How to divide using area model
Answers
Answer:
In mathematics, an area model is a rectangular diagram or model used for multiplication and division problems, in which the or the and define the length and width of the rectangle.
We can break one large of the rectangle into several smaller boxes, using number bonds, to make the calculation easier. Then we add to get the area of the whole, which is the or quotient.
To multiply two 2-digit numbers, using the area model, follow the given steps:
Write the multiplicands in expanded form as tens and ones.
For example, 27 as 20 and 7, and 35 as 30 and 5.
Draw a 2 × 2 grid, that is, a box with 2 rows and 2 columns.
Write the terms of one of the multiplicands on the top of the grid (box). One on the top of each cell.
On the left of the grid, write the terms of the other multiplicand. One on the side of each cell.
Write the product of the number on the tens in the first cell. Then write the product of the tens and ones in the second and third cell. Write the product of the ones in the fourth cell.
write the product in the cell
Finally, add all the partial products to get the final product.
Here, for example, the area model has been used to multiply 27 and 35.
area model multiplication
Let us see how to find the product of 3-digit number by a 2-digit number using the area model.
Find the Product using Area Model
Let us now use the area model for the division. Here, we divide 825 by 5.
Area Model Division 1
Area Model Division 2
Fun Facts
The area model is also known as the box model.
The area model of solving multiplication and division problems is derived from the concept of finding the area of a rectangle. Area of a rectangle = Length × Width.
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Related Questions
The average of two numbers is 5x. If one of the numbers is 2x + 3, find the other number.
Answers
Answer:
8x-3
Step-by-step explanation:
Average of 2 numbers means add the two numbers and divide by 2
(y+z)/2 = 5x
Let z = 2x+3
(y+2x+3)/2 = 5x
Multiply each side by 2
y+2x+3 = 10x
Subtract 2x from each side
y+3 = 10x-2x
y+3 = 8x
Subtract 3
y = 8x-3
The other number is 8x-3
Use the information below to complete the problem: p(x)=1/x+1 and q(x)=1/x-1 Perform the operation and show that it results in another rational expression. p(x) + q(x)
Answers
Answer:
hope u will understand...if u like this answer plz mark as brainlist
Answer:
[tex]\displaystyle p(x) + q(x) = \frac{2x}{(x+1)(x-1)}[/tex]
The result is indeed another rational expression.
Step-by-step explanation:
We are given the two functions:
[tex]\displaystyle p(x) = \frac{1}{x+1}\text{ and } q(x) = \frac{1}{x-1}[/tex]
And we want to perform the operation:
[tex]\displaystyle p(x) + q(x)[/tex]
And show that the result is another rational expression.
Add:
[tex]\displaystyle = \frac{1}{x+1} + \frac{1}{x-1}[/tex]
To combine the fractions, we will need a common denominator. So, we can multiply the first fraction by (x - 1) and the second by (x + 1):
[tex]\displaystyle = \frac{1}{x+1}\left(\frac{x-1}{x-1}\right) + \frac{1}{x-1}\left(\frac{x+1}{x+1}\right)[/tex]
Simplify:
[tex]=\displaystyle \frac{x-1}{(x+1)(x-1)} + \frac{x+1}{(x+1)(x-1)}[/tex]
Add:
[tex]\displaystyle = \frac{(x-1)+(x+1)}{(x+1)(x-1)}[/tex]
Simplify. Hence:
[tex]\displaystyle p(x) + q(x) = \frac{2x}{(x+1)(x-1)}[/tex]
The result is indeed another rational expression.
please help! 50 points!
Answers
Answer:
a) forming a bell
b) 5
c) 4.7
d) mean
is the correct answer
pls mark me as brainliest
A 230 pound man, a 140 pound woman, a 750 pound crate of equipment, an 80 pound bag of concrete. What percent of the total weight was concrete?
What percent of the total weight was human?
Answers
Human percent: 370/1200 = .308333 = 30.8 %
why infinity ( ) can’t be included in an inequality?
Answers
Answer:
Step-by-step explanation:
Because then the value on the other side will be unbounded by the infinity sign while expressing the answers on a number line.
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Please answer this question
Answers
Translate this phrase into an algebraic expression.
61 less than twice Jenny's age
Use the variable j to represent Jenny's age.
Answers
j = Jenny's age
What is A11 for the geometric sequence 3,072, −1,536, -768, −384...?
Answers
Answer:
3
Step-by-step explanation:
The general formula of the series is 3072/(-2)^(n-1). A11=3072/(-2)^10=3
10. (30-i)-(18+6i)+30i
Answers
Answer:
[tex]12+23i[/tex]
Step-by-step explanation:
[tex](30−i)−(18+6i)+30i[/tex]
[tex]30−i−18−6i+30i[/tex]
[tex]12−i−6i+30i[/tex]
[tex]12−7i+30i[/tex]
[tex]12+23i[/tex]
Hope it is helpful....Addition prop of equality
subtraction prop of quality
multiplication prop of equality
Division prop of equality
simplifying
distrib prop
Answers
2simplifying
3 Addition prop
4 simplifying
what is the slope and point
Answers
Answer:
Step-by-step explanation:
Again need help with these ones I don’t understand and they have to show work
Answers
[tex]x^2 - 18x + 81= 65 + 81[/tex]
[tex](x - 9)^2 = 146[/tex]
Taking the square root of both sides, we get
[tex]x - 9 = \pm\sqrt{146}[/tex]
or
[tex]x = 9 \pm \sqrt{146} = 9 \pm 12.1 = 21.1\:\text{and}\:-3.1[/tex]
use undetermined coefficient to determine the solution of:y"-3y'+2y=2x+ex+2xex+4e3x
Answers
First check the characteristic solution: the characteristic equation for this DE is
r ² - 3r + 2 = (r - 2) (r - 1) = 0
with roots r = 2 and r = 1, so the characteristic solution is
y (char.) = C₁ exp(2x) + C₂ exp(x)
For the ansatz particular solution, we might first try
y (part.) = (ax + b) + (cx + d) exp(x) + e exp(3x)
where ax + b corresponds to the 2x term on the right side, (cx + d) exp(x) corresponds to (1 + 2x) exp(x), and e exp(3x) corresponds to 4 exp(3x).
However, exp(x) is already accounted for in the characteristic solution, we multiply the second group by x :
y (part.) = (ax + b) + (cx ² + dx) exp(x) + e exp(3x)
Now take the derivatives of y (part.), substitute them into the DE, and solve for the coefficients.
y' (part.) = a + (2cx + d) exp(x) + (cx ² + dx) exp(x) + 3e exp(3x)
… = a + (cx ² + (2c + d)x + d) exp(x) + 3e exp(3x)
y'' (part.) = (2cx + 2c + d) exp(x) + (cx ² + (2c + d)x + d) exp(x) + 9e exp(3x)
… = (cx ² + (4c + d)x + 2c + 2d) exp(x) + 9e exp(3x)
Substituting every relevant expression and simplifying reduces the equation to
(cx ² + (4c + d)x + 2c + 2d) exp(x) + 9e exp(3x)
… - 3 [a + (cx ² + (2c + d)x + d) exp(x) + 3e exp(3x)]
… +2 [(ax + b) + (cx ² + dx) exp(x) + e exp(3x)]
= 2x + (1 + 2x) exp(x) + 4 exp(3x)
… … …
2ax - 3a + 2b + (-2cx + 2c - d) exp(x) + 2e exp(3x)
= 2x + (1 + 2x) exp(x) + 4 exp(3x)
Then, equating coefficients of corresponding terms on both sides, we have the system of equations,
x : 2a = 2
1 : -3a + 2b = 0
exp(x) : 2c - d = 1
x exp(x) : -2c = 2
exp(3x) : 2e = 4
Solving the system gives
a = 1, b = 3/2, c = -1, d = -3, e = 2
Then the general solution to the DE is
y(x) = C₁ exp(2x) + C₂ exp(x) + x + 3/2 - (x ² + 3x) exp(x) + 2 exp(3x)
Subtract the integers. 22−(−10)
Answers
Answer:
32
Step-by-step explanation:
Step 1: change 22 - ( - 10) into 22 + 10
Step 2: solve it like normal
If per unit variable cost of a product is Rs.8 and fixed cost is Rs 5000 and it is sold for Rs 15 per unit, profit in 1000 units is.......
a.. rs 7000
b. rs 2000
c. rs 25000
d. rs 0
Answers
Answer:
a.. rs 7000
Because 15×1000=15000 it is SP when selling 1000units in the rate of Rs 15/unit& 8×1000=8000 this is cp when buying 1000 units in the rate of Rs 8/unit.
So,by formula of profit,
Rs (15000-8000)=Rs7000
help with 1 b please. using ln.
Answers
Answer:
[tex]\displaystyle \frac{dy}{dx} = \frac{1}{(x - 2)^2\sqrt{\frac{x}{2 - x}}}[/tex]
General Formulas and Concepts:
Pre-Algebra
Equality PropertiesAlgebra I
Terms/CoefficientsFactoringExponential Rule [Root Rewrite]: [tex]\displaystyle \sqrt[n]{x} = x^{\frac{1}{n}}[/tex]Algebra II
Natural logarithms ln and Euler's number eLogarithmic Property [Exponential]: [tex]\displaystyle log(a^b) = b \cdot log(a)[/tex]Calculus
Differentiation
DerivativesDerivative NotationImplicit DifferentiationDerivative Property [Multiplied Constant]: [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]
Derivative Property [Addition/Subtraction]: [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]
Basic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Derivative Rule [Quotient Rule]: [tex]\displaystyle \frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}[/tex]
Derivative Rule [Chain Rule]: [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]
Step-by-step explanation:
*Note:
You can simply just use the Quotient and Chain Rule to find the derivative instead of using ln.
Step 1: Define
Identify
[tex]\displaystyle y = \sqrt{\frac{x}{2 - x}}[/tex]
Step 2: Rewrite
[Function] Exponential Rule [Root Rewrite]: [tex]\displaystyle y = \bigg( \frac{x}{2 - x} \bigg)^\bigg{\frac{1}{2}}[/tex][Equality Property] ln both sides: [tex]\displaystyle lny = ln \bigg[ \bigg( \frac{x}{2 - x} \bigg)^\bigg{\frac{1}{2}} \bigg][/tex]Logarithmic Property [Exponential]: [tex]\displaystyle lny = \frac{1}{2}ln \bigg( \frac{x}{2 - x} \bigg)[/tex]Step 3: Differentiate
Implicit Differentiation: [tex]\displaystyle \frac{dy}{dx}[lny] = \frac{dy}{dx} \bigg[ \frac{1}{2}ln \bigg( \frac{x}{2 - x} \bigg) \bigg][/tex]Logarithmic Differentiation [Derivative Rule - Chain Rule]: [tex]\displaystyle \frac{1}{y} \ \frac{dy}{dx} = \frac{1}{2} \bigg( \frac{1}{\frac{x}{2 - x}} \bigg) \frac{dy}{dx} \bigg[ \frac{x}{2 - x} \bigg][/tex]Chain Rule [Basic Power Rule]: [tex]\displaystyle \frac{1}{y} \ \frac{dy}{dx} = \frac{1}{2} \bigg( \frac{1}{\frac{x}{2 - x}} \bigg) \bigg[ \frac{2}{(x - 2)^2} \bigg][/tex]Simplify: [tex]\displaystyle \frac{1}{y} \ \frac{dy}{dx} = \frac{-1}{x(x - 2)}[/tex]Isolate [tex]\displaystyle \frac{dy}{dx}[/tex]: [tex]\displaystyle \frac{dy}{dx} = \frac{-y}{x(x - 2)}[/tex]Substitute in y [Derivative]: [tex]\displaystyle \frac{dy}{dx} = \frac{-\sqrt{\frac{x}{2 - x}}}{x(x - 2)}[/tex]Rationalize: [tex]\displaystyle \frac{dy}{dx} = \frac{-\frac{x}{2 - x}}{x(x - 2)\sqrt{\frac{x}{2 - x}}}[/tex]Rewrite: [tex]\displaystyle \frac{dy}{dx} = \frac{-x}{x(x - 2)(2 - x)\sqrt{\frac{x}{2 - x}}}[/tex]Factor: [tex]\displaystyle \frac{dy}{dx} = \frac{-x}{-x(x - 2)^2\sqrt{\frac{x}{2 - x}}}[/tex]Simplify: [tex]\displaystyle \frac{dy}{dx} = \frac{1}{(x - 2)^2\sqrt{\frac{x}{2 - x}}}[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
Book: College Calculus 10e
Find the sum of ∑3/k=0 k^2
Answers
Answer:
[tex]14[/tex]
Step-by-step explanation:
Given
[tex]\displaystyle \sum_{k=0}^3k^2[/tex]
Let's break down each part. The input at the bottom, in this case [tex]k=0[/tex], is assigning an index [tex]k[/tex] at a value of [tex]0[/tex]. This is the value we should start with when substituting into our equation.
The number at the top, in this case 3, indicates the index we should stop at, inclusive (meaning we finish substituting that index and then stop). The equation on the right, in this case [tex]k^2[/tex], is the equation we will substitute each value in. After we substitute our starting index, we'll continue substituting indexes until we reach the last index, then add up each of the outputs produced.
Since [tex]k=0[/tex] is our starting index, start by substituting this into [tex]k^2[/tex]:
[tex]0^2=0[/tex]
Now continue with [tex]k=1[/tex]:
[tex]1^1=1[/tex]
Repeat until we get to the ending index, [tex]k=3[/tex]. Remember to still use [tex]k=3[/tex] before stopping!
Substituting [tex]k=2[/tex]:
[tex]2^2=4[/tex]
Substituting [tex]k=3[/tex]:
[tex]3^2=9[/tex]
Since 3 is the index we end at, we stop here. Now we will add up each of the outputs:
[tex]0+1+4+9=\boxed{14}[/tex]
Therefore, our answer is:
[tex]\displaystyle \sum_{k=0}^3k^2=0+1+4+9=\boxed{14}[/tex]
Answer:
14
Step-by-step explanation:
∑3/k=0 k^2
Let k=0
0^2 =0
Let k = 1
1^2 =1
Let k =2
2^2 = 4
Let k = 3
3^2 = 9
0+1+4+9 = 14
We are given a weighted coin (with one side heads, one side tails), and we want to estimate the unknown probability pp that it will land heads. We flip the coin 1000 times and it happens to land heads 406 times. Give answers in decimal form, rounded to four decimal places (or more). We estimate the chance this coin will land on heads to
Answers
Answer:
0.4060
Step-by-step explanation:
To calculate the sample proportion, phat, we take the ratio of the number of preferred outcome to the total number of trials ;
Phat = number of times coin lands on head (preferred outcome), x / total number of trials (total coin flips), n
x = 406
n = 1000
Phat = x / n = 406/ 1000 = 0.4060
The estimate of the chance that this coin will land on heads is 0.406
Probability is the likelihood or chance that an event will occur.Probability = Expected outcome/Total outcomeIf a coin is flipped 1000 times, the total outcomes will 1000
If it landed on the head 406 times, the expected outcome will be 406.
Pr(the coin lands on the head) = 406/1000
Pr(the coin lands on the head) = 0.406
Hence the estimate of the chance that this coin will land on heads is 0.406
Learn more on probability here: https://brainly.com/question/14192140
Which equation is represented by the graph below?
Answers
Answer:
Hello,
Answer C
Step-by-step explanation:
Since ln(1)=0
if x=1 then y=4 ==> y=ln(x)+4
y=ln(x) is translated up for 4 units.
12) Find the angles between 0o and 360o where sec θ = −3.8637 . Round to the nearest 10th of a degree:
Please show all work
Answers
9514 1404 393
Answer:
105.0°, 255.0°
Step-by-step explanation:
Many calculators do not have a secant function, so the cosine relation must be used.
sec(θ) = -3.8637
1/cos(θ) = -3.8637
cos(θ) = -1/3.8637
θ = arccos(-1/3.8637) ≈ 105.000013°
The secant and cosine functions are symmetrical about the line θ = 180°, so the other solution in the desired range is ...
θ = 360° -105.0° = 255.0°
The angles of interest are θ = 105.0° and θ = 255.0°.
The perimeter of a triangle is 83 centimeters. If two sides are equally long and the third side is 8 centimeters longer than the others, find the lengths of the three sides.
Answers
Answer:
25, 33
Step-by-step explanation:
let the length of the one with equal sides be x
third side = x+8
x+x+x+8 = 83
3x+8 = 83
3x = 75
x = 25
x+8 = 25+8 = 33
A tour bus is traveling along a triangular path. The three straight lines form a right triangle. One leg of the triangle represents a distance of 8 miles. The other leg of the triangle is 4 miles shorter than the hypotenuse. What is the length of the hypotenuse of this triangle? Of the other leg?
Answers
Answer:
Hypotenuse=10 miles.
Short leg=6 miles.
Step-by-step explanation:
Set up triangle, leg 8 miles, hypotenuse x miles, short leg x-4 miles.Input into Pythagoras theorem.Simplify.how many feet is in one centimeter and how many inches is in 1 feet?
Answers
Answer:
12 inches r in a foot
0 feet r in a centimeter
Step-by-step explanation:
Answer:
0.032 feet in a centimeter and 12 inches in 1 foot
Step-by-step explanation:
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WORTH 100 POINTS!
The function h(x) is quadratic and h(3) = h(-10) = 0. Which could represent h(x)?
1) h(x) = x2 - 13x - 30
2) h(x) = x2 - 7x - 30
3) h(x) = 2x2 + 26x - 60
4) h(x) = 2x2 + 14x - 60
Answers
Answer:
h(x) = 2x^2 +14x -60
Step-by-step explanation:
A quadratic is of the form
h(x) = ax^2 + bx +c
h(3) = h(-10) = 0
This tells us that the zeros are at x=3 and x = -10
We can write the equation in the form
h(x) = a( x-z1)(x-z2) where z1 and z2 are the zeros
h(x) = a(x-3) (x- -10)
h(x) = a(x-3) (x+10)
FOIL
h(x) = a( x^2 -3x+10x-30)
h(x) = a(x^2 +7x -30)
Let a = 2
h(x) = 2x^2 +14x -60
It means
zeros are 3 and -10
Form equation
y=x²-(3-10)x+(-10)(3)y=x²+7x-30Multi ply by 2
y=2x²+14x-60Option D
Illustrate the 7th pattern of the sequence of square numbers.
Answers
1,4,9,16,25,36,49,........
7th pattern =49.....
Answer:
1, 4, 9, 16, 25, 36, 49…................the 7 the pattern is 49
If the terminal side of an angle (θ) goes through the point (4 , -3) what is (θ)?
Answers
Answer:
The family of directions of the given vector is represented by [tex]\theta = 323.130^{\circ} \pm 360\cdot i[/tex], [tex]\forall \,i\in \mathbb{N}_{O}[/tex].
Step-by-step explanation:
According to the given information, vector stands in the 4th Quadrant ([tex]x > 0[/tex], [tex]y < 0[/tex]) and direction of the vector ([tex]\theta[/tex]) in sexagesimal degrees, is determined by following definition:
[tex]\theta = 360^{\circ} - \tan^{-1} \left(\frac{|y|}{|x|} \right)\pm 360\cdot i[/tex], [tex]\forall \,i\in \mathbb{N}_{O}[/tex]
Please notice that angle represents a function with a periodicity of 360°.
If we know that [tex]x = 4[/tex] and [tex]y = -3[/tex], then the direction of the vector is:
[tex]\theta = 360^{\circ}-\tan^{-1}\left(\frac{|-3|}{|4|} \right)\pm 360\cdot i[/tex]
[tex]\theta = 323.130^{\circ} \pm 360\cdot i[/tex]
The family of directions of the given vector is represented by [tex]\theta = 323.130^{\circ} \pm 360\cdot i[/tex], [tex]\forall \,i\in \mathbb{N}_{O}[/tex].
if point B is the midpoint of points A and C, find the value of x and AC. AB= 5x - 2, BC= 9x -10
Answers
9514 1404 393
Answer:
x = 2AC = 16Step-by-step explanation:
The midpoint divides the segment into two equal lengths:
AB = BC
5x -2 = 9x -10
8 = 4x
2 = x
AB = 5(2) -2 = 8
AC = 2AB = 2(8) = 16
Find the multiplicative inverse of: -3/7 X -4/9
Answers
Hi there!
»»————- ★ ————-««
I believe your answer is:
[tex]\frac{21}{4}[/tex]
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
[tex]\boxed{\text{Calculating the answer...}}\\\\---------------\\\rightarrow -\frac{3}{7} * -\frac{4}{9}\\\\\rightarrow \frac{12}{63} \\\\\rightarrow \frac{12/3}{63/3}\\\\\rightarrow\boxed{\frac{4}{21}}\\--------------\\\rightarrow \frac{4}{21}* x= 1\\\\\rightarrow (21)*\frac{4}{21}x= 1(21)\\\\\rightarrow 4x=21\\\\\rightarrow \frac{4x=21}{4}\\\\\rightarrow \boxed{x=\frac{21}{4}}[/tex]
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
A.) V’ (-3,-5), K’ (-1,-2), B’ (3,-1), Z’(2,-5)
B.) V’(-4, 1), K’(-2, 4), B(2,5) Z’ (1, 1)
C.) V’ (-3,-4), K’(-1,-1) B’ (3,0), Z’(2,-4)
D.) V’ (-1,0), K’ (1, 3), B’(5,4), Z’(4,0)
Answers
Answer:
C
Step-by-step explanation:
this is a "translation" - a shift of the object without changing its shadow and size.
this shift is described by a "vector" - in 2D space by the x and y distances to move.
we have here (1, 0) - so, we move every point one unit to the right (positive x direction) and 0 units up/down.
therefore, C is the right answer (the x coordinates of the points are increased by 1, the y coordinate are unchanged).
Which expression defines the given series for seven terms?
–4 + (–5) + (–6) + . . .
Answers
Answer: -n+(-n-1)
Step-by-step explanation:
Expression will be -n + (-1)
Series
-4 +(-5)+(-6)+(-7)+(-8)+(-9)+(-10)+(-11)+(-12)+(-13) and so on
Here number -n has + (-n-1) being added to it
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