A farmhouse shelters 15 animals. Some are goats and some are ducks. Altogether there are 42 legs. How many of each animal are there? Use the variable g to represent goats Use the variable d to represent ducks
Part A: Create a system of equations that can model this scenario.
Part B: Solve the system of equations Algebraically
Answer:g+d=152
g+2d=30
4g+2d=42
4g+2d-(2g+2d)=42-30
4g+2d-2g-2d =12 2g. =12
g=6
d+6=15
d=15-6
d=9
6 goats and 9 ducks
The number of animals are 6 goats and 9 ducks.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. Unitary method is a technique by which we find the value of a single unit from the value of multiple devices and the value of more than one unit from the value of a single unit. It is a method that we use for most of the calculations in math.
We are given that;
Number of farmhouse shelters=15
Total number of legs=42
Now,
Part A:
Let's use g to represent the number of goats and d to represent the number of ducks in the farmhouse.
We know that there are 15 animals in total, so:
g + d = 15
We also know that goats have 4 legs and ducks have 2 legs, and there are a total of 42 legs:
4g + 2d = 42
Part B:
We can solve this system of equations algebraically by using substitution or elimination.
Substitution Method:
Solve for one variable in terms of the other in one equation, and substitute into the other equation.
Solve for the remaining variable.
From the first equation, we know that:
g = 15 - d
Substitute g = 15 - d into the second equation:
4g + 2d = 42
4(15 - d) + 2d = 42
60 - 4d + 2d = 42
-2d = -18
d = 9
So there are 9 ducks in the farmhouse.
To find the number of goats, substitute d = 9 into g = 15 - d:
g = 15 - 9
g = 6
Therefore, by the unitary method the answer will be 6 goats and 9 ducks
Learn more about the unitary method, please visit the link given below;
https://brainly.com/question/23423168
#SPJ3
Please help!!!!!
Billy and Susie were saving up to buy the new Xbox. Billy got $50 for his birthday and saved $20 each week. Susie already had $25 and saved $40 each week. Write a system of equations to describe this situation.
Answer:
50+ 20x= y
25+ 40x= y
Explanation:
For Billy and Susie, the starting values are $50 and $25. You simply add that to the money saved per week ($20 and $40).
x= number of weeks
What is the degree measure of z
A.29
B.39
C.68
D.41
Answer:
[tex]\Huge\boxed{C.68}[/tex]
Step-by-step explanation:
Hello There!
The exterior angle of a triangle rule is that the exterior angle is equal to the sum of the interior opposite angles
So essentially what I'm saying is that
z = 29 + 39
29+39=68 therefore the measure of angle z is 68
the value of n. 3n = (3^2)8
Answer:
Step-by-step explanation:
3n = 3² × 8 3² = 3 × 3
n × 3 = 3 × 3 × 8 notice a times 3 on both sides of the equation
divide both sides by 3
n = 3 × 8
n = 24 <---------------- FINAL ANSWER
if f(1)= 4 and f(n) = -3f(n-1) then find the value of f(6)
Answer:
-972
Step-by-step explanation:
if f(1)= 4 and f(n) = -3f(n-1) then find the value of f(6)
If f(1)= 4
f(2) = -3f(2-1)
f(2) = -3f(1)
f(2) = -3(4)
f(2) = -12
f(3) = -3f(3-1)
f(3) = -3f(2)
f(3) = -3(-12)
f(3) = 36
f(4) = -3f(4-1)
f(4) = -3f(3)
f(4) = -3(36)
f(4) = -108
f(5) = -3f(5-1)
f(5) = -3f(4)
f(5) = -3(-108)
f(5) = 324
f(6) = -3f(6-1)
f(6) = -3f(5)
f(6) = -3(324)
f(6) = -972
hence the sixth term of the sequence is -972
the equations in the triangle consist of (2x +1) and (5x +5)
The area of a semicircle is 0.2512 square inches. What is the semicircle's radius?
Answer:
0.28277
I got this by plugging in 0.2512 for "A" ( A = π r² ) Then I solved the rest ( divide both sides by pie, then taking the square root from that.
Step-by-step explanation:
Cos Milky Said it.
5x-5=-3+b+(a-1)x
sat math
Answer:
81
Step-by-step explanation:
PLEASE HELP The perimeter of an equilateral triangle is 48 cm . Find the height of the triangle to the nearest whole number please
*UNKNOWN LINKS WILL BE REPORTED
Answer:
17.2 cm
Step-by-step explanation: Each side would be 19 cm since a triangle has three sides. Next, we will use pythagorean theory. Since the equation would be a^2 + b^2 = c^2. Since 19^2 is 361 and is getting subtracted by 64 (we get it because at the bottom, we have to split it. also, 8 squared is 64). Then we get 297, which the base root with one number behind the decimal would be 17.2 cm.
Which equation describes a line with
y-intercept (0,5) that passes through
the point (2, 1)?
Answer:
Step-by-step explanation:
CAN SOMEONE PLEASE HELP ME WITH THIS ASSIGMENT WILL MARK BRAINLIEST
Stephanie adds pennies, nickels and quarters to a scale until the mass of the combined coins is $75$75 grams. Each penny has a mass of $2.5$2.5 grams, each nickel has a mass of $5$5 grams and each quarter has a mass of $5.7$5.7 grams.
Create an equation to model this situation, where $x$x is the number of pennies, $y$y is the number of nickels and $z$z is the number of quarters that Stephanie can put on the scale so that the mass of the combined coins is exactly $75$75 grams.
In AMNP, what is sin M?
12
P
M
5
13
N
Answer:
A
Step-by-step explanation:
triangle ez ez and yes i am smart big brain
(I’m marking brainliest) plzzz help me out!!!
Answer:
14, 16, 18, 20
Step-by-step explanation:
To be labeled as a jumbo egg, the egg is supposed to weigh 2.5 oz. Jandeliz buys a carton of jumbo eggs and measures one of the eggs as 2.4 oz. What is the MEASUREMENT error?
1, 0.96
2. 0.1
3. 0.042
4. 0.04
Answer: 0.04
Step-by-step explanation:
The measurement error is calculated as:
= Error / Ideal value
= (2.5 - 2.4) / 2.5
= 0.1/2.5
= 0.04
Therefore, the correct option is D.
The following graph describes function 1, and the equation below it describes function 2. Determine which function has a greater maximum value, and provide the ordered pair. Function 1 graph of function f of x equals negative x squared plus 8 multiplied by x minus 15 Function 2 f(x) = −x2 + 4x + 1 Function 1 has the larger maximum at (4, 1). Function 1 has the larger maximum at (1, 4). Function 2 has the larger maximum at (2, 5). Function 2 has the larger maximum at (3, 2).
Answer:
wait can we have the graph
Step-by-step explanation:
Answer:
Function 2 has the larger maximum at (2, 5).
Step-by-step explanation:
PLEASE HELP ASAP!! WILL MARK BRAINLIEST
Match the points on
the number line with the rational numbers they represent.
A
B
C
D
E
1.3
-1.7
1.7
-0.8
-0.2
Answer:
A: 1.7
B: 1.3
C: -0.2
D: -0.8
E: -1.7
Step-by-step explanation:
Will mark brainlist plz anwser
Answer:
1,740 is the width.
frist one to do it gets brainist
Answer:
tennis and chess
Step-by-step explanation:
Evaluate without using a calculator (x2y-3)0+x1/3-(4x)1/2 when x = 64 and y = 27. Show work.
Given:
The expression is:
[tex](x^2y-3)^0+x^{\frac{1}{3}}-(4x)^{\frac{1}{2}}[/tex]
To find:
The value of the given expression when [tex]x=64[/tex] and [tex]y=27[/tex].
Solution:
We have,
[tex](x^2y-3)^0+x^{\frac{1}{3}}-(4x)^{\frac{1}{2}}[/tex]
Putting [tex]x=64[/tex] and [tex]y=27[/tex], we get
[tex]=((64)^2(27)-3)^0+(64)^{\frac{1}{3}}-(4(64))^{\frac{1}{2}}[/tex]
It can be written as
[tex]=((64)^2(27)-3)^0+(4^3)^{\frac{1}{3}}-(4)^{\frac{1}{2}}(64)^{\frac{1}{2}}[/tex]
[tex]=1+4-2(8)[/tex] [tex][\because a^0=1,a\neq 0][/tex]
[tex]=5-16[/tex]
[tex]=-11[/tex]
Therefore, the value of the given expression [tex]-11[/tex] when [tex]x=64[/tex] and [tex]y=27[/tex].
Write the sentence as an equation.
306 is equal to 80 subtracted from q
Answer:306 = 80-q is the answer
Plsssssss help i need an answer look in the pic below
Answer:
A. 120 cm²Step-by-step explanation:
10 cm x 12 cm = 120 cm²
For the two right triangles above, explain why a/8=x/12 . What trigonometric ratio is also equal to the two given ratios?
Answer:
sin trigonometry ratio
Step-by-step explanation:
Given
See attachment for triangles
Required
Explain why [tex]\frac{a}{8} = \frac{x}{12}[/tex]
From the attached diagram, both triangles are similar triangles because
(1) the second triangle is a dilation of the first triangle by a ratio of 1.5
i.e
[tex]k = \frac{12}{8}[/tex]
[tex]k = 1.5[/tex]
(2) They have angle 30 degrees, and have their right angles located at the same point
In the first triangle, the sine of 30 degrees is represented as:
[tex]sin(30) = \frac{Opp}{Hyp}[/tex]
This gives:
[tex]sin(30) = \frac{a}{8}[/tex]
In the second triangle:
[tex]sin(30) = \frac{Opp}{Hyp}[/tex]
So:
[tex]sin(30) = \frac{x}{12}[/tex]
By comparison:
[tex]sin(30) = sin(3)[/tex]
Hence:
[tex]\frac{a}{8} = \frac{x}{12}[/tex]
He has 834 cups of chocolate chips. Use the guess, check, and revise strategy to solve the equation 114b=834 to find b, the number of batches of muffins he can make if he uses Recipe 2.
Answer:
vas dir que no sóc jo, sóc una mica, però vull que tornem a casa i ens ocupem de tots els altres
Please helppp me with me ASAP
Answer:
the formula for a triangle is height*base/2
plug it in and you get (3*6)/2=18/2=9
so, the answer is 9 mm2
A box has a volume given by the trinomial x^3 + 4x^2 — 32x. What are the possible dimensions of the box?
Answer:
x(x-4)(x+8)
Step-by-step explanation:
Factor.
x(x^2+4x-32)
x(x-4)(x+8)
A train with a mass of 1570 kg is moving at 3.2 m/s collides with a train at rest with a mass of 1224 kg. They stick together and move as one. What is the velocity of both trains together?
m1V1 + m2V2 = total total
Solve for x in the following diagram. Round your answer to nearest tenth.
Answer:
48.3
Step-by-step explanation:
→ See what side is not given
Opposite
→ Find a triangle with out an O in it
Cos = Adjacent / Hypotenuse
→ Make what you want to find the subject
Hypotenuse = Adjacent / Cos
→ Substitute the numbers into the formula
41 / cos (32) = 48.3
What is the approximate area of the garden?
Answer:
Option D
Step-by-step explanation:
By applying Pythagoras theorem in triangle ABC,
(Hypotenuse)²= (Leg 1)² + (Leg 2)²
AC² = AB² + BC²
AC² = (40 - 15)² + (80 - 75)²
AC² = (25)² + 5²
AC² = 650
AC = √650
AC = 25.495 ft
Since, area of a rectangle = Length × Width
Therefore, area of the garden = 25.495 × 6
= 152.97
≈ 153 ft²
Since, 150 is very close to 153, approximate area of the rectangular garden is 150 ft².
Option D is the answer.
Libby takes a test that has a total possible score of 800. Each question is worth the same
number of points. If she misses 3% of the questions, what is her score?
Answer:
Step-by-step explanation:
800(1-3/100)
800(100-3)/100
800(97)/100
77600/100
776 is her score.