In the triangle below, what is the length of the side opposite the 30° angle?
30"
3
60"
O A. 213
O B. 313
O c.
3
2
O D. 13

Answer:

112 cm.

Step-by-step explanation:

A triangle is a polygon with three sides and three angles. The types of triangles are scalene triangle, equilateral triangle, right angled triangle and obtuse triangle.

Cosine rule states that given a triangle with sides a, b, c and their corresponding angles opposite to the sides as A, B, C. Then:

[tex]a^2=b^2+c^2-2bc*cos(A)[/tex]

In triangle IJK:

We can find the length of j using cosine rule:

[tex]j^2=k^2+i^2-2ik*cos(J)\\\\substituting:\\\\j^2=59^2+80^2-2(80)(59)cos(106)\\\\j^2=3481+6400-(-2602)\\\\j^2=3481+6400+2602\\\\j^2=12483\\\\j=\sqrt{12483} \\\\j=112\ cm[/tex]

Answer:

200miles

Step-by-step explanation:

Given data

Rent-For-Less

charges $50 for a deposit and $1.25 per mile

let the number of miles be x

and the total distance be y

y=50+1.25x-------------1

Cheap Rides

charges $1.30 per mile and a $40 deposit

y=40+1.30x-------------2

Equate 1 and 2 above we have

50+1.25x=40+1.30x

collect liker terms

50-40= 1.3x-1.25x

10=0.05x

divide both side by 0.05

x= 10/0.05

x=200 miles

Hence the distance in miles is 200miles

Answer:

x can be all real numbers

Step-by-step explanation:

1 - 5x = -5x + 1

-5x+5x=1-1

0=0

Answer:

1/10

Step-by-step explanation:

5x=-5x+1

Move the variable to the left hand and change its sign

5x+5x=1

10x=1

x=1/10

Answer:

The answer is below

Step-by-step explanation:

A parabola is the locus of a point such that its distance from a given line (directrix) and a fixed point (focus) is always the same.

The equation of a parabola with a horizontal line as directrix is given by:

(x - h)² = 4p(y - k)

where y = k - p is the directrix and the focus = (h, k + p)

Given that parabola has a directrix at y = 2 and a focus at (5, 0)

Therefore:

y = k - p

k - p = 2          (1)

focus = (h, k + p) = (5, 0)

h = 5, k + p = 0

k + p = 0         (2)

Solve equation 1 and 2 simultaneously by adding both equations together:

2k = 2

k = 1

Substitute k = 1 in k + p = 0 to find p:

1 + p = 0

p = -1

Therefore h = 5, p = -1 and k = 1

Substitute the values of h, k and p into the equation of a parabola:

(x - h)² = 4p(y - k)

(x - 5)² = 4(-1)(y - 1)

(x - 5)² = -4(y - 1)

x² - 10x + 25 = -4y + 4

-4y = x² - 10x + 21

4y = 10x - x² - 21

Answer:

no because she would get the same total if she added it before or after

Step-by-step explanation:

Answer:

[tex]2950 - 125 - 50 \\ = 2950 - (125 + 50) \\ = 2950 - 175 \\ = \boxed{2775}[/tex]

Answer:

she washes 5 cars per hour

Answer:

Sue washes 5 cars an hour

Step-by-step explanation:

25/5 = 5 cars an hour

Answer:

I did this test a while ago I chose A and it was right I beleieve.

Step-by-step :

Answer:

m

Step-by-step explanation:

Answer:

Any scalene quadrilateral will serve as a counterexample. For a conditional (if-then) statement, a counterexample must be an instance which satisfies the hypothesis , but not the conclusion .

Step-by-step explanation:

Answer:

if your considering 1 each, 20.

Step-by-step explanation:

1 goes into 20,20 times

although....its 2021 now so I dont know (answer: 20).

Answer:

20

Step-by-step explanation:

Answer:

x=-5

Step-by-step explanation:

-4(x-5)=40

-4x+20=40

-4x=40-20

x=20/-4

x=-5

Isolate the variable by dividing each side by factors that don't contain the variable.

Inequality Form:

X< -10/3

Interval Notation:

(-∞, - 10/3)

Hope this is right :)

Answer:

180-(67+52)

Step-by-step explanation:

angles on a straight line add up to 180 degress

Answer:

the angle measurement is 75

Step-by-step explanation:

Answer:

($5000 x 4% ) * 2 = $400

The ending balance : $5000 + $400 = $5400

Step-by-step explanation:

Answer:160

Step-by-step explanation:

Answer:

$5,308.42

Step-by-step explanation:

(see attached for reference)

recall that the formula for Depreciation

is given by

A = P ( 1 - r)^t,

where

A = final amount

P = principal amount = given as $6,000

r = depreciation rate = given as 4% = 0.04

t = time in years = given as 3,

Simply substitute these into the equation to get:

A = P ( 1 - r)^t

= 6000( 1 - 0.04) ^ 3

= 6000 (0.96)^3

= $5,308.42

Answer:

A. x = -3

B. x = 2

C. x = 9/10

Step-by-step explanation:

(A) –12x + 9 = –15x

Collect like terms

9 = -15x + 12x

9 = -3x

x = 9 / -3

x = -3

(B) 4.5x + 11.5 = 8.5x + 3.5

4.5x - 8.5x = 3.5 - 11.5

-4x = -8

x = -8 / -4

x = 2

(C) 23x – 9 = 13x

-9 = 13x - 23x

-9 = -10x

x = -9 / -10

x = 9/10

Answer:

A) x= -3

B) x = -2

C) x = 27

Explanation: I did the lesson

Answer:

40

Step-by-step explanation:

4 times 10 equals 40

i news more sownfjdhe

Answer:

The probability of snow is about 0.75

Step-by-step explanation:

Answer:

[tex]37.7\ \text{foot}[/tex]

Step-by-step explanation:

The length of the edging will be equal to the circumference of the circular flower garden.

Here, the diameter of the circular garden is [tex]d=12\ \text{foot}[/tex]

Circumference of a circle is given by

[tex]C=\pi d\\\Rightarrow C=3.14\times 12\\\Rightarrow C=37.68\approx 37.7\ \text{foot}[/tex]

The length of the edging is [tex]37.7\ \text{foot}[/tex].

Answer:

20

Step-by-step explanation:

use ur head

DG, DM, DS, DT GD, GM, GS, GT MD, MG, MS, MT, SD, SG, SM, ST, TD, TG, TM, TS. Those are all the possible combinations using each letter only once in each set.

In short, you can make 20 sets.

Answer:

Unit rate is 1.5

Step-by-step explanation:

4 pounds  = $6

Divide 6 by 4 = 1.5

Check: 4 * 1.5 = 6

Hence,

1 pound = $1.5

Hope this helps :)