→MP bisects ∠L M N, →MQ bisects ∠L M P, and →MR bisects ∠QMP. If m∠R M P=21, find m∠LMN. Explain your reasoning.

Answer:10:05

Step-by-step explanation:

subtract 45 from 50!

Answer:

She started the test at 10:05 am

Step-by-step explanation:

Take the end time and subtract the time of the test

10:50-45 = 10:05

She started the test at 10:05 am

Answer:

12 and 8

Step-by-step explanation:

Answer:

3/32

Step-by-step explanation:

1. 3/8 (3/4 + 5/6) - 1/2

2. 3/8 x 19/12 - 1/2

3. 19/32 - 1/2

4. 3/32

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

First, you do the operation order. In this equation, parentheses goes first. You add the fractions to get 19/12.

Then, we multiply the sum from the parentheses and 3/8, 19/32.

Finally, we subtract the product we got from the parentheses and 3/8 with 1/2, each lead us to our final answer 3/32.

~~~Hope this helps~~~

The general solution of the given homogeneous differential equation is:y = ±x√(Cx² + 2)

The given differential equation is: 2xyy' + (x² - y²) = 0

We have to find the general solution of the given homogeneous differential equation. To solve the above differential equation, we will use the substitution method.

Put y = vx and y' = v + xv'

Differentiating both sides w.r.t x: y' = v + xv' ⇒ v' = (y' - v)/x

Differentiating again w.r.t x: y'' = v' + xv'' + v' ⇒ y'' = (y'' - 2y'v + v² + xv')/x

Substituting these values in the given differential equation:

2x(v)(v + xv') + (x² - v²x²) = 0

2v + 2x²v' + x - v² = 0

2x²v' + 2v/x - v³/x = -1/x

We can write the above differential equation as:

2x²dv/dx + 2v/x = v³/x - 1/x

Separating the variables and integrating both sides:

∫dx/x = ∫[v/(v² - 2)]dv/x

⇒ ln |x| + ln |v² - 2| + C

⇒ ln |x(v² - 2)| = ln |Cx|

⇒ v² - 2 = Cx² (where C is a constant)

⇒ v = ±√(Cx² + 2)

Putting the value of v in y = vx, we get:

y = x√(Cx² + 2) and y = -x√(Cx² + 2)

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12 and 13 are the the two consecutive positive integers whose product is 156.

Let x and x+1 are the two consecutive positive integers whose product is 156.

Let x represent the first number and x+1 is second number

x(x+1) = 156

Expanding the left side:

x² + x = 156

Bringing everything to one side:

x² + x - 156 = 0

The equation is in the form of quadratic

x² + 13 x - 12x - 156 = 0

x(x+13)+12(x+13)=0

(x-12)(x+13)=0

x=12 and x=-13

Therefore, the two consecutive positive integers are 12 and 13, since their product is 156.

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Answer:

√27

Step-by-step explanation:

3×√3 = 5.196

√27 = 5.196

Answer:

27

Step-by-step explanation:

StartRoot 27 EndRoot cm

Answer:

(3,1)

Step-by-step explanation:

Answer:

5x+55=100

Step-by-step explanation:

Therefore , the solution of the given problem of circumference statement is proved by the following below explanation.

Any great circle's circumference, or the distance between the center of the sphere and any plane running through it, is measured in meters. Any large circle that passes through a pole-designated location is referred to as a meridian.

Here,

An arc PQ of a circle that subtends angles POQ at its center O and PAQ at one of its points A on the circumference.

To prove : <POQ = 2<PAQ

To prove this theorem we consider the arc AB in three different situations, minor arc AB, major arc AB and semi-circle AB.

Construction:

Join the line AO extended to B.

Proof :

<BOQ = ZOAQ + ZAQO .....(1)

Also, in A OAQ,

OA = OQ

Therefore,

[Radii of a circle]

ZOAQ = ZOQA

[Angles opposite to equal sides are equal]

<BOQ = 2ZOAQ

.......(2)

Similarly, BOP = 220AP

.(3)

Adding 2 & 3, we get,

<BOP + <BOQ = 2(ZOAP + ZOAQ)

<POQ = 2<PAQ

.......(4)

For the case 3, where PQ is the major arc, equation 4 is replaced by

Reflex angle, <POQ = 2ZPAQ

Therefore , the solution of the given problem of circumference statement is proved by the following below explanation.

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The demand function for good X is Qx = m - 3Px + 2Py, where Qx is the quantity demanded of X, m is income, Px is the price of X, and Py is the price of a related good Y. The equation shows that the demand for X is inversely related to its price and directly related to the price of Y. Income, price of X, and price of Y collectively affect the overall demand for X.


The demand function for good X is given by Qx = m - 3Px + 2Py, where Qx represents the quantity demanded of good X, m is the income, Px is the price of good X, and Py is the price of a related good Y. In this equation, the income and prices are assumed to be positive.

To determine the demand for good X, we can analyze the equation. The coefficient -3 in front of Px indicates that the demand for good X is inversely related to its price. As the price of X increases, the quantity demanded of X decreases, assuming other factors remain constant. On the other hand, the coefficient 2 in front of Py indicates that the demand for good X is directly related to the price of the related good Y. If the price of Y increases, the quantity demanded of X also increases, assuming other factors remain constant.

Furthermore, the term (m - 3Px + 2Py) represents the overall effect of income, price of X, and price of Y on the quantity demanded of X. If income (m) increases, the quantity demanded of X increases. If the price of X (Px) increases, the quantity demanded of X decreases. If the price of Y (Py) increases, the quantity demanded of X increases.

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If C and D are square matrices of size m x m, then the statement that is not true is \((5) det(C^-1) = 1/det(C)\). The determinant is a mathematical object that is used in linear algebra to define scalar invariants of square matrices.

The determinant can also be viewed as the matrix's scaling factor, which changes the magnitude of a matrix's linear transformation in order to describe how the linear transformation alters the volume of any shape. The adjugate matrix is the transpose of the matrix of cofactors for a square matrix. The product of two matrices A and B is a matrix C such that A is a matrix with m rows and n columns and B is a matrix with n rows and p columns. A matrix with the same number of rows and columns is called a square matrix. It is a matrix in which the number of rows and columns is the same, i.e., it has an equal number of rows and columns. The determinant of a 2x2 matrix can be found using the formula ad - bc. If C and D are square matrices of size m X m, then the statement that is not true is \((5) det(C^{-1}) = 1/det(C)\).

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The statement that x = 0 is the only solution to ax = 0 if and only if the rank of the p × q matrix a equals q, the number of unknowns, can be proven as follows:

First, assume that x = 0 is the only solution to ax = 0. This means that there are no nonzero solutions to the equation, implying that the null space of the matrix a is trivial (only containing the zero vector). By the rank-nullity theorem, the nullity of a matrix is equal to the dimension of its null space. Since the null space of a is trivial, its nullity is zero.

Next, consider the rank of the matrix a. By the rank-nullity theorem, the rank of a plus its nullity is equal to the number of columns in a, which is q. Therefore, if the nullity is zero, the rank of a must be equal to q.

Conversely, if the rank of the matrix a equals q, it implies that the nullity of a is zero. This means that the only solution to the equation ax = 0 is the zero vector, x = 0.

x = 0 is the only solution to ax = 0 if and only if the rank of the matrix a equals q, the number of unknowns. This result highlights the relationship between the null space and the rank of a matrix, providing insights into the solutions of linear equations and the properties of the matrix.

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Answer:

Your answer will be 1.5

Step-by-step explanation:

I used my calculator to find out, your welcome:)

Answer:

Step-by-step explanation

Frist, the area = ab = 30 m^2 and the perimeter = 2(a + b) = 34 m or a + b = 17 m (2). Solving (1) and (2), a = 15 m and b = 2 m. Since it is a rectangle, the dimensions are (all in m) so the answer is: 15, 2, 15, 2.

Answer:

THe kitchen is 8 by 10

Step-by-step explanation:

x = width

y = length

Area = xy = 80 m²

Perimeter = 2x + 2y = 36 m

2x = 36 - 2y

x = 18 - y   substitute into equation 1

(18 - y)(y) = 80

-y² + 18y - 80 = 0    find roots of y by factoring

y² - 18y + 80 = 0

(y - 8)(y - 10) = 0

y = 8, 10

Since xy = 80, then:

x = 80/10 = 8, or, x = 80/8 = 10

Now you have your dimensions: 8 and 10

To check the answers:

8 x 10 = 80 m²

2(8) + 2 (10) = 36 m

Answers are correct!

1

The exact value of tan(π4) tan ( π 4 ) is 1 .

Answer:

$8 per pound

Step-by-step explanation:

40 ÷ 5 = 8

$40 per 5 pound= 8

$8 per 1 pound = 8

The difference in salary options for the month of February would be $9,875.

In Option #1, you would earn $100 per week plus 7.5% commission on sales. In Option #2, you would earn a fixed salary of $350 per week, with no commission. To calculate the difference in salary options for the month of February, we need to calculate the earnings for each option and then subtract Option #2 from Option #1.

In Option #1, the commission on sales would be 7.5% of $145,000, which is $10,875. The weekly earnings would be $100 per week. Since there are four weeks in February, the total earnings for Option #1 would be $100 * 4 + $10,875 = $11,275.

In Option #2, the weekly earnings would be a fixed $350 per week. So, the total earnings for Option #2 in February would be $350 * 4 = $1,400.

To find the difference in salary options, we subtract the earnings of Option #2 from Option #1: $11,275 - $1,400 = $9,875.

Therefore, the difference in salary options for the month of February would be $9,875.


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Answer:

x = -10

Step-by-step explanation:

5 (x + 8) = -10

5x + 40 = -10

5x = -50

x= -10

Answer:

x= -10

Step-by-step explanation:

5(x+8)=-10

5x+40=-10

move the 40 to the other side

5x=-10-40

5x= -50

divide 5 by both sides to get rid of the x.

x=-10

Answer:

B. 3.6 = 3h

Step-by-step explanation:

Area of rectangle formula :-

A = L × W

3.6 = 3 × W OR the answer choic it gave is 3.6 = 3h.

Hope this helps, thank you !!

Answer: The answer to the question is $\boxed{\text{(d)}\ 4}$. This is because a polynomial of degree 4 can have at most 4 zeros, and those zeros can be either real or complex numbers. Since the question asks for the maximum number of positive real zeros, the answer is $\boxed{\text{(d)}\ 4}$.

Step-by-step explanation: The maximum number of positive real zeros that a polynomial function of degree 4 can have is 4. This is because a polynomial of degree 4 can have at most 4 zeros, and those zeros can be either real or complex numbers. Since the question asks for the maximum number of positive real zeros, the answer is $\boxed{\text{(d)}\ 4}$.

The table representing the relationship between hours of lawn care and the amount of money the company charges is:

8 $220

10 $275

12 $330

14 $385.

Equations are mathematical expressions with two algebraic expressions flanking the equals (=) symbol on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS (left hand side equals right hand side) is the most widely accepted theorem.

Let x be the charge of lawn care for 1 hour.

Given, charge for 4 hours of lawn care =$110

So, x= Amount charged/ Hours of lawn care

x=110/4

x=27.5

Now, the company charges $27.5 for 1 hour of lawn care.

So now we can find the amount charged by the company for

"y" no. of hours by using the equation. x × y = z

Here x, y and z are variables, where x is the charge of lawn care for 1 hour. y is the number of hours of lawn care and z is the total amount

charged by the company.

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Answer:

1-5

Step-by-step explanation:

Answer:

C: (2,3)

Step-by-step explanation:

to solve this algebraically just plug in the x and y values of the points and see if they are true, but here is the graph to juse show you

If A limousine service has 15 cars available for rides: then the number of different collections C of 5 limousines are possible is 3003 .

To find the number of different collections C of five limousines, we can use combinations. A combination is a way to choose a subset of items from a larger set, without regard to order.

Let the number of Cadillac models n.

Then, 15 - 8 = 7 cars are Cadillacs. So, n = 7.

The number of different collections of 5 limousines from the 15 cars is given by the number of combinations of 5 items taken from a set of 15 items:

⇒ ¹⁵C₅ = 15!/(5!×(15 - 5)!) = 15!/(5!×10!) = 3003.

Therefore , there are 3003 different collections C of five limousines that the event organizer can choose from the limousine service's fleet of 15 cars.

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