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Suppose a triangle has two sides of length 3 and 4 and that the angle
between these two sides is pi/3 What is the length of the third side of the
triangle?
A. sqrt13
B. 4sqrt3
C. sqrt3
D. 3

Answer:

B

Step-by-step explanation:

Answer: y = -3x + 5

Step-by-step explanation:

slope = m

[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{2-(-4)}{1-3}=\frac{6}{-2}=-3[/tex]

y = mx + b, (3,-4), (1,2), m = -3

(both points work for the y = mx + b equation)

[tex]y=mx+b\\2=-3(1)+b\\2=-3+b\\b=5\\y=-3x+5[/tex]

Answer:

115 in.^2

Step-by-step explanation:

The total surface area is the sum of the areas of the square base and the 4 congruent triangular faces.

SA = b^2 + 4 * bh/2

SA = (5 in.)^2 + 4 * (5 in.)(9 in.)/2

SA = 25 in.^2 + 2 * 45 in.^2

SA = 115 in.^2

Answer:

14.4 i hope it helped you

Answers:

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Work Shown:

AP = arithmetic progression, which is the same as arithmetic sequence

d = common difference

Notice how we scale up the d terms d, 2d, 3d, counting up by 1 each time.

So that must mean 25 is the same as 20+4d

20+4d = 25

4d = 25-20

4d = 5

d = 5/4

d = 1.25

and therefore,

We could convert these to fraction form, but I find decimal form is easier in this case.

Answer:

[tex] \rm\cos({600}^{ \circ} ) =-1/2 [/tex]

Step-by-step explanation:

we would like to solve the following using double-angle formula:

[tex] \displaystyle \cos( {600}^{ \circ} ) [/tex]

there're 4 double Angle formulas of cos function which are given by:

[tex] \displaystyle \cos(2 \theta) = \begin{cases} i)\cos^{2} ( \theta) - { \sin}^{2}( \theta) \\ii) 2 { \cos}^{2}( \theta) - 1 \\iii) 1 - { \sin}^{2} \theta \\ iv)\dfrac{1 - { \tan}^{2} \theta}{1 + { \tan}^{2} \theta } \end{cases}[/tex]

since the question doesn't allude which one we need to utilize utilize so I would like to apply the second one, therefore

step-1: assign variables

to do so rewrite the given function:

[tex] \displaystyle \cos( {2(300)}^{ \circ} ) [/tex]

so,

Step-2: substitute:

[tex] \rm\cos(2 \cdot {300}^{ \circ} ) = 2 \cos ^{2} {300}^{ \circ} - 1[/tex]

recall unit circle thus cos300 is ½:

[tex] \rm\cos(2 \cdot {300}^{ \circ} ) = 2 \left( \dfrac{1}{2} \right)^2 - 1[/tex]

simplify square:

[tex] \rm\cos(2 \cdot {300}^{ \circ} ) = 2\cdot \dfrac{1}{4} - 1[/tex]

reduce fraction:

[tex] \rm\cos(2 \cdot {300}^{ \circ} ) = \dfrac{1}{2} - 1[/tex]

simplify substraction and hence,

[tex] \rm\cos({600}^{ \circ} ) = \boxed{-\frac{1}{2}}[/tex]

Answer:

x=110.6

Step-by-step explanation:

sin(19)=36/x. x=36/sin(19)=110.6

Answer:

12.92

Step-by-step explanation:

rounding the 1 hundredth up to 2 because of the 5 thousandth

Answer:

Step-by-step explanation:

See explanation in attached image

The area of one side of the coin is 41.605 mm².

Given that, the diameter of a $1 coin is 26.5 mm.

We need to find the area of one side of the coin.

The area of a circle formula is A=πr².

Now, radius=26.5/2=13.25 mm.

Area of a coin=3.14×13.25=41.605 mm².

Therefore, the area of one side of the coin is 41.605 mm².

To learn more about the area of the circle visit:

https://brainly.com/question/11952845.

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Given:

The population, P, of six towns with time t in years are given by the following exponential equations:

(i) [tex]P=1000(1.08)^t[/tex]

(ii) [tex]P = 600 (1.12)^2[/tex]

(iii) [tex]P =2500 (0.9)^t[/tex]

(iv) [tex]P=1200 (1.185)^t[/tex]

(v) [tex]P=800 (0.78)^t[/tex]

(vi) [tex]P=2000 (0.99)^t[/tex]

To find:

The town whose population is decreasing the fastest.

Solution:

The general form of an exponential function is:

[tex]P(t)=ab^t[/tex]

Where, a is the initial value, b is the growth or decay factor.

If b>1, then the function is increasing and if 0<b<1, then the function is decreasing.

The values of b for six towns are 1.08, 1.12, 0.9, 1.185, 0.78, 0.99 respectively. The minimum value of b is 0.78, so the population of (v) town  [tex]P=800 (0.78)^t[/tex] is decreasing the fastest.

Therefore, the correct option is b.

Answer:

Step-by-step explanation:

Total frequencies:

Median group is the containing the middle - 25th and 26th frequencies. This is the 11-15 interval.

Estimated median formula:

Substitute values and work out the number:

Answer:

$968.78

Step-by-step explanation:

multiply worked hours by her pay per hour

38.52×$25.15=

38.52×$25.15=$968.778

then you round it to the nearest hundredth

since the thousandth is greater than 5 the 8 will round the 7 to an 8

giving you $968.78

Answer: $977.50

Step-by-step explanation:

(38)(25.15)=955.70

(52)(25.15)/60=21.80

955.70 + 21.80 = 977.50

Answer:

24

Step-by-step explanation:

The question is asking for the net area from x=3 to x=10.

It gives you the net area from x=3 to x=5 being -18.

It gives you the net area from x=5 to x=10, being 42.

Together those intervals make up the interval we want to find the net area for.

-18+42=42-18=24

Answer:

[tex]\displaystyle \int\limits^{10}_3 {f(t)} \, dt = 24[/tex]

General Formulas and Concepts:

Calculus

Integration

Integration Property [Splitting Integral]:                                                               [tex]\displaystyle \int\limits^c_a {f(x)} \, dx = \int\limits^b_a {f(x)} \, dx + \int\limits^c_b {f(x)} \, dx[/tex]

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle \int\limits^{5}_3 {f(t)} \, dt = -18[/tex]

[tex]\displaystyle \int\limits^{10}_5 {f(t)} \, dt = 42[/tex]

[tex]\displaystyle \int\limits^{10}_3 {f(t)} \, dt[/tex]

Step 2: Integrate

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Integration

The total distance the particle travels from t=0 seconds to t=4 seconds would be 11.33 meters.

Used the concept of integration that states,

In Maths, integration is a method of adding or summing up the parts to find the whole. It is a reverse process of differentiation, where we reduce the functions into parts.

Given that,

A particle moves along a line with a velocity v(t) = t² - t - 6, measured in meters per second.

Now the total distance the particle travels from t=0 seconds to t=4 seconds is,

D = ∫₀⁴ |(t² - t - 6)| dt

D =  ∫₀⁴ (t²) dt - ∫₀⁴ (t) dt -  ∫₀⁴ (6) dt

D = (t³/3)₀⁴ - (t²/2)₀⁴ - 6 (t)₀⁴

D =| (64/3) - (16/2) - 6 (4)|

D = | (64/3) - 8 - 24 |

D = | (64/3) - 32|

D = 11.33 meters

Therefore, the total distance is 11.33 meters.

To learn more about integration visit:

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Answer:

900°

Step-by-step explanation:

The interior angles sum = 180° ( n - 2 )

~~~~~~~~

n = 7

180° ( 7 - 2 ) = 900°

Answer:

900 degrees

Step-by-step explanation:

just apply the formulas discussed in class !

The sum of interior angles in a triangle is 180°. To find the sum of interior angles of a polygon, multiply the number of triangles in the polygon by 180°.

The number of triangles in each polygon is two less than the number of sides.

The formula for calculating the sum of interior angles is:

(n−2)×180∘ (where n is the number of sides)

in our case we have 7 sides.

so, we could split this polygon into 5 triangles.

each of these triangles would have an angle sum of 180°.

so, the angle sum of the polygon is

5×180 = 900°

Answer:

Step-by-step explanation:

Because those lines are parallel, that means that the angle measuring 75 and the angle measuring 4x + 7 are alternate interior and by definition are congruent. Therefore,

75 = 4x + 7 and

68 = 4x so

x = 17

Answer:

[tex]ST = 6cm[/tex]

Step-by-step explanation:

Given

[tex]RS =2x[/tex]

[tex]ST = 3x[/tex]

[tex]RT = 10[/tex]

Required

Find ST

From the question, we understand that S is between R and T.

So:

[tex]RS + ST = RT[/tex]

Substitute known values

[tex]2x + 3x = 10[/tex]

[tex]5x =10[/tex]

Divide both sides by 5

[tex]x =2[/tex]

Given that:

[tex]ST = 3x[/tex]

[tex]ST = 3 * 2[/tex]

[tex]ST = 6cm[/tex]

Answer:

C or 6 centimeters

Step-by-step explanation:

Answer:

[tex]x = \frac{-(-2) \± \sqrt{(-2)^2 - 4*1*-3}}{2*1}[/tex]

Step-by-step explanation:

Given

[tex]0 = x^2 - 2x -3[/tex]

Required

The correct quadratic formula for the above

A quadratic equation is represented as:

[tex]ax^2 + bx + c = 0[/tex]

And the formula is:

[tex]x = \frac{-b \± \sqrt{b^2 - 4ac}}{2a}[/tex]

So, we have:

[tex]0 = x^2 - 2x -3[/tex]

Rewrite as:

[tex]x^2 - 2x - 3 = 0[/tex]

By comparison:

[tex]a= 1; b = -2; c = -3[/tex]

So, we have:

[tex]x = \frac{-b \± \sqrt{b^2 - 4ac}}{2a}[/tex]

[tex]x = \frac{-(-2) \± \sqrt{(-2)^2 - 4*1*-3}}{2*1}[/tex]