If the sin of angle x is four fifths and the triangle was dilated to be two times as big as the original, what would be the value of the sin of x for the dilated triangle? Clue: Use the slash symbol ( / ) to represent the fraction bar, and enter the fraction with no spaces.

[tex]\dfrac{x}{4}=\dfrac{x+9}{4+12}\\\\16x=4(x+9)\\16x=4x+36\\12x=36\\x=3[/tex]

Answer:

C=252

Step-by-step explanation:

Given:

x^5y^5

(x+y)^10

Find the coefficient of x^5y^5

To get the coefficient of x^5y^5,

we will put r = 5, in the below given general term.

The general term is : nCr =x^ry^n-r

We get:

Coefficient is = 10C5

= 10!/5!*5!

= 252

The coefficient of x^5y^5 is 252

C. 252

Answer:

4*10^6

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]\frac{8\times 10^2^4}{2\times 10^1^8}=\\\\\mathrm{Divide\:the\:numbers:}\:\frac{8}{2}=4\\\\=\frac{10^{24}\times \:4}{10^{18}}\\\\\mathrm{Apply\:exponent\:rule}:\quad \frac{x^a}{x^b}=x^{a-b}\\\\\frac{10^{24}}{10^{18}}=10^{24-18}\\\\=4\times \:10^{24-18}\\\\\mathrm{Subtract\:the\:numbers:}\:24-18=6\\\\=10^6\times \:4\\\\10^6=1000000\\\\=1000000\times \:4\\\\=4000000\\\\= 4\times10^6[/tex]

Since ∠COA and ∠BOD are vertical angles, they are congruent.

You are also given that ∠ACO ≅ ∠DBO and BO ≅ CO.

By ASA (Angle-Side-Angle) congruency, you know that △ACO ≅ △DBO

The proof is shown below:

If the three angles and the three sides of a triangle are equal to the corresponding angles and the corresponding sides of another triangle, then both the triangles are said to be congruent.

In Δ PQR and ΔXYZ, as shown below, we can identify that PQ = XY, PR = XZ, and QR = YZ and ∠P = ∠X, ∠Q = ∠Y and ∠R = ∠Z. Then we can say that Δ PQR ≅ ΔXYZ.

ASA criterion stands for Angle-Side-Angle criterion. Under the ASA criterion, two triangles are congruent if any two angles and the side included between them of one triangle are equal to the corresponding angles and the included side of the other triangle.

Given:

∠ACO ≅ ∠DBO, and BO ≅ CO

as, ∠COA =∠BOD (vertically opposite angles)

∠ACO ≅ ∠DBO ( given)

BO ≅ CO ( given)

So, By ASA (Angle-Side-Angle) congruency,  △ACO ≅ △DBO

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Answer:

[tex]3 + 3^2 + 3^3 ...+ 3^n = \frac{3(3^n - 1)}{2}[/tex]

Step-by-step explanation:

Given

[tex]3 + 3^2 + 3^3 ...+ 3^n[/tex]

Required

Show that the sum of the series is [tex]\frac{3(3^{n}-1)}{2}[/tex]

The above shows the sum of a geometric series and this will be calculated as shown below;

[tex]S_n = \frac{a(r^n - 1)}{r - 1}[/tex]

Where

a = First term;

[tex]a = 3[/tex]

r = common ratio

[tex]r = \frac{3^2}{3} = \frac{3^3}{3^2}[/tex]

[tex]r = 3[/tex]

Substitute 3 for r and 3 for a in the formula above;

[tex]S_n = \frac{a(r^n - 1)}{r - 1}[/tex] becomes

[tex]S_n = \frac{3(3^n - 1)}{3 - 1}[/tex]

[tex]S_n = \frac{3(3^n - 1)}{2}[/tex]

Hence;

[tex]3 + 3^2 + 3^3 ...+ 3^n = \frac{3(3^n - 1)}{2}[/tex]

The construction that you can use to prove the Pythagorean Theorem based on similarity of triangles is 2nd construction. Please see the attached file.

Two triangles are similar triangles of their corresponding angles are equal corresponding sides are in equal ratios.

The Pythagorean theorem, also known as Pythagoras's theorem, is a fundamental relation in Euclidean geometry among the three sides of a right triangle. It mentions that the sum of the squares of the other two sides is equal to the square of the hypotenuse (the side opposite the right angle).

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Answer Step one x=16/9 =1.778

Last step is x²=0

Hope I helped you

Answer:

the roots are {0, 0, 16/9}

Step-by-step explanation:

The trick to solving this is to factor out x^2 from both terms on the left:

x^2*9*x - 16x^2=0, or

x^2(9x - 16) = 0

Then, either x^2 = 0 or (9x - 16) = 0.

Thus, the roots are {0, 0, 16/9}

Answer:

69

Step-by-step explanation:

Answer:

k=-6

Step-by-step explanation:

Answer:

[tex]\Large \boxed{k=-6}}[/tex]

Step-by-step explanation:

35 = -5(2k+5)

Expand brackets.

35 = -10k - 25

Add 25 on both sides.

60 = -10k

Divide both sides by -10.

-6 = k

Hi there! :)

Answer:

[tex]\huge\boxed{f(1) + f(5) = 30}[/tex]

Given:

[tex]f(x) = x^{2} + 2[/tex]

Evaluate [tex]f(1) + f(5)[/tex]

Solve for each:

[tex]f(1) = (1)^{2} + 2 = 3[/tex]

[tex]f(5) = (5)^{2} + 2 = 27[/tex]

[tex]27 + 3 = 30[/tex]

Answer:

30

Step-by-step explanation:

Answer:

Step-by-step explanation:

To find the side adjacent to the 50° angle we use tan

[tex] \tan( \alpha ) = \frac{opposite}{adjacent} [/tex]

From the question

The opposite is 6m

The adjacent is ?

So we have

[tex] \tan(50) = \frac{6}{?} [/tex]

[tex]? \tan(50) = 6[/tex]

[tex]? = 6 \times \frac{1}{ \tan(50) } [/tex]

But

[tex] \frac{1}{ \tan(x) } = \cot(x) [/tex]

So we have

[tex] \frac{1}{ \tan(50) } = \cot(50) [/tex]

Substitute it into the expression

That's

We have the final answer as

[tex]? = 6 \cot(50) [/tex]

Hope this helps you

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

Explanation:

We're given an opposite side and an adjacent side. The tangent rule ties these two sides together. "tangent" is nowhere to be found in any of the answer choices, but cotangent is. Recall that

cot = 1/tan

which means

tan = opposite/adjacent

cot = adjacent/opposite

one is the reciprocal of the other

-----------

This means

cot(angle) = adjacent/opposite

cot(50) = x/6

6*cot(50) = x

x = 6*cot(50)

If you want to set up the equations:

let the cost of one apple cheesecake be [tex] a[/tex] and the cost of one pecan cheesecake be $p$

from Abby, $14p+3a=113$

and from Katy....?

then solve for both variables

can you take it from here?

Answer:

[tex]\boxed{x = 40}[/tex]

Step-by-step explanation:

Hey there!

Well angles like 142 and 2x + 22 equal each other because they are across from each other.

So we can set up the following,

142 = 3x + 22

Single out x

-22 to both sides

120 = 3x

Divide both sides by 3

x = 40

Hope this helps :)

Answer:

x=40

Step-by-step explanation:

142=3x+22

3x+22-22=142-22

3x=120

120/3=40

Answer: 11x - 8y = -9

Step-by-step explanation:

Subtract it by terms.

8x - (-3x) = 11x  

-4y - (4y) = -8y

-4-5= -9    

order it

11x - 8y =-9

Answer:

27

Step-by-step explanation:

By the theorem of intersecting secant and tangent out side of a circle, we have:

[tex] {60}^{2} = 48 \times (48 + x) \\ 3600 = 48 \times (48 + x) \\ \frac{3600}{48} = 48 + x \\ 75 = 48 + x \\ 75 - 48 = x \\ x = 27 \\ [/tex]

Answer:

The least number of steps she takes to reach 20 m is 118 steps

Step-by-step explanation:

For Laura, the length of a walking step = 50 cm = 0.5 m

The repeating number of steps she takes = Two steps forward one step backwards

The number of forward steps it would take for her to reach 20 m = (20 m)/(0.5 m) = 40 steps

Given that she always takes two steps forward and one step backwards, we have;

The number of steps forward every three steps = 2 step forward + (-1) step (backward)

The number of steps forward every three steps = 2 - 1 = 1 step forward

To reach 39 steps forward, she would need 39 × 3 =  117 steps

To get to the 40 steps she needs just a step forward, making the total number of steps to reach 40 steps = 117 + 1 = 118 steps

Therefore, the least number of steps she takes to reach 20 m = 118 steps.

Answer:

7/6

Step-by-step explanation:

We can find the slope by using the slope formula

m = (y2-y1)/(x2-x1)

    = ( -3 -4)/(5 -11)

  -7/-6

  =7/6

Answer:

7/6

Step-by-step explanation:

m = (y2 - y1)/(x2 - x1)

m = (-3 - 4)/(5 - 11)

m = -7/(-6)

m = 7/6

Sry i couldn't find the answer

Answer:

(2) 42°

Step-by-step explanation:

Copy of the given problem:

4. Multiple-Choice

1. Two complementary angles measure (12r - 18)° and (5x + 23)°. What

is the measure of the smaller angle?

(1) 5°

(2) 42°

(3) 48°

(4) 90°

Solution:

The sum of the measures of complementary angles is 90 deg.

12r - 18 + 5x + 23 = 90

We have 1 equation with two different variables, so we cannot solve the equation to find unique values of the variables.

I assume the above is an error, and both variables should be the same.

12r - 18 + 5r + 23 = 90

Combine like terms on the left side. Terms with r are combined. Terms with no variable are combined.

12r + 5r - 18 + 23 = 90

17r + 5 = 90

Subtract 5 from both sides.

17r = 85

Divide both sides by 5.

r = 5

The measures of the angles are:

12r - 18 = 12(5) - 18 = 60 - 18 = 42

5r + 23 = 5(5) + 23 = 25 + 23 = 48

The measures of the two angles are 42°  and 48°.

The smaller angle measures 42°

Answer: (2) 42°

Answer:

5/6, 0.23, -5 3/8

Step-by-step explanation:

Answer:

a 0,1 and b 1,0

Step-by-step explanation:

exam took

Answer:

The other answer is incorrect the answer is

D) The locations of A' and B' are A' (0, 6) and B' (6, 0); lines f and f' are parallel.

260 units2 is the answer

Answer:

$12165.97

Step-by-step explanation:

100 + 4.1 = 104.1%

104.1% = 1.041

$5670 x 1.041^19 = $12165.97

Answer:

daily

Step-by-step explanation:

To answer this try plugging in each type of compund: daily, monthly, quarterly, and annually.

5670(1+0.041/365)^(365*19)

= 12356.04

365= daily

so your answer would be that the interest compounds daily.

Answer:

1. b.  2. a.  3. a.

Step-by-step explanation:

1. (f + g)x = f(x) + g(x)

= x^2 + 2x + 4

(f + g)(-1) =  (f + g)(x)  where x = 1 so it is

(-1)^2 + 2(-1) + 4

=  1 - 2 + 4

= 3.

2.  We find (f o g)(x) by replacing the x in f(x) by g(x):

= √(x + 1) and

(f o g)(3) =  √(3 + 1)

= √4

= 2.

3. (f/g) c  = f(x) / g(x)

= (x - 3)/(x + 1)

The domain is the values of x which give real values of (f/g).

x cannot be - 1 because the denominator x + 1 = -1+1 = 0 and dividing by zero is undefined. So x can be all real values of x except x = -1.

The domain is (-∞, -1) U (-1, ∞)

Answer:

Yes, that is correct.

Step-by-step explanation:

W = x

L = ?

A = x^2 + 12x

(x^2 + 12x)/x = x + 12

L = x + 12

Subbing in 10 for each X, we get:

Perimeter: 64

2(10) + 2(10 + 12) = 20 + 44 = 64

Area: 220

10 * 22 = 220

Part A looks perfect. You've shown that x^2+12x factors into x(x+12) indicating that x is the width and x+12 is the length. Convention usually has the length be longer than the width, but to be honest, the order doesn't really matter (since we can multiply in any order we want).

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

Part B is a bit hazy. You show that 10 * 22 = 220 is the area, so you imply that the rectangle has width 10 and length 22. However, you don't directly mention the dimensions of the rectangle.

You can pick either x^2+12x or x(x+12). I prefer x(x+12) as its easier in my opinion. You don't need to do both.

All you really need to do is say that if x is the width and x = 10, then the width is 10. Furthermore, if x+12 is the length then x+12 = 10+12 = 22 is the length.

Answer: 24

Step-by-step explanation:

R= 3

You can find this using simple algebra

The measure of RA is 24 units after using the concept of congruent triangle option (A) 24 is correct.

Congruent triangles are those that are exactly the same size and shape. Congruent is represented by the symbol ≅ When the three sides and three angles of one triangle match the dimensions of the three sides and three angles of another triangle, they are said to be congruent.

We have a triangle shown in the picture.

It is required to find the measure of the RA

To find the measure of the RA we can apply the concept of congruent triangle:

In the triangle LRU and triangle LAU

LU = LU (common side)

LR = LA (equal sides)

Angle RLU = Angle ALU (equal)

The triangles are congruent.

RU = UA

18 - 2r = 4r

6r  = 18

r = 18/6 = 3

The measure of the RA = 18 - 2r + 4r = 18 + 2r

The measure of the RA = 18 + 2(3) = 18+6 = 24 units

Thus, the measure of RA is 24 units after using the concept of congruent triangle option (A) 24 is correct.

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Answer:

x = 162 degrees.

Step-by-step explanation:

m < RSP = 180 - 72

= 106 degrees (adjacent angles)

m < Q = m < RSP ( Opposite angles in a parallelogram are equal).

So m < Q = 180 degrees.

m < x = 360 - 90 - 108

= 360 - 198

= 162 degrees.

Using the appropriate angle theorems, the value of the angle, x in the parallelogram would be 162°

At angle S :

S + 72 = 180 (sum of straight line angles)

S = 180° - 72°

S = 108°

S = Q (opposite angles of a parallelogram)

Q = 108°

Hence,

108° + x + 90 = 360

x = 360 - (108 + 90)

x = 162°

Hence, the value of x is 162°

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Answer:

[tex] 2w^2(w + 2)(4w - 3) [/tex]

Step-by-step explanation:

[tex] 8w^4 + 10w^3 − 12w^2 = [/tex]

First, factor out the GCF of all terms, 2w^2:

[tex] = 2w^2(4w^2 + 5w - 6) [/tex]

Now we work on the trinomial.

Think of ax^2 + bx + c.

Multiply ac

ac = 4 * (-6) = -24

Now we need two numbers whose product is -24 and whose sum is 5.

They are -3 and 8.

We break up the middle term, 5w, into a sum using these two numbers.

5w = 8x - 3w

[tex] = 2w^2(4w^2 + 8w - 3w - 6) [/tex]

Now we factor by parts. We factor a common factor out of the first two terms, and we factor a common factor out of the last two terms.

[tex] = 2w^2[4w(w + 2) - 3(w + 2)] [/tex]

[tex] = 2w^2(w + 2)(4w - 3) [/tex]

Step-by-step explanation:

V=(4/3) * πr^3

V=(4/3) * π * 7.6 ^3

V=(4/3) * π * 438.976

V= π * 585.301333

V = 1837.85 inch^3

3.14 for pi btw

Answer: 14 1-cent stamps (in case anyone else still needs)

Step-by-step explanation:

1-cent stamps=x

8-cent stamps=x-4

12-cent stamp=.5x

x+x-4+.5x=31

2.5x-4=31

2.5x=35

x=14

You can use the $1.78 to double check:

(1*14)+(8*10)+(12*7)

14+80+84=178 cents (or $1.78)