Answer:
5,424 ft.
Step-by-step explanation:
For every 1 foot the ski lift goes up by, it travels west 4 feet. So, because we know that the lift will be 1,356 feet higher at the top of the mountain, all we have to do is multiple 1,356 by 4.
1,356 * 4 = 5,424 ft.
I hope this helps. :)
You buy a used car for $20,000. It depreciates at the rate of 21% per year. Find the value of the car for the given years.
A. 5 years.
B. 8 years.
Answer:
a is 840 ,b is 525
Step-by-step explanation:
At the end of each year, its value is down to 79%, which is 0.79 times its value at the start of the year. Keep this up for n years and the value is
V(n) = $20,000 (0.79)n,
where n is the number of years elapsed from when the value was $20,000. Just plug in n=5 and n=8, evaluate, and get your 2 answers.
Answer:
A. 5 years
Step-by-step explanation:
21% of 20,000 is 4200, mutiply that by 5 and get $20,000
PLEASE HELP HURRY!! What is the value of x?
The question is Find the constant of proportionality in the graph below
Answer:
4.5
Step-by-step explanation:
Graph a scatter plot using the given data.
Answer:
Here is the answer.
Step-by-step explanation:
HELP IT'S URGENT.
Please show workings.
No 4 (see image)
Answer:
(i) (b² - 2ac)/c²(ii) (3abc - b³)/a³Step-by-step explanation:
α and β are the roots of the equation:
ax² + bx + c = 0Sum of the roots is:
α + b = -b/aProduct of the roots is:
αβ = c/aSolving the following expressions:
(i)
1/α² + 1/β² =(α² + β²) / α²β² =((α + β)² - 2αβ) / (αβ)² = ((-b/a)² - 2c/a) / (c/a)² = (b²/a² - 2c/a) * a²/c² = b²/c² - 2ac/c² =(b² - 2ac)/c²----------------
(ii)
α³ + β³ =(α + β)(α² - αβ + β²) =(α + β)((α + β)² - 3αβ) = (α + β)³ - 3αβ(α + β) =(-b/a)³ - 3(c/a)(-b/a) =-b³/a³ + 3bc/a²= 3abc/a³ - b³/a³=(3abc - b³)/a³[tex] \huge \underline{\tt Question} :[/tex]
If α and β are the roots of the equation ax² + bx + c = 0, where a, b and c are constants such that a ≠ 0, find in terms of a, b and c expressions for :
[tex] \tt \dfrac{1}{\alpha ^2} + \dfrac{1}{\beta ^2}[/tex]α³ + β³[tex] \\ [/tex]
[tex] \huge \underline{\tt Answer} :[/tex]
[tex] \bf \dfrac{1}{\alpha ^2} + \dfrac{1}{\beta ^2} = \dfrac{b^2 - 2ac}{c^2 }[/tex][tex] \bf \alpha ^3 + \beta ^3 = \dfrac{ - b^3 + 3abc}{a^3}[/tex][tex] \\ [/tex]
[tex] \huge \underline{\tt Explanation} :[/tex]
As, α and β are the roots of the equation ax² + bx + c = 0
We know that :
[tex] \underline{\boxed{\bf{Sum \: of \: roots = \dfrac{- coefficient \: of \: x}{coefficient \: of \: x^2}}}}[/tex][tex] \underline{\boxed{\bf{Product \: of \: roots = \dfrac{constant \: term}{coefficient \: of \: x^2}}}}[/tex][tex] \tt : \implies \alpha + \beta = \dfrac{-b}{a}[/tex]
and
[tex] \tt : \implies \alpha\beta = \dfrac{c}{a}[/tex]
[tex] \\ [/tex]
Now, let's solve given values :
[tex] \bf \: \: \: \: 1. \: \dfrac{1}{\alpha ^2} + \dfrac{1}{\beta ^2}[/tex]
[tex] \tt : \implies \dfrac{\beta ^2 + \alpha ^2}{\alpha ^2 \beta ^2}[/tex]
[tex] \tt : \implies \dfrac{\alpha ^2 + \beta ^2}{\alpha ^2 \beta ^2}[/tex]
[tex] \\ [/tex]
Now, by using identity :
[tex] \underline{\boxed{\bf{a^2+ b^2 = (a+b)^2 -2ab}}}[/tex][tex] \tt : \implies \dfrac{(\alpha + \beta)^2 - 2 \alpha\beta}{(\alpha\beta)^2}[/tex]
[tex] \\ [/tex]
Now, by substituting values of :
[tex] \underline{\boxed{\bf{\alpha + \beta = \dfrac{-b}{a}}}}[/tex][tex] \underline{\boxed{\bf{\alpha\beta = \dfrac{c}{a}}}}[/tex][tex] \tt : \implies \dfrac{\Bigg(\dfrac{-b}{a}\Bigg)^2 - 2 \times \dfrac{c}{a}}{\Bigg(\dfrac{c}{a}\Bigg)^2}[/tex]
[tex] \tt : \implies \dfrac{\dfrac{b^2}{a^2} - \dfrac{2c}{a}}{\dfrac{c^2}{a^2}}[/tex]
[tex]\tt : \implies \dfrac{\dfrac{b^2}{a^2} - \dfrac{2ac}{a^{2} }}{\dfrac{c^2}{a^2}}[/tex]
[tex]\tt : \implies \dfrac{\dfrac{b^2 - 2ac}{a^2 }}{\dfrac{c^2}{a^2}}[/tex]
[tex]\tt : \implies \dfrac{b^2 - 2ac}{\cancel{a^2} } \times \dfrac{ \cancel{a^2}}{c^2}[/tex]
[tex]\tt : \implies \dfrac{b^2 - 2ac}{c^2 }[/tex]
[tex] \\ [/tex]
[tex] \underline{\bf Hence, \: \dfrac{1}{\alpha ^2} + \dfrac{1}{\beta ^2} = \dfrac{b^2 - 2ac}{c^2 }}[/tex]
[tex] \\ [/tex]
[tex] \bf \: \: \: \: 2. \: \alpha ^3 + \beta ^3 [/tex]
[tex] \\ [/tex]
By using identity :
[tex] \underline{\boxed{\bf{a^3+ b^3 = (a+b)(a^2 -ab + b^2)}}}[/tex][tex] \tt : \implies (\alpha + \beta)(\alpha ^2 - \alpha\beta + \beta ^2)[/tex]
[tex] \tt : \implies (\alpha + \beta)(\alpha ^2 + \beta ^2 - \alpha\beta)[/tex]
[tex] \\ [/tex]
By using identity :
[tex] \underline{\boxed{\bf{a^2+ b^2 = (a+b)^2 -2ab}}}[/tex][tex] \tt : \implies (\alpha + \beta)(\alpha + \beta)^2 -2 \alpha\beta - \alpha\beta)[/tex]
[tex] \tt : \implies (\alpha + \beta)((\alpha + \beta)^2 -3 \alpha\beta)[/tex]
[tex] \\ [/tex]
Now, by substituting values of :
[tex] \underline{\boxed{\bf{\alpha + \beta = \dfrac{-b}{a}}}}[/tex][tex] \underline{\boxed{\bf{\alpha\beta = \dfrac{c}{a}}}}[/tex][tex] \tt : \implies \Bigg(\dfrac{-b}{a}\Bigg)\Bigg( \bigg(\dfrac{-b}{a} \bigg)^2 -3 \times \dfrac{c}{a}\Bigg)[/tex]
[tex] \tt : \implies \Bigg(\dfrac{-b}{a}\Bigg)\Bigg(\dfrac{b^2}{a^2} - \dfrac{3c}{a}\Bigg)[/tex]
[tex]\tt : \implies \Bigg(\dfrac{-b}{a}\Bigg)\Bigg(\dfrac{b^2}{a^2} - \dfrac{3ac}{a^{2} }\Bigg)[/tex]
[tex]\tt : \implies \Bigg(\dfrac{-b}{a}\Bigg)\Bigg(\dfrac{b^2 - 3ac}{a^2} \Bigg)[/tex]
[tex]\tt : \implies \dfrac{-b}{a} \times \dfrac{b^2 - 3ac}{a^2} [/tex]
[tex]\tt : \implies \dfrac{ - b(b^2 - 3ac)}{a \times a^2} [/tex]
[tex]\tt : \implies \dfrac{ - b^3 + 3abc}{a^3} [/tex]
[tex] \\ [/tex]
[tex] \underline{\bf Hence, \: \alpha ^3 + \beta ^3 = \dfrac{ - b^3 + 3abc}{a^3}}[/tex]
please help i will give brainliest
Answer:
n<-0.6
Step-by-step explanation:
7.2>0.9(n+8.6)
8>n+8.6
-0.6>n
n<-0.6
So there would be an open circle at the point -0.6 (because the "less than" sign shows that -0.6 is not included), and then an arrow pointing left to show solutions that are less than -0.6
I will assume you know what buttons to press.
Answer:
Step-by-step explanation:
7.2>0.9(n+8.6)
n< -0.6
(-∞,-0.6)
open circle on -0.6 and go to the left
does opposites name the same location on a number line.
Answer:
I'm not sure but maybe this will help
Step-by-step explanation:
- 3 and 3 are located on opposite sides of zero. They are the same distance from zero. 3 and -3 are called opposites.
phoebe, andy and polly share €270
phoebe gets three times as much as and who gets twice as much as polly
work out how much they each get
Answer:
Polly=30
Andy=60
Phoebe=180
Step-by-step explanation:
Polly=x
Andy=2x
Phoeby 3(2x)=6x
x+2x+6x=270
9x=270
x=30
Polly=x=30
Andy = 2x=60
Phoebe=6x=180
which number does Not represent 4.701
Answer:
4.702 does not represent 4.701
Step-by-step explanation:
#teamtrees #WAP (Water And Plant)
Answer:
WHAT ARE THE NUMBERS?
Step-by-step explanation:
YOU DIDNT WRITE THEM
PLZ HELP ME ILL GIVE U 20 POINTS!!!!!!!!!!!!!!!!
Answer:
1. y < 4
2. x </= -3
3. y >/= 2
4. x > -2
5. x </= 2
6. x < 0
7. t > -2
8. N >/= 3
9. n < -4
10. x < 5
Step-by-step explanation:
Sally buys a pair of shoes that are discounted 60% off the original price. If Sally pays $50 for the shoes, what was the original price of the shoes?
Answer:
90$
Step-by-step explanation
Step 1: You need to find how much was the 60% discount
Step 2: To find that multiply .6 by 50 you will get 30
Now you know how much was 60% discount
Step 3: Add 30(the discount) + 50(the prce sally pays) = 90 (the oriagnal price)
plz help!! serious answers only
Answer:
line t = -9/8
Step-by-step explanation:
Parallel lines have the same slope, so line t will have a slope of -9/8 as well
what the slope of(-1,8) (8,-4)
Answer:
-4/3
Step-by-step explanation:
I think :\
I like ice cream :D
Answer:
-4/3
Step-by-step explanation:
We can use the slope formula
m = ( y2-y1)/(x2-x1)
= ( -4-8)/(8 - -1)
= ( -4-8)/(8+1)
= -12/9
= -4/3
The function g(x) is a transformation of f(x). If g(x) has a y-intercept of -2, which of the following functions could represent g(x)?
A. g(x) = f(x) - 5
B. g(x) = f(x - 5)
C. g(x) = f(x) - 2
D. g(x) = f(x + 2)
Answer:
A.
Step-by-step explanation:
It just is trust
The bottom of a ladder leaning against a wall is 1.5 m from the bottom of the wall. The ladder is 5.5 m long. Find how high the top of the ladder is above the ground, correct to one decimal place.
A. 5.8 m
B. 5.7 m
C. 5.2 m
D. 5.3 m
Answer: D. 5.3 m
Step-by-step explanation:
The ladder leaning against the wall causes it to forma right angle.
The right angle has two sides , which is the two legs, and the hypotenuse.
Using the formula a^2 + b^2 = c^2 , a and b are the two legs and c is the hypotenuse. In this case, a will be the wall, b will be 1.5 m and the ladder which is 5.5 m will be the hypotenuse.
Input the values for a and c to sole for b using the formula.
1.5^2 + b^2 = 5.5^2
2.25 + b^2 = 30.25
-2.25 -2.25
b^2 = 28
b = [tex]\sqrt{28}[/tex]
b = 5.2915 rounded to one decimal place is the same as rounding it to the nearest tenth, and 5.29 rounded to the nearest tenth is 5.3.
Height of top of ladder above the ground that is resting on the wall, correct to one decimal place is 5.3 m
hence option D is correct.
According to Pythagoras theorem
In a right triangle
[tex]\rm H^2 = P^2 + B^2[/tex]
[tex]\rm P = \sqrt {H^2 - B^2 }.........(1)\\where \\H = Hypotenuse \; of \; right\; triangle\\B = Base\; of \; the \; right\; triangle \\P = Perpendicular \; of \; the\; right\; triangle[/tex]
In the given situation the the ladder forms the right triangle with the wall
Length of the ladder = 5.5 m
Length of the base of ladder from the wall = 1.5 m
Let K be the height of top of ladder above the ground that is resting on the wall.
Hence from equation (1) we can write
[tex]\rm K = \sqrt{5.5^2 - 1.5^2} = \sqrt{28} = 5.291 \approx \bold{5.3}[/tex] m
Height of top of ladder above the ground that is resting on the wall, correct to one decimal place is 5.3 m
hence option D is correct.
For more information please refer to the link given below
https://brainly.com/question/16426393
Need help pls like I really need help
Answer:
4
Step-by-step explanation:
PLZ MARK BRAINLIEST
Answer:
y=1.5x
Step-by-step explanation:
3/2=1.5
9/6=1.5
HELP ASAP WILL MARK BRAINLIEST UTS DUE IN 5!!!
Find the slope of the line.
O -2/5
O 2/5
O 5/2
O None of the above
Answer: 2/5
Step-by-step explanation:
Samantha paid $26.25 for three books that all cost the same amount. What was the cost per book?
Answer:
$8.75 per book
Step-by-step explanation:
26.25/3 = 8.75
Answer:
$8.75
Step-by-step explanation:
26.25 divided by 3 = 8.75
Identify the real and imaginary parts of the given number. Then identify whether the number belongs to each of the following sets: real numbers, imaginary numbers, and complex numbers.
−9 + 9i
The real part of −9 + 9i is ____ and the imaginary part is ____.
The number −9 + 9i belongs to which of the following sets. Select all that apply.
A real numbers
B imaginary numbers
C complex numbers
See image.
Answer:
-9 is real, 9i is imaginary, C
Step-by-step explanation:
-9 is real because you can literally draw nine things.
9i is imaginary because i is √-1 and square roots of negatives are imaginary.
It is complex because complex expressios are written as a+bi.
Which of the following correctly lists the following equations in order from most steep to least steep?
Help please it’s needed!
Hurryyyy
Which system of linear inequalities is graphed?
Answer:
y ≥ 3x-1
x+3y ≤ 6
Step-by-step explanation:
Solving equations with like terms -8 -3y + 2y =32
Answer:
y= -40
Step-by-step explanation:
y= (x + 4)2 + 8
how do you simplify this equation
Answer:
Step-by-step explanation:
you could distribute and combine like terms
y=(x+4)2+8
y=2x+8+8
y=2x+16
Factorize completely
X^2/25-y^2/16
Answer:
16x^2-25y^2/400
Step-by-step explanation:
The 16 and 25 are grouped and both over the 400. I really hope this helps pls consider giving brainliest I would really appreciate it.
One plant container holds 14 seedlings, you have 1,113 seedlings. how many plant containers will hold all the seedlings.
ANSWERS:
A. 79 containers, do not use the remainder
B.80 containers no remainder
C. 85 containers, use the remainder to make 1 more container= 86 total containers (Asking For Little Brother)
Answer: the answer wwas c
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
How would you graph the solution to -5w + 9 = 14 on a number line?
Answer:
Step-by-step explanation:
w= -1
Your circle will be on the -1
Answer:
Taft
Step-by-step explanation:
PLEASEE HELP.!! ILL GIVE BRAINLIEST.!! *EXTRA POINTS* DONT SKIP:((
Answer:
-12
Step-by-step explanation:
Answer:
-12
Step-by-step explanation:
Its -12 for sure!!!!!
1. NC.6.RP.3 An airplane travels at a constant speed of 360 miles per hour. How far, in
miles, will the airplane travel in 45 minutes?
a. 270 miles
b. 16,200 miles
C. 60 miles
d 720 miles
9514 1404 393
Answer:
a. 270 miles
Step-by-step explanation:
In 3/4 of an hour, the plane will fly 3/4 of 360 miles, so 270 miles.
HELP ME PLEASE! how do you write 0.0370 as a scientific notation