MATHEMATICS HIGH SCHOOL

1. Round to the nearest hundredth. 1.824
A. 1.82
B. 1.83
C. 2
D. 1.8

Answers

Answer 1
Answer: Considering 1.824 (2 being hundredth) it would mean that this is 1.82 
Answer 2
Answer: A because 1.824 is rounded to 1.82 when rounding to the nearest hundredth.

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21 is a supplement of 22, and mZ1 = 123°. Z2 is a complement of 23. Find m23.OmZ3 =

2x-3y=-143x-2y=-6
if (x,y) is a solution to the system of equations above, what is the value of x-y?
A)-20
B)-8
C)-4
D)8
can you show your work please

Answers

Answer:

Step-by-step explanation:

The given system of equations :

2x-3y=-14.............................(1)\n3x-2y=-6.........................(2)

Multiply equation (1) with 3 and equation (2) with 2 , we get

6x-9y=-42.............................(3)\n6x-4y=-12.........................(4)

Now subtract equation (4) from equation (3), we get

5y=30\n\n\Rightarrow\ y=6

Substitute the value of y in equation (1), we get

2x-3(6)=-14\n\n\Rightarrow\ 2x=-14+18\n\n\Rightarrwo\ 2x=4\n\n\Rightarrow\ x=2

Hence, the solution of the system : (x,y)=(2,6)

Now, consider  x-y and substitute the value of x and y , we get

2-6=-4

The solution to the equation is x - y = -4

Given data ,

To solve the system of equations, we can use the method of substitution or elimination. Let's use the method of elimination:

Multiply the first equation by 3 and the second equation by 2 to make the coefficients of x in both equations equal:

(3)(2x-3y) = (3)(-14)

(2)(3x-2y) = (2)(-6)

Simplifying these equations gives:

6x-9y = -42

6x-4y = -12

Now, subtract the second equation from the first equation:

(6x-9y) - (6x-4y) = (-42) - (-12)

-5y = -30

Divide both sides by -5:

y = 6

Substitute this value of y back into one of the original equations, let's use the first equation:

2x - 3(6) = -14

2x - 18 = -14

2x = 4

x = 2

Now , the value of x - y is given by

A = x - y

A = 2 - 6

A = -4

Hence , the equation is solved

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What is the value of g(-4)?

Answers

The value of g(-4) is 1. The correct option is C

What is a Piece-Wise Function?

A function that has a different sub-function for different intervals of the domain is called  Piece-Wise Function

The functions for the different interval is

g(x)= \rm \sqrt[3]{x+5} , x ≤ -4

     = -x² +11 , x > -4

The value of g(-4) will be determined by using g(x)= \rm \sqrt[3]{x+5}

Substituting the value x = -4

g(x) = \rm \sqrt[3]{-4+5}

g(x) = ∛1

g(x) = 1

Therefore, The value of g(-4) is 1. The correct option is C

To know more about piece-wise function

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1.the typical school lunch milk carton is a half pint. how many ounces is this?2.you need a quart of water but you only have a measuring cup. how many times do you need to fill the cup in order to get a quart?

3.what is the speed of a car in feet/second that is traveling 60 miles/hour?

Answers

1 pint = 16 ounces
1/2 pint = 16/2 = 8 ounces.

What are the solutions to X2 + 8X + 7 = 0?

Answers

Answer:

x = - 7, x = - 1

Step-by-step explanation:

Given

x² + 8x + 7 = 0

Consider the factors of the constant term (+ 7) which sum to give the coefficient of the x- term (+ 8)

The factors are + 7 and + 1 , since

7 × 1 = 7 and 7 + 1 = 8 , then

(x + 7)(x + 1) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 7 = 0 ⇒ x = - 7

x + 1 = 0 ⇒ x = - 1

Answer:

x=-1,-7

Step-by-step explanation:

x^2+8x+7=0 where a \neq 0 so a = 1 b = 8 c = 7

Quadratic Formula: x=-b(√(b^2-4ac) )/(2a)

x=-8(√(8^2-4(1)(7)) )/(2(1))

x=-8(√(64-28) )/(2)     Evaluate the exponent and multiply 4ac

x=-8(√(36) )/(2)          Subtract b^2 - 4ac and multiply 2a

x=-8(√(6) )/(2)           Solve for the sqrt root of 35

x = - 8 ± 6/2 =

x = - 8 + 6/2 = -1

x = - 8 - 6/2 = -7

5 is a ________ of 20.
multiple
factor

Answers

5 is a factor of 20

The multiples of 20 are

20, 40, 60, 80, 100, etc.

A and B are independent events. Which equation below must be true?A. P(A) = P(B)
B. P(A | B) = P(A)
C. P(A ∩ B) = P(A)
D. P(B) = P(A | B)

Answers

The correct answer for this question is B. P(A | B) = P(A). Another equation used for independent events is P(B | A) = P(B). When the multiplication rule is applied, this gives an alternative definition of independence which is:

P(A ∩ B) = P(A)*P(B)

Independent events are events that can occur without affecting or changing the probability of the other.

Answer with Step-by-step explanation:

A and B are independent events.

Then, we have to find,which equation below must be true.

A. P(A) = P(B)

No, this is not true, example

A: Occurence of 1 in rolling a die  P(A)=1/6

B: occurence of an even number on rolling a die P(B)=1/2

B. P(A | B) = P(A)

This is true

since, P(A|B)+P(A)/P(A∩B)  and, P(A∩B)=P(A)P(B)

C. P(A ∩ B) = P(A)

This is not true

since, P(A∩B)=P(A)×P(B)

D. P(B) = P(A | B)

This is not true
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