Given the first three terms of Geometric Sequence: 2b+2, b+4, b, where each of the tem is
positive, find
1) the value of b. (8)
ii) the first term and common ratio. (18,2/3)
(2009)
Answer:
1. b = 8
2. First term (T₁) = 18
Common ratio (r) = 2/3
Step-by-step explanation:
1. Determination of the value of b.
2b+2, b+4, b
First term (T₁) = 2b + 2
2nd term (T₂) = b + 4
3rd term (T₃) = b
The value of b can be obtained as follow:
Common ratio = T₂/T₁ = T₃/T₂
T₂/T₁ = T₃/T₂
(b + 4)/(2b + 2) = b/(b + 4)
Cross multiply
(b + 4)(b + 4) = b(2b + 2)
Expand
b(b + 4) + 4(b + 4) = b(2b + 2)
b² + 4b + 4b + 16 = 2b² + 2b
b² + 8b + 16 = 2b² + 2b
Rearrange
2b² – b² + 2b – 8b – 16 = 0
b² – 6b – 16 = 0
Solving by factorisation
b² – 8b + 2b – 16 = 0
b(b – 8) + 2(b – 8) = 0
(b – 8)(b + 2) = 0
b – 8 = 0 or b + 2 = 0
b = 8 or b = –2
Since each of the terms are positive, therefore, b is 8.
2. Determination of the first term and common ratio.
2b+2, b+4, b
First term (T₁) = 2b + 2
b = 8
First term (T₁) = 2(8) + 2
First term (T₁) = 16 + 2
First term (T₁) = 18
2nd term (T₂) = b + 4
b = 8
2nd term (T₂) = 8 + 4
2nd term (T₂) = 12
Common ratio (r) = T₂/T₁
First term (T₁) = 18
2nd term (T₂) = 12
Common ratio (r) = 12/18
Common ratio (r) = 2/3
What are the roots of the equation?
x2 + x - 6 = 0
Can someone tell me how to do this and give me the answer please
Answer:
C. 94 Supplementary angles
Step-by-step explanation:
if QS= 13 and RS= 12 what is the length of QR
40 POINTS !! 40 POINTS !!
PLEASE HELP , DONT SKIP !
NO LINKS OR FILES.
Answer:
??????
Step-by-step explanation:
Answer:
wow this is not 40 points there u get no help
Step-by-step explanation:
Ben ran 2/3 of a mile and walked 5/12 of a mile. How much farther did Ben run than walk?
Answer:
1.016 of a mile.
Step-by-step explanation:
If a bakery produces 1,215 cupcakes during a 9 hour shift, what is the production rate of cupcakes per hour?
Answer:
135
Step-by-step explanation:
Answer:
135 cupcakes
Step-by-step explanation:
You would do 1,215 divided by 9 to get your answer. So the answer would be 135 cupcakes.
1. What is the slope of the line
given by the equation
y = 2x +7
Answer:
2
Step-by-step explanation:
What is sin ?
What is a cos?
Answer:
Cos: adjacent / hypotenuse
In a right angled triangle, the cosine of an angle is: The length of the adjacent side divided by the length of the hypotenuse. The abbreviation is cos. cos(θ) = adjacent / hypotenuse. Well Done!
Sin: In mathematics, the sine is a trigonometric function of an angle. The sine of an acute angle is defined in the context of a right triangle: for the specified angle, it is the ratio of the length of the side that is opposite that angle, to the length of the longest side of the triangle.
hope this helps out, if not, i'm sorry
Step-by-step explanation:
Answer:
Sin=O/H
Cos=A/H
Step-by-step explanation:
Sin in full is some, a trigonometric ratio calculated by dividing the opposite over the hypotenuse.
Cos is in full cosine , also a trigonometric ratio calculated by dividing the adjacent over the hypotenuse.
A landscaping company placed two orders with a nursery. The first order was for 13 bushes and 4 trees, and totaled $327.50. The second order was for 6 bushes and 2 trees, and totaled $142.96. Sam tried to use system of equation to solve the problem If "b" represents bushes and "t" represents trees which system can Sam use?
A 13b + 2t = 327.50 6b + 4t = 142.96
B. 13b + 4t = 142.96 6b + 2t = 327.50
C 4b + 13t = 327.50 2b + 6 = 142.96
D 13b + 4t = 327.50 6b + 2t = 142.96
Answer:
A
Step-by-step explanation:
because mathematics of mathatics equals mathematics
PLEASE HURRY THIS IS DUE IN 20MIN
The Green River Freeway has a minimum and a maximum speed limit. Tony drove for 4 hours at the minimum speed limit and 7 hours at the maximum limit, a distance of 710 miles. Rae drove 4 hours at the minimum speed limit and 6 hours at the maximum limit, a distance of 640 miles SOLVE USING elimination
This is not my answer I found it from another brainly
From the beginning we know we are dealing with two different rates. Distance is equal to (Speed X Time). We have two different speeds though. We will call the min speed = x and the max speed = y. With those two ideas in place we can make two equations for both Tony and Rae.
Tony:
2x+3.5y=355
Rae:
2x+3y=320
Now you can solve the equations by subtracting Rae's equation from Tony's
.5y=35 solve for y and you get 70
Now plug that y value back into either equation and you can solve for x. I'll use Rae's distance:
2x+3(70)=320
x=55
Obtain the truth value of
(i)
If 5 + 6 = 11, then 11 – 6 = 5.
(ii)
If 5 + 8 = 12, then 12 + 8 = 20.
(iii)
If 6 + 9 = 14, then 14 – 7 = 8
(iv)
If 7 + 8 = 15, then 8 – 7 = 2
Simplify 42 ⋅ 48.
Please help with this!
Answer:
Step-by-step explanation:
a^x. a^y=a^{x+y}
4²*4^8=4^{10}
Answer:
4 to the power of 10
Step-by-step explanation:
Geometry please help!!!!!
What is 5 3/4 -1 5/12= ?
Answer:
4.33333333333 or 4 and 1/3
Step-by-step explanation:
Answer:
4 1/3
Step-by-step explanation:
1) Convert 5 3/4 to improper fraction.
2) Simplify 5x4 to 20.
3) Simplify 20+3 to 23.
4) Convert 1 5/12 to an improper fraction.
5) Simplify 1x12 to 12.
6) Simplify 12+5 to 17.
7) Find the least common denominator of 23/4 & 17/12.
8) Make the denominators the same.
9) Join the denominators.
10) Simplify 52/12 ( 4 1/3 )
Hope this helped!
.
x
What are the perimeter and area
of a square with side length of 12 in.?
A. P= 24 in., A = 24 in.?
B. P= 144 in., A = 48 in.2
O
C. P = 24 in., A = 144 in.2
O
D. P= 48 in., A = 144 in.2
Answer: P = 48 in, A = 144 in.2
Step-by-step explanation: Since a square has equal sides and we know one side length is 12 inches, then all the sides are 12 inches. For perimeter, we add all sides, which would equal 48 and for area, we multiply 2 of the sides, which would be 144.
Am I correct? I put
Answer:
yes
Step-by-step explanation:
Find the areas of the trapezoids
Answer:
figure 1 - 10.5 unit^2
figure 2 - 12 unit^2
Step-by-step explanation:
figure 1
1. find the area of the rectangle
3*2 = 6 unit^2
2. find the area of the triangle
(3*3)/2 = 4.5 unit^2
3. add the area of the rectangle and the area of the triangle together. The sum would be the area of the trapezoid.
6 + 4.5 = 10.5 unit^2
figure 2
1. find the area of the rectangle
2*4 = 8 unit^2
2. find the area of both triangles
(1*4)/2 = 2 unit^2
3. add the area of the rectangle and the area of both triangles together. The sum would be the area of the trapezoid.
8 + 2 + 2 = 12 unit^2
7. Mrs. Paulson is constructing a 90% confidence interval for the difference of means based on independent
simple random samples from two populations. The sample sizes are n, = 6 and n, =14. She draws dotplots
of the sample data to check one of the conditions for using two-sample i procedures. Which of the following
descriptions of those dotplots would suggest that it is safe to perform inference?
(a) Both dotplots are roughly symmetric. There are no outliers in either dotplot.
(b) Both dotplots are roughly symmetric. The dotplot of sample 2 has an outlier.
(c) Both dotplots are strongly skewed to the right. There are no outliers in either dotplot.
(d) Both dotplots are roughly symmetric. Both dotplots have one upper outlier
(e) i procedures are not recommended in any of these cases.
The description that will show that it is safe to perform inference is that (a) Both dotplots are roughly symmetric. There are no outliers in either dotplot.
What description would make it possible to make inferences?In order to use the two-sample t procedure to make inferences, certain conditions need to be met such as the sample being random and independent.
The variances for the groups in the data need to be equal which is why the presence of no outliers in either dotplot would present an safe opportunity to be able to perform inferences on the data.
In conclusion, option A is correct.
Find out more on two-sample t-tests at https://brainly.com/question/17438355.
Please help me
This is analytic geometry
Answer:
The coordinates of point B are (-3,-3).
Step-by-step explanation:
Let [tex]A(x,y) = (6,-6)[/tex], [tex]C(x,y) = (-6,-2)[/tex] and [tex]\overrightarrow{AB} = \frac{3}{4}\cdot \overrightarrow{AC}[/tex], then we have the following formula by vectorial definition of a line segment:
[tex]\overrightarrow{AB} = \frac{3}{4}\cdot \overrightarrow{AC}[/tex]
[tex]B(x,y) -A(x,y) = \frac{3}{4}\cdot [C(x,y)-A(x,y)][/tex]
[tex]B(x,y) = \frac{3}{4}\cdot C(x,y) +\frac{1}{4}\cdot A(x,y)[/tex]
[tex]B(x,y) = \frac{3}{4}\cdot (-6,-2)+\frac{1}{4}\cdot (6,-6)[/tex]
[tex]B(x,y) = (-3, -3)[/tex]
What would you multiply by to find 80% of an amount
Answer:
× [tex]\frac{80}{100}[/tex]
Step-by-step explanation:
For example-
80% of 400 (working in the attachment)
HOPE IT HELPS
Can someone please help me?
9514 1404 393
Answer:
C. 0.25, 1, 2, 4.75
Step-by-step explanation:
The solutions are the x-values of the points where the curves intersect. There are 4 intersection points to the right of the y-axis. Choice C is the only one with four (4) positive values for x.
the equation is
Y=4x + 2
-6x+ 2y=8
I'm trying to figure out whats the value of x +y
Answer:
Y = 4x +2
substitute Y into the second equation
-6x +2[4x +2] =8
-6x +8x +4 =8
collect like terms
-6x +8x =8-4
2x=4
x=2
Substitute (x=2) into the first equation
Y= 4(2) +2
Y= 8+2
Y= 10
I need help Asap please
9514 1404 393
Answer:
c
Step-by-step explanation:
Choice A lists most of them, but choice C lists them all.
__
Vertical angles are on opposite sides of the intersection of crossing lines. They share a vertex, and have sides that are opposite rays.
If g(x) = 2 | x| − 1, what is g(−2.3)?
a.-7
b.-5
c.-4
d.-3
Answer:
-7
Step-by-step explanation:
Try Again
The price of an item has been reduced by 70%. The original price was $49.
Use the ALEKS calculator to find the price of the item now.
s
Answer:
$34.30
Step-by-step explanation:
Use the equation:
F=P(r)
F=final price
P=principal (starting) amount
r=rate, normally a percent and has to be converted to a decimal
**Since this problem asks us to go down, there is no 1+r. That's when it gives us the final price and asks us to find the original.
Plug in the values: F = 49(.7)
F=$34.30 (don't forget the $ sign)
A jacket was originally $284. It is discounted 20%, but doesn’t sell, so it is discounted again by 20% off the sale price. Finally, after sitting in the store for 6 months, it is marked as clearance, at 50% of the lowest sale price. What is the clearance price of the jacket?
Parker ran 100 meters, 6 kilometers, and 4,000 centimeters. How many meters did he run all together
Answer:
4,106
Step-by-step explanation:
you jus add all the numbers up.
The hypotenuse of a right triangle is 12.4 ft. One of the other two sides is 5.8 ft How
long is the third side?
The value of 8 units is 11. What is the value of 1 unit?