Answer:
(a) The common difference is 4
(b) The 25th term is 108
Step-by-step explanation:
Given
[tex]T_7 = 36[/tex]
[tex]T_{14} = 64[/tex]
Solving (a): The common difference
The nth term of an AP is:
[tex]T_n = a + (n -1)d[/tex]
For the 7th term, we have:
[tex]36 = a + (7 -1)d[/tex]
[tex]36 = a + 6d[/tex]
For the 14th term, we have:
[tex]64 =a + (14 -1)d[/tex]
[tex]64 =a + 13d[/tex]
Subtract both equations
[tex]64 - 36 = a - a +13d-6d[/tex]
[tex]28 = 7d[/tex]
Divide by 7
[tex]d = 4[/tex]
Solving (b): The 25th term
First, we calculate the first term (a)
The 7th term of the progression is:
[tex]36 = a + 6d[/tex]
Substitute [tex]d = 4[/tex]
[tex]36 = a + 6 * 4[/tex]
[tex]36 = a + 24[/tex]
Subtract 24
[tex]a = 36 -24[/tex]
[tex]a = 12[/tex]
The 25th term is:
[tex]T_{25} = a + (25 - 1)d[/tex]
[tex]T_{25} = 12 + (25 - 1)*4[/tex]
[tex]T_{25} = 12 + 24*4[/tex]
[tex]T_{25} = 108[/tex]
Someone please help me thanks
Answer:
a. 7.2
Step-by-step explanation:
CAH (cos = adj/hyp)
cos53 = b/12; cross multiply
cos53*12 = 7.2
Pls help me no files just type it in thank you<333
Answer:
[tex] \large{ \tt{❃ \: EXPLANATION}} : [/tex]
We're provided - Number of kids playing soccer = 8 , Number of kids playing basketball = 16. Total number of kids at the park = 8 + 16 = 24. Now , divide 24 by 2 , you'll get 12 and that's your final answer.[tex] \boxed{ \boxed{ \large{ \tt{۵ \: OUR \: FINAL \:ANSWER : \underline{ \tt{12}}}}}}[/tex]
-Yey! We're done ツ
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Help is needed please!!!!
Answer:
31/20
Step-by-step explanation:
You need to plug in x as y-3.
so instead of 10x+10y=1 it is 10(y-3)+10y=1
Then just simplify the equation to find the value of y
Compare. Use >, <, or =.
123,546,789 >, <, or =, 123,456,789
please help
Step-by-step explanation:
123,546,789 > 123,456,789
#CMIIW
Work out m and c for the line:2y+3x=5
Answer:
[tex]{ \tt{2y + 3x = 5}} \\ { \tt{2y = - 3x + 5}} \\ { \tt{y = - \frac{3}{2} x + \frac{5}{2} }} \\ { \boxed{ \bf{general \: equation : { \tt{y = mx + c}}}}} \\ by \: relation : \\ { \tt{m = - \frac{3}{2} }} \\ \\ { \tt{c = \frac{5}{2} }} \\ \\ { \underline{ \blue{ \tt{becker⚜jnr}}}}[/tex]
A biologist is researching a newly-discovered species of bacteria. At time t = 0 hours, he puts one hundred bacteria into what he has determined to be a favorable growth medium. Six hours later, he measures 450 bacteria. Assuming exponential growth, what is the growth constant "k" for the bacteria? (Round k to two decimal places.) find the
number of bacteria after 13 hours
Answer:
k=.25068
Step-by-step explanation:
450 = 100 [tex]e^{6k}[/tex]
4.5 = [tex]e^{6k}[/tex]
ln(4.5) = 6k
k= ln(4.5)/6
k=.25068
The number of bacteria after 13 hours will be 2579.
What is an exponential expression?Powers can simply be expressed in concise form using exponential expressions. The exponent shows how many times the base has been multiplied. Since 2 is the "base" and 5 is the "exponent," it can be represented as 2x2x2x2=25 for the number 32. This phrase should be understood as "two to the fifth power."
Given that a biologist is researching a newly-discovered species of bacteria. At time t = 0 hours, he puts one hundred bacteria into what he has determined to be a favourable growth medium. Six hours later, he measures 450 bacteria.
The bacteria after 13 hours will be calculated as,
[tex]N=100(e)^{13\times 0.25)[/tex]
[tex]N = 100\times e^{3.25}[/tex]
N = 2579.
Therefore, the number of bacteria after 13 hours will be 2579.
To know more about an exponential expression follow
https://brainly.com/question/12940982
#SPJ2
Based on the picture below (note that it is not drawn to scale), Maggie says that . Is she correct? Explain why or why not.
Answer:
Step-by-step explanation:
By using the property of similar triangles,
"Corresponding sides of two similar triangles are proportional"
If ΔSMA ~ ΔPOD
[tex]\frac{SM}{PO}=\frac{MA}{OD}=\frac{SA}{PD}[/tex]
[tex]\frac{6}{10}=\frac{5}{10}=\frac{5}{12}[/tex]
[tex]\frac{3}{5}=\frac{1}{2}=\frac{5}{12}[/tex]
Since, ratios of corresponding sides are not equal,
Therefore, the given triangles are not similar.
Find f(3) given f(x) = -3x^3 + 2x^2 + 24
A. 123
B. -39
C. 69
D. 99
n is an integer
Write the values of n such that [tex]-8\leq 4n\ \textless \ 12[/tex]
Answer:
-2, -1, 0, 1, 2,
Step-by-step explanation
Divide the whole thing by 4.
You will have -2 [tex]\leq[/tex] n < 3
The only values that fit range from -2 to 2.
¿Cuánto mide el lado de un terreno cuadrado, si su área 144 m2?
Answer:
72
Step-by-step explanation:
all you had to do was divide by 2
The length of the missing sides
Answer:
length-14cm width-7cm
Step-by-step explanation:
To work out the sides, you can use 2l+2w=42. Since the length is twice the width, this becomes 2(2w)+2w=42.
This can be expanded to 4w+2w=42 or 6w=42.
From there, we can divide both sides by 6 to isolate w, meaning w=7.
Since the length is twice the width, it is given by l=2×7 or l=14.
**This question involves writing and solving algebraic equations from worded questions, which you may wish to revise. I'm always happy to help!
Sam and Mary collect marbles. “If you give me 5 marbles I’ll have twice as many as you.” said Sam to Mary.
“But if you give me 4 marbles wwe would have the same number said Mary to Sam.
How many marbles do they have altogether?
Answer:
54 marbles
Step-by-step explanation:
The question is a word problem leading to a simultaneous equation
Let 'x' represent the initial number of marbles with Sam, and let 'y' represent the initial number of marbles with Mary,
If Mary gives Sam 5 marbles, we have;
x + 5 = 2 × (y - 5)...(1)
If Sam gives Mary 4 marbles, we get;
x - 4 = y + 4...(2)
From equation (1), we get;
x + 5 = 2 × (y - 5) = 2·y - 10
x = 2·y - 10 - 5 = 2·y - 15
x = 2·y - 15...(3)
From equation (2), we have;
x - 4 = y + 4
∴ x = y + 4 + 4 = y + 8
x = y + 8...(4)
Equating the two values of 'x' in equation (3), and equation (4), we get;
2·y - 15 = y + 8
2·y - y = 8 + 15 = 23
∴ y = 23
From equation (4), we get;
x = y + 8 = 23 + 8 = 31
x = 31
The total number of marbles they have altogether = x + y
However, x + y = 23 + 31 = 54
Therefore;
The total number of marbles they have altogether = 54 marbles.
plsss help (on pic)
First will put brainliest
Answer:
7 over 2x-2
Step-by-step explanation:
Answer:
g^-1 •7
7g^-1
7•1/g
answer is 7/g
I hoped I helped!! :)
Math help please show work thanks
=====================================================
Work Shown:
36 inches = 3 feet
Divide by 12 to go from inches to feet
The block has the dimensions
L = 5 ftW = 8 ftH = 3 ftUse the formula below to calculate the surface area
SA = 2*(LW+LH+WH)
SA = 2*(5*8+5*3+8*3)
SA = 2*(40+15+24)
SA = 2*(79)
SA = 158 square feet
So if you had 158 square feet of wrapping paper, then you can cover this entire 3D box without any gaps or overlaps. The paper can be folded over the box, or you can cut/glue the pieces on, but make sure there isn't any leftover scraps of paper.
Help pls!! this is a presentation I’m doing in class and I NEED this completed rn, ASAP!!! . What I need is just the answers for the picture below and I NEED the explanation to all of them, and if you can pls try to give a similar example to these and solve it or what did u use to solve it. (Only 1 example that is similar) Thank you so much!
15. 70° because a right angle is 90° and we have the angle of ADB which is 20°. So 90°-20°=70°.
16. 70° because angle PSQ is 60° and angle QSR is 10°. So 60°+10°=70°.
17. 55° because it says it in the explanation. I assume this is a typo and they meant to ask the measurement of ADC and in that case it would be 130° because angle ADB is 75° and angle BDC is 55°. 75°+55°=130°.
18. 40° because angle PSQ is a right angle which means it's 90°. So 130°-90°=40°.
19. 140° because angle ADB is 120° and angle BDC is 20° so 120°+20°=140°.
20. 125° because again it's in the explanation. But if it's a typo and they meant what is the measurement of PSQ then it is 50° because PSR is 125° and QSR is 75° so 125°-75°=50°.
Hope this helps! :)
NEED HELP; What is the value of x?
X/8=6/12
A. 3
B. 5
C. 4.
D. 0.5
Answer:
the answer is 4
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Consider angle θ in Quadrant II, where cosθ=−12/13. What is the value of sinθ?
Answer:
The value of sin theta is 5/13
Step-by-step explanation:
In the second quadrant, sin is positive and cos is negative
Cos theta = -12/13 = adjacent/hypotenuse
Sin theta = opposite/hypotenuse
opposite = sqrt(hyp² - adj²) = sqrt (13² - 12²) = sqrt (169 - 144) = sqrt (25) = 5
Sin theta = opposite/hypotenuse = 5/13
3. Which of the following is equivalent to
3-3
Step-by-step explanation:
must be _1/27 in my opinion it's that
The value of a car has decreases by 5% each year. Sophie bought a car two years ago for £10000 work out the value now .
Answer:
£9000
Step-by-step explanation:
= £10 000× 5 ×2
100
= 1000
= £10 000-1000
= £9000
binomial theorem to expand (x+4)^4
Answer:
Step-by-step explanation:
(x+4)^2.(x+4)^2
= x^4 +16x^3+96x^2+256x+256
Practice D. Factor each trinomial.
1.
x² – 2x- 8
I
2.
y2 – 13y + 42
3.
m2 - 6m - 7
Help me answer those three factor please
Answer:
So 1) x²-2x-8
= x(x-2-8/x)
2) y²-13y+42
= y(y-13+42/y)
3) m²-6m-7
= m(m-6-7/m)
Hope it helps
What is the explicit formula for this arithmetic sequence?
-10,-17, -24, -31
Answer:
[tex]x_{n} =[/tex] -10 - 3(n-1)
Step-by-step explanation:
The answer is
xn = -10 - 3(n-1)
Please help I’ll give brainliest
Answer:
2 is the base
Step-by-step explanation:
2^12
The 2 is the base and the 12 is the exponent
which event has exactly 12 possible outcomes?
tossing a coin 6 times
tossing a coin and randomly choosing 1 of 4 different cards
rolling a number cube with sides labeled 1 -6 and then rolling the number cube again
rolling a number cube with sides labeled 1-6 and tossing a coin
please help me TwT
Answer:
rolling a number cube with sides labeled 1-6 and tossing a coin
Step-by-step explanation:
Which number(s) below belong to the solution set of the equation? Check all
that apply
x + 9 = 26
A. 17
B. 234
C. 52
D. 35
E. 26
F. 3
Answer:
A
Step-by-step explanation:
x + 9 = 26
x = 17
Answer:
A.17
Step-by-step explanation:
17+9=26
Can someone please solve this?
Does anyone know the answer ?!?
Answer:
40/100 = .4 = 40%
Step-by-step explanation:
Consider the trapezoid shown below.
6 in.
4 in.
6 in.
6 in.
(not drawn to scale)
Answer:
36
Step-by-step explanation:
1/2bh
1/2 (6*4) =12
Considering there are three triangles we will multiply by 3
12*3=36
Doughnuts are sold in bags and cartons
A bag holds four doughnuts and a carton holds ten doughnuts
Tom buys B bags of doughnuts and C cartons of doughnuts
He buys a total T doughnuts
Writs down a formula for T in terms of B and C
Answer:
Doughnuts are sold in bags and cartons
A bag holds four doughnuts and a carton holds ten doughnuts
Tom buys B bags of doughnuts and C cartons of doughnuts
He buys a total T doughnuts
Writs down a formula for T in terms of B and C
Step-by-step explanation:
Doughnuts are sold in bags and cartons
A bag holds four doughnuts and a carton holds ten doughnuts
Tom buys B bags of doughnuts and C cartons of doughnuts
He buys a total T doughnuts
Writs down a formula for T in terms of B and C
pls help my computers about to die lol
Answer:
Elapsed 10 hours and 50 minutes
Step-by-step explanation:
So it's 5:25 pm to 4:15 am.
It goes by 50 mins to get from 5:25 to 6:15.
Now the hours.
It has passed 10 hours to get 6:15 pm to 4;15 am.
