Answers
Let the number of chickens = c.
Let the number of pigs = p.
A chicken has 1 head and 2 legs.
c number of chickens have c heads and 2c legs.
A pig has 1 head and 4 legs.
p number of pigs have p heads and 4p legs.
There are 40 heads.
Equation for heads:
c + p = 40
There are 110 legs.
Equation for legs:
2c + 4p = 110
System of equations:
c + p = 40
2c + 4p = 110
Solve the first equation of the system of equations for c:
c = 40 - p
Substitute 40 - p for c in the second equation:
2c + 4p = 110
2(40 - p) + 4p = 110
80 - 2p + 4p = 110
80 + 2p = 110
2p = 30
p = 15
Now substitute p = 15 in the first equation to find c.
c + p = 40
c + 15 = 40
c = 25
There are 25 chickens and 15 pigs.
Related Questions
Jada makes sparkling juice by mixing 2 cups of sparkling water and 3 cups of apple juice.
Let s represent the number of cups of sparkling water and j represent the number of cups of apple juice . Write an equation that shows how s and j are related.
-Please comment equation or explanation.
Answers
Answer:
Step-by-step explanation:
So what you do is
1 cup = 8 fluid ounces
(Don’t use that)
So you is
“Since 1 cup= 8 fluid ounces, what you do is multiply by 2. 8 times 2 is 16 , 3 times 8 is 24. 24+16 is 40” there’s your answer
The equation that shows the relation between the cups of sparkling water (s) and apple juice (j) mixed by Jada is 2s = j, meaning that the quantity of apple juice is always twice the quantity of sparkling water.
Explanation:
In the question provided, we're given that Jada makes her sparkling juice by mixing 2 cups of sparkling water and 3 cups of apple juice. Let's define s as the number of cups of sparkling water, and j as the number of cups of apple juice. Given this, the equation that shows how s and j are related is 2s = j. This equation expresses that the quantity of apple juice (j) is always twice the quantity of sparkling water (s).
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Triangle ABC with vertices A(4, −6), B(2, −8), and C(−10, 4) is dilated by a scale factor of 2 to obtain triangle A′B′C′. Which statement best describes triangle A′B′C′?
It is similar to triangle ABC and has coordinates A′(2, −3), B′(1, −4), and C′(−5, 2).
It is similar to triangle ABC and has coordinates A′(8, −12), B′(4, −16), and C′(−20, 8).
It is congruent to triangle ABC and has coordinates A′(2, −3), B′(1, −4), and C′(−5, 2).
It is congruent to triangle ABC and has coordinates A′(8, −12), B′(4, −16), and C′(−20, 8).
(Please answer asap ;-;)
Answers
Answer:
It is similar to triangle ABC and has coordinates A'(2, -3), B'(1, -4), and C'(-5, 2)
I am having a hard time simplifying (x^2 - 4x + 8)(2x - 1), can you help me out?
Answers
Answer:
2x^3 +3x^2 + 12x - 8
Step-by-step explanation:
(x^2- 4x + 8)(2x-1)
we expand the notation by using (2x-1)
2x(x^2 - 4x + 8) -1(x^2- 4x +8)
= 2x^3 -8x^2 +16x -x^2 + 4x -8
collect like terms
2^3 - 8x^2 - x^2 +16x + 4x -8
2x^3 + 7x^2 + 20x - 8
Help 30 Points! Show ALL Work! Image Attached.
Answers
Answer:
a. x = 13
b. x = 7
c. x = 24
d. x = Undefined
Step-by-step explanation:
Since all the bases are the same the power it is raised by is equivalent to the sum's power.
In mathematical terms
.
.
x^a + x^b = x^a+b
So all we have to do is add up the exponents and make them equivalent to each other.
For the last question, it is impossible since the powers added cannot ever be equal to each other.
9+x can never equal 4+x so it is undefined.
Explanation please how to do it
Answers
Answer:
I can't see the whole problem but if it says how many times per week does he practice it would be 13 times
Step-by-step explanation:
9 3/4 divided by 3/4.
39/4 times 4/3=13
What is the attribute being measured?
A)
inches
B)
height
C)
overweight males
D)
number of adult males
Answers
Answer:
What is the attribute being measured?
A) inches
B) height
C) overweight males
D) number of adult males
Step-by-step explanation:
Answer:It´s B, just did the assessment.
Step-by-step explanation:
A car travels 55.9 in an hour. If the car continues at the same speed, for 12 hours how many will it travel?
Can someone help me please
Answers
Answer:
670.8
Step-by-step explanation:
55.9x12=670.8
Yasmin has a bag containing 165 colored beads. Her classmates take turns selecting one bead from the bag without looking, recording the color in the table, and replacing the bead. Based on the table, about how many beads of each color are in Yasmin’s bag? Enter your answers in the boxes. Color Red Brown Orange Yellow Number of Beads 10 15 17 13 red, brown, orange, yellow
Answers
Answer:
30 , 45 , 51 , 39
Step-by-step explanation:
You just add up the numbers until you get 165
Number of beads of each color in Yasmin's bag is:
Red-- 30
Brown-- 45
Orange-- 51
Yellow-- 39
Step-by-step explanation:The record of experiment are as follows:
Color Red Brown Orange Yellow
Number of Beads 10 15 17 13
Total number of beads recorded=10+15+17+13=55 beads
Also, the Probability of Red bead is=10/55
Probability of Brown bead is=15/55
Probability of Orange bead is=17/55
Probability of Yellow bead is=13/55
Number of red beads in Yasmin's bag are:
[tex]\dfrac{10}{55}\times 165=30[/tex]
Number of brown beads in Yasmin's bag are:
[tex]\dfrac{15}{55}\times 165=45[/tex]
Number of orange beads in Yasmin's bag are:
[tex]\dfrac{17}{55}\times 165=51[/tex]
Number of yellow beads in Yasmin's bag are:
[tex]\dfrac{13}{55}\times 165=39[/tex]
URGENT!! Solve the following for θ, in radians, where 0≤θ<2π.
−4sin2(θ)−3sin(θ)+5=0
Select all that apply:
2.21
1.19
1.92
0.93
0.31
2.63
Answers
Answer: 0.93 radians & 2.21 radians
Step-by-step explanation:
[tex]-4sin^2\theta-3sin\theta+5=0\\\\\text{Since this is not factorable, use the quadratic formula to find the roots:}\\\\sin\theta=\dfrac{-(-3)\pm \sqrt{(-3)^2-4(-4)(5)}}{2(-4)}\\\\\\.\quad=\dfrac{3\pm \sqrt{9+80}}{-8}\\\\\\.\quad=\dfrac{3\pm\sqrt{89}}{-8}\\\\\\.\quad=\dfrac{3\pm9.43}{-8}\\\\\\.\quad=\dfrac{12.43}{-8}\quad and\quad \dfrac{-6.43}{-8}\\\\\\.\quad=-1.55\quad and\quad 0.80\\\\\\\theta=sin^{-1}(-1.55)\quad and\quad \theta=sin^{-1}(0.80)[/tex]
[tex]\theta=not\ valid\qquad and\quad \theta=0.927[/tex]
[tex]\theta = 0.927\ radians\text{\ in the 1st quadrant and}\\\pi-0.927=2.21\ radians\text{\ in the 2nd quadrant}[/tex]
Answer:
2.21
0.93
Step-by-step explanation:
Given that; [tex]-4\sin^2\theta-3\sin \theta+5=0[/tex]
This is a quadratic equation is [tex]\sin \theta[/tex], where [tex]a=-4,b=-3,c=5[/tex]
We want to solve for [tex]\theta[/tex] in radians, where 0≤θ<2π.
We apply the quadratic formula given by;
[tex]\sin \theta=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]
We substitute the given values to obtain;
[tex]\sin \theta=\frac{--3\pm\sqrt{(-3)^2-4(-4)(5)}}{2(-4)}[/tex]
Simplify;
[tex]\sin \theta=\frac{3\pm\sqrt{9+80}}{-8}[/tex]
[tex]\sin \theta=\frac{3\pm\sqrt{89}}{-8}[/tex]
[tex]\sin \theta=0.804[/tex] or [tex]\sin \theta=-1.55[/tex]
When [tex]\sin \theta=0.804[/tex] , [tex]\theta=\sin^{-1}(0.804)[/tex]
[tex]\Rightarrow \theta=0.93[/tex] --In the first quadrant.
In the second quadrant;
[tex]\theta=\pi-0.93=2.21[/tex]
When [tex]\sin \theta=-1.55[/tex] , [tex]\theta[/tex] is not defined.
A map has a scale of 1:25 000.
David walks 3.5 km in real life.
How far will this be on the map?
Answers
Answer:
250 m
Step-by-step explanation:
Final answer:
To find how far 3.5 km will be on a map with a scale of 1:25,000, convert the distance to meters (3,500 m) and then divide by the scale factor (25,000) to get the map distance, which is 14 centimeters.
Explanation:
When working with map scale, it's essential to understand how to convert distances on a map to actual distances in the real world. In this particular case, we have a map with a scale of 1:25,000, which means that 1 unit on the map is equivalent to 25,000 units in real life. David has walked a distance of 3.5 km in reality, and we need to calculate how far this would be represented on the map.
To convert David's actual walking distance to the map distance, we first need to express the 3.5 km in the same unit that is used in the map scale, which is meters. Since 1 km equals 1,000 meters, David walked 3,500 meters. Simply divide the actual distance walked by the scale factor to find the distance on the map:
Map distance = Actual distance / Scale
Map distance = 3,500 meters / 25,000
Map distance = 0.14 meters
Map distance = 14 centimeters
Thus, on the map, David's 3.5 km walk will be represented by a line that is 14 centimeters long.
Find the solution of the equation from the given numbers. x + 14 = 23; 9, 55, 37, or 30 55 9 37 30
Answers
The equation is X + 14 = 23.
To solve for X subtract 14 from each side:
x+14 = 23
x = 23 - 14
x = 9
x+14=23
x=23-14
x=9
9+14=23
How much money has to be invested at 2.9% interest compounded continuosly to have 34,000 after 18 years
Answers
Answer:
[tex]\$20,173.31[/tex]
Step-by-step explanation:
we know that
The formula to calculate continuously compounded interest is equal to
[tex]A=P(e)^{rt}[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
e is the mathematical constant number
we have
[tex]t=18\ years\\ A=\$34,000\\ r=0.029[/tex]
substitute in the formula above
[tex]34,000=P(e)^{0.029*18}[/tex]
[tex]P=34,000/((e)^{0.029*18})=\$20,173.31[/tex]
A scientist needs 70 liters of a 40% solution of alcohol. He has a 30% and a 60% solution available. How many liters of the 30% and how many liters of the 60% solutions should he mix to make the 40% solution?
Answers
The answer is:
There are needed 46.67 liters of the 30% solution and 23.33 liters of the 60% solution in order to make 70 liters of a 40% solution.
Why?We can solve this problem creating a system of equations. Let's make the two equations that will help us to solve the problem.
From the statement we know that a solution of 70 liters of a 40% is needed, and there are two differents solutions available, of 30% and 60% and we need to use them to make 70 liters of a 40% solution, so:
So:
[tex]30(Percent)SolutionVolume=X\\60(Percent)SolutionVolume=Y[/tex]
If both solutions will make a 70 liters solution, so the first equation will be:
[tex]x+y=70L[/tex]
Let's work with real numbers converting the percent values into real numbers by dividing it into 100, so:
[tex]30(Percent)=\frac{30}{100}=0.3\\\\40(Percent)=\frac{40}{100}=0.4\\\\60(Percent)=\frac{60}{100}=0.6[/tex]
Then, we know that both solutions will make 70 liters of a 40% solution, so the second equation will be:
[tex]0.30x+0.60y=0.4*70[/tex]
Therefore, from the first equation we have:
[tex]x=70-y[/tex]
Then, substituting x into the second equation to find y, we have:
[tex]0.30(70-y)+0.60y=28\\21-0.30y+0.60y=28\\0.3y=28-21\\y=\frac{7}{0.3}=23.33[/tex]
Hence, substituting y into the first equation to find x, we have:
[tex]x=70-y=70-23.33=46.67[/tex]
So, there are needed 46.67 liters of the 30% solution and 23.33 liters of the 60% solution in order to make 70 liters of a 40% solution.
Have a nice day!
Final answer:
To prepare 70 liters of a 40% alcohol solution, a scientist should mix equal amounts of the 30% and 60% alcohol solutions that are available. In this case, the scientist would need to mix 35 liters of the 30% solution with 35 liters of the 60% solution.
Explanation:
To solve the problem, we need to set up a system of equations based on the volumes and concentrations of the alcohol solutions. Let's define x as the volume in liters of the 30% alcohol solution and y as the volume in liters of the 60% alcohol solution.
First, we know that the total volume of the two solutions must add up to 70 liters:
x + y = 70
Second, we also know that the total amount of pure alcohol in the final 40% solution must be 40% of 70 liters. We can express the amount of pure alcohol in the 30% solution as 0.30x and in the 60% solution as 0.60y. The equation representing the alcohol concentration is:
0.30x + 0.60y = 0.40 × 70
Next, we solve these equations simultaneously to find the values of x and y.
Multiply the second equation by 10 to clear out decimals: 3x + 6y = 280.Subtract the first equation from this new equation to eliminate y: 2y = 210, so y = 105.Since the total volume is 70 liters, x + 105 = 70, which means x = -35. However, a negative volume doesn't make sense, so there must have been a mistake. Let's correct it and find the right value for x.From the corrected second equation 3x + 6y = 280, we rewrite it as x = (280 - 6y) / 3.Substitute y = 70 - x into the equation: x = (280 - 6(70 - x)) / 3.Simplify and solve for x to find that x = 140/4 = 35 and y = 70 - x = 70 - 35 = 35.Therefore, the scientist needs 35 liters of the 30% alcohol solution and 35 liters of the 60% alcohol solution to make a 40% solution.
At what x-values do the graphs of the functions y=cos 2x and y = cos^2 x-1 intersect over the interval 0 ≤ x ≤ pi. There must be two selections there are two anwsers!
Answers
Answer:
[tex]x=\frac{\pi}{2}[/tex] and [tex]x=\frac{3\pi}{2}[/tex]
Step-by-step explanation:
We need to solve the 2 equations to figure out the x-values (intersecting points).
Note: The identity [tex]cos^{2}x=\frac{1}{2}+\frac{1}{2}cos(2x)[/tex]
[tex]cos(2x)=cos^{2}(x)-1\\cos(2x)=(\frac{1}{2}+\frac{1}{2}cos(2x))-1\\cos(2x)=\frac{1}{2}cos(2x)-\frac{1}{2}\\\frac{1}{2}cos(2x)=-\frac{1}{2}\\cos(2x)=-1\\2x=cos^{-1}(-1)\\2x=\pi, 3\pi\\x=\frac{\pi}{2}, \frac{3\pi}{2}[/tex]
So they intersect at [tex]x=\frac{\pi}{2}, \frac{3\pi}{2}[/tex]
Answer:
x=pi/2 and x=3pi/2
Step-by-step explanation:
Need help please help me
Answers
Answer:
Exterior Angle Theorem states the exterior angle is the sum of the interior angles opposite it.
Angle 4 = 75
Step-by-step explanation:
The exterior angle theorem states that the two interior angles across from the exterior angle add to the degree of the exterior angle.
Angle 4 = 20 + 55 = 75
Garth has x books which is 20 more books than Henrietta has. If Garth gives Henrietta 7 books how many books does Henrietta now have
Answers
Answer:
she should have x-27 books left
Step-by-step explanation:
The number of books Henrietta has is x-13.
Given that, Garth has x books which are 20 more books than Henrietta has.
We need to find out how many books Henrietta now has.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Now, the number of books with Garth has =x
The number of books with Henrietta has =x-20
Garth gave Henrietta 7 books =x-20+7
=x-13
Therefore, the number of books Henrietta has is x-13.
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which equation represents the pattern in the table below
a.) s = c+4
b.) s= 4c
c.) c= s + 4
d.) c= 4s
Answers
3) c = s + 4
Answer:
C=s+4
Step-by-step explanation:
Hope this helps!
Explain how to use multiplication to find 4÷1/5=
Answers
Final answer:
To find 4 divided by 1/5, multiply 4 by the reciprocal of 1/5, which is 5, resulting in an answer of 20.
Explanation:
To solve the division problem 4 ÷ 1/5, you can utilize multiplication by the reciprocal of the fraction. Recall that dividing by a fraction is equivalent to multiplying by its reciprocal. In this case, the reciprocal of 1/5 is 5/1, because when you flip the numerator and denominator of 1/5, you get 5.
Now, you can rewrite the original equation as a multiplication problem: 4 × 5/1. When you multiply fractions, you multiply the numerators with numerators and the denominators with denominators. Since the denominator of 5/1 is 1, multiplying by it doesn't change the value of the numerator. Thus, multiplying 4 by 5 gives you the answer 20.
Which inequality is equivalent to -6x
30?
1.X greater than or equal to 5
2.X greater than or less than -5
3.X less than or equal to 5
4. X less than or equal to -5
Answers
Step-by-step explanation:
How to simplify
-6x (some sign, it didn't show in the question)30
Divide by -6 on both sides to isolate the variable.
30 divided by -6 is -5, so x=-5.
Answer:
,
Step-by-step explanation:
The first term of a Geometric progression is 16 and the fifth term is 9. what is the values of the seventh term?
Answers
Answer:
18
Step-by-step explanation:
Given the geometric sequence where a1=3 and the common ratio is -1, what is the domain for n?
Answers
Answer:
natural numbers: integers n for n ≥ 1
Step-by-step explanation:
As it is for any sequence, the domain of term numbers (n) is the positive integers, the natural numbers.
__
In general, the domain of any "n' that represents something being counted will be the counting numbers. These are also referred to as "natural numbers" or "positive integers." For integer n, n ≥ 1.
__
Additional comment
The geometric sequence described in this problem statement is represented by the exponential function ...
a(n) = 3(-1)^n
This evaluates to a real number (3 or -3) for all integer values of n, and for some fractional values of n. In the complex numbers, the function is defined for all real and complex values of n.
Answer:
All integers where n ≥ 1
Step-by-step explanation:
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3. What is the area of the figure below? O26 in. 27 in. 52 in.2 54 in.2
Answers
Answer:
26 in²
Step-by-step explanation:
area of triangle half base times height
gives you 20 and 6
Hey I need help plz help me now 13points
Answers
Answer:
1
Step-by-step explanation:
common denominator is 12
6 11/12 - (2 3/12 + 3 8/12)
6 11/12 - 5 11/12
1
Janice bought her mother a bunch of 10 flowers two of the flowers are daisies one half of the remaining flowers are tulips write the fraction of the flowers that are daisies
Answers
Answer:
2/10 or 1/5 of the flowers are daises.
4/10 of the flowers are tulips.
Since there is 10 flowers, that will be your denominator. 2 out of the ten flowers, so 2 is your numerator. There is 8 flowers left over and half of that is 4.
I need to find the volume of the shapes. Can you help me on 5and6.
Answers
Answer:
5. 96 ft³
6. 108 cm³
Step-by-step explanation:
I will answer in spite.
5. To find the volume, seperate the figure into two separate rectangles (one long one along the bottom, and one small one sitting on top).
The volume of rectangle one is 4ft × 9 ft × 2ft = 72 ft³.
The volume of rectangle two is 4ft × 3ft × 2ft = 24 ft³.
72 ft³ + 24 ft³ = 96 ft³.
6. Patty treated the figure as two separate rectangles with the dimensions 2x3x11 and 2x3x10, not taking into account the space where the rectangles meet.
She should have calculated (2x3x11) + (2x3x7), which is 108 cm³.
You're welcome Mr. Harvard.
Helpp
Given: m AB =32°, AC ≅BC, tangent AS
Find: m∠CAO, m∠SAC
Answers
Answer:
m∠CAO=8º
m∠SAC=82º
Step-by-step explanation:
We know that m∠OAS is 90º because it is a radius to a tangent. This will be useful later.
OA=OB because they are both radii. If we draw a line from A to B, this makes an isosceles triangle ABO with a vertex angle of 32 because of the central angle theorem. This means that m∠OAB and m∠OBA are both 74º.
Isosceles triangle CAB is also formed with the construction of AB. Using the inscribed angle theorem, we can find ACB, which is 16º. Solve for the other angles and you get 82º. To find m∠CAO, subtract m∠OAB from m∠CAB, and this returns 8.
To find m∠SAC, subtract m∠CAO from m∠OAS, which is 90º-8º, and you get 82º.
PLEASE HELP : A cylindrical fish tank has a base radius of 7 inches . The volume of the tank is approximately 3,080 cubic inches . What is the approximate height of the fish tank A) 62 in. B) 20 in C) 11in D) 10 in
Answers
Answer: B) 20 in
I plugged it into a calculator for this specific formula.
PLEASE HELP WITH MY MATH
1. What is thw width of a rectangular room with a area of 90 square feet and a length of 9ft?
2. What is the width of a rectangular swimming pool with a rea of 180 square feet and a width of 12 feet?
3. What is the perimeter of a rectangular rose garden that mesures 8 meters by 10meters
4. What is the width of a rectangular ping pong table that messures 8ft in length with a area of 32 square feet?
Answers
1. 10 ft
2. 15 ft
3. 36 meters
4. 4 ft
Hope this helps!
Mike is renting a boat. The hourly rental fee is the same per hour for any boat. Mike paid $50 to rent a canoe, and then $25 to rent a kayak. which is the dependent variable in the situation!
Answers
Answer:
The dependent variable is the cost of renting a boat
Step-by-step explanation:
Let
x-----> the number of hours
y----> the cost of renting a boat
In this problem
The independent variable is the number of hours
The dependent variable is the cost of renting a boat
Answer:
cost
Step-by-step explanation:
Write the equation that represents the line use exact numbers
Answers
Answer:
[tex]y=1.5x+3[/tex]
Step-by-step explanation:
Observing the graph
Let
[tex]A(0,3)[/tex] -----> this point is the y-intercept of the line
[tex]B(2,6)[/tex]
we know that
The equation of the line into slope intercept form is equal to
[tex]y=mx+b[/tex]
where
m is the slope
b is the y-coordinate of the y-intercept
In this problem
[tex]b=3[/tex]
Find the slope of the line m
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
substitute the values
[tex]m=\frac{6-3}{2-0}[/tex]
[tex]m=\frac{3}{2}[/tex]
[tex]m=1.5[/tex]
The equation of the line is
[tex]y=1.5x+3[/tex]
The equation of the line that passes through the points (0, 3) and (2, 6) is y = 1.5x + 3. The slope (m) is calculated as 1.5 and the y-intercept (b) is 3.
Explanation:To find the equation of a line that passes through two points, you'll first have to find the slope (m), and then find the y-intercept (b). Linear equations are typically represented in the form y = mx + b, where m is the slope and b is the y-intercept.
The line passes through points (0, 3) and (2, 6). To calculate the slope m, we use the formula (y2-y1)/(x2-x1). Plugging in our points, we get (6-3)/(2-0) = 1.5. This is our slope.
Next, we want to use the formula y = mx + b to calculate b. Since the line passes through the point (0,3), we know that when x = 0, y = 3. Plugging these values into the equation along with our determined slope, we get 3 = 1.5*0 + b. Solving for b reveals that our y-intercept is 3.
Therefore, the equation for this line appears as: y = 1.5x + 3.
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