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.
3.
(03.06)
Using the completing-the-square method, rewrite f(x) = x2 − 8x + 3 in vertex form. (2 points)
f(x) = (x −8)2
f(x) = (x −4)2−13
f(x) = (x −4)2 + 3
f(x) = (x −4)2 + 16
Answer: f(x) = (x −8)2
Step-by-step explanation:
Suppose you have a coin collection of dimes and quarters containing 46 coins. If you have $6.70, how many of each type of coin do you have?
answer:
32 dimes and 14 quarters
step by step:
32 x 10 = 320
14 x 25 = 350
320 + 350 = 670
670¢ = 6.70$
helppppp plzzzz is fue today
Answer:
0
Step-by-step explanation:
There is no gradient there.
Find the quarter point of y=1/2sin(2x+π)
Answer:
32
Step-by-step explanation:
y = 1/2sin[2(x + π/2)]. Now you can read that the graph is shifted from its standard starting position at (0, 0) left by π/2 and the period ...
-5/6e-2/3=-24 what does e=
Answer:
-5e/6-2/3=-24
Step-by-step explanation:
How many permutations are there of the letters APPLE, if the arrangement must begin with a
vowel and end with a consonant?
Answer:
[tex]18[/tex].
Step-by-step explanation:
Start by considering the two "[tex]\verb!P![/tex]"'s as being different from one another. That way, all five letters in this word would be distinct. With this assumption, the number of arrangements would be [tex]\left(\genfrac{}{}{0}{}{2}{1}\right) = 2[/tex] times that of the actual value.
Start by fixing the first and the last letter since they come with special requirements.
There are [tex]2[/tex] choices for the first letter (the vowel: [tex]\verb!A![/tex] and [tex]\verb!E![/tex].)
Under the assumption that the two "[tex]\verb!P![/tex]"'s are distinct, there would be [tex]3[/tex] choices for the last letter ([tex]\verb!L![/tex] and the two
After choosing the first and the last letters, there would be [tex](5 - 1 - 1) = 3[/tex] choices for the second letter, [tex](3 - 1) = 2[/tex] choices for the third, and [tex](2 - 1) = 1[/tex] for the fourth.
Thus, under the assumption that the two "[tex]\verb!P![/tex]"'s are distinct, there would be [tex](2 \times 3) \times (3 \times 2 \times 1) = 36[/tex] ways to choose the new word. Since this assumption doubles the number of arrangements, dividing the [tex]36[/tex] by [tex]\left(\genfrac{}{}{0}{}{2}{1}\right) = 2[/tex] would give the actual number of arrangements:
[tex]\begin{aligned}\frac{36}{\genfrac{(}{)}{0}{}{2}{1}} = \frac{36}{2} = 18\end{aligned}[/tex].
[tex]\begin{aligned}& 1 && \verb!APPEL!\\& 2 && \verb!APLEP!\\& 3 && \verb!APEPL!\\& 4 && \verb!APELP!\\& 5 && \verb!ALPEP!\\& 6 && \verb!ALEPP!\\& 7 && \verb!AEPPL!\\& 8 && \verb!AEPLP!\\& 9 && \verb!AELPP!\\& 10 && \verb!EAPPL!\\& 11 && \verb!EAPLP!\\& 12 && \verb!EALPP!\\& 13 && \verb!EPAPL!\\& 14 && \verb!EPALP!\\& 15 && \verb!EPPAL!\\& 16 && \verb!EPLAP!\\& 17 && \verb!ELAPP!\\& 18 && \verb!ELPAP!\end{aligned}[/tex].
3/4+4y÷3;y=1 1/22 please help
Answer:3
4
+
4
(
y
3
)
.
3
4
+
4
(
y
3
)
=
4
y
3
+
3
4
y
=
11
22
=
=
1
2
Step-by-step explanation: :)
I WILL GIVE BRAINLIEST!! PLS HELP
Answer:
Angle PRQ is the same as NRM so therefore one of the three angles for both triangles is the same. Angle QPR and NMR are both 90 degrees and so the last angle must be the same in order for the three angles to be 180 degrees in total.
Step-by-step explanation:
Hope This Helps!!!
Selena and Demi run a gift delivery business. Selena charges a delivery fee that is $18, and she also charges $6 per gift delivered. Demi charges $16, and she also charges $8 per gift delivered. How many gifts have to be delivered before they charge the same amount?
Answer:
1 gift
Step-by-step explanation:
Cost per gift + delivered cost
Selena $6x + $18
Demi $8x + $16
$8x + $16 = $6x + $18
$2x - $16 = $18
$2x = $18 - $16
$2x = $2
x = 1
I need help with this please.
1. Which value is the closest to 1/9 • 24/25 (fractions)
a. 0
b. 0.5
c. 1
d. 21/20 (fraction)
Explain your answer:
Answer:
Option A: 0
Step-by-step explanation:
Given the multiplication of fractions, [tex]\huge\mathsf{\frac{1}{9} \:\times\frac{24}{25}}[/tex]:
Simply multiply the numerators (together), as well as the denominators.
In other words:
[tex]\huge\mathsf{\frac{1}{9} \:\times\frac{24}{25}\:=\frac{1\:\times\:24}{9\:\times\:25}\:=\:\frac{24}{225}}[/tex]
Since 24 and 225 do not have common multiples, then we cannot simplify the fraction into its lowest terms.
Next, in order to find out which is the closest value to the product, [tex]\huge\mathsf{\frac{24}{225}}[/tex], divide the numerator by the denominator, which gives you the following quotient:
[tex]\huge\mathsf{\frac{24}{225}\:=\:24\:\div\:225\:=\:0.1067}[/tex] or 0.11.
We must compare this quotient with the other options:
Option A) 0: This is a possible answer, since rounding 0.11 to the nearest ones (whole number) is 0.
Option B) 0.5: Unlikely a valid answer, since the digit on the hundreths place is 0.11, and rounding it up to the nearest tenths will become 0.1.
Option C) 1: Definitely not a valid answer, according to the explanations provided in Options A and B.
For Option D) [tex]\huge\mathsf{\frac{21}{20}}[/tex] , we need to find its equivalent decimal form by dividing its numerator by the denominator: [tex]\huge\mathsf{\frac{21}{20}\:=\:21\:\div\:20\:=\:1.05}[/tex]. Hence, it is also not a valid answer, according to the explanations provided in Options A and B.
Therefore, the closest value to [tex]\huge\mathsf{\frac{24}{225}\:=\:0.11}[/tex] is Option A) 0.
Find the unit rate for each problem.
Answer:
1. 11 players per team
2. 60 miles per hour
3. 25 games per season
4. 60 words per minute
Step-by-step explanation:
1) 132 players divided by 12 teams = # of players per team
132/12 = 11 players per team
2) 240 miles divided by 4 hours = # of miles per hour
240/4 = 60 miles per hour
3) 125 games divided by 5 seasons = # of games per season
125/5 = 25 games per season
4) 180 words divided by 3 minutes = # of words per minute
180/3 = 60 words per minute
What is the answer of this question please reply!
0.00536 by 25
Answer:
0.134
Step-by-step explanation:
"By" means multiplied by, so the question is, what's 0.00536 multiplied by 25?
In the first step, we multiply all the numbers in the decimal by 5, and we get 0.02680. In the second, we multiply all the numbers in the decimal by 20, and we get 0.10720. Then we add the two together and get 0.134.
I hope that helped :)
would this be A? Im not too sure about this.
Answer:
You're correct
Step-by-step explanation:
Basically, just add the answers with the given 67° until you get 180°
Help me ..Answer should be well explained..
9514 1404 393
Answer:
6. see attached
7. (a, b) = (-2, 3)
8. equation has issues
Step-by-step explanation:
6. Matrix addition is defined for corresponding terms, so the usual associative and commutative properties of addition apply. That is, ...
A₁₁ +B₁₁ = (A+B)₁₁ . . . . . and the same for other corresponding terms
The attachment shows the sums are equal. (It is convenient to let a spreadsheet do the tedious repetitive work.)
__
7. To find 'a' and 'b', we only need to consider the matrix elements that involve those variables.
element 11: 5 = b +2 ⇒ b = 3
element 21: a = 2 +2a ⇒ a = -2 (add -a-2 to both sides to get this)
__
8. There are issues with this equation. It is incomplete and inconsistent.
element 11: p = p+4 ⇒ no solution
element 21: r = 0 +(2r s) ⇔ missing math symbol; problem is incomplete
element 12: q = 6 + (p +q) ⇒ p = -6; q = anything
element 22: s = 2s +2 ⇒ s = -2 (add -s-2 to both sides)
_____
Additional comment
When a problem has issues of the kind that show up in question 8, I suggest that you have your teacher show you how to work the problem. If they're paying attention, they will discover the issues for themselves.
If they are able to work the problem, it will be because they filled in the missing information and resolved the inconsistencies. This will let you see the intended question.
Mike has $84 less than three times as much as Dave. Together they have $132. How much money does Mike have?
I have to use either the system of equation strategy of elimination or substitution to solve this. I realize that the first equation is
m + d = 132. But I don’t get what the second equation should be!
Answer: $48
Step-by-step explanation:
132 - 84 = 48
Solve the inequality and enter your solution as an inequality.
X-4<6
Answer:
x < 10
Step-by-step explanation:
Given: x -4 < 6
Add four to both sides: x < 10
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
(X-2)(x+1)
Expand and simplify
(x - 2)(x + 1) = ...
= x² + (-2 + 1)x + (-2•1)
= x² - x - 2
A homeowner collects data about the amount of oil, in gallons, used to heat the house per month for 5 months and the average monthly temperature, in degrees Fahrenheit, for those months. The scatter plot shows the data. The function best fits these data.
Use the function A(t)to determine which of the following statements are true. Select all that apply.
A The homeowner would use about 82 gallons of oil to heat the house for a month with an average temperature of 10 °F.The homeowner would use about 82 gallons of oil to heat the house for a month with an average temperature of 10 ° F.
B The homeowner would use about 85 gallons of oil to heat the house for a month with an average temperature of 15 °F.The homeowner would use about 85 gallons of oil to heat the house for a month with an average temperature of 15 ° F.
C The homeowner would use about 0 gallons of oil to heat the house for a month with an average temperature of 68.5 °F.The homeowner would use about 0 gallons of oil to heat the house for a month with an average temperature of 68.5 ° F.
D The homeowner would use about 5 gallons of oil to heat the house for a month with an average temperature of 55 °F. The homeowner would use about 5 gallons of oil to heat the house for a month with an average temperature of 55 ° F.
E The homeowner would use about 96 gallons of oil to heat the house for a month with an average temperature of 0 °F.
They are doing the calculations, we can say that the alternatives are:
A) True
B) False
C) False
D) False
E) True
For this exercise, the equation should be used:
[tex]A(t)=-1.4t+96[/tex]
So analyzing the first given statement we will have to:
[tex]A(t)=-1.4t+96\\t=10\\A(t)=-14+96=82[/tex]
Based on the calculations, this statement is true, for the second statement we will have:
[tex]A(t)=-1.4t+96\\t=15\\A(t)=-21+96=75[/tex]
From the calculations this statement is false, so for the alternative we will have:
[tex]A(t)=-1.4t+96\\t=55\\A(t)=-77+96=19[/tex]
From the calculations this statement is false, so for the alternative we will have:
[tex]A(t)=-1.4t+96\\t=0\\A(t)=96[/tex]
Based on the calculations, this statement is true.
Learn more: brainly.com/question/516840
3x + 9 - 2x + 1 + 5x + 11
Please please help meee please help meeee
Answer:
i. $3000
ii. $9000
Step-by-step explanation:
25%=1/4, so we find one fourth of 12000, which is 3000, which is how much he lost, and remove that from the price he bought it, and we get the selling price, $9000.
Order the numbers from least to greatest.
1,553
1,347
1,644; 1,553; 1,347
b. 1,347; 1,553; 1,644
1,644
a.
C.
1,553; 1,347; 1,644
Please select the best answer from the choices provided
Ο Α
Ο Ο Ο
B
Answer:
b even though you made this hard to read lol, its b
Step-by-step explanation:
help help help plssss
Answer:
6.5
Step-by-step explanation:
bc I just no plus or it's 5
Help Me Within 7 Minutes for brainliest. I already have a sorta guess But I'm not positive, A little help here? I want to confirm my answers and it seems no one else ever posted this question out.
y=3x+5
m=3Parallel lines has equal slope .
So equation of parallel line also have slope 3Take the 2nd option
[tex]\\ \sf\longmapsto 6x+2y=12[/tex]
Cut 3[tex]\\ \sf\longmapsto 3x+y=4[/tex]
[tex]\\ \sf\longmapsto y=-3x+4[/tex]
Note the answerTake 3rd option
[tex]\\ \sf\longmapsto -3x+y=8[/tex]
[tex]\\ \sf\longmapsto y=3x+8[/tex]
Take the 1st option
[tex]\\ \sf\longmapsto 3y=9x[/tex]
[tex]\\ \sf\longmapsto y=3x[/tex]
Option C and A is correct
Answer:
C and A
Step-by-step explanation:
Parallel means same slope, which is 3. Just solve for y in each equation, and see if 3 is the slope.
a. 3y = 9x
y = 3x
---
b. 6x + 2y = 12
2y = -6x + 12
y = -3x + 6
---
c. -3x + y = 8
y = 3x + 8
---
d. y = -1/3 x
answer to this question please
Answer:
Volume is 21
Explanation
Base length is 4.5
Widgth is 3.5
and height is 4 (I can't tell if its 2 because picture is blurry)
V=lwh/3=4.5·3.5·4= 21
What is the constant of proportionality in the equation
Below
Answer:
k = 9/2
Step-by-step explanation:
Constant of proportionality, k = y/x
given: x/y = 2/9
since k = y/x, therefore, k value will now be inverse of 2/9, which is 9/2
1 Solve for the unknown variable:
Answer:
Hypotenuse^2 = Opposite^2 + Adjacent^2
Step-by-step explanation:
Here hypotenuse is c, opposite is a and adjacent is b.
c^2 = a^2 + b^2
16^2 = a^2 + 12^2
a^2 = 16^2 - 12^2
a^2 = 112
a = √112 or 10.58
As the question uses inches I think it would be better if you wrote 10.58 in.
Hopefully this helps!!
ANSWER FAST PLEASE !!
Use synthetic division and the remainder theorem to find P(a).
P(x) = x^3 + 5x^2 - 6x +6; a = 4
P(a) =
Simplify your answer
Answer:
[tex]1 + 2 = [/tex]
answer
1 inch = 2feet . what would be the real life measurement of an object that measures 3 inches on a scale drawing
Given,
1 inch = 2 feet
3 inches = ? feet
3 inches = (2 × 3) feet
3 inches = 6 feet
=》3 inches in the scale drawing is 2 feet in real life.
_______
Hope it helps ⚜
what is the value x in following sequences 3,12,x,48,75,...
Answer:
30
Step-by-step explanation:
12-3= 9
75-48= 27
This is quadratic because it is like saying what is in between 9 and 27.
So the pattern is 9, 18, 27
so 12-3= 9
30-12= 18
48-30= Also 18
75-48= 27
Hope this helped :)
Find the inverse function in slope-intercept form (mx+b):
f(x) = -x - 5
Answer:
In order to find the inverse of a function, we flip it over the line y=x, or we switch the x and y values in the equation and solve it for y. So let's do the latter:
m(x) = 5x - 5
y = 5x - 5
x = 5y - 5
5y = x + 5
y = (x + 5)/5
Step-by-step explanation:
hope this is helpful
Answer: f ^−1(x)=x+5