Answer:
22%
Step-by-step explanation:
Well if the ramp can hold 1000lbs and 6 people all weight 780 in total (they must be really fat lol, but anyway) we can make the following fraction.
780/1000
So now we simplify the fraction to 39/50.
And do 39 / 50 = .78
To make that a percent we move the decimal point 2 times to the right so 78% of the ramp‘s capacity is being used meaning there is stil 22% capacity left.
HELPPP DO NOT LOOK IT UP PLS
Two pathways meet at 30° to each other. One pathway has lighting and the other does not.
The distance between successive lights on the lighted pathway is 5 metres. Each light has a
range of effective illumination of 6 metres.
What length of the pathway without lights is illuminated by the pathway with lights?
Answer:
12 meters
Step-by-step explanation:
Draw a picture of the two pathways 30° apart. Add a circle representing the illumination of the light on one of the pathways. Draw a line from the center of the circle to the last point where it intersects the pathway without lights.
This forms a triangle. One leg is x, the length of the pathway without lights. Another leg is 5n, where n is an integer. This represents how far the light is from where the pathways meet. The third and final leg is 6, the radius of the illumination.
Use law of cosine to solve:
6² = x² + (5n)² − 2x(5n) cos 30°
36 = x² + 25n² − 5√3 xn
0 = x² − 5√3 xn + 25n² − 36
In order to have a solution, the discriminant must be greater than or equal to 0.
b² − 4ac ≥ 0
(-5√3 n)² − 4(1)(25n² − 36) ≥ 0
75n² − 100n² + 144 ≥ 0
144 − 25n² ≥ 0
144 ≥ 25n²
144/25 ≥ n²
12/5 ≥ n
So n must be an integer less than 12/5, or 2.4. Therefore, the largest value of n is 2. Substituting:
0 = x² − 5√3 x(2) + 25(2)² − 36
0 = x² − 10√3 x + 64
Solve with quadratic formula:
x = [ 10√3 ± √(300 − 4(1)(64)) ] / 2(1)
x = (10√3 ± √44) / 2
x = 5√3 ± √11
x ≈ 5.34 or 11.98
We want the larger value of x. So approximately 12 meters of the pathway without lights is illuminated.
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
Determine if the coordinate (6, 8) lies on the circle x^2 + y^2 = 100.
Answer:
x² + y² = 100
6² + 8² = 100
36 + 64 = 100
100 = 100
Because this is a true statement, the answer is yes, it does lie on the circle.
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
New packaging for fruit snacks contains 10% less weight than the original packaging. If the new package costs 15% more than the original package, by what fraction did the unit price increase? Express your answer as a common fraction.
Answer:
5/18
Step-by-step explanation:
Let's say the original packaging was 1 lb of packaging for $1.
The cost was $1/lb.
Then the weight went down by 10% and the price went up by 15%.
Now 0.9 lb of packaging cost $1.15.
The new unit cost is $1.15/(0.9 lb)
The difference is
$1.15/(0.9 lb) - $1/lb =
= $1.15/(0.9 lb) - $0.9/(0.9 lb)
= $0.25/(0.9 lb)
=$25/(90 lb) = $5/(18 lb)
The price went up by 5/18.
use the elimination method to solve the system of equations. choose the correct ordered pair x+y=3 y=8
Answer:
(-5, 8)
Step-by-step explanation:
Step 1: Multiply 2nd equation by -1
x + y = 3
-y = -8
Step 2: Elimination
x = -5
Step 3: Find y
y = 8
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)
Solve this a² ÷ a⁴ × a²
Step-by-step explanation:
a^4 - a^4 = (a^2 +a^2)(a^2-a^2)
a^4 - a^4 = (a^2 + a^2)(a+a)(a-a)
there is no need of this solution, because it equal to 0 because a^4 - a^4 will be equal then it will be 0
i hope this will help you
Answer:
Hello There!
~~~~~~~~~~~~~~~
a² ÷ a⁴ × a² =
1
Step-by-step explanation: Simplify the expression.
Hope this helped you! Brainliest would be nice!
☆_____________❤︎______________☆
Helppp!!!! please!!!
Answer: B. rectangular pyramid
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.
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 answer it in two minutes
Answer:
p = 3
Step-by-step explanation:
We have a right triangle with both legs equal, whose hypotenuse is 3 times the root of 2.
We know both legs are equal because we have identical opposite angles in this right rectangle.
If we apply the Pythagorean theorem, we obtain:
[tex]p^2+p^2=(3\sqrt{2})^2=9\cdot 2=18\\\\2p^2=18\\\\p^2=18/2=9\\\\p=\sqrt{9}\\\\p=3[/tex]
The planet mercury is approximately 6*10^7 miles from the sun. The distance between the sun and mars is approximately 2*10^8 miles. About how many times farther from the sun is mars than mercury.
Answer:
Around 10/3 or 3.33 times farther.
Step-by-step explanation:
We simply divide the larger distance by the smaller distance to find our ratio:
2(10⁸)/6(10⁷)
10/3
*Remember when you divide exponents, you subtract them
Consider the following 8 numbers, where one labelled x is unknown.
11, 1, 34, x, 41, 10, 47, 2
Given that the range of the numbers is 67,
work out 2 values of x.
Answer:
x=-20 or x=68
Step-by-step explanation:
you can either make it so 47 remains the largest number and so take 67 from 47 (=-20) or you can leave 1 as the smallest number and add 67 to 1 (=68)
Which number(s) below belong to the solution set of the inequality Check all that apply. x + 30 < 60 a.50 b.45 c.300 d.1 e.29 f.30
Answer:
e.29 d.1
Step-by-step explanation:
x+30<60 :we will replace with the values we have :
300 that's a big number . Obviously it isn't a solution 50 : 30+50 = 80>60 so no 45: 30+45= 75 >60 so no 30+30 = 60 we have < not ≤ so no 1 yes . it's obvious 29 +30 = 59<60 so yes !It takes me 10 minutes to swim 2 laps. How long will it take
me to swim 5 laps?
Answer:
25 minutes
Step-by-step explanation:
10 ÷ 2 = 5
1 lap = 5 minutes
5/1 × 5 = 25
25 minutes
Hope this helped! :)
Answer:
25 minutes
Step-by-step explanation:
Let's set up a proportion using the following setup:
minutes/laps=minutes/laps
It takes 10 minutes to swim 2 laps.
10 minutes / 2 laps = minutes/laps
We don't know how long it will take to swim 5 laps. Therefore, we can say it takes x minutes to swim 5 laps.
10 minutes/ 2 laps= x minutes / 5 laps
10/2= x/5
We want to find out what x is. Therefore, we need to get x by itself.
x is being divided by 5. The inverse of division is multiplication. Multiply both sides by 5.
5*(10/2)=(x/5)*5
5*10/2=x
5*5=x
25=x
It takes 25 minutes to swim 5 laps.
If n is the term, what is the first integer value of n where the sequence 2n² is greater than 50?
Answer:
The 6th term is first integer value of n greater then 50 in the 2n^2 sequence.
Step-by-step explanation:
2n^2 sequence:
2,8,18,32,50,72
please help ASAP: Factorise the following:
Answer:
hope u will understand it....
Answer:
Hello!
___________________
A)Factor x^2 - 12x + 32 using the AC method. ( x - 8 ) ( x - 4)
B) Factor x^2 - 14x + 48 using the AC method. ( x - 8) ( x - 6)
C) Factor x^2 - 3x + 2 using the AC method. ( x - 2) ( x - 1)
Step-by-step explanation: Always factor by x^2 while using the AC method.
Hope this helped you! :D
Dos familias asisten a un sitio de comidas rápidas de la ciudad, una de ellas pide 4 perros calientes y 3 hamburguesas y pagan 43000 pesos, la otra familia, piden 5 perros calientes y 1 hamburguesa y pagan 34500 pesos, se desea saber ¿cuál es el valor de cada perro y de cada hamburguesa?.
Answer:
Cada perro caliente cuesta 5,500 pesos y cada hamburguesa cuesta 7,000 pesos.
Step-by-step explanation:
Sea x el precio de los perros calientes y y el precio de las hamburguesas.
Escribiendo los datos de la primera familia en forma de ecuación tenemos:
[tex]4x+3y=43,000[/tex] (4 perros calientes y 3 hamburguesas cuestan 43,000 pesos)
Escribiendo los datos de la segunda familia:
[tex]5x+y=34500[/tex] (5 perros calientes y 1 hamburguesa cuestan 34,500 pesos)
Vamos a resolver este sistema de ecuaciones por el método de suma y resta:
[tex]4x+3y=43,000\\5x+y= 34,500[/tex]
Multiplicando la segunda ecuación por -3 y sumando ambas tenemos:
[tex]4x+3y=43,000\\-15x-3y= -103,500\\\\-11x=-60,500\\x=-60,500/-11\\x= 5,500[/tex]
Por lo tanto, un perro caliente cuesta 5,500 pesos.
Ahora sustituimos este valor en nuestra segunda ecuación para encontrar el precio de las hamburguesas:
[tex]5x+y=34500\\5(5,500)+y=34,500\\27,500 +y=34,500\\y=34,500-27,500\\y=7,000[/tex]
Por lo tanto, las hamburguesas cuestan 7,000 pesos cada una
If (ax+b)(bx+a)=26x^2+ Box(x) +26, where a, b, and Box are distinct integers, what is the minimum possible value of Box, the coefficient of x?
Question in latex: If $(ax+b)(bx+a)=26x^2+\Box\cdot x+26$, where $a$, $b$, and $\Box$ are distinct integers, what is the minimum possible value of $\Box$, the coefficient of $x$?
Answer:
16.59
Step-by-step explanation:
Given:
[tex](ax+b)(bx+a)=26x^2+\Box\cdot x+26[/tex]
Expanding the left hand side, we have:
[tex](ax+b)(bx+a)=abx^2+a^2x+b^2x+ab\\=abx^2+(a^2+b^2)x+ab\\=26x^2+\Box\cdot x+26\\ab=26 \implies b=\frac{26}{a}[/tex]
Therefore:
[tex]a^2+b^2=a^2+\dfrac{26}{a} =\dfrac{a^3+26}{a}[/tex]
To find the minimum value, we take the derivative and solve for its critical point.
[tex]\frac{d}{da} (\frac{a^3+26}{a})=\frac{2a^3-26}{a^2}\\$Setting the derivative equal to zero, we have:\\2a^3-26=0\\2a^3=26\\a^3=13\\a=\sqrt[3]{13}[/tex]
Recall that:
[tex]\Box=a^2+b^2=\dfrac{(\sqrt[3]{13}) ^3+26}{\sqrt[3]{13}}\\=\dfrac{13+26}{\sqrt[3]{13}}\\\\\Box=16.59[/tex]
The minimum possible value of the coefficient of x is 16.59.
Answer:
173
Step-by-step explanation:
For sympliciy let the box equal y.
Expanding the left side we get (a*x+b)(b*x+a) = (a*b*(x)^2 + (a^2 + b^2)x + a*b). Hence we have that (a*b*(x)^2 + (a^2 + b^2)x + a*b) = 26*(x)^2 + x*y + 26. Scince the coefficients of like terms in our equation must be equal, ab=26. Hence (a,b) = (1,26),(26,1),(-1,-26),(-26,-1),(2,13),(13,2),(-2,-13),(-13,-2). Since a^2 + b^2 = y we can see that the only 2 values of y are 677 and 173 (by simply plug in the values of (a,b)), taking the smaller of the two our answer is [173].
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
2+2 what does it 1+!
Answer:
4 AND 2
Step-by-step explanation:
Answer:
Hello!
______________________
This question is very easy.
2 + 2 = 4
1 + 1 = 2
Step-by-step explanation: Add.
Hope this helped you!
Can anyone help with this?
Answer:
115/5 23 so 20% =23 23x4 =92
please i know the awnser is 60 but i cant explain it
Answer:
a) 60 degrees
Step-by-step explanation:
b) The triangle shown is an equilateral triangle as all the sides are the same. This means that all the angles are the same as well.
Angles in a triangle add up to 180 degrees. There are 3 angles. Each angle is 60 degrees.
Angle x is an exterior corresponding angle and hence, that is why x = 60 degrees.
hope this helps : )Answer:
All of the measures of the interior angles of an equilateral triangle are 60°. Because x and 60° are alternate interior angles of parallel lines, this means that they are equal, therefore x = 60°.
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
What is the equation of a horizontal line that passes
through the point (-4, -5)?
Answer: y=-5
Step-by-step explanation:
A horizontal line appears on the graph if it goes through the y-axis. Knowing this, the coordinate tells us that the y-coordinate is -5. This tells us that the equation of the line is y=-5.
Urgent ‼️50 POINTS NO BS OR I WILL REPORT YOU Why is partitioning a directed line segment into a ratio of 1:3 not the same as finding 1/3 the length of the directed line segment?
Answer:
3rd option
Step-by-step explanation:
The ratio of 1:3 mean that one part is 1 to the other part being 3.
That means the total is 1 + 3 = 4.
1 part to 3 parts is the same as 1 part to a whole of 4 and 3 parts to a whole of 4.
Answer: 3rd option
Answer:
The ratio given is part to part. The total number of parts in the whole is 1 + 3 = 4.
Step-by-step explanation:
I like to call the numbers in the ratio 1 : 3 "ratio units".
That is, the short length is 1 ratio unit long, and the longer length is 3 ratio units long. The total (whole) length is 1+3 = 4 ratio units long. Then the short length (1 ratio unit) is 1/4 of the whole length (4 ratio units).
_____
Coment on the answer wording
I think you need to be careful with terminology. The word "part" has a different meaning in the first answer sentence "... part to part" than it does in the second answer sentence "... parts in the whole ...".
In the first sentence, it refers to "a piece of the line, no matter its length." In the second sentence, it refers to "that length of the line represented by 1 in the ratio."
Find the area of a trapezoid with bases of 5 feet and a 7 feet, and a height of 3 feet a. 18 b. 36 c. 72 d. 40
Answer:
The answer is option A. 18Step-by-step explanation:
Area of a trapezoid = 1/2(a + b) × h
where
h is the height
a and b are the other sides
From the question
h = 3 feet
a = 5 feet
b = 7 feet
Area = 1/2(5+7) × 3
= 1/2 ( 12) × 3
= 6 × 3
The answer is
= 18
Hope this helps you.
Find the total surface area of this triangular prism...
Answer:
144 cm^2
Step-by-step explanation:
8x6+4x10+4x8+4x6
48+40+32+24
80+40+24
120+24
144