The sum of the measures of the angles of a triangle is 180°. The middle-sized angle measures 3° more than 2 times the smallest angle. The middle-sized angle measures 109° less than the largest angle. Find the measure of each angle.​

Answer:

is this tye required answer

The value of (1+tanx)(1-tanx)+sec²x is 0 and the value of [tex]\frac{sec^{2}-4 }{sec+2}[/tex] is [tex]sec\theta \ -2[/tex].

Given that, (1+tanx)(1-tanx)+sec²x.

Now, (1-tan²x)+sec²x

=1-tan²x+sec²x

=1+sec²x-tan²x

=1-1=0

Now, evaluate [tex]\frac{sec^{2}-4 }{sec+2}[/tex]

[tex]=\frac{sec^{2} \theta \ -2^{2} }{sec\theta \ +2} =\frac{(sec \theta \ +2)(sec \theta \ -2)}{sec \theta \ +2}[/tex] (∵a²-b²=(a+b)(a-b))

[tex]=sec \theta \ -2[/tex]

Hence, the value of (1+tanx)(1-tanx)+sec²x is 0 and the value of [tex]\frac{sec^{2}-4 }{sec+2}[/tex] is [tex]sec\theta \ -2[/tex].

To learn more about trigonometric identities visit:

https://brainly.com/question/12537661.

#SPJ1

In 2.44 seconds lindsey be 30 feet in the air.

A quadratic equation is a second-order polynomial equation in a single variable x, ax²+bx+c=0. with a ≠ 0 .

Given:

y= -16x²+33x+45

If the height is 30 feet.

30= -16x²+33x+45

-16x²+33x+45-30=0

-16x²+33x+15=0

16x²-33x-15=0

Solving the quadratic equation

x=-b±√b²-4ac/ 2a

x= 33 ± √2049/32

x= (33+ √2049)/32    and x=33-√2049/32

x=2.44 and -0.3833

Learn more quadratic equation here:

https://brainly.com/question/2263981

#SPJ1

Now, ORQ is a straight angle and RS its bisector.

It means:

So, ∠ORS and ∠QRS are supplementary.

We also have ray RP, that divides the angles ORQ and QRS.

It gives us one more pair of supplementary angles:

Since ∠QRS is right angle, its parts are forming a pair of complementary angles:

The sum of the unknown angle and 33 degrees are supplementary. The measure of x is 147 degrees

The sum of the unknown angle and 33 degrees are supplementary to have:

x + 33 = 180

Subtract 33 from both sides

x + 33 - 33 = 180 - 33

x = 180 - 33

x = 147degrees

Hence the measure of x is 147 degrees

Learn more on supplementary angles here: https://brainly.com/question/12919120

#SPJ1

Answer:

Step-by-step explanation:

x + 33° = 180°

reason :( they are cointerior angle )

x = 180° - 33°

x = 147°

Answer: a

Step-by-step explanation:

[tex]\left(\frac{f}{g} \right)(x)=\frac{f(x)}{g(x)}=\frac{\sqrt{x^{2}-1}}{\sqrt{x-1}}}=\sqrt{\frac{x^{2}-1}{x-1}}=\sqrt{\frac{(x-1)(x+1)}{x-1}}=\boxed{\sqrt{x+1}}[/tex]

One can determine the number of roots by seeing the degree of the given polynomial.

The number of roots can be determined by just seeing the highest power of the given equation.

1) for the equation  x-4=0

here, the highest power of the equation is one. So, it will have one root.

A polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtract multiplication, on,  and non-negative integer exponentiation of variables.

Let's check it by simplifying x-4=0  which implies x=4

Hence, the equation has only one root namely x = 4.

2) Consider a quadratic equation,

10t^2-t-3=0

here, the highest power of the equation is two. So, it will have two roots.

Let's check it by simplifying using the middle term splitting method,

10t^2+5t-6t-3=0

5t(2t+1)-3(2t+1)=0

(5t-3)(2t+1)=0

t=-3/5 or t=-1/2

Thus, the equation has two roots.

Hence, one can determine the number of roots by seeing the degree of the given polynomial.

To learn more about the polynomial visit:

https://brainly.com/question/2833285

#SPJ1

Step-by-step explanation:

the answer is C) 8x^5y - 6x^4y^2

pls like and follow.

hope you understand as well

Using a piece-wise function, the representation of the graph is given as follows:

Walking uphill for 3 hours and downhill for 1 hour.

A piece-wise function is a function that has multiple definitions, depending on the input.

In this problem, we have that:

Hence the meaning of the graph is:

Walking uphill for 3 hours and downhill for 1 hour.

More can be learned about piece-wise functions at https://brainly.com/question/27262465

#SPJ1

Step-by-step explanation:

It is given that Joe paid 14.00 for a board game this is 70% of the original price what is the original price.

Let the original price of board game be

X.

x * 70/100 = 14

x * 7/10 = 14

Multiply both sides by 10.

7x = 140

Divide both sides by 7.

x = 20

Answer:

c because have great day

Answer:

Inversión en una circunferencia es una transformación que conserva la magnitud de los ángulos pero cada ángulo se transforma en un ángulo de signo opuesto . El sentido o dirección de cada ángulo se invierte. La inversión en una circunferencia es una transformación anti-conforme(como la reflexión en una recta).

Step-by-step explanation:

El sentido o dirección de cada ángulo se invierte. La inversión en una circunferencia es una transformación anti-conforme(como la reflexión en una recta).

Answer:

inversion transformations are a natural extension of Poincaré transformations to include all conformal one-to-one transformations on coordinate space-time.

Answer:

the median is 9

Explanation

Finding the median is easy, all you need to do is put the numbers in numeric order and the one that's in the middle of the numbers is the median

9 , 9 , 9 , 4 , 9 , 1 , 10  =   1, 4, 9, (9), 9, 9, 10

                                              (median)

[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]

Given the Ages of students: 9,9,9,4,9,1,10. State the median

[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]

[tex]\boxed{\begin{minipage}{7cm} Before finding the median, we\\ need to arrange \\ our data from least to greatest. \end{minipage}}[/tex]

Thus,

[tex]\bf{1,4,9,9,9,9,10}[/tex].

[tex]\fbox{The median is the number in the middle.}[/tex]

Thus,

[tex]\bf{9}[/tex]

[tex]\cline{1-2}[/tex]

[tex]\bf{Result:}[/tex]

            [tex]\bf{=9}[/tex]

[tex]\begin{tabular}{c | 1} Data Parameter & What to Do \\ \cline{1-2} \\ Mean & Add all the numbers and divide by how many there are \\ Median & Arrange the numbers from least to greatest and take the number \\ & in the middle. Take the mean of the 2 numbers in the middle \\ & if there's an even amount of numbers \\ Mode & The number that occurs the most \\ Range & The largest number minus the smallest number \\ Minimum & The smallest value \\ Maximum & The largest value \end{tabular}[/tex]

[tex]\LARGE\boxed{\bf{aesthetic\not1\theta\ell}}[/tex]

A team of 3 boys and 3 girls be selected from 5 boys and 4 girls in 40 ways

The selections are given as:

3 boys from 5 boys

3 girls from 4 girls

Each selection is calculated using:

[tex]^nC_r = \frac{n!}{(n- r)!r!}[/tex]

So, we have:

[tex]Ways = ^5C_3 * ^4C_3[/tex]

Apply the combination formula

[tex]Ways = \frac{5!}{2!3!} * \frac{4!}{1!3!}[/tex]

Expand

[tex]Ways = \frac{5 * 4 * 3!}{2 * 3!} * \frac{4 * 3!}{1 * 3!}[/tex]

Simplify

Ways = 5 * 2 * 4

Evaluate

Ways =40

Hence, the number of ways is 40

Read more about combination at:

https://brainly.com/question/11732255

#SPJ1

Answer:

nth term: 0.5n² + 2.5n + 3

Explanation:

pattern 1 = 6 bowls

pattern 2 = 10 bowls

pattern 3 = 15 bowls

pattern 4 = 21 bowls

First difference:

Second difference:

This is not an arithmetic nor a geometric sequence.

Solve:

2a  = 2nd difference

2a = 1

a = 1/2 or 0.5

===================

3a + b = 1st difference

3a + b = 4

b = 4 - 3(1/2)

b = 2.5

====================

a + b + c = first term

1/2 + 2.5 + c = 6

c = 3

Quadratic nth term:

0.5n² + 2.5n + 3

Answer:

y = -1.5x

How to build equation?

Given points: (0, 0), (2, -3)

Find slope:

[tex]\sf slope: \dfrac{y_2 - y_1}{x_2- x_1} \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points[/tex]

[tex]\rightarrow \sf slope \ (m) = \dfrac{-3-0}{2-0} = -1.5[/tex]

Then find equation:

[tex]y-y_1 = m(x - x_1)[/tex]

[tex]y - 0 = -1.5(x -0)[/tex]

[tex]y = -1.5x[/tex]

Answer:

y = (-3/2)x

Step-by-step explanation:

I am going to answer this question in slope-intercept form, which is y = mx + b (m is the slope, b is the y-intercept). The question already gives us the y-intercept, or the point at which the graph crosses the y-axis. It is (0, 0). Now, all we have to do is find the slope, which we can do using the following formula:

[tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1}}[/tex]

In this formula, (x1, y1) and (x2, y2) are two points that are given to us [the first point is (0,0) and the second point is (2,-3). We can solve for the slope by plugging in:

[tex]m=\frac{-3-0}{2-0}=\frac{-3}{2}[/tex]

Now that we have m and b, we can plug into slope-intercept form to get our equation: y = (-3/2)x + 0 or y = (-3/2)x

Answer:

[tex]sin\theta=\dfrac{1}{2}[/tex]

=============

Use identity [tex]sin^2\theta+cos^2\theta=1[/tex] :

Answer:

Options (1), (5), and (6)

Step-by-step explanation:

See attached image

Three pairs of measurements which are possible side lengths for the triangle are,

1.  AB = 4, BC = 4√3

5 AB = 7, AC = 14.

6. AB = 11, BC = 11√3

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Now, We get;

The sides of this triangles has lengths in the ratio x : √3x : 2x

where 2x is the hypotenuse.

Now, When C = 30,  the side AB is the small leg (=x).

When B = 90, the hypotenuse is AC ( =2x).

When A =  60, the larger leg is BC (=√3x).

1.  AB = 4, BC = 4√3 :- Are possible legs.

5 AB = 7, AC = 14. :-  AB = small leg, AC = hypotenuse.

6. AB = 11, BC = 11√3:-   AB = small, BC = larger leg.

Learn more about the triangle visit;

brainly.com/question/1058720

#SPJ5

The maximum height of the projectile fired from the ground with an upward speed of 245 m/s is 3001.25 m

An equation is an expression that shows the relationship between two or more variables and numbers.

The maximum height (H) of a projectile is given as:

H = u²/2g

Where u is the initial speed = 145 m/s, g is the acceleration due to gravity = 10 m/s²

H = 245²/ 2(10) = 3001.25 m

The maximum height of the projectile fired from the ground with an upward speed of 245 m/s is 3001.25 m

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

The solution to the system of equations is x = -1 and y = 4

The system of equations is given as:

5x + 2y = 3

2x + 3y = 10

Multiply the first equation by 2 and the second by 5.

10x + 4y = 6

10x + 15y= 50

Subtract the above equations

10x - 10x + 4y - 15y = 6 - 50

This gives

-11y = -44

Divide by -11

y = 4

Substitute y = 4 in 5x + 2y = 3

5x + 2 * 4 = 3

This gives

5x + 8 = 3

Subtract 8 from both sides

5x = -5

Divide by 5

x = -1

Hence, the solution to the system of equations is x = -1 and y = 4

Read more about system of equations at:

https://brainly.com/question/12895249

#SPJ1

The percentage depreciation is 27 % .

What is percentage ?

Given ,

         from 4500 to 3285 is depreciation value of a motor bike.

So,

         =      [tex]\frac{( 4500 - 3285 )} {4500} * 100[/tex]

         =       [tex]\frac{1215}{4500} * 100\\[/tex]

           = [tex]\frac{121500}{4500}[/tex]

          = 27 %

Therefore, The percentage depreciation is 27 % .

Learn more about percentage depreciation brainly.com/question/13894858

#SPJ4

Limit of x approaches two from the left of f of x: 3. Limit of x approaches two from the right of f of x: - 1 (negative 1)

If limits exist, we can take limits of the function, where x tends to -∞ or ∞, and that limiting value will be the value the function will approach.

In order to find the limit as x approaches two from the left of f of x:

Lim x→2- f(x) = ?

According to the graph, when x approaches two from the left (x<2), the function approaches 3:

Lim x→2- f(x) = 3

IN order to find the limit as x approaches two from the right of f of x:

Lim x→2+ f(x) = ?

According to the graph, when x approaches two from the right (x>3), the function approaches -1:

Lim x→2+ f(x) = - 1

Learn more about one-sided limits here:

https://brainly.com/question/23625942

#SPJ1

If the function is translated 4 units down, the resulting function will be

y = x - 4 while the vertical stretch by 3units will be y = 3(x-4)

Transformation of function is a way of changing the position of a line or curve on an xy place.

Given the equation of a line as shown;

y = x (This will serve as the parent function)

If the function is translated 4 units down, the resulting function will be

y = x - 4. If the resulting function is stretched by a factor of 3, the final function will be y = 3(x - 4)

Learn more on translation here: https://brainly.com/question/12861087

#SPJ1

Answer:

true

Step-by-step explanation:

Since their wise or intelligent guess

Considering her change, it is found that she will donate $0.28 to the animal shelter.

The amount of change is given by the subtraction of the total paid and the price of the products.

In this problem, the price of the products bought is given by:

$15.74 + $3.98 = $19.72

She paid $20, hence the change is given by:

$20 - $19.72 = $0.28.

More can be learned about the amount of change in a purchase at https://brainly.com/question/10866253

#SPJ1

The equation representing the cost in The Free Press is 12 + 5d.

The equation representing the cost in The Free Press will be:

= 12 + (5 × d)

= 12 + 5d

The equation representing the cost in The Banner will be:

= 8 × d

= 8d

The table of value for Free Press will be:

1st day = 12

2nd day = 17

3rd day = 22

4th day = 27

5th day = 32

The table of value for the Banner will be:

1st day = 8

2nd day = 16

3rd day = 24

4th day = 32

5th day = 40

The newspaper that will be used to run the advertisement for the first day is Free Press since it's cheaper.

The newspaper that will be used to run the advertisement for twelve days will be:

Free press = 12 + 5d

= 12 + 5(12)

= 12 + 60 = 72

The banner = 8d = 8 × 12 = 96

Therefore, for 12 days, Free Press is cheaper.

Learn more about equations on:

brainly.com/question/2972832

#SPJ1

Answer:

22x^2-9x+32

Step-by-step explanation:

(21x² - 6x +14) + (x²-3x+18)

To add, we need to combine like terms

21x^2+x^2     -6x-3x    +14+18

22x^2-9x+32

Answer:

22x² - 9x + 32

Step-by-step explanation:

(21x² - 6x +14) + (x²-3x+18)

Get rid of the parenthesis:

21x² - 6x + 14 + x² - 3x + 18

Group like terms:

22x² - 9x + 32

the answer is

X=5

y=3

hope you like it

Answer:

(2 + StartRoot 3 EndRoot) – (1 + StartRoot 3 EndRoot)i

Step-by-step explanation:

I'm 100% sure! ^^

Answer:

B: (2 + StartRoot 3 EndRoot) – (1 + StartRoot 3 EndRoot)i

Step-by-step explanation:

Took the quiz