A student solved the equation sin2x/cos x = 2, 0 ≤ x ≤ pi, and got pi/2. What was the student's error?

[tex]\bold{\huge{\underline{ Solution \:1}}}[/tex]

If we look at the both the triangles then the

From above, we can conclude that :-

Both the triangles are similar by AA Similarity

Hence, Option A is correct.

[tex]\bold{\huge{\underline{ Solution \:2}}}[/tex]

Let consider the given triangle be ABC and the line that divides the triangle consider it as DE

So,

We have to find the value of x

In ΔABC, By using BPT theorem

That is,

[tex]\sf{\dfrac{ AD }{ AB }}{\sf{ = }}{\sf{\dfrac{DE}{BC}}}[/tex]

Subsitute the required values,

[tex]\sf{\dfrac{ 6 }{ 6 + 4 }}{\sf{ = }}{\sf{\dfrac{8}{x}}}[/tex]

[tex]\sf{\dfrac{ 6 }{ 10 }}{\sf{ = }}{\sf{\dfrac{8}{x}}}[/tex]

[tex]\sf{\dfrac{ 3 }{ 5 }}{\sf{ = }}{\sf{\dfrac{8}{x}}}[/tex]

[tex]{\sf{ x = 8{\times} }}{\sf{\dfrac{5}{3}}}[/tex]

[tex]{\sf{ x = }}{\sf{\dfrac{40}{3}}}[/tex]

[tex]{\sf{ x = 13}}{\sf{\dfrac{1}{3}}}[/tex]

Hence, Option C is correct

[tex]\bold{\huge{\underline{ Solution \:3}}}[/tex]

Here,

For x,

By using BPT theorem,

[tex]\sf{\dfrac{ AB }{ RS }}{\sf{ = }}{\sf{\dfrac{BC}{ST}}}[/tex]

Subsitute the required values,

[tex]\sf{\dfrac{ 2 }{ 4 }}{\sf{ = }}{\sf{\dfrac{x}{6}}}[/tex]

[tex]\sf{\dfrac{ 1 }{ 2 }}{\sf{ = }}{\sf{\dfrac{x}{6}}}[/tex]

[tex]\sf{ x = }{\sf{\dfrac{6}{2}}}[/tex]

[tex]\sf{ x = 3 }[/tex]

Thus, The value of x is 3

For y

Again by using BPT theorem,

[tex]\sf{\dfrac{ AB }{ RS }}{\sf{ = }}{\sf{\dfrac{AC}{RT}}}[/tex]

Subsitute the required values,

[tex]\sf{\dfrac{ 2 }{ 4 }}{\sf{ = }}{\sf{\dfrac{5}{y}}}[/tex]

[tex]\sf{\dfrac{ 1 }{ 2 }}{\sf{ = }}{\sf{\dfrac{5}{y}}}[/tex]

[tex]\sf{ y = 5{\times}2 }[/tex]

[tex]\sf{ y = 10 }[/tex]

Thus, The value of y is 10

Hence, Option A is correct.

Answer:

26 children

Step-by-step explanation:

346-8*40

346-320

26

Answer:

  4

Step-by-step explanation:

The proportional relationship can be described by the equation ...

  [tex]f=\dfrac{k}{\sqrt{g}}[/tex]

We can fill in the given values to find k:

  15 = k/√144 = k/12

  15·12 = k = 180 . . . . . . multiply by 12

Then for f = 90, we have ...

  90 = 180/√g

  1/2 = 1/√g . . . divide by 180; next multiply by 2√g and square both sides

  g = 2² = 4 . . . . the value of g when f=90

Answer:

30,000

Step-by-step explanation:

26,490 becomes 30,000

Answer:

(1)8 + (5)3=23 or if your in middle/elm use this 8x1 + 5x3=23       Step-by-step explanation:  if you do 8x1=8 5x3=15  

8+15=23

Answer:

The break even point is the production level at which total revenues for a product equal total expenses.

Step-by-step explanation:

Answer:

x= 13 degrees

Step-by-step explanation:

This is a 90 degree angle. We can create an equation to find x

68+x+9= 90

77+x= 90

-77     -77

x= 13 degrees

Hope this helps!

Answer:

x = 13

Step-by-step explanation:

The given angles are,

→ 68°

→ (x + 9)°

Now we have to,

→ Find the required value of x.

Forming the equation,

→ 68° + (x + 9)° = 90°

Then the value of x will be,

→ 68° + (x + 9)° = 90°

→ 68° + x + 9° = 90°

→ (68 + 9)° + x = 90°

→ 77° + x = 90°

→ x = 90° - 77°

→ [ x = 13 ]

Hence, the value of x is 13.

Answer:

24 ways

Step-by-step explanation:

4 things can be placed in 4! = 4 × 3 × 2 × 1 = 24 different ways

The number of different ways 4 brands can be arranged is 24.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Number of brands = 4

Number of different ways 4 brands can be arranged.
= 4!

= 4 x 3 x 2 x 1

= 24

Thus,

The number of different ways 4 brands can be arranged is 24.

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ2

9514 1404 393

Answer:

  9.  vertex: (1, -2)

  10.  dashed line, shaded inside, opens down, (neither point is a solution)

Step-by-step explanation:

The graph is attached. Either the graph or the equation will tell you the vertex is (1, -2). Since the leading coefficient is negative, the parabola opens downward. Since the comparison is "y < ( )", shading is below the boundary line, so shading is inside the parabola.

The point (0, 0) is outside the parabola, so is not a solution. The point (2, -3) is on the (dashed) boundary line, so is not a solution. (The boundary line is dashed because points on it are not part of the solution set.)

__

The inequality is written in vertex form:

  y < a(x -h)^2 +k . . . . . . . . has vertex (h, k)

The value of h in your inequality is 1, and the value of k is -2, so the vertex is (1, -2) as read from the inequality itself. (No graphing needed.)

Answer:

4/7 x 2 = 8/14

4/7 x 3 = 12/21

4/7 x 4 = 15/28

4/7 x 5 = 20/35

Step-by-step explanation:

4/7 x 2 = 8/14

4/7 x 3 = 12/21

4/7 x 4 = 15/28

4/7 x 5 = 20/35

Have an amazing day!!!

PLEASE RATE!!

Hello.

Please remember that equivalent means equal.

So we need to find 4 fractions that are equal to

[tex]\displaystyle\frac{4}{7}[/tex]

There are infinitely many fractions equal to the given fraction; we need just 4 of them.

First, let's multiply the numerator (4) and the denominator (7) times 2:

[tex]\displaystyle\frac{8}{14}[/tex]

Now, let's multiply the numerator and denominator of this fraction by 2:

[tex]\displaystyle\frac{16}{28}[/tex]

Multiply by 2 once more:

[tex]\displaystyle\frac{32}{56}[/tex]

I hope it helps.

Have an outstanding day. :)

[tex]\boxed{imperturbability}[/tex]

Answer:

Step-by-step explanation:

From the information given:

Neighbourhood A = 30  homes and the number increases by 20% each year

Neighbourhood B = 45  homes, and each year 3 new homes are built.

A.

The function representing the numbers of homes in  Neighbourhood A and B are as follows:

For neighbourhood A: f(x) = [tex]\mathbf{30 \times (1.2)^x}[/tex]

For neighbourhood B: f(x) =  45 + 3x

B.

After five years;

Neighbourhood A has = [tex]\mathbf{30 \times (1.2)^x}[/tex]

Neighbourhood A  = [tex]\mathbf{30 \times (1.2)^5}[/tex]

Neighbourhood A  =  74.65 homes

Neighbourhood B: =   45 + 3(5)

Neighbourhood B: =   45 + 15

Neighbourhood B: =   60 homes

C.

To determine how many years the number of homes are the same for neighbourhood A and B, we need to equate both together.

i.e.

[tex]\mathbf{30 \times (1.2)^x= 45 + 3x}[/tex]

[tex]\mathbf{ (1.2)^x= \dfrac{45 + 3x}{30}}[/tex]

[tex]\mathbf{ (0.4)^x= \dfrac{15 + x}{10}}[/tex]

x = 3.3

Thus, after 3.3 years, the number of homes will be the same.

Answer:

D.) QS ≅ NR

Step-by-step explanation:

Congruency between QS and NR can be assumed because the angles they make at points T and U are both right angles and the 6.7 seems to be indicating the same length of the lines (?)

Nonetheless, they look to be about equal in size and angle, so D.) QS ≅ NR is your best answer.

Answer:

12^2

Step-by-step explanation:

the pemas first you do the "(" and then what ever 12^2 is. i got the same question on mine and i got it correct. if this is correct write brainiest.

Answer:

[tex]2+\sqrt{3}[/tex]

Step-by-step explanation:

tan(-105°) is equal to 3.73205081, and [tex]2+\sqrt{3}[/tex] is equal to 3.73205081 as well.

Step-by-step explanation:

see pictures above or below

Answer:

29.92 m²

Step-by-step explanation:

Area of the rectangle = 5.5 * 4 = 22 m²

Radius of the circle = 5.5 m

Area of the sector of the circle = π*(5.5)² * 30/360 = 7.92 m²

Total area = 22 + 7.92 = 29.92 m²

Answer:

Distributive

Let's say each row sums to 15

If we had 3 rows, then the total sum would be 3*15 = 45

If we added all of the values in the 3x3 magic square, then we'd get 45 as well.

This is one example showing that

sum of all values = (number of rows)*(magic constant)

You can replace "rows" with columns to get the same idea, because each column also adds to the same magic constant. The diagonals are an exception since we only have two of them.

Answer:

42º

Step-by-step explanation:

The angle on a straight line is always equal to 180º.

So here we know that angles AEB, BEC and CED add up to 180º. Now we simply have to rearrange to find angles AEB, seeing as we know all the others.

180 - (BEC + CED) = AEB

180 - (48º + 90º)

= 180 - 138º

= 42º

:

a bottle has 1 3/4 liters. The first thing to do is convert this mixed fraction to an improper fraction. 1 equals 4/4, so 4/4+3/4=7/4, it says they want to take 6 1/4 glasses, we convert this to a fraction, we multiply 6*1/4=6/4 and this simply we have to subtract it from 7/4 which are the liters

7/4-6/4= 1/4

so we have 1/4 of a liter left over

una botella tiene 1 3/4 de litros. Lo primero que hay que hacer es convertir esta fracción mixta en fracción impropia. 1 equivale a 4/4, entonces 4/4+3/4=7/4, dice que quieren llevar 6 vasos de 1/4, esto lo convertimos en fracción, multiplicamos 6*1/4=6/4 y esto simplemente lo tenemos que restar a 7/4 que son los litros

7/4-6/4= 1/4

entonces nos sobra 1/4 de litro

Answer:

See below.

Step-by-step explanation:

2 x 36 = 72

3 x 18 = 54

6 x 12 = 72

8 x 8 = 64

A and C are the answers.

-hope it helps

Answer:

1. The total distance will be equal to 20 miles plus the remaining distance which would be obtained when you multiply the speed to time t. The equation would be written as follows:

120 = 20 + 50t

2. The minimum time would be 0 hours. The maximum time is when the total distance of 120 is fully covered.

t ≤ (120 - 20)/50

t ≤ 2 hours

Thus, the domain would be 0 < t ≤ 2.

Step-by-step explanation:

Answer:

1 First blank; f(1.5)=95    2 Blank; 1.5    3 Blank; 95

Step-by-step explanation:

you use the equation f(x)=50x+20 and put 1.5 in

f(1.5)=50(1.5)+20   =    f(1.5)=95

you get 95, and that is the number of miles

1.5 is number of hours

Answer:

here ,

origin means (0,0)

so ,

h and k are 0 and 0

and diameter ( d) is 4

r = d/2

using formula

(x-h)^2 +( y-k)^2 = r^2

(x-0)^2 +( y-0)^2= 2^2

x^2+y^2= 4 is the equation.

Answer:

The number you're looking for is 18.

Step-by-step explanation:

18/2=9

9 + 15 = 24

Therefore you get 18

Answer:

a

Step-by-step explanation:

Answer:

More than 30 items

Step-by-step explanation:

C(x)=300x+6,000

First, find c(x), the average cost function.

c(x)c(x)=C(x)x=300x+6,000x

The average cost function is shown below.

c(x)=300x+6,000x

We want the function c(x) to be less than 500.

c(x)<500

Substitute the rational expression for c(x).

300x+6,000x<500x≠0

Subtract 500 to get 0 on the right.

300x+,6000x−500<0

Find the LCD, and rewrite the left side as one quotient.

300x+6,000x−500xx−200x+6,000x<0<0

Factor the numerator to show all factors.

−200(x−30)x<0

Find the critical points when the numerator or denominator are equal to 0.

−200(x−30)−200≠0x−30x=0x=0=0=30

More than 30 items must be produced to keep the average cost below $500 per item.

Answer:

m=8

Step-by-step explanation:

4hours after time?

Hour. will be changed only

The time in 24hr format is 14:17 and in 12 hr format it's 2:17

Answer:

[tex]\huge\boxed{\bf\:14:17}[/tex]

Step-by-step explanation:

Given information,

Since the question doesn't provide whether [tex]10:17[/tex] is in Post Meridiem(P.M) or Ante Meridiem (A.M), we'll be using the 24-hour clock format.

In the 24-hour clock format, the clock goes from 12:01 to 23:59 each day. Each full rotation of the clock from this period shows that a day has passed by.

In the above case, if Maria starts her work by [tex]10:17[/tex], then,

Time Maria finishes her work by

[tex]=\sf\: 10:17 + (4 \: one-hour \:clock \: rotations)\\= \sf\:10:17 \rightarrow (11:17\rightarrow12:17\rightarrow13:17\rightarrow14:17)\\= \boxed{\bf\:14:17}[/tex]

[tex]\rule{150pt}{2pt}[/tex]

Answer:

  (0, -4)

Step-by-step explanation:

The y-intercept is the point on the line where it crosses the y-axis. That point has x-coordinate equal to zero. To find the y-intercept, set x=0 in the equation and solve for y:

  3y = -12

  y = -12/3 = -4

The y-intercept is -4. The point coordinates are (0, -4).

__

Additional comment

You may notice that in the standard form equation, ...

  ax +by = c

The x-intercept is c/a, and the y-intercept is c/b.

Answer:

$36

Step-by-step explanation:

27 x 2/1.50 = 36