y is directly proportional to (x-1)2.
When x = 3, y = 24.
Find y when x = 6.
Answers
Answer:
y = 150
Step-by-step explanation:
Proportions
It's given y is directly proportional to the square of x-1. It can be expressed as:
\(y=k(x-1)^2\)
Where k is the constant of proportionality. We know y=24 when x=3. Substituting:
\(24=k(3-1)^2\)
\(24=k(2)^2=4k\)
Solving for k:
k = 24/4 = 6
Thus, the equation is:
\(y=6(x-1)^2\)
When x=6:
\(y=6(6-1)^2=6(5)^2=6*25\)
y = 150
Related Questions
The diameter of a circle is 20 ft. Find its area in terms of T.
Answer: A=
ft2
Submit Answer
7
Answers
Answer:
314.2ft^2
Step-by-step explanation:
Given data
Diameter= 20ft
Radius r= 20/2= 10ft
The expression for the area is
A= πr^2
A= 3.142*10^2
A= 3.142*100
A= 314.2ft^2
Hence the area is 314.2ft^2
Which values are solutions to the inequality below? Check all that apply.
√x <10
A. 100
B. 25
C. -100
D. 105
E. 36
F. 9
Answers
Answer:
The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²vvvThe diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²v
Step-by-step explanation:
its E and A
Answer:
The solutions to the inequality are B, E, and F: 25, 36, and 9.
Step-by-step explanation:
The solutions to the inequality √x < 10 are the values of x that make the inequality true when plugged in. To find these values, we can square both sides of the inequality:
√x < 10
x < 10^2 = 100
So, the values of x that make the inequality true are those that are less than 100. The options that satisfy this condition are:
A. 100 (not a solution)
B. 25 (solution)
C. -100 (not a solution)
D. 105 (not a solution)
E. 36 (solution)
F. 9 (solution)
E(y∣x)=β 0 +β 1 x (a) Now apply the properties of expected value to write the unconditional expectation E(y) as a function of the unconditional expectation E(x). That is, simplify the following expression. [Hint: you should recognize the result as following from the Law of Iterated Expectations.] E(y)=E(β 0 +β 1 x+u)=
Answers
The unconditional expectation of y (E(y)) equals β0 + (β1 * E(x)), derived using the Law of Iterated Expectations.
To simplify the expression for the unconditional expectation E(y), we can apply the properties of expected value and the Law of Iterated Expectations. The Law of Iterated Expectations states that the unconditional expectation of a conditional expectation is equal to the unconditional expectation itself.
Starting with the expression for E(y):
E(y) = E(β0 + β1x + u)
We can break down this expression using the linearity of expectation:
E(y) = E(β0) + E(β1x) + E(u)
Since β0 and β1 are constants, their expected values are equal to themselves:
E(y) = β0 + β1E(x) + E(u)
Now, since u is the error term and it is assumed to have a mean of zero (E(u) = 0), the expression simplifies to:
E(y) = β0 + β1E(x)
Therefore, we can conclude that the unconditional expectation of y (E(y)) is equal to the constant term β0 plus the product of the slope coefficient β1 and the unconditional expectation of x (E(x)). This result follows from the Law of Iterated Expectations, which allows us to simplify the expression by considering the expected values of the individual terms separately.
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Which type of sampling is used in the statement, On the day of the last presidential election, ABC News organized an exit poll in which
specific polling stations were randomly selected and all voters were surveyed as they left the premises.
O Systematic
O Stratified
O Cluster
A
O Convenience
Answers
Based on the analysis, the type of sampling used in the given scenario is Cluster Sampling.
Understanding the scenario
ABC News organized an exit poll on the day of the last presidential election, where specific polling stations were randomly selected, and all voters were surveyed as they left the premises. We need to determine the type of sampling used in this scenario.
Steps to identify the sampling type
1. Systematic Sampling: In systematic sampling, every nth item in the population is selected to be included in the sample. This method involves selecting a random starting point and then including every kth element in the sample. However, the scenario does not mention any systematic selection based on a fixed interval or pattern, so we can rule out systematic sampling.
2. Stratified Sampling: In stratified sampling, the population is divided into subgroups or strata based on certain characteristics, and then samples are randomly selected from each stratum. This ensures representation from each subgroup. The scenario does not mention any stratification or dividing the population into subgroups, so stratified sampling is not applicable.
3. Cluster Sampling: In cluster sampling, the population is divided into clusters or groups, and a random sample of clusters is selected. All individuals within the selected clusters are included in the sample. This method is often used when it is difficult to obtain a complete list of individuals in the population. The scenario mentions that specific polling stations were randomly selected, and all voters at those polling stations were surveyed. This indicates that the sampling was done by selecting specific clusters (polling stations) and including all individuals (voters) within those clusters. Therefore, cluster sampling is the most appropriate type of sampling for this scenario.
4. Convenience Sampling: Convenience sampling involves selecting individuals who are readily available and convenient to access. This method may introduce bias and may not provide a representative sample of the population. The scenario does not indicate that the polling stations or voters were selected based on convenience, so convenience sampling is not applicable.
Based on the analysis, the type of sampling used in the given scenario is Cluster Sampling.
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Bill plans to save for a pair of headphones that are 89.00.The sales tax rate is 8% how much will bill need to save
Answers
Answer: 96.12
Step-by-step explanation:
The amount that Bill will need to save will be for the cost of the headphones and the sales tax that will be applied. This will be:
= 89 + (8% × 89)
= 89 + (0.08 × 89)
= 89 + 7.12
= 96.12
Therefore, Bill will need to save 96.12.
Chart Rodrigo's total utility for lattes and the marginal utility for the same using information
from the table.
Quantity
Utility
0
14
2
3
4
on ANO
22
28
32
35
5
1)
40
30
Units of Total Utility
20
10
0
1
2
3
4
N
5
Number of Lattés
2)
)
20
15
Units of Total Utility per Latte
10
5
0
1
2
3
4 5
Number of Lattés
Answers
The marginal utility is the extra satisfaction derived from the consumption of a product.
How to illustrate the marginal utility?Your information isn't well written. Therefore, an overview of utility will be given. The total utility is the total amount of satisfaction that a consumer derives from a product.
The marginal utility simply means the extra satisfaction that's gotten from a product when an additional unit is consumed.
The formula for marginal utility will be:
= Total utility difference/Quantity of goods difference
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Amanda is building a soft triangular kennel for her dog. she has four wooden planks of lengths 2 feet, 3 feet, 5 feet, and 6 feet. determine which planks amanda should use to build the triangular-shaped kennel. enter the lengths from least to greatest. a triangular kennel made of carpet-covered planks
Answers
Amanda would use 3 planks of lengths 3 feet, 5 feet, and 6 feet.
What is a triangle?A triangle is a three-edged polygon with three vertices. It is a fundamental shape in geometry. Triangle ABC denotes a triangle with vertices A, B, and C. In Euclidean geometry, any three non-collinear points define a unique triangle and, by extension, a unique plane.To determine which planks Amanda should use to build the triangular-shaped kennel:
To build a kennel for dog, we would try to make it the largest possible with what we have.So, we would go with the 3 longest planks: 3ft, 5ft, and 6ft.By looking at the length, we see that we could make something very close to a right triangle since we could use the 6ft as a hypotenuse, and have the two other sides as 3ft and 5 ft (6² is almost 3²+5², which equals 34).That means our corner angle would be slightly over 90 degrees.Therefore, Amanda would use 3 planks of lengths 3 feet, 5 feet, and 6 feet.
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we want to select a random sample of five dealers. the random numbers are: 38, 52, 3, 62, 46, 59, 32, 11, 79, 13, 93, and 24. which dealers would be included in the sample? (enter the numbers as they appear.)
Answers
The dealers included in the random sample would be: 38, 52, 3, 62, and 46.
To select a random sample of five dealers from the given list of numbers, we can simply choose the first five numbers in the list: 38, 52, 3, 62, and 46.
The random sample is obtained by selecting a subset of individuals from a larger population, in this case, the dealers. The numbers provided represent the random numbers used for selection. Since we need to select five dealers, we choose the first five numbers in the list.
Therefore, the dealers included in the sample are 38, 52, 3, 62, and 46. These dealers were selected based on the order of the random numbers given.
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How to Find the Height of a Triangle
Answers
Answer:divide your base in half and use the pythagorean theorem to solve for the height
Step-by-step explanation:
Suppose that the function g is defined, for all real numbers, as follows.
1x²-5 ifx#-2
g(x)=-
4
if x = -2
Find g (-5), g (-2), and g (5).
8 (-5) = 0
8 (-2) = 0
8 (5) = 0
8
X
Ś
Answers
The value of g(-5) is 7.5, g(-2) is 4, and g(5) is 7.5 if the value of function g(x) = 1/2x²-5 if x≠-2 and g(x) = 4 if x = -2.
A function is a rule that associates each element in a set (called the domain) with a unique element in another set (called the range). A function takes an input from the domain and produces an output in the range.
To find the value of g(-5), substitute the value in given function
g(-5) = 1/2×(-5)² - 5
= 1/2×25 - 5
= 12.5 - 5 = 7.5
The value of g(-2) is 4 as it is defined in the question only.
To find the value of g(5), substitute the value in given function
g(5) = 1/2×(5)² - 5
= 1/2×25 - 5
= 12.5 - 5 = 7.5
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Need help with my math hw
Answers
Determine if the following equation is linear. If the equation is linear, convert i to standard form: ax+by=c
Answers
Given the equation:
\((10+y)^2-y^2=-3x+11\)Then, expanding and operating this equation leads to:
\(\begin{gathered} 10^2+2\cdot10\cdot y+y^2-y^2=-3x+11 \\ 100+20y=-3x+11 \end{gathered}\)There are no quadratic terms, so the equation is linear. Now, converting it to standard form:
\(20y+3x=-89\)Exponential Functions
Write a review question over this material
DO NOT Solve
Answers
Review question can be "What is the relationship between the rate of growth or decay and the value of the base in an exponential function?".
Answer to that question can be, The rate of growth or decay in an exponential function is directly proportional to the value of the base. Specifically, if the base is greater than 1, the function represents exponential growth, where the function value increases at an accelerating rate as x increases. On the other hand, if the base is between 0 and 1, the function represents exponential decay, where the function value decreases at a decelerating rate as x increases. The larger the base, the faster the function grows or decays. Therefore, the base determines the behavior of the exponential function and its rate of growth or decay.
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Which values of x are solutions to the equation below 15x^2 - 56 = 88 - 6x^2?
a. x = -4, x = 4
b. x = -4, x = -8
c. x = 4, x = 8
d. x = -8, x = 8
Answers
A quadratic equation is a polynomial equation of degree 2, which means the highest power of the variable is 2. It is generally written in the form: ax^2 + bx + c = 0. Option (d) x = -8, x = 8 is the correct answer.
The given equation is 15x^2 - 56 = 88 - 6x^2.
We need to find the values of x that are solutions to the given equation.
Solution: We are given an equation 15x² - 56 = 88 - 6x².
Rearrange the equation to form a quadratic equation in standard form as follows: 15x² + 6x² = 88 + 56 21x² = 144
x² = 144/21 = 48/7
Therefore x = ±sqrt(48/7) = ±(4/7)*sqrt(21).
The values of x that are solutions to the given equation are x = -4/7 sqrt(21) and x = 4/7 sqrt(21).
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The given equation is 15x² - 56 = 88 - 6x². Values of x are solutions to the equation below 15x² - 56 = 88 - 6x² are x = -2.62, 2.62 or x ≈ -2.62, 2.62.
Firstly, let's add 6x² to both sides of the equation as shown below.
15x² - 56 + 6x² = 88
15x² + 6x² - 56 = 88
Simplify as shown below.
21x² = 88 + 56
21x² = 144
Now let's divide both sides by 21 as shown below.
x² = 144/21
x² = 6.86
Now we need to solve for x.
To solve for x we need to take the square root of both sides.
Therefore, x = ±√(6.86).
Therefore, the values of x are solutions to the equation below are x = -2.62, 2.62 or x ≈ -2.62, 2.62.
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A line with a slope of 3 passes through (2,5). Which choice is an equation of this line?
Answers
Answer:
y=3x-4
Step-by-step explanation:
a slope of 3 means that the equation will definitely start like this
y=3x +/- b
to find b, substitute the coordinates given, so
5=3 x 3 +/- b
5=9 +/- b
5-9=b
-4=b
so the equation would be
y=3x-4
15.95 to the nearest cent
Answers
Step-by-step explanation:
95 95 branded to the nearest 10 with the number line
deter determine the two constructive multiples of 10 that bracket 95
9 is between 90 and 100
asteroid on the number line 95 is the midpoint between the 90 and 100
therefore 95 rounding to the nearest 10 is equal to 100
because 95 rounds to 100 which makes 15.95 into 16
an unnormalized relation is a table that has more than one row.
Answers
An unnormalized relation refers to a table in a relational database that contains more than one row. This means that there are duplicate rows in the table, which violates the rules of normalization.
Normalization is a process in database design that aims to eliminate data redundancy and ensure data integrity. It involves breaking down a database into multiple tables and defining relationships between them. By doing so, we can efficiently store and retrieve data while minimizing inconsistencies.
In an unnormalized relation, duplicate rows can lead to various problems. For example, it can result in data inconsistencies, as updating one instance of a row may not reflect changes in other duplicate rows. Additionally, it can cause unnecessary storage and maintenance overhead.
To normalize an unnormalized relation, we need to identify the functional dependencies in the table and create separate tables for related data. This helps organize the data and reduces redundancy.
In summary, an unnormalized relation is a table in a relational database that has duplicate rows. It is important to normalize such relations to ensure data integrity and efficiency.
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Jason and Pam recently bought a house. They financed the house with a $250,000, 30-year mortgage with a nominal interest rate of 77% compounded monthly. Mortgage payments are made at the end of each month. What would be their house payment?
Answers
Answer:
Annual payument (PMT)= $1,663.19
Step-by-step explanation:
Giving the following information:
Loan (PV)= $250,000
Monthly interest rate (i)= 0.07/12= 0.005833
Number of periods (n)= 12*30= 360 months
To calculate the monthly payment, we need to use the following formula:
Annual payument (PMT)= (PV*i) / [1 - (1+i)^(-n)]
Annual payument (PMT)= (250,000*0.005833) / [1 - (1.005833^-360)]
Annual payument (PMT)= $1,663.19
The Sumerians used rubber stamps to show ownership of objects.
True Or false
Answers
Answer:
I think False not sure
Step-by-step explanation:
Josh works for a driving company. It has been a little over six years since he was hired. He now makes $64,500 per year. When he was hired, he was told that he had 10 days of paid vacation time. For each year that he worked at the company, he would gain another three days of paid vacation time to a maximum of 30 days. How many paid vacation days does he now get at the end of six years of employment and how much will he make during the time he is on vacation?
Answers
Answer:
Step-by-step explanation:
What is the value of x in the figure shown below?
2.8
2.8
A
96°
53°
2.8
5.4
5.4
D
B
Answers
Answer:
Step-by-step explanation:
∠EAD = ∠CAB = 53°
By Side-angle-side, △EAD is congruent to △CAB
∠E = 96°
∠D = 180-96-53 = 31°
x = 31°
square root of 5 times square root of 8
Answers
Answer:
6.32455532034
Rounded: 6.32
Hope this helps! :)
The relationship between hours practice and coordinate video game is modeled by the equation Y = 10x graph this relationship on the graph below what is the slope and what does it mean for the situation
Answers
answer:
provided in the explanation.
step-by-step explanation:
the graph would contain the points (0,0), (1,10), (2,20), etc. the slope is 10, which represents the number of coordinate video games practiced in x number of hours. the representation for the slope depends on whether coordinate video game or hours practiced is on the x or y axis. hope that helps!
in regression models, we use both numerical and dummy (categorical) variables as predictor variables.what are the 3 interaction variables discussed in the chapter? select all that apply!
Answers
Interaction are variables that are created by combining two or more predictor variables. The three interaction variables discussed in the chapter.
Interaction Terms: An interaction term is a product of two (or more) predictor variables. It is used to capture the combined effect of two variables, and is usually represented as an equation of the form y = β0 + β1X1 + β2X2 + β3X1X2. Interaction Effects: An interaction effect occurs when the effect of one predictor on the dependent variable depends on the value of another predictor. It is usually represented as an equation of the form y = β0 + β1X1 + β2X2 + β3X1X2 + β4X2X2. Interaction Coefficients: An interaction coefficient is a parameter that is estimated by the model and measures the strength of the interaction between two predictors. It is usually represented as an equation of the form y = β0 + β1X1 + β2X2 + β3X1X2 + β4X2X2 + β5X1X2.
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what is 47/14 as a decimal rounded to the nearest hundredth
Answers
Answer:
\( \frac{47}{14} \dashrightarrow \: 3.36\)
The value of the fraction number 47/14 into a decimal number will be 3.36.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
The numerical expression is given below.
⇒ 47/14
Convert the fraction number into a decimal number. Then we have
⇒ 47/14
⇒ 3.36
The worth of the part number 47/14 into a decimal number will be 3.36.
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someone answer this correctly please, I’ll give you brainliest and your getting 50 points someone answer this no fraud answers don’t be weird.
Answers
The proof of the congruent sides RU and TS is given below.
What is congruent triangles?
In any orientation, two triangles are said to be congruent if their three sides and three angles are equal.
Therefore, if two triangles have the same number of sides on each side, they are said to be congruent. Additionally, we can determine that they are congruent if we have a side, an angle between the sides, and then another side that is congruent, in that order: side, angle, side.
Let the given figure is a rectangle RSTU.
Since the all four angles of rectangle are of 90 degree.
So, each angle of rectangle RSTU is 90 degree.
Let, US divides the angle RUT and angle RST and form two new triangles, ΔSRU and ΔSTU.
Both the triangles having same measure of angles and sides.
⇒ ΔSRU ≅ ΔSTU
As the triangles are congruent so their sides are congruent.
Hence, RU is congruent to TS.
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\( \mathrm{m}_{1} \) and \( \mathrm{m}_{2} \) is \( 120 \mathrm{lbs} \) and 210 Ibs respectively. What is \( r_{2} \) if \( r_{1} \) \( =1.8 \mathrm{~m} \) ? \( 3.15 \mathrm{~m} \) \( 1.25 \mathrm{~m}
Answers
The value of \( r_{2} \) is approximately 1.028 m. The moment or torque is calculated by multiplying the force applied by the distance from the point of rotation.
To find the value of \( r_{2} \), we need to use the concept of moments or torques in a system. The moment or torque is calculated by multiplying the force applied by the distance from the point of rotation.
In this case, if we assume that \( r_{1} \) and \( r_{2} \) are the distances of masses \( m_{1} \) and \( m_{2} \) from the point of rotation respectively, then the torques exerted by \( m_{1} \) and \( m_{2} \) should be equal since the system is in equilibrium.
Using the equation for torque:
Torque = Force × Distance
The torque exerted by \( m_{1} \) is given by:
\( \text{Torque}_{1} = m_{1} \cdot g \cdot r_{1} \)
where \( g \) is the acceleration due to gravity.
The torque exerted by \( m_{2} \) is given by:
\( \text{Torque}_{2} = m_{2} \cdot g \cdot r_{2} \)
Since the system is in equilibrium, \( \text{Torque}_{1} = \text{Torque}_{2} \), we can equate the two equations:
\( m_{1} \cdot g \cdot r_{1} = m_{2} \cdot g \cdot r_{2} \)
Now, let's substitute the given values into the equation and solve for \( r_{2} \):
\( 120 \, \text{lbs} \cdot 9.8 \, \text{m/s}^{2} \cdot 1.8 \, \text{m} = 210 \, \text{lbs} \cdot 9.8 \, \text{m/s}^{2} \cdot r_{2} \)
Simplifying the equation:
\( 2116.8 \, \text{N} \cdot \text{m} = 2058 \, \text{N} \cdot r_{2} \)
Dividing both sides of the equation by 2058 N:
\( r_{2} = \frac{2116.8 \, \text{N} \cdot \text{m}}{2058 \, \text{N}} \)
\( r_{2} \approx 1.028 \, \text{m} \)
Therefore, the value of \( r_{2} \) is approximately 1.028 m.
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if the length of a rectangular field is 2 feet less than four times its width, and the perimeter is 106 feet.
Answers
The length and width of the rectangle are: 42 feet and 11 feet.
What is a rectangle?Rectangle refers to a plane shape, as opposed to a square, with four straight sides and four right angles, particularly one with uneven neighboring sides.
Given:
Perimeter of the rectangular field = 106 feetLength of the field is 2 feet less than 4 times the width.To find: the length and width of the rectangular field.
Finding:
Let the width of the rectangular field be 'x'
Then the length of the field = 4x - 2
Perimeter of rectangle = 2 (width + length)
=> 106 = 2 ( x + 4x -2)
=> 53 = 5x - 2
=> 55 = 5x
=> 11 = x, i.e., the width of the field = 11 feet
The length of the field = 11(4) - 2 = 42 feet.
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please help me with this problem
Answers
Answer:
140 cm^2
Step-by-step explanation:
Area of rectangular = L x W
14 times 10 = 140cm^2
13. Select all the expressions equivalent to (4x5)(5x6).
(2x5)(10x6 )
(4x5)(6x5)
(4x6)(5x5)
20x11
20x30
Answers
Answer:
(4×6)(5×5)
20 × 30
(4×5)(6×5)
(2×5)(10×6)