The arrangement of the rose plants on the triangular plot is such that they
form a series, or progression that is defined.
The number of rows on Bill's plot is; 8 rowsReasons:
The given parameters for the triangular plot are;
Number of plants at the corner = 1 plant
Number of additional plant per row = 6 plants
Number of rose plants = 150 rose plants
Required:
The number of rows in the plot.
Solution;
The difference between successive rows, d = 6
The number rose at the top vertex, a = 1
Therefore, the rose in the garden form an arithmetic progression
The first term, a = 1
The common difference, d = 6
The number of rows Bill's plot will have, n, is given by the sum of n terms of
an arithmetic progression, [tex]\mathbf{S_n}[/tex], is given as follows;
[tex]\displaystyle S_n = \mathbf{\frac{n}{2} \cdot \left[2 \cdot a + (n - 1)\cdot d \right]}[/tex]
When Sₙ = 150, we get;
[tex]\displaystyle 150 = \frac{n}{2} \cdot \left[2 \times 1 + (n - 1)\times 6 \right] = n + 3 \cdot n^2 - 3 \cdot n = 3 \cdot n^2 - 2 \cdot n[/tex]
150 = 3·n² - 2·n
3·n² - 2·n - 150 = 0
Taking only the positive solution for n, we have;
[tex]\displaystyle n = \frac{2 \pm\sqrt{(-2)^2 -4 \times 3 \times (-150) } }{2 \times 3} \approx \mathbf{ 7.3965}[/tex]
The number of rows Bill's plot has, n ≈ 7.3965
Given that the 7th row is completed, an 8th row will be present on Bill's plot
The number of rows Bill's plot will have = 8 rowsLearn more about arithmetic progression here:
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which equation represents the parabola?
What is the domain of y =
cos-1^x?
Answer:
A
Step-by-step explanation:
correct on edge
Answer:
A) [-1,1]
Step-by-step explanation:
The function of y=cos⁻¹(x) has a domain of [-1,1] and a range of [0,π]. Observe the graph.
Scalar and Matrix Multiplication:
Answer:
C
Step-by-step explanation:
When multiplying scalars and matrices, just distribute the scalar to every component of the matrix. So 4*6=24, -2*6= -12, 6*6 = 36, 7*6 = 42, 3*6 = 18, and 0*6 = 0.
Luis needs 3 1/8 cups of blueberries for his pie. A store sells containers of blueberries that each hold 3/4 cups.
How many containers will Luis use to make his pie? Move numbers and a symbol to the lines to create an equation that shows the answer.
Answer:
3 1/8 divided by 3/4 = 4 1/6. basically 5 containers.
5^2+5^2=c^2 solve pythagorean theorem
Answer:
[tex]\sqrt 50[/tex]
Step-by-step explanation:
You are at (1,5). The zombie is six units to the right. Enter the correct coordinates of the zombie below.
Answer:
(7, 5)
Step-by-step explanation:
Right = movement on the x axis
X coordinate - 1
+6 units to the right = 7,5
(Keep y axis)
Answer:
(7,5)
Step-by-step explanation:
PLEASE HELP!! Step by step if possible
Answer:
r = 9
Step-by-step explanation:
[tex] In\: \odot O, [/tex] QP is tangent at point P and OP is radius.
[tex] \therefore OP\perp QP[/tex]
[tex] \therefore m\angle OPQ = 90\degree [/tex]
So, [tex] \triangle OPQ[/tex] is a right angled triangle. Hence, OQ will be its HYPOTENUSE such that OQ = r + 32
Now, by Pythagoras theorem:
[tex] OQ^2 = OP^2 + PQ^2 [/tex]
[tex] \therefore (r + 32)^2 = r^2 + (40)^2 [/tex]
[tex] \therefore\cancel {r^2} + 64r + 1024 = \cancel {r^2} + 1600 [/tex]
[tex] \therefore 64r = 1600-1024 [/tex]
[tex] \therefore 64r = 576 [/tex]
[tex] \therefore r = \frac{576}{64}[/tex]
[tex] \therefore r = 9[/tex]
How many terms are in the algebraic expression 1 ly +3?
A. 3
B. 4
O
C. 2.
D. 11
Answer:
Step-by-step explanation:
Answer:
The correct answer is 2 which is ;
C. 2.
Find the circumference of the circle.
please help me baby
surface area of prisms. please help with the work shown because i can't figure out how to solve these :(
here: :)
I did the work, and basically i solved for the area of the faces and then multiplied that by two to get the total surface area of the faces. Then I added in the areas of the sides connecting the two faces:
just as a referral: the formulas to find the faces are as follows:
rectangle: length times width
circle: pi x r^2
trapezoid: h(base1 + base2)
and triangle: (b x h)/2
What is the inverse function of f(x)=x^3+8
Answer:
[tex]\sqrt[3]{x-8}[/tex]
Step-by-step explanation:
y-8 = x^3
// -8 on both sides
[tex]\sqrt[3]{y-8}[/tex] = x
// cube root both sides
// then just switch x and y
Answer:
Step-by-step explanation:
[tex]f^{-1}(x)=\sqrt[3]{x-8}}[/tex]
a group of 100 people, some students, and some faculty attended a museum opening. Each student paid $10 per person for entrance to a museum and each of the faculty paid $ 25 per person for entrance. if the total paid, for all 100 people, was $1300, how many, students attended the museum opening?
a. 20
b. 70
c. 80
d. 50
Answer: 80
Step-by-step explanation:
Let the number of students be represented by x
Let the number of faculty be represented by y.
Based on the information in the question, we can form an equation which will be:
x + y = 100 ..... i
10x + 25y = 1300 ....... ii
From equation i,
Make y the subject of the formula
y = 100 - x ...... iii
Put the value of equation iii into ii
10x + 25y = 1300
10x + 25(100 - x) = 1300
10x + 2500 - 25x = 1300
10x - 25x = 1300 - 2500
-15x = -1200
x = 1200/15
x = 80
There were 80 students who attended the museum opening
What is 2 over 5 x 5 over 8
Answer:
the answer is 1/4
Step-by-step explanation:
2/5 × 5/8
2× 5/ 5 × 8
= 10/40
=1/4
Answer:
1/4
Step-by-step explanation:
You would do 2/5 times 5/8 which would equal 10/40 cause 5 times 2 is 10 and then 5 times 8 is 40 and then you would simplify the fraction 10/40 which would make it 1/4
what number must i add to complete the square x^2+8x=-3
Answer:
16
Step-by-step explanation:
(b/2)^2
(8/2)^2 = (4)^2 = 16
(x^2+8x+16) = -3+16
(x+4)^2 = 13
so on so forth, but basically you add 16 which completes the square
A train travels 120 mi in 1 hour and 20 minutes. How many miles will the train go in 6 hours traveling at the same rate?
Answer: 541.32 miles
Step-by-step explanation:
First find the speed of the train in miles per hour.
1 hour 20 minutes needs to be converted to decimal:
= 1 20/60
= 80/60
= 1.33 hours
Speed is:
= Distance / Time
= 120/ 1.33
= 90.22 miles an hour
If the train is traveling 6 hours at the above speed, it will travel:
= Speed * time
= 90.22 * 6
= 541.32 miles
Determine a series of transformations that would map figure F onto figure G.
PLEASE ASAP
Answer:
reflection, translation
Step-by-step explanation:
I can explain it if you want if you reply to this but since you are in a hurry that'll take too long to type right now haha
In ΔSTU, t = 3.4 cm, u = 6.9 cm and ∠S=21°. Find the area of ΔSTU, to the nearest 10th of a square centimeter.
Answer:
4.2
Step-by-step explanation
Delta
The area of the triangle STU to the nearest of a square centimeter is 4.2 cm².
Area of a trianglearea of the triangle = 1 / 2 tu sin S
where
height = u sin STherefore,
t = 3.4 cm
u = 6.9 cm
∠S = 21°
Hence,
area of the triangle = 1 / 2 × 3.4 × 6.9 sin 21°
area of the triangle = 23.46 sin 21 / 2
area of the triangle = 23.46 × 0.35836794954 / 2
area of the triangle = 8.40731209633 / 2
area of the triangle = 4.20365604817
area of the triangle = 4.2 cm²
learn more on triangle here: https://brainly.com/question/22252675
Identify the equation of the circle B that passes through (4, -6) and has center (3, -2).
Answer:
solution given :
centre (h,k)=(3,-2)
another point (a,b)=(4,-6)
now
radius =[tex] \sqrt{(3-4)²+(-2+6)²} [/tex]=√17
We have
equation of a circle is:
(x-h)²+(y-k)²=r²
(x-4)²+(y+6)²=17 is a required equation.
A medical device company knows that the percentage of patients experiencing injection-site reactions with the current needle is 11%. What is the mean of X, the number of patients seen until an injection-site reaction occurs?
3.1289
8.5763
9.0909
11
Answer:
The answer is 9.0909
Step-by-step explanation:
n=1 p=.11
mean = 1/0.11 = 9.0909
The mean of X, the number of patients seen until an injection-site reaction occurs is 9.0909.
What is mean?The mean refers to "the average set of values".
According to the question,
The percentage of patients experiencing injection- site reactions with the current needle is 11%.
Mean = [tex]\frac{sum of the all values}{Total number of values}[/tex]
Total number of values = 11% = 0.11 and n = 1.
Mean = [tex]\frac{1}{0.11}[/tex]
=9.0909.
Hence, the mean of X, the number of patients seen until an injection-site reaction occurs is 9.0909.
Learn more about mean here
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#SPJ2
Please help me choose the right answer
What kind of triangle would this one be?
Answer:
Scalene right
Step-by-step explanation:
It has a right angle, and two 45 degree angles as well as two sides of equal length
Answer:
I believe its scalene obtuse
so sorry if I'm wrong
Solve by completing the square.
x2 + 12x + 8 = 0
I need help ASAP . Brainlist will be given !!
Answer:
5,4 and 4,4
Step-by-step explanation:
Jared is mailing 10 packages. The line plot shows the weight of the packages.
XXX
х
X
Х
1
13
13
2
11
13
1
Weight of Packages (pounds)
How many more pounds are all the packages that weigh 1 pounds than all the packages that weigh lậ?
O A. Špound
O c. 24 pounds
B.
1 pounds
O d. 3 pounds
Answer:
C.
(I did the quiz aswell, i scored 100)
hey! i’ll give brainliest please help
Answer:
Conjunction
Step-by-step explanation:
Have a good day :)
Answer:
[tex]Conjuction[/tex] (๑・ω-)～♥”
In the figure below, GRAH is a rectangle, RA=7, and GA=10. Determine AH.
Answer:
AH = [tex]\sqrt{51}[/tex]
Step-by-step explanation:
The opposite sides of a rectangle are congruent , so
GH = RA = 7
Using Pythagoras' identity in right Δ GHA
AH² + GH² = GA²
AH² + 7² = 10²
AH² + 49 = 100 ( subtract 49 from both sides )
AH² = 51 ( take the square root of both sides )
AH = [tex]\sqrt{51}[/tex] ≈ 7.14 ( to 2 dec. places )
Answer:
√51 (or in LaTeX $sqrt51$)
Step-by-step explanation:
We know that Triangle GRA is a right triangle because Angle GRA is one of the angles of rectangle GRAH, and all interior angles of a rectangle are right.
We also know the lengths of two sides of GRA, so we can use the Pythagorean Theorem to solve for the third side. Specifically, the Pythagorean Theorem tells us that
(GR)^2 + (RA)^2 = (GA)^2.Plugging in RA=7 and GA=10, we get
(GR)^2 + 49 = 100,so (GR)^2=51. We know that GR is positive, so we conclude that $GR=\sqrt{51}$. Finally, since GRAH is a rectangle, its opposite sides have equal length. Thus AH = GR, and so AH = √51, which cannot be simplified.
Use substitution method to solve for x and y.
y = -8x -23 ...........(i)
y = 4x + 1 ............(ii)
Answer:
X=-2, y=-7
Step-by-step explanation:
f(x)=4x^2-17x+3 how many distinct real number zeros does f have?
Answer:
2
Step-by-step explanation:
2 distinct real number zeros
Step-by-step explanation:
The discriminant b^2 - 4ac
= (-17)^2 - 4*4*3
= 241
So it has 2 distinct roots.
What is the largest integer value of x such that the value of f(x) = x ^ 2 - 6x + 40 exceeds the value of g(x) =; 2 * (1.5) ^ x
Answer:
1
Step-by-step explanation:
2#&&#&÷&7*÷**#*×*×*÷(×(×¥=111
X Plus 2/4 equals 20