A certain mapping in the xy-plane has the following properties:
• For the point A, the image A' is at the same point as A.
• A point P that is not at A maps counterclockwise to point P' such that mZPAP = 0.
• The lengths of AP and AP are equal.

Answer/Step-by-step explanation:

Recall: SOH CAH TOA

✔️Find <A:

Reference angle (θ) = A

Opposite side = 14 cm

Hypotenuse = 20 cm

Apply SOH:

Sin θ = Opp/Hyp

Substitute

Sin A = 14/20

A = [tex] sin^{-1}(\frac{14}{20}) [/tex]

m<A = 44° (nearest whole number)

✔️Find <C:

Reference angle (θ) = C

Adjacent side = 14 cm

Hypotenuse = 20 cm

Apply CAH:

Cos θ = Adj/Hyp

Substitute

Cos C = 14/20

C = [tex] cos^{-1}(\frac{14}{20}) [/tex]

m<C = 46° (nearest whole number)

✔️Find AB:

Reference angle (θ) = C = 46°

Opposite side = AB

Hypotenuse = 20 cm

Apply SOH:

Sin θ = Opp/Hyp

Sin 46° = AB/20

20*Sin 46° = AB

AB = 14.4 cm (one decimal place)

Answer:

20

Step-by-step explanation:

a²+b²=c²

25²-15²=b²

625-225=b²

400=b²

√400=√b²

20=b

Answer:

B) 5 units

Step-by-step explanation:

The distance between these points (0, 2) and (5, 2) will be 5 units. Then the correct option is B.

It is the measure of distance between the two points and is known as length. The length is measured in meters generally.

Let one point be (x, y) and another point be (h, k).

Then the distance between the points will be

D² = (x - h)² + (y - k)²

The two pints are given below.

(0, 2) and (5, 2)

Then the distance between these points (0, 2) and (5, 2) will be given as,

D² = (5 - 0)² + (2 - 2)²

D² = 5²

D = 5 units

The distance between these points (0, 2) and (5, 2) will be 5 units. Then the correct option is B.

Learn more about the distance between two points here:

https://brainly.com/question/18296211

#SPJ2

Answer:

It is A

Step-by-step explanation:

Your welcome

Let me know if you ever need help! :)

Answer:

[tex] \sqrt{48} \times \sqrt{3} \\ \sqrt{144} \\ 12[/tex]

Answer:

the answer is the second number line

Answer:

The largest number of mini cakes Nicole can make with the butter she has is 9.

Step-by-step explanation:

Given that Nicole has 2/3 of the butter needed to make a cake, and the same amount of butter is needed to make 1 cake as it does to make 14 mini cakes, to determine what is the largest number of mini cakes Nicole can make with the butter she has, the following calculation must be performed:

2/3 = 0.666

1 = 14

0.666 = X

0.666 x 14/1 = X

9.333 = X

Therefore, the largest number of mini cakes Nicole can make with the butter she has is 9.

Answer:

(b) is true

Step-by-step explanation:

Given

Molly

[tex]a = 500[/tex] --- starting balance

[tex]m = 10[/tex] --- monthly rate

Her brother

[tex]a = 100[/tex] ---- starting balance

[tex]r = 10\%[/tex] --- annual rate

Required

Determine which option is true

First, we calculate her brother's function.

The function is an exponential function calculated as:

[tex]y = ab^x[/tex]

Where [tex]b = 1 + r[/tex]

So, we have:

[tex]y = ab^x[/tex]

[tex]y = 100 *(1 + 10\%) ^x[/tex]

[tex]y = 100 *(1 + 0.10) ^x[/tex]

[tex]y = 100 *(1.10) ^x[/tex]

Hence:

[tex]g(x) = 100 *(1.10) ^x[/tex]

Next, we calculate Molly's function (a linear function)

The monthly function is:

[tex]y = mx + a[/tex]

So, we have:

[tex]y = 10x + 500[/tex]

Annually, the function will be:

[tex]y = 10x*12 + 500[/tex]

[tex]y = 120x + 500[/tex]

So, we have:

[tex]f(x) = 120x + 500[/tex]

At this point, we have:

[tex]f(x) = 120x + 500[/tex] ---- Molly

[tex]g(x) = 100 *(1.10) ^x[/tex] ---- Her brother

Next, we test each option

(a): Molly's account will have a faster rate of change over [32,40]

We calculated Molly's function to be:

[tex]y = 120x + 500[/tex]

The slope of a linear function with the form: [tex]y = mx + b[/tex] is m

By comparison:

[tex]m = 120[/tex]

Since Molly's account is a linear function, the rate of change over any interval will always be the same; i.e.

[tex]m = 120[/tex]

For his brother:

Rate of change is calculated using:

[tex]m = \frac{g(b) - g(a)}{b - a}[/tex]

[tex]m = \frac{g(40) - g(32)}{40 - 32}[/tex]

[tex]m = \frac{g(40) - g(32)}{8}[/tex]

Calculate g(40) and g(32)

[tex]g(x) = 100 *(1.10) ^x[/tex]

[tex]g(40) = 100 * 1.10^{40} =4526[/tex]

[tex]g(32) = 100 * 1.10^{32} = 2111[/tex]

So, we have:

[tex]m = \frac{4526 - 2111}{8}[/tex]

[tex]m = \frac{2415}{8}[/tex]

[tex]m = 302[/tex]

By comparison: [tex]302 > 120[/tex]

Hence, her brother's account has a faster rate over [32,40]

(a) is false

(b): Molly's account will have a slower rate of change over [24,30]

[tex]m = 120[/tex] --- Molly's rate of change

For his brother:

[tex]m = \frac{g(b) - g(a)}{b - a}[/tex]

[tex]m = \frac{g(30) - g(24)}{30 - 24}[/tex]

[tex]m = \frac{g(30) - g(24)}{6}[/tex]

Calculate g(30) and g(24)

[tex]g(x) = 100 *(1.10) ^x[/tex]

[tex]g(40) = 100 * 1.10^{30} =1745[/tex]

[tex]g(32) = 100 * 1.10^{24} = 985[/tex]

So, we have:

[tex]m = \frac{g(30) - g(24)}{6}[/tex]

[tex]m = \frac{1745 - 985}{6}[/tex]

[tex]m = \frac{760}{6}[/tex]

[tex]m = 127[/tex]

By comparison: [tex]127 > 120[/tex]

Hence, Molly's account has a slower rate over [24,30]

(b) is false

(c): Molly's account will have a slower rate of change over [0,4]

[tex]m = 120[/tex] --- Molly's rate of change

For his brother:

[tex]m = \frac{g(b) - g(a)}{b - a}[/tex]

[tex]m = \frac{g(4) - g(0)}{4 - 0}[/tex]

[tex]m = \frac{g(4) - g(0)}{4}[/tex]

Calculate g(4) and g(0)

[tex]g(x) = 100 *(1.10) ^x[/tex]

[tex]g(4) = 100 * 1.10^4 =146[/tex]

[tex]g(0) = 100 * 1.10^{0} = 100[/tex]

So, we have:

[tex]m = \frac{g(4) - g(0)}{4}[/tex]

[tex]m = \frac{146 - 100}{4}[/tex]

[tex]m = \frac{46}{4}[/tex]

[tex]m = 11.5[/tex]

By comparison: [tex]120>11.5[/tex]

Hence, Molly's account has a faster rate over [0,4]

(c) is false

The area of the sector that is not shaded is 120π units²

Option C is the correct answer

A circle is a two-dimensional figure with a radius and circumference of 2pir.

The area of a circle is pir^2.

We have,

The circle has 360°.

This can be written as,

Area = πr² x 360/360

Now,

The area of the not-shaded part has (360 - 60)°

So,

Area = πr² x 300/360

Now,

r = 12 units

Area = π x 12 x 12 x 300/360

Area = 120π units²

Thus,

The area of the sector that is not shaded is 120π units²

Learn more about circle here:

https://brainly.com/question/11833983

#SPJ7

Answer:

[tex]x = 3 + i\ or\ x = 3 - i[/tex]

Step-by-step explanation:

Given

[tex]x = \frac{-(-6) \± \sqrt{(-6)^2 - 4(1)(10)}}{2*1}[/tex]

Required

Solve, in terms of i

We have:

[tex]x = \frac{-(-6) \± \sqrt{(-6)^2 - 4(1)(10)}}{2*1}[/tex]

Solve the expressions in bracket

[tex]x = \frac{-(-6) \± \sqrt{36 - 40}}{2*1}[/tex]

[tex]x = \frac{-(-6) \± \sqrt{-4}}{2}[/tex]

Express -4 as 4 * -1

[tex]x = \frac{-(-6) \± \sqrt{-4*1}}{2}[/tex]

Split

[tex]x = \frac{-(-6) \± \sqrt{4}*\sqrt{-1}}{2}[/tex]

In complex numbers;

[tex]i = \sqrt{-1[/tex]

So, we have:

[tex]x = \frac{-(-6) \± 2*i}{2}[/tex]

[tex]x = \frac{6 \± 2i}{2}[/tex]

Factorize

[tex]x = \frac{2(3 \± i)}{2}[/tex]

[tex]x = 3 \± i[/tex]

Split

[tex]x = 3 + i\ or\ x = 3 - i[/tex]

Answer:

the answer is A

Step-by-step explanation:

its because -4 is the coldest and 3 is the warmest out of the rest

It is formed by two non collinear rays with the same point.

I think your answer is:

Angle

Answer:

$13.4

Step-by-step explanation:

Given that :

Tip percentage = 20%

Amount of bill = $67.13

Rounding the bill Amount to then nearest dollar :

$67.13 = $67

Tip amount = 20% of $67

Tip amount = 0.2 * $67

Tip amount = $13.4

Answer:

The table does not represent a function.

Step-by-step explanation:

Every function must have a exactly one y-value for every x-value. Two different x-values can have the same y-value, but two different y-values cannot have the same x-value.

In the table, we see that the same x-value has two different y-values:

[tex](15, \textbf{10}),\\(15, \textbf{10.5})[/tex]

Thus, the table does not represent a function.

Answer:

option a) 30 : 19

Step-by-step explanation:

[tex]Length = 7 \frac{1}{2} = \frac{15}{2}\\\\Width = 4\frac{3}{4} = \frac{19}{4}[/tex]

Ratio of length to width:

      [tex]\frac{15}{2} : \frac{19}{4}[/tex]

    [tex]=\frac{\frac{15}{2}}{\frac{19}{4}}\\\\=\frac{15}{2 } \times \frac{4}{19}\\\\=15\times \frac{2}{19}\\\\=\frac{30}{19}\\\\30 : 19[/tex]

Answer:

2(x+3)

Hope u get it correct!!!

Step-by-step explanation:

Answer:

(5/1)(4-0)-(-5)(-4-3)

Step-by-step explanation:

You could also get an undefined number by putting any number divided by 0.

Answer:

0 comes before any fractions

Step-by-step explanation:

All fractions are greater than 0, because remember, fractions are a part of a  number and are always greater than 0.

Answer:

Number of additional inches= x

Number of additional topping= y

Total cost= 8+1.5(x)+0.75(y)

-----------------------

hope it helps...

have a great day!!

Answer:

c. 2.5

Step-by-step explanation:

4×2.5 => 10

6×2.5 => 15

so scale factor = 2.5

The answer would be $53

Answer:

m = -4

Step-by-step explanation:

The given y= -4x + 5 exactly matches the format of the slope-intercept equation   y = mx + b.

Thus, the gradient (slope) of the given line is -4.

Answer:

3966

Step-by-step explanation:

Use order of operations to solve this problem:

In your case, there are no parentheses or exponents, so we can skip right the the multiply and divide step. The first multiplication is 98*63=6174. The next step is to do 32*69=2208. Then you minus 6174-2208=3966.

Hope this helps!

Answer:

Step-by-step explanation:

m3= 29%

m6= 35%

m7= 90%

Answer:

Area=12.56

Circumference= 12.56

Step-by-step explanation:

Area formula is [tex]\pi r^{2}[/tex]

Circumference is [tex]2\pi r[/tex]

Answer:

radius=diameter/2

=4/2=2

circumference of a circle= 2πr

=2*3.14*2

=12.56ft

area of a circle=πr2

=3.14*2*2

=12.56ft

Answer:

Step-by-step explanation:

Five rational number from 68 to 72

69, 70 , 71, 71.1 , 71.2

Answer:

The equation is unsolvable when the 'a' variable is in it, so if we take it out, then all of them would make the equation open up.

Sorry for not giving a definite answer, but that is what I got.

Hope that this helps!