Step-by-step explanation:
let's subtract it from the first one
8x -4y -(-3x + 4y) = -4 -5
8x -4y +3x - 4y= -9
11x -8y =-9
An arithmetic sequence has this recursive formula. a1=9 and 1-3 .
The required explicit formula for the sequence is [tex]a_n = 9+(n+1)(-3)[/tex]. Option B is correct.
Given, an arithmetic sequance is given in the form of [tex]\left \{ {{a_1=9} \atop {a_n =a_{n-1}-3} \right.[/tex] .
Explicit formula for the sequence is to be determined.
Arithmetic progression is the sequence of numbers that have common differences between adjacent values.
Example, 1, 2, 3, 4, 5, 6. this sequence as n = 6 number with a = 1 (1st term) and common differene d = 2- 1 = 1.
Given arithmetic sequance is in the form of [tex]\left \{ {{a_1=9} \atop {a_n =a_{n-1}-3} \right.[/tex]
From above expression
[tex]a_n-a_{n-1}= -3[/tex]
common difference (d) = -3
with d = -3 and [tex]a_1 = 9[/tex]
The equation for the nth term in an arithmetic sequence is given by
[tex]a_n =a +(n-1)d[/tex]
[tex]a_n = 9 +(n-1)(-3)[/tex]
The above expression is the explicit form of the arithmetic equation.
Thus, the required explicit formula for the sequence is [tex]a_n = 9+(n+1)(-3)[/tex]. Option B is correct.
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PLZZZZ HLPPPPP MEEEEEEEE
write the slope intercept inequality for the graph below. if necessary use <= or >=
Answer: y ≥ (3/5)*x - 3
Step-by-step explanation:
In the graph, we can see that we are above a bold line, that goes through the points (0, -3) and (5, 0)
First, let's find the equation for this line:
y = a*x + b
the value of a is the slope and is equal to:
a = (0 - (-3))/(5 -0) = 3/5
and the value of b is the point where the line intersects the y-axis, in this case, b = -3
then our line is
y = (3/5)*x - 3
As the shaded part is above the line, this equality represents the minimum value that y can take for a given x, and because the line is not a doted line, we know that the equality is valid, so we must use the ≥ symbol.
y ≥ (3/5)*x - 3
which of these statements us true for f(x)=3•(9)^x
Answer:
C
Step-by-step explanation:
The y-intercept is at x=0, y=3.
Approximate the value of positive square root 5 to the nearest hundredth
Answer:
2.2
Step-by-step explanation:
Arnold always sits in the second row of seats in his classroom. If there are 5 rows of seats behind Arnold and each row has 6 seats, how many seats are in the classroom?
Answer:
42 Seats.
Step-by-step explanation:
If Arnold is in the second row and there are 5 rows behind him, there are 7 rows because 2 + 5 equals 7.
So then, you multiply 6 times 7 since there are 7 rows and 6 seats in each row. And that equals 42.
Answer:
b:42
Step-by-step explanation:
help me with this problem and show your work
Answer:
10x - 15
Step-by-step explanation:
let Emily's be x hrs
Abbey = 3x-5 hrs
Nathan = 2 * Abbey's time= 2(3x-5)
= 6x-10 hrs
Expression= x + 3x-5 + 6x-10 = 10x - 15 hrs
Therefore, 10x - 15 is the EXPRESSION THAT DENOTES THE TOTAL NUMBER OF HOURS SPENT FOR DOING HOMEWORK COLLECTIVELY.
which is a valid proportion? 4/18=6/27 4/6=16/36 3/4=9/12 5/9=8/12 Check all that apply
Answer:
Given
Hope it helps..
Step-by-step explanation:
The options that apply are:
4/18= 6/27
3/4= 9/12
How to check:
Multiple the middle two terms
Then divide the product by one of the outer terms
If you get the other outer term, its a valid proportion
A rectangular field measures 616m by 456m. Fencing posts are placed along it's sides at equal distances. What will be the distance between the posts if they are place as far apart as possible?
Answer: 766.41m
Step-by-step explanation:
Hi, since the situation forms 2 right triangles (see attachment) we have to apply the Pythagorean Theorem for one triangle.
c^2 = a^2 + b^2
Where c is the hypotenuse of the triangle (in this case the diagonal distance between corners of the field, which is the distance between the posts if they are placed as far apart as possible ) and a and b are the other sides.
Replacing with the values given:
c^2 = 616^2 + 456^2
c^2 = 379,456+207,936
c^2 =587,392
c = √587,392
c = 766.41m
So, she is within the area serviced by the tower (20 miles)
Feel free to ask for more if needed or if you did not understand something.
A student does an experiment and wants to make a graph comparing various amounts of materials. Which type of graph should the student choose?
Answer:
The plotting the points 1 and then you will be able to compare the materials and how they work in comparison to the other material
Answer:
Bar graph
Step-by-step explanation:
Cuz he will make bars in order to show the materi
i hate math bro please help me ill mark u brainliest
Answer:
B. A reflection across the y axis.
Step-by-step explanation:
Only B. A reflection across the y axis will work because all the other options make it move somewhere else or flip it upside down. The trapezoid has a line of symmetry down the y-axis so reflecting it across the y-axis will make the same exact figure in the same exact spot.
Billy’s Boat Rentals charges a yearly fee of $105 and $9.50 each time a member wants to rent a boat. Lisa’s Boat Rentals does not charge a yearly fee but charges $14.75 every time a member rents a boat. How many times does a person have to rent a boat for Billy’s and Lisa’s to cost the same amount?
Answer:
It will take 20 times for both cost to be same
Step-by-step explanation:
What we want to do here is to calculate the number of times it will take someone who’s wants to rent a boat by Billyboat will be able to rent Lisa boat.
The first thing to do here is calculate how much that is charged to rent Billyboats
That would be;
Let the number of times be n
so the amount will be
105 + 9.50n
Now, renting at 14.75 at n times would be 14.75n
Mathematically, we equate both
14.75n = 105 + 9.5n
14.75n - 9.5n = 105
5.25n = 105
n = 105/5.25
n = 20 times
Rewrite
y +2>1/3 (6x – 9) to isolate the yterm.
Answer:
[tex]y>2x-5[/tex]
Step-by-step explanation:
[tex]y +2>1/3 (6x-9)[/tex]
Expand 1/3(6x-9).
[tex]y +2>6/3x-9/3[/tex]
[tex]y +2>2x-3[/tex]
Subtract 2 on both sides.
[tex]y +2-2>2x-3-2[/tex]
[tex]y>2x-5[/tex]
The rewritten form of y +2 > 1/3 (6x – 9) where the y-term us isolated is; y > 2x -5
To isolate the y-term;
The following operations are carried out;
y +2 >1/3 (6x – 9)y +2 > 2x – 3By finally isolating y; we have;
y > 2x -5
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Can some please help me with this question? And can you show your work too? I will mark the best answer Brainliest
Answer:
Finding the vertex by completing the square
1) The vertex = (4/3, -4/3)
2) The vertex = (-1/2, 36)
3) The vertex = (2/3, 26/3)
Finding the value of x by completing the square
1) x = 1 or -4
2) x = 3/2 or -7/2
3) x = 1 or -3
Step-by-step explanation:
Finding the vertex by completing the square
The vertex form of the quadratic equation y = ax² + bx + c is written as follows;
y = a(x - h) + k
Therefore, we have;
Y = 3·x² + 4 - 8·x = a(x - h)² + k
Hence, a = 3
Which gives;
3×(x² - 2·x·h + h²) + k
Hence, we have 3×2×h = 8
h = 8/6 = 4/3
The constant term = k
We note that 3 × h² + k = 4
∴ k = 4 - 16/3 = -4/3
The vertex form is therefore;
Y = 3(x - 4/3)² - 4/3
The vertex = (4/3, -4/3)
2) Where Y = 4·x² + 4·x + 36
a = 4
4× -2·h = 4
∴ h = 4/(4 × (-2)) = 4/-8 = -1/2
Also, 4 × h² + k = 36
Which gives;
4 × (-1/2)² × k = 36
k = 36
The vertex form becomes
y = 4(x - (-1/2)) + 36
The vertex = (-1/2, 36)
3) Where Y = -3·x² + 4·x + 10, we have
a = -3
3×2×h = 4
∴ h = 4/(2×3) = 2/3
a×h² + c = k
-(3)×(2/3)² + 10 = 26/3
Which gives;
Y = -3(x - 2/3) + 26/3
The vertex = (2/3, 26/3)
To find the value of x by completing the square, we have;
1) 2·x² = -6·x + 8
2·x² + 6·x = 8
2·(x² + 3·x) = 8
x² + 3·x = 8/2 = 4
x² + 3·x + (3/2)² = 4 + (3/2)² = 25/4
(x + 3/2)² = 25/4
∴ x + 3/2 = ±5/2
x = 5/2 - 3/2 or -5/2 - 3/2
x = 1 or -4
2) 8·x² + 16·x = 42
8·(x² + 2·x) = 42
x² + 2·x = 42/8 = 21/4
x² + 2·x + 1 = 21/4 + 1 = 25/4
(x + 1)² = 25/4
x + 1 = √(25/4) = ± 5/2
x = 5/2 - 1 or -5/2 - 1
∴ x = 3/2 or -7/2
3) -x² + 2·x = -3
-x² + 2·x = -3
-1×(-x² + 2·x) = -1 ×-3 = 3
x² - 2·x = 3
x² - 2·x + 1 = 3 + 1 = 4
(x - 1)² = 4
x - 1 = √4 = ±2
∴ x = 2 - 1 or -2 - 1
x = 1 or -3
Use the graphing method to solve the equation 5(1/2)^x=30 Round to the nearest thousandth
Answer:
x = -2.585
Step-by-step explanation:
You will have to plug this into your graphing calculator.
In y=, type 5(1/2)^x in the Y1 and type 30 in Y2.
When you hit 2nd trace and hit find intersections, you will get (-2.585, 30).
The answer is x = -2.585
Find the surface area of this triangular prism shown below
Answer:
Step-by-step explanation:
area of side triangles=2(1/2×6×4)=24 units²
area of 3 rectangles=6×7+2(5×7)==42+70=112 units²
or=(6+5+5)×7=16×7=112 units²
Total surface area=24+112=136 units²
In △ABC, AB = 13.2m,
BC = 6.9m and ∠ACB = 90°. H lies on AC such that
∠BHC = 46°. Find
(i) ∠ABH
(ii) The length of AH
Answer:
(i) ∠ABH = 14.5°
(ii) The length of AH = 4.6 m
Step-by-step explanation:
To solve the problem, we will follow the steps below;
(i)Finding ∠ABH
first lets find <HBC
<BHC + <HBC + <BCH = 180° (Sum of interior angle in a polygon)
46° + <HBC + 90 = 180°
<HBC+ 136° = 180°
subtract 136 from both-side of the equation
<HBC+ 136° - 136° = 180° -136°
<HBC = 44°
lets find <ABC
To do that, we need to first find <BAC
Using the sine rule
[tex]\frac{sin A}{a}[/tex] = [tex]\frac{sin C}{c}[/tex]
A = ?
a=6.9
C=90
c=13.2
[tex]\frac{sin A}{6.9}[/tex] = [tex]\frac{sin 90}{13.2}[/tex]
sin A = 6.9 sin 90 /13.2
sinA = 0.522727
A = sin⁻¹ ( 0.522727)
A ≈ 31.5 °
<BAC = 31.5°
<BAC + <ABC + <BCA = 180° (sum of interior angle of a triangle)
31.5° +<ABC + 90° = 180°
<ABC + 121.5° = 180°
subtract 121.5° from both-side of the equation
<ABC + 121.5° - 121.5° = 180° - 121.5°
<ABC = 58.5°
<ABH = <ABC - <HBC
=58.5° - 44°
=14.5°
∠ABH = 14.5°
(ii) Finding the length of AH
To find length AH, we need to first find ∠AHB
<AHB + <BHC = 180° ( angle on a straight line)
<AHB + 46° = 180°
subtract 46° from both-side of the equation
<AHB + 46°- 46° = 180° - 46°
<AHB = 134°
Using sine rule,
[tex]\frac{sin 134}{13.2}[/tex] = [tex]\frac{sin 14.5}{AH}[/tex]
AH = 13.2 sin 14.5 / sin 134
AH≈4.6 m
length AH = 4.6 m
What is the approximate area of the shaded sector in the circle shown below
Answer: B
Step-by-step explanation:
The area of a circle is pi*radius^2. But only a diameter is given, so in order to find the radius, you must divide the diameter by 2:
3.6/2 = 1.8
Now, you can plug the radius, 1.8, into the equation pi*radius^2 ([tex]\pi r^{2}[/tex]):
[tex]\pi (1.8)^2 = \pi(3.24)[/tex] = about 10.18
Lastly, you must divide the area 10.18 by 2 because you are looking for only half the area.
10.18/2 = 5.09
The area of the shaded region is 5.09 square cm if the radius of the circle is 1.8 cm, option (B) is correct.
What is a circle?It is described as a set of points, where each point is at the same distance from a fixed point (called the centre of a circle)
We have:
The diameter of the circle = 3.6 cm
The radius of the circle = 3.6/2 = 1.8 cm
Area of shaded region = (180/360)π(1.8)²
Area of the shaded region = 5.089 ≈ 5.09 square cm
Thus, the area of the shaded region is 5.09 square cm if the radius of the circle is 1.8 cm, option (B) is correct.
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Can someone help? It’s about 2 column proofs
Step-by-step explanation:
1. AB = BC (B is the midpoint of AC)
2. DE = EF (E is the midpoint of DF)
3. EB is common
4. ∠ABE = ∠CBE; ∠BED = ∠BEF (EB⊥AC, EB⊥DF)
5. ΔDEB ≅ ΔFEB (RHS)
6. DB = FB (corresponding ∠s of ≅ Δs)
7. ∠EFB = ∠CBF; ∠EDB = ∠ABD (alternate interior angles, AC║DF)
8. ΔABD ≅ ΔCBF (SAS)
If point P is 4 over 7 of the distance from M to N white ratio does the point P partioned the directed line segments from M to N into
Answer:
4 : 3
Step-by-step explanation:
The first segment is 4/7 of the whole, so the second segment is 1 - 4/7 = 3/7 of the whole. Then the ratio of the two segments is ...
(4/7) : (3/7) = 4 : 3
Evaluate -31-8+31 what’s the answer
Answer:
i believe that would be -8...
Step-by-step explanation:
Answer:
the correct answer is -8
plz mark as brainliest
Step-by-step explanation:
(root6-root5)(root8+root15)
Answer:root10 root3
Step-by-step explanation:since when you look for the square of root six you will get 2*3 then you will look for the root of 8 then you get 2*4 then you get 3*5 after that you multiply all then collect like times
Please help, I need this answer
Answer:
6.4
Step-by-step explanation:
By the Pythagorean Theorem:
[tex]c=\sqrt{5^2+4^2}= \\\\\sqrt{25+16}= \\\\\sqrt{41}\approx 6.4[/tex]
Hope this helps!
Answer:
To solve we need to use pythogorean theorm. So first we take the square of both giving us 25, 16. Then we add them and get 41. So the answer is squareroot of 41 and if you round you get 6.4
Answer: is approx. 6.4Natalie made a mistake in the following problem.
The mistake was made in Line ___. Only input the number of the first incorrect line
Line 1
6(4) ÷ 2 − 1 + 5
Line 2
6(4) ÷ 1 + 5
Line 3
24 ÷ 1 + 5
Line 4
24 + 5
Line 5
29
Answer:
The mistake is in line 2
Step-by-step explanation:
(BODMAS) bracket (multiplication) before subtraction
Which of the following expressions are equivalent to this expression: –1(0) = ? im lazy and dont wanna do it
Answer:
0
Step-by-step explanation:
Okay...um. Any number times 0 is 0 so the expression you choose should equal 0.
5662 to the nearest 10
Answer:
[tex]5660[/tex]
Step-by-step explanation:
Rounded to the nearest tenth.
Answer:
5660
Step-by-step explanation:
When finding the nearest 10 u need to start counting from the last figure your zeros and tenth(10) start it
Can you guys teach me how to do this??
The usual margin of error we strive for is a 95% probability that our estimate is within the margin. Assuming a normal distribution (and that we have a big enough sample not to worry about t tests) that corresponds to between minus and plus two standard deviations of the mean (remember the 68-95-99.7 rule). So our margin of error is plus or minus two standard deviations.
Answer: ±2%
chromesway you're smart please help me
Answer:
A
Step-by-step explanation:
If since y = 0 is a line of symmetry for the rectangle, reflection over y = 0 will just map the rectangle onto itself.
Please help which figure represents an under defined term?
Answer:
D
Step-by-step explanation:
Because its a line and the only three undefined terms are line,point,plane
find the coordinate of H' after a Glide reflection of the triangle translation 3 units up and 1 unit right then a reflection across the x-axis. answer in (a,b).
Part 1a
Answer:
H' = (4, -2)
Step-by-step explanation:
Translating point H three units up and one unit right places it at (4, 2).
Then after a reflection across the x-axis, the y value is reversed, and the point is placed at (4, -2)
what is the interquartile range(IQR) of the data set represented by this box plot?
A.37
B.17
C.5
D.22
Answer:
Answer:22
Step-by-step explanation: