Answer:
[tex]a = -9[/tex]
[tex]b = 4[/tex]
Step-by-step explanation:
Given
Sequence: a+3b, a+7b, a+11b
2nd term = 19
5th term = 67
Required
Find a and b
First, the 5th term needs to be calculated;
Using formula for Arithmetic Progression (AP), the formula goes thus
[tex]T_n = T_1 + (n - 1)d[/tex]
Where n = 5
T_1 = a + 3b ------------ FIrst term
[tex]d = T_2 - T_1 or T_3 - T_2[/tex] --- Difference between two successive terms
[tex]d = a + 7b - (a + 3b)[/tex]
[tex]d = a + 7b -a - 3b[/tex]
[tex]d = a - a + 7b - 3b[/tex]
[tex]d = 4b[/tex]
So, [tex]T_n = T_1 + (n - 1)d[/tex] becomes
[tex]T_5 = a + 3b + (5 - 1)4b[/tex]
[tex]T_5 = a + 3b + (4)4b[/tex]
[tex]T_5 = a + 3b + 16b[/tex]
[tex]T_5 = a + 19b[/tex]
Now that we have values for 2nd and 5th term;
From the second, T2 = 19 and T5 = 67
This gives
[tex]a + 7b = 19[/tex] --- Equation 1
[tex]a + 19b = 67[/tex] ---- Equation 2
Make a the subject of formula in (1)
[tex]a = 19 - 7b[/tex]
Substitute these values in equation 1
[tex]a + 19b = 67[/tex] becomes
[tex]19 - 7b + 19b = 67[/tex]
[tex]19 + 12b = 67[/tex]
Collect like terms
[tex]12b= 67 - 19[/tex]
[tex]12b = 48[/tex]
Divide both sides by 12
[tex]\frac{12b}{12} = \frac{48}{12}[/tex]
[tex]b = 4[/tex]
Recall that b = 4
Substitute a = 19 - 7b and nothing will hire
[tex]a = 19 - 7(4)[/tex]
[tex]a = 19 - 28[/tex]
[tex]a = -9[/tex]
Hence, the values of a and b are -9 and 4 respectively.
Um homem estava indo para a Bahia com suas sete irmãs. Cada irmã carregava sete caixas, cada caixa tinha sete gatos,cada gato estava com sete filhotes. Quantos estavam indo para a Bahia?
Answer:
2,752
Step-by-step explanation:
English Translation
A man was going to Bahia with his seven sisters. Each sister carried seven boxes, each box had seven cats, each cat had seven puppies. How many were going to Bahia?
Solution
1 man was going to Bahia
With his 7 sisters.
Total nunber of humans = 1 + 7 = 8 humans
Each of the 7 sisters carried 7 boxes.
Each of the 49 boxes had 7 cats
Total number of cats = 7 × 7 × 7 = 343 cats
Each of the 343 cats had 7 puppies
Total number of puppies = 7 × 343 = 2401 puppies.
Total number of living things going to Bahia
8 humans + 343 cats + 2401 puppies
= 2,752
Hope this Helps!!!
What is the perimeter of the triangle?
Answer:
To find the perimeter of the triangle, you need to add up the three sides of the triangle
/\
1 /__\ 5
9
1+5+9
_________________________________
Hey!!
The formula to find perimeter of triangle is a+b+c
For example:
If a triangle has the sides of 5,4 and 3 respectively,then to find the perimeter of triangle,we have to use the formula a+b+c which equals to 12.
Hope it helps
Good luck on your assignment
___________________________________
Use the data in the table to answer the question. Citations are "speeding tickets." You may fill in the table to help you answer the question. Original data Line of "best guess" Line of best fit Mph greater than speed limit Number of citations Outputs Residuals Outputs Residuals 5 3 7.5 6 10 10 15 5 20 6 Use a calculator or online resource to find the line of best fit. Note that values have been rounded. y = 0.7 x - 5.2 y = 0.7 x + 5.2 y = 0.07 x + 5.2 y = 0.07 x - 5.2
Answer: ŷ = 0.07X + 5.2
Step-by-step explanation:
Given the following :
Number of citations 5 - 7.5 - 10 - 15 - 20
Outputs Residuals 3 - - 6 - - 10 - 5 - - 6
Using the online regression calculator :
Line of best fit is represented by the equation:
ŷ = 0.06897X + 5.2069
ŷ = 0.07X + 5.2
From the line equation:
y = mx + c
With 0.07 = slope of gradient(m)
Intercept (c) = 5.2 (point where the line of best fit intersect the y_axis
x and y are values of x and y respectively
I need to know the answer
Answer:
y=3.65
X=11.85
Step-by-step explanation:
sin(60)=y/12
sin(60)×12=y
y=3.65
sin(30)=X/12
sin(30)×12=X
X=11.85
Which translation maps the graph of the function f(x)=x2 onto the function g(x)=x2+_2x+6?
Answer:
idk
Step-by-step explanation:
20% of a number is 58
Answer:
290
Step-by-step explanation:
The reason this is the answer is because if you divide 100% by 20% it will give you 5% so then you have to multiply 58 times 20 which will give you 290.
Answer:
290
Step-by-step explanation:
Find the perimeter of the figure. If you need to use Pi in your computation, approximate its value as 3.14. Rectangle topped by a semicircle A rectangle topped by a semicircle. The rectangle has length of 6 meters and width of 5 meters. The circle has diameter 5 meters. a. 29.85 m b. 18.57 m c. 32.70 m d. 24.85 m
Answer:
l think the answer is C
32.70m
Step-by-step explanation:
we all know that perimeter is the distance round the shape.
so the first step is adding 6 +6 because the other side of the shape is also 6 then add 5 and this equals to 17.
After that we find the area of the circle
which is 3.14*5= 15,7
After getting this value we add it to 17
then we get 32.70m
Answer:C
Step-by-step explanation:
Help pls :/.
The net of a triangular prism and its dimensions are shown. What is the total surface area, in square inches, of the triangular prism?
A) 240 sq inches
B) 120 sq inches
C) 96 sq inches
D) 24 sq inches
Answer:
120 sq inches
Step-by-step explanation:
I just did the quiz just now
as an estimation 5 miles is 8km. convert 16km to miles
Answer:
if its 8 to 5 then 16 is 10
answer: 10 miles
Answer:
10 miles
Step-by-step explanation:
8 km = 5 miles
So, Let's use the unitary method
1 km = [tex]\frac{5}{8}[/tex] miles
Multiplying both sides by 16, we get
16 km = [tex]\frac{5}{8} * 16[/tex] miles
16 km = 5 × 2 miles
16 km = 10 miles
Complete the sentence.
The bases of a circular cylinder are two ___
ao circles.
Answer:
congruent & parallel
Step-by-step explanation:
The bases of a circular cylinder are congruent and parallel to each other. If you need more explanation, reply to my answer.
What is the area of a rectangles with the side lengths 7/6 inches and 6/7 inches?
Answer:
1 in^2
Step-by-step explanation:
area of a rectangle=l*w
l=7/6
w=6/7
7/6 * 6/7 = 1
please help a struggling man
Answer:
x is all real numbers
Step-by-step explanation:
The domain is the input to the function. It is the values that x can take.
For this function, x can be any real value
4x+2/2 -(-2) find the answer
Answer:
[tex]4x+3[/tex]
Step-by-step explanation:
[tex]4x+2/2 -(-2)[/tex]
[tex]4x+1 -(-2)[/tex]
[tex]4x+1 +2[/tex]
[tex]4x+3[/tex]
Answer: =4x+3
Step-by-step explanation:
4x+ 2 /2 −(−2)
=4x+1+2
then you Combine the Like Terms:
=4x+1+2
=(4x)+(1+2)
=4x+3
Hope this helps :)
Nick simplified this expression. Is his answer correct?
O No Nick multiplied before dividing
O No. Nick should have converted to all decimals first.
O No. The first step should be division
O Yes. Nick did not make a mistake
Answer:
is A
Step-by-step explanation:
No. Nick multiplied before dividing
Answer:
the answer is nick multiplied before dividing.
Step-by-step explanation:
Which of the following pair of angles is the complementary angle? 25 and 65 31 and 71 60 and 40 145 and 35
Answer:
Step-by-step explanation:
If the sum of a pair of angles is 90, then they are complementary angles.
25 + 65 = 90
So, 25 and 65 are complementary angles
Answer:
25 and 65
Step-by-step explanation:
complementary angle= either of two angles whose sum is 90°
25 and 65, sum = 90°
yes31 and 71, sum = 102°
no60 and 40, sum = 100°
no145 and 35, sum = 180°
noi need help im too lazy still :)
Answer:
w=-16
Step-by-step explanation:
divide -192 by 12 to isolate w
Answer:
w=-16
Step-by-step explanation:
Ms Adams shares out 21 pencils between Niamah and Jack in the ratio 2:5 how many pencils does each child get
Answer:
niamah : jack
2 : 5
2×3 : 5×3
6 : 15
niamah gets 6 pencils
jack gets 15 pencils
*6+15 = 21
Answer:
Step-by-step explanation:
If the ratio of Niamah to Jack is 2:5, that means that for every 2 pencils that N gets, J gets 5. If there are a total of 21 pencils, then
2x + 5x = 21 and
7x = 21 so
x = 3.
That means that N gets 2(3) which is 6, and J gets 5(3) which is 15. Notice that 6:15 is the same ratio as 2:5 when it is reduced.
A farmer finds that if she plants 25 trees per acre, each tree will yield 41 bushels of fruit. She estimates that for each additional tree planted per acre, the yield of each tree will decrease by 1 bushel. How many trees should she plant per acre to maximize her harvest?
Answer:
17
Step-by-step explanation:
Let F be the number of fruit per acre
F = (25 + x) × (41 - x)
F=1025 -25x + 41x -x²
F=-x²+16x+1025
The maximum yield is at the maximum of that expression, which is at
[tex]x=-\frac{b}{2a} =>-\frac{16}{-2\times1}[/tex]
x=8
So apparently she currently has far too many trees per acre. To get the maximum yield, she needs to reduce the number of trees per acre by 8.
So the number of trees per acre for maximum yield is 25-8 = 17.
write the next three multiples of 9
36,
Answer:
45,54,63
Step-by-step explanation:
The multiples of 9 are
9,19,27,36,45,54,63,72,81
The three multiples are 36 are
45,54,63
Answer:
9, 36, 45, 54, 63
Step-by-step explanation:
XYZ is a right-angled triangle. Calculate the length of XZ. Give your answer correct to 2 decimal places. PLEASE ANSWER MY QUESTION
Answer:
3.52 m
Step-by-step explanation:
The question is not complete.
Let us assume XY = 1.35 m and YZ = 3.25 m.
If XZ is the longest side of the right-angled triangle (that is the hypotenuse), we can calculate XZ using the Pythagoras theorem.
The Pythagoras theorem state that the square of the hypotenuse side is equal to the sum of the square of the other two sides of the triangle.
That is for Triangle XYZ with XZ as hypotenuse:
XZ² = XY² + YZ²
Substituting:
XZ² = 1.35² + 3.25²
XZ² = 1.8225 + 10.5625
XZ² = 12.385
XZ = √12.385 = 3.5192
XZ = 3.52 m to 2 decimal places
Solve 3 (3 - 3x) +4= -5.
Answer:
x=2
Step-by-step explanation:
3 (3 - 3x) +4= -5
Subtract 4 from each side
3 (3 - 3x) +4-4= -5-4
3 (3 - 3x)= -9
Divide by 3
3/3 (3 - 3x) = -9/3
3-3x = -3
Subtract 3 from each side
3-3x-3 = -3-3
-3x = -6
Divide by -3
-3x/-3 = -6/-3
x = 2
b.
C.
Which triangles are similar?
12
16
6
ob
Answer:
a, b, and d.
Step-by-step explanation:
They have a common angle = 25 deg.
The pair of sides created that common angle share the same ratio = 1/2
(6/12 = 3/6 = 8/16 = 1/2)
Hope this helps!
Solve for x.
8x - 4 = 2x - 3
8x-4=2x-3
One solution was found :
x = 1/6 = 0.167
Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
8*x-4-(2*x-3)=0
Step by step solution :
Step 1 :
Solving a Single Variable Equation :
1.1 Solve : 6x-1 = 0
Add 1 to both sides of the equation :
6x = 1
Divide both sides of the equation by 6:
x = 1/6 = 0.167
One solution was found :
x = 1/6 = 0.167
i am not solving for x i am solving for you lol!!!
The price of an item has been reduced by 15%. The original price was $17
Answer:
17/100*85= $14.45
Step-by-step explanation:
Divide by 100 and multiply by (100-15) 85 to get the result.
You and your bestfriend are both on the swim team. You want to beat your bestfriend at the next swim meet so you decide to swim 15 minutes longer than she does on day at practice write an equation for the number of minutes you swim,y, when you bestfriend swims x number of minutes
Answer:
y = x + 15
Step-by-step explanation:
You swim 15 minutes more than a friend.The friend swims x minutes.
The amount of time you swim is 15 more than x.
Your time is y
Therefore y = x + 15 would be the equation.
Part 3. Identify the X intercepts for
y = (x+4)^2-9
Answer:
x = -1 or x = -7
Step-by-step explanation:
y = (x + 4)^2 - 9
To find x-intercept, set y = 0
=> (x + 4)^2 - 9 = 0
=> ( x + 1)( x + 7) = 0
=> x = -1 or x = -7
To find the x intercepts, plug in y = 0 and solve for x
y = (x+4)^2 - 9
0 = (x+4)^2 - 9 ... replace y with 0
9 = (x+4)^2
(x+4)^2 = 9
x+4 = plus/minus sqrt(9)
x+4 = sqrt(9) or x+4 = -sqrt(9)
x+4 = 3 or x+4 = -3
x = 3-4 or x = -3-4
x = -1 or x = -7 You have the correct answers. Nice work.-----------------------------------------------------------------
Checking each answer:
Plug x = -1 into the original equation. You should get y = 0 as a result
y = (x+4)^2 - 9
y = (-1+4)^2 - 9
y = (3)^2 - 9
y = 9-9
y = 0 .... so this confirms x = -1 as a solution
The same should apply for the other potential solution x = -7
y = (x+4)^2 - 9
y = (-7+4)^2 - 9
y = (-3)^2 - 9
y = 9-9
y = 0 .... this confirms x = -7 as well
Richard's Rental Car charges a $55 rental fee and $0.25 per mile. Freddy's Rental Car charges a
$45 rental fee and $0.35 per mile. For how many miles, X, will the total charge of Richard's
Rental Car be no more than the total charge of Freddy's Rental Car?
2 < 10
> 10
> 100
2 < 100
Answer:
Correct option: third one -> X > 100
Step-by-step explanation:
The equation for the price of Richard's Rental Car is:
P1 = 55 + 0.25*X
The equation for the price of Freddy's Rental Car is:
P2 = 45 + 0.35*X
To find for how many miles will the total charge of Richard be less than Freddy, we have that P1 < P2, so:
55 + 0.25*X < 45 + 0.35*X
0.25*X - 0.35*X < 45 - 55
-0.1*X < -10
0.1*X > 10
X > 100
Correct option: third one
X-9 = -27
2
0-24
0-12
11
O 12
______________________________
Hey!!
Solution,
x-9=-27
or, X= -27+9
x=-18
So the value of X is -18
hope it helps..
Good luck on your assignment
__________________________
5 + 3 + 2 = 151022
9 + 2 + 4 = 183652
8 + 6 + 3 = 482466
5 + 4 + 5 = 202541
Then ...
7 + 2 + 5 = ??????
Answer:
7 + 2 + 5 = 143547
Step-by-step explanation:
This question needs to identify the pattern
the pattern
is
5 + 3 + 2 = 151022
First two digits: 5*3 = 15 multiple of first and second term
third and fourth digit: 5*2 = 10 multiple of first and third term
last two digit = First two digits + third and fourth digit - second term
= 15+10 - 3 = 22
similarly
9 + 2 + 4 = 183652
9*2 = 18
9*4 = 36
18+36 - 2 = 52
____________________________________
5 + 4 + 5 = 202541
5*4 = 20
5*5 = 25
20+25-4 = 41
_______________________
7 + 2 + 5 = ??????
7*2 = 14
7*5 = 35
14+35-2 = 49-2 = 47
thus, 7 + 2 + 5 = 143547
8 divided by 4106 long division
Answer:
513.25 or 0.001
How i got the answer:
As we that 06 + 4 = 10. 10 is not divisible by 8. It means that 4106 is also not divisible by 8. The correct answer will be 4106 divided by 8 is 513.25.
If you asking only 8 divided by 4106 the answer is 0.00194836824. In short form it is 0.001.
If you asking if 8 is divisible by 4106 the answer is 513.25. Steps are added above.
Answer: 513.25 or 0.001
Please mark me brainliest
Hope this helps.
answer is 8/4106 or 0.002
Just follow the rules for multiplication and keep going till the end