Answer:
9. a₁ = 13, aₙ = aₙ₋₁ × (-2)
10. aₙ = 2 (-3)ⁿ⁻¹
Step-by-step explanation:
9. aₙ = 13 (-2)ⁿ⁻¹
This is a geometric sequence where the first term is 13 and the common ratio is -2.
So the recursive formula is:
a₁ = 13, aₙ = aₙ₋₁ × (-2)
10. a₁ = 2, aₙ = aₙ₋₁ × (-3)
This is a geometric sequence where the first term is 2 and the common ratio is -3.
So the explicit formula is:
aₙ = 2 (-3)ⁿ⁻¹
The digits of both the two-digit numbers in the first calculation below have been reversed to give the two-digit numbers in the second calculation. The answers to the two calculations are the same. 62 × 13 = 806 26 × 31 = 806 For which one of the calculations below is the same thing true
Answer:
42x48
Step-by-step explanation:
Convert the following equation
into slope intercept form.
3x + y = -3
Answer: y = -3x -3
Step-by-step explanation:
y = mx + b
3x + y = -3
y = -3x -3
Answer:
slope intercept form: y=mx+c
*m = gradient
*c = y-intercept
3x + y = -3
y = -3x - 3
The tip jar at a sandwich shop has been found to have a dollar value 0.65ℎ +1.25, where ℎ is the number of hours since the shop opened.
a. By how much is the value of the tip jar increasing
The tip jar is increasing by 65 cents per hour
b. How much is the initial value of the tip jar when the store opens?
Answer:
The intial value is 1.25
Step-by-step explanation:
Work out the area of this circle with a radius of 6mm. Give your answer in terms of pi
Answer:36π mm^2
Step-by-step explanation:
Formula for area of a circle =
πr^2
r=6mm
π*6^2
π*36
36π mm^2
Answer:
36 π mm²
Step-by-step explanation:
r= 6 mm
A= πr²
A= π* 6²= 36 π mm²
what is the nth term rule of the linear sequence below 15, 7, -1, -9, -17
Answer:
8n+7
Step-by-step explanation:
3. Nancy and Harry are sliding a stone statue and moving it to a new location in their garden. Nancy is pushing the statue with a force of 120N at a 60° angle to the horizontal and Harry is pulling the statue with a force of 180N at a 40° angle with the horizontal. What is the magnitude of the horizontal force exerted on the statue?
Answer:
197,8879 N.
Step-by-step explanation:
The magnitude of the horizontal force exerted on the statue can be calculated using trigonometric functions.
The question given says that Nancy is pushing the statue with a force of 120 N at a 60° angle to the horizontal and Harry is pulling the statue with a force of 180 N at a 40° angle with the horizontal.
With that information can be calculated the horizontal force exerted on the statue by Nancy, the horizontal force exerted on the statue by Harry and, adding that results, the total horizontal magnitude can be calculated.
The cosine function can be used to calculate the horizontal component of the forces exerted by Nancy and Harry, to determine the horizontal component of the force exerted on the statue.
F= (120 N cos 60°) + (180 N x cos 40°)
F= 197,8879 N
The surface area of a sphere with a diameter of 12 units is:
Answer:
Surface area of sphere = 4πr²
r = radius
radius = diameter /2
= 12/2
= 6units
Surface area = 4π×6²
= 144π
= 452.4 square units
Hope this helps.
A standard six-sided die is thrown. What is the probability that the number
that comes up is less than or equal to 2?
Answer:
2/6 or 1/3
Step-by-step explanation:
There are two numbers who are equal or less than 2 its 1 and 2
And the total is 6 so its 2/6 which is 1/3
Sorry if this is late
Answer:
0.33
Step-by-step explanation:
Which of the binomials below is a factor of this trinomial?
X2-16x + 28
O A. x+7
O B. x2 + 7
O c. x+4
O D. X-14
Answer:
x-14
Step-by-step explanation:
The binomial which is a factor of this trinomial is (x- 14).
What is Trinomial?An algebraic expression with three terms is called a trinomial.
Examples of a trinomial expression: x + y + z is a trinomial in three variables x, y and z.
Given:
p(x) = x²-16x + 28
If x+ a is factor of any polynomial p(x) then x= -a satisfy the polynomial.
factorizing p(x)
x²-16x + 28
= x²-14x + 2x + 28
= x( x- 14) + 2 (x+ 14)
= (x- 14)(x+ 2)
Hence, the binomial is (x- 14).
Learn more about Trinomial here:
https://brainly.com/question/16347049
#SPJ2
What is 12 1/2 - (-4 1/2)
Answer:
the correct answer is
Step-by-step explanation:
= 12 1/2 - (-4 1/2)
=17
hope this helps you!!!!!
Answer:
17
Step-by-step explanation:
12 1/2 - (-4 1/2)
Turn to improper fractions.
25/2 - (-9/2)
Negative times negative is positive.
25/2 + 9/2
Add fractions with common denominators.
34/2
Divide.
= 17
please help.. GP is geometric progression
Answer:
unanswerable,don't censore the question
Step-by-step explanation:
sorry pal
Answer:
n is the seventh term=5832
Step-by-step explanation:
a1=8
r=3
a(n)=a1*r^(n-1)=
an=8*3(n-1)
8+24+72+216+648+1944+5832=8744
The volume of a cube is 8cm3, find the length of one of it's sides
Answer:
The side length is 2 cm
Step-by-step explanation:
The volume of a cube is s^3
V = s^3
8 = s^3
Take the cube root of each side
8 ^ 1/3 = s^3 ^ 1/3
2 = s
The side length is 2 cm
Answer:
2 cm
Step-by-step explanation:
The volume of a cube can be found using the following formula:
V=s^3
where s is the length of one side. We know the volume is 8 cm^3, therefore we can substitute that value in for V.
8 cm^3=s^3
We want to find what the side length is. The side length is being cubed. The inverse of a cube is the cube root. Therefore, we must take the cube root of both sides, or raise both sides to the power of 1/3.
(8 cm^3)^1/3=(s^3)^1/3
(8 cm^3)^1/3=s
2 cm=s
The length of one side is 2 centimeters.
Find the product: (50z + 20)(10z + 4) ( 1 ) 12. Find the product: (88a + 80)(8a + 8)
Answer:
1. 60z, 36
2. 96a, 88
Step-by-step explanation:
1.
First, find the like terms for z. (60z)
Second, find the like terms for 20, 4, and 12. (36)
2.
Combine the 88a and 8a (96a)
Then combine 8 plus 80 (88)
Answer:
(50z+20)(10z+4)
=50z(10z+4)+20(10z+4)
=500z²+200z+200z+80
=500z²+400z+80
(88a+80)(8a+8)
=88a(8a+8)+80(8a+8)
=704a²+704a+640a+640
=704a²+1344a+640
Step-by-step explanation:
i hope this will help you:)
I NEED HELP PLEASE, THANKS! :)
Answer: b) increasing for x < -4/3 and x > 4/3
decreasing for -4/3 < x < 4/3
Step-by-step explanation:
Graph the equation and the follow the curve from left to right. When you are going up, it is increasing. When you are going down, it is decreasing.
see the image below. Red is increasing. Blue is decreasing.
The vertices occur when x = -4/3 and x = 4/3
A school crossing sign is shown. Find the measures of angle A and angle C
Answer:
m∠A = 135°
m∠C = 135°
Step-by-step explanation:
There are 540° in a pentagon.
You are given 3 90° angles
540-90(3) = 270
∠A and ∠C are congruent
270/2 = 135° each
Sylvie finds the solution to the system of equations by graphing.
y =2/3x + 1 and y = -2/3x-1. Which graph shows the solution to Sylvie's system of equations?
Answer:
The third graph is your answer.
Step-by-step explanation:
I included a graph below with the correct graphing.
The figure shows the dimensions of a wall having a door and window of a room. Write an algebraic expression for the area of the wall to be painted. PLEASE FAST
Answer:
Area of the wall to be painted = (11x² + 12x) square units
Step-by-step explanation:
The figure that should be attached to this question is missing. The figure was obtained and is attached to this solution provided.
From the image attached, it is given that the dimension of the rectangular wall to be painted is (4x+3) by (4x), the dimensions of the window is (2x) by (x) and the dimensions of the door is (x) by (3x).
Since, the window space and the door space cannot be painted along with the wall, the Area of the rectangular wall that will be painted will be given by the expression
(Total Area of the rectangular wall) - [(Area of window space) + (Area of door space)]
Area of a rectangular figure = Length × Breadth
Total area of rectangular wall = (4x+3) × 4x = (16x² + 12x) square units
Area of window space = (2x) × (x) = (2x²) square units
Area of door space = (x) × (3x) = (3x²) square units
Area of the wall to be painted = (16x² + 12x) - (2x² + 3x²)
= 16x² + 12x - 5x²
= (11x² + 12x) square units
Hope this Helps!!!
PLS ANSWER FOR BRANINETEST
Answer:
3(3/7)
Step-by-step explanation:
Just by doing the math.
If y varies directly with x, and y is 14 when x is 2,
what is the value of x when y is 35?
X =
DONER
nt of
Answer: x = 5
Step-by-step explanation:
14 / 2 = 7
7 * 5 = 35
Same applies for x
2 / 2 = 1
1 * 5 = 5
Which value would make the statement true?
what is the area of the figure below use 3.14 for pie
Answer:
Answer CL 586 cm^2
Step-by-step explanation:
Hello. It's pi, not pie.
The area of the triangle is A1 = (1/2)(base)(height) = (1/2)(18 cm)(7 cm), or
A1 = 63 cm^2.
The area of the rectangle is A2 = (base)(height) = (18 cm)(22 cm) = 396 cm^2.
The area of the semicircle is A3 = (1/2)(pi)(9 cm)^2 = 3.14(81 cm^2)(1/2) = 127 cm^2
Thus, the total area of the figure is A = 127 cm^2 + 396 cm^2 + 63 cm^2, or
586 cm^2 approximately.
please see the attached picture for full solution...
Hope it helps...
Good luck on your assignment....
Very buys a basket of mangoes that is priced $14 before tax. The sales tax is 6%. What is the total price Avery pays for the basket of mangoes
Answer:
Avery needs to pay $14.84
Step-by-step explanation:
When there's a tax we need to sum the original value of the product with the tax's value. To find the amount of money Avery needs to pay in taxes we can apply a rule of three as shown below:
[tex]\frac{14}{x} = \frac{100}{6} \frac{\%}{\%}[/tex]
Where "x" is the tax value, and $14 represents 100%, since it's the value used to calculate the tax. We have:
[tex]x = \frac{14*6}{100}\\x = \frac{84}{100}\\x = 0.84[/tex]
The value to be paid is the product value plus the tax, therefore:
[tex]\text{paid} = 14 + 0.84 = 14.84[/tex]
Avery needs to pay $14.84
A car travels at the speed x + 30 kilometers in one hour, where x is an unknown. Find x if this car covers 300 kilometers in 3 hours?
Answer:
[tex]x=70[/tex]
Step-by-step explanation:
We know that the car travels at speed [tex]x+30[/tex] per hour. Thus, after [tex]h[/tex] hours, it will have traveled [tex]h(x+30)[/tex] kilometres.
We are given that it traveled 300 kilometres after 3 hours. So, we have...
[tex]300=3(x+30)[/tex]
[tex]100=x+30[/tex]
[tex]x=70[/tex]
What is the product?
1
12
64
2
78
30
6
32
78 30
6
64
78 30
6
32
39
15
6
64
39 30
Answer:
9.3526131e+34
Step-by-step explanation:
112*642=71904*4948560=355821258240*7830*664=1.8499574e+18*7830*632=9.1546252e+24*3915*664=6.7577122e+12*3930=2.6557809e+16=9.3526131e+34
Answer:
Answer:
9.3526131e+34
Step-by-step explanation:
112*642=71904*4948560=355821258240*7830*664=1.8499574e+18*7830*632=9.1546252e+24*3915*664=6.7577122e+12*3930=2.6557809e+16=9.3526131e+34
ANSWER THIS AND ILL FRIEND YOU What is 4(5x+7)/2+5x simplified
Answer:
15x+14Step-by-step explanation:
[tex]4(5x+7)/2+5x\\\\\frac{20x+28}{2} +5x\\Simplify\\ 10x +14+5x\\10x+5x+14\\15x+14[/tex]
At a certain high school, 35 students play only stringed instruments, 10 students play only brass instruments, and 5 students play both. There are also 5 students who play neither stringed nor brass instruments. what is the probability that a randomly selected student plays both a string and a brass instrument?
Answer:
0.09
Step-by-step explanation:
Total = 35+5+10+5 = 55
P(string&brass) = 5/55
= 1/11 = 0.09090909
What is the decimal multiplier to decrease by 1.7%?
Answer:
0.983
Step-by-step explanation:
100(0.983)=98.3
Answer:
[tex]0.983[/tex]
Step-by-step explanation:
[tex]\frac{100-17/10}{100}[/tex]
[tex]\frac{100-1.7}{100}[/tex]
[tex]=0.983[/tex]
A girl was born 35 years after her mother what fraction of the mother's age would the girl be at age 15
Answer: 3/10
Step-by-step explanation:
Equations:
m = d + 35
When girl is 15, mom is 35+15 = 50
Ans: girl = (15/50) = 3/10 of the mother's age.
5.
The total length of 2 pieces of rope is
108cm. If one piece is 18cm shorter, what is
the length of the longer piece?
Answer:
63 cm
Step-by-step explanation:
piece 1: x
piece 2: x - 18
First you would subtract 2x - 18 = 108
Second you would add 108 + 18 = 2x
Third you would divide 126 divided by 2x = 63
So that would mean x = 63
Answer:
63cm
Step-by-step explanation:
2 pieces of rope, and one is shorter by 18cm.
piece 1: x
piece 2: x-18
Add the equations together, combine both pieces
2x-18
2x-18 = 108
108+18 = 2x
126 = 2x
x = 63
Given the line of best fit for a set of data points with the equation y=5x-2.5, what is the residual for the point (3,6)?
========================================================
Explanation:
For the x value x = 3, the observed y value is y = 6 which is from the point (3,6).
The predicted y value is found by plugging x = 3 into the line of best fit equation
y = 5x-2.5
y = 5(3)-2.5
y = 12.5
The residual is the difference between the two y values
e = residual
e = (observed y value) - (predicted y value)
e = 6 - 12.5
e = -6.5
The negative residual tells us the observed y value is smaller than the predicted y value for this given x value.