Which number line represents the solutions to |-2x| = 4?

The length of each side of an equilateral triangle is increased by 20%, resulting in triangle ABC. If the length of each side of

kompoz [17]

Answer: Area of ΔABC is 2.25x the area of ΔDEF.

Step-by-step explanation: Because equilateral triangle has 3 equal sides, area is calculated as

$A=\frac{\sqrt{3} }{4} a^{2}$

with a as side of the triangle.

Triangle ABC is 20% bigger than the original, which means its side (a₁) measures, compared to the original:

a₁ = 1.2a

Then, its area is

$A_{1}=\frac{\sqrt{3} }{4}(1.2a)^{2}$

$A_{1}=\frac{\sqrt{3} }{4}1.44a^{2}$

Triangle DEF is 20% smaller than the original, which means its side is:

a₂ = 0.8a

So, area is

$A_{2}=\frac{\sqrt{3} }{4} (0.8a)^{2}$

$A_{2}=\frac{\sqrt{3} }{4} 0.64a^{2}$

Now, comparing areas:

$\frac{A_{1}}{A_{2}}= (\frac{\sqrt{3}.1.44a^{2} }{4})(\frac{4}{\sqrt{3}.0.64a^{2} } )$

$\frac{A_{1}}{A_{2}} =$ 2.25

The area of ΔABC is 2.25x greater than the area of ΔDEF.

7 0

2 years ago

Can I have help with this, I have drawn out a graph and marked my points so far.

Sidana [21]

Answer:

D. 2x²

Step-by-step explanation:

Ok, so the first thing to do is remember the first number in parentheses is x, and the second number is y.

You're trying to figure out which expression turns x into y in each set.

Just by plugging in the numbers into each expression I found that the answer is 2x².

I'll prove this starting with (1, 2).

1² = 1

2 x 1 = 2

So, y = 2x²!

Next, (2, 8).

2² = 4

2 x 4 = 8

So, y = 2x²!

I'm not going to demonstrate with the other two but I hope you understand. Just plug the values of x and y into the equation and see which is correct.

4 0

3 years ago

Match solutions and differential equations. Note: Each equation may have more than one solution. Select all that apply. (a) 7y''

Nonamiya [84]

Answer:

a- $e^x,e^{-x}$

b- $x^{-2}$

c- $x^3$

Step-by-step explanation:

a.7 y''-7 y =0

Auxillary equation

$D^2-1=0$

$(D-1)(D+1)=0$

D=1,-1

Then , the solution of given differential equation

$y=e^x,y=e^{-x}$

2. $7x^2y''+14xy'-14 y=0$

Y= $y=x^3$

$y=3x^2$

$y''=6x$

Substitute in the given differential equation

$42x^3+42x^3-14x^3\neq 0$

Hence, $x^3$ is not a solution of given differential equation

$e^x,e^{-x}$ are also not a solution of given differential equation.

y= $x^{-2}$

$y'=-2x^{-3}$

$y''=6x^{-4}$

Substitute the values in the differential equation

$7x^2(6x^{-4})+14x(-2x^{-3})-14 x^{-2}$

= $42x^{-2}-28x^{-2}-14x^{-2}=0$

Hence, $x^{-2}$ is a solution of given differential equation.

c. $7x^2y''-42y=0$

$y=x^3$

$y'=3x^2$

$y''=6x$

Substitute the values in the differential equation

$42x^3-42x^3=0$

Hence, $x^3$ is a solution of given differential equation.

a- $e^x,e^{-x}$

b- $x^{-2}$

c- $x^3$

6 0

3 years ago

Read 2 more answers

The scatter plot shows the relationship between the test scores of a group of students and the number of hours they spend on soc

kolbaska11 [484]

First I let's represent our data in the table and make a scatter plot ( i attached the image).
$\begin{tabular}{ll} x & y \\ 0.5 & 100 \\ 2 & 100 \\ 1 & 95 \\ 3 & 85 \\ 3 & 78 \\ 5 & 75 \\ 5 & 72 \\ 6 & 70 \\ 6 & 98 \\ 7 & 60 \\ \end$
Points labeled A are called data set.
Point labelled B is called the outlier. The outlier is a point that does not fit well with the rest of our data set. Posible reason for point B is that someone is super smart and they don't need to spend a lot of time studying to achieve good results.
PartB
We can see from the graph that the number of hours spent on social media and test scores are negatively correlated. See a scatter plot, I added the trend line.
In other words, the more hours you spend on social media the lower your test scores should be.

7 0

2 years ago

Read 2 more answers

The freshman class at West High is planning an adventure park event. The park charges $300 for a group day pass with an addition

Elanso [62]

Answer:

C

Step-by-step explanation:

Key in the expression is "s" that represents students going to the trip

The first part shows what the adventure park is going to charge, a group day charge of $300 and $30 more for the students taking the ropes course

300+30*s

The second being the amount the class can get, $500 the have in the account and $25 per student in tickets they have to sell

500+25s

The result of this subtraction is the money they need to raise to complete

C: The expression shows how much money the freshman class may need to raise in order to afford the event

7 0

3 years ago