can someone help asap!!​

Answers:

16. sin(A) = a/12

17. tan(A) = a/9

18. sin(B) = 3/4    (reduced from 9/12)

19. cos(B) = a/12

===================================================

Explanation:

The sine of an angle is equal to the ratio of the opposite side over the hypotenuse. For reference angle A, the opposite side is BC = a. The hypotenuse is always the longest side. The hypotenuse is AB = 12.

sin(angle) = opposite/hypotenuse

sin(A) = BC/AB

sin(A) = a/12

Similarly,

sin(B) = opposite/hypotenuse = AC/AB = 9/12 = 3/4.

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

Tangent is the ratio of opposite over adjacent

tan(angle) = opposite/adjacent

tan(A) = BC/AC

tan(A) = a/9

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

Cosine is the ratio of adjacent over hypotenuse

cos(angle) = adjacent/hypotenuse

cos(B) = BC/AB

cos(B) = a/12

we see that this is the same result as sin(A). It turns out that sin(A) = cos(B) if and only if A+B = 90. In other words, the sin(A) = cos(B) when A and B are the acute angles of a right triangle.

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

Side note: you could use the Pythagorean theorem to solve for the value of 'a'. All of this assumes that triangle ACB is a right triangle.

Answer:

7

Step-by-step explanation:

It is easier to find the area of green triangle as the difference of the area of the square and adjacent triangles, see attached picture for reference.

Area of the square:

Area of adjacent blue triangles:

Area of green triangle:

Answer:

[tex](C) \dfrac{x+3}{x}[/tex]

Step-by-step explanation:

We want to determine an  equivalent expression to:

[tex]\dfrac{x}{x-3} \div \dfrac{x^2}{x^2-9}[/tex]

Step 1: Factorise [tex]x^2-9[/tex] using the difference of two squares.

[tex]x^2-9=x^2-3^2=(x-3)(x+3)[/tex]

Step 2: Change the division sign to multiplication

[tex]\dfrac{x}{x-3} \times \dfrac{(x-3)(x+3)}{x^2}[/tex]

Step 3: Cancel out common terms and simplify

[tex]= \dfrac{x+3}{x}[/tex]

The correct option is C.

The expression equivalent to given expression is [tex]\frac{x+3}{3}[/tex]

Given expression is,

                        [tex]\frac{x}{x-3}\div\frac{x^{2} }{x^{2} -9}[/tex]

Use factorization,   [tex]x^{2} -9=(x-3)(x+3)[/tex]

Now simplify the given expression.

                       [tex]\frac{x}{x-3}\div\frac{x^{2} }{x^{2} -9}\\\\=\frac{x}{x-3}*\frac{(x-3)(x+3)}{x^{2} } \\\\=\frac{x+3}{x}[/tex]

Hence, the expression equivalent to given expression is [tex]\frac{x+3}{3}[/tex]

Learn more:

https://brainly.com/question/1280754

Answer:

[tex]1 \times 10^{10}[/tex] more pieces of mail were handled in 1995 than in 2010.

Step-by-step explanation:

We are given that in 1995, the USPS approximated that they handled  [tex]1.8 \times 10^{11}[/tex] pieces of mail and in 2010, the USPS reported that they handled [tex]1.7 \times 10^{11}[/tex]  pieces.

To find how many more pieces of mail were handled in 1995 than in 2010, we do subtraction of the pieces of mail that were handled in both the years.

Pieces of mail handled in 1995 = [tex]1.8 \times 10^{11}[/tex]

Pieces of mail handled in 2010 = [tex]1.7 \times 10^{11}[/tex]  

As it is clear that more pieces of mail were handled in 1995.

So, Pieces of mail handled in 1995 - Pieces of mail handled in 2010 = [tex](1.8 \times 10^{11}) -(1.7 \times 10^{11})[/tex]

=  [tex]10^{11} \times (1.8 -1.7)[/tex]

=  [tex]10^{11} \times 0.1[/tex] = [tex]1 \times 10^{10}[/tex]

Hence, [tex]1 \times 10^{10}[/tex] more pieces of mail were handled in 1995 than in 2010.

Answer:

D.

Step-by-step explanation:

ΔABC ≅ ΔEFD

This is because:

∠A ≅ ∠E (30°)

∠B ≅ ∠F (100°)

∠C ≅ ∠D (50°)

Answer:

h=5/2

Step-by-step explanation:

200h=180h+50

20h=50

Answer:

1) 38

2) 160

3) 40

Step-by-step explanation:

Answer:

23, 42, 12

Step-by-step explanation:

Answer:

436

Step-by-step explanation:

[tex]45-29\times 16 + 875-20= \\\\45-464+875-20= \\\\-419+855=\\\\436[/tex]

Hope this helps!

Answer:

480 in.^3

Step-by-step explanation:

volume of pyramid = (1/3) * (area of base) * height

Since this pyramid has a square for the base, the area of the base is

A = s^2, where s = length of the side of the square

volume = (1/3) * s^2 * h

volume = (1/3)(12 in.)^2 * (10 in.)

volume = (1/3)(144)(10) in.^3

volume = 480 in.^3

The volume of the square-based pyramid is 480 cubic inches as per the concept of the pyramid.

To find the volume of a square-based pyramid, we can use the formula:

Volume = (1/3) x base area x height.

In this case, the base of the pyramid is a square with a side length of 12 inches, and the height of the pyramid is 10 inches.

First, we calculate the base area of the pyramid, which is the area of the square base:

Base area = side length x side length

                = 12 in x 12 in

                = 144 square inches.

Now, we can substitute the values into the volume formula:

[tex]Volume = \frac{1}{3} \times 144 \times 10[/tex].

Multiplying these values, we get:

[tex]Volume = \frac{1}{3} \times1440 {in}^3[/tex]

Simplifying the expression, we have:

[tex]Volume = 480\ in^3[/tex].

To learn more about the pyramid;

https://brainly.com/question/17615619

#SPJ2

Answer:

m<EAD=29°

m<CAB=119°

Solution,

< CAE+<EAD+90°=180°( angles on a straight line)

61+<EAD+90°=180°

<EAD=180-(90+61)

=180-151

=29°

<CAB+<FAB=180°( Linear pair)

<CAB+61°=180°

<CAB=180°-61°

<CAB=119°

hope this helps ..

Good luck on your assignment..

Answer:

  C, D

Step-by-step explanation:

Any rigid transformation (rotation, translation, reflection) will result in a congruent polygon. To make a similar (smaller) polygon, a dilation by a factor less than 1 must be used.

C. a dilation about the origin by a scale factor of 2/3 followed by a rotation of 90° counterclockwise about the origin and a translation 5 units left

D. a dilation about the origin by a scale factor of 5/7 followed by a reflection over the y–axis and a dilation about the origin by a scale factor of 3/4

Answer:

c and something is not d

Step-by-step explanation:

Answer:

Step-by-step explanation:

The formula for simple interest is prt = I, where p is the initial investment (our unknown in this case), r is the interest rate in decimal form, t is the time in years, and I is the interest earned. That is NOT the same as the amount of money in the account t years later.

For us,

p = ??,

r = .05,

t = 18, and

I = 225.

Filling in:

p(.05)(18) = 225 and

.9p = 225 so

p = 250

Answer:

The answer is $250.

Step-by-step explanation:

First, the money that his grandmother deposited is called the principal, P. Substitute the given values into the formula, interest equals principal times rate times time, and solve for P. Here, I is 225 dollars and t is 18 years.

Next, the percent given represents the interest rate, r, but first it must be changed to a decimal. To change it, move the decimal point 2 places to the left.

Now, multiply point 0, 5, and 18 to simplify the right side of the equation. The product is point nine.

Finally, divide both sides of the equation by .9 . The result is P equals $225 The principal, or original deposit, is $250.

Answer:

Read below.

Step-by-step explanation:

There is an infinite amount of numbers larger than 0.68 but here are some for you:

1, 2, 3.4, 4.1289, 190, 2198, 0.7, 0.72578

Answer:

Please see the attached picture...

Hope it helps...

Good luck on your assignment....

Answer:

D.

Step-by-step explanation:

The graph increases when y hits its lowest point and then starts to go back up again. In this case, when x = 10, it starts to go back up again.

Answer:

D. (10, ∞).

Step-by-step explanation:

Got Correct on MyPath.

Answer:

f(-7)=224

Step-by-step explanation:

[tex]f(x) = 4x^2 -4x\\f(-7)= 4(-7)^2 - 4(-7)\\= 4(49) -+28\\=196+28\\f(-7) = 224[/tex]

Answer:

The number Alexis thinks of first is 6.7.

Step-by-step explanation:

Let the number Alexis thinks of be x and the first answer he got be y.

Since he multiplies the number by x and divides the answer by 100, the equation is

10x = y

10x = [tex]\frac{y}{100}[/tex]

Then, he multiplies this answer, [tex]\frac{y}{100}[/tex], by 1000 and gets a final answer of 67. The equation is

[tex]\frac{y}{100}[/tex] × 1000 = 67

To find y, you divide 1000y by 100 which gives 10y.

i.e. [tex]\frac{1000y}{1000} = 67[/tex]

10y = 67

Divide both sides of the equation by the coefficient of y (which is 10)

[tex]\frac{10y}{10} = \frac{67}{10}[/tex]

y = 6.7

Substituting 6.7 for y in 10x = y

10x = 6.7

Divide both sides of the equation by the coefficient of x (which is 10)

[tex]\frac{10x}{10} = \frac{6.7}{10}[/tex]

x = 0.67

∴ The number Alexis thinks of first is 0.67.

Hope this helps!!! :))

Answer:

0.67

Step-by-step explanation:

Solution 1

We can work out the initial number by going backwards from the end:

67/1000= 0.067

0.067*100= 6.7

6.7/10= 0.67

Solution 2

(x*10/100)*1000= 67

x/10*1000= 67

100x= 67

x=67/100

x=0.67

Answer:

Slope-intercept form is y = mx + b where m and b are the slope and y-intercept respectively. Since we know the values of m and b (-1 and 7) the answer is y = -x + 7.

Answer:

y=-x+7

Step-by-step explanation:

y=-x+7

Answer:

C. y < -1/5x + 1

Step-by-step explanation:

We can eliminate A and B because the inequality sign is incorrect. If we were to graph those, the shaded area would be above the line, not below. We are left with C and D. Notice in our given graph that the line is dotted, so solution on the line are not included. So our answer would be C. because the inequality sign is y is less than and not y is less than or equal to.

Answer:

3, 12, 27 and 300

Step-by-step explanation:

Plug n as 1, 2, 3 and 10.

3(1)² = 3

3(2)² = 12

3(3)² = 27

3(10)² = 300

Answer/Step-by-step Explanation:

==>Given:

Ratio of cost of 1m polyester fabric to 1m of cotton fabric = 2:7

I.e. if 1m of polyester fabric = £2, then 1m of cotton fabric = £7.

==>Required:

a. Cost of polyester fabric for the following lengths:

i) 6m ii) 8m iii) 9m

Thus, having known that cost of 1m polyester fabric = £2, therefore,

i) 6m polyester fabric = 6×2 = £12

ii) 8m polyester fabric = 8×2 = £16

iii) 9m polyester fabric = 9×2 = £18

b. Cost 8 cotton fabric for the following lengths:

i) 2m ii) 6m iii) 8m iv) 9m

Thus, since 1m of cotton fabric = £7, therefore,

i) 2m cotton fabric = 2×7 = £14

ii) 6m cotton fabric = 6×7 = £42

iii) 8m cotton fabric = 8×7 = £56

iv) 9m cotton fabric = 9×7 = £63

Answer:

Graph (B)

Step-by-step explanation:

Given inequality is,

x + 2y ≤ 47

This inequality has a sign of less than equal to ( ≤ ).

Properties of this inequality when graphed will be,

1). Sign of equal to in the given inequality shows that the graph of the line will be a solid line.

2). Sign of less than represents the shaded region below the line.

Therefore, Graph (B) will be the answer.

Answer:

x = 2

Step-by-step explanation:

We are given the equation 3 - 4x - 2 = 2x - 11;

[tex]3 - 4x - 2 = 2x - 11,\\3 - 2 = 6x - 11,\\1 = 6x - 11,\\12 = 6x,\\\\x = 2\\Conclusion, x = 2[/tex]

If you want this explanation in a " statement reasoning " format refer to the attachment below;

Answer:

see explanation

Step-by-step explanation:

∠ 1 and ∠ 2 are adjacent angles and supplementary, thus

∠ 2 = 180° - ∠ 1 = 180° - 110° = 70°

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

The chord- chord angle 3 is half the sum of the measures of the arcs intercepted by the angle and its vertical angle, thus

∠ 3 = [tex]\frac{1}{2}[/tex] (100 + 60)° = 0.5 × 160° = 80°

∠ 3 and ∠ 4 are adjacent angles and supplementary, thus

∠ 4 = 180° - 80° = 100°

Thus

Angle    Value

   1           110

   2            70

   3             80

   4            100

Answer:

3.98 cm

Step-by-step explanation:

V= πr²h

V= 200 cm³, r= 4 cm, h=?

h= V/(πr²)= 200/(3.14*4²)= 3.98 cm

Hey there! :)

Answer:

x = -24.

Step-by-step explanation:

Plug in the values to find the value of 'k':

-3 = k(6)

Divide both sides by 6 to solve for 'k':

-3/6 = k

k = -1/2

Plug this into the equation to solve for the value of x when y= 12:

12 = -1/2(x)

Divide both sides by -1/2:

-24 = x

x = -24.

Answer:

x would be -24

Step-by-step explanation:

since k is a constant, we have to find out what k is from the equation

. -3=6(k) divide both sides by 6 to get that k is -0.5/-1/2.

then, solve for what x is when y is 12 by setting up the equation 12=(-0.5)x. this would result in x being -24

Answer:

$2466.55

Step-by-step explanation:

We use the formula for Compound Amount, the amount gotten after a particular time, to find the balance:

[tex]A = P(1 + r)^t[/tex]

where P = Principal = $700

r = rate = 6.5% = 0.065

t = time elapsed 20 years

Therefore:

[tex]A = 700(1 + 0.065)^{20}\\\\A = 700(1.065)^{20}\\[/tex]

A = $2466.55

The balance of the account will be $2466.55

Answer: divide both numbers

Step-by-step explanation:

20.95

Answer:

C) [tex]n^3+4n^2+8n-16[/tex]

Step-by-step explanation:

[tex]2n^3+4n^2-7+(-n^3)+8n-9=\\n^3+4n^2-7+8n-9=\\n^3+4n^2+8n-9-7=\\n^3+4n^2+8n-16[/tex]

(Just combine like terms)

Only C) [tex]n^3+4n^2+8n-16[/tex] fits our answer.

Answer:

[tex] {n}^{3} + 4 {n}^{2} + 8n - 16[/tex]

Option C is the right option

Solution,

[tex]2 {n}^{3} + 4 {n}^{2} - 7 + ( - {n}^{3} + 8n - 9) \\ = 2 {n}^{3} + 4 {n}^{2} - 7 - {n}^{3} + 8n - 9 \\ [/tex]

combine like terms

[tex]2 {n}^{3} - {n}^{3} + 4 {n}^{2} + 8n - 7 - 9 \\simplify \\ = {n}^{3} + 4 {n}^{2} + 8n - 16[/tex]

hope this helps...

Good luck on your assignment..

Answer:

12.1 =x

Step-by-step explanation:

Since this is a right triangle, we can use  trig functions

cos theta = adj/ hyp

cos 30 = x/14

14 cos 30 = x

12.12435565 =x

12.1 =x