Show the steps please.

What is the image of point (0,3) for mapping (x,y) (x-2,y-3)

Ann [662]

When it asks for the image, that means what are your new coordinates after doing the rules they give you. In this, the rule is to subtract 2 from your x value and subtract 3 from the y value. So you subtract 2 from 0 and subtract 3 from 3. This will give you the values to use for the x and y of your answer:)

5 0

3 years ago

What is the lowest common multiple of 120 160 180

Anna11 [10]

20 it the least common multiple of the numbers given

4 0

4 years ago

Jose asks his friends to guess the higher of two grades he received on his math tests. He gives them two hints. The difference o

denis23 [38]

Option D. 96 is the correct answer.

Explanation:

Let the higher grade be = x

Let the lower grade be = y

As given, The difference of the two grades is 16

$x-y=16$ or $x=16+y$ .... (1)

The sum of one-eighth of the higher grade and one-half of the lower grade is 52.

$\frac{1x}{8}+\frac{1y}{2}=52$ ... (2)

Putting the value of x=16+y in equation (2)

$\frac{16+y}{8}+\frac{y}{2}=52$

$\frac{16+y+4y}{8}=52$

$\frac{16+5y}{8}=52$

$16+5y=416$

$5y=400$

$y=80$

As x=16+y

x=16+80 = 96

Hence, higher grade is 96.

8 0

3 years ago

The diagram shows a regular octagon ABCDEFGH. Each side of the octagon has length 10cm. Find the area of the shaded region ACDEH

Zolol [24]

The area of the shaded region /ACDEH/ is 325.64cm²

Step 1 - Collect all the facts

First, let's examine all that we know.

We know that the octagon is regular which means all sides are equal.
since all sides are equal, then all sides are equal 10cm.
if all sides are equal then all angles within it are equal.
since the total angle in an octagon is 1080°, the sum of each angle within the octagon is 135°.

Please note that the shaded region comprises a rectangle /ADEH/ and a scalene triangle /ACD/.

So to get the area of the entire region, we have to solve for the area of the Scalene Triangle /ACD/ and add that to the area of the rectangle /ADEH/

Step 2 - Solving for /ACD/

The formula for the area of a Scalene Triangle is given as:

A = $\sqrt{S(S-a)(S-b)(S-c) square units}$

This formula assumes that we have all the sides. But we don't yet.

However, we know the side /CD/ is 10cm. Recall that side /CD/ is one of the sides of the octagon ABCDEFGH.

This is not enough. To get sides /AC/ and /AD/ of Δ ACD, we have to turn to another triangle - Triangle ABC. Fortunately, ΔABC is an Isosceles triangle.

Step 3 - Solving for side AC.

Since all the angles in the octagon are equal, ∠ABC = 135°.

Recall that the total angle in a triangle is 180°. Since Δ ABC is an Isosceles triangle, sides /AB/ and /BC/ are equal.

Recall that the Base angles of an isosceles triangle is always equal. That is ∠BCA and ∠BAC are equal. To get that we say:

180° - 135° = 45° [This is the sum total of ∠BCA and ∠BAC. Each angle therefore equals

45°/2 = 22.5°

Now that we know all the angles of Δ ABC and two sides /AB/ and /BC/, let's try to solve for /AC/ which is one of the sides of Δ ACD.

According to the Sine rule,

$\frac{Sin 135}{/AC/}$ = $\frac{Sin 22.5}{/AB/}$ = $\frac{Sin 22.5}{/BC/}$

Since we know side /BC/, let's go with the first two parts of the equation.

That gives us $\frac{0.7071}{/AC/} = \frac{0.3827}{10}$

Cross multiplying the above, we get

/AC/ = $\frac{7.0711}{0.3827}$

Side /AC/ = 18.48cm.

Returning to our Scalene Triangle, we now have /AC/ and /CD/.

To get /AD/ we can also use the Sine rule since we can now derive the angles in Δ ABC.

From the Octagon the total angle inside /HAB/ is 135°. We know that ∠HAB comprises ∠CAB which is 22.5°, ∠HAD which is 90°. Therefore, ∠DAC = 135° - (22.5+90)

∠DAC = 22.5°

Using the same deductive principle, we can obtain all the other angles within Δ ACD, with ∠CDA = 45° and ∠112.5°.

Now that we have two sides of ΔACD and all its angles, let's solve for side /AD/ using the Sine rule.

$\frac{Sin 112.5}{/AD/}$ = $\frac{Sin 45}{18.48}$