Answers
2l +3t +3b = 156 . . . . . . . 156 meals per day are supplied
l +t = 3b . . . . . . . . . . . . . . there are 3 times as many great cats as bears
l +t +b = 68 . . . . . . . . . . . there are a total of 68 animals
_____
The last 2 equations tell you
.. 4b = 68
.. b = 17
Subtracting 3 times the last equation from the first gives
.. -l = -48
There are 48 lions, 3 tigers, and 17 bears.
Let T = number of tigers
Let B = number of bears
If one lion eats 2 meals per day, then L number of lions eat 2L meals per day.
Tigers eat 3T meals per day, and bears eat 3B meals per day.
In one day, all animals combined ate 156 meals.
That gives us our first equation.
2L + 3T + 3B = 156
The lions and tigers are considered great cats. The bears are not cats.
There are 3 times as many great cats as bears.
This gives us our second equation.
L + T = 3B
In all there are 68 animals in the zoo.
From here we get our third equation.
L + T + B = 68
Our system of equations is:
2L + 3T + 3B = 156
L + T = 3B
L + T + B = 68
Now we solve the system of equations.
Subtract the second equation from the third equation.
B = -3B + 68
4B = 68
B = 17
Substitute B = 17 into the first and second equations.
2L + 3T + 3B = 156
2L + 3T + 3(17) = 156
2L + 3T + 51 = 156
2L + 3T = 105 New Equation A
L + T = 3B
L + T = 3(17)
L + T = 51 Equation B
Equations A and B have only two variables, so we can solve them as a system of two equations in two unknowns.
2L + 3T = 105
L + T = 51
Rewrite equation A. Multiply Equation B by -2 and write underneath Equation A. Then add the equations.
2L + 3T = 105
+ -2L - 2T = -102
-------------------------
T = 3
Now use B = 17 and T = 3 in the original third equation to solve for L.
L + T + B = 68
L + 3 + 17 = 68
L + 20 = 68
L = 48
Answer: There are 48 lions, 3 tigers, and 17 bears
Check:
"Lions eat 2 meals per day, tigers and bears eat 3 meals each per day."
Number of meals:
2 * 48 + 3 * 3 + 3 * 17 = 96 + 9 + 51 = 156
"There are 3 times as many great cats in the zoo as bears."
48 + 3 = 51, and 51 is 3 times 17
"There are 68 animals in the zoo."
48 + 3 + 17 = 68
All statements are satisfied by our solution, so the answer above is correct.
Related Questions
Write an expression to show the sum of fourteen and triple eight.
Answers
Really need help! Been trying to solve for a while.
1. Solve the system by using a table. 3y=4x+7 , -4x-4y=28. These are the possible solutions:(–4, –3),(–3, –4), (4, 3),(3, 4).
2.Solve by graphing. -3x-y=-10, 4x-4y=8. possible solutions:(-1,3), (3-1), (1,3), (3,1)
Answers
-4x - 4y = 28
=========
-7y = 21 ; y = 21/-7 = -3
Substituting value of y in equn 1
4x - 3(-3) = -7
4x +9 = -7
4x = -7 -9
4x = -16
x = -4
Solution : (-4, -3)
-------------------------------------
-3x - y = -10 .... equn 1
4x - 4y = 8 .... equn 2
=========
x - 5y = -2 ; x = 5y - 2
Substituting value of x in equn 1
-3(5y - 2) -y = -10
-15y + 6 -y = -10
-16y = -10 - 6
-16y = -16
y = 1
Substituting value of y in equn 1
-3x - 1 = -10
-3x = -9
x = 3
Solution : (3,1)
help with these two please....
Answers
Answer: fourth choice 6, - 3+3√3 i, and -3 - 3√3 i
Solution:
1) Factor x^3 - 216 as a difference of cubes:
(x)^3 - (6)^3 = (x - 6) (x^2 + 6x + 6^2) = (x - 6) (x^2 + 6x + 36) = 0
3) first factor = 0 => x - 6 = 0 => x = 6
4) second factor = 0 => x^2 + 6x + 36 = 0
Using the quadratic formula:
x = [ - 6 +/- √(6^2 - 4*1*36) ] / (2)
=> x = [ - 6 +/- √ (-108) ] / 2 = -3 +/- 3√3 i
=> x = - 3 + 3√3 and x = - 3 - 3√3 i
Answer: 3, - 3+3√3 i, and -3 - 3√3 i
2) Which is equivalent to (2p^2 + 5pq - q^2) + (p^2 + 3pq - 2q^2) ?
Answer: first option 3p^2 + 8pq - 3q^2
Solution:
1) eliminate parenthesis:
2p^2 + 5pq - q^2 + p^2 + 3pq - 2q^2
2) combine like terms:
2p^2 + p^2 = 3p^2
5pq + 3pq = 8pq
-q^2 - 2q^2 = - 3q^2
3) The result is 3p^2 + 8pq - 3q^2, which is the first option.
Find the supplement to the angle whose measure is 70 degrees. Show all your work
Answers
therefore the sum of our angles will be:
x+70=180
solving for x we get:
x=180-70
x=80°
hence the value of the supplement of 70° is 80°
Your school raise 125% of its fundraising goal. The goal raised $6,750. What was the goal?
Answers
100/x = 125 / 6750
100% is to x and 125 is 6750
100/x = 125/6750 Cross multiply.
100 * 6750 = 125x Divide by 125
100 * 6750 / 125 = x
x = 5400 was the initial goal.
Jason is buying hamburgers and hot dogs for a barbecue. One package of hamburgers costs $10. One package of hotdogs costs $5. He has $60 to spend, and must buy AT LEAST 3 packages of hot dogs.
What 2 inequalities can be used?
Answers
he needs AT LEAST 3 packages of hotdogs
so
[tex]d \geqslant 3[/tex]
each packet costs $5 so he must spend $15 in total on hotdogs
so he can spend NO MORE than $45 on hamburgers so can buy no more than 4 packs of hamburgers
so
[tex]b \leqslant 4[/tex]
Answer:
10x + 5y ≤ 60 & y ≥ 3Step-by-step explanation:
Let x = the number of hamburgers
Let y = the number of hotdogs
Let us first represent the amount of food:
10x + 5y ≤ 60
This means x packages of $10 hamburgers plus y packages of $5 hotdogs is greater than or equal to $60.
However, we have also been given another important piece of information and that is that he must buy at least three packages of hotdogs.
y ≥ 3
this means that the packages of hotdogs must be no less than 3.
Hence or two inequalities are 10x + 5y ≤ 60 & y ≥ 3.
This also means that the least he can spend on hotdogs is $15. The most he can spend on hamburgers is $45, meaning the most packages of hamburgers he can get is 4
PLEASE MARK BRAINLIEST
If y is directly proportional to x and y is 12 when x = 10, what is the constant of variation?
Answers
constant of variation = 1.2
Explanation:
y varies directly with x means that as x increases, y increases and vice versa.
This can be translated into the following equation:
y = kx
where k is the constant of pvariation.
We are given that:
y = 12 when x = 10.
Therefore, we will substitute with these values in the above equation and solve for k as follows:
y = kx
12 = k * 10
k = 12 / 10
k = 1.2
This means that the equation relating x and y is:
y = 1.2x
where 1.2 is the constant of variation.
Hope this helps :)
Answer:constant of variation = 1.2
Step-by-step explanation:
For model 5, the tip of the blade travels 0.18 mile per revolution. What is the approximate speed, in revolutions per minute,for model 5?
Answers
need the answer tooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo
The approximate speed of model 5's 148-foot blade travels at 0.18 miles per revolution converted to feet is approximately 385.8 revolutions per hour.
To find the number of revolutions per minute for Model 5 with a blade length of 148 feet and a tip speed of 0.18 miles per revolution,
use the following calculation:
First, convert the tip speed from miles to feet:
0.18 miles × 5280 feet per mile = 950.4 feet per revolution
Now, divide this by the length of the blade in feet:
950.4 feet per revolution / 148 feet = 6.43 revolutions per minute
Finally, multiply this by 60 minutes per hour to get the number of revolutions per hour:
6.43 revolutions per minute × 60 minutes per hour = 385.8 revolutions per hour
Therefore, the required speed of model 5 has a blade that makes approximately 385.8 revolutions per hour.
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can you please help me with this I will crown you brainly
Answers
It's identical on both sides.
A soccer ball has a radius of 6 inches, what is the approximate volume of the ball? Pi =3.14 *
Answers
4/3 * 3.14 * 216
4/3 * 678.24
904.32
Answer is 904.32
Select the statements that are true for the graph of y=(x−1)^2(−6)
The vertex is (1, −6) .
The vertex is (−1, −6) .
The graph has a minimum.
The graph has a maximum.
Answers
Hope this helps<3
From the graph of given function, we have vertex (1, -6). Therefore, option A is the correct answer.
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
The given function is y=(x-1)²-6.
Graph the parabola using the direction, vertex, focus, and axis of symmetry.
Direction: Opens Up
Vertex: (1, -6)
Focus: (1, -23/4)
Axis of symmetry: x=1
Directrix: y=-25/4
The coordinate points to plot are (-1, -2), (0, -5), (1, -6), (2, -5) and (3, -2).
Therefore, option A is the correct answer.
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Which sets of the real number system does − 2 belong to?
Answers
Which diagram shows parallel lines cut by a transversal?
Answers
Answer:
The third diagram.
Step-by-step explanation:
When we have two parallel lines cut by a transversal, vertical angles are congruent; alternate interior angles are congruent; alternate exterior angles are congruent; corresponding angles are congruent; and same-side interior angles are supplementary.
In the first diagram, we have two angles on the same side of their respective parallel lines and the same side of the transversal. These are by definition corresponding angles. Since they are not congruent, these lines are not truly parallel.
In the second diagram, we have two angles on opposite sides of the transversal and outside the block of parallel lines. These are by definition alternate exterior angles. Since they are not congruent, these lines are not truly parallel.
In the third diagram, we have two angles inside the block of parallel lines and on the same side of the transversal. These are by definition same-side interior angles. Since they are congruent, these are parallel lines.
The sum of two consecutive integers is 37. Write an equation that models this situation and find the values of the two integers.
Answers
n+n + 1 = 37
2n + 1 = 37
2n = 36
n = 18
n+1 = 19
18 and 19
Hope this helps ^_^
Write an equation of the line that passes through the points (-2,-2) and (0,5)
Answers
PLEASE HELP NOW I ONLY NEED TO KNOW NUMBER 5. 25 POINTS!!!
Points C and D are equidistant from point A. Complete the following table to prove that AEC ≅ AED.
Answers
AC = AD (S) (Points C and D are equidistant from point A)
AE = AE (S) (The two triangle shared the same side)
∠CAE = ∠EAD (A) (This angle is between the two sides that we just proved to be equal)
By SAS,
ΔEAD ≡ ΔEAC
This net folds into a cube. Which two letters appear on opposite faces?
-D and A
-A and E
-C and D
-B and E
Answers
Answer:
- B and EStep-by-step explanation:
If this net folds into a cube, then, when we form the cube, side B and side E becomes opposite sides, because side D and side F would be placed next to side B, having side E as opposite.
Therefore, the right answer is the last choice. Sides B and E appear on opposite sides.
Suppose that a car rental agency charges a fixed amount per day plus an amount per mile for renting a car. heidi rented a car one day and paid $58 for 190 miles. on another day she rented a car from the same agency and paid $86 for 330 miles. find the linear function f(x) (where x is in miles and f(x) is in dollars) that the agency could use to determine its daily rental charges.
Answers
The linear function f (x) hat the agency could use to determine its daily rental charges will be;
⇒ f (x) = 0.2x + 20
Where, f (x) is in dollars and x is in miles.
What is linear expression?
A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power.
Given that;
Heidi rented a car for one day and paid $58 for 190 miles.
And, On another day she paid $86 for 330 miles.
Now,
We find the linear function for f (x), where f (x) is in dollars and x is in miles as;
Here the two situations are given for miles and dollars as;
(190, 58) and (330, 86)
Thus, The linear function with two points (190, 58) and (330, 86) is defined as;
⇒ y - y₁ = (y₂ - y₁)/(x₂ - x₁) (x - x₁)
⇒ y - 58 = (86 - 58) / (330 - 190) (x - 190)
⇒ y - 58 = 28 / 140 (x - 190)
⇒ y - 58 = 1/5 (x - 190)
⇒ y - 58 = 0.2 (x - 190)
⇒ y - 58 = 0.2x - 38
⇒ y = 0.2x - 38 + 58
⇒ y = 0.2x + 20
⇒ f (x) = 0.2x + 20
Thus, The linear function f (x) hat the agency could use to determine its daily rental charges will be;
⇒ f (x) = 0.2x + 20
Where, f (x) is in dollars and x is in miles.
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To determine the daily rental charges at a car rental agency based on fixed and per mile fees, the linear function f(x) is found to be $40 + $0.15 per mile.
Linear function f(x):
Define variables: Let d = daily rental charge, m = per mile charge.Form equations based on given data: $58 = d + 190m and $86 = d + 330m.Solve the system of equations to find f(x): d = $40 and m = $0.15. Therefore, f(x) = 40 + 0.15x.A sphere has a radius of 26 inches. a horizontal plane passes through the center of the sphere describe the cross section formed by the plane and the sphere.
Answers
When a horizontal plane passes through the center of a sphere with a radius of 26 inches, the cross-section formed is a circle with a radius of 26 inches.
let's break down the problem into two parts:
Describe the cross-section: We'll describe the shape formed when a horizontal plane passes through the center of the sphere.
Calculate the dimensions of the cross-section: We'll calculate the dimensions of the cross-section, such as its radius or diameter.
1. Describe the cross-section:
When a horizontal plane passes through the center of a sphere, it divides the sphere into two equal halves. The cross-section formed by this plane and the sphere will be a circle. Since the plane passes through the center of the sphere, the circle will be perfectly centered.
2. Calculate the dimensions of the cross-section:
Since the radius of the sphere is given as 26 inches, the radius of the cross-section (which is also the radius of the circle formed) will also be 26 inches.
So, the cross-section formed by the plane and the sphere is a circle with a radius of 26 inches.
Mr Daniels is organizing a class field trip on a budget of $900.The bus rental costs $600. Mr.daniels will also buy tickets that will cost $9.50 per student. Write an inequality to represent the number students,y, that he can bring on the trip.
Answers
600 fixed amount
9.5 is the variable changing amount and differs among number of students taken
Answer:
y ≤ 31 students
Step-by-step explanation:
The rental cost is a fixed cost that will be incurred irrespective of the number of students embarking on the class field trip. This cost added to the total ticket cost must be less than or equal to the budget.
the total ticket cost for y number of students
= 9.5y
Hence the total cost = 9.5y + 600 ( measured in $)
In inequality form,
9.5y + 600 ≤ 900 (all in $)
9.5y ≤ 900 - 600
9.5y ≤ 300
y ≤ 300/9.5
y ≤ 31 students
A Rectangle launch tray has a length of X centimeters and a width of 15 cm the trays length is at least 20% greater than it's width. right an inequality to represent this situation. suppose X is a whole number find the least possible permitted and the least possible area of the lunch tray
Answers
x-------------> length rectangle launch tray
w------------< width rectangle launch tray------> 15 cm
length is at least 20% greater than it's width
x>=1.2w---------> x>=1.2*15
the answer part a) is
x>=18 ---------------> ( inequality to represent this situation)
part b) suppose X is a whole number find the least possible permitted and the least possible area of the lunch tray
the least possible permitted length is 18 cm
the least possible area of the lunch tray is 18*15=270 cm²
Solve the system of equations using the linear combination method.
{5p−3q=−39
{−2p−3q=3
Enter your answers in the boxes.
Answers
- (-2p - 3q = 3)
==> 7p = -42 ==> p = -6
==> p = -6
-2(-6) - 3q = 3 ==> 12 - 3q = 3
==>p = -6
-3q = 3 - 12 ==> -3q = -9
==> p = -6
q = 3
By solving the equations through linear combination method we are going to get the values of p and q are -6 and three.
What is linear combination method?It is a bit like elimination method of solving equations within which one variable is eliminated so we'll get the worth of another variable.
How to solve an equation?We are having two equations:
5p-3q=-39-------------1
-2p-3q=3---------------2
equation1 * 2 and equation 2 *5
10p-6q=-78
-10p-15q=15
Now add both equations
10p-6q-10p-15q=-78+15
-21q=-63
q=3
Put the worth of q in 1
5p-3(-3)=-39
5p+9=-39
5p=-30
p=-6
Hence the system of equations have the worth of p=-6 and q=3.
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HELP!!!!!!!!!Which geometric series converges?
Answers
The second series does converge. As the sequence continues, the numerator will stay 1 and the denominator will continue to increase. This means the overall fraction gets smaller and smaller, approaching 0. Thus the sum will approach a finite number.
The third series does not converge. As the exponents get larger and larger, the answers will swing to larger positives and larger negatives each time. As the sum goes on, the absolute value of it will get larger and the sign will switch.
The fourth series does not converge. As 2 gets raised to a higher and higher exponent, the product of it and 1/5 will be a larger and larger number. It will approach infinity, not a finite number.
Answer:
its b
Step-by-step explanation:
Nancy randomly scattered one handful of seeds in her garden. The garden is circular and has a radius of 5 feet. Somewhere in the garden is a 2 feet by 2 feet square patch that has especially good soil for the seeds. If it is equally likely for a seed to land anywhere in the garden, what is the probability that a seed will land in the 2 feet by 2 feet square?
Answers
the garden is circular--------------> r=5 ft
Area1=pi*r²=pi*5²=78.50 ft²
path 2 feet by 2 feet square (good soil for the seeds)
Area2=2*2=4 ft²
the probability that a seed will land in the 2 feet by 2 feet square=Area2/Area1
P=4/78.5=0.051 (5.1%)
the answer is 0.051 (5.1%)
The vertex of a quadratic function is located at (1, 4), and the y-intercept of the function is (0, 1). What is the value of a if the function is written in the form y = a(x – h)2 + k?
a=____
Answers
[tex]y=a(x-1)^{2} +4[/tex]
The y-intercept of the parabola is (0,1). Which means for x=0, y=1 for the given parabola. Using these values of x and y in above equation, we can find the value of a for the parabola.
[tex]1=a (0-1)^{2} +4 \\ \\ 1-4=a \\ \\ a=-3[/tex]
The equation of parabola thus becomes:
[tex]y=-3 (x-1)^{2} +4[/tex]
Answer:
-3
Step-by-step explanation:
right on edge
Look at the rational expression below. x^2-4/2-x Which value of x makes the expression undefined?
Answers
Answer:
given rational function is undefined for x = 2
Step-by-step explanation:
The given rational function is
[tex]\frac{x^2-4}{2-x}[/tex]
The rational function is undefined if the denominator is zero.
Hence, the given rational function is undefined if
[tex]2-x=0[/tex]
Solve the equation for x
[tex]x=2[/tex]
Therefore, the given rational function is undefined for x = 2
Gina sells 216 cakes in the ratio small :medium:large 5:7:12. The profit for one medium cake is twice the profit for one small cake. The profit for one large cake is three times the profit for one small cake. Her total profit id £648.45. Work out the profit for one small cake.
Answers
Answer:
£1.31
Step-by-step explanation:
5+7+12=24
216÷24=9
Small=9x5=45
Medium=9x7=63
Large=9x12=108
2x= Medium, Large= 3x, Small=x
Small=45x, Medium= 63x2=126x, Large=108x3=324x
45x+126x+324x=495x
£648.45=495x
£648.45÷495=x
£1.31=x
The profit for one small cake will be £ 1.31. The profit of the one small cake is the amount of benifit obtained to sell one cake.
What is profit?When money generated from a commercial activity exceeds the expenses, costs, and taxes involved in maintaining the activity in question, profit is earned.
The ratio of the small :medium: large cake is 5:7:12.
Let the cake is considered to be x;
The sum of alll the cakes is;
5x+7x+12x=24 x
The total no of cake is 216
Each no of cake is found as;
[tex]\rm 24 x = 216 \\\\ x = 9[/tex]
The number of the small cake;
N(s) = 9 ×5 =45
N(m)=9×7=63
N(l)=9×12=108
Let the small cake is x
The profit for one medium cake is twice the profit for one small cake;
P(m)=2x
P(l)=3x
P(s)=x
The small medium and the large cake according to the new condition will be 45 x,126x,324x respectively.
The sum of all the cakes according to the new condition is found as;
[tex]4s x +126 x+324 c \\\\ 495 x=648.45 \\\\ x=\£ \ 1.31[/tex]
Hence the profit for one small cake will be £ 1.31.
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A square banner has an area of (4x^2-12x+9) square inches. Write an expression for the perimeter of the banner.
Answers
Ans since it is square, then we can take the root of the equation to find on side of the square, which is (2x-3) and by multiplying it by4, we can find the perimeter.
The radius of the bulls-eye of the dartboard is 8 inches. The radius of each concentric circle (there are 4 labeled A, B, C, D from the inside out) is 14 inches more than the radius of the circle inside it. If a dart lands at random on the dartboard, the probability that the dart will hit in area C is what percent?
Answers
The area for B (including the area of A) is A=3.14(8+14)²=1519.76 in².
The area for C (including the areas of A and B) is A=3.14(8+14+14)²=4069.44.
The area for D (including the areas of A, B and C) is A=3.14(8+14+14+14)²=7850 in².
We now need to know how much the ring for circle C takes up. We take the entire area for C and subtract the total area for B (since it includes A):
4069.44-1519.76=2549.68 in².
To find the percent, we divide this amount by the total area of the board, 7850:
2549.68/7850=0.3248
The probability of hitting circle C would be 32.48%.
Charlie used these steps to solve the equation 6x+5=1+2(3x+2)6x+5=1+23x+2. Which choice describes the meaning of his result, 5=5
Answers
[6x+5]=1+2*(3x+2)
[6x+5]=1+2*3x+2 --------> is not correct ------->1+ 2*(3x+2)=1+2*3x+2*2
then
[6x+5]=1+6x+4---------------> [6x+5]=[6x+5]
this equation is an identity, all real numbers are solutions.
Answer:
All values of x make the equation true. It is an infinite solution.