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Answer:

  (-1.570796, 0.666239) ∪ (1.570796, 2.475353)

Step-by-step explanation:

A graphing calculator can give you the numerical values that limit the intervals of the solution. The attachment shows this solution.

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We can multiply by cos(x) and solve the resulting quadratic inequalities. Two cases arise:

  tan(x) -cos(x) < 0 . . . . . . subtract cos(x)

  sin(x) -cos(x)² < 0 . . . . . . . for cos(x) > 0

  sin(x) -cos(x)² > 0 . . . . . . . for cos(x) < 0 (inequality is reversed)

Replacing cos(x)² with (1 -sin(x)²) gives quadratic equations in sin(x). (We're using <> to mean "could be greater than; could be less than, depending on cos(x)".)

  sin(x) -(1 -sin(x)²) <> 0

  sin(x)² +sin(x) -1 <> 0 . . . . put in standard form

  (sin(x)² +sin(x) +1/4) -1 -1/4 <> 0 . . . . complete the square

  (sin(x) +1/2)² -5/4 <> 0 . . . . . write as a square

  ((sin(x) +1/2)-√(5/4))·((sin(x) +1/2) +√(5/4)) <> 0 . . . . factor

Note that the second factor is always positive, so it has no impact on the intervals of solution.

__

The zeros of the first factor are located at ...

  sin(x) = 1/2(-1 +√5)

  x ≈ 0.666239 radians, and π - 0.666239 radians ≈ 2.475353 radians

The sine function will be positive between these angle values.

__

However, the intervals of solution to the inequality depend on the cosine function. Effectively, the solution space is where  (sin(x) +(1-√5)/2) and cos(x) have opposite signs.

The cosine function is positive for -π/2 < x < π/2, so one of the intervals of solution will be ...

  -π/2 < x < arcsin((√5 -1)/2), approximately (-1.570796, 0.666239)

The cosine function is negative for -π < x < -π/2 and for π/2 < x < π. The other interval of solution will be ...

  π/2 < x < (π -arcsin((√5 -1)/2)), approximately (1.570796, 2.475353)

_____

Additional comment

In the above, we have used α=arcsin( ) to mean the values of angle in the principal branch: -π/2 ≤ α ≤ π/2. That is why we have to subtract it from π to find the other end of the interval of interest.

Answer:

98.75 tickets

Step-by-step explanation:

395/4 = 98.75 (adult tickets)

check answer:

98.75 x 3= 296.25

296.25 + 98.75 = 395

hope this helps:)

[tex]\frac{1}{2} (n+8) + \frac{3}{4} [/tex]

[tex]\frac{1(n+8)}{2} + \frac{3}{4} [/tex]

[tex]\frac{n+8}{2} + \frac{3}{4} [/tex]

[tex]\frac{2(n+8)}{4} + \frac{3}{4} [/tex]

[tex]\frac{2(n+8) + 3}{4} [/tex]

[tex]\frac{2n + 16 +3}{4} [/tex]

[tex] \frac{2n + 19}{4} [/tex]

Answer: 6x^2

Step-by-step explanation:

Answer:

Step-by-step explanation:

Trignomentary - real life problem.

We can find the height of the tower without measuring it. WE can find the height  of the tower when we know,

1.  A point which at a distance 'x' from the foot of the tower.

2. The angle of elevation is known  

Eg: A tower stands vertically on the ground. From a point on the ground which is 15 m away from the foot of the tower, the angle of elevation  of the top of the tower is 60°. Find the height of the tower.

AB - tower

We know the adjacent side of 60°  and we have to fing the opposite side of 60°. So, we have to use

[tex]\sf \ Tan \ 60^\circ=\dfrac{Opposite \ side \ of \ 60^\circ}{Adjacent \ side \ of \ 60^\circ}[/tex]

[tex]1.732 = \dfrac{AB}{BC}\\\\1.732=\dfrac{AB}{15}\\\\1.732*15=AB[/tex]

AB = 25.98 m

Height of the tower ≈ 26 m

Answer: 5miles

Step-by-step explanation: Convert 8800yards to miles. Divide by 1760

Answer:

460

Step-by-step explanation:

23+23=46. 20+20=40. 46+40=86. 23×20= 460

Answer:

blm is the correct answer

Step-by-step explanation:

The number of the two-slice sandwich will be 10.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that there are 20 slices of bread in a loaf. The number of the sandwiches will be calculated as below:-

Number of the sandwiches = 20 / 2 = 10 sandwitch

Therefore, the number of the two-slice sandwich will be 10.

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Answer:

64 textbooks

Step-by-step explanation:

the first two teachers had 21 students each that's 21+21=42

the other teacher had 22 students so apparently all the textbooks handed to the students are,21+21+22=64

Answer:

top answer is 'c' and the bottom is 'a'

Answer:

3

Step-by-step explanation:

Answer:

>

Step-by-step explanation:

1 mile =1760 yards

so 3 mile= 1760x3=5280yard

so, 5280 yards is more than 5000 yards

I think it’s -2(-2x + 3y) but I am unsure because I got -4 instead of 4

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

40,000 x 3^1 = 120,000

120,000 x 3 = 360,000

40,000 x 3^2 = 360,000

Therefore, it is the second option, or B.

Answer:

The answer is 10 and i know because im smart

Step-by-step explanation:

because im smart

Answer:

24

Step-by-step explanation:

add 8 and 12 and 4 and its 24

Answer:

[tex]c + c \: + 40 + 12 = 100 \\ 2c + 52 = 100 \\ 2c = 100 - 52 \\ 2c = 48 \\ c = \frac{48}{2} \\ c = 24cm[/tex]

Answer: 24

Explanation: 12+40 is 52, perimeter is adding up all the sides. since perimeter is 100, then you have to see what numbers you add to get 100. 100-52 is 48. since there are 2 sides, you divide 48 by 2, which is 24.

I hope this is helpful xx

Answer:

302.5 miles

Step-by-step explanation:

using the relationship

D = ST ( D is distance, S is speed and T is time in hours )

given he  drove 140 miles in 2 [tex]\frac{1}{2}[/tex] = 2.5 hours , then

S = [tex]\frac{D}{T}[/tex] = [tex]\frac{140}{2.5}[/tex] = 56 mph

the next part of his journe is 6mph slower, that is 50 mph for 3 [tex]\frac{1}{4}[/tex] = 3.25 hours, then

D = ST = 50 × 3.25 = 162.5 miles

total distance travelled = 140 + 162.5 = 302.5 miles

y=1/3x

A linear function is a relationship that has a degree of 1 and a constant slope. Linear functions are written in the form of y=mx+b, where m is the slope and b is the y-intercept.

Y-intercept

The y-intercept of a function is the y-value when x=0. In this case, we are given all of the coordinates. One of the coordinates is (0,0), which means that when x=0, y=0. So, the y-intercept is 0.

Slope

The slope is the change in y over the change in x. Using the coordinates we can find the slope through the formula [tex]\frac{y_{2} -y_{1} }{x_{2}- x_{1} }[/tex]. It will be easiest to use the coordinates (0,0) and (3,1). Plug these points into the formula to find the slope.

This means that the slope is 1/3.

Answer

Using the information found in the previous sections we can create the final answer, y=1/3x+0, or just y=1/3x.

Answer:

a rotation followed by a translation

Step-by-step explanation:

i did it

The rotation is followed by a translation.

We have given that,

a glide reflection

a rotation followed by a translation

a rotation followed by a reflection

reflection followed by a translation

We have to determine the tessellation below, and what transformation(s) maps Brick A onto Brick B.

Rotation is the circular movement of an object around an axis of rotation. A three-dimensional object may have an infinite number of rotation axes.

Therefore the rotation is followed by a translation.

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Answer:

A.

Divide each dimension by scale factor of 5

Big Δ dimensions : Small Δ dimensions

35 : 7

30 : 6

15 : 3

a = 7 in

b = 6 in

c = 3 in

Hope this helps and God bless!

Answer:

Option 1

Step-by-step explanation:

Answer:

it is A the meidian is the middle number in a orderd set

Answer:

22

Step-by-step explanation:

Reflection on x axis

P(x, y) =P'(x,-y)

Therefore, D(2,3 ) =D'(2,-3)

Answer:

8:18

Step-by-step explanation:

The approximate area of the sketch for the new lamp is : A = 70 [tex]in^{2}[/tex]

A trapezium is one pair of parallel sides and one pair of non-parallel sides.

from the diagram we can extract the necessary information needed to find the area of the trapezium.

for the first trapezium (lamp shade)

a = 4 in

b = 6 in

h = 6 in

[tex]A_{1}[/tex] = [tex]\frac{a + b}{2}[/tex] * h

[tex]A_{1}[/tex] = [tex]\frac{4 + 6}{2}[/tex] * 6

[tex]A_{1}[/tex] = [tex]\frac{10}{2}[/tex] * 6

[tex]A_{1}[/tex] = 5 * 6 = 30[tex]in^{2}[/tex]

For the area of the second trapezium (lamp base)

a = 4 in

b = 6 in

h = 4 in

[tex]A_{2}[/tex]  = [tex]\frac{a + b}{2}[/tex] * h

[tex]A_{2}[/tex]  = [tex]\frac{4 + 6}{2}[/tex] * 4

[tex]A_{2}[/tex]  = [tex]\frac{10}{2}[/tex] * 4

[tex]A_{2}[/tex]  = 5 * 4 = 20[tex]in^{2}[/tex]

For the area of the third trapezium (lamp base)

a = 6 in

b = 4 in

h = 4 in

[tex]A_{3}[/tex]  =  [tex]\frac{a + b}{2}[/tex] * h

[tex]A_{3}[/tex]  =  [tex]\frac{6 + 4}{2}[/tex] * 4

[tex]A_{3}[/tex]  =  [tex]\frac{10}{2}[/tex] * 4

[tex]A_{3}[/tex]  =  5 * 4 = 20[tex]in^{2}[/tex]

The total Area of the trapezium (lamp)

A = [tex]A_{1}[/tex]  +  [tex]A_{2}[/tex]  +  [tex]A_{3}[/tex]

A = 30 + 20 + 20

A = 70 [tex]in^{2}[/tex]

Inconclusion The approximate area of the sketch for the new lamp is : A = 70 [tex]in^{2}[/tex]

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Answer:

Step-by-step explanation:

20, 30, 70

Answer:

[tex]y=3(x-50)[/tex]

Please Give Brainliest if this is correct!

(Which I am pretty confident in...)

Answer:

5

Step-by-step explanation:

70% is 0.7, multiply 0.7×50=35 points on Jenny's test. Hannah scored 0.8×50=40 points on the test. Subtract 40-35 for the answer of 5

Answer:

We can see that the number in the middle is 36. Hence the median of the data set is 36 the median of a data set is the number placed at the middle of a data after rearrangement either in ascending order or descending order.

Given the dataset 10, 15, 27, 33, 33, 36, 42, 47, 45, 56, 78

Step-by-step explanation:

36

Answer:

36

Step-by-step explanation:

10, 15, 27, 33, 33, 36, 42, 47, 45, 56, 78

The median is the middle number of the set

There are 11 data points so the middle is 11/2 = 5.5

Round up so the middle is the 6th data point

10, 15, 27, 33, 33,     36,       42, 47, 45, 56, 78

The median is 36