where is the example? What are the binomials?- or do we use any three?
divide 210 between James and John in ratio 3:4
well, we can simply divide 210 by (3 + 4) and then distribute accordingly
[tex]\stackrel{James}{3}~~ : ~~\stackrel{John}{4} ~~ \implies ~~ \stackrel{James}{3 ~~ \cdot \frac{210}{3+4}}~~ : ~~\stackrel{John}{4~~ \cdot \frac{210}{3+4}} ~~ \implies ~~ \stackrel{James}{3 \cdot \frac{210}{7}}~~ : ~~\stackrel{John}{4 \cdot \frac{210}{7}} \\\\\\ \stackrel{James}{3(30)}~~ : ~~\stackrel{John}{4(30)} ~~ \implies ~~ \stackrel{James}{90}~~ : ~~\stackrel{John}{120}[/tex]
Answer:
James- 90 and John- 120
Step-by-step explanation:
Since you want to divide 210 with a ratio of 3:4. It's easiest to first add your 3 and 4. This =7. Now you know you have to divide 210 by 7 before you give them to James and John. 210 divided by 7 = 30. Now do 30 times each ratio.
James has 30 x 3 and John has 30 x 4
this leaves you with 90 and 120
The remainder is what’s left when you divide. The part you cannot divide.
You can divide 75 by 3 = 25, so the remainder is 1.
The correct dividend of 76 is required to yeild a quotient of 25 and a remainder of 1 when divided by 3.
Division FormulaWe can know the dividend, the quotient and the remainder of the division using the division formula: (Divisor x Quotient) + Remainder = Dividend
Divisor = 3
Quotient = 25
Remainder = 1
(3 × 25) + 1 = 75 + 1
(3 × 25) + 1 = 76
Thus, the dividend 76 divided by the divisor 3 have the quotient 25 and a remainder when of 1.
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A family buys a studio apartment for $200,000. They pay a down payment of $50,000. a. Their down payment is what percent of the purchase price? b. What percent of the purchase price would a $90,000 down payment be?
Hence, in option (A) the down payment is what percent of the purchase price is [tex]25[/tex]% and in option (B) the purchase price would be [tex]90000[/tex] $ down payment is [tex]45[/tex] %.
What is the installation amount?
Installation Cost means the total cost payable by the Lessee to the Lessee’s direct contractor under the contract for the carpet installation works.
Payment of the Attendance Fees for the Designated Works may be made by the Lessee progressively in the course of the relevant Designated Works being carried out.
Here given that,
A family buys a studio apartment for $[tex]200,000[/tex]. They pay a down payment of $[tex]50,000[/tex].
(A)
The down payment is the percentage of purchase price is
[tex]\frac{50000}{200000}[/tex] × [tex]100[/tex] [tex]=[/tex] [tex]25[/tex] %
(B)
The percent of the purchase price would be [tex]90000[/tex] $ down payment is
[tex]\frac{90000}{200000}[/tex] ×[tex]100[/tex] [tex]=45[/tex] %
Hence, in option (A) the down payment is what percent of the purchase price is [tex]25[/tex]% and in option (B) the purchase price would be [tex]90000[/tex] $ down payment is [tex]45[/tex] %.
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solve ((-3) x (10 + (-7))) to the power of 2 divided by 3 - (-9) to the power of 2)
The solution of the given expression will be 9/16.
What is an expression?Expressions in maths are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.
Given an expression, [-3*(10+(-7))]²÷[(3-(-9)]²
= [-3*(10+(-7))]²÷[(3-(-9)]² = (-9)²/12²
= 9/16
Hence, The solution of the given expression will be 9/16.
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the least-squares solution of a x = b is the vector in the column space of a closest to b. true or false?
The statement that least-squares solution of a x = b is the vector in the column space of a closest to b is; true
How to interpret least square solution of matrix vector?
One method for computing a least-squares solution of Ax = b is;
Compute the matrix A T A as well as the vector A T b .Form the needed augmented matrix for the given matrix equation A T Ax = A T b , and then row reduce.This equation is always consistent, and as such any solution K x will be a least-squares solution.Now, If b is in the column space of A then it tells us that there is at least one exact solution to the system Ax = b. In this case, it means that every solution to the system minimizes |Ax − b| (makes it zero) and as such is a least squares solution.
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4[tex]\left \{ {{y=2} \atop {x=2}} \right. \left \{ {{y=2} \atop {x=2}} \right. \int\limits^a_b {x} \, dx \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right][/tex]
Answer:
5 4/9
Step-by-step explanation:
our equation is 4 2/3+7/9
2/3=6/9.
So we have 4 6/9+7/9
Simplify:
4 13/9
5 4/9
A. Directions: Add the following decimals and mixed decimals. Write your answer on the
spaces provided.
1. 8.9395 +1.2973=
2.2.8862 +8.2758=
3. 5.9529 +2.0043 =
4. 1.223+0.4643=
5. 3.2292 +9.45 =
=
100.0
6. 2.421 +6.0473=
7. 5.2697 + 4.4603
8. 0.0003 +2.6035 =
9. 3.7092 +9.2965-
10. 7.0551 +0.8388:
=
The answer for 8.9395 +1.2973 is 10.2368 for .2.8862 +8.2758=11.162, and for 5.9529 +2.0043 = 7.9572.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.
1. 8.9395 +1.2973=10.2368
2.2.8862 +8.2758=11.162
3. 5.9529 +2.0043 = 7.9572
4. 1.223+0.4643=1.6873
5. 3.2292 +9.45 =12.6792
6. 2.421 +6.0473=8.4683
7. 5.2697 + 4.4603=9.73
8. 0.0003 +2.6035 =2.6038
9. 3.7092 +9.2965=13.0057
10. 7.0551 +0.8388=7.8939
Thus, the answer for 8.9395 +1.2973 is 10.2368 for .2.8862 +8.2758=11.162, and for 5.9529 +2.0043 = 7.9572.
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a group of friends were working on a student flim. they spent $504 on props, which was 42% of their total budget. What was the total budget for the student film.
Answer:
1200 dollars
Step-by-step explanation:
1.) Create an equation. If we use x as a variable for the total money, we get [tex]\frac{504}{x}=\frac{42}{100}[/tex] .
2.) By solving this equation, we get 42x = 50400, and x = 1200.
Therefore, their total budget was 1200 dollars.
Resuelva:
1) |3 x-1|-|2 x+5-(5-x)|=0
2) |2(x+1)-4|=|2-2(2-x)|
3) |x-2/4|-1/3=x
4) 1/2|x-3|-1=|x-3|+2
The absolute functions |3x - 1| - |2x + 5 - (5 - x)| = 0, |2(x + 1) - 4| - 4| = |2 - 2(2 - x)|, |(x - 2) / 4| - 1/3 = x and 1/2|x - 3| - 1 = |x - 3| + 2 have solutions of 1/6, 1, 2/15 and no solutions respectively
Absolute FunctionAn absolute value function is a function in algebra where the variable is inside the absolute value bars. This function is also known as the modulus function and the most commonly used form of the absolute value function is f(x) = |x|, where x is a real number. Generally, we can represent the absolute value function as, f(x) = a |x - h| + k, where a represents how far the graph stretches vertically, h represents the horizontal shift and k represents the vertical shift from the graph of f(x) = |x|. If the value of 'a' is negative, the graph opens downwards and if it is positive, the graph opens upwards.
In the questions given;
1) |3x - 1| - |2x + 5 - (5 - x)| = 0
x = 1/6
2) |2(x + 1) - 4| - 4| = |2 - 2(2 - x)|
x = 1
3) |(x - 2) / 4| - 1/3 = x
x = 2 / 15
4) 1/2|x - 3| - 1 = |x - 3| + 2
The equation has no solution
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Girard buys 9 tons of rocks to build a long rock wall. Each section
of the wall weighs 500 pounds, or ¼
ton. How many sections can
Girard build?
Answer: 36
Step-by-step explanation:
4 sections are 2,000 lbs or 1 ton
To find the pounds Girard has to build, we know we have 9 tons, therefore if each ton is 2,000 lbs, multiply 2,000 by 9 to get 18,000 lbs to use
2,000 lbs per ton x 9 tons= 18,000 lbs to use
now take the 18,000lbs and divide by 500 to find the number of sections we can build
18,000lbs / 500 pounds per section = 36
36 sections is the answer
When Ibuprofen is given for fever to children 6 months of age up to 2 years, the usual dose is 5 milligrams (mg) per kilogram (kg) of body weight when the fever is under 102.5 degrees Fahrenheit. How much medicine would be usual dose for a 18 month old weighing 22 pounds?
If Ibuprofen is given for fever to children 6 months of age up to 2 years.The amount of much medicine that would be usual dose for a 18 month old weighing 22 pounds is 50kg.
How to find the medicine dose?1 pound = 0.45 kg
Hence,
22 pounds = 22×0.45 Kg
22 pounds = 9.9Kg
Now let find the the amount of medicine that would be the usual dose
Medicine dose = 5mg × 9.9kg
Medicine dose =49.5 kg
Medicine dose = 50 kg
Therefore the medicine dose is 50kg.
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A bird sits on the branch of a tree, then starts to fly. The height of the bird is described by the function y = 0.6sin(πx/12) + 35, where y represents the height of the bird measured in meters, and x represents the number of seconds since the bird left the branch.
Which function expresses y, the number of seconds since the bird left the branch, as a function of x, the height of the bird in meters?
A.y=12/πsin^-1(x-35/0.6)
B.y=12/πsin^-1(x+35/0.6)
C.y=π/12sin^-1(x/0.6)-35
D.y=π/12sin^-1(x/0.6)+35
y=12/πsin⁻¹(x-35/0.6) is the function which expresses y, the number of seconds since the bird left the branch, as a function of x, the height of the bird in meters
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given,
A bird sits on the branch of a tree, then starts to fly.
The height of the bird is described by the function y = 0.6sin(πx/12) + 35
Where y represents the height of the bird measured in meters,
x represents the number of seconds since the bird left the branch
We need to find the function expresses y, the number of seconds since the bird left the branch, as a function of x, the height of the bird in meters
y=12/πsin⁻¹(x-35/0.6)
Hence, y=12/πsin⁻¹(x-35/0.6) is the function which expresses y, the number of seconds since the bird left the branch, as a function of x, the height of the bird in meters
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Answer:
Answer is A
Step-by-step explanation:
got it right on assignment.
100 POINTS + BRAINLIEST IF CORRECT
See attached screenshot
Answer:
[tex] p(x)= -2x^3-4x^2+6x[/tex]
Step-by-step explanation:
We need to write a polynomial with zeroes -3 , 0 and 1 , with a leading coefficient of 2 . We know that if a polynomial has 3 zeroes say [tex]\alpha[/tex] , [tex]\beta[/tex] and [tex]\gamma[/tex] , then the polynomial can we written as ,
[tex]\longrightarrow p(x) = k[ ( x -\alpha)(x-\beta)(x-\gamma)] [/tex]
where k is a constant , and here k = -2 .So , similarly we can write it as;
[tex]\longrightarrow p(x) = -2[ (x -(-3)) (x-0) (x-1)\\[/tex]
Simplify,
[tex]\longrightarrow p(x) = - 2[ (x+3)(x)(x-1) ]\\[/tex]
[tex]\longrightarrow p(x) = -2[ (x^2+3x)(x-1)]\\[/tex]
[tex]\longrightarrow p(x) = -2[ x(x^2+3x)-1(x^2+3x)\\ [/tex]
[tex]\longrightarrow p(x) = -2[ x^3 +3x^2 -x^2-3x ]\\[/tex]
[tex]\longrightarrow p(x)= -2[ x^3 +2x^2 -3x]\\[/tex]
[tex]\longrightarrow\underline{\underline{ p(x)= -2x^3-4x^2+6x }} [/tex]
And we are done!
Write the point-slope form of the equation of the line that passes through the points (6, -9) and (7, 1). a. Using variables, write out the formula for the point-slope form of the equation. b. Determine the slope of the line. c. Write the point-slope form of the line. Show all work on how you found the slope. Use the box provided to submit all of your calculations and final answers. Simplify the answer as needed.
The point slope form of the equation of the line that passes through the points (6, -9) and (7, 1) is y - 1 = 10(x - 7)
How to represent equation in point slope form?Linear equation can be represented in different form such as point slope form, slope intercept from, standard form and general form.
The line passes through the points (6, -9) and (7, 1). The point slope form can be represented as follows:
y - y₁ = m(x - x₁)
where
m = slopex₁ and y₁ are variablesTherefore, let's find the equation of the line that passes through the points (6, -9) and (7, 1).
Let's find the slope.
slope = m = 1 + 9 / 7 - 6
slope = 10 / 1
slope = 10
Therefore,
y - 1 = 10(x - 7)
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1) A bus stops every 400m. How many stops does it make in travelling a distance of 20kmaround a city?
2: A kitchen garden is made up of a rectangle and a square as shown in Fig. 4.2. What is the perimeter of the garden in
(a) metres?
(b) centimetres?
Answer: 1. 50 stops.
Step-by-step explanation:
There is 1,000 meters in a Kilometer. So 20,000/400=50
Answer:
1) 50 stops
2) a: 60 meters
b: 6,000 centimeters
Step-by-step explanation:
A) we have to convert 20k into meters to solve it
To do that we multiply by 1000
20x1000
20,000 meters now we divide by 400 to see how many stops
20,000/400
50 stops
2)
to find perimeter is meters we add all of the sides together
20+10+5+5+15+5
30+10+20
30+30
60 m is the perimeter
Now in centimeters we multiply by 100
60x100
6,000 centimeters
Hopes this helps please mark brainliest
Which expression is equivalent to ↓
Step-by-step explanation:
Answer is D.
Breaking it down;
1/3 + 2/6 = 4/6.
4/6 - 5/6 = -1/6
-1/6 × 3/11 = -3/66
Encuentra la ecuación de la parábola y los elementos que se solicitan, sabiendo que su vértice está en el origen y su foco está en F (0, -15).
The equation of parabola for the given statement is: [tex]x^{2} = -60y[/tex]
What is Parabola ?The locus of points where point moves under a restriction that its distance from a fixed point Focus(F) and fixed line Directrix always remain constant
Solution: here focus of parabola is on -ve y axis so we will take general equation of parabola whose focus is on -ve y axis and directrix will be above x axisi.e[tex]x^{2} =-4ay[/tex]
here a is the distance between vertex and focus and here vertex is origin so by distance formula it comes out to be a = 15
put back in above equation we get its equation[tex]x^{2} = -60y[/tex]which is our required equation of parabola.
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Does the equation describe a function?
y=8
yes or no?
Yes, the equation:
y = 8
describes a function.
Does the equation describe a function?A function is a relation that maps elements x into elements y, such that each element x is mapped into a single value of y.
In this case, we have the equation:
y = 8
So all our points are of the form (x, 8).
Notice that all the inputs x are mapped into a single output y = 8, then this relation is a function.
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3. Four relationships are given.
Relationship A: x 3 2 1 y 2 2/3 1 2 / 3 2/3 Relationship B: 2x=y
Relationship C: y=2+x
Relationship D: x 3 6 y 6 12 In which two relationships are the constant of proportionality 2?
Of the four relationships the ones that have the constant of proportionality of 2 are
Relationship B and Relationship DHow to show the the constant of proportionality existing between themThe constant of proportionality is the constant that relates the input with output terms
Relationship A
the output, y dies it equal 2 * input
an instance = 2 * 3 = 6 not 2 2/3
Relationship B
y = 2x has the constant written out already
Relationship C
Represents a linear function
Relationship D
y = 6, x = 3
y = 2x
when x = 3 y = 6
when x = 6 y = 12
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The length of a rectangle is 4 inches more than its width. The area of the rectangle is equal to 4 inches less than 4 times the perimeter. Find l and w
Answer:
Step-by-step explanation:
[tex]l=w+4[/tex]
[tex]A=l*w\\l=w+4\\A=(w+4)w\\A=w^2+4w[/tex]
[tex]P=2l+2w\\A=4p-4\\A=4(2l+2w)-4\\A=8l+8w-4\\l=w+4\\A=8(w+4)+8w-4\\A=8w+32+8w-4\\A=16w+28[/tex]
[tex]16w+28=A=w^2+4w\\16w+28=w^2+4w\\w^2-12w-28=0\\w^2-14w+2w-28=0\\(w^2-14w)+(2w-28)=0\\w(w-14)+2(w-14)=0\\w+2=0=w-14\\w=-2and14[/tex]
Since w represents a measurement of a physical object in inches, it cannot be negative. So, [tex]w\neq-2[/tex]. The width of the rectangle is 14 inches.
The length is given as 4 inches more than the width, so the length is 18 inches.
This satisfies all the requirements of the question:
[tex]4P-4=A\\P=2(18)+2(14)=64in\\4P=64in(4)=256in\\A=18in*14in=252in^2\\256-4=252\\252=252[/tex]
I need help with this fast. Can anyone help me thank you
Part (a)
4, read it off the diagram.
Part (b)
(4 in)(1 ft/12 in) = 1/3 ft
Part (c)
(60 ft)(20 ft)(1/3 ft)=400 cu ft
Part (d)
(66 ft)(26 ft)(1/3 ft)=572 cu ft
Part (e)
572 cu ft - 400 cu ft = 172 cu ft
The side ratio of two shapes is 3:4.
The ratio of the area of the two squares is 9:16.
A square has four corners and is a closed, two-dimensional (2D) object. A square has equal and parallel sides on all four sides.
A square is a closed object with four sides that are all the same length, and its interior angles are all 90 degrees. A square can have many different characteristics. The following list includes some of a square's key characteristics.
A quadrilateral with four sides and four vertices is called a square.The square's four sides are equal to one another.A square's diagonals are parallel to one another.Each vertex of a square has a 90° internal angle.360° is the total of all interior angles.If it is square:
The ratios of the sides of two squares = 3:4
Let the common multiple of the above ratio be x.
So, side of one square = 3x
and side of the other square = 4x
Area of square = (side)²
Area of square with side 3x = (3x)² = 9x²
Area of square with side 4x = (4x)²= 16x²
Ratio of the areas of the two squares = Area of square with side 3x/Area of square with side 4x = 9x²/16x² = 9/16 = 9:16
Therefore, the ratio of the area of the two squares is 9:16.
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Does the equation describe a function? y=8
The equation y = 8 does not describe a function
How to determine if an equation describes a function?
A function is an equation that has only one output or answer (y) for every input (x) e.g y = 2x
If we plot y =8 on a coordinate plane, you would see that at the point of (0, 8) is a horizontal line.
Also, no matter the value of the input (x), the value of when of the output (y) will always remain 8. This does not fit the description of a function
Therefore, the equation y =8 does not describe a function
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A triangular prism is 17 meters long and has a triangular face with a base of 16 meters and a height of 15 meters. The other two sides of the triangle are each 17 meters. What is the surface area of the triangular prism?
The surface area of the triangular prism is 1090 metres squared.
How to find the surface area of a triangular prism?A triangular prism is a polyhedron made up of two triangular bases and three rectangular sides.
Therefore, let's find the surface area of the triangular prism.
Surface area of the triangular prism = bh + l(a + b + c)
where
b = base of the triangular faceh = height of the trianglesa, b and c are the sides of the trianglel = height of the prismTherefore,
Surface area of the triangular prism = 16 × 15 + 17(17 + 17 + 16)
Surface area of the triangular prism = 240 + 17(50)
Surface area of the triangular prism =240 + 850
Surface area of the triangular prism = 1090 metres squared
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If f(x)=x^(2 )+4 then verify (fof^(-1))(x)=(f^(-1) of)(x)=x. (Consider the positive values only)
Answer:
Step-by-step explanation:
If f(x)=x²+4 then (fof⁻¹)(x)=(f⁻¹of)(x)=x is proved
What is a function?A relation is a function if it has only One y-value for each x-value.
Composite functions are when the output of one function is used as the input of another.
If f(x)=x²+4
Then we have to prove f⁻¹of(x)=f⁻¹(f(x)
Let us consider fof⁻¹(x)
f(f⁻¹(x))
x
So (fof⁻¹(x))=x
Now f⁻¹of(x)=f⁻¹(f(x)
=x
Hence, If f(x)=x²+4 then (fof⁻¹)(x)=(f⁻¹of)(x)=x is proved
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You are baking chocolate chip cookies. One batch makes 5 dozen big cookies. The recipe calls for 3/4 cup brown sugar. How many cups of brown sugar would you need it you wanted to make 13 dozen cookies?
Answer:
1 [tex]\frac{19}{20}[/tex] cups
Step-by-step explanation:
[tex]\frac{cookies}{sugar}[/tex] = [tex]\frac{cookies}{sugar}[/tex]
[tex]\frac{5}{\frac{3}{4} }[/tex] = [tex]\frac{13}{x}[/tex] Cross multiply and solve for x
5x = (13)([tex]\frac{3}{4}[/tex])
5x = [tex]\frac{39}{4}[/tex] Divide both sides by 5
x = [tex]\frac{39}{4}[/tex]÷5
x = [tex]\frac{39}{4}[/tex] x [tex]\frac{1}{5}[/tex]
x = [tex]\frac{39}{20}[/tex]= 1 [tex]\frac{19}{20}[/tex]
I NEED HELP ASAP WITH THIS QUESTION
Answer: B. The Total profit made when a person buys a car for $10,000 and sells it for $10,000.
Step-by-step explanation:
Answer A would be wrong since when there is a temperature change from 15 degrees to -15 degrees would lead to an overall change of 30 degrees.
Answer C would be wrong as well since it is decreasing 500 feet in altitude, meaning that there is a negative change in altitude.
Answer D would also be wrong since the train is traveling 35 miles north, then south. That means that even though the train is in the same place that is was before, it traveled a total of 70 miles to return to where it was previously at.
Hope this helps!
Find the area and the circumference of a circle with radius 7 m.
Use the value 3.14 for π, and do not round your answers.
Area=?
Circumference=?
Answer:
[tex]Area = 153.938040026m^2[/tex]
[tex]Circumference= 43.9822971503m[/tex]
Step-by-step explanation:
Area
[tex]Area = \pi r^2\\Area = \pi *7^2\\Area = 49\pi\\Area = 153.938040026[/tex]
Circumference
[tex]C = 2\pi r\\C = 2\pi*7\\C= 14\pi\\C=43.9822971503[/tex]
Part of the proceeds from a garage sale was $500 worth of $10 and $20 bills. If there were 11 more $10 bills than $20 bills, find the number of each denomination.
There were
enter your response here $10 bills
enter your response here $20 bills.
From the given parameters of linear equation, we can say that;
The number of $10 bills is; 24
The number of $20 bills is; 13
How to solve linear equation word problems?Let x be the number of the $20 dollars bills.
Then the number of the $10 dollars bills is (x + 11), according to the condition.
The money equation is expressed as;
20x + 10*(x + 11) = 500
Simplify and solve for x.
20x + 10x + 110 = 500
30x = 500 - 110
30x = 390
x = 390/30
x = 13
Then number of $10 bills is 13 + 11 = 24
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Given the following table of values for f(x), find f(5).
x −4 0 1 4 5 7
f(x) 3 −3 −3 −5 5 9
Check the picture below.
