The angle a lies between 0° and 90° and is such that
2 tan²a + sec²a = 5-4 tana

Show that

3 tan²a +4 tana -4 = 0
and hence find the exact value of tan a

Answer:

solve the following system of equations by using gauss elimination method

Answer:

sama sma tayi

Step-by-step explanation:

3×3()56(7)

Answer: Look at step by step

Step-by-step explanation:

(ax + b)(ax + b) = [tex]a^{2}[/tex] [tex]x^{2}[/tex]+ 2abx + [tex]b^{2}[/tex]

Substitute g into x

[tex]a^{2}[/tex] = 7

a = [tex]\sqrt{7}[/tex]

2ab = -3

b = -3 / (2 x [tex]\sqrt{7}[/tex])

[tex]b^{2}[/tex] = 9 / (4 x 7) = 9/28

So the term to be added to make a perfect square is 9/28

When factorized would get ([tex]\sqrt{7}[/tex]x - 3/2[tex]\sqrt{7}[/tex])([tex]\sqrt{7}[/tex]x - 3/2[tex]\sqrt{7}[/tex])

If this doesn't help, maybe it is best you ask your teacher instead of listening to a random person on the internet. Hope this helps though

Check the picture below.

The expressions which is equivalent to 2x + 3 would be 4x + 6.

Those expressions who might look different but their simplified forms are same expressions are called equivalent expressions. To derive equivalent expressions of some expression, we can either make it look more complex or simple. Usually, we simplify it.

We need to find the expressions which is equivalent to 2x + 3

Thus, we will Use the Distribute Property of Multiplication by multiplying the number outside the parenthesis with the numbers inside.

Let the expression be multiplying by 2 then;

2(2x + 3)

4x + 6

Hence, we can say that the expressions which is equivalent to 2x + 3 would be 4x + 6.

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Answer:

4 books a day

Step-by-step explanation:

$30 ÷7=4.28

so If you sell 4 books a day you get $30 I'n the end of the week

Answer:

AS shown in the purse

Step-by-step explanation:

A. The school attendance happens in the sixth week

B. A(13) ≈ 42$

meaning : In the Thirdteenth week. The student attendance rate is 425

C. A(x)=400 =) x = 10

in the tenth week.The student attendance rate is 400

D.in the fourth week the least attendance nce.

E. It has 450 students

The number of attendance increased to 450.

And the area was flat

Answer:4,3,8

Step-by-step explanation:

The statements that are true about the quadratic function and its graph include the following:

In Mathematics, the graph of any quadratic function or equation always forms a parabola because it is a u-shaped curve. For the given quadratic function, the graph is a upward parabola because the coefficient of x² is positive i.e when the value of "a" is greater than zero.

Next, we would determine the statements about the quadratic function and its graph that are true:

At point (-10, 82), we have:

f(x) = 1/5 x² – 5x + 12

f(x) = x²/5 – 5x + 12

f(-10) = -10²/5 – 5(-10) + 12

f(-10) = 82

At point (20, -8), we have:

f(x) = 1/5 x² – 5x + 12

f(x) = x²/5 – 5x + 12

f(20) = 20²/5 – 5(20) + 12

f(20) = -8

In conclusion, the graph of this quadratic function does not contain the point (0, 0) as shown in the image attached below.

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Complete Question:

Consider the quadratic function f(x) = 1/5 x² – 5x + 12. Which statements are true about the function and its graph? Select three options. The value of f(–10) = 82 The graph of the function is a parabola. The graph of the function opens down. The graph contains the point (20, –8). The graph contains the point (0, 0).

Solution

Given the graphs below

For the graph of figure A and B:

Figure A and figure B are congruent.

Hence, yes they are congruent.

The transformation that map figure A onto figure B is to rotate figure A clockwise 90° about the origin.

For the graph of C and D:

Figure C and figure D are congruent.

Hence, yes they are congruent.

The transformation that map figure C onto figure D is reflect figure C over the y-axis

The division of (4+5i) / (2-4i) is performed by multiplying the numerator and denominator by 2+4i and the result of the given expression is (-3/5) + (13/10) i

The given expression is

(4+5i) / (2-4i)

Here we have to divide the given complex number

First multiply both numerator and denominator by 2+4i

(4+5i) / (2-4i) × (2+4i) / (2+4i)

= [tex]\frac{(4+5i)(2+4i)}{(2-4i)(2+4i)}[/tex]

Multiply the terms in the numerator and denominator.

= [tex]\frac{8+16i+10i-20}{2^2+4^2}[/tex]

= (-12+26i) / 20

= (-12/20) + (26/20)i

Divide both numerator and denominator by common terms

= (-3/5) + (13/10)i

Hence, the division of (4+5i) / (2-4i) is performed by multiplying the numerator and denominator by 2+4i and the result of the given expression is (-3/5) + (13/10)i

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If wasps had eaten 20 apples then, 50 rotten apples were there and the rest of the apples were quality apples in the ratio of 4: 10: 20 respectively.

This is a problem from simple mathematical equations. We can solve this problem by following a few steps.

Let's consider x as the highest common factor of apples eaten by wasps, rotten and quality apples.

So, the number of apples eaten by wasps is, 4 × x = 4x

The number of rotten apples is, 10 × x = 10x

The number of quality apples is, 20 × x = 20x

As, we all know HCF of the numbers × ratio of numbers = The numbers

So, 4x = 20 as per the question.

Therefore, x = 5.

Now, we can write that the HCF is 5.

So, the number of rotten apples ≡ HCF × 10 = 5× 10 = 50.

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Answer:

[tex] \huge \sf \: x = 30[/tex]

Step-by-step explanation:

x/3 = 10

[tex] \frac{x}{3} = \frac{10}{1} [/tex]

Cross multiply

x = 30

Answer: 2.5 meters below sea level

Step-by-step explanation:

0.5 + 2 = 2.5

Hope this Helps!

The value of the variable x is 2 and length of the segment AB = 25 and length of segment BC is 14.

If a Line segment AC is given in a plane and B is some point between the points A and C on the line segment AC. Then two segments of the line segment ac are formed that are AB and BC. and length of AC is equal to the sum of lengths of AB and BC.

Then AC = AB +BC

Given that  B is point on the line segment AC

Length of AB line = 9x+7

Length of BC = -3x +20

Length of AC = 39

Using segment addition postulate,

we have AC = AB +BC

⇒ 39 = 9x+7 + (-3x) +20

⇒ 39 = 9x -3x +7+20

⇒39 = 6x +27

⇒ 39-27 = 6x

⇒ 12 = 6x

⇒ 2 = x

∴ Length of AB will be = 9(2) +7 = 25

∴ Length of BC will be = -3x + 20 = -3(2) +20 = 14

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The complete question is mentioned in the picture below:

The pair of vertical angles are

There are four angles made by the intersection of two lines. Those are ∠1, ∠2, ∠3 and ∠4

Vertical angles are the each of opposite angles formed when two lines meet each other at a point. So whenever two lines intersect each other four angles are formed and each set of opposite angles are called vertical angles

Here, two lines intersect each other and ∠1, ∠2, ∠3 and ∠4 are formed.

∠1,∠3 and ∠2,∠4 are the opposite angles

So the vertical angles are ∠1,∠3 and ∠2,∠4

Hence, the pair of vertical angles are

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The mean of the 10 sales amounts for store A is $40,000

The  least-squares regression line is

y=-3000+1.2x

where

x represents the sales amounts each day at store A

y represents the sales amounts each day at store B

we have

y=$45,000

substitute the value of y in the linear equation and solve for x

45000=-3000+1.2x

1.2x=48000

x=40000

therefore

The mean of the 10 sales amounts for store A is $40,000

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Answer:

-5 2

Step-by-step explanation:

       A mathematical statement indicating an order relationship between two numbers or algebraic expressions, such as greater than, greater than or equal to, less than, or less than or equal to.

|x+1/3| < 3/2.

Consider the center of the group of numbers that fulfill 2|x+1/3|3 to be x = -1/3.

The maximum value of this set is obtained by adding 3/2 to this -1/3:

-1/3 + 3/2, or -2/6 + 9/6, or 7/6.

The bottom limit of this solution set is obtained by subtracting 3/2 from this and then -1/3:

-1/3 - 3/2, or -2/6 - 9/6, or - 11/6.

The answer range is (7/6, -11/6).

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For the given function g(x) , the values at given points :

a. g(9) = 2

b. g(0) = -2.5

c. g(3) = -1

d. g(17) = 6

A function is a set of rules that assigns each element of a set a unique element of another set.

If f is a function and f(x) = x+2, then if we have to find value of at x= 1 ,put 1 in place of x,

Then f(1 ) = 1+2 =3

Given that a function g is such that

g(x) = (x -5)/2

This the values of the function g at given points:

a. g(9) = (9-5)/2 = 4/2 = 2

b. g(0) = (0-5)/2 = -5/2 = -2.5

c. g(3) = (3-5)/2 = -2/2 = -1

d. g(17 ) =  (17-5)/2 = 12/2 = 6

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(x-2) is not a factor of f([tex]x[/tex]) = [tex]3x^{4}-3x^{3}-9x^{2} +5x-2[/tex].

Remainder Theorem is an approach of Euclidean division of polynomials. According to this theorem, if we divide a polynomial P(x) by a factor ( x – a) that isn't essentially an element of the polynomial, you will find a smaller polynomial along with a remainder.

The Remainder Theorem: If (x-a) is a factor of the f(x) then f(a) = 0

Here,

f([tex]x[/tex]) = [tex]3x^{4}-3x^{3}-9x^{2} +5x-2[/tex]

substitute a = 2

[tex]f(2)=3(2^{4}) -3(2) ^{3}-9(2)^{2}+5(2)-2[/tex]

      = 48-24-36+10-2

      = 32-36

f(2)  = -4

f(2) [tex]\neq 0[/tex]

Hence, (x-2) is not a factor of f([tex]x[/tex]) = [tex]3x^{4}-3x^{3}-9x^{2} +5x-2[/tex].

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Explanation:

ASA = angle side angle

It refers to knowing two pairs of congruent angles, and a pair of congruent sides between the angles.

The angle markers tell us which angles are congruent. The shared overlapped sides are congruent (since any segment is congruent to itself; aka reflexive property).

ASA is slightly different from AAS in that the congruent sides for AAS are not between the congruent angles.

The coordinates of  Point O that is on MN and divides it such that MO:NO is 2:1 is; (10, 10)

We are given a line segment as MN with its' endpoint coordinates as;

M(4,14) and N(13,8)

Now, point O divides MN such that MO:NO is 2:1.

Now, the formula for the coordinate of the point that divides a line segment in the ratio a:b is;

(x, y) = (ax₂ + bx₁)/(a + b), (ay₂ + by₁)/(a + b)

Since point O is the point that divides the line segment in the ratio 2:1, we have;

O(x, y) = (2*13 + 1*4)/(2 + 1), (2*8 + 1*14)/(2 + 1)

O(x, y) = (30/3), (30/3)

O(x, y) = (10, 10)

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Answer:

D

Step-by-step explanation:

Look at the original figure that is complete.  The left side of the figure has a length of 3 units, the top of the figure has a length of 2 units and the bottom of the figure has a length of 3 units.  

If you multiply each of those lengths, you will have  9 (3x3), 6 (2x3) and 9 (3x3).  Do you see in the large figure to the right, that you have a left side of 9, a top of 6 and a bottom of 9?  That is what you original figure looks like if we multiply the sides by 3.  We are missing the right side point.  That is the point on the right side that points inward.

If you look at the original shape and start at the left had bottom corner, you would have to move up one and one to the right to plot the point to finish the figure.  So, for the new figure we would need to go up three and three to the right to put the last point.  That would be point D.

Answer:

130 m

Step-by-step explanation:

See the attached, pleasantly presented, worksheet.

Answer: 13 and 5= coeeficients, x and y = variables,  -2 and 3 =constants

Step-by-step explanation:

Answer: v = 2

Step-by-step explanation:

1. Distribute the 5 to the items within the parenthesis.

-3v + 5v - 10 = -6

2. Combine V terms and Isolate V from other terms.

2v = 4

3. Divide both sides by 2.

v = 2

The solution of the given conditions are;

a. Smallest possible value of 100 draws = 100

b. Largest possible value of 100 draws = 600

c. Average of the box = 3.6

d. The expected value of the sum = 360

e. Standard Error = 0.189

Given tickets: 5, 1, 2, 4, 3, and 6.

Value of n = 100

Question a :

Smallest possible value of 100 draws = 100 * (Least of the ticket values)

                                                              = 100 * 1

                                                              = 100

Question b :

Largest possible value of 100 draws = 100 * (Highest of the ticket values)

                                                             = 100 * 6

                                                             = 600

Question c :

Average of the box = (5+1+2+4+3+6) / 6

                                = 22/6

                                = 3.6

Question d :

The expected value of the sum = 100 * the Average of the box

                                                     = 100 * 3.6

                                                     = 360

Question e :

Given, SD = 1.89

Standard Error =?

Standard Error = SD/[tex]\sqrt{n}[/tex]

SE = 1.89/√100

    = 1.89 / 10

    = 0.189

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By using the table of values, we have the following:

A function can be defined as a mathematical expression which is used to define and represent the relationship that exists between two or more variables. This ultimately implies that, a function is typically used for mapping an input variable (x-value) to an output variable (y-value or f(x)).

In this exercise, you're required to determine the value of each function based on the value of x shown in the table above. Therefore, you would identify the input variable (x-value) that corresponds to the value of the output variable (y-value or f(x)) in the given table and vice-versa.

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