Answer:
Ellie's age is 41, Edna's age is 40, Elsa's age is 42
Step-by-step explanation:
Let Ellie's age be x. Because they're consecutive integers, Edna's age is x-1 and Elsa's age is x+1. Therefore, 3x=123, x=41, so Ellie's age is 41, Edna's age is 40, Elsa's age is 42
Answer:
Edna is 40, Ellie is 41 and Elsa is 42.
Step-by-step explanation:
let Edna be m years old
m - Edna
m+1 - Ellie
m+2 - Elsa
m+m+1+m+2=123
Collect like terms
3m+3=123
3m=123-3
3m=120
Divide through by 3
m=40
Therefore, Edna is m=40 years old
Ellie=m+1=41 years old
Elsa=m+2=42 years old.
If x is increasing at a
rate of 2 units per second,
find the rate of change of theta
at the instant when x= 12 units.
Answer:
[tex]\frac{d\theta}{dt}=-\frac{2}{5}[/tex] at [tex]x=12[/tex]
Step-by-step explanation:
[tex]\frac{dx}{dt}=2[/tex]
[tex]\frac{d\theta}{dt}=?[/tex]
[tex]x=12[/tex]
[tex]cos(\theta)=\frac{adjacent}{hypotenuse}[/tex]
[tex]cos(\theta)=\frac{x}{13}[/tex]
[tex]\frac{d}{dt}cos(\theta)=\frac{d}{dt}\frac{x}{13}[/tex]
[tex]-sin(\theta)\frac{d\theta}{dt}=\frac{1}{13}\frac{dx}{dt}[/tex]
[tex]-sin(\theta)\frac{d\theta}{dt}=\frac{1}{13}(2)[/tex]
[tex]-sin(\theta)\frac{d\theta}{dt}=\frac{2}{13}[/tex]
[tex]\frac{d\theta}{dt}=\frac{2}{-13sin(\theta)}[/tex]
[tex]cos(\theta)=\frac{x}{13}[/tex]
[tex]cos(\theta)=\frac{12}{13}[/tex]
[tex]\theta=cos^{-1}(\frac{12}{13})[/tex]
[tex]\frac{d\theta}{dt}=\frac{2}{-13sin(\theta)}[/tex]
[tex]\frac{d\theta}{dt}=\frac{2}{-13sin(cos^{-1}(\frac{12}{13}))}[/tex]
[tex]\frac{d\theta}{dt}=\frac{2}{-13(\frac{5}{13})}[/tex]
[tex]\frac{d\theta}{dt}=\frac{2}{-5}[/tex]
[tex]\frac{d\theta}{dt}=-\frac{2}{5}[/tex]
The value of θ is given by the inverse sine function, from which the rate of
change of θ with respect to x can be derived.
The rate of change of θ at the instant when x = 12 units is -0.4 rad/sReasons:
[tex]\displaystyle \frac{dx}{dt} = \mathbf{2 \ units \ per \ second}[/tex]
[tex]\displaystyle cos(\theta) = \frac{x}{13}[/tex]
[tex]\displaystyle \theta = arccos \left(\frac{x}{13}\right)[/tex]
[tex]\displaystyle \frac{d}{dx} \theta = \frac{d\left(arccos \left(\frac{x}{13}\right)\right)}{dx} = \mathbf{\frac{\sqrt{169-x^2} }{x^2-169}}[/tex]
Using chain rule of differentiation, we have;
[tex]\displaystyle \frac{d\theta}{dt} = \mathbf{ \frac{d\theta}{dx} \times \frac{dx}{dt}}[/tex]
Therefore;
[tex]\displaystyle \frac{d\theta}{dt} =\frac{\sqrt{169-x^2} }{x^2-169}\times \frac{dx}{dt} = \mathbf{\frac{\sqrt{169-x^2} }{x^2-169}\times 2}[/tex]
When x = 12, we get;
[tex]\displaystyle \frac{d\theta}{dt} =\frac{\sqrt{169-12^2} }{12^2-169}\times 2 = -\frac{2}{5} = -0.4[/tex]
The rate of change of the angle, θ, with time at the instant when x = 12 is -0.4 rad/s
Learn more about rate of change here:
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Find x given the prism has a surface area of 286 in². Explain your thoughts
Answer:
h
=
3
r
=
4
h
=
2
r
=
6
h
=
4
l
=
4
w
=
4
Step-by-step explanation:
Big Sam, an engineer of the Oval Express says: "We blew off a cylinder head an hour after leaving the station and had to continue the trip at three-fifths of the former speed, which brought us in two hours late. If the accident had occurred fifty miles father on, the train would have arrived forty minutes sooner". Based on Sam's description, how long was the run between the two train stations?
A. 150 miles
B. 200 miles
C. 250 miles
D. 300 miles
Answer:
Ig 200 miles
Step-by-step explanation:
I am guessing
James is observing the population of the fish he put into a pond. He built a pond and
populated it with 700 fish. The population of the fish doubles every year.
The exponential equation is given by y = 700(2)ˣ
An exponential function is given by:
y = abˣ
where y, x are variables, a is the initial value of y and b is the multiplier.
Let y represent the population of fish after x hours.
Given that he starts with 700 fishes, hence
a = 700
The population of the fish doubles every year, hence:
b = 2
The exponential equation becomes:
y = 700(2)ˣ
Find out more at: https://brainly.com/question/12490064
hi so my teacher gave me this and i am not sure if i did it right, this is what i put for the first Question
degree = 3
leading coefficient = 1
and the it is the arrows are going up/down so its a odd degree
and i put that the answer is d i did the rest like this please tell me where i went wrong/if i did
Answer:
First, let's look at some polynomials of even degree (specifically, quadratics in the first row of pictures, and quartics in the second row) with positive and negative leading coefficients:❤
Mrs. Harris treated her 1st period with donuts for averaging the highest on the midterm exam. She bought 25 donuts, By the end of the period, there were 3 donuts remaining. What is the percent decrease?
Answer:
88% decrease
Step-by-step explanation:
3 is only 12% of 25 so there was a 88% decrease
7+x÷y is a ______( type of polynomial)
PLEASE ANSWER FOR 30 POINTS
Answer:
One Solution
Step-by-step explanation:
x + 3y = 3
x - y = -3
4y = 6 Subtract to solve by elimination.
y = [tex]\frac{3}{2}[/tex] Divide by 4.
x - [tex]\frac{3}{2}[/tex] = -3 Substitute [tex]\frac{3}{2}[/tex] for y in the original equation.
x = -[tex]\frac{3}{2}[/tex] Add [tex]\frac{3}{2}[/tex].
Planes A and B are shown.
If a new line, p, is drawn parallel to line I, which
statement is true?
ZA
O Line p must be drawn in plane B.
O Line p must be perpendicular to line m.
O Line p must be drawn so that it can lie in the same
plane as line 1
O Line p must be drawn in the same plane as line n.
m
Which item produces the magnetic field in the electromagnet?
A-paperclips
B- a switch
C-paint brushes
D- a magnet
Answer:
Its ethier a switch or magnet
Ms.Gómez ran 3/5 of a mile in 5 minutes. Mr. Hernández ran 3/5 of a mile in 3 minutes. How far did Ms gomez and mr Hernandez each run in 1 minute?
Show work or explain
Answer:
Ms G ran 3/25 mile per minute
Mr H ran 1/5 mile per minute
Step-by-step explanation:
Ms G:
create a proportion from mile/minutes = mile/minutes
let 'm' = amount of miles
3/5÷5 = m÷1
cross-multiply to get:
3/5 = 5m
m = 3/5 × 1/5 = 3/25
Mr H:
3/5÷3 = m÷1
cross-multiply to get:
3/5 = 3m
15m = 3
m = 3/15 or 1/5
Someone help?
Find the problem:
-5x - 16 = 8x - 1
Fix the problem:
?
[tex]-5x -16 = 8x -1\\\\\implies 8x +5x = -16 +1 \\\\\implies 13x = -15\\\\\implies x = -\dfrac{15}{13}[/tex]
what is 1/4 of 5/6???
you search the LCD then you subtracted the top and left the bottom the same
Step-by-step explanation:
im not sure
5(x-a)=3(x+b)
Solve for x
Answer:
[tex]x=\frac{3b}{2} +\frac{5a}{2}[/tex]
Step-by-step explanation:
Answer:
Step-by-step explanation:
5(x - a) = 3(x + b)
5x - 5a = 3x + 3b
2x = 5a + 3b
x = 2.5a + 1.5b
I was absentee and i dont know how to solve it help plz
Answer:
-1/3 or 1/-3 (it doesn't matter which one you pick because its still the same)
Step-by-step explanation:
You find slope by doing rise over run. Its left to right so you start on the left dot and go down one. This makes it -1 because you're going down, not up. You move 3 to the right which makes it positive. Once you do this itll lead you right the the 2nd point. 1 down= -1
3 right= 3
-1/3
What is the change in elevation for
(3)(4)(-3.5)
Hey there!
(3)(4)(-3.5)
= 12(-3.5)
= -42
Therefore, your answer SHOULD be: -42
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
A rocket is launched from a tower. The height of the rocket, y in feet, is related to the time after launch, x in seconds, by the given equation. Using this equation, find the maximum height reached by the rocket, to the nearest tenth of a foot.
y=−16x^2+160x+150
Answer:
Answer below
Step-by-step explanation:
Time can not be negative from any perspective. Hence, the correct answer is 10.16 seconds.
The equation of the path of a rocket is given that is y= x^2 + 153x + 98
We need to determine the time that the rocket will hit the ground.
Now, if the rocket hits the ground after the launching then the overall displacement at the time of hitting the ground will be zero.
Therefore, the value of y is 0.
Thus, -16x^2 +153x + 98 = 0
Now, the formula for finding the roots of the quadratic equation
ax^2 +bx +c = 0 is given as:
[tex]x^{1} =\frac{-b+\sqrt{b^2 -4ac} }{2a}[/tex]
[tex]x^2 = \frac{-b -\sqrt{b^2 -4ac} }{2a}[/tex]
Comparing the expression with the standard form of the equation.
a = -16b = 153 and c = 98
By applying the formula there are two values are come that is,
x^1 = -0.602555
x^2 = 10.1651
Time can not be negative from any perspective.
Hence, the correct answer is 10.16 seconds.
———————————————————————————————————————-
(Hope this helps can I pls have brainlist (crown)☺️)
Which equation below represents an equation in standard form?
Answer:
C
Step-by-step explanation:
standard form is ax + by = c, which is true for the third option.
The variables x and y are directly
related. When x=15, y = 6. What is the
value of x when y = -4?
Work out the area of the shaded shape.
Answer:
61 m²
Step-by-step explanation:
Find the area of the whole rectangle and subtract the part that is cut off
Area = [tex]11 *8 - 9 *(8-5)[/tex]
= [tex]88 - 9*3[/tex]
= [tex]88 - 27[/tex]
= [tex]61[/tex]
Units = m * m or m²
61 m²
-Chetan K
The hypotenuse is NOT located across from the right angle
True or false
The statement, The hypotenuse is NOT located across from the right angle is false.
What is a right angled triangle?
A right-angled triangle is a type of triangle that has an angle that measures 90 degrees. The triangle has three sides. The hypotenuse is the longest side of a right-angled triangle. Other sides are the base and the length. The sum of sides in a a right-angled triangle is 180 degrees.
Please find attached an image of a right-angled triangle. To learn more about a triangle, please check: https://brainly.com/question/9329354
Pls answer will give brainiest
Answer:
8/15
Step-by-step explanation:
1/5 + 1/3 = 3/15 + 5/15 = 8/15
7. (6 points) For the following geometric sequence, 3 ,- 1, 1/3,-1/9, …
Find the formula for the nth term
Answer:
The formula of the nth term is a₇=48(1/2)⁷⁻¹=48×1/64=3/4
Step-by-step explanation:
A shed has dimensions of 12m in length and 5 m in width. Both the length and width are increased by the same amount in order to increase the floor area by more than double the original area?
The amount by which the length and width of a shed can be increased to
more than double the area, depends on the initial dimensions.
The amount that can be added to both the length and the width to increase the floor area by more than double the original area is more than 3 meters.Reasons:
The given parameters of the shed are;
The length of the shed = 12 m
Width of the shed = 5 m
The amount by which the length and the width are increased = The same amount
The new area after the increase in the length and width of the shed = More than double the initial area
Required:
The amount of increase in the length.
Solution:
Let the amount by which the length and width are increased = x
We have;
Initial area of the shed = 12 m × 5 m = 60 m²
The new area = (12 + x) × (5 + x) > 2 × 60
By multiplication, we get;
(12 + x) × (5 + x) = x² + 17·x + 60 > 2 × 60 = 120
x² + 17·x + 60 - 120 > 120 - 120 = 0
x² + 17·x - 60 > 0
By factorization, we get;
(x + 20)·(x - 3) > 0
x > -20, or x > 3
The increase (positive) amount of the solution is x > 3
Therefore, the amount by which both the length and the width can be increased to more than double the area is x > 3 meters
Learn more about the area of a rectangle here:
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What is the mean , median , and sum
Step-by-step explanation:
sum was the first name of integral
and the median is something in the middle
for example :
A . B . C
the median is B
The Kicking Cacti and the Sprinting Stingrays met in their town's annual kickball championship this year. They were so evenly matched that the game lasted 11 innings! The Stingrays had 3 pitchers, and each of them pitched for the same number of innings.
How long did each of the pitchers for the Stingrays pitch?
Answer:
11/3 = 3 2/3 innings
Step-by-step explanation:
3 pitchers = 11 innings
1 pitcher = x innings
in the first equation, divide both sides by 3 to get 1 pitcher on one side
1 pitcher = 11/3 innings = 3 2/3 innings
A CD is on sale for $100.00. The sales tax rate is 6%. How much will the total cost be for the CD
Answer: $106.00
Step-by-step explanation:
88, 89, 86, 90, 83, 81, 89
What is the median number
A 88
B. 89
C 90
D. 86
Please answer this I really need help
Answer:
The answer is 90.
Step-by-step explanation:
90 is in the middle
Answer:
d
Step-by-step explanation:
cause i said so
What is the mass of an object that has 50 newtons of force and is accelerating at the rate of 2 m/s/s
HELP PLEASE!! Do not explain need full answer
Answer:
F= ma
m = F/a
m = 50/2
m = 25
Answer equal 25
Help me with this question thanks so much
