MATHEMATICS HIGH SCHOOL

Directed line segment porque is shown on the coordinate plane. What are the coordinates of the point 1/3 of the way from point P(4,4) to point Q(-2,1)?

Answers

Answer 1

Answer:

Answer: (2,3).

Step-by-step explanation:

We need to find the coordinates of the point 1/3 of the way from point P(4,4) to point Q(-2,1).

Let the point be A.

$PA:PQ=1:3$

$PA:AQ=PA:(PQ-PA)=1:(3-1)=1:2$

It means the point A divide the segment PQ in 1:2.

Section formula: If a point divide a segment is m:n.

$\left((mx_2+nx_1)/(m+n),(my_2+ny_1)/(m+n)\right)$

$A=\left((1(-2)+2(4))/(1+2),(1(1)+2(4))/(1+2)\right)$

$A=\left((-2+8)/(3),(1+8)/(3)\right)$

$A=\left((6)/(3),(9)/(3)\right)$

$A=\left(2,3\right)$

Therefore, the required coordinates are (2,3).

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the sides of a rectangle are in the ratio 5:7 and the perimeter of the rectangle is 96cm. What is the area of the rectangle?

Answers

width = 5x
length = 7x

Perimeter = 10x + 14x = 24x = 96cm
x = 96/24 = 4cm

width = 5x = 20cm
length = 7x = 28cm

Area = (20cm x 28cm) = 560 cm²

Help me plz with this question

Answers

Answer:

y= -6x+23

Step-by-step explanation:

perpendicular: opposite signs and reciprocal

m= 1/6 and y-intercept = 23

y= -6x+23

please help :) Geography doesn’t simply begin and end with maps showing the location of all the countries of the world. In fact, such maps don’t necessarily tell us much. No—geography poses fascinating questions about who we are and how we got to be that way, and then provides clues to the answers. ~Kenneth Davis The speaker in the passage above is stating that a. maps are not helpful to historians. b. human geography is more important than physical geography. c. historians want to know where people settled. d. physical features and locations tell historians about the ways people lived.

Answers

Answer:

d. physical features and locations tell historians about the ways people lived.

Step-by-step explanation:

I believe this is the correct answer

Help please i don’t kneo

Answers

Answer:

x=4

Step-by-step explanation:

Log3x-log3 (x − 8) = 2?

Answers

Answer: To solve the equation log3x - log3(x - 8) = 2, we can use the properties of logarithms to simplify and solve for x.

First, let's apply the quotient rule of logarithms. The quotient rule states that log(base a)(b) - log(base a)(c) = log(base a)(b/c).

Using this rule, we can rewrite the equation as log3(x / (x - 8)) = 2.

Next, let's rewrite 2 as a logarithm. The logarithmic form of 2 is log(base a)(b) = c, where a^c = b. In this case, a^c = 3^2 = 9. Therefore, we can rewrite the equation as log3(x / (x - 8)) = log3(9).

Now that the bases are the same, we can set the arguments of the logarithms equal to each other. Therefore, x / (x - 8) = 9.

To solve for x, we can multiply both sides of the equation by (x - 8) to eliminate the fraction. This gives us x = 9(x - 8).

Expanding the right side of the equation, we get x = 9x - 72.

Next, we can subtract 9x from both sides of the equation to isolate x. This gives us -8x = -72.

Dividing both sides of the equation by -8, we find that x = 9.

Therefore, the solution to the equation log3x - log3(x - 8) = 2 is x = 9.

Step-by-step explanation:

Harriet earns the same amount of money each day. Her gross pay at the end of 7 work days is 35h + 56 dollars. Which expression represents her gross pay each day

Answers

In the question "Harriet earns the same amount of money each day. Her gross pay at the end of 7 work days is 35h + 56 dollars. Which expression represents her gross pay each day" To obtain the expression that represents her gross pay each day, we divide the given expression by 7 to get (35h + 56) / 7 = 35h / 7 + 56 / 7 = 5h + 8 Therefore, the expression that represents her gross pay each day is 5h + 8.

Answer:

Step-by-step explanation:

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