A tiger in captivity is fed 13.5 pounds of food an elephant in captivity eats per day. Compare the function by comparing their rates of change.
Answers
SEE ATTACHED IMAGE.
The first thing that we are going to do in this case is to find the slope of the line for the function that simulates the amount of food of the elephant.
We have then:
m = (y2-y1) / (x2-x1)
Substituting any two points:
m = (625-125) / (5-1)
m = 125 pounds / day
125> 13.5
Answer:
The elephant eats more than the tiger daily.
Related Questions
Easy Geometry! Easy Geometry! Easy Geometry!
Answers
b. Linear Pair
c. Definition of supplementary
d. Substitution; Combine like terms
e. Division Property of Equality
f. Definition of Right Angle
g. Definition of Perpendicular
=========================================
Further Explanations:
b. A linear pair is simply a result of cutting a straight angle into two pieces. They are adjacent and supplementary (add to 180 degrees)
c. If two angles are supplementary then they add to 180. This is simply a definition to memorize.
d. The "m < 2" is replaced with "m < 1" through the substitution property. This is possible because of statement (a) on the first line of the proof. The teacher has also combined like terms. Technically this step would require its own line.
e. Think of this as 2x = 180 solving to x = 90. The step done here is dividing both sides by 2, which uses the division property of equality. Alternatively you can use the multiplication property of equality to multiply both sides by 1/2 = 0.5
f. If an angle is 90 degrees, then by definition it is considered a right angle. This is another thing you memorize.
g. Also to be memorized is the fact that if two segments form a right angle, then they are considered perpendicular segments. The upside down T symbol means "perpendicular to"
Answer:
b) Linear Pair
c) Definition of supplementary
d) Substitution; Combine like terms
e) Division Property of Equality
f) Definition of Right Angle
g) Definition of Perpendicular
Ninas car exponentially depreciates at a rate of 7 percent per year. If nina bought the car when it was 6 years old for 12000, what was the original price of the car
Answers
hope this helps
Answer:
[tex] A(6) = 12000 = A_o e^{-0.07 *6}[/tex]
And solving for the initial amount [tex] A_o[/tex] we got:
[tex] A_o = \frac{12000}{e^{-0.07*6}}= 18263.539[/tex]
So then the original price for the car would be approximately 18263.539$
Step-by-step explanation:
For this case we can use the exponential model given by:
[tex] A(t) = A_o e^{bt}[/tex]
Where:
[tex]A_o[/tex] represent the initial amount for the car
[tex]b=-0.07[/tex] represent the exponential growth/decay rate
t represent the number of years. With t =0 at the begin
After 6 year we have that t =6, and we know this condition:
[tex] A(6) = 12000[/tex]
So then we can use the exponential model formula and the condition given and we have this:
[tex] A(6) = 12000 = A_o e^{-0.07 *6}[/tex]
And solving for the initial amount [tex] A_o[/tex] we got:
[tex] A_o = \frac{12000}{e^{-0.07*6}}= 18263.539[/tex]
So then the original price for the car would be approximately 18263.539$
What is the area of a sector with a central angle of π3 radians and a radius of 12.4 m? Use 3.14 for π and round your final answer to the nearest hundredth.
Answers
Answer:
80.47
Step-by-step explanation:
This is correct! :D
Your team gets an ice sculpture in the shape of a basketball. It has a radius of 12 inches. What is the volume of the ice? Use 3.14 for pi. Round your answer to the nearest hundredth.
Answers
The equation would be 4/3 * 3.14 * 12^3.
4/3 * 3.14 * 1728
4/3 * 5425.92
7234.56
The original price of sn item is $25, but after the discount, you only have to pay $18.50. what is the discount (as a percent)?
Answers
The discount is 26%.
What is Discount?The discount equals the difference between the price paid for and it's par value. Discount is a kind of reduction or deduction in the cost price of a product.
Given:
Marked price = $25
Selling price = $18.50
So,
Discount = MP - SP
Discount = 25-18.50
Discount = 6.50
Now,
D% = D/MP *100
D% = 6.5 /25*100
D% = 26%
Hence, the discount percent is 26%.
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What is 59.69 in expanded form
Answers
50 +9 + 0.6+ 0.09
Expanded Factors Form:
5 × 10 +9 × 1 +6 × 0.1+9 × 0.01
Expanded Exponential Form:
5 × 101+9 × 100+6 × 10-1+9 × 10-2
Word Form:
fifty-nine and sixty-nine hundredths
which figures can be precisely defined by using only undefined terms? check all that apply
1) angle
2) arc
3) circle
4) line segment
5) parallel lines
Answers
HELP PLEASE HELP HELP
Answers
The answer is D
Please solve these for me. I need them for a quiz.
Answers
I'm going to use the Substitution method
c = 160 + 67t
55 + 82t = 160 + 67t .... replace c with 55+82t; solve for t
55 + 82t - 55 = 160 + 67t - 55
82t = 67t + 105
82t - 67t = 67t + 105 - 67t
15t = 105
15t/15 = 105/15
t = 7
Use t = 7 to find that
c = 160 + 67t
c = 160 + 67*7
c = 629
You can use the other equation as well to get the same answer for c.
It takes 7 months for the cost to be the same. That cost is $629
===========================================================
4b)
I'm going to use the Elimination method
Subtract the equations to get
x+y = 20
x-4y = -15
-----------
0x+5y = 35
If 5y = 35, then y = 7 after we divide both sides by 5
Plug y = 7 into the first equation and solve for x
x+y = 20
x+7 = 20
x+7-7 = 20-7
x = 13
So x = 13 and y = 7 are the solutions
Max exercises 13 hours a week while Sasha exercises 7 hours a week
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4c)
I'm going to use the Substitution method
x = price for one adult ticket (in dollars)
y = price for one student ticket (in dollars)
Fact #1
4 adult tickets + 2 student tickets = 64 dollars
4x + 2y = 64
Fact #2
3 adult tickets + 3 student tickets = 60 dollars
3x + 3y = 60
3(x + y) = 60
3(x + y)/3 = 60/3
x + y = 20
x + y-x = 20-x ... subtract x from both sides
y = 20 - x
Plug that into the first equation
4x + 2y = 64
4x + 2(y) = 64
4x + 2(20-x) = 64 ... replace y with 20-x; solve for x
4x + 40-2x = 64
2x + 40 = 64
2x + 40-40 = 64-40
2x = 24
2x/2 = 24/2
x = 12
Use x = 12 to find y
y = 20 - x
y = 20 - 12
y = 8
In summary, x = 12 and y = 8, which means...
One adult ticket costs $12
One student ticket cost $8
The area of a playground is 204 yards squared the width of a playground at 5 yards longer than its length whats the length and the width of the playground
Answers
L= length
Area= 204
Area= LW
204 square yards= LW
substitute w=L+5 for w
204= (L)(L+5)
204= L^2 + 5L
subtract 204 from both sides
0= L^2 + 5L - 204
factor
0= (L+17)(L-12)
0= L+17
-17= L
0= L-12
12 yards= L
WIDTH
Since the area cannot be a negative number, we'll use L=12 to find the width.
w=L+5
w=12+5
w=17 yards
CHECK:
204=(12)(17)
204=204
ANSWER: The length is 12 yards and the width is 17 yards.
Hope this helps! :)
Solve for x in the equation x2+20x+100=36
Answers
[tex] x = - 64 \div 22 = -2.909091[/tex]
But if x2 was supposed to be x^2 then the answer is:
[tex]x = - 4.-16[/tex]
Answer:
x = -4 and x = -16.
Step-by-step explanation:
We have the equation,
[tex]x^{2}+20x+100=36[/tex]
i.e. [tex]x^{2}+20x+64=0[/tex]
As the solution of a quadratic equation [tex]ax^{2}+bx+c=0[/tex] is given by [tex]x=\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}[/tex].
On comparing, a = 1, b = 20, c = 64.
So, the solution is,
[tex]x=\frac{-20\pm \sqrt{(20)^{2}-4\times 1\times 64}}{2a\times 1}[/tex].
i.e. [tex]x=\frac{-20\pm \sqrt{400-256}}{2}[/tex].
i.e. [tex]x=\frac{-20\pm \sqrt{144}}{2}[/tex].
i.e. [tex]x=\frac{-20\pm 12}{2}[/tex].
i.e. [tex]x=\frac{-20+12}{2}[/tex] and [tex]x=\frac{-20-12}{2}[/tex].
i.e. [tex]x=\frac{-8}{2}[/tex] and [tex]x=\frac{-32}{2}[/tex].
i.e. x = -4 and x = -16
Thus, the solution of the given equation is x = -4 and x = -16.
Please help out with this question! Thanks :)
Answers
If 11 is among the choices, that is the answer I'd choose.
Amir's checking account charges a $9.75 monthly service fee and a $0.12 per-check fee. If Amir writes 15 checks per month, should he switch to a checking account that charges an $11.50 monthly service fee and no per-check fee
Answers
[tex]0.12(15) = 1.80 [/tex]
[tex]1.80 + 9.75 = 11.55[/tex]
Yes Amir should switch because it's a nickel less
Simplify. −5x4(−3x2+4x−2)
1:−8x^6−x^5−7x^4
2:15x^8−20x^4+10
3:15x^6−20x65+10x64
4:−15x^8−20x^5+10x^4
Answers
Answer:
[tex]15x^{6}-20x^{5}+10x^4)[/tex]
Step-by-step explanation:
We have been given an expression [tex]-5x^4(-3x^2+4x-2)[/tex] and we are asked to simplify our given expression.
We will use distributive property [tex]a(b+c)=a*b+a*c[/tex] to simplify our given expression.
Upon distributing [tex]-5x^4[/tex] we will get,
[tex](-5x^4*-3x^2)+(-5x^4*4x)-(-5x^4*2)[/tex]
Using exponent property [tex]a^b*a^c=a^{b+c}[/tex] we will get,
[tex](15x^{4+2})+(-20x^{4+1})-(-10x^4)[/tex]
[tex](15x^{6})+(-20x^{5})-(-10x^4)[/tex]
[tex]15x^{6}-20x^{5}+10x^4)[/tex]
Therefore, our given expression simplifies to [tex]15x^{6}-20x^{5}+10x^4)[/tex].
The equation y=4.75x+20 gives the cost y of towing a car if the car is towed x miles.
According to to the model, what is the best estimate of the cost for towing a car 22 miles.
A. $24.75
B $46.25
C $104.50
D $124.50
Answers
Answer: $124.50
Step-by-step explanation:
We are given that the equation y=4.75x+20 gives the cost y of towing a car if the car is towed x miles.
To find the best estimate of the cost for towing a car 22 miles., we substitute x= 22 in the above equation, we get
Cost of towing a car 22 miles=[tex]y=4.75(22)+20=[/tex]
[tex]\rightarrow\ y=104.50+20=124.50[/tex]
Therefore, the best estimate of the cost for towing a car 22 miles = $124.50
The perimeter of the rectangle is 34 cm. Find the value of x.
A. 2
B. 17
C. [tex] \frac{34}{33} [/tex]
D. 20
Answers
3x + 11 = 34/2
3x + 11 = 17
3x = 17 - 11
3x = 6
x = 6/3
x = 2
what Is the product? 4n/4n-4*n-1/n+1
Answers
Answer:
n/(n+1) . . . . n ≠ 1
Step-by-step explanation:
As written, there is no product. There is ony the sum ...
[tex]4\dfrac{n}{4}-4n-\dfrac{1}{n}+1[/tex]
With appropriate parentheses, this becomes the product of rational functions ...
... (4n)/(4n-4)·(n-1)/(n+1)
[tex]=\dfrac{4n(n-1)}{4(n-1)(n+1)}=\dfrac{n}{n+1}[/tex]
_____
At n=1, the product has a "hole" where the denominator of the original expression is zero, so the expression is undefined. Hence the domain of the product must be restricted to n≠1 (as well as n≠-1).
Hellllllllłllllllllllllllllllllllllllllllllllpp
Answers
PLEASE HELP I NEED THE ANSWER TO THIS ASAP. YOU JUST NEED TO MATCH EACH THING ON THE LEFT TO ITS CORRECT ANSWER ON THE RIGHT.
Match the following items.
Complete the proof for Theorem 3-13. (if you dont know what this theorem is i added a picture that explains it so you can help)
Answers
But I'll give it a try:
1) l // m ___ Given
2) <1 = <3 ___ if parallel lines, then corresponding angles (<s) are equal
3) <2 = <3 ___ Vertical <s are equal
4) <1 = <2 ___ Substitution
The complete proof of the theorem in chronological order is;
GivenIf lines are ∥, corresponding angles are equal.Vertical angles are equalSubstitutionHow to complete a proof?The proof that when a transversal cut two parallel lines, alternate angles are equal.
1.
Statement: l ∥ m
Reason: Given
2.
Statement: m ∠ 1 = m ∠ 3
Reason: If lines are ∥, corresponding angles are equal.
3.
Statement: m ∠ 2 = m ∠ 3
Reason: Vertical angles are equal
4.
Statement: m ∠ 1 = m ∠ 2
Reason: Substitution
Therefore, alternate exterior angles are equal when a transversal cut two parallel lines,
Read more on vertical angles:
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For the figures below, assume they are made of semicircles, quarter circles and squares. For each shape, find the area and perimeter. Give your answer as a completely simplified exact value in terms of π (no approximations).
Answers
Area of the quarter circle = 1/4 πr²
= 1/4π 12²
= 36π cm²
Area of the triangle = 1/2×base×height
= 1/2 × 12×12
= 72 cm²
Thus the area of the region
= (36π-72) cm²
2. Perimeter of the first figure
The length of the arc AC is 2πr/4
= 2π×12/4
= 6π cm
the length of line AC
√(12² +12²) = 16.97
Thus the perimeter of the figure
= (6π+16.97) cm
3. The are of figure 2
Area of the semi circle πr²/2
= 12²π/2 = 72π cm²
The area of the square
= 24 × 24 =576 cm²
Area of the semi circle = 72 π cm²
Thus the area of the part of the square
= (576-72π) cm²
total area
72π +576-72π
= 576 cm²
4. Perimeter of figure 2
The length of arc AD = (2πr)/2
= 2π×12/2 = 12π cm
but length of arc AD is equal to that of arc BC
Thus arc BC = 12πcm
Therefore, total perimeter
= 12π +12π +24 +24
= (24π +48) cm
Answer:
The perimeter of the first figure is [tex]6\pi +12\sqrt{2}[/tex]
Step-by-step explanation:
Besides that, they got everything right.
helppppppppppppppppppppppppppppp
Answers
We have then:
2 (16x ^ 3y) ^ (1/3) + 4 (54x ^ 6y ^ 5) ^ (1/3)
We then have to use properties of exponents:
4 ((2 ^ (1/3) xy ^ (1/3)) + 12 ((2 ^ (1/3)) x ^ 2y ^ (5/3))
4 ((2 ^ (1/3) xy ^ (1/3)) + 12 ((2 ^ (1/3)) x ^ 2 * y * y ^ (2/3))
We rewrite:
4x ((2y) ^ (1/3)) + 12 * x ^ 2 * y ((2y ^ 2) ^ (1/3))
Answer:
4x ((2y) ^ (1/3)) + 12 * x ^ 2 * y ((2y ^ 2) ^ (1/3))
option 1
With $3500 each, Martin and Edward opened separate accounts. Each account offered 4.5% interest over 10 years. At the end of 10 years, Edward earned more than Martin. Why? A. Edward invested for a different amount of time than Martin. B. Edward had a different interest rate than Martin. C. Edward earned compound interest, and Martin earned simple interest. D. Edward e
Soomeone helpppp meeee
Answers
The interest earned from above cash under simple interest will be:
S.I=(PRT)/100
S.I=3500*4.5/100*10=$1575
the total amount after 10 years will therefore be:
1575+3500
=$5075
The same amount if it was compounded annually, the amount after 10 years will be:
FV=P(1+r/100)^n
FV=3500(1+3.5/100)^10
FV=4,937.10
we therefore conclude that the answer is:
Edward must have earned simple interest while Martin earned compound interest.
The hypotenuse of a right triangle is 50 and the short leg is 30, find the projection of the leg onto the hypotenuse
Answers
CB/CA = CD/CB
30/50 = projection/30
projection = 30^2/50
projection = 18
If the circumference of a circle is 11inches, which is closest to its area?a.380 square inchesb.95 square inchesc.17 square inchesd.35 square inches
Answers
11=6.28*r
r=1.75
A=pi r^2
A=3.14* (1.75)^2=9.625
this number is closer to 17 square inches
look at the pictures bellow
Answers
C=-2
Simplify (3x − 5) − (5x + 1).
−2x + 6
−2x − 6
2x − 6
2x + 6
can you please work this out for me?
thank you verymuch.
Answers
we have been asked to simplify
[tex] (3x-5)-(5x + 1) [/tex]
To Simplify this, we will first open the parenthesis, as below
[tex] (3x-5)-(5x + 1)=3x-5-5x-1\\
\\
\text{take the like terms together and simplify we get}\\
\\
(3x-5)-(5x + 1)=3x-5x-5-1\\
\\
(3x-5)-(5x + 1)=-2x-6\\
\\
[/tex]
Hence the simplified expression is -2x-6
Answer:
-2x-6
Step-by-step explanation:
A chef has less than 25.8 pounds of rice. She takes out 5 pounds to use during the day and stores the rest in containers. Each container has 2.5 pounds of rice. Let x represent the number of containers. What is the maximum number of containers the chef will be able to fill with rice? 13 12 8 7
Answers
The chef has less than 25.8 pounds of rice.
She takes out 5 pounds to use during the day and stores the rest in containers.
Quantity of rice stored = 25.8 - 5 = 20.8 pounds
Each container can store 2.5 pounds of rice.
Let x represent the number of containers.
The number of containers that can be filled = 20.8/2.5 = 8.32
So, the maximum number of containers the chef will be able to fill with rice is 8
Is it possible to toss a coin 20 times and have it land heads-up 20 times? Is this likely to happen? explain.
Answers
A field test for a new exam was given to randomly selected seniors. The exams were graded, and the sample mean and sample standard deviation were calculated. Based on the results, the exam creator claims that on the same exam, nine times out of ten, seniors will have an average score within 6% of 80%.
Is the confidence interval at 90%, 95%, or 99%? What is the margin of error? Calculate the confidence interval and explain what it means in terms of the situation.
Answers
Is the system of equations is consistent, consistent and coincident, or inconsistent?
y=−3x+12y=−6x+2
Select the correct answer from the drop-down menu.
Answers
Coincident is one line on the graph
Consistent is two parallel lines
Answer:
The given system of equations is inconsistent.
Step-by-step explanation:
We have been given a system of equations and we are asked to find whether our given system of equation is consistent, consistent and coincident, or inconsistent.
[tex]y=-3x+12...(1)[/tex]
[tex]y=-6x+2...(2)[/tex]
Since we know that a system of equations is inconsistent if it has no solution. Parallel lines are inconsistent because they do not intersect.
Consistent system of equations can have one or infinitely many solution. As if two lines are same then they will have infinitely many solution. If lines intersect at only one point, then they will have only one solution.
Now let us check slope of given lines.
Upon dividing equation (2) by 2 we will get,
[tex]y=-3x+1...(2)[/tex]
We can see that both lines have slope of negative 3. Since y-intercept of both equations are different, so they will not intersect at any point.
Since our given equations represent parallel lines, therefore, our given system of equations is inconsistent.