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3 years ago

You invest $5,000 in a savings account that earns 6% interest each year.

1 answer:

4 0

A. Multiply $5000 by .06, and add it back to $5000 to get the total after one year. This is $5300.
B. Multiply the new amount, or $5300 by .06, and add it back to $5300 to get the total after 2 years. This is $5618.

A. $5300
B. $5618

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Quadrilateral ABCD is transformed to create A'B'C'D'. Match the coordinates of A' with the transformations that create it

SashulF [63]

The three basic types of rigid transformations are rotation, reflection and translation transformation

The correct options are;

Quadrilateral ABCD is reflected over the x-axis → (2, 4)

Quadrilateral ABCD translated 2 units right and 1 unit down → (4, -5)

Quadrilateral ABCD dilated about the origin by a scale factor of 3 → (6, -12)

Quadrilateral ABCD rotated 180° clockwise about the origin → (-2, 4)

The reasons the above matches are correct are as follows:

The given coordinates of the preimage are A(2, -4)

The image of (x, y) following a reflection over the x-axis is (x, -y)

Therefore

A(2, -4) in Quadrilateral ABCD is reflected over the x-axis → A'(2, 4)

The image of (x, y) following a translation of 2 units right and 1 unit down → (x + 2, y - 1)

Therefore;

A(2, -4) in Quadrilateral ABCD translated 2 units right and 1 unit down → A'(4, -5)

The image of (x, y) following a dilation about the origin by a scale factor of 3 is (3×x, 3×y)

Therefore;

A(2, -4) in Quadrilateral ABCD dilated about the origin by a scale factor of 3 → A'(6, -12)

The image of the point (x, y) rotated 180° clockwise about the origin is (-x, -y)

Therefore;

A(2, -4) in Quadrilateral ABCD rotated 180° clockwise about the origin → A'(-2, 4)

Learn more about rigid transformations here:

brainly.com/question/11018647

3 0

3 years ago

What are the missing numbers?<br> 1, -7, -15_, _, 39

CaHeK987 [17]

Answer:

23 and4o

Step-by-step explanation:

8 0

3 years ago

Huw do I combine like terms

dybincka [34]

I'll give you an example

y= 2x+56a-16a+14x

y=16x+40a

you basically just do the letters that are the same together i hope it make sense to you

8 0

3 years ago

Given the equation y = mx + b, which variable represents the slope of the line?

Savatey [412]

Answer:

Variable "m"

Step-by-step explanation:

Hello!

The equation $y = mx +b$ is perhaps the most used equation when representing a line. The parts of the equation:

y = output, y-value, ordinate...
m = slope, rate of growth, rise over run...
x = input, x-value, abscissa...
b = y-intercept

____________________________________________

Let's use an example: y = 2x + 5

We want to find the y-value when x is 2.

To solve, simply plug in 2 for x:

y = 2(2) + 5
y = 4 + 5
y = 9

So, the coordinate when x is 2 is (2,9), remember that coordinates are written in (x,y) format.

Image: y = 2x + 5

7 0

2 years ago

How do you solve tan(sin^-1 x/2)? (show steps)

andrew11 [14]

First: Equations are solved. $\tan\left(\sin^{-1}\dfrac x2\right)$ is an expression, and expressions can be simplified.

Now suppose $y=\sin^{-1}\dfrac x2$ . Imagine a right triangle with one angle (not the one opposite the hypotenuse, of course) labeled $y$ . This relation suggests that

$\sin y=\dfrac x2$

and under the hood, we're assuming that $-\dfrac\pi2$ , because otherwise we wouldn't be able to properly alternate from $x$ to $y$ so seamlessly.

Now,

$\tan\left(\sin^{-1}\dfrac x2\right)=\tan y$

so the given expression is the same as the tangent of that same angle $y$ .

If $\sin y=\dfrac x2$ , then in the triangle, the leg opposite the angle $y$ occurs with the length of the hypotenuse in a ratio of $x$ to 2. By the Pythagorean theorem, the remaining side - call it $z$ - satisifies

$z^2+x^2=2^2\implies z=\sqrt{4-x^2}$

and we have

$\tan y=\dfrac xz=\dfrac x{\sqrt{4-x^2}}$

4 0

3 years ago