What is the sum and classification of 3/20 + the square root of 10 and is it rational

Answer:

it denotes distributive property of multiplication over addition

distributive property of multiplication over addition. The distributive property states that multiplying a sum by a number gives the same result as multiplying each addend by the number and then adding the products together.

Answer:

θ  = [tex]30^{0}[/tex]

Step-by-step explanation:

Since the vertical height of the mountain is 800 feet, and the distance from the top to its base is 1600 feet. Let the angle of elevation be represented by θ, applying the required trigonometric function;

Sin θ = [tex]\frac{opposite}{hypotenuse}[/tex]

Sin θ = [tex]\frac{800}{1600}[/tex]

        = 0.5

θ = [tex]Sin^{-1}[/tex] 0.5

θ  = [tex]30^{0}[/tex]

Thus, the angle of elevation from the base to the top of the mountain is [tex]30^{0}[/tex].

Answer: C) 2/3

========================================================

Explanation:

Let's cross multiply and then get everything to one side

x/(2x-1) = (2x+1)/(x+2)

x(x+2) = (2x-1)(2x+1)

x^2+2x = 4x^2-1

0 = 4x^2-1-x^2-2x

0 = 3x^2-2x-1

3x^2-2x-1 = 0 .... see note below

x^2-(2/3)x-1/3 = 0

In that last step, I divided everything by the leading coefficient 3. That way, the leading coefficient becomes 1.

It turns out that anything in the form x^2-px+q has roots m and n such that

p = m+n

q = m*n

In short, the roots add to the negative of the middle coefficient, and they also multiply to the constant term. Again this only applies to quadratics where the leading coefficient is 1.

Comparing x^2-(2/3)x-1/3 with the form x^2-px+q, we see that

p = 2/3

q = -1/3

Therefore, p = m+n = 2/3

If you're curious why this works, it's because (x+a)(x+b) expands out to x^2+(a+b)x+ab, and note how the roots here are x = -a and x = -b.

-------------------------

Note: Another route would be to solve 3x^2-2x-1 = 0 for x using any method you prefer (I recommend the quadratic formula). You would get the two solutions x = -1/3 and x = 1. They add to (-1/3)+1 = (-1/3) + (3/3) = (-1+3)/3 = 2/3.

Answer:

A)

The simplest way to solve A is by checking 1st digit one-by-one.

selecting 1 as 1st digit, we have 2 ways

1324 and 1423

selecting 2 as 1st digit, we have 3 ways

2143, 2314, and 2413

selecting 3 as 1st digit, we have 3 ways

3142, 3241, and 3412

selecting 4 as 1st digit, we have 2 ways

4132 and 4231

=> 2 +3 + 3 + 2 = 10 ways in total.

B)

Use the same strategy as A)

selecting 1st digit that is greater than 6, there are 3 digits: {9, 8, 7}

selecting 9 as 1st digit => 967, 968

selecting 8 as 1st digit => 867, 869

selecting 7 as 1st digit => 768, 769

=> 3 x 2 = 6 ways

selecting 1st digit that is smaller than 6, there are 5 digits: {5, 4, 3, 2, 1}

selecting 5 as 1st digit => 565, 564, 563, 562, 561, 560

similarly, selecting 4, 3, 2, 1, there are 6 ways to select that last digit

=> 5 x 6 = 30 ways

=> 30 + 6 = 36 ways in total

C)

a 7-digit snakelike number starts with digit 9 (the largest digit)

=> 2nd digit is smaller than 9

=> 3rd digit is larger than 2nd digit

=> 4th digit is smaller than 3rd digit

=> 5th digit is larger than 4th digit

=> 6th digit is smaller than 5th digit

=> 7th digit is larger than 6th digit (this is impossible because 0 is smallest digit)

Answer:

Perpendicular line through a point off a line

Step-by-step explanation:

Based on the markings in the diagram, we have;

Marking points E and F along AB extended forms two points equidistant from the point C on the line AB

Construction of the line HI by using equal arc lengths from E and F creates two points equidistant from E and F on either side of the line AB such that HI passes through C forming a perpendicular bisector from C to AB.

Therefore, a perpendicular line has been constructed from the point C off the line AB to the line AB

Hence the correct option is the construction of a perpendicular line through a point off a line.

Answer:

C. Perpendicular line through a point off a line (its off not on)  Took the test and got it right

Step-by-step explanation:

Answer:

5/8

Step-by-step explanation:

slope: (y₂ - y₁) / (x₂ - x₁)

(3 - 8) / (1 - 9) = -5/-8 = 5/8

Answer:

m= 5/8

Step-by-step explanation:

The slope of a line can be found using the following formula:

[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1} }[/tex]

where (x₁, y₁) and (x₂, y₂) are the points the line passes through.

The points given are: (1,3) and (9,8). Therefore,

[tex]x_{1}=1 \\y_{1}=3 \\x_{2}=9 \\y_{2}=8[/tex]

Substitute the values into the formula.

[tex]m=\frac{8-3}{9-1}[/tex]

Perform the operation in the numerator. Subtract 3 from 8.

[tex]m=\frac{5}{9-1}[/tex]

Perform the operation in the denominator. Subtract 1 from 9.

[tex]m= \frac{5}{8}[/tex]

The slope of the line is 5/8

Answer:

$6650

Step-by-step explanation:

→ Calculate the decimal multiplier

100 - 30 = 70

70 ÷ 100 = 0.7

→ Multiply the decimal multiplier by the cost

9500 × 0.7 = 6650

Answer:

$6,650

Step-by-step explanation:

This is called percentage decrease:

(100 - 30)% = 70%

9500 × 70/100

= $6,650

Answer:

1,116

Step-by-step explanation:

2568 + ( - 1452)

= 2568 - 1452 ( because + × - makes -)

= 2568 - 1452

= 1,116

Answer:

the answer is 1116 I hope it's right

The value of the given expression (7m - 2m²n)² = 34,596 at m = -6 and n = 2.

An expression consists of variables, constants, and operators. Based on the number of terms in an expression, they are named linear, binomial, and so on.

The given expression is (7m - 2m²n)²

It is given that m = -6 and n = 2

To evaluate the given expression, the given values are substituted in it.

On substituting these values,

(7m - 2m²n)² = (7(-6) - 2(-6)²(2))²

⇒ (-42 - 4(36))²

⇒ (-42 - 144)²

⇒ (-186)²

∴ (7m - 2m²n)² = 34,596

Therefore, the required value of the given expression is 34,596.

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Answer: The equations are y = 4x-3  and y= 3x -1

Step-by-step explanation:

So lets say both equations will have positive slopes. Using that, we can input any slope  and solve for the y intercept using the coordinates.We will use the formula, y=mx + b  where m is the slope and b is the y-intercept

Let's say the slope is 3.

5 = 3(2) + b

5= 6 + b

-6  -6  

b= -1  

We can now come up with the equation, y= 3x -1  

We need to find another equation that will intersect with it at the point (2,5)

For lines to intersect, they need to have different slopes and different y-intercepts.

We need to come up with a new slope, the slope of the second equation could be 4. Now using the formula, use the coordinates so solve for the y intercept.

5= 4(2) + b

5 = 8 + b

-8   -8

b = -3

The equation will be   y = 4x -3  

We now have the equations y=4x -3   and  y = 3x -1  

To find that their solution is (2,5)  substitute one of the y-values into the other and solve for x then solve for y.  

4x -3 = 3x -1

    +3        +3

4x = 3x + +2

-3x   -3x

1x = 2

x = 2  

We know now that the value of x is true because the value of x is 2.Input it into one of the equations and solve for y.

y = 4(2) - 3

y = 8-3

y = 5

The solution is indeed (2,5) .

Answer:

it is 17.2 + 16.4

Step-by-step explanation:

because 8.6x2= 17.2

then 5.2x2=10.4

then 3+3=6

lastly 10.4+6= 16.4

so that makes it 17.2+16.4

Answer:

Step-by-step explanation:

2(3x+5) = 4(2x - 3)

First expand the terms

That's

6x + 10 = 8x - 12

6x - 8x + 10 = - 12

- 2x + 10 = - 12

Subtract 10 from both sides

That's

- 2x + 10 - 10 = - 12 - 10

- 2x = - 22

Divide both sides by - 2

We have the final answer as

Hope this helps you

Answer: 145

Step-by-step explanation:

Answer: 145

Step by step explanation:

Answer:

3

Step-by-step explanation:

The Greatest Common Factor between 42 and 45 is 3.

Greatest Common Factor of two or more numbers is defined as the largest number that is a factor of all the numbers.

Given two numbers are 42 and 45,

42 = 7*2*3

45 = 5*3*3

GCF = 3

Hence, The Greatest Common Factor between 42 and 45 is 3.

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Answer:

DBH is an obtuse angle.

Step-by-step explanation:

D is around the 15 degree mark. h is around the 144 degree mark. Subtract 15 by 15 and 144 by 15 degrees, so that way angle D would be on the 0. You would get 129 degrees, which still makes it obtuse because is greater than 90 degrees

I hope this helps

Answer:

[tex]x = 7[/tex]

Step-by-step explanation:

Given

[tex]\frac{4}{3}x - \frac{1}{3} = 9[/tex]

Required

Solve for x

[tex]\frac{4}{3}x - \frac{1}{3} = 9[/tex]

Add [tex]\frac{1}{3}[/tex] to both sides

[tex]\frac{4}{3}x - \frac{1}{3} + \frac{1}{3} = 9 + \frac{1}{3}[/tex]

[tex]\frac{4}{3}x = 9 + \frac{1}{3}[/tex]

Take LCM

[tex]\frac{4}{3}x = \frac{27 + 1}{3}[/tex]

[tex]\frac{4}{3}x = \frac{28}{3}[/tex]

Multiply both sides by [tex]\frac{3}{4}[/tex]

[tex]\frac{3}{4} * \frac{4}{3}x = \frac{3}{4} *\frac{28}{3}[/tex]

Evaluate the left hand side

[tex]x = \frac{3}{4} *\frac{28}{3}[/tex]

[tex]x = \frac{28}{4}[/tex]

Divide 28 by 4

[tex]x = 7[/tex]

Answer:

x=7 we are both correct

Step-by-step explanation:

Answer:

$18.15

Step-by-step explanation:

You need 3 numbers, divide the total by 3:

84/3 = 28

This is the middle value.

Now you use the one lower and the one higher:

27 + 28 + 29 = 84

The numbers are 27, 28, 29

Answer: 26, 28, 30

Step-by-step explanation:

26, 28, and 30 follow each other in consecutive order without haps of more than two and are arranged smallest to largest.

Answer:

9

Step-by-step explanation:

Use PEMDAS

Parentheses (Bracketts go after parentheses but are not included in PEMDAS)

Exponents

Multiplication

Division

Addition

Subtraction

Answer:

3

Step-by-step explanation: 15-(10+(3-2)2)+6

3-2=1x2=2+10=12 15-12=3

Answer:

10

Step-by-step explanation:

(10y+6) + (8y-6) =180

18y=180

y=10

JKM=10y+6=10(10)+6=106

MKL=8y-6=8(10)-6=74

Answer:

Step-by-step explanation:

10y+6+8y-6=180

then,y=10

therefore,

angle(JKM)=106

angle(MKL)=74

Answer:

True

Step-by-step explanation:

the parent function f(x) = 1/x has a vertical asymptote at x = 0 and a horizontal asymptote at y = 0

Answer:

Step-by-step explanation:

4(2x-1)=3x+5-x

8x-4=3x+5-x

8x-4=2x+5

6x-4=5

6x=9

x=3/2

Answer: x=1.3

Explanation: Just simplify the equation so there is a variable on one side and a number on the other.

Answer:

g-1(4)=-5

Step-by-step explanation:

because inverse mean that you will switch every x and y on the original graph

for example; point( 4,-2) inverse will be (-2,4)

so to find x=4 on the inverse than just find y=4 on the origin graph

Answer:

60 inches

Step-by-step explanation:

12 feet=144 inches

28in x 3 = 84

144-84= 60

Sarah is left with 60 inches of the board, after cutting three pieces of 28 inches of the board from 12 feet long board which is equal to 144 inches converted using the conversion factor.

The conversion of units is the process of converting a quantity between multiple units of measurement, usually using multiplicative conversion factors.

The conversion factor between inch and foot are:

1 foot = 12 inches,

or, 1 inch = 1/12 feet.

We are informed that Sarah has a wooden board that is 12 feet long.

We are asked that if she cuts three 28-inch pieces from the board, how many inches of the board will she have left.

To solve the problem, we convert the length of the wooden board from feet to inches.

The board is 12 feet long. We know 1 foot = 12 inches.

∴ 12 feet = 12*12 inches = 144 inches.

∴ Length of the board = 144 inches.

Size of the piece cut by Sarah = 28 inches.

She cuts 3 such pieces,

∴ Total piece of board cut = 3*28 inches = 84 inches.

∴ Length of the board Sarah is left with = Total length of the board - Total piece cut from the board = 144 - 84 inches = 60 inches.

∴ Sarah is left with 60 inches of the board, after cutting three pieces of 28 inches of the board from 12 feet long board which is equal to 144 inches converted using the conversion factor.

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Answer:

Video Games = $5.25

Movies = $1.25

Step-by-step explanation:

(3x + 5y = 30)2

6x + 2y = 18

                                           Video Games (y) = 5.25

  6x + 10y = 60

-  6x + 2y = 18  

      (8y)/8 = (42)/8

6x + 2(5.25) = 18

6x + 10.5 = 18

6x = 7.5

x = 1.25

Double Check by plugging in the numbers

Answer:

this is a correct answer

Answer:

The answer is A. (3x^4-5x^3+5x+2) =(x-2)

Step-by-step explanation:

we see that the polynomial that gives the remainder as 20 is

(3[tex]x^{4}[/tex] - 5x³ + 5x + 2) ÷ (x - 2)

Option A is our correct answer.

The remainder theorem states that when a polynomial p(x) is divided by

(x - a), then the remainder = f(a).

We have,

(3[tex]x^{4}[/tex] - 5x³ + 5x + 2) ÷ (x - 2) ____(1)

We can directly find the remainder as:

x - 2 = 0

x = 2

Putting x = 2 in (1) we get,

= 3 x 16 - 5 x 8 + 5 x 2 + 2

= 48 - 40 + 10 + 2

= 20

The remainder is 20.

(3x³ + 7x² + 5x + 2) ÷ (x - 2) ) _______(2)

x - 2 = 0

x = 2

Putting x = 2 in (2) we get,

= 3 x 8 + 7 x 4 + 5 x 2 + 2

= 24 + 28 + 10 + 2

= 64

The remainder is 64.

(x³ + 5x² - 4x + 6) ÷ (x + 5) ______(3)

x + 5 = 0

x = -5

Putting x = -5 in (3) we get,

= - 125 + 5 x 25 - 4 x (-5) + 6

= -125 + 125 + 20 + 6

= 20 + 6

= 26

The remainder is 26.

([tex]x^{4}[/tex] - 8x² + 16) ÷ (x + 4) _______(4)

x + 4 = 0

x = -4

Putting x = -4 in (4) we get,

= 256 - 8 x 16 + 16

= 256 - 128 + 16

= 144

The remainder is 144.

Thus we see that the polynomial that gives the remainder as 20 is

(3[tex]x^{4}[/tex] - 5x³ + 5x + 2) ÷ (x - 2)

Option A is our correct answer.

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Answer:

C

Step-by-step explanation:

Given

[tex]\frac{-m}{2}[/tex] - [tex]\frac{5}{4}[/tex] ≤ [tex]\frac{5m}{12}[/tex] - [tex]\frac{7}{6}[/tex]

Multiply through by 12 to clear the fractions

- 6m - 15 ≤ 5m - 14 ( subtract 5m from both sides )

- 11m - 15 ≤ - 14 ( add 15 to both sides )

- 11m ≤ 1

Divide both sides by - 11, reversing the symbol as a result of dividing by a negative quantity

m ≥ - [tex]\frac{1}{11}[/tex] → C

Answer:

2/5

Step-by-step explanation:

3/5 + ____ = 5/5

2/5

Answer:

coordinate of M (8,13)

Step-by-step explanation:

LM has L(-2,-9), P(3,2) mid point of LM

coordinate of mid point= x=x1+x1/2 and y=y1+y2/2

x1=-2 , x2 is the x of point M

xof P= (-2+x2)/2

3(2)=-2+x2

6=-2+x2 ⇒ x2=6+2=8

y of P= y1+y2/2

2=-9+y2/2

y2=2(2)+9⇒ y2=13

coordinate of M (8,13)