Answer:
[tex]x = 2[/tex]
[tex]S_n = 63[/tex]
Step-by-step explanation:
Given
[tex]a_1 = x + 1[/tex]
[tex]a_2 = 4x -2[/tex]
[tex]a_3 = 6x -3[/tex]
[tex]a_n = 18[/tex]
Solving (a): x
To do this, we make use of common difference (d)
[tex]d = a_2 - a_1[/tex]
[tex]d = a_3 - a_2[/tex]
So, we have:
[tex]a_3 - a_2 = a_2 - a_1[/tex]
Substitute known values
[tex](6x - 3) - (4x - 2) = (4x - 2) - (x + 1)[/tex]
Remove brackets
[tex]6x - 3 - 4x + 2 = 4x - 2 - x - 1[/tex]
Collect like terms
[tex]6x - 4x- 3 + 2 = 4x - x- 2 - 1[/tex]
[tex]2x- 1 = 3x- 3[/tex]
Collect like terms
[tex]2x - 3x = 1 - 3[/tex]
[tex]-x = -2[/tex]
[tex]x = 2[/tex]
Solving (b): Sum of progression
First, we calculate the first term
[tex]a_1 = x + 1[/tex]
[tex]a_1 = 2 + 1 = 3[/tex]
Next, calculate d
[tex]d = a_2 - a_1[/tex]
[tex]d = (4x - 2) - (x +1)[/tex]
[tex]d = (4*2 - 2) - (2 +1)[/tex]
[tex]d = 6 - 3 = 3[/tex]
Next, we calculate n using:
[tex]a_n = a + (n - 1)d[/tex]
Where:
[tex]a_n = 18[/tex]
[tex]d = 3; a = 3[/tex]
So:
[tex]18 = 3 +(n - 1) * 3[/tex]
Subtract 3 from both sides
[tex]15 = (n - 1) * 3[/tex]
Divide both sides by 3
[tex]5 = n - 1[/tex]
Add 1 to both sides
[tex]6 = n[/tex]
[tex]n = 6[/tex]
The sum of the progression is:
[tex]S_n = \frac{n}{2} * [a + a_n][/tex]
So,, we have:
[tex]S_n = \frac{6}{2} * [3 + 18][/tex]
[tex]S_n = 3 * 21[/tex]
[tex]S_n = 63[/tex]
Can someone help me solve this problem ?
Answer:
B
Step-by-step explanation:
Since x= 3/4
To take the fraction on left hand side, inverse 4/3
Take π as denominator
Then cube root the entire equation on the left hand side.
Answer:
Step-by-step explanation:
Jack’s backpack weighs 15 pounds. Fernando’s backpack weighs less than Jack’s. Which graph shows how much Fernando’s backpack can weigh?
Answer:
A
Step-by-step explanation:
c and d out of the question
b has its circle filled in meaning it could be 15lbs, which it's not
A correct answer by default
Answer:b
Step-by-step explanation: it has a filled in diamond which mean it's that...
Simplify the following expression
Answer:
[tex]\frac{98p^{6}}{q}[/tex]
Step-by-step explanation:
Distribute the exponents
[tex](\frac{(7^{-2}p^{-6}q^{-8})}{2q^{-9}} )^{-1}[/tex]
[tex](\frac{q}{98p^{6}} )^{-1}[/tex]
Distribute the -1
[tex]\frac{98p^{6}}{q}[/tex]
Can someone do #4 and #5
Answer:
First, find two points on the graph:
(x₁, y₁) = (0, 2)(x₂, y₂) = (2, 8)Slope = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1}} = \frac{8-2}{2-0} =\frac{6}{2}=3[/tex]
16 + (-3) = 16 - 3 = 13
A 90% confidence interval is (35 45). What is the margin of error?
A. 5
B.4.5
C.9
D.10
Answer:
option A 5
I hope it's correct
.....
How to make my answer for 0.70 a fraction
Answer:
0.70 = 7/10
Step-by-step explanation:
Answer:
70/100 or 7/10 (Simplified)
Step-by-step explanation:
0.70 is basically .70 of 1. You can wrote this as a fraction, 70/100. If you divide 70 by 100, it gives you .70.
If you want to simplify it, it becomes 7/10, and if you divide 7 by 10, it also gives you 0.70.
Depends if you want your fraction simplified or not.
have a great day.
Please I need the answer according to steps
Answer:
Factorise out x and y terms:
[tex]{ \tt{ = \frac{ {x}^{2} {y}^{4} (5x - 3y)}{45} }} \\ [/tex]
please can anyone help me with this question what is the probability of the spinner landing on an even number.
find the sum of all multiples of 9 between 0 and 200
Answer:
I thick the answer is 2277
Trish's punch recipe calls for 8 liters of lemon-lime soda and 4 liters of cranberry juice, Jenny's punch recipe requires 7
liters of lemon-lime soda and 6 liters of cranberry juice. Which recipe has a higher ratio of lemon-lime soda to cranberry
juice?
( A, neither, the ratios are equivalent
B. Trish's recipe
c. Jenny's recipe
D. not enough information
According to this diagram, what is tan 62°?
62°
17
18
280
90°
15
O A.
8
17
OB.끝
O c. 1
8
15
D.
15
8
O
E.
17
15
F.
15
17
Answer:
15/8
Step-by-step explanation:
tan(62)=P/B
tan(62)=15/8
5 A machine puts tar on a road at the rate of 4 metres in 5 minutes.
a) How long does it take to cover 1 km of road
b) How many metres of road does it cover in 8 hours?
Answer:
5 a) Total = 20.83 hrs = 20 hrs and 50 mins (1250mins total)
5 b) Total = 96 meters. = 0.096km in 8 hrs.
Step-by-step explanation:
1km = 1000 meters
5 mins = 4 meters
1000/4 = 250 multiplier
250 x 5mins = 1250 minutes
1250/60 = 20hrs + 50 minutes
50 / 60 = 0.83 = 20.83hrs
b) 8 hrs = 8 x 60 = 480 minutes
480/5 = 24 multiplier of 4 meters
24 x 4 = 96 meters
What is the volume of the cone
Answer:
The volume of this cone would be approximately equal to 2787.64 [tex]yd.^2[/tex].
Step-by-step explanation:
The formula used to calculate the volume of a cone is [tex]\pi r^2*\frac{h}{3}[/tex] where [tex]r[/tex] represents the radius of the circle at the base of the cone, and [tex]h[/tex] represents the vertical height of the cone. In this case, [tex]r[/tex] equals the diameter of the base divided by two, which is [tex]\frac{22}{2}[/tex] or 11 yards; and [tex]h[/tex] is equivalent to 22 yards. Insert these values into the formula and you'll get that the volume of this cone is equal to [tex]11^2*\pi*\frac{22}{3} = 121\pi * \frac{22}{3}[/tex] ≈ 2787.64 [tex]yd.^2[/tex], so that is the correct answer.
Pls if anyone knows the answer with work included/steps that will be greatly appreciated :) for 6 just want to know is it w y x or z
Answer:
Step-by-step explanation:
Let's begin calculating the MPH for Fran.: Joanne's MPH is 250 / 2.5 = 100 MPH.
Now I'm going to subtract the 100 MPH by Fran. going 10 MPH less: 100 - 10 = 90.
I can't see the bottom part of the graph, so based on the MPH, it might be X, if you could put a better picture it would be better!
Which two shapes make up the digital camera below?
Rectangular prism and cylinder make up a camera.
What is rectangular prism and cylinder?A cube is a rectangular prism with all of its sides being the same length, a triangular prism has a triangle as its base, and a rectangular prism has a rectangle as its foundation. Another form of right prism that has a circle as its basis is a cylinder.
A rectangular prism includes a total of 6 faces, 12 sides, and eight vertices. Like a cuboid, it contains three dimensions- the base width, the height, and the length. The top and base of the rectangular prism exist rectangular. The pairs of opposite faces of a rectangular prism exist as identical or congruent.
A cylinder contains traditionally been a three-dimensional solid, one of the most essential curvilinear geometric shapes. Geometrically, it includes been regarded as a prism with a circle as its base.
Hence, Rectangular prism and cylinder make up a camera.
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This graph represents which of these expressions?
Answer:
x > 43
Step-by-step explanation:
Open circle at 43, which means it is not equal to 43
Line goes to the right, which means x is greater than
x > 43
Answer:
B
Step-by-step explanation:
Write the ratio as a fraction in simplest form, with whole numbers in the numerator and denominator.
4L TO 7.2 L
9514 1404 393
Answer:
5/9
Step-by-step explanation:
[tex]\dfrac{4\text{ L}}{7.2\text{ L}}=\dfrac{40}{72}=\dfrac{5\cdot8}{9\cdot8}=\boxed{\dfrac{5}{9}}[/tex]
What is the value of the capacitance of a capacitor that stores 40
μ
C on each plate, when a potential difference of 10 V is applied to it?
We know
[tex]\boxed{\sf Q=CV}[/tex]
[tex]\\ \large\sf\longmapsto C=\dfrac{Q}{V}[/tex]
[tex]\\ \large\sf\longmapsto C=\dfrac{40}{10}[/tex]
[tex]\\ \large\sf\longmapsto C=4\mu F[/tex]
A number is equal to twice a smaller number plus 3. The same number is equal to twice the sum of the smaller number and 1. How many solutions are possible for this situation?
* Infinitely many solutions exist because the two situations describe the same line.
* Exactly one solution exists because the situation describes two lines that have different slopes and different y-intercepts.
* No solutions exist because the situation describes two lines that have the same slope and different y-intercepts.
* Exactly one solution exists because the situation describes two lines with different slopes and the same y-intercept.
Answer:
There is no solution to this.
Explanation :
We have a double system of equation to solve. Let x be the big number and let y be the smaller number, such that y < x.
x is equal to twice a smaller number plus 3, which translates into : x = 2y + 3
and x is equal to twice the sum of the smaller number and 1 : x = 2 * (y + 1)
We get this system to solve : [tex]\left \{{{x=2y+3} \atop {x=2(y+1)}} \right. \left \{{{x-2y=3} \atop {x-2y=2}} \right.[/tex]
It's either x minus 2y equals 3, or x minus 2y = 2 but it can't be both. No solutions exist because the situation describes two lines that have the same slope and different y-intercepts
solve similar triangles (advanced)
solve for x
Answer:
x = 27/8
Step-by-step explanation:
We can write a ratio to solve
x 3
------- = ----------
x+9 11
Using cross products
x*11 = 3(x+9)
11x = 3x+27
Subtract 3x from each side
8x = 27
8x/8 = 27/8
x = 27/8
2(4×+2)=10
[tex]6 \times + 4 = 10 \\ \\ 6 \times = 10 - 4 \\ \\ 6 \times = 6 \\ \\ [/tex]
that is the answer
Answer:
x = 3/4
Step-by-step explanation:
2(4x + 2) = 10 Remove the brackets
8x + 4 = 10 Subtract 4 from both sides
8x = 6 Divide by 8
x = 6/8
x = 3/4
Check
2(4*3/4 + 2) =?10
2( 3 + 2) = 10
2*5 = 10
10 = 10
Your parents deposit 2 50-dollar bills at the bank.
How much money did they deposit?
Answer: $100
Step-by-step explanation:
Considering 50 + 50 = 100
This means that the amount of money is $100
Find the product:
1 -1 2
12 1 0] -1 -2 1 [a b c
0 1 1
a
12
b=0
Answer:
[tex][1, -4 ,5][/tex]
Step-by-step explanation:
In this question we are multiplying together two matrices. When we multiply a (1 x 3) matrix with a (3 x 3) matrix, we get a (1 x 3) matrix.
To compute each value, all you need to do is take the each value in each row in the first matrix, and multiply it by each value in each column of the second matrix and add up the result. So let's do that.
[tex]a = (2 * 1) + (1 * -1) + (0 * 0) = 2 - 1 + 0 = 1[/tex]
[tex]b = (2 * -1) + (1 * -2) + (0 * 1) = -2 -2 = -4[/tex]
[tex]c = (2 * 2) + (1 * 1) + (0 * 1) = 4 + 1 + 0 = 5[/tex]
What is the lengh of the line
Answer:
√45 or 3√5
Step-by-step explanation:
Which set of angles are complementary
Answer:
A. <ECF and <BCF
Step-by-step explanation:
Complementary angles are angles that add up to give 90°
m<BCE = m<BCA = 90° (right angles)
m<ECF + m<BCF = m<BCA
m<ECF + m<BCF = 90° (Substitution)
Therefore, <ECF and <BCF are complementary angles.
> There are 14 books on a shelf. 6 of these books are new. The rest of them are used (a) What is the ratio of new books to used books? (b) What is the ratio of used books to all books on the shelf
Answer:
a) 6:8
Because you have 14 books total if you substract 14 - 6= 8, so now you have
14 Books total
6 New Books
8 Used Books.
So, the ratio of new books to used books is 6:8 or if you simplified is 3:4.
b) 8:14
Because you have 8 used books compare to 14 books total. If you simplified your fraction you'll have 4:7
Step-by-step explanation:
Complete the table for the given rule.
Rule: y is 0.75 greater than x
x y
0
3
9
The complete table is
x y
0 0.75
3 3.75
9 9.75
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
What is substitution?Substitution means putting numbers in place of letters to calculate the value of an expression or equation.
According to the given question.
We have values of x.
Also, one rule that y is 0.75 greater than x.
So, we have a equation for finding the value of y i.e.
[tex]y = x + 0.75..(i)[/tex]
For finding the value of y
At x = 0, substitute x = 0 in equation (i)
[tex]y = 0 + 0.75\\\implies y = 0.75[/tex]
At x = 3, substitute x = 3 in equation (i)
[tex]y = 3+0.75\\\implies y = 3.75[/tex]
At x = 9, substitute x = 9 in equation (i)
[tex]y = 9+0.75\\\implies y = 9.75[/tex]
Hence, the complete table is
x y
0 0.75
3 3.75
9 9.75
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2( 1/5 m− 2/5 )+ 3/5
Answer:
2m/5-1/5
Step-by-step explanation:
2*m-2/5+3/5
2(m-2)/5+3/5
2(m-2)/5+3/5
2m-4/5+3/5
2m/5-1/5
How do you Find the acute Angle A when sinA=0.616?
Answer:
arcsin0.616
Step-by-step explanation:
arcsino.616
30 is what percent of 44?
Answer:
68.18
Step-by-step explanation:
→ Set up an equation
[tex]\frac{44x}{100} =30[/tex]
→ Times both sides by 100
44x = 3000
→ Divide both sides by 44
68.18
