prove that:tan²0-cot²0=sec²0(1-cot²0)

For the given systems of equations, we have that:

17. The solution is: x = 3, y = 4.

18. The company can afford to promote 2 engineers to level II.

19. The substitution method was used, as writing x as a function of y in the given equation was quite straight forward, as was replacing into the second equation to find y.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

For item 17, the system is:

Adding the equations, we can eliminate y and solve for x, hence:

7x = 21

x = 3.

Then the solution for y is given as follows:

3x + 2y = 17

3(3) + 2y = 17

2y = 8

y = 4.

For item 18, the variables are given as follows:

The company has 8 engineers, hence:

x + y = 8 -> x = 8 - y.

The company can afford to pay a total of $472,000 to the engineers, hence, considering the salaries(in thousands of dollars) of each:

56x + 68y = 472.

We want to solve for y, hence, since x = 8 - y:

56x + 68y = 472.

56(8 - y) + 68y = 472.

12y = 24.

y = 2.

The company can afford to promote 2 engineers to level II.

The substitution method was used, as writing x as a function of y in the given equation was quite straight forward, as was replacing into the second equation to find y.

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Answer:

This is my other account. I just needed 1+ answers togive brainliest for the other person. dont mind this

Step-by-step explanation:

Answer: ∠L = 102°

               ∠N = 78°

Step-by-step explanation:

Quadrilaterals can be classified into Parallelograms, Squares, Rectangles, and Rhombuses. Square, Rectangle, and Rhombus are also Parallelograms.

A quadrilateral is called a parallelogram, if both pairs of its opposite sides are parallel. AB ∥ DC and AD ∥ BC. So, ABCD is a parallelogram. A parallelogram having all sides equal, is called a rhombus.

Given data,

In □KLMN, side LM ∥ side KN, side KL ≅ side NM If ∠K = 78°

then find the measure of ∠L, and ∠N                          

                           side LM∥ side KN

Interior angles on the same side of the transversal are supplementary.

                    ∠K + ∠L = 180°

                    78° + ∠L = 180°

                     ∠L = 180° -  78°

                      ∠L = 102°

Construction:

Draw LP ∥ MN

So, LM ∥ KN and LP ∥ MN

PLMN is a parallelogram

                   MN ≅ LP

Now MN  = LP and MN = KL

                     LP = KL

              ∠LKP = ∠LPK = 78°

LP ∥ MN so,

           ∠MNP =  ∠LPK = 78° (corresponding angles are equal)

                               ∠L = 102°

                               ∠N = 78°

Therefore,

                             ∠L = 102°

                               ∠N = 78°.

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Answer:

x = 10

One angle is 13 and the other angle is 13

Step-by-step explanation:

Vertical angles have the same measurement, so set the angles equal to each other and solve for x.

2x - 7 = x + 3  Subtract x from both sides of the equation

x - 7 = 3  Add 7 to both sides of the equation

x = 10  Now use this to solve for both angles

2(10) - 7 =

20 - 7 =

13

x + 3

10 + 3 =

13

Answer:

From the Soldier's point of view, the American Civil War was not a continuous battle. Instead, it was long monotonous marches and long residency in camps punctuated by the terror and chaos of combat. When winter set in and the campaigning season came to a close, most Soldiers counted on a long, cold stay in a winter camp. The four log cabins at the center of the Army Heritage Trail represent the types of buildings which Soldiers in both the Union and the Confederate Armies spent the long dreary months of winter. The cabins are modeled after images from the USAHEC collection, including the Army of the Potomac's winter camp at Brandy Station and the Confederate camp at Centerville

Answer:

Step-by-step explanation:

The simplification by combining like terms of 5v-3(2 -v)  is 8v - 6.

According to the given question.

We have an expression5v - 3(2 - v).

As we know that, like terms are terms whose variables (and their exponents such as the 2 in x2) are the same.  when we combine like terms, such as 2x and 3x, we add or subtract their coefficients.

Since, we have to combine the like terms of the given expression

5v - 3(2 - v).

Here 5v, and 3v both are the like terms.

So, we add coeffcients of v to simplify the given expression.

Therefore, the simplification of 5v -3 (2 -v ) is given by

5v - 3(2 - v)

= 5v - 6  + 3v

= 8v - 6

Hence, the simplification by combining like terms of 5v - 3(2 - v) is 8v - 6.

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The value of the function is x = 3 is 11

Functions are expressions that consists of dependent and independent variables. This variables are represented using letters. For instance, f(x) is a function of x.

Given the function below

f(x) = 3(x-1)² + 2x - 7

Given that the value of x is 3, hence;

f(x) = 3(3-1)² + 2(3) - 7

Expand to have:

f(3) = 3(2)² + 2(3) - 7

f(3) = 3(4) + 6 - 7

f(3) = 12 - 1

f(3) = 11

Hence the value of the function is x = 3 is 11

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You will wait for 11 minutes

Find the number of minutes between 5:00am and 8:37am

60 mins in an hour.

8-5=3 hours

60x3=180+37=217 minutes

Divide 217 by 12 to see how many bus stops have already been made

217/12=18

18*12=216

217-216=1 minute

12-1=11 minutes

Therefore you will have to wait 11 minutes.

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Answer: 2, -4, -10. -16, ..., -6n+8  n=1, 2, 3, ...

Step-by-step explanation:

2, -4, -10, -16

a₁=2

a₂=-4

a₃=-10

a₄=-16

a₂-a₁=-4-2=-6

a₃-a₂=-10-(-4)=-6

a₄-a₃=-16-(-10)=-6

Hence, this is an arithmetic progression: a₁=2    d=-6

[tex]a_n=a₁+(n-1)d\\a_n=2+(n-1)(-6)\\a_n=2-6n+6\\a_n=-6n+8[/tex]

Answer:

17 1/

Step-by-step explanation:

first you have to find a common denominator, so you multiply 1/8 by 3 and get 3/24. then you add the two numbers getting 17 8/24 but you have to simplify it so it's 17 1/

Answer:

Step-by-step explanation:

15L

15000 divided by 1000

Answer:

15 liters

Step-by-step explanation:

1000=1

15000=x..... (cross multiply)

15000=1000x...... (divide both sides by 1000)

=15

We have proved that PA = 1/2 PB using the SAS rule or Side Angle Side rule.

A right angle triangle is given.

We have to prove that measure of the segment that joins the vertex of the right angle in a right triangle to the midpoint of the hypotenuse is one-half the measure of the hypotenuse.

What is a triangle ?

A triangle is a 3-sided shape. There are three sides and three angles in every triangle, some of which may be the same.

As per the question ;

Let's assume P is the midpoint of the hypotenuse of the right angle △ABC and it is right angled at B. Also , D is the midpoint of AB.

Now ;

Draw a line parallel to BC from P meeting B at O and join PB.

Here ;

In △PAD and △PBD

∠PDA =∠PDB = 90°

and

PD = PD common)

AD = DB (As D is mid point of AB)

So ;

△ PAD ≅ PBD

by SAS rule

and

PA = 1/2 PB

Thus , we have proved that PA = 1/2 PB using the SAS rule or Side Angle Side rule.

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Given the task content, the cost, y, of any number of puppies, x is modeled by the equation y = mx + b where cost of any number of puppies is $12

There are three major types of equation. Namely,

An equation can be solved through the following methods:

Given:

6 puppies costs $172

10 puppies costs $220

y = mx + b

Where,

172 = m(6) + b

220 = m(10) + b

172 = 6m + b

220 = 10m + b

48 = 4m

m = 48/4

m = 12

172 = 6m + b

172 = 6(12) + b

172 = 72 + b

172 - 72 = b

100 = b

Therefore, the cost of any number of puppies is $12

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Answer:120 yards

Step-by-step explanation:

10/5=2 2*60= 120 yards

The line created by 1st and 2nd is making the same angle with 3rd so all three will be colinear and 3rd is the midpoint of 1st and 2nd.

A graph is a diagram that shows the fluctuation of one variable in relation to one or more other variables.

In order to plot the graph, we need to find out y's values corresponding to x's value

After that, we need to substitute the values of x's and y's into the coordinate geometry.

Given the condition making a graph as shown below,

Now in ΔAOC and ΔBOC, the angle x is the same.

Distance AO = BO and CO is common side.

So both triangles will be congruent.

Since all corresponding side of two congruent triangles is the same.

So,

AC = BC hence C will be the midpoint of A and B.

Hence "The line created by 1st and 2nd is making the same angle with 3rd so all three will be colinear and 3rd is the midpoint of 1st and 2nd".

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The solution of the given equation y/y+1 = 2/3 is calculated as (y = 2).

In cross-multiplication, the numerator of the first fraction is multiplied by the denominator of the second fraction, and the numerator of the second fraction is multiplied by the denominator of the first fraction.

Now, the given equation is as follows;

y/y+1 = 2/3

Cross-multiplying the values;

3y = 2(y + 1)

3 y = 2y + 2

Bring the variable on the single side and constants on the other.

3y - 2y = 2

y = 2

Therefore, the solution of the given equation y/y+1 = 2/3 is computed as (y = 2).

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Answer:

Area = 792 m

Step-by-step explanation:

You can cut the polygon into 2 rectangles.
Subtracting 18 from 60 can give you the length of rectangle A, so 42 will be the new length for rectangle A.

Multiply 6 and 42 to get 252 for the area of rectangle A.

Multiply 18 and 30 to get 540 for the area of rectangle B.

(You multiply to find the area.)

Lastly you add both areas, 252 + 540, and the final result is:

Area = 792 m

Answer:

Step-by-step explanation:

Solve each equation. Check your answer.

2x - 5 = 17

2x = 12

x = 22 : 2

x = 11

------------------

check

2 * 11 - 5 = 17

22 - 5 = 17

17 = 17

the answer is good

The simplification of the given complex fraction 2/(x +y/3) is

6/(3x + y).

Accoring to the given question.

We have a complex fraction.

2/(x +y/3)

As we know that, complex fraction is a rational expression that has a fraction in its numerator, denominator or both.

For example:  (2/3)/(4/6)

So, the above complex fraction can be simplified by

(2/3) × (6/4)

= (2/3) ×  (3/2)

= 1

Thereofore, the siplification of the complex fraction 2/(x +y/3) is given by

[tex]\frac{2}{x + \frac{y}{3} }[/tex]

= [tex]\frac{2}{\frac{3x+y}{3} }[/tex]

= 2(3)/(3x + y)

= 6/(3x + y)

Hence, the simplification of the given complex fraction 2/(x +y/3) is

6/(3x + y).

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The simplified form of the given expression is 4.3⁹. The correct option is the third option (4.3)^9

From the question, we are to simplify the given expression

The given expression is

(4.3)(4.3^2)^4

This can be written as

(4.3)(4.3²)⁴

Applying the law of exponents, we get

(4.3)(4.3² ˣ ⁴)

(4.3)(4.3⁸)

Then,

4.3 × 4.3⁸

NOTE: 4.3 = 4.3¹

Thus,

4.3¹ × 4.3⁸

Applying the multiplication law of indices, we get

4.3¹ ⁺ ⁸

= 4.3⁹

Hence, the simplified form of the given expression is 4.3⁹. The correct option is the third option (4.3)^9

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Answer:

2m - 59 = Matt's savings

Step-by-step explanation:

520÷13=40..............

Answer:

The answer is C 40

Step-by-step explanation:

520/ 13 = 40

:) have a nice day

As per question, ‘Z’ is a standard normal random variable. And the value of ‘z’ is [tex]0.9878.[/tex]

According to the question, the area to left of ‘z’ and the equation can be written as:

[tex]P(Z > z) =0.01222[/tex]

Therefore,[tex]P(Z < z) =1-0.01222=0.9878[/tex]

Now the desired z-score corresponding to z-table graph = [tex]2.25[/tex]

What is Probability?

The term probability means the study of the occurrence or the outcomes of the event. It is the measurement of the events that occurred during events. And many uncertain events cannot be measured.

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Answer: Hercules has the fastest pace

Step-by-step explanation:

L=Leah. l=lee. H=Hercules

**Since the speeds are in fractions, make the denominators the same.

L=13/6

l=5/3

l=(5*2)/(3*2)

l=10/6

H=36/8

H=(36*6/8)/(8*6/8)

H=(216/8)/(48/8)

H=27/6

27/6 > 13/6 > 10/6

H>L>l

Hercules has the fastest pace

Answer:Your answer is the fourth one

Step-by-step explanation:Please give brainliest if right

43/49= 0.93

To express each fraction into its decimal we need to bring 100 at the denominator.

Fraction = numerator\denominator

For example :

1>    4\5

= 4*20\ 5* 20

      = 80\ 100

      = 0.80

2>   1\4

= 1 *20\ 4 *20

      = 20\ 100

       = 0.20

3>  49/50

= 49*2/50*2

= 98/100

=0.98

There are some numbers where it is not possible to make the denominator 100

So by the process of division method, we can convert the fraction into decimal form

43/46

0.93

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The length of an inscribed angle is half the length of the central angle. The circumscribed angle's measure is 180 degrees less the central angle's measure.

In geometry, an inscribed angle is the angle formed in the interior of a circle when two chords intersect on the circle. It is also the angle formed by two given points on a circle at a given point on the circle.

The length of an inscribed angle is half the length of the central angle. The circumscribed angle's measure is 180 degrees less the central angle's measure.

m ∠ABC =  m ∠ABD +  m ∠DBC  (∠ Addition Postulate)

m ∠ABD = 1/2 m(arc AD)    

m ∠DBC = 1/2 m(arc DC)  

(The measure of an inscribed ∠ whose side is diameter is half the measure of the intercepted arc (Case 1)).

m ∠ABC = 1/2 m(arc AD) + 1/2 m(arc DC) (Substitution)

m ∠ABC = 1/2 [m(arc AD) + m(arc DC)] (Factor)

m(arc AD) + m(arc DC) = m(arc AC) (Arc Addition Postulate)

m ∠ABC = 1/2 m(arc AC) (Substitution)

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Answer:

Step-by-step explanation:

the horizontal line is x and 8=x so the point has to be where 8 is in the horizontal line. Then y is 3 so the point is gonna be in the vertical line then you connect those two-points and you have your line.

Answer: C

Step-by-step explanation:

Since the inequalities for all 4 options are different, all you need to look at are the inequality signs.

For the line with a positive slope (bottom left to top right), the point it ends at is not filled in, so that point is not included meaning it is x > 1.

For the line with a negative slope (top left to bottom right), the point it ends at is filled in, so that point is included meaning it is x [tex]\leq[/tex] 1.

C. is the only one that has these inequalities.