
What angle is congruent to ∠C?
Step-by-step explanation:
Order of congruence does not matter. For any angles A,B, and C , if ∠A≅∠B and ∠B≅∠C , then ∠A≅∠C . If two angles are both congruent to a third angle, then the first two angles are also congruent.
Please find x and y... I will mark you brainliest
Answer:
Step-by-step explanation:
Dodoodo
Step-by-step explanation:
x=30 and y=30. I have solve it. See the picture that I have attached.
Find the perimeter. Simplify your answer.
Answer:
20u-26
Step-by-step explanation:
To find the perimeter we have to add up all the sides
9u-6+u-7+9u-6+u-7
Combine light terms and we get
20u-26
Modeling Real Life A principal invites 138 students to a reward breakfast. Nine students sit at each table. How many tables are there?
Answer:
16 tables
Step-by-step explanation:
So there are 138 students, and 9 sit at each table. This means you do 138/9, which leaves you with 15.3333. However you cant have .3 of a table so there must be 16 tables!