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3 years ago

a square painted measures 2 meters on each side. what is the area of the painting in square centimeters

1 answer:

6 0

Area of a square = side * side

If each side of a square measures, 2 metres, then

area = 2m * 2m
= 200 cm * 200 cm
= 40,000 cm^2

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Write the slope-intercept form of the equation of the line that is parallel to AB and passes through Point X. Show all

DanielleElmas [232]

find y=mx+b for line parallel to AB.

The line that is parallel will have the same slope as line AB:

the slope of line AB is

m=(8-3)/(-10-2)

=5/-12

=-5/12

Since the line going through X is parallel the vertical distance of the new line to AB is the same for all values of the domain(x-axis).

at x=-5 the point X has the y value of 10 which is 4 more than the y value for AB based on the graph.

To find the intercept b of the line going through X that is parallel to AB we just add 4 to the intercept of AB, which is 4 so

4+4=8

7 0

2 years ago

If α and β are the zeros of the quadratic polynomial f(x) = 3x2–4x + 5, find a polynomialwhose zeros are 2α + 3β and 3α + 2β.

Lelechka [254]

Answer:

$\boxed{\sf \ \ \ 3x^2-20x+37\ \ \ }$

Step-by-step explanation:

Hello,

a and b are the zeros, we can say that

$f(x)=3(x^2-\dfrac{4}{3}x+\dfrac{5}{3}) = 3(x-a)(x-b)=3(x-(a+b)x+ab)$

So we can say that

$a+b=\dfrac{4}{3}\\ab=\dfrac{5}{3}$

Now, we are looking for a polynomial where zeros are 2a+3b and 3a+2b

for instance we can write

$(x-2a-3b)(x-3a-2b)=x^2-(2a+3b+3a+2b)x+(2a+3b)(3a+2b)\\= x^2-5(a+b)x+6a^2+6b^2+9ab+4ab$

and we can notice that

$a^2+b^2=(a+b)^2-2ab$ so

$(x-2a-3b)(x-3a-2b)=x^2-5(a+b)x+6[(a+b)2-2ab]+13ab\\= x^2-5(a+b)x+6(a+b)^2+ab$

it comes

$x^2-5*\dfrac{4}{3}x+6(\dfrac{4}{3})^2+\dfrac{5}{3}$

multiply by 3

$3x^2-20x+2*16+5=3x^2-20x+37$

4 0

3 years ago

Liana started to evaluate the function f(x) = 2x^2 – 3x + 7 for the input value 2.

Igoryamba

I hope this helps you

6 0

3 years ago

Read 2 more answers

4x and 16y are like terms. O A. True O B. False

Gekata [30.6K]

B. False

X and Y are two different variables.

7 0

3 years ago

Read 2 more answers

In the form of a paragraph, explain in complete sentences, your answers to the following questions. Include the final answer in

Yanka [14]

Lisa is an avid runner and is training for a marathon, so she runs everyday to achieve this purpose. In this way, she goes out to run for six days, so we have the following data set regarding the miles she runs:

1st day = 3.2 miles
2nd day = 7.5 miles
3rd day = 9.8 miles
4th day = 11.5 miles
5th day = 2.9 miles
6th day = 3.5 miles

Finally, she ran a total of:

3.2+7.5+9.8+11.5+2.9+3.5 = 38.4 miles

What was the average distance of each run?

This result can be get as the sum of each run (or the total of miles she run) divided by the numbers of days she ran.

 $A=\frac{38.4}{6}=6.4mi$

Lisa's goal for this week is to run an average of 6 miles per day. How many miles does she need to run tomorrow (the 7th day) in order to achieve her goal of 6 miles per day for the week?

Let's name x the distance she must run tomorrow. Therefore, the equation for this purpose is given as follows:

 $\frac{3.2+7.5+9.8+11.5+2.9+3.5+x}{7}=6$

∴ $\frac{38.4+x}{7}=6$

Isolating x:

$38.4+x=42$

∴ $x=42-38.4=3.6$

Therefore, she need to run:

$\boxed{3.6mi}$ in order to achieve the goal of 6 miles per day.

4 0

3 years ago