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3 years ago

Find the distance between the points A(-4, -3) and B(-8, 7). Round your answers to the nearest tenth.

Mathematics

1 answer:

Firlakuza [10]3 years ago

6 0

Answer:

distance = 10.8

Step-by-step explanation:

the distance between 2 points is the Hypotenuse of the right angled triangle of the x and y coordinate differences.

so, Pythagoras is used.

c² = a² + b²

c = the Hypotenuse (the side of the triangle being opposite to the 90 degree angle).

x- difference : -4 - -8 = +4

y- difference : -3 - 7 = -10

c² = +4² + (-10)² = 16 + 100 = 116

c = sqrt(116) = 10.8

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14. Write a two-column proof.

scZoUnD [109]

Given:

$\bold{ 8x=4y-20} \\\\ \bold{ y=13}$

Prove:

$\bold{x=4}$

Solution:

$\to \bold{8x=4y-20}..........(i)\\\\\to \bold{ y=13}........................(ii)$

Putting the value of equation (ii) into the equation (i):

$\to \bold{8x=4(13)-20}\\\\\to \bold{8x=52-20}\\\\\to \bold{8x=32}\\\\\to \bold{x=\frac{32}{8}}\\\\\to \bold{x= 4}\\\\$

putting the value x into the equation (i):

$\to \bold{8(4)=4y-20}\\\\\to \bold{32=4y-20}\\\\\to \bold{32+20=4y}\\\\\to \bold{52=4y}\\\\\to \bold{y=\frac{54}{4}}\\\\\to \bold{ y= 13.5}$

Therefore, the value of x= 4

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3 years ago

Marlene rides her bike at a rate of 16 miles per hour. The time in hours that she rides is represented by the variable t, and th

Gemiola [76]

A function assigns the values. The correct option is B and E.

<h3>What is a Function?</h3>

A function assigns the value of each element of one set to the other specific element of another set.

Given Marlene rides her bike at a rate of 16 miles per hour. Therefore, Marlene Speed is 16 miles/hour. Now if speed is 16 miles/hour, then time is the independent variable and distance is the dependent variable. And the speed is the slope of the function, therefore, the statements that are true of the scenario are,

The distance traveled depends on the amount of time Marlene rides her bike.

The function f(t) = 16t represents the scenario.

Hence, the correct option is B and E.

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2 years ago

A house painter has $100 to buy paint. If each can of paint costs $10, how many cans of paint can the painter buy?

Tasya [4]

Answer:

The house painter can buy 10 cans of paint.