MATHEMATICS HIGH SCHOOL

Find the distance between the points L(7,−1) and M(−2, 4).

Answers

Answer 1

Answer:

Answer:

$d=√(106)$

$d \approx 10.3$

Step-by-step explanation:

Consider the vector

$\vec v = \overrightarrow{LM}$

$\overrightarrow{LM}=M-L=(-2, 4)-(7-1)=(-9, 5)$

The distance is equal to the norm:

$d=||\vec v || = √((-9)^2 + 5^2)= √(81+25)= √(106)$

$d \approx 10.3$

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Using solving systems by substitution, how do you solve Y=5x-7
6x-5y=12Solve for x and y (x,y)

Answers

$y=5x-7 \n6x-5y=12 \n \n\hbox{substitute 5x-7 for y in the 2nd equation:} \n6x-5(5x-7)=12 \n6x-25x+35=12 \n6x-25x=12-35 \n-19x=-23 \nx=(-23)/(-19) \nx=(23)/(19) \n \ny=5x-7=5 * (23)/(19)-7=(115)/(19)-(133)/(19)=-(18)/(19) \n \n(x,y)=((23)/(19),-(18)/(19))$

Point M with coordinates (3,4) is the midpoint of the line AB and A has the point (-1,6). What is thepoint of B?

Answers

The midpoint of a line segment divides the line segment into equal halves. The point of B is (7,2)

Given that:

$A = (-1,6)$

$M = (3,4)$

Point B is represented as:

$B = (x_2,y_2)$

To calculate the coordinate of B, we use the following midpoint formula:

$M = ((x_1 + x_2)/(2),(y_1 + y_2)/(2))$

So, we have:

$(3,4) = ((-1 + x_2)/(2),(6 + y_2)/(2))$

Multiply through by 2

$2 * (3,4) = (-1 + x_2,6 + y_2)$

$(6,8) = (-1 + x_2,6 + y_2)$

By comparison:

$6 = -1 +x_2$ and

$8 = 6 + y_2$

So, we have:

$6 = -1 +x_2$

$x_2 =6 + 1$

$x_2 =7$

$8 = 6 + y_2$

$y_2 = 8 - 6$

$y_2 = 2$

Hence, the coordinate of B is (7,2)

Answers

Answer:

x=3.5

Step-by-step explanation:

$9^(x - 2) = 27$

To solve for x , we need to make same base on both sides

9 can be written as 3^2

27 can be written as 3^3

$9^(x - 2) = 27$

[tex[](3^2)^{x - 2} = 3^3[/tex]

multiply the inside exponent with inside exponent

$3^(2(x-2))= 3^3$

Both sides have same base 3

so we equation the exponents

$2(x-2)= 3$

$2x-4= 3$

add 4 on both sides

$2x=7$

divide by 2 on both sides

$x=(7)/(2) =3.5$

To solve this question rewrite 27 as 3 to power 3. And 9 as 3 to power 2. Then distribute 2 in 3 to the power of 2 to the expression of (X-2). Cancel out 3 base at the end. Then set the equation 2x-4=3. Solving for X gives me 7/2 or 3.5.

Solve the following proportion for u.
17/13=u/4

Answers

Answer:

u=5.23

Step-by-step explanation:

$(17)/(13) =(u)/(4)\n13u=68~by~cross-multiplication\nu=5.23~rounded~to~the~nearest~hundreds$

What is 940 divided by
58 equals what's

Answers

154.13793103 it gave it in decimal form

The answer is16.20689655172414

Whats the difference of 89,24&17

Answers

I interpret the first number to be 89.24, so 84 and 24 hundredths.

The difference would be by how many numbers they differ, so we subtract the smaller from the bigger:

89.24-17=12.24

this would be their difference!

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