let x = horses
5x = cows
x + 5x = 132
6x = 132
Divide both sides by 6
X = 22
he has 22 horses and 110 cows
There are 22 horses and 110 cows.
What is an equation?"It is a mathematical statement which consists of equal symbol between two mathematical expressions."
For given question,
Let 'c' represents the number of cows and 'h' represents the number of horses.
A rancher raises 5 times as many cows as horses.
So, we get an equation,
⇒ c = 5 × h .................(i)
There are 132 animals.
So, we get an equation,
⇒ c + h = 132 ..................(ii)
Substitute the value of c = 5h in equation (ii)
⇒ c + h = 132
⇒ 5h + h = 132
⇒ 6h = 132
⇒ h = 22
This means, there are 22 horses.
Substitute the vale of h in equation (i),
⇒ c = 5 × h
⇒ c = 5 × 22
⇒ c = 110
This means, there are 110 cows.
Therefore, there are 22 horses and 110 cows.
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The half-life of cobalt-60 (used in
radiation therapy) is 5.26 years (actual
data). How much of a 200 g sample of
cobalt-60 will remain after 26.3 years?
Answer:
6.25 gm left
Step-by-step explanation:
Find the number of half lives in 26.3 years
26.3 / 5.26 = 5 half lives
(1/2) ^5 = 1/32 nd of the original will be left
1/32 * 200g = 6.25 gm left
Which expression is equivalent to -1/2 (1/4 x - 3/8). SHOW WORK
A. -1/8x + 3/16
B. -1/8 x + 3/8
C. 1/8x - 3/16
D. 1/8x - 3/8
Answer:
A. -1/8 x + 3/16
Step-by-step explanation:
Distribute -1/2 over the parentheses
-1/2 ( 1/4 x - 3/8 )
-1/2 (1/4 x) - 1/2 (-3/8 )
multiply fractions to simplify
-1/8 x + 3/16
A is correct
what are the amounts of interest and maturity value of a loan for 25,000 at 12% simple interest for 5 years
Answer:
Interest= 15,000
Maturity Value=40,000
Step-by-step explanation:
Simple Interest
V= (principal) * (rate) * (# of periods)
=(25,000)*(0.12)*(5)
=15,000
Maturity Value
V= P*(1+rt)
=25,000*(1+(.12)(5))First, converting R percent to r a decimal
r = R/100 = 12%/100 = 0.12 per year.
Solving our equation:
V = 25000(1 + (0.12 × 5)) = 40000
V = 40,000.00
hope it will help you
thank u
Goal
Your task is to create a monthly budget given certain circumstances.
Role
You are a single person who just received a full-time job in a factory (40 hours). You will make $12.00 an hour.
Audience
You need to convince your parents that you can maintain a budget to live in a one-bedroom apartment that costs $300 for rent a month.
Situation
The challenge involves dealing with finding average heating, water, sewage bills in your area so that you can include those in your budget.
Product, Performance, and Purpose
You need to develop a monthly budget so that you can show your parents that you can afford the expenses.
Please upload your completed assignment here. Be sure you have included your name at the top of your document and as part of the file name.
The development of the personal budget that convinces parents that one can maintain an independent living is detailed as follows using the 50: 30: 20 rule:
50% for necessities (housing, food, transportation, utilities) $740
30% for luxuries, savings, vacations, entertainment, etc. $461
20% for Emergency Funds and Retirement $335
What is a personal budget?A personal budget is the household budget for a single person for a period.
The personal budget shows an estimate of the person's revenue and expenses over the period.
Data and Calculations:Hourly rate of earnings = $12
Working hours per week = 40 hours
Working hours per month = 160 hours (40 x 4 weeks)
Total monthly earnings = $1,920 ($12 x 160)
Assumed tax rate = 20%
After-tax take-home pay = $1,536 ($1,920 x 1 - 20%)
Monthly Necessities:Rent of apartment = $300
Heating = $40
Water cost = $20
Sewage bill = $10
Food = $300
Transportation = $50
Other costs = $20
Total cost for necessities = $740
Thus, the development of the personal budget shows that one can maintain an independent living from the parents as a single person.
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Question 1: 5 pts
Bill wants to plant roses in his triangular plot. There will be 1 plant at a corner. Each row will have 6
additional plants. He wants the plot to have as many lows as possible with 150 rose plants. How many
rows will Bill's plot have?
O 7 rows
O 8 rows
O 6 rows
O 5 rows
The arrangement of the rose plants on the triangular plot is such that they
form a series or progression that is defined.
The number of rows on Bill's plot is; 8 rows
The given parameters for the triangular plot are;
Number of plants at the corner = 1 plant
Number of additional plants per row = 6 plants
Number of rose plants = 150 rose plants
The number of rows in the plot.
The difference between successive rows, d = 6
The number rose at the top vertex, a = 1
Therefore, the rose in the garden forms an arithmetic progression
The first term, a = 1
The common difference, d = 6
The number of rows Bill's plot will have, n is given by the sum of n in terms of
an arithmetic progression, Sn, is given as follows;
[tex]S_n=\frac{n}{2}[2a+(n-1)\times d[/tex]
When Sn = 150, we get;
[tex]150=\frac{n}{2} [2\times 1+(n-1)\times 6[/tex]
150 = 3·n² - 2·n
3·n² - 2·n - 150 = 0
Taking only the positive solution for n, we have;
[tex]n_{1,\:2}=\frac{-\left(-2\right)\pm \sqrt{\left(-2\right)^2-4\cdot \:3\left(-150\right)}}{2\cdot \:3}[/tex]
[tex]n_{1,\:2}=\frac{-\left(-2\right)\pm \:2\sqrt{451}}{2\cdot \:3}[/tex]
[tex]n=\frac{1+\sqrt{451}}{3},\:n=\frac{1-\sqrt{451}}{3}[/tex]
The number of rows Bill's plot has, n ≈ 7.3965
Given that the 7th row is completed, an 8th row will be present on Bill's plot
The number of rows Bill's plot will have = 8 rows
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A circle has four sections. Only three sections are labeled. The labels are 29.78% 24.73% and 19.49%. What is the missing section should be?
Answer:
26
Step-by-step explanation:
You would add the 3 numbers and then minus that from 100
The length of a new rectangular playing field is 4 yards longer than quadruple the width. If the perimeter of the rectangular playing field is 558 yards, what are its dimensions?
The width is yards.
Answer:
55 x 224 yards
Step-by-step explanation:
w + w + 2 * ( 4 + 4w) = 558 (given)
10 w + 8 =558
w = 55 then L = 4 + 4w = 224 yards
i needs help with it please
Answer:
(i) (0, -32)
(ii) (-4, 0) and (8, 0)
(iii) x = 2
(iv) (2, -36)
(v) (2, -36) minimum
Step-by-step explanation:
Given quadratic equation:
[tex]y=x^2-4x-32[/tex]
Part (i)
The y-intercept is the point at which the curve crosses the y-axis.
To find the y-intercept, substitute x = 0 into the given equation:
[tex]\implies (0)^2-4(0)-32=-32[/tex]
Therefore, the y-intercept is at (0, -32)
Part (ii)
The zeros are the points at which the curve crosses the x-axis.
To find the zeros, substitute y = 0 into the given equation and factor:
[tex]\implies x^2-4x-32=0[/tex]
[tex]\implies x^2-8x+4x-32=0[/tex]
[tex]\implies x(x-8)+4(x-8)=0[/tex]
[tex]\implies (x+4)(x-8)=0[/tex]
Therefore:
[tex](x+4)=0 \implies x=-4[/tex]
[tex](x-8)=0 \implies x=8[/tex]
So the zeros are (-4, 0) and (8, 0)
Part (iii)
The axis of symmetry is a vertical straight line that divides the curve into two symmetrical parts. The axis of symmetry is the x-value of the mid-point of the zeros.
[tex]\sf \implies midpoint=\dfrac{8+(-4)}{2}=2[/tex]
Therefore, the axis of symmetry is: x = 2
Part (iv)
The vertex is the turning point of the parabola.
If the leading coefficient is positive, the parabola opens upwards and the vertex is the minimum point.
If the leading coefficient is negative, the parabola opens downwards and the vertex is the maximum point.
The axis of symmetry is the x-value of the vertex.
To find the y-value, substitute x = 2 into the equation:
[tex]\implies (2)^2-4(2)-32=-36[/tex]
Therefore, the vertex is (2, -36)
Part (v)
The optimal value is also known as the vertex.
Therefore, the optimal value is (2, -36).
As the leading coefficient of the given quadratic equation is positive, the parabola opens upwards and so the optimal value is a minimum.
1. Find the equation of a normal to the curve y= 2² - 2x +3 at the point (3,0)
I think you meant to say the equation is
y = 2x² - 2x + 3
Differentiate both sides with respect to x :
dy/dx = 4x - 2
At the point (3, 0), the slope of the tangent line is dy/dx(3) = 4•3 - 2 = 10. Then the normal line to the curve at (3, 0) has slope -1/10.
Using the point-slope formula, the equation of the normal line is
y - 0 = -1/10 (x - 3) ⇒ y = (3 - x)/10
Los disminuyentes de liquido normal en ula persona sana es de 0.6mL/kg/hr. Sabiendo que don pedro cuenta con 39 grados de fiebre y pesa82 kg. Calcule la perdida de liquido/h
The question requires the computation of loss body fluid. The results show that Don Pedro's loss of body fluid per hour is 54,234ml/hours. See computation below.
What is the loss of body fluid?This refer to the rate at which a human being loses water on the hour. The formula for this is given as:
The Body weight in lb x percentage rate of dehydration (given in decimal form) x 500.
Hence, Don Pedro's loss of fluid per house is:
82 x 0.6 x 500;
Recall that in the formula, the weight is given in lb. So we convert Pedro's weight to Lb.
1kg = 2.20462Lb
Hence
80kg = 80 * 2.20462 = 176.37
Hence
Pedro's loss of fluid per house =
180.779 x 0.6 x 500
= 54,233.70
≈ 54, 234 ml/h
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Need a little help!
Find the volume of the sphere. Round your answer to the nearest tenth.
Use 3.14 for .
A sphere has a radius of 12 centimeters.
The volume of the sphere is about
cm³.
Find the height of a trapezium below with are 90cm and parallel sides 6 and 19.
Answer:
7.2 cm
Step-by-step explanation:
The height of the trapezium can be found by making use of the area formula with known values filled in.
__
solve for heightThe area of a trapezium is given by ...
A = 1/2(b1 +b2)h . . . . b1, b2 are the parallel sides, h is the height
Using the given values, we have ...
90 cm² = 1/2(6 cm +19 cm)h . . . . . . use the known values
(90 cm²)/(12.5 cm) = h = 7.2 cm . . . . divide by the coefficient of h
The height of the trapezium is 7.2 cm.
PLS PLS PLS HELP!!!
The perimeter of a square is given as 6c - 4(c-5) Which expression give the length of one side of the square?
A 2c + 20
B 1/2c + 20
C 1/2c+5
D 8c+20
Are the two expressions, 6c-4(c-5) and the answer you chose to the
question above equivalent?
Explain why or why not in 1 to 2 sentences.
Answer:
( we know that square of perimeter is 4L now,4L=6c-4(c-5),4L=6c-4c+20,4L=2c+20,then L=(c+10)/2
The side of a given square is c/2+5. Therefore, option C is the correct answer.
What is the perimeter?The perimeter of a shape is defined as the total distance around the shape. It is the length of the outline or boundary of any two-dimensional geometric shape. The perimeter of different figures can be equal in measure depending upon the dimensions.
Given that, the perimeter of a square is 6c-4(c-5).
We know that, the perimeter of a square is 4a, where a is the side.
Now, 4a=6c-4(c-5)
4a=6c-4c+20
4a=2c+20
a=c/2+5
Therefore, option C is the correct answer.
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Given that these simultaneous equations
x-y=k
2x²+y²-15
have exactly one pair of solutions, find k.
The answer is supposedly (±3√10)/2, but I don't know how to get to the answer
The value of k is[tex](3\sqrt{ 10})/2[/tex]
How to solve the simultaneous equation?Given:
x-y=k.............(eq i)
2x²+y²-15..............(eq ii)
We would make y the subject formula in eq ii
2x²+y²-15= 0
2x² + y²= 15
y²= 15-2x²
y= [tex]\sqrt{15-2x^2}[/tex]...........(eq iii)
Substitute the value of y into eq i
x-([tex]\sqrt{15-2x^2}[/tex]= k
x- ([tex]\sqrt{15} - 2x[/tex]= k
k= [tex](3\sqrt{ 10})/2[/tex]
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which expression represent the quotient of seven and four
The expression that represents the quotient of seven and four is 7/4
How to determine the expression?The statement is given as:
quotient of seven and four is 7/4
Quotient means divide
So, the interpretation of the expression is seven divide four i.e. 7/4
Hence, the expression that represents the quotient of seven and four is 7/4
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Which one is the right conversion?
Answer:
1, 4, 5, 6
Step-by-step explanation:
to convert a rational to an exponential it's the index (number left of radical) over the power (number on the right).
you can also double check by plugging both into a calculator and see if they equal the same number.
What is angle Data please help
Answer:
C. 74°
Step-by-step explanation:
Cosine Rule (for finding angles)
[tex]\sf \cos(C)=\dfrac{a^2+b^2-c^2}{2ab}[/tex]
where:
C = anglea and b = sides adjacent the anglec = side opposite the angleGiven:
C = [tex]\theta[/tex]a = 5b = 11c = [tex]\sf \sqrt{115}[/tex]Substitute these values into the formula:
[tex]\implies \sf \cos(\theta)=\dfrac{5^2+11^2-(\sqrt{115})^2}{2(5)(11)}[/tex]
[tex]\implies \sf \cos(\theta)=\dfrac{25+121-115}{110}[/tex]
[tex]\implies \sf \cos(\theta)=\dfrac{31}{110}[/tex]
[tex]\implies \sf \theta=\cos^{-1}\left(\dfrac{31}{110}\right)[/tex]
[tex]\implies \sf \theta=74^{\circ} \quad (nearest\:degree)[/tex]
Subtract (-2x4-4y3+4z3+6) - (-9x4-3y3+4z3+9)
Answer:
Step-by-step explanation:
-2x^4 - 4y^3 + 4z^3 + 6 + 9x^4 + 3y^3 - 4z^3 - 9
7x^4 - y^3 - 3
Answer:
28x-3y-3
Step-by-step explanation:
(-2x × 4 - 4v × 3 + 4z× 3 + 6) - (-9× × 4 - 3v× 3 + 4
Multiply the monomials
（-8×-4y×3+ 42×3+6)-（-9××4-3y×3+42×3+9
Multiply the monomials
(-8x-12y + 4z × 3 + 6) - (-9x× 4 - 3y × 3 + 4z × 3 + 9)
Multiply the monomials
(-8x - 12y + 12z +6) - (-9× × 4 - 3y × 3 + 4z × 3 + 9)
Multiply the monomials
(-8x-12y +12z +6) - (-36x -3y × 3+ 4z × 3 + 9)
Multiply the monomials
(-8x-12y + 12z + 6) - (-36x - 9y + 4z × 3 + 9)
8×-12y+122+6-（-36×-9y+122+9
Remove the parentheses for addition or
subtraction
-8x - 12y + 12z + 6 + 36x + 9y - 12z - 9
-8x - 12y + 12z + 6 + 36x + 9y - 12z - 9
Reorder and gather like terms
(-8x + 36x) + (-12y + 9y) + (12z - 12z) + (6 - 9) 3 steps
Collect coefficients of like terms
(-8+36) ××+ (-12 + 9) × y+ (12 - 12) × z+ (6 - 9)
an airplane has an airspeed of 530 kilometers per hour bearing N45 degrees E. The wind velocity is 30 kilometers per hour in the direction N30 degrees W. Find the resultant vector representing the path of the plane relative to the ground. What is the ground speed of the plane? What is its direction?
For an airplane has an airspeed of 530 kilometers per hour bearing N45 degrees E, the ground speed of the plane and its direction is mathematically given as
Vg=556.10km/hr[tex]\theta=52.99East[/tex]What is the ground speed of the plane and its direction?Generally, the equation for the velocity of the plane is mathematically given as
[tex]Vp=Fcos\thetai+Fsin\theta j[/tex]
Therefore
Vp=530cos45i+530sin45j
Vp= 374.76i+374.76j
For wind speed
Vm=80cos(90+30)i+80sin(90+30)j
Vm=-40i+69.28j
Hence, there resultant is
Vr=Vm +Vp
Vr=374.76i+374.76j + 40i+69.28j
Vr=334.77i+1444.05j
In conclusion, the Ground speed is
[tex]Vg=\sqrt{334.77^2+1444.05^2}[/tex]
Vg=556.10km/hr
Direction
[tex]Tan \theta=\frac{444.05}{334.77}[/tex]
[tex]\theta=52.99East[/tex]
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5x+3
Write the fraction below as a sum or difference.
=?
4
(Simplify your answer. Use integers or fractions for any numbers in the
expression.)
To write this sum as a fraction, you can use the following formula: 5x/4 + 3/4.
How to transform a fraction into a sum?To transform a fraction into a sum we must perform the following procedure:
[tex]\frac{5x + 3}{4}[/tex] = [tex]\frac{5x}{4} + \frac{3}{4}[/tex]According to the above, all we have to do is divide the fraction using each digit of the numerator and put the same denominator.
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4.
Solve the system of inequalities graphically. Label the solution set with an S.
Help asap
Answer:
Step-by-step explanation:
Please help we’re stuck
Answer:
Divide 12 by -6
Using the diagram of a regular hexagon, fill in the blanks for the steps to solve for the area of a hexagon with sides equal to 14 cm.
(1) How many equilateral triangles are there? _____
(2) What is the measure of each of the three angles in the equilateral triangle? _____
(3) If we cut an equilateral triangle down the middle (segment a), what special right triangle do you create? _____
(4) What is the vocabulary word for the segment a? _____
(5) What is the length of the short side of one of the 30-60-90 triangles? _____
(6) What is the length of the hypotenuse of one of the 30-60-90 triangles? _____
(7) Using the properties of 30-60-90 triangles, calculate the length of the long leg of one of the 30-60-90 triangles. _____
(8) What is the height of one of the the equilateral triangles? _____
(9) Apply the formula for the area of a triangle to find the area of one equilateral triangle. _____
(10) Calculate the area of the complete hexagon by multiplying the area of one equilateral triangle by the number of triangles. _____
Find answers to the questions in the attached file.
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how do you get 14 divided by 9 as a decimal
Answer:
14 divided by 9 = 1.5
The result of 14/9 is a non-terminating, repeating decimal.
Answer:
1.56 [?]
this question's wording was slightly confusing but I think this is what you meant
Step-by-step explanation:
by dividing the two numbers, (you can use long division or a calculator) while they are not in a fraction state (don't rewrite it as [tex]\frac{14}{9}[/tex], actually divide
14 by 9) you will end up with a number:
1.55555556
(repeating decimal)
So, you can either write this as 1.5 with a little dash over the 5
Or, you can round the decimal to 1.56 .
(method: by actual division)
[Worth 30 Points] NEED HELP!!!
To estimate the height of a mountain, two students find the angle of elevation from a point (at ground level) b=740meters from the base of the mountain to the top of the mountain is β=60∘. The students then walk a=1850 meters straight back and measure the angle of elevation to now be α=37∘. If we assume that the ground is level, use this information to estimate the height of the mountain.
The height of the mountain is: ______ Meters.
Explain how your answer measure below. Be sure to show all of your work.
The height of the mountain estimated by two students is 2,467.98 meters.
Height of the mountain
The height of the mountain is calculated as follows;
tanα = h/( a + b + x)
where;
x is the distance between end of b and htan37 = h/(1850 + 740 + x)
tan37 = h/(2590 + x)
h = tan37(2590 + x)
h =1,951.82 + 0.7536x ---- (1)
tanβ = h/(b + x)
tan60 = h/(740 + x)
h = tan60(740 + x)
h = 1,281.68 + 1.732x ---- (2)
Solve (1) and (2) together
1,951.82 + 0.7536x = 1,281.68 + 1.732x
1,951.82 - 1,281.68 = 1.732x - 0.7536x
670.14 = 0.9784x
x = 684.93 m
h = 1,281.68 + 1.732x
h = 1,281.68 + 1.732(684.93)
h = 2,467.98 m
Thus, the height of the mountain estimated by two students is 2,467.98 meters.
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Which of the following is the graph of y = |x - 3|?
Answer:
D
Step-by-step explanation:
with this functional definition y can never have a negative value.
so, A and C are automatically out.
and then find some core points (like x = 0 and y = 0).
for x = 0 we get y = 3. ok, that fits to both B and D.
for y = 0 x must be 3.
and that leaves only D as right answer.
Answer:
the answer is a on my test
Step-by-step explanation:
Ian buys 4 bananas and 2 apples. Each banana has a mass of 120 grams. Each apple has a mass of 180 grams.
Which is the total mass of the fruit that Ian buys?
A.
300 grams
B.
580 grams
C.
840 grams
D.
960 grams
Answer:
THE ANSWER IS A CORRECT ME IF I WRONG
Suppose y varies inversely with x, and y = 49 when x = 17. What is the value of x when y = 7 ?
[tex]\qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}} ~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\cfrac{\stackrel{\downarrow }{k}}{x}~\hfill } \\\\ \textit{\underline{x} varies inversely with }\underline{z^5} ~\hspace{5.5em} \stackrel{\textit{constant of variation}}{x=\cfrac{\stackrel{\downarrow }{k}}{z^5}~\hfill } \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{\underline{y} varies inversely with \underline{x}}}{y=\cfrac{k}{x}}\qquad \textit{we also know that} \begin{cases} y=49\\ x=17 \end{cases} \\\\\\ 49=\cfrac{k}{17}\implies 833=k~\hfill \boxed{y=\cfrac{833}{x}} \\\\\\ \textit{when y = 7, what is "x"?}\qquad 7=\cfrac{833}{x}\implies x=\cfrac{833}{7}\implies x=119[/tex]
Identify the composition that is represented by: r (90, 0) T(−2,4)
A translation left 2, up 4 and then a reflection of 90°
A rotation of 90° and then a translation left 2, up 4.
A translation of left 2, up 4 and then a rotation of 90°.
A reflection of 90° and then a translation left 2, up 4.
The composition of the transformation is (b) A rotation of 90° and then a translation left 2, up 4.
How to determine the transformation?The transformation rule is given as:
r (90, 0) T(−2,4)
The r(90,0) represents a rotation of 90 degrees.
The other part of the transformation rule can be rewritten as:
T(-2,4) => (x - 2,y + 4)
This means a translation right by 2 units and up by 4 units
Hence, the composition of the transformation is (b)
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Answer: left 2
Step-by-step explanation:
1. Ms. Cedric bought a jar for 25 dimes. If she had 75
nickels, how much money is left in her bag?