Determine whether the ratios form a proportion.
16/9, 28/15

Answer:

[tex]x=32[/tex]°

Step-by-step explanation:

The law of sines is a property of all triangles that relates the sides and angles of a triangle. This property states the following:

[tex]\frac{sin(a)}{A}=\frac{sin(b)}{B}=\frac{sin(c)}{C}[/tex]

Where side (A) is the side opposite angle (<a), side (B) is the side opposite angle (<b), and side (C) is the property opposite angle (<c).

Substitute each of the sides and respective angles into the formula, and solve for the unknown angle (<x). Please note that a triangle with two congruent sides (referred to as an isosceles triangle) has a property called the base angles theorem. This states that the angles opposite the congruent sides in an isosceles triangle are congruent. Therefore, there can be two (<x)'s in this triangle.

[tex]\frac{sin(a)}{A}=\frac{sin(b)}{B}=\frac{sin(c)}{C}[/tex]

[tex]\frac{sin(x)}{10}=\frac{sin(116)}{17}=\frac{sin(x)}{10}[/tex]

One can shorten the equation so it only holds the parts that will play a role in solving this equation,

[tex]\frac{sin(x)}{10}=\frac{sin(116)}{17}[/tex]

Now take the cross product in this equation to simplify it further,

[tex]\frac{sin(x)}{10}=\frac{sin(116)}{17}[/tex]

[tex]17(sin(x))=10(sin(116))[/tex]

Inverse operations, solve this equation for (x),

[tex]17(sin(x))=10(sin(116))[/tex]

[tex]sin(x)=\frac{10(sin(116))}{17}[/tex]

[tex]x=sin^-^1(\frac{10(sin(116))}{17})[/tex]

[tex]x=31.91782...[/tex]

[tex]x\approx32[/tex]

Answer:

hello,

Step-by-step explanation:

the triangle is isocele,

x+x+116=180

x=(180-116)/2

x= 32° (thirty-two , trente-deux in french)

Answer:

j = 10.1

Step-by-step explanation:

The difference between 9.5 and 11.3 is

11.3 - 9.5 = 1.8

This is split into 3 divisions, that is

1.8 ÷ 3 = 0.6

Then

j = 9.5 + 0.6 = 10.1

Answer: 360 - 44 - 80 = 236

236 ÷ 2 = 118

both angle equal to 118

Step-by-step explanation:

The measure of angle 1 is 118 degrees and the measure of angle 2 is 118 degrees.

It is defined as the four-sided polygon in geometry having four edges and four corners.

We know that kite is quadrilateral, having :

It has one pair of opposite congruent angles.

One diagonal is bisected.

The top and bottom angles are bisected but

As we know from the kite properties it has one pair of opposite congruent angles

From the properties of the quadrilateral the sum of the interior angles is 360 degrees

44 + angle 1 + angle 2 + 80 = 360

Angle 1 = angle 2 = x(say)

44 + x + x + 80 = 360

2x + 124 = 360

2x = 236

x = 118 degrees

Angle 1 = angle 2 = 118 degrees

Thus, the measure of angle 1 is 118 degrees and the measure of angle 2 is 118 degrees or m∠1 = 118° and m∠2 = 118°.

Learn more about the quadrilateral here:

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Answer:

$4,100

Step-by-step explanation:

Interest = principal * rate * time

Let entire principal = amount invested = p

Investment A :

Rate, r = 7%, principal = p/2, time, = 1

Investment B :

Rate, r = 13%, principal = p/2, time = 1

Total interest = $4.10

(p/2 * 0.07 * 1) + (p/2 * 0.13 * 1) = 410

0.035p + 0.065p = 410

0.1p = 410

p = 410 / 0.1

p = $4100

Answer:

45 hours

Step-by-step explanation:

1 mile * 1609 meters  *     1 s           = 160900 sec

               1 mile               .01 meters

160900 sec / 60 /60 = 44.7 = 45 hours

Step-by-step explanation:

This is a cute question lol.

So this lil snail is trying to go 1609 meters, at a speed of 0.01 m/s (meters per second). Lets see how long that takes.

The way I like to do conversion problems is by starting with the value that doesn't have something on the bottom (1609 m) then multiplying to get rid of that variable.

I'll show you what I mean:

[tex]\frac{1609 m}{1} *\frac{1 s}{0.01 m} *\frac{1 min}{60s} *\frac{1 hr}{60 min}[/tex]

Then, we just multiply everything.

[tex]\frac{1609 *1*1}{1*0.01*60*60}hr[/tex]

Simplify.

[tex]\frac{1609}{36}hr[/tex]

Divide.

[tex]44.694444444...hr[/tex]

Round to the nearest whole hour.

[tex]45 hr[/tex]

Answer:

45 hours

Answer:

i dont know the total sum of marbles

Step-by-step explanation:

A fraction is written in the form of a numerator and a denominator

where the denominator is greater than the numerator.

1/4 of 80 is 20.

The number of white marbles is 20.

A fraction is written in the form of a numerator and a denominator where the denominator is greater than the numerator.

Example: 1/2, 1/3 is a fraction.

We have,

Total marbles = x

The number of white marbles = 1/4x

The number of blue marbles = 3/8x

The number of yellow marbles = 30

Total marbles.

x = (1/4)x + (3/8)x + 30

x - (1/4)x - (3/8)x = 30

(8x - 2x - 3x) / 8 = 30

3x/8 = 30

3x = 30 x 8

3x = 240

x = 80

The number of white marbles.

= (1/4)x

= (1/4) x 80

= 20 marbles.

Thus,

The number of white marbles is 20.

Learn more about fractions here:

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Answer:

answer is 21..............

Explanation:

p(x) = x⁴ + 2x³- 3x² + x - 1

Factor of p(x)

x-2=0

x=2

Then by using synthetic division

Answer:

0.62kg

Step-by-step explanation:

Let

x = 40/kg coffee

y = 11/kg coffee

two equations can be derived from the question

x + y = 12 equation 1

40x + 11y = 114 (9.5 x 12)  equation 2

multiply equation 1 by 11

11x + 11y = 132 equation 3

subtract eqn 3 from eqn 2

29x = 18

divide both sides of the equation by 29

x = 0.62kg

Answer:

Step-by-step explanation:

Answered by Gauthmath

Answer:

B

Step-by-step explanation:

The slope is zero is the answer

Answer:

Carrying forward.

Step-by-step explanation:

Answer:

25%

Step-by-step explanation:

40-30=10

10/40*100

25%

Answer:

4

Step-by-step explanation:

A=ch

then,

2ft×2ft

4ft

Answer:

x=8

Step-by-step explanation:

(3x-8)/1=4x/2. 3x-8=2x, x=8

Answer:

42.1

Step-by-step explanation:

The height of the main triangle is,

h = 47√3/2 (since it's an 30-60-90 triangle)

so to find x,

tan(44) = h/x

x = h/tan(44)

x = 42.1 (rounded to the nearest tenth)

Answered by GAUTHMATH

Answer:

[tex]Total = 15 + 6 x[/tex]

Step-by-step explanation:

Given

Option 1

[tex]Admission = 0[/tex]

[tex]Rate = \$5/game[/tex]

Option 2

[tex]Admission = 15[/tex]

[tex]Rate = \$6/game[/tex]

Required

The total cost for option 2

This is calculated as:

[tex]Total = Admission + Rate * x[/tex]

Where:

[tex]x \to[/tex] games

So, we have:

[tex]Total = 15 + 6 * x[/tex]

[tex]Total = 15 + 6 x[/tex]

Answer:

C.) [tex]350\pi[/tex] [tex]cm^{2}[/tex]

Step-by-step explanation:

Since we are given the radius of the cone's base and the slant height, we can use the following equation to solve for surface area:

[tex]A = \pi r^{2} + \pi rl[/tex]

Now we just plug in the given information and solve:

[tex]A = \pi (10cm)^2 + (\pi) (10cm)(25cm)\\A = 100\pi cm^2 + 250\pi cm^2\\A = 350\pi cm^2[/tex]

Answer:

20

Step-by-step explanation:

(6x3=18)  (6x1/3=2)  (18+2=20)

First things first!

Multiply 6 by 3 (18).

Mulitply 6 by 1/3 (2).

Add 18 and 2, and ... *drum roll*, the final answer is 20!

Hope this helps :)

Answer:

The equation of the line is [tex]y = \frac{3}{5}\cdot x -\frac{26}{5}[/tex].

Step-by-step explanation:

Given the values of the slope and a point of the line, we can derive the equation of the line by means of this formula:

[tex]y-y_{1} = m\cdot (x-x_{1})[/tex] (1)

Where:

[tex]x[/tex] - Independent variable.

[tex]y[/tex] - Dependent variable.

[tex]m[/tex] - Slope.

[tex](x_{1}, y_{1})[/tex] - Coordinates of the given point.

If we know that [tex]m = \frac{3}{5}[/tex] and [tex](x_{1},y_{1}) = (2, -4)[/tex], then the equation of the line is:

[tex]y+4 = \frac{3}{5}\cdot (x-2)[/tex]

[tex]y + 4 = \frac{3}{5}\cdot x -\frac{6}{5}[/tex]

[tex]y = \frac{3}{5}\cdot x -\frac{26}{5}[/tex]

The equation of the line is [tex]y = \frac{3}{5}\cdot x -\frac{26}{5}[/tex].

Answer:

y = -3x+9

Step-by-step explanation:

Parallel lines have the same slope

y = -3x+2  

This is in slope intercept form where y =mx+b where m is the slope

The slope is -3

y = -3x+b

Using the point (2,3)

3 = -3(2)+b

3 = -6+b

Add 6 to each side

3+6 = b

9=b

y = -3x+9

Answer:

slope (m) = -3

3= -3(2)+b

b = 9

y=mx+b → y= -3x+9

OAmalOHopeO

Answer:

the trapiezium

Step-by-step explanation:

It has a area of 4 which is the highest

Answer:

C

Step-by-step explanation:

Given 2 intersecting chords in a circle, then

The product of the parts of one chord is equal to the product of the parts of the other chord, that is

DK × KB = AK × KC , substitute values

12(4x + 1) = 14(3 + 3x) ← distribute parenthesis on both sides )

48x + 12 = 42 + 42x ( subtract 42x from both sides )

6x + 12 = 42 ( subtract 12 from both sides )

6x = 30 ( divide both sides by 6 )

x = 5 → C

Answer:

but what to do in do I have to find the area of the particular Region or a length of that

Answer: AS = 46

Step-by-step explanation:

Since we know that a circumcenter is equidistant from all three vertices, we know that segment BS is congruent to segment CS which is congruent to segment AS. By the definition of congruent segments, BS = AS. Since BS is 46, we know that AS will also be 46.

(v^3)(w^-3) / (-v^-6)(w^3)

(-v^9)(w^-3) / (w^3)

(-v^9)(w^-6)

ANSWER: Option 4

Hope this helps!

Answer:

A) 3

B)60

C)4

Step-by-step explanation:

y = kx

36 = 12k

A)k=3

~~~~~~~~~~

b) 60

12*5

c) 4  

12/3

Answer:

8.18

Step-by-step explanation:

r = square root of A/ pi

R = square root 210/ 3.14

I hope the formula helped!

Answer:

m∠1 = 90º

m∠2 = 25º

Step-by-step explanation:

m∠1

diagonals of a kite are perpendicular by definition

m∠2

the 65º angle, the angle to the right of ∠1, and ∠2 form a triangle

we know that triangles are 180º

65º + 90º + m∠2 = 180º

m∠2 = 25º

Answer:

Option C

Step-by-step explanation:

A function's input is assigned to exactly one output. Any input must not repeat.

Option A's not a function because the input of 3 repeats.

Option B's not a function because the input of -4 repeats.

Option C's a function because no inputs repeat.

Option D's not a function because the input of 5 repeats.

Hope this helps.