The original scale factor for a scale drawing of a house plan is 180, and the length of the original scale drawing is 12 inches. What is the length of a new scale drawing if the scale factor of the new scale drawing to actual length of the house is 1180?.

Step-by-step explanation:

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The product of A x B of matrix is

a)  [tex]C = \left[\begin{array}{ccc}8 & 12 \\ 10 &15 \\\end{array}\right][/tex]

b) [tex]C = \left[\begin{array}{ccc}3 &6 \\ 4 &8 \\\end{array}\right][/tex]

c) [tex]C = \left[\begin{array}{ccc}-7 &-2 \\ 42 &12 \\\end{array}\right][/tex]

d) [tex]C = \left[\begin{array}{ccc}24 &-96 \\ 15 &-60 \\\end{array}\right][/tex]

What is multiplication of matrices?

The product of two matrices A and B is defined if the number of columns of A is equal to the number of rows of B. The first matrix must have the same number of columns as the second matrix has rows. The number of rows of the resulting matrix equals the number of rows of the first matrix, and the number of columns of the resulting matrix equals the number of columns of the second matrix

Given data ,

a)

Let the 2 matrices be A and B

The value of matrix A is

[tex]A = \left[\begin{array}{ccc}4\\5\\\end{array}\right][/tex]

The value of matrix B is

[tex]B = \left[\begin{array}{ccc}2&3\\\end{array}\right][/tex]

Now , the dimensions of matrix A is 2 x 1 and of matrix B is 1 x 2

So , matrix multiplication is possible

Now , let C be the result of A x B

And ,

[tex]C = \left[\begin{array}{ccc}4\\5\\\end{array}\right] *\left[\begin{array}{ccc}2&3\\\end{array}\right][/tex]

So  , the value of matrix C is calculated as

[tex]C = \left[\begin{array}{ccc}( 4 * 2 ) &( 4 * 3 )\\( 5 * 2 ) &(5 * 3 )\\\end{array}\right][/tex]

On simplifying the matrix , we get

[tex]C = \left[\begin{array}{ccc}8 & 12 \\ 10 &15 \\\end{array}\right][/tex]

Therefore , the value of matrix C is   [tex]C = \left[\begin{array}{ccc}8 & 12 \\ 10 &15 \\\end{array}\right][/tex]

b)

C be the result of A x B

The value of matrix A

[tex]A = \left[\begin{array}{ccc}3\\4\\\end{array}\right][/tex]

The value of matrix B is

[tex]B = \left[\begin{array}{ccc}1&2\\\end{array}\right][/tex]

Now , let C be the result of A x B

And ,

[tex]C = \left[\begin{array}{ccc}( 3 * 1 ) &( 3 * 2 )\\( 4 * 1 ) &(4 * 2 )\\\end{array}\right][/tex]

On simplifying the matrix , we get

[tex]C = \left[\begin{array}{ccc}3 &6 \\ 4 &8 \\\end{array}\right][/tex]

Therefore , the value of matrix C is [tex]C = \left[\begin{array}{ccc}3 &6 \\ 4 &8 \\\end{array}\right][/tex]

c)

C be the result of A x B

The value of matrix A

[tex]A = \left[\begin{array}{ccc}-1\\6\\\end{array}\right]\\[/tex]

The value of matrix B

[tex]B = \left[\begin{array}{ccc}7&2\\\end{array}\right][/tex]

Now , let C be the result of A x B

And ,

[tex]C = \left[\begin{array}{ccc}-7 &-2 \\ 42 &12 \\\end{array}\right][/tex]

Therefore , the value of matrix C is [tex]C = \left[\begin{array}{ccc}-7 &-2 \\ 42 &12 \\\end{array}\right][/tex]

d)

C be the result of A x B

The value of matrix A

[tex]A = \left[\begin{array}{ccc}8\\5\\\end{array}\right]\\[/tex]

The value of matrix B

[tex]B = \left[\begin{array}{ccc}3&-12\\\end{array}\right][/tex]

Now , let C be the result of A x B

And ,

[tex]C = \left[\begin{array}{ccc}24 &-96 \\ 15 &-60 \\\end{array}\right][/tex]

Therefore , the value of matrix C is [tex]C = \left[\begin{array}{ccc}24 &-96 \\ 15 &-60 \\\end{array}\right][/tex]

Hence , the matrix multiplication is done and the results are given

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The value of a , b and c are 7, 11 and 1 respectively.

173a is divisible by 9.

Rule of divisible by 9 is:

The number itself is divisible by 9 if its digit sum is also divisible by 9.

digits sum  =  1+7+3+a  = 11+a.

11+a is divisible by 9. a can be 7 so that 11+7 = 18 is divisible by 9.

minimum positive value of a = 7.

173b is divisible by 11

Rule of divisible by 11 is:

A number is completely divisible by 11 if the difference between the sum of its alternative digits is divisible by 11.

sum of its alterative digits:

1+3 =4  

7+b =7+b

difference of alternative digits sum = 7+b-4 = b+3 is divisible by 11 b = 8

so that 8+3 = 11 is divisible by 11.

minimum positive value of b = 11.

173c is divisible by 6.

Rule of divisible by 11 is:

Any number that can be divided by both 2 and 3 is also divisible by 6.

sum of digits of number = 1+7+3+c = 11 + c if divisible by 2 then it should be even if we put c = 1  , 11+1 = 12 which is divisible by both 2 and 3.

minimum positive value of c = 1.

So the value of a ,b and c are 7, 11 and 1 respectively.

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Drawing an altitude and computing the side lengths of the resulting half triangle for an equilateral and isosceles triangle, would give the trigonometric functions for multiples of 30 and 45 respectively.

In a 30°-60°-90° right triangle, the longer leg is [tex]\sqrt{3}[/tex] times longer than the shorter leg, and the hypotenuse is twice as long. In a 45°-45°-90° right triangle, sides opposite to the equal angles (45°) are equal and the hypotenuse is [tex]\sqrt{2}[/tex] times the other sides.

To find the trigonometric functions of multiples of 30°, first consider a equilateral triangle of, say, side-length 2. Draw an altitude for the triangle. Each of the half triangle are 30°-60°-90° right triangle. Clearly the base will be divided into 2 equal parts of length 1 each. Now using Pythagorean Theorem on one of the 30°-60°-90° right triangle, trigonometric functions for multiples of 30° could be obtained.

Draw x and y axis. Now take a length of , say , 2 in the x-axis and using a compass pointed at origin and mark the point on y axis with a length 2. Now join these points on x and y axis. A 45°-45°-90° isosceles right triangle with side-length 2 is obtained. Now using Pythagorean Theorem, trigonometric functions for multiples of 45° could be obtained.

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The equation that represents this situation is y=  4x

From the question, we have the following parameters that can be used in our solution:

Point = (8, 36)

This point can be represented as

(x, y) = (8, 36)

From the above parameter, we can calculate the constant of variation

The constant of variation is calculated as

Constant of variation = y/x

Substitute the known values in the above equation

So, we have the following equation

Constant of variation = 36/8

Evaluate the quotient

Constant of variation = 4

Recall that:

Constant of variation = y/x

So, we have

y/x = 4

This gives

y = 4x

Hence, the equation is y = 4x

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The decimal fraction as a decimal number.14,25

What is decimal?

The base-10 number system, arguably the most widely used number system, is referred to as decimal. The 10 single-digit digits of the decimal number system are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. The number following nine is 10. 19 is followed by 20, and so on.

The accepted method for representing both integer and non-integer numbers is the decimal numeral system. It is the expansion of the Hindu-Arabic numeral system to non-integer values. Decimal notation is the term used to describe the method of representing numbers in the decimal system.

14 25/100= 14*100+25/100=

1400+25/ 100

= 1425/100

= 14.25

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Answer:

2.44$ per muffin

Step-by-step explanation:

15/6.15

Answer:

2

Step-by-step explanation:

y would be the first number in the equation on the left side of the equal sign. This looks lik the y=mx+b formula, so m, being slope, would be 7, -3 would be x, and b would be 4.

Answer:

2

Step-by-step explanation:

take an example like

u have one apple then someone gives you another one apple

when you add them,

you get 2

Answer:

12 - 12 a

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

an open circle on a value means that x cannot equal that value

a closed circle on a value means that x can equal that value

from the number line

closed circle at - 3 means x can equal 3

open circle at 2 means that x cannot be equal to 2

all values between - 3 and 2 are solutions for x, then

x ≥ - 3 and x < 2 or - 3 ≤ x < 2

The principal amount for account A is $200 and for account B is $700.

Account B earns more simple interest than account B in first month.

Given,

Account A

Simple interest, SI = $9.25

Time period, T = 15 months = 1 1/4 = 5/4 years

Rate of interest, R = 3.7%

Account B

Simple interest, SI = $25.20

Time period, T = 18 months = 1 1/2 = 3/2 years

Rate of interest, R = 2.4%

We have to find the principal amount for each account and also the account which earned the more simple interest;

Here,

Simple interest, SI = PRT/100

P is the principal amount

Now,

Account A.

SI = PRT/100

9.25 = (P × 3.7 × 5/4) / 100

9.25 × 100 = P × 4.625

P = 925/4.625

P = $200

SI = PRT/100

SI = (200 × 3.7 × 1/15) / 100

SI = 2 × 3.7 × 1/15

SI = $0.493

Next,

Account B

SI = PRT/100

25.20 = (P × 2.4 × 3/2) / 100

25.20 × 100 = P × 3.6

P = 2520/3.6

P = $700

SI = PRT/100

SI = (700 × 2.4 × 1/18) / 100

SI = 7 × 2.4 × 1/18

SI = $0.933

Here,

The principal amount for account A is $200

The principal amount for account B is $700

Simple interest for first month;

Account A = $0.493

Account B = $0.933

Therefore,

In first month account B earns more simple interest than account A.

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Answer:

2 5/6 OR 3

Step-by-step explanation:

1. Divide Both sides by four.

2. -15/-4 can be simplified to 15/4 by removing the negative sign from both the numerator and the denominator.

3. Add 1/2 to both sides

4. Least common multiple of 4 and 2 is 4. Convert 15/4 and 1/2 to fractions with the denominator 4.

5. Since 15/4 and 2/4 have the same denominator, add them by adding their numerators.

6. Add 15 and 2 to get 17.

7. Multiply each side by 2/3, the reciprocal of 3/2 (cancel out 3/2 and leave only X)

8. multiply 17/4 by 2/3 by multiplying numerator times numerator and denominator times denominator.

9. By doing the multiplications 17x2/4x3 you should get 34/12

10. Reduce the fraction 34/12 to lowest terms by extracting and cancelling out 2.

11. You should get 17/6.

Final Step: if you are asked for a mixed number, the answer is 2 5/6 OR if asked for a decimal, put 2.833333333 or 3 IF asked to round.

$7325.98  is the amount you have in the account in 5 years

Compound interest is the interest determined on the principal and the interest accumulated over the previous period.

Given that: You deposit $6000 in an account earning 4% interest compounded monthly.

Amount (A) = P(1+r)^t

Where P is the principal, r is the interest rate and t is the time

P = $6000, r =  4% / year = 4/12 = 1/3 % / month = 1/300 , t = 5 years = 5×12 = 60 months

A = P(1+r)^t

A = 6000(1 + 1/300)⁶⁰

A = $7325.98

Thus, you will have $7325.98  in the account in 5 years

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 168 divided by 12  is 14.

 14 <-- quotient

 ---

168

  12

  --

   48

   48

   --

      <-- remainder

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The solution to the given system of equation has exactly one solution at (0,2).

The addition property of equality is used in the elimination technique to solve systems of linear equations.

To create an equation in one variable using the elimination approach, you can either add or subtract the equations. To eliminate a variable, add the equations when the coefficients of one variable are in opposition, and subtract the equations when the coefficients of one variable are in equality.

Given pair of equations is

18x - 2y = -4  ....(i)

4x - y = -2    .....(ii)

To solve the equation apply elimination method.

Multiply equation (ii) by 2 and subtract it from (i):

18x - 2y = -4

8x - 2y = -4

(-)  (+)     (+)

_________

10x = 0

x = 0

Putting x = 0 equation (ii)

0 - y = -2

y = 2

So there is exactly one solution (0,2).

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The solution to the given system of equation has exactly one solution at (0,2).

Which property is used in elimination method?
The addition property of equality is used in the elimination technique to solve systems of linear equations.

What is elimination formula?

To create an equation in one variable using the elimination approach, you can either add or subtract the equations. To eliminate a variable, add the equations when the coefficients of one variable are in opposition, and subtract the equations when the coefficients of one variable are in equality.
Given pair of equations is
18x - 2y = -4  ....(i)
4x - y = -2    .....(ii)
To solve the equation apply elimination method.
Multiply equation (ii) by 2 and subtract it from (i):
18x - 2y = -4
8x - 2y = -4
(-)  (+)     (+)
_________
10x = 0
x = 0
Putting x = 0 equation (ii)
0 - y = -2
y = 2
So there is exactly one solution (0,2).

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Therefore the solution of this problem is a)critic value t = 2.8982 b)margin of error=  2.985146

In statistics, the standard deviation measures how widely distributed or how much a set of values might vary. In contrast to a high standard deviation, which indicates that values are widely dispersed, a low standard deviation indicates that values are typically close to the set's mean.

Here ,

where s is the sample's standard deviation

Finding the number of degrees of freedom is the first step in solving this problem. The sample size has been reduced by 1.

So

df = 18 - 1 = 17

99% confidence interval

We must now determine the value of T, which can be done by consulting the t table, which has 17 degrees of freedom (on the y-axis) and a confidence level of).

[tex]1 - \frac{1-0.99}{2} =0.995[/tex]

So we have T = 2.8982.

The margin of error is:

M = T*s = 2.8982*1.03 = 2.985146

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The length of each identical section of pipe is 2.51 meters

Define Algebraic Expression

In mathematics, an expression that includes variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.)

Given,

Billy bought 18 identical sections of pipe.

Total length of pipes = 45.18 meters

The length of each pipe is = 45.18 / 18

                                            = 2.15 meters

Hence, the length of each identical section of pipe is 2.51 meters

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The demand function for the marginal revenue function is found as; p(x) = 0.02x² - 0.025x + 138.

For the given question;

R′(x) = 0.06x² − 0.05x + 138

R(x) = ∫R′(x)dx

R(x) =  ∫[0.06x² − 0.05x + 138] dx

R(x) = 0.06x³/3 - 0.05x²/2 + 138x + C

R(x) = 0.02x³ - 0.025x² + 138x + C

If R(0) = 0, revenue is 0.

Put x = 0.

0.02x³ - 0.025x² + 138x + C = 0

c = 0

Thus,

R(x) = 0.02x³ - 0.025x² + 138x

Factorizing the function,

R(x) = 0.02x³ - 0.025x² + 138x

R(x) = x(0.02x² - 0.025x + 138)

R(x) = xp(x) . Thus,

p(x) = 0.02x² - 0.025x + 138

Therefore, the demand function for the marginal revenue function is found as; p(x) = 0.02x² - 0.025x + 138.

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Answer:

(not a possible parabola)

Step-by-step explanation:

see the plot...

[tex]f(x)=-\cfrac{1}{2}x^2 + 5x\hspace{13em}g(x)=x^2+2 \\\\[-0.35em] ~\dotfill\\\\ g(-2)=(-2)^2+2\implies g(-2)=4+2\implies g(-2)=6 \\\\[-0.35em] ~\dotfill\\\\ f(~~g(-2)~~)\implies f(6)\implies f(6)=-\cfrac{1}{2}(6)^2+5(6) \\\\\\ f(6)=-\cfrac{36}{2}+30\implies f(6)=-18+30\implies \stackrel{f(~~g(-2)~~)}{f(6)}=12[/tex]

The value of the expression in the form of the scientific notation is 7.539 x 10⁵.

Numbers that are either too large or too little to be conveniently stated in decimal form can be expressed using scientific notation. It may be called scientific form.

When a number is written using only the digits of the number, that is considered standard notation. Since words are not used in conventional number notation, this is the way that numbers are typically written.

The expression is (7.62 × 10⁵) – (8.1 × 10³). The expression will be solved as,

E = (7.62 × 10⁵) – (8.1 × 10³)

E = (7.62 × 10⁵) – (0.081 × 10⁵)

E = 7.539 x 10⁵

Therefore, the value of the expression in the form of the scientific notation is 7.539 x 10⁵.

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Answer: it’s already in its simplest form

Step-by-step explanation:

Answer: The fraction [tex]\frac{1}{12}[/tex] is already at its simplest form.

Step-by-step explanation: Sorry if this isn't correct, hope this helps!

Answer:

  3⁰ = 1

  x⁰ = 1

Step-by-step explanation:

You want powers of 3 filled in your table from an exponent of 4 down to an exponent of 0.

3⁴ = 3·3·3·3 = 81 . . . . . . 3 is a factor 4 times

3³ = 3·3·3 = 27 . . . . . . .  3 is a factor 3 times

Each row of the table has 3 being a factor of 3^x one fewer times, so each value of 3^x is 1/3 of the previous value.

The last two rows of the table are ...

  3¹ = 3

  3⁰ = 1

See the attachment for the whole table.

In general, the meaning of x⁰ is ...

  x⁰ = 1

__

Additional comment

In algebra, 0⁰ = 1 is the usual definition. In some contexts (mathematical analysis, calculus), it may be "undefined."

That means x⁰ = 1 for all real numbers x, including x = 0.

Answer: 6.5

Step-by-step explanation:

To perform this kind of exercise, it is necessary to replace the value indicated in each variable each time you find the variable in the equation.

Answer:

6.5

Step-by-step explanation:

Substitute the known variables into the equation

7(0.5) + 5 - 8(0.25)

Multiply: 3.5+5-2

Solve: 6.5

The constant of variation when the amount of money that Mary earns varies directly with the number of hours is 8.

According to the question,

We have the following information:

The amount of money that Mary earns varies directly with the number of hours worked. And Mary earns $320 for working 40 hours.

Now, following expression can be used to express this relationship where y is the amount of money and x is the number of hours.

y = kx

320 = 40k

Dividing by 40:

k = 320/40

k = 8

Hence, the constant of variation when the amount of money that Mary earns varies directly with the number of hours is 8.

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The answer to this Question based on Linear pair is 180 degree

What is Linear Pair?

A linear pair is a pair of adjacent angles that are supplementary, meaning they add up to equal 180 degrees. Linear pairs can be found in many shapes and geometric shapes, such as squares, rectangles, and parallelograms. Linear pairs can also be found in the angles of intersecting lines. When two lines intersect, four angles are formed, and two of them will always form a linear pair. Linear pairs can also be found in circles, as the angles formed by two chords that intersect with each other will always form a linear pair.

Suppose any triangle we are given 6 angles in which 3 are interior and 3 are exterior

suppose we take any pair of interior and exterior and we can see that it will always form a linear pair and its sum will be equal to 180 degree

Here in this question sum of angle 1 and 2

sum of angle 5 and 6

sum of angle 3 and 4

all will be same and will be equal to 180 degree by Linear Pair

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Answer:

a,b,c

Step-by-step explanation:

a) m∠3 + m∠4 = 180°

b) m∠2 + m∠4 + m∠6 = 180°

c) m∠2 + m∠4 = m∠5

these are the correct answers  for edge 2023 geometry assignment; Triangle Angle Theorems

hope this helps!