The length of the opposite side of a right triangle is 2cm longer than the length of the adjacent side. The hypotenuse is 4cm longer than the adjacent side. Use a quadratic equation to determine the perimeter of the triangle.
PLEASE HELP
Answer:
Step-by-step explanation:
Let x be the adjacent side length in cm
opposite side is x + 2 cm
hypotenuse is x + 4 cm
x² + (x + 2)² = (x + 4)²
x² + (x² + 4x + 4) = (x² + 8x + 16)
x² - 4x - 12 = 0
(x - 6)(x + 2) = 0
so either
x - 6 = 0 x = 6
or
x + 2 = 0 x = -2
positive answer is x = 6 as negative length does not make sense
opposite side is 6 + 2 = 8
hypotenuse is 6 + 4 = 10
perimeter is 6 + 8 + 10 = 24 cm
To prepare for a wedding, Aiden bught 60 candles. He paid $0.37 for each candle. His sister bought 170 candles at a sale where she paid $0.05 less for each candle than Aiden did. How much did Aiden spend on candles, how much did his sister spend on candles, and who spent more on candles (how much more when you answer this question).
Answer:
Aiden spent $22.20. His sister spent $54.40. His sister spent $32.20 more than Aiden.
Step-by-step explanation:
Answer each part. If necessary, round your answers to the nearest hundredth. (a) A color printer prints 9 pages in 3 minutes. How many pages does it print per minute? | pages per minute (b) At Hoffman's Bike Rentals, it costs $37 to rent a bike for 7 hours. How many hours of bike use does a customer get per dollar? hours per dollar
Answer:
Q1: 3 pages per minute
Step-by-step explanation:
time = 3 minutes
pages = 9 pages
answer = 9 divided by 3 = 3
Answer:
3 pages per minute
1 hour per $5.29
Step-by-step explanation:
9÷3= 3
37÷7= 5.29
0.03249 in standard form to 3 significant figures is
(A) 3.24 × 10−1
(B) 3.24 × 10−2
(C) 3.25 × 10−2
(D) 3.25 × 10−3
In order to meet ADA (Americans with Disabilities Act) requirements, a wheelchair ramp must have an angle of elevation of no more than 4.8. . A builder needs to install a ramp to reach a door that is 2.5 feet off the ground.Is 20 feet long enough for the straight line distance of the ramp to meet the requirements? What angle of elevation will this ramp have?
Answer:
Yes, 35 feet is enough
The angle of elevation is 4.1º
can someone please tell me whether the answer is a, or b? or if it’s none of those. ty :)
The area of the rectangular roof on a dollhouse is 756 square inches. The length of the roof is 108 inches. How many inches wide is the roof?
Answer:
7 inches
Step-by-step explanation:
756÷108=7
that's about it, but I just divided the area and length.
I NEED HELP WITH PRECALC PLEASE
Answer: First question: D, Second question: A
Step-by-step explanation:
Note: I'm not so good at expanding so I'll just solve it :)
So this leaves either C or D
Apply the sum rule:
8-70=-62
The only one that gives a negative sum is D
For the second picture, the one you have chosen is correct
a1 = 3 and r = -5 so:
an = 3/5 * (-5)^n
Plugging in 8 for n (the first choice) we get the given term: -234,375
Answer:
(d) 2 +(-5) +(-12) +... (a) a8Step-by-step explanation:
1.Putting n = 0 and n = 1 into the expression being summed will show you which series is correct.
2 -7n for n=0 is 2 -7·0 = 2
2 -7n for n=1 is 2 -7·1 = -5
The series of the last choice (d) is correct.
__
2.The given sequence is exponential with a first term of 3 and a common ratio if -5. Then the n-th term is ...
an = 3(-5)^(n -1)
We want to find n for an = -234,375.
-234375 = 3(-5)^(n-1)
-78125 = (-5)^(n-1)
For n to be a real number, we must have n even. In that case, the value of n is equivalent to the value that is the solution to ...
78125 = 5^(n -1)
Taking logs of both sides, we get ...
log(78125) = (n -1)·log(5)
log(78125)/log(5) = n -1 . . . . . . . . . . . . divide by log(5)
n = 1 +log(78125)/log(5) = 1 +7 = 8 . . . add 1 and evaluate
-234,375 is the 8th term of the sequence.
If 18 is subtracted from twice the square of an integer, the result is equal to nine times the integer. What is the value of the integer?
Answer:
6 or -1.5
Step-by-step explanation:
We can let this integer be x.
Therefore, according to the question we have:
[tex]2x^2-18=9x[/tex]
Subtracting 9x, we have a quadratic:
[tex]2x^2-9x-18=0[/tex]
Plugging into the quadratic equation:
[tex]\frac{9+\sqrt{81+144}}{4}, \frac{9-\sqrt{81+144}}{4},[/tex]
the square root of 81+144 is 15, so the answer is either 6 or -1.5
f(x)=x^2-12x+20
a. f(0) = ?
b. f(2) = ?
c. f(x) = 0,x = ?
d. f(x)= 9,x = ?
Answer:
c . f(x)=0,x=????????????
Is it possible to have a bounded feasible region that does not optimize an objective function?
It is not possible to have a bounded feasible region that does not optimize an objective function.
What is the feasible region?The viable zone is the common area that the linear programming problem's constraints all dictate.
There is an optimum value of the objective function if the feasible region is bounded and the function attains its optimum values at the extremes of the feasible region.
Hence, it is not possible to have a bounded feasible region that does not optimize an objective function.
Learn more about the feasible region:
https://brainly.com/question/29314086
#SPJ2
joey’s town voted on a new speed limit . 40 % of the 25 votes were in favor of the new speed limit . How many votes were in favor ?
Step-by-step explanation:
I don't know the answer really
CAN SOMEONE TELL ME IF I CLICKED THE RIGHT AWNSER PLEASE
Answer:
yes your absolutely right
Step-by-step explanation:
you just are
How do u solve this?
Answer:
first you need a problem to solve.
Step-by-step explanation:
what is the question here?
Which statement is true about point Y?
Point Y is the center of the circle that passes through points D, F, and N.
Point Y is the center of the circle that passes through points M, N, and E.
Point Y is the center of the circle that passes through points L, M, and N.
Point Y is the center of the circle that passes through points D, E, and F.
Answer:
D, E and F
Step-by-step explanation:
Beause y is a point. It is a prime example physics.
Pls help!! What is the equation for the line in slope-intercept form
Answer:
y = -4x + 9
Step-by-step explanation:
using any two points, in this case (0, 5) and (3, -7) you can find slope by using this formula: [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
plug in the x- and y- values of the two points above
[tex]m=\frac{-7-5}{3-0}=\frac{-12}{3}=-4[/tex]
y = -4x + b
use any point of the line and plug it into the equation above
5 = -4(0) + b
5 = -4 + b
5 + 4 = -4 + b +4
9 = b
the equation in full is y = -4x +9
A television is advertised as having a 65-inch measurement. Brenan measures the width of the television while at the store and finds that it is 57 inches wide.
If the space where Brenan plans to hang the television is 32 inches high, will he have enough vertical space to hang the 65-inch television?
Answer: the answer would be C
Yes, the television is approximately 8 inches shorter than the space.
Step-by-step explanation: My name is Ebenezer Haile
Help as soon as possible
Marisol has 5 times as many books as jerry. Jerry has 15 books. How many more books does marisol have
Answer:
5 times more books
Step-by-step explanation:
In total Marisol has 75 books. She has 5 times as many books and Jerry has 15. 5*15=75
PLZ HURRY IT'S URGENT!!!
What is the value of x? Leave answer in **simplest radical form.***
options:
4
4√3
8
8√3
Stuck on this, need help on this.
Answer:
Domain: (-∞ , ∞)
Range: y <= 8 [8 , -∞)
Step-by-step explanation:
x = 2
f(x) = 8
x<=2
f(x) <=8
Please help solve for a in the equation in the photo
[tex]\huge\bf Question:—[/tex]
[tex] \sf \longmapsto \: g=a(4− {d}^{2} )[/tex]
[tex]\huge\bf Solution:—[/tex]
[tex] \underline{\bf \: Flip \: the \: equation:—}[/tex]
[tex] \sf \longmapsto \: −a {d}^{2} +4a=g[/tex]
[tex] \underline{\bf \: Factor \: out \: variable \: (a):—}[/tex]
[tex] \sf \longmapsto \: a(− {d}^{2} +4)=g[/tex]
[tex]\underline{ \bf \: Divide \: both \: sides \: by -d^2+4 :—} [/tex]
[tex]\sf \longmapsto \: \dfrac{a( - {d}^{2} + 4) }{ { - d ^2+ 4}^{} } = \dfrac{g}{{ - d ^2+ 4}^{}} [/tex]
[tex]\sf \longmapsto \:1 a = \dfrac{g}{{ - d^2 + 4}^{}} [/tex]
[tex]\underline{\bf Answer:—}[/tex]
[tex]\boxed{ \bf \: a = \dfrac{g}{ - d^2 + {4}^{} } }[/tex]
Answer:
[tex]\boxed{\boxed{\sf a=\cfrac{G}{4-d^2} }}[/tex]
Step-by-step explanation:
[tex]\sf G=a(4-d^2)[/tex]
Use the Distributive Property to multiply a by (4-d^2):
[tex]\sf G=4a-ad^2[/tex]
Now, we'll swap sides so that all variable terms are on the left hand side.
[tex]\sf 4a-ad^2=G[/tex]
Combine like terms:
[tex]\sf (4-d^2)\:a =G[/tex]
Divide both sides by 4-d^2:
[tex]\sf \cfrac{(4-d^2)a}{4-d^2} =\cfrac{G}{4-d^2}[/tex]
Dividing by 4-d^2 undoes the multiplication by 4-d^2.
[tex]\sf a=\cfrac{G}{4-d^2}[/tex]
_______________________________________
Jason stands in the corner of a very large field. He walks, on a bearing of 030°,
a distance of d metres. Jason then changes direction and walks twice as far on a new
bearing of 120°. At the end of the walk Jason calculates both the distance he must
walk and the bearing required to return to his original position. Given that the total
distance walked is 120 metres, what answers will Jason get if he is correct?
Answer:
Step-by-step explanation:
d + 2d = 120
3d = 120
d = 40 m
east distance was 40cos30 + 80cos120 = -5.35898 m
north distance was 40sin30 + 80sin120 = 89.282032
as 30° and 120° bearings are 90° apart, Jason needs to walk
D = √(d² + (2d)²) = d√5 or 40√5 meters or about 89.44 m to return to his original position.
we could also use √(-5.35898² + 89.282032²) = 89.44 m
direction will be
θ = arctan -89.28/5.359 = -86.565° or a bearing of 273.4°
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
Use the quadratic formula to solve the equation.
X^2 - 7x – 6 = 0
Step-by-step explanation:
[tex]x = \frac{ - b + - \sqrt{ {b}^{2} - 4ac} }{2a} [/tex]
a=1.
b=-7
c=-6
x=
[tex] \frac{ - ( - 7) + \sqrt{ (- 7)^{2} - 4(1)( - 6)} }{2(1)} [/tex]
OR
[tex] \frac{ - ( - 7) - \sqrt{ (- 7) ^{2} - 4(1)( - 6)} }{2(1)} [/tex]
Therefore x= 7,772
OR
x=-0,772
b) How fast should a boy of 40kg mass run so that the kinetic energy becomes 800J?
Answer:
v = 6.32 m/s
Step-by-step explanation:
Given Data:
Mass = m = 40 kg
Kinetic Energy = KE = 800 J
Required:
Speed = v = ?
Formula:
[tex]\displaystyle KE = \frac{1}{2} mv^2[/tex]
Solution:
Rearrange the formula for speed
[tex]\displaystyle v =\sqrt{\frac{2KE}{m} } \\\\Put \ values\\\\v = \sqrt{\frac{2(800)}{40} } \\\\v = \sqrt{2(20) } \\\\v = \sqrt{40} \\\\\boxed{v = 6.32 \ m/s}\\\\\rule[225]{225}{2}[/tex]
Hope this helped!
~AH1807What is equivalent to 56 − 7 + ( 26 − 4 ) ÷ 2
Answer:
60
Step-by-step explanation:
56-7+22÷2
56-7+11
67-7=60
hope it helps thanks
y=(x^4)-(6^3)+(50x^2)+122x=65
find the zeros
[tex]\sf 3x+6y=12[/tex]
Answer:
[tex]3x + 6y = 12[/tex]
[tex]3x + 6y - 6y = 12 - 6y[/tex]
[tex]3x = 12 - 6y[/tex]
[tex] \frac{3x}{3} = \frac{12}{3} - \frac{6y}{3} [/tex]
[tex] \frac{3x}{3} = 1 = x[/tex]
[tex] \frac{12}{3} - \frac{6y}{3} [/tex]
[tex] = \frac{12 - 6y}{3} [/tex]
[tex] = \frac{6(2 - y)}{3} [/tex]
[tex] \frac{6}{3} = 2[/tex]
[tex] = 2( - y + 2)[/tex]
[tex]x = 2( - y + 2)[/tex]
Answer:
x=2(3-y)
Step-by-step explanation:
3x+6y=12
x+2y=4
x=4-2y
=2(2-y)
Judith is getting older and feels like she should donate her collection of stuffed animals to children who are less fortunate. She has 16 stuffed cats and 8 stuffed dogs, which she wants to divide into identical groups, with no stuffed animals left over. What is the greatest number of groups Judith can place her stuffed animals into?
Answer:iojoenckcnurmum
Step-by-step explanation:
the sum of three terms in a GP is 14 and the sum of their squares is 84, find the terms
Answer:
The terms are 2, 4, and 8
Step-by-step explanation:
a+b+c=14
a^2+b^2+c^2=84
Plug in numbers.
3+6+5=14
3^2+6^2+5^2=70
This is too little, meaning the some of the terms have to be larger.
1+7+6=14
1^2+7^2+6^2=86
This is too much, meaning smaller terms are needed.
2+8+4=14
2^2+8^2+4^2=84
This is perfect.