Answer:
8/15 acres per hour
Step-by-step explanation:
To find acres per hour, divide acres by hours:
(2/5 ac)/(3/4 h) = (2/5)(4/3) ac/h = 8/15 ac/h
Derek can cover 8/15 acres per hour.
Which of the following is the equation of a line in slope-intercept form for a
line with slope = 5 and y-intercept at (0, -3)?
O A. y = 5x - 3
O B. y = 5x + 3
O C. y=-3x + 5
D. x = 3y-5
Answer:
The answer is option A
y = 5x + 3Step-by-step explanation:
Equation of a line is y = mx + c
where m is the slope
c is the y intercept
From the question
Slope or m = 5
y intercept is ( 0 , - 3) which is - 3
So the equation of the line is
y = 5x - 3
Hope this helps you
In circle o, the length of radius OL is 6 cm and the length
of arc LM is 6.3 cm. The measure of angle MON is 75º.
Rounded to the nearest tenth of a centimeter, what is the
length of arc LMN?
L
0 7.9 cm
6.3 cm
O 10.2 cm
6 cm
M
0 12.6 cm
0 14.2 cm
0 75
N
Answer:
14.2cm
Step-by-step explanation:
The diagram representing the circle and its attributes has been attached to this response.
As shown in the diagram;
The circle is centered at o,
The length of radius OL = 6cm
The length of the arc LM = 6.3cm
The angle MON = 75°
The angle LOM = θ
Remember that;
The length, L, of an arc is given by;
L = (θ / 360) x (2πr) -------------(i)
Where;
θ is the angle subtended by the arc
r = radius of the circle.
Using the formula in equation (i), let's calculate the angle θ subtended by arc LM as follows;
L = (θ / 360) x (2πr)
Where;
L = length of arc LM = 6.3cm
r = radius of the circle = length of radius OL = 6cm
Substitute these values into the equation to get;
6.3 = (θ / 360) x (2 x π x 6)
6.3 = (θ / 360) x (12 x π)
6.3 = (θ / 30) x (π) [Take π = 22/7]
6.3 = (θ / 30) x (22 / 7)
θ = [tex]\frac{6.3*30*7}{22}[/tex]
θ = 60.14°
Therefore, the angle subtended by arc LM is 60.14°
Now, from the diagram,
The angle subtended by arc LMN is;
θ + 75° = 60.14° + 75° = 135.14°
Let's now calculate the length of arc LMN using the same equation (i)
L = (θ / 360) x (2πr)
Where;
L = length of arc LMN
θ = angle subtended by LMN = 135.14°
r = radius of the circle = length of radius OL = 6cm
Substitute these values into the equation;
L = (135.14° / 360°) x (2 x π x 6) [Take π = 22/7]
L = 14.15cm
Therefore, the length of arc LMN is 14.2cm to the nearest tenth.
Answer:
14.2
Step-by-step explanation:
Edge
20 POINTS!! WILL GIVE BRAINLIEST!! ANSWER SOON PLEASE!!
You own a restaurant and want to “carpet” the floor with coins. What kind of coin would you use and why? How much would it cost to cover the floor with the coin you chose? Explain your reasoning. Include calculations in your reasoning.
Answer: I would use pennies. It is the lowest cost per unit of area.
The cost of the "penny carpet" would be about $ 5,319
Step-by-step explanation:
Each penny is 19.05mm or 1.905cm in diameter 100 centimeters per meter, so 100/1.905 = 52.493 pennies per meter in width, Squared to find number per square meter: 52.493² = 2755.5
The total area of the floor is 23 × 12 in the main area and 3×3 in the entrance,
184 m² + 9 m² = 193 m² . Multiplied by the cost per square meter, $27.56
Total cost: $5,919
The closest comparison would be the nickel. At 2.121 cm, it would take slightly fewer coins per m² , about 2223, but at $0.05 each, the cost per m² is about $111.15. The nickel carpet would cost 4 times as much as the penny carpet.
What is the total cost of troys order?
PLEASE HELP ME WITH THIS QUESTION :0
Marco is investigating some of the business models of SureSpin, one of Faster Fidget's top competitors. He has learned that they model their cost of production for one type of spinner with the function C(x) = 13,450 + 1.28x, where x is the number of spinners produced. Interpret the model to complete the statement. Type the correct answer in each box. Use numerals instead of words. Based on the model, the fixed cost of production is $
Answer:
$13,450
Step-by-step explanation:
The fixed costs of production, are the costs incurred that are independent from the production volume, that is, regardless of how many spinners the company produces, those costs will remain the same. If 'x' is the number of spinners produced, interpreting the cost function, we can see that it costs $1.28 to produce each spinner and that there is a cost that does not rely on production of $13,450. Therefore, the fixed cost of production is $13,450.
HELP NOW PLZ 20-30 POINTS FOR BRAINLIEST LOOK AT MY PROFILE FOR THE SAME QUESTION WITH MORE POINTS Step 1: Write a quadratic equation in standard form choosing your own coefficients and constant! (Recall: Standard Form of a quadratic equation is Ax^2 + Bx + C ). You need to choose a value for A, B, and C that satisfies each of the following conditions. You can use a value of 0 for B for no more than 1 of the 5 questions! Step 2: Solve each of the equations you create. YOU MUST SHOW YOUR WORK TO RECEIVE CREDIT FOR THIS STEP! Write your Exact answer in simplest form AND if necessary, round your estimate to the nearest tenth. 1) Equation 1 should represent a parabola that opens up and has a negative y-intercept. Equation 1: ____________________________________________________________ What strategy are you using to solve this equation and why? ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ Show your work and solution for solving this equation: 2) Equation 2 should represent a parabola that opens down and has a negative y- intercept. Equation 2:___________________________________________________________________ What strategy are you using to solve this equation and why? ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ Show your work and solution for solving this equation: 3) Equation 3 should represent a parabola that is a vertical stretch of the parent function and has a y-intercept greater than 3 and opens down. Equation 3:___________________________________________________________________ What strategy are you using to solve this equation and why? ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ Show your work and solution for solving this equation: 4) Equation 4: You decide what type of parabola you would like to create by answer the following questions: Does your parabola open up or down? _______________ Is there a vertical stretch or vertical compression? _______ What is the y-intercept? __________ Equation 4: ____________________________________________________________________ What strategy are you using to solve this equation and why? ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ Show your work and solution for solving this equation: 5) Write a quadratic equation that can only be solved using the quadratic formula. Equation 4: _________________________________________________________________ Show your work for how you use the quadratic formula to solve this equation:
Step-by-step explanation:
Equation 2: -[tex]x^{2}[/tex] + 3x - 6
Equation 2 should represent a parabola that opens down and has a negative y-intercept.
Parabola that opens down = a<0
Ax^2 + Bx + C
-[tex]x^{2}[/tex] + 3x - 6
Negative y-intercept: -(0)^2 +3(0) -6 = y= -6
Strategy to solve: Quadratic formula
Why? - This equation doesn't factor cleanly.
Show your work:
a= -1 b= 3 c= -6
Write the quadratic formula down ([tex]x= \frac{-b + \sqrt{b^{2} - 4ac } }{2a}[/tex]) ± not just +
Show step, solve.
x= 1.5 + 1.9365i
Equation 3:
Sorry, I can't do this.
Equation 4 :[tex]x^{2} -1[/tex]
You decide.
Alright, easy parabola.
1. Does parabola open up or down. UP
2. Is there a vertical stretch or compression? NO
3. What is the y-intercept- (0,-1)
[tex]x^{2} -1[/tex]
Strategy: Simple factoring patterns (Difference of squares) -
(x+1)(x-1)
x = + 1
Show work: x^2 is square of x,
Equation 5: [tex]x^{2} -3x+15[/tex]
x^2−3x+15
a=1 b= -3 c=15
([tex]x= \frac{-b + \sqrt{b^{2} - 4ac } }{2a}[/tex]) ± not just +
Good luck! Sorry that I couldn't do equation 3, vertical stretches are not my thing.
If A=2+i, O=-4, P=-i, and S=2+4i, find A-O+P+S.
==================================================
Work Shown:
A = 2+i
O = -4, this is the letter 'oh' not to be confused with the number zero
P = -i
S = 2+4i
A-O+P+S = (2+i) - (-4) + (-i) + (2+4i)
A-O+P+S = (2+i) + 4 + (-i) + (2+4i)
A-O+P+S = (2+4+2) + (i-i+4i)
A-O+P+S = 8+4i
Complete the following theorem.
Answer:
m⊥n
Step-by-step explanation:
the answer is n⊥m
Which expressions are equivalent to 6 +(–x) + 2x + (–7) + 2x? Check all that apply. Which expression is equivalent to 2(a+2b)-a-2b
Answer:
1 and 3
Step-by-step explanation:
The equation can be arranged to form equations 1 and 3.
Hope this helps!!! Please mark brainliest and thanks!!
I need to find the derivative. I’m not very good at this so I am answer asap would be sosososo helpful
Answer:
See below.
Step-by-step explanation:
First, notice that this is a composition of functions. For instance, let's let [tex]f(x)=\sqrt{x}[/tex] and [tex]g(x)=7x^2+4x+1[/tex]. Then, the given equation is essentially [tex]f(g(x))=\sqrt{7x^2+4x+1}[/tex]. Thus, we can use the chain rule.
Recall the chain rule: [tex]\frac{d}{dx}[f(g(x))]=f'(g(x))\cdot g'(x)[/tex]. So, let's find the derivative of each function:
[tex]f(x)=\sqrt{x}=x^\frac{1}{2}[/tex]
We can use the Power Rule here:
[tex]f'(x)=(x^\frac{1}{2})'=\frac{1}{2}(x^{-\frac{1}{2} })=\frac{1}{2\sqrt{x}}[/tex]
Now:
[tex]g(x)=7x^2+4x+1[/tex]
Again, use the Power Rule and Sum Rule
[tex]g'(x)=(7x^2+4x+1)'=(7x^2)'+(4x)'+(1)'=14x+4[/tex]
Now, we can put them together:
[tex]y'=f'(g(x))\cdot g'(x)=\frac{1}{2\sqrt{g(x)}} \cdot (14x+4)[/tex]
[tex]y'=\frac{14x+4}{2\sqrt{7x^2+4x+1} } =\frac{7x+2}{\sqrt{7x^2+4x+1} }[/tex]
Two ships are located 200 m and 300 m respectively from a lighthouse. If the angle formed by their paths to the lighthouse is 96°. What is the distance between the two ships?
Answer:its from applications of trignometry
The distance between the two ships is 377.54 m.
Given that, two ships are located 200 m and 300 m respectively from a lighthouse and the angle formed by their paths to the lighthouse is 96°.
We need to find the distance between the two ships.
What is the cosine rule to find the side?The cosine rule is c²=a²+b²-2abcosC
Now, c²=200²+300²-2×200×300cos96°
⇒c²=40000+90000-1,20,000×(-0.1045)
⇒c²=40000+90000+12,540
⇒c=377.54 m
Therefore, the distance between the two ships is 377.54 m.
To learn more about trigonometry application visit:
https://brainly.com/question/11687813.
#SPJ2
2/3 x +3 =1/4x-7
solve with work
Answer:
x=-24
Step-by-step explanation:
2/3 x +3 =1/4x-7
8/12x+3= 3/12x-7
5/12x + 3 = -7
5/12x = -10
5/12x (12/5) = -10(12/5)
x=-120/5
x=24
Simplify 5x5^2 leaving answers in index form
Answer:
5^3
Step-by-step explanation:
5*5^2
We are multiplying when the bases are the same
5^1 * 5^2
Add the exponents
5^(1+2)
5^3
Answer:5^3
Step-by-step explanation:Its a fact
please help me 4 1/7 + 1/2
Answer:
Exact Form:65/14
Mixed number Form:4 9/14
Step-by-step explanation:
Answer:
4 9/14
as an improper fraction: 65/14
hopefully this helped :3
Ray and Kelsey have summer internships at an engineering firm. As part of their internship, they get to assist in the planning of a brand new roller coaster. For this assignment, you help Ray and Kelsey as they tackle the math behind some simple curves in the coaster's track.
Part A
The first part of Ray and Kelsey's roller coaster is a curved pattern that can be represented by a polynomial function.
Ray and Kelsey are working to graph a third-degree polynomial function that represents the first pattern in the coaster plan. Ray says the third-degree polynomial has 4 intercepts. Kelsey argues the function can have as many as 3 zeros only. Is there a way for the both of them to be correct? Explain your answer.
Kelsey has a list of possible functions. Pick one of the g(x) functions below and then describe to Kelsey the key features of g(x), including the end behavior, y-intercept, and zeros.
g(x) = x3 − x2 − 4x + 4
g(x) = x3 + 2x2 − 9x − 18
g(x) = x3 − 3x2 − 4x + 12
g(x) = x3 + 2x2 − 25x − 50
g(x) = 2x3 + 14x2 − 2x − 14
Create a graph of the polynomial function you selected from Question 2.
Part B
The second part of the new coaster is a parabola.
Ray needs help creating the second part of the coaster. Create a unique parabola in the pattern f(x) = ax2 + bx + c. Describe the direction of the parabola and determine the y-intercept and zeros.
The safety inspector notes that Ray also needs to plan for a vertical ladder through the center of the coaster's parabolic shape for access to the coaster to perform safety repairs. Find the vertex and the equation for the axis of symmetry of the parabola, showing your work, so Ray can include it in his coaster plan.
Create a graph of the polynomial function you created in Question 4.
Part C
Now that the curve pieces are determined, use those pieces as sections of a complete coaster. By hand or by using a drawing program, sketch a design of Ray and Kelsey's coaster that includes the shape of the g(x) and f(x) functions that you chose in the Parts A and B. You do not have to include the coordinate plane. You may arrange the functions in any order you choose, but label each section of the graph with the corresponding function for your instructor to view.
Part D
Create an ad campaign to promote Ray and Kelsey's roller coaster. It can be a 15-second advertisement for television or radio, an interview for a magazine or news report, or a song, poem, or slideshow presentation for a company. These are just examples; you are not limited to how you prepare your advertisement, so be creative. Make sure to include a script of what each of you will say if you are preparing an interview or a report. The purpose of this ad is to get everyone excited about the roller coaster.
Step-by-step explanation:
Part A
A 3rd degree polynomial can have no more than 3 x-intercepts or zeros. Kelsey is correct. However, Ray stated it had 4 intercepts which can include 3 x-intercept and 1 y-intercept.
Graph the function g(x) = x3 − x2 − 4x + 4. See attached picture.
It has x-intercepts at (-2,0), (1,0) and (2,0). The y-intercept is (0,4). As x-> -∞ then y -> -∞. As x->∞, y->∞.
Part B
Use the quadratic function f(x) = -x^2 - 6x. The parabola faces downward with y -intercept (-3,9) and zeros (-6,0) and (0,0). See the attached graph.
The axis of symmetry will serve as a ladder through the coaster at x = -3.
Part C and D will use the math above to create the coaster and ad campaign.
Any point on the parabola can be labeled (x,y), as shown. What are the distances from the point (x,y) to the focus of the parabola and the directrix? Select two answers.
distance to the focus: (x+3)2+(y−3)2−−−−−−−−−−−−−−−√
distance to the focus: (x−2)2+(y+3)2−−−−−−−−−−−−−−−√
distance to the focus: (x+3)2+(y−2)2−−−−−−−−−−−−−−−√
distance to the directrix: |x−4|
distance to the directrix: |y−4|
distance to the directrix: |y+4|
Answer:
Step-by-step explanation:
Standard form of the equation:
y = [tex]-\frac{1}{4} (x+3)^2+3[/tex]
Directrix: y=4
Focus: (-3,2)
Points on the parabola (x,y):
(-5,2) (-3,3) (-1,2)
Distance from points to focus:
(-5,2) = (-3,2)
Answer choices: (x+3)^2+(y−3)^2, (x−2)2+(y+3)2, (x+3)2+(y−2)2
(-5+3)^2+(2-3)^2=5
(-5-2)^2+(2+3)^2=74
(-5+3)^2+(2-2)^2=4
(-1,2)
The polynomial 6x2 + x − 15 has a factor of 2x − 3. What is the other factor? A. 3x − 5 B. 3x + 5 C. 4x − 5 D. 4x + 5
Answer:
B: 3x+5
Step-by-step explanation:
You can solve this equation by doing the following steps:
6x2 + x - 15 is your polynomial. So take your polynomial and factor it down.
6x^2 + x - 15 = 6x^2 - 9x + 10x - 15 = 3x(2x - 3) + 5(2x - 3) = (3x+5)(2x - 3).
Check your answers again.
A) 3x - 5
Would this be possible considering our last answer? Which was (3x + 5)(2x - 3). No, it's not adding, so it's wrong.
B) 3x + 5
Could this be possible? Yes, it could because it has the first half of our answer. (3x + 5), keep this in mind.
C) 4x - 5
There was no 4 in the last part, so no. It's wrong. We're working with 2, 3, and 5 only. No 4.
D) 4x + 5
Again, no 4. Make sure to double-check your answers before clicking.
The answer is B) 3x + 5. Hope you found this helpful! Have a wonderful day and stay safe! (/O^O)/ *In 2008 a newspaper sold 120 thousand papers, and had 60 thousands people reading online. Their online readership has been increasing by 8 thousand people each year, while their physical paper sales have decreased by 6 thousand papers a year. In what year does online readership exceed physical sales?
Answer:
t = 5 years
online readership will exceed physical sales in 5 years
Step-by-step explanation:
The number of physical readership can be represented by the equation;
P(t) = 120 - 6t
The number of Online readership can be represented by the equation;
K(t) = 60 + 8t
For online readership to exceed physical sales
K(t) > P(t)
60 + 8t > 120 - 6t
Collecting the like terms;
8t+6t > 120-60
14t>60
t > 60/14
t > 4.29
To the nearest year greater than 4.29.
t = 5 years
online readership will exceed physical sales in 5 years
...........................
Answer:
3/5 or 0.6
Step-by-step explanation:
Here, given the value of tan theta , we want to find the value of sine theta
Mathematically;
tan theta = 0pposite/adjacent
Sine theta = opposite/hypotenuse
Firstly we need the length of the hypotenuse
This can be obtained using the Pythagoras’ theorem which states that the square of the hypotenuse equals sum of the squares of the two other sides.
Let’s call the hypotenuse h
h^2 = 3^2 + 4^2
h^2 = 9 + 16
h^2 = 25
h = √(25)
h = 5
Now from the tan theta, we know that the opposite is 3
Thus, the value of the sine theta = 3/5 or simply 0.6
what are the values of a and b?
I hope this helps you
Step-by-step explanation:
By using cosine rules:
6/sin45° = b/sin90°
b = 6× sin45°/sin90°
b = 9.124(3d.p)
Also,
using Pythagoras theorm of right-triangle
b² = 6² + a²
9.124² = 6² + a²
83.247376 = 36 + a²
83.247376-36 = a²
47.247376 = a²
√47.247376 = a
6.874 = a
What is the solution to the equation
?
1/x=x+3/2x2
Answer:
x = 0 , 3
Step-by-step explanation:
[tex]\frac{1}{x}=\frac{x+3}{2x^{2}}\\\\1*2x^{2}=x*(x+3)\\\\2x^{2}=x*x+x*3\\\\2x^{2}=x^{2}+3x\\\\2x^{2}-x^{2}-3x = 0\\\\x^{2}-3x =0\\\\x(x-3)=0[/tex]
x = 0 ; x - 3 = 0
x = 0 ; x = 3
HELPPPPPP ASAP!!!!!!!!!!!!!!!!!!!!!!! PLS DO NOT LOOK IT UP
Answer:
The constant proportionality of the table above is 16.
Step-by-step explanation:
In order to solve this problem, you must divide the weight of cat food by the number of bags. You must also continue doing this for each of the ratios shown in the table.
64 ÷ 4 = 16
80 ÷ 5 = 16
96 ÷ 6 = 16
So, the proportionality of the table is 16. As you can see, when we divided the numbers, they all had a quotient of 16, which is our proportion.
please help me out with these questions. It's trigonometry
Step-by-step explanation:
LOOK AT THE PICTURE
In ΔABC:
[tex]\sin\alpha=\dfrac{x}{y+p}\\\\\cos\alpha=\dfrac{q}{y+p}\\\\\tan\alpha=\dfrac{x}{q}[/tex]
In ΔADC
[tex]\sin\alpha=\dfrac{y}{x}\\\\\cos\alpha=\dfrac{z}{x}\\\\\tan\alpha=\dfrac{y}{z}[/tex]
In ΔBCD
[tex]\sin\alpha=\dfrac{z}{q}\\\\\cos\alpha=\dfrac{p}{q}\\\\\tan\alpha=\dfrac{z}{p}[/tex]
To write a fraction as a decimal, you divide the denominator by the numerator.
Answer:
"The decimal number is just a shorthand way of writing a fraction with a denominator of one thousand. It means the very same thing as . But this is just the algorithm for dividing the numerator by the denominator to get the decimal digits ."
Step-by-step explanation:
For what value of k will k + 9, 2k -1 and 2k + 7 are the consecutive terms of an A.P.?
Answer:
18
Step-by-step explanation:
Since, k + 9, 2k -1 and 2k + 7 are the consecutive terms of an A.P.
Therefore, their common differences would be same.
Hence,
(2k - 1) - (k + 9) = (2k + 7) - (2k - 1)
2k - 1 - k - 9 = 2k + 7 - 2k + 1
k - 10 = 8
k = 8 + 10
k = 18
Robyn saves up $204 and spends $32.50 on books. She wants to purchase more books from a sale where they cost $8.15 each. Which answer gives the best estimate for the number of books Robyn can buy?
Answer: 21 books
Step-by-step explanation:
I am estimating $32.50 to $33.
Remaining amount= 204 - 33 = $171
$8.15 = $8
$171 ÷ $8 = 21.375
Estimated answer = 21 books.
By reading the question it feels like there are options to choose from for the final answer. If it is, then choose the one which seems as close as possible to what I have got above.
Hope this helps :)
What do I do next please help
Answer:
13
Step-by-step explanation:
Since a point on the line is (0, 13) we know that the y-intercept is 13. The answer is already written in slope-intercept form so the answer is 13.
Answer:
13
Step-by-step explanation:
Let the missing value be c.
y = -3x + c
Put x as 0, and y as 13.
13 = -3(0) + c
13 = 0 + c
13 = c
Find the lateral area of the cone in terms of pi.
To find the lateral area of a cone, use this formula:
[tex]\pi r\sqrt{h^2+r^2}[/tex]
where r is the radius (in this case, 11) and h is the height (in this case, 26)
Try plugging the values in. If you need additional help, feel free to ask!
Please please please someone help me
Which of the following expressions is a factor of the polynomial x 2 +3/2x-1
Answer:
[tex]\large \boxed{\sf \ \ \ (x+2)(x-\dfrac{1}{2}) \ \ \ }[/tex]
Step-by-step explanation:
Hello,
let's solve
[tex]x^2+\dfrac{3}{2}x-1=0\\\\<=> 2x^2+3x-2=0 \ \text{multiply by 2}\\\\\\[/tex]
[tex]\Delta=b^2-4ac=9+4*2*2=9+16=25[/tex]
There are two solutions
[tex]x_1=\dfrac{-3-\sqrt{25}}{4}\\\\x_1=\dfrac{-3-5}{4}\\\\x_1=\dfrac{-8}{4}\\\\\boxed{x_1=-2}[/tex]
And
[tex]x_2=\dfrac{-3+\sqrt{25}}{4}\\\\x_2=\dfrac{-3+5}{4}\\\\x_2=\dfrac{2}{4}\\\\\boxed{x_2=\dfrac{1}{2}}[/tex]
So we can write
[tex]x^2+\dfrac{3}{2}x-1\\\\=(x-x_1)(x-x_2)\\\\=(x+2)(x-\dfrac{1}{2})[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you