Find x for m and n. Identify the postulate or theorem

Answer:

B

Step-by-step explanation:

Since x is 3, you go 3 units right. Since y is -2, you go 2 units down.

Answer:

Approximately 57 minutes.

Step-by-step explanation:

5 ÷ 45 = 1/9

1/9 · 8.5 = 17/18

An hour = 60 mins so

60 ÷ 18 = 10/3

10/3 · 17 = 56.6666667

also known as 56.67 minutes if rounded to hundreds, 56.7 minutes if rounded to the tenths, and 57 minutes if rounded to a whole number.

Answer: 50 feet, 150 feet, 75 feet, and 180 feet

Step-by-step explanation:

The side lengths are x, 3x, 1.5x and 180 (in feet) and they must all add up to 455 feet, so ....

x + 3x + 1.5x + 180 = 455

(1+3+1.5)x + 180 = 455

5.5x + 180 = 455

Subtract 180 from both sides

5.5x = 275

x = 275/5.5

x = 50 feet  , but that was not really the question.

The question was the 4 side lengths.

The lengths are x, 3x, 1.5x and 180, all in feet.

x =    50 feet     ---->  50 feet

3x = 3(50 feet) ---> 150 feet

1.5x = 1.5(50 feet) ---> 75 feet

180 feet (given)

We check our work by adding the four sides ---> 50+150+75+180 = 455, so that looks good.

Don't forget to label the lengths in feet!

I hope this helps.

Answer:

I think it is b

Step-by-step explanation:

Where the above factors are given, a sale price of approximately $84 for the immersion blenders will allow Kitchen Masters to achieve a profit of $89,300.

The profit equation for the sale of pressure cookers for the company Kitchen Masters is:

P = −120p² + 19,800p − 727,450

To find the sale price for the immersion blenders, p, that will allow Kitchen Masters to achieve a profit, P, of $89,300,


Let the profit equation =  89,300.

Now, we solve for p:

89,300 = −120p² + 19,800p − 727,450

Adding 727,450 to both sides:

816,750 = -120p² + 19,800p

Dividing both sides by -120:

-6,805 = p² - 165p

Rearrange the equation to make it Quadratic

p² - 165p + 6,805 = 0

Now we can solve for p using the quadratic formula:

p = (-b ± √(b² - 4ac)) / 2a

where a = 1, b = -165, and c = 6,805.

p = (-(-165) ± √((-165)² - 4(1)(6,805))) / 2(1)

p = (165 ± √((27,225 - 27220)) / 2

p ≈ 83.618 or p ≈ 81.382

Therefore, a sale price of approximately $84 for the immersion blenders will allow Kitchen Masters to achieve a profit of $89,300.

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Step-by-step explanation:

the area of a rectangle is

a × b

with a, b being the length and width (in any sequence).

a×b = 800

a = 800/b

the perimeter is

2a + 2b

one side is not needed, so we take one of them off. e.g. we take off one a.

a + 2b need to be a minimum

800/b + 2b

f(b) = 800/b + 2b

the extreme value(s) we find as the zero points of the first derivative.

f'(x) = -800/(b²) + 2 = 0

2 = 800/(b²)

2b² = 800

b² = 400

b = ±20 ft

negative lengths don't make sense, so, 20 ft is the solution.

a×b = 800

a×20 = 800

a = 40 ft

so, the minimum fencing is for

a = 40 ft

b = 20 ft (2 times)

the second a is covered by the barn.

Answer:

x=65

Step-by-step explanation:

Both sides have to equal the same, which is 145. 145-15=130, 130/2=65. So basically you have to do inverse operation to solve this.

For figure {0}, the number of tiles will be equal to 2.

Function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function

Expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators

Equation : A mathematical equation is used to equate two expressions.

Given is a graph as shown in the image.

The line passes through point -

(3, 8) and (4, 10)

So, the slope of the line will be -

m = (10 - 8)/(4 - 3)

m = 2

y = 2x + c

For the point (3, 8), we can write -

8 = 6 + c

c = 2

For figure {0}, the number of tiles will be equal to 2.

Therefore, for figure {0}, the number of tiles will be equal to 2.

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Therefore, the equation for that value x = 6, and m(A) = 90.

A mathematical equation expresses two things as being equal to one another, or as having the same value and worth. A specific equation that expresses a significant link between variables and numbers is called a formula.

The fact that the sum of a triangle's angles is 180 degrees must be used to determine the value of x. Angles J, A, and K in the triangle AJK allow us to write:

m(J) + m(A) + m(K) = 180

We can substitute the given angle measures into this equation:

(8x - 7) + m(A) + (x + 7) = 180

Simplifying this equation, we get:

9x + m(A) = 180 - 7 - 7

9x + m(A) = 166

We can use the same reasoning for triangle AJL:

m(J) + m(A) + m(L) = 180

Substituting the given angle measures, we get:

(8x - 7) + m(A) + (2x + 15) = 180

Simplifying this equation, we get:

10x + m(A) = 172

The two unknowns in our current set of equations are x and m(A). By removing the first equation from the second, we can find m(A):

10x + m(A) = 172

(9x + m(A) = 166)

x = 6

Now that we know x, we can substitute it into either equation to find m(A):

8x - 7 + m(A) + x + 7 = 180

15x + m(A) = 180

m(A) = 180 - 15x

Substituting x = 6, we get:

m(A) = 180 - 15(6) = 90

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For the given expression, the addition of coefficients is \(5x^2 + 2x - 7\).

In algebra, a coefficient is a numerical or constant quantity placed before and multiplying the variable in an algebraic expression. In other words, it is the number that is being multiplied by the variable.

Addition is a basic mathematical operation that combines two or more numbers or quantities to produce a sum. It is denoted by the plus sign (+). When two or more numbers are added, the result is called the sum or total.

First, we need to combine like terms by adding the coefficients of terms with the same variable(s) raised to the same power.

\((6x^2 + 10x - 7) + (-x^2 - 8x)\)

\(= 6x^2 + (-x^2) + 10x + (-8x) - 7\) (grouping like terms together)

\(= (6x^2 - x^2) + (10x - 8x) - 7\) (rearranging terms)

\(= 5x^2 + 2x - 7\) (combining the coefficients)

Therefore, the final answer for the addition of coefficients is \(5x^2 + 2x - 7.\)

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Answer:

4 + 13x

Step-by-step explanation:

add 8x and 5x which makes 13x. Since 4 doesn't have variable x in it then you can't add it to 13x.

The interest rate paid by Scott is 4.25% for the 72 months.

We can determine the simple interest of the given problem by the simple interest formula which is given as :

I=PRT

Where,

I=Interest

P=principal

R=rate in decimal

T=time in years

Converting the given 72 months into years we get time t :

1 year = 12months

72 months / 12months = 6 years

t=6

From the given data

I=8925

P=35000

R=r

T=6

Substituting the above values in the simple interest equation we get:

8925 = 35000*r*6

8925 = 210000*r

divide both sides by 210000

R = 0.0425

Therefore, the interest rate is 4.25%

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Answer:

This formula has no values, it is a false inequality. X can not be greater than 5, and less than 3.

Step-by-step explanation:

x < 3 or x > 5

This means, x is less than 3, but greater than 5.

Technically, you would write this as 5 < x < 3, however, this is a false inequality, and does not work.

The average normal stress in the links connecting:

(a) points B and D is:

|σ_max| = 13.7 MPa

(b) points C and E is:

|σ_max| = 13.0 MPa

To determine the maximum value of the average normal stress in the links connecting points B and D, we need to calculate the bending moment and the axial force in the link. Assuming the links are in pure bending, we can use the bending stress formula to calculate the maximum normal stress:

σ_max = Mc / I

where M is the bending moment, c is the distance from the neutral axis to the outer fiber, and I is the moment of inertia of the cross-sectional area.

The bending moment in the link BD can be calculated as the sum of the moments due to the applied loads and the reactions at the pins. The axial force can be calculated as the sum of the forces in the link due to the applied loads.

M = 4kN * 80mm - 8kN * 120mm = -640 Nm

F = 4kN - 8kN = -4kN

        I = bh³ / 12

        I = (8mm) * (36mm)³ / 12 = 186624 mm⁴

       σ_max = (-640 Nm) * (4mm) / 186624 mm⁴ = -13.7 MPa

        |σ_max| = 13.7 MPa

       M = 4kN * 40mm + 8kN * 80mm = 800 Nm

        F = 4kN + 8kN = 12kN

I = bh³ / 12 = (36mm) * (8mm)³ / 12 = 24576 mm⁴

       σ_max = (800 Nm) * (4mm) / 24576 mm⁴ = 13.0 MPa

       |σ_max| = 13.0 MPa

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Step 1: Isolate the Sin Operator

\(8 sin(\frac{\pi }{6} x)=2\\sin(\frac{\pi }{6} x)=0.25\\\\\)

Step 2: Use Inverse Sin(arcsin) to isolate the term with the x variable

Note that since trig functions have 2 general solutions, this will give us one of our general solutions.

\(x=\frac{6 arcsin(0.25)}{\pi } =0.48\)

x₁= 0.48

Solving for x₂

Use the period identity for Sin Functions

\(sin(x)=sin(\pi -x)\)

X in this case is arcsin(0.25)

\(\frac{\pi }{6} x=\pi -arcsin(0.25) = 5.52\)

So our two general solutions are 0.48 and 5.52

Step 3: Period

Trig Functions have periodic behavior and this function period is

\(\frac{2\pi }{1} (\frac{6}{\pi } )= 12\)

So our general solutions are

0.48±12k, where k is an integer

5.52±12k, where k is an integer

Let k=1, and we get our next set of solutions:

12.48 and 17.52

So our answer is 0.48,5.52,12.48,17.52

Answer:

No

Step-by-step explanation:

70 is divisible by 5. 5 is not an even number.

Answer:

No

Step-by-step explanation:

The factors of 70 are 1, 2, 5,7,10, 14, 35, and 70. the even numbers are 2, 10,14, and 70. but there are odd numbers, like 1, 5, 7, and 35. And since we know there are odd factors, the answer is No. 70 has even AND odd factors.

The correct answer is Option D. The ratio for cos A is 15/17.

The cosine of an angle is defined as the ratio of the adjacent side to the hypotenuse in a right-angled triangle.

It is frequently denoted as cos.

Consider a right-angled triangle with sides a, b, and c.

The cosine of angle A, denoted as cos(A), can be calculated as follows:

cos(A) = a/cIn the given case, the ratio for cos A is given as 15/17, which implies that:

cos(A) = 15/17

Therefore, in the right-angled triangle, the adjacent side is 15 units and the hypotenuse is 17 units.

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Jake measured a hotel and made a scale drawing, the length of the room in the drawing is 24 inches.

If the scale of the drawing is 8 inches : 7 feet, this means that for every 8 inches in the drawing, there are 7 feet in real life.

To find out length of the room is in the drawing, we need to set up a proportion:

8 inches / 7 feet = x inches / 21 feet

where x is the length of the room in the drawing.

We can cross-multiply and solve for x:

8 inches × 21 feet = 7 feet × x inches

168 inches = 7 feet × x inches

Dividing both sides by 7, we get:

24 inches = x

Therefore, the length of the room in the drawing is 24 inches.

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Answer:

the lines are perpendicular to each other

Step-by-step explanation:

The standard form of equation of a line is y = mx+c

m is the slope of the line

c is the intercept

Given the equations

10x – 3y = 3

3x + 10y = 30

Get the individual slopes

For 10x – 3y = 3

Rewrite in standard form

-3y = -10x + 3

y = 10/3 x - 3/3

y = 10/3 x  - 1

Slope of the line is 10/3

For the equation 3x + 10y = 30

10y = -3x+30

y = -3/10 x + 3

Slope of the line is -3/10

Take the product of the slopes

10/3 * -3/10 = -1

Since the product of their slopes is -1, hence the lines are perpendicular to each other

Answer:

B is the correct one. Second.

Answer:

B

Step-by-step explanation:

To find the value of x, we can set the two angle measures equal to each other and solve for x.

Given:

mZA = (4x - 2)°

mZB = (6x - 20)°

Setting them equal to each other:

4x - 2 = 6x - 20

Now, we can solve for x:

4x - 6x = -20 + 2

-2x = -18

Dividing both sides by -2:

x = -18 / -2

x = 9

Therefore, the value of x is 9.

Answer:

The answer is 9.

Step-by-step explanation:

We need to use the fact that the sum of the angles in a triangle is 180 degrees. Let A, B, and C be the three angles in the triangle. Then we have:

mZA + mZB + mZC = 180°

Substituting the given values, we get:

(4x - 2)° + (6x - 20)° + mZC = 180°

Simplifying the left side, we get:

10x - 22 + mZC = 180°

Next, we use the fact that angles opposite congruent sides of a triangle are congruent. Since we know that segment AC and segment BC are congruent, we have:

mZA = mZB

Substituting the given values and simplifying, we get

4x - 2 = 6x - 20

Solving for x, we get:

x = 9

Therefore, the value of x is 9.

The two prime numbers that add up to 100005, based on the properties of prime numbers would be 2 and 100003.

To find the two prime numbers, the relevant relationship would be  the Goldbach's Conjecture. This posits that every even number greater than 2 can be expressed as the sum of two prime numbers.

So, to write an odd number as the sum of two prime numbers, one of the prime numbers has to be 2 because we know that 2 is the only even prime number.

The other number would therefore be:

= 100005 - 2

= 100003

100003 is a prime number so the two prime numbers are 2 and 100003.

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Answer:

Step-by-step explanation:

Reflection: the conceptual operation of inverting a system or event with respect to a plane, each element being transferred perpendicularly through the plane to a point the same distance the other side of it.

- the leaf

Rotation: The movement of something around anouther or clockwise/counter-clockwise (this one makes no since as an exsplination)

- Phone and the tire

Translation: The movement of something from one place to anouther

- the checker piece.

Based on the information given, we know that the two triangles have two pairs of congruent angles. This is sufficient to prove that the two triangles are congruent using the AAS (Angle-Angle-Side) postulate. Therefore, the method I would use to prove the two triangles congruent is **AAS**.

Answer:

It has a slope of -2/3 and the y intercept is 3

Step-by-step explanation:

The amount of cost to carpet the entire rectangular living room floor of the cabin is given by A = $ 420

The area of the rectangle is given by the product of the length of the rectangle and the width of the rectangle

Area of Rectangle = Length x Width

Given data ,

Let the area of the rectangular living room be A

The scale factor is 1 cm of graph = 4 feet

Now , the length of rectangular floor be L = 5 cm

So , the length of the rectangular floor L = 20 feet

And , the width of the rectangular floor W = 3.5 cm

So , the width of the rectangular floor W = 14 feet

The cost per unit area of carpet = $ 1.50

The area of rectangular floor = L x W

On simplifying , we get

The area of rectangular floor = 20 x 14 = 280 feet²

Now , the cost to carpet 280 feet² of living room = 280 x cost per unit area of carpet

The amount of cost to carpet the entire living room floor = 280 x 1.5

The amount of cost to carpet the entire living room floor = $ 420

Hence , the cost to carpet the living room is $ 420

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The complete question is :

If carpet cost s $1.50 per square foot including the cost of installation how much would it cost to carpet the entire living room floor of the cabin shown at the right?

Answer:

7/12 (seven over twelve)

Step-by-step explanation:

1/3 -1/4 =4/12- 3/12=1/12

1/2+1/12=6/12+1/12=7/12

so the answer is 7/12

hopefully this helps

Ones is the place value of the digit 6 in the number 2,016 and 6 is the face value of the digit 6 in the number 2,016.

Given, a number 2,016

we have to find the place and face value of 6 in the given number 2,016.

So, the Place value of 6 in the given number is ones.

Ones is the place value of the digit 6 in the number 2,016

Also, the Face value of 6 in the given number is 6.

6 is the face value of the digit 6 in the number 2,016

Hence, Ones is the place value of the digit 6 in the number 2,016 and 6 is the face value of the digit 6 in the number 2,016.

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The expected total dollar net operating Income for next year = $70,000

1) The contribution format income statement for the game last year, and the degree of operating leverage is computed below:

Contribution format income statement for the game last year Sales (15,000 × $20) = $300,000

Variable expenses (15,000 × $6) = $90,000

Contribution margin = $210,000

Fixed expenses = $182,000Net operating income = $28,000

Degree of operating leverage = Contribution margin / Net operating income= $210,000 / $28,000= 7.5 2)

The expected percentage increase in net operating income for next year:

The expected sales in next year = 18,000

games selling price per game = $20

Therefore, Total sales revenue = 18,000 × $20 = $360,000

Variable expenses = 18,000 × $6 = $108,000

Fixed expenses = $182,000

Expected net operating income = Total sales revenue – Variable expenses – Fixed expenses

= $360,000 – $108,000 – $182,000= $70,000

The expected percentage increase in net operating income = (Expected net operating income - Last year's net operating income) / Last year's net operating income*100= ($70,000 - $28,000) / $28,000*100= 150%

The expected total dollar net operating income for next year = $70,000

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