The peasant had 28 hens and 42 rabbits
How to determine the number of hens and rabbits?Represent hens with h, eggs with e and rabbits with r.
So, we have:
2r = 3h
e = 1/3h
Make h the subject in e = 1/3h
h = 3e
He got 72 pennies.
So, we have:
r + h = 72
Multiply through by 2
2r + 2h = 144
Substitute 2r = 3h in 2r + 2h = 144
3h + 2h = 144
Evaluate the sum
5h = 144
Divide by 5
h = 28.8
Remove decimal
h = 28
Recall that:
2r = 3h
So, we have:
2r= 3 * 28
Divide by 2
r = 3 * 14
Evaluate the product
r = 42
Hence, the peasant had 28 hens and 42 rabbits
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If y varies directly as x, and y is 18 when x is 5, which expression can be used to find the value of when x is 11?
Answer:
[tex]\frac{18}{5}[/tex] (11)
Step-by-step explanation:
If it varies directly, you need to find k, the constant of proportionality.
This is done by plugging the values in for x & y that are known.
y = kx
18 = k(5)
[tex]\frac{18}{5}[/tex] = k
Now solve for y when x is 11.
y = [tex]\frac{18}{5}[/tex] (11)
y = 39.6
Determine if the lines through each set of ordered pairs are parallel, perpendicular, or neither. Explain your answer. Ordered pairs: (8, 3) (-2, 5) and (-2, -5) (-1, -10)
Considering the slope of the lines, it is found that the lines going through the points are neither parallel nor perpendicular.
When are lines parallel, perpendicular or neither?The slope, given by change in y divided by change in x, determines if the lines are parallel, perpendicular, or neither, as follows:
If they are equal, the lines are parallel.If their multiplication is of -1, they are perpendicular.Otherwise, they are neither.In this problem, the slopes are given as follows:
m1 = (5 - 3)/(-2 - 8) = -2/10 = -1/5 = -0.2.m2 = (-10 - (-5))/(-1 -(-2)) = -5/1 = -5.The multiplication is of 1, not -1, hence they are neither parallel nor perpendicular.
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5. Use the law of Cosines to find each missing sides. Round to the nearest tenth
The measure of angle x will be 88 degrees. Then the correct option is C.
The complete question is attached below.
What is law of cosine?Let there is a triangle ABC such that |AB| = a units, |AC| = b units, and |BC| = c units and the internal angle A is of θ degrees, then we have:
2ab cos θ = a² + b² – c²
The triangle is shown below.
Then the value of the variable x will be
2 · 7 · 10 · cos x = 7² + 10² – 12²
140 · cos x = 49 + 100 – 144
cos x = (149 – 144) / 140
x = 87.95 ≈ 88°
Then the correct option is C.
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Which statement is true?
O When an altitude is drawn from the right angle in a right triangle it creates two similar triangles.
O When an altitude is drawn from an acute angle in a right triangle it creates three similar triangles.
O When an altitude is drawn from the right angle of a right triangle it creates three similar triangles.
O When an altitude is drawn from an acute angle in a right triangle it creates two similar triangles.
Answer:
C) When an altitude is drawn from the right angle of a right triangle it creates three similar triangles.
Step-by-step explanation:
The Inscribed Similar Triangles Theorem states that if an altitude is drawn from the right angle of any right triangle, then the two triangles formed are similar to the original triangle and all three triangles are similar to each other.
complete each
1. 570 mL = _______________ L
2. 623 cm3 = _______________ m3
3. 38 gal. = _______________c
4. 585mL = ________________tbsp
5. 20 fl. oz. = ________________ tsp
6. 12 hrs =________________ min
Answer:
1. 570 mL = 0.57 L
2. 623 cm3 = 0.000623 m3
3. 38 gal. = 608 cups
4. 585mL = 39.5624 tbsp
5. 20 fl. oz. = 120 tsp
6. 12 hrs = 720 min
Step-by-step explanation:
1. 570 mL to L
divide the volume value by 1000, 570 / 1000 = 0.57
2. 623 cm3 to m3
divide the volume value by 623/10^6 = 0.000623
3. 38 gal. to c
1 gallon is 16 cups,
multiply the volume value by 16, 38 x 16 = 608c
4. 585mL to tbsp
for an approximate result, divide the volume value by 14.787
14.787 x 585 = 39.5624
5. 20 fl. oz. to tsp
multiply the volume value by 6, 20 x 6 = 120
6. 12 hrs to min
1 hour is 60 minutes
multiply the time value by 60
12 x 60 = 720
What are all of the possible classifications for a 3 × 3 system?.
Answer:
consistent and dependent
consistent and independent
Step-by-step explanation:
If a system of equations has no solutions, it is said to be inconsistent.
If a system of equations has at least one solution, it is said to be consistent.
If there is just one solution to a system of equations, it is said to be independent.
If a system of equations has an unlimited number of solutions, it is dependent.
A 3 x 3 system of equations is a three-variable system of equations. That is correct (x, y, z)
A three-by-three-equation system might be dependent, independent, or inconsistent.
A 3 x 3 system of equations can be written as follows:
consistent and self-sufficient (This indicates that there is just one answer.)
Dependable and consistent (It has infinite solutions)
If it is inconsistent, it can neither be dependent nor independent
Can anyone help me with this it would be great.
Answer:
11. The student put 24 as the diameter instead of the radius.
12. 48 pi
Step-by-step explanation:
The formula for the circumference of a circle is c = pi x diameter.
However, the question says that the radius is 24m, not the diameter.
To fix it, all you need to to is double the radius to get 48m for the diameter.
48 x pi = 48 pi
Answer:
The error is that he made the radius a diameter.The circumstances is 150.8571428 mStep-by-step explanation:
π = 22/7 or 3.14
Circumference= diameter × 22 / 7
= 2 × radius × 22 / 7
= 2 × 24 × 22/ 7
= 48 × 22 / 7
= 48 / 1 × 22 / 7
= 1056 / 7
= 150.8571428 m
I also need help on 3 4 5 if some one can explain it will be really helpful
And I will give 65 points
The equation that shows the relationship between the variables are T = 0.112N, D = 54A and T = 62.5A
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let k represent the constant of proportionality
3) T = kN
28 = 250k
k = 0.112
i) T = 0.112N
ii) T = 0.112(300) = 33.6
iii) 98 = 0.0112N
N = 875
4) D = kA
270 = 5k
k = 54
i) D = 54A
ii) D = 54(4.5) = 243
iii) 324 = 54A
A = 6
5) T = kA
150 = 2.4k
k = 62.5
i) T = 62.5A
ii) T = 62.5(1.8) = 112.5
iii) 3(60) = 62.5A
A = 2.88
The equation that shows the relationship between the variables are T = 0.112N, D = 54A and T = 62.5A
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Show how you would convert 500 A.U. into light-years.
Someone please help I’m so lost
Answer:
0.00790625
Step-by-step explanation:
499.9997656975
Astronomical unit
=
0.00790625
Light-year
Formula
for an approximate result, divide the length value by 63240
What is the missing fifth term in the
pattern below?
1, 8, 27, 64, ?
Options:
101
125
128
202
250
Answer:
The answer would be 125, because 1*1 = 1 2*2*2= 8 and so forth
Step-by-step explanation:
I hope this helps
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Your equation:}[/tex]
[tex]\mathsf{1, 8, 27, 64, ?}[/tex]
[tex]\huge\textbf{LET'S CONVERT IT TO FOR EASIER}\\\\\huge\textbf{TO UNDERSTAND A WHOLE LOT}\\\\\huge\textbf{BETTER.}[/tex]
[tex]\mathsf{1^3, 2^3, 3^3, 4^3, ?}[/tex]
[tex]\huge\textbf{Notice the pattern?}\\\\\\\\\huge\textbf{So, that means your mystery number}\\\\\huge\textbf{has to be squared (also known as to the}\\\\\huge\textbf{power of 3}[/tex]
[tex]\huge\textbf{Breaking down the exponents}[/tex]
[tex]\mathsf{1^3}\\\mathsf{= 1\times1\times1}\\\mathsf{= 1\times1}\\\mathsf{= \bf 1}[/tex]
[tex]\mathsf{2^3}\\\mathsf{= 2\times2\times2}\\\mathsf{= 4\times2}\\\mathsf{= \bf 8}[/tex]
[tex]\mathsf{3^3}\\\mathsf{= 3\times3\times3}\\\mathsf{= 9\times3}\\\mathsf{= \bf 27}[/tex]
[tex]\mathsf{4^3}\\\mathsf{= 4\times4\times4}\\\mathsf{= 16\times4}\\\mathsf{= \bf 64}[/tex]
[tex]\huge\textbf{If you didn't notice that your}\\\\\huge\textbf{exponents went like 1,2,3,4.}\\\\\\\\\huge\textbf{so that your mystery number has to}\\\\\huge\textbf{be 5 squared}[/tex]
[tex]\mathsf{5^3}\\\\\huge\textbf{That is what I meant \& this should give}\\\\\huge\textbf{you your result to this question.}[/tex]
[tex]\mathsf{5^3}\\\mathsf{= 5\times5\times5}\\\mathsf{= 25\times5}\\\mathsf{=125}[/tex]
[tex]\huge\textbf{The result:}[/tex]
[tex]\huge\boxed{\mathsf{Option\ B. \ 125}}\huge\checkmark[/tex]
[tex]\huge\textbf{The outro}[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
[tex]\huge\textbf{Signature}[/tex]
~[tex]\huge\boxed{\frak{Amphitrite1040:)}}[/tex]What is the area of the trapezoid? If necessary, round your answer to the nearest tenth.
A trapezoid with bottom side length of 8.5 feet, top side length of 5.5 feet, and height of 6.5 feet.
35.8 feet squared
45.5 feet squared
46.8 feet squared
The area of the trapezoid is calculated as 45.5 feet squared.
What does Area of Trapezoid mean?
The entire area occupied by the sides of a trapezoid is its area. It's important to notice that if we know the lengths of all the sides, we can divide the trapezoid into smaller polygons, such as triangles and rectangles, calculate their areas, and then sum them all together to determine the area of the trapezoid.
The formula for Trapezoid Area:If the parallel sides of the trapezoid are known, along with their height, it is possible to determine their area. It is expressed as,
A=[tex]1/2[/tex](a+b) h
where, A= the area of the trapezoid
h= height
'a' & 'b' = parallel side bases
Solution:a=5.5 feet , b= 8.5 feet & h=6.5 feet
A=[tex]1/2[/tex](a+b)h
∴A=[tex]1/2[/tex](5.5+8.5)*6.5
⇒A=[tex]1/2[/tex](14)*6.5
⇒A=7*6.5
⇒A=45.5 feet squared
Therefore, the solution is (b) 45.5 feet squared.
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Which number can each term of the equation be multiplied by to eliminate the fractions before solving?
-m-2=2+
m
O 2
O 3
04
O 5
A machinist who had been producing 40 parts per day increased to the out put of 60 parts per day by going to a faster machine. How many times faster is the new machine? Wright your answer as a mixed number.
5.7x10^6 as an ordinary number
Answer:
5700000
Step-by-step explanation:
Quadrilateral ABCD was rotated 360° clockwise with the origin as the center of rotation to create a new figure. Which rule describes this transformation?
A (x, y)-(x,y)
B(x, y)(x, y)
c(x, y)-(x, y)
D (x, y)-(x, y)
The rules describes the transformation is (x, y)(x, y).
The correct option is (B)
what is Transformation?A transformation is a general term for four specific ways to manipulate the shape and/or position of a point, a line, or geometric figure.
If the figure is rotated 360 degrees then the coordinates remains unchanged.
This is because when from where it started it stops there again.
As the 360 degree rotation is complete circle rotation.
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Circle Q is shown. Line segments P Q and R Q are radii. The length of R Q is 6. Angle P Q R is 45 degrees. Sector P Q R is shaded.
Which statements are true about circle Q? Select three options.
The ratio of the measure of central angle PQR to the measure of the entire circle is One-eighth.
The area of the shaded sector is 4 units2.
The area of the shaded sector depends on the length of the radius.
The area of the shaded sector depends on the area of the circle.
The ratio of the area of the shaded sector to the area of the circle is equal to the ratio of the length of the arc to the area of the circle.
The statements that are true about circle Q are:
The ratio of the measure of central angle PQR to the measure of the entire circle is 1/8.The area of the shaded sector depends on the length of the radius.The area of the shaded sector depends on the area of the circle.How to explain the circle?The measure of the central angle is 45°. The measure of the entire circle is 360°. This makes the ratio of the central angle to the entire circle 45/360 = 9/72 = 1/8
To find the area of the shaded sector, this will be:
A = πr² = π(6²) = 36π
1/8(36π) = 36π/8 = 18π/4 = 9π/2 = 4.5π square units. This is not 4 square units.
The ratio of the area of the shaded sector to the area of the circle would not be the same as the ratio of the length of the arc to the area of the circle.
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Answer:
1,3,4
Step-by-step explanation:
What is the solution set for -1<-2f+1<9? Please show work and chose a b c and d
The solution set is 1 ≥ f ≥ -4, and the correct number line is the one in option A.
How to find the solution set?
Here we have the inequality:
-1 ≤ -2f + 1 ≤ 9
To solve this, we need to isolate the "f" on the middle.
First, we can subtract 1 in both sides to get:
-2 ≤ -2f ≤ 8
Now we need to divide both sides by -2, remember that this will change the direction of the symbols:
-2/-2 ≥ f ≥ 8/-2
1 ≥ f ≥ -4
So we need to have a line that starts at -4 and ends at 1, the correct option is number line A.
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Use set notation to describe the domain and range of each graph. Use set notation to describe the domain and range of each graph .
The range and domain of the graphs have been determined .
What is Domain and Range of a Function ?Domain is the value that can be an input to the function and the range is all the value a function can obtain.
From the given graphs ,
For Graph 1
It can be seen that the line extends from x = -5 to +4
where -5 is not included
therefore the domain is given by
D = { x| -5 < x ≤4}
and the range is
R = {y | -3 < y≤4}
For Graph 2
The input value x extends from -∞ to +∞
so the domain is
D = { x| - ∞ ≤ x ≤ +∞ }
and the range is given by
R = {y | - ∞ ≤ y ≤ 3}
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Give the fact that connects the look below there is image two angles labelled below.
Use this fact to find the value of c in degrees ().
C
74°
Not to scale
Assuming that both lines are parallel, we conclude that C = 74°.
How to find angle C?
Here we can see that both of the lines that go upwards are parallel lines. This means that C and the 74° angles are opposite angles.
Then if we say that x is the angle at the right of the 74°, we must have that:
x + 74° = 180°
x = 180° - 74° = 106°
And we also must have that:
x + C = 106° + C = 180°
Solving for C:
C = 180° - 106° = 74°
C = 74°.
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The volume of the cube is given as V= x³, where x is the side length of the cube. Find the domain of the volume of
the cube.
Answer: None of the choices
Step-by-step explanation:
1. It couldn't be integers (whole numbers positive or negative), because a cube couldn't have a negative volume.
2. It could be natural numbers, but the problem is, that a volume could have decimal values, for example, 3.62 meters cubed which a natural number doesn't support.
3. Set of whole numbers is the same as integers, so it can't be that.
4. None of the choices, which in my opinion is the correct one.
I'm not sure it is correct, but I hope I helped you!
find the area of the rectangle below
(3x+4) feet x
(x+3) feet
select the correct answer
Answer:
3x^2+ 13x + 12
Step-by-step explanation:
Multiply the length and width:
(3x+4) * (x+3)
FOIL method:
3x^2 + 9x + 4x + 12
Combine like terms
3x^2+ 13x + 12
A shipment of tile cost $64,500. each tile costs 15 dollars. how many pieces of tile are in the shipment?
Answer:
4,300
Step-by-step explanation:
total cost of the shipment of tile cost =$64,500
each tile cost =$15
how many pieces will now be the total cost of shipment tile divided by the cost of each tile
which will be
64500/15
=4,300 tiles are there
i am glad I helped
Mr. Sanchez’s class sold fruit pies for $1.73 each and Mr. Kelly’s class sold bottles of fruit juice for $1.44 each. Together, the classes sold 83 items and earned $130.83 for their school. Write and solve a system of equations that models this problem. Show all your work.
Answer:
p = 39 f = 44
Step-by-step explanation:
p = $ 1.73
f = $ 1.44
equation
p + f = 83
1.73 p + 1.44 (83 - p) = $ 130.83
p = 39 (amount of times fruit pies were sold).
Therefore,
p = 39
f = 44
A school stores expenses and sales for a three-month period are shown in the table below. Month Expense Sales September $125.00 $47.00 October$0.00 $65.00 November $57.00 $28.00 Based on the data in the table, what is the loss or pro t for the store for the three-month period? A. $182.00 loss B. $42.00 loss C. $15.00 profit D. $140.00 profi
t
The school store is in $42 loss , Option B is the correct answer.
What is Profit and Loss ?When the sales is more than the expenses then it is called profit and vice versa is called Loss.
The sales and expenses for three months are given
To calculate overall Profit/Loss
Total Expenses = $125 + $0 +$ 57 = $182
Total Sales = $47 +$65 + $28 = $140
Therefore as sales is less than the expense , The school is in loss
Loss = $ 182 -$ 140 = $42
Thus Option B is the correct answer.
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Peter uses the equation y = StartFraction 13 over 4 EndFraction x to model the number of miles that he has walked in x hours. Which statement is true about the proportional relationship that is modeled by Peter’s equation?
Regarding the proportional connection that Peter's equation simulates, claim C is accurate. Peter moves along at a 13/4 mph walking pace.
What is the equation?An equation is a mathematical statement that uses an equal sign to join two algebraic expressions having the same value.
The complete question is
"Peter uses the equation Y=13/4x to model the number of miles that he has walked in x hours. Which statement is true about the proportional relationship that is modeled by the peat there's the equation?
A:Peter walks a rate of 4/13 miles per hour.
B: Peter walks at a rate of 4 miles per hour.
C: Peter walks at a rate of 13/4 miles per hour.
D: Peter walks at a rate of 13 miles per hour."
Provided equation
Y=13/4x
where y is the distance traveled and x denotes the amount of time.
According to the equation, Peter moves along at a speed of 13/4 miles per hour.
As a result, the proportional connection represented by Peter's equation is valid as stated in assertion C.
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If F(x) = 7x - 3 and g(x) = x2, what is (g ° f)(1)?
Answer:
16
Step-by-step explanation:
If f(x)=7x-3 and g(x)=x²,
(g•f)(1)= g(f(1))
bit : f(1) =7(1)-3 = 4
(g•f)(1)= g(f(1)) = g(4) = 1² = 16
I hope this was helpful :)
What is the solution set for Ix+3| =5?
S-8 and s-8
s=-2 and s=2
s=-8 and s=2
s = 2 and s= 8
When f(a) = 227 + 32 - 3, evaluate f( - 1)
helpp
Step-by-step explanation:
[tex]f(x) = 2 {x}^{2} + 3x - 3[/tex]
[tex]f( - 1) = 2. {( - 1)}^{2} + 3.( - 1) - 3[/tex]
[tex]f( - 1) = 2 - 3 - 3[/tex]
[tex]f( - 1) = - 4[/tex]
The cash price of a mobile phone is $540. Andrea bought the mobile phone by paying $42 monthly instalments over 15 months. Find the flat rate interest of the instalments, give your answer correct to 3 significant figures.
The rate of interest of the instalment is 13%
What is Instalments ?The part payment of a loan is called Instalment
It is given that
The Cash price is $540
Instalment of $42
Time = 15 month = 15/12 = 1.25 years
Total Amount paid = 42 * 15 =$630
Interest Paid is $90
90 = 540 * 1.25 *Rate
Rate = 13%
The rate of interest of the instalment is 13%
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What are the solutions of the equation x4 - 5x2 - 14 = 0? Use factoring
to solve.
Answer:
x = ±√7, ±i√2
Step-by-step explanation:
[tex]x^4-5x^2-14=0\\(x^2-7)(x^2+2)=0\\[/tex]
[tex]x^2 - 7 = 0[/tex] or [tex]x^2 + 2 = 0\\[/tex]
x^2 - 7 = 0
x^2 = 7
x = ±√7
or x^2 + 2 = 0
x^2 = -2
x = ±i√2
