3) Solve the following system by elimination:
3x – 2y = 2
5x - 5y = 10
I

Answer:

Step-by-step explanation:

When you list the trigonometic ratios for both acute angles in a right triangle, you notice some interesting developments.

Let's concentrate on sine and cosine:

Observation from the table above: notice1

In a right triangle, the sine of one acute angle, A, equals the cosine of the other acute angle, B.

If ∠A and ∠B are the acute angles of a right triangle,

sin A = cos B

Since the measures of these acute angles of a right triangle add to 90º, we know these acute angles are complementary. ∠A is the complement of ∠B, and ∠B is the complement of ∠A.

If we write, m∠B = 90º - m∠A    (or m∠A = 90º - m∠B ), and we substitute into the original observation, we have:

      notice4

If θ is substituted for m∠A , we establish the following relationship between sine and cosine:

sincosrule

The sine of any acute angle is equal to the cosine of its complement.

The cosine of any acute angle is equal to the sine of its complement.

Sine and cosine are called "cofunctions", where the sine (or cosine) function

of any acute angle equals its cofunction of the angle's complement.

FYI: What about tangent?

Yes, there is a "relationship" regarding the tangent of the two acute angles (A and B) in a right triangle. It is not, however, the same type of relationship that exists between sine and cosine.

The tangent of ∠A is the reciprocal (flip over) of the tangent of ∠B.

The angles being used in the following examples are acute angles.

ex1

If sin 30º = ½ and cos θ = ½,

find θ.  Solution: Since both trig functions = ½,

30º and θ must be complementary.

θ = 60º

ex2

If sin(3x + 10)º = cos(x + 24)º,

find x.  Solution: In order for the sine and cosine to be equal, the angles must be complementary.

3x + 10 + x + 24 = 90

4x + 34 = 90

4x = 56

x = 14

ex3

If sin(15º) = 0.26 and

cos (15º) = 0.97,

find sin(75º) and the cos(75º).  Solution: The sine of an angle and the cosine of its complement are equal.

15º and 75º are complementary.

sin(75º) = cos(15º) = 0.97

cos(75º) = sin(15º) = 0.26

ex4

In right ΔABC, m∠C = 90º,

sin A = x + 0.1 and cos B = 2x - 0.4. Find x.  Solution: If A and B are the acute angles of a right triangle, sin A = cos B.

x + 0.1 = 2x - 0.4

0.5 = x

Answer:

13/45

Step-by-step explanation:

9 times 5 is 45 and 15 times 3 is also 45 after 5 times 5 is 25 and 4 times 3 is 12

25/45- 12/45= 13/45

(because u only have to subtract 12 from 25)

Answer:

Level 2:

45 x 45 = 2025

28 x 28 = 784

2025 + 784 = 2809

(sqrt)2809 = 53

53 units

Level 3:

(Start by graphing the coordinates)

Your shape should have one leg of 14 units, and one leg of 8 units.

14 x 14 = 196

8 x 8 = 64

196 + 64 = 260

(sqrt)260 = 16.1245155

(rounded to nearest tenth)

16.1 units

I`m not sure about the other two though, sorry :/

3. Using the Pythagorean theorem, x = 53 in.

4. 6, 9, and 11 does not form a right triangle because they are not a Pythagorean triple. i.e. 11² ≠ 9² + 6².

5. Using the distance formula, AB = 16.1 units

7. Height of the Pyramid using the Pythagorean theorem is: h = 5.2 units.

8. Length of diagonal = 10.2 units.

If c is the hypotenuse of a right triangle with a and b as its legs, the Pythagorean theorem states that c² = a² + b².

Diagonal (d) = √(l² + h² + w²)

l = length

w = width

h = height

3. Find x using the Pythagorean theorem:

x = √(45² + 28²)

x = 53 in.

4. 6, 9, and 11 does not form a right triangle because they are not a Pythagorean triple. i.e. 11² ≠ 9² + 6².

5. Using the distance formula, find AB:

AB = √(5−(−3))² + (6−(−8))²

AB = √260

AB = 16.1 units

7. Height of the Pyramid using the Pythagorean theorem:

h = √(6² - 3²)

h = 5.2 units.

8. Diagonal of the Rectangular Prism:

Length of diagonal = √(l² + h² + w²) = √(8² + 5² + 4²)

Length of diagonal = 10.2 units.

Learn more about Pythagorean Theorem on:

https://brainly.com/question/21332040

Answer:

So a batch is 5/8

There are THREE 3/4th cups of flour in the cupboard.

So 3 three fourths so basically
3/4 * 3 = 9/4 or

3/4 + 3/4 + 3/4 = 9/4

9/4 and each batch is 5/8.
9/4 ÷ 5/8 = 72/20 or 3 1/10

3 batches of cookies.

Answer:

Write the equation of the line parallel to x = 5 that passes through (2, 7)

The sum of forty-five and a number n is 46.1, and the expression that can represent this can be written "45+n" where the value of n is 1.1

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The statement that is given to us is" the sum of forty-five and a number", therefore, the expression that will represent this can be written as,

45 + n,

Now, if the value of n is 1.1. Then the sum will be,

[tex]45+n\\\\=45+1.1\\\\=46.1[/tex]

Hence, the sum of forty-five and a number n is 46.1, and the expression that can represent this can be written "45+n" where the value of n is 1.1

Learn more about Expression:

https://brainly.com/question/13947055

Answer:

x = 24°

Step-by-step explanation:

What do the sum of all angles in a triangle add up to?

First, let's find the missing angle of the big triangle (the angle next to 111°).

Now, we can find the value of x given the smaller triangle's angle.

Therefore, x = 24°.

Have a lovely rest of your day/night, and good luck with your assignments! ♡

Answer:

24 degrees

Step-by-step explanation:

Right corner angle

= 180 - 94 - 41

= 180 - 135

= 45 degrees

angle x

= 180 - 111 - 45

= 180 - 156

= 24 degrees

Answer:

No chart is provided

Step-by-step explanation:

Answer

The anwser is B

Step-by-step explanation:

I did this test as well earlier this year

Equation x=3 represents a line perpendicular to the x-axis. Therefore, the correct answer is option A.

The general equation of a straight line is y=mx+c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis.

here, we have,

A) x=3

Graph the line using the slope and y-intercept, or two points.

Slope: Undefined

y-intercept: No y-intercept

The coordinate points are (3, 0) and (3, 1).

B) Graph the line using the slope and y-intercept, or two points.

Slope: 1

y-intercept: (0,0)

The coordinate points are (0, 0) and (1, 1)

C) x=y

Graph the line using the slope and y-intercept, or two points.

Slope: 1

y-intercept: (0,0)

The coordinate points are (0, 0) and (1, 1)

D) x=-3y

Graph the line using the slope and y-intercept, or two points.

Slope: -1/3

y-intercept: (0,0)

The coordinate points are (0, 0) and (-3, 1)

Therefore, option A is the correct answer.

To learn more about the the equation of a line visit:

brainly.com/question/2564656.

#SPJ7

Answer:

103,140.82, or 103,141 since it asks for the whole number.

Step-by-step explanation:

[tex]45000(1.05)^17[/tex]

the 17 is supposed to be the whole power, not sure why the 7 is lower. but since she is making 45k a year, at a 5% increase in wages per year, this is how we would set up the equation. the number, multiplied by the percentage which is written as 1.05, since it is an increase, not a decrease, then we set that to the power of 17 since it is 17 years.

hope this helps, please mark as brainlest.

360 - 120 = 240

240 / 21 = 11.4

11.4cm

Answer:

The amount per pound would be:
$2.40

Step-by-step explanation:

720 divided by 3 = 240
We can then conclude that:
$7.20 divided by 3 = $2.40


Have a great rest of your day
#TheWizzer

Answer:

0.15 dollars, of 15 cents (I believe)

Step-by-step explanation:

3 pounds, 16 oz per pound is 48 oz. 7.20 divided by 48 oz is 0.15, which should be equal to 15 cents. Hope this helps :)

Answer:

Step-by-step explanation:

Factorize

Answer:

y = - [tex]\frac{2}{3}[/tex] x + 8

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Given

2x + 3y = 24 ( subtract 2x from both sides )

3y = - 2x + 24 ( divide all terms by 3 )

y = - [tex]\frac{2}{3}[/tex] x + 8 ← in slope- intercept form

The equation 2x+3y=24 in the slope-intercept form can be written as [tex]y = -\frac{2}{3}x+8[/tex]

From the question,

We are to write the given equation in the slope-intercept form

The slope-intercept form of an equation of straight line is written as

y = mx +c

To write the equation, 2x+3y=24, in the slope-intercept form, we will make y the subject of the equation

[tex]2x+3y=24[/tex]

First, subtract 2x from both sides of the equation

That is,

[tex]2x -2x +3y = 24 -2x[/tex]

This becomes

[tex]3y = 24 -2x[/tex]

Now, divide both sides by 3

[tex]\frac{3y}{3} =\frac{24-2x}{3}[/tex]

∴ [tex]y = \frac{24}{3}-\frac{2x}{3}[/tex]

[tex]y = 8-\frac{2}{3}x[/tex]

In the slope-intercept form, we get

[tex]y = -\frac{2}{3}x+8[/tex]

Hence, the equation 2x+3y=24 in the slope-intercept form can be written as [tex]y = -\frac{2}{3}x+8[/tex]

Learn more here: https://brainly.com/question/20076300

Answer:

Step-by-step explanation:

total surface area = 584 m2

lateral surface area = 504 m2

top surface area = 40 m2

bottom surface area = 40 m2

Answer:

subtract? this is put together weird maybe add a screenshot so we know what to solve

Step-by-step explanation:

Answer:

36

Step-by-step explanation:

21+15 is 36 so there for u just add 15 to 21 giving you 36

Answer:

40%

Step-by-step explanation:

Answer:

3 pounds and 8 ounces

Step-by-step explanation:

1 pound is 16 ounces, 1/2 pound is 8 ounces.

If you need further help, let me know!

-profparis

Answer:

The dimensions on paper are 1.992ft by 5.976ft with a scale factor of 7.53

Step-by-step explanation:

The first step will be to find the diagonal of the rea life mural.

We can use Pythagoras' Theorem to do this.

Diagonal = [tex]\sqrt{15^2 +45^2 }[/tex] =47.43 feet.

Now we have the real-life diagonal, we will now relate the diagonal of the painting outside with the one on paper. We can do this by dividing the two diagonals.

This will be 47.43 / 6.3 units = 7.53.

The scale factor is 7.53

To get the dimensions of the length and the breadth on paper, we divide the outside dimensions by the scale factor.

This will be

Length = 15/ 7.53 = 1.992

Breadth = 45/7.53 = 5.976

Therefore, the dimensions on paper are 1.992ft by 5.976ft with a scale factor of 7.53

Answer:

Q1: No solutions

Q2: x=2, y=-2

Q3: x=1, y=4

Step-by-step explanation:

Q1: Found out 0y = 18 which is impossible therefore no solution.

Q2:

In the first equation: [tex]2x - 4y = 12[/tex]

Let's express x in terms of y by changing the subject. Follow my steps.

[tex]2x = 12+4y[/tex]

[tex]x = \frac{12+4y}{2}[/tex]

Now let's put the x above into the second equation: [tex]-14x-4y=-20[/tex]

It becomes: [tex]-14(\frac{12+4y}{2})-4y=-20[/tex]. Follow my steps.

[tex]-7(12+4y)=-20+4y[/tex]

[tex]-84-28y=-20+4y[/tex]

[tex]-32y=64[/tex]

[tex]y=-2[/tex]

Put y = -2 into the first equation:

[tex]2x-4(-2)=12[/tex]

[tex]2x+8=12[/tex]

[tex]2x=12-8[/tex]

[tex]2x=4[/tex]

[tex]x=2[/tex]

Q3:

Multiply the first equation by 3 and the second equation by 7, so that both are 21x.

1st equation:
[tex]3(7x-3y)=3(-5)[/tex]
[tex]21x-9y=-15[/tex]

2nd equation:

[tex]7(3x+2y) = 7(11)[/tex]

[tex]21x+14y = 77[/tex]

We can now substract the 2nd equation with the 1st equation so that both 21x cancels out and only the variable y remains.

[tex]21x-9y-(21x+14y)=-15-77[/tex]

[tex]21x-9y-21x-14y=-92[/tex]

[tex]-23y=-92[/tex]

[tex]y=4[/tex]

Put y = 4 into the second equation to find x.

[tex]3x+2(4)=11[/tex]

[tex]3x+8=11[/tex]

[tex]3x=11-8[/tex]

[tex]3x = 3[/tex]

[tex]x=1[/tex]

Answer:

23

Step-by-step explanation:

To get to 17 degrees, you need to add 6 to -6 to get to 0.

And to get to 17 from 0, you need to add 17.

So then you add 6 and 17 together.

6+17=23

The vertex form of the function g(x)=40x-4x² is g(x) = 4(x + 5)² - 100, where the vertex lies at (-5, -100).

The  general equation of a parabola is given as,

y = a(x-h)² + k

where,

(h, k) are the coordinates of the vertex of the parabola in form (x, y);

a defines how narrower is the parabola, and the "-" or "+" that the parabola will open up or down.

As we want to write a function g(x) = 40x + 4x² in vertex form, and we know that the vertex form of a parabola, with vertex at (h,k) is written as,

[tex]f(x) = a(x-h)^2 + k[/tex]

Also, the algebraic identity  [tex](x + a)^2[/tex] is written as,

[tex](x + a)^2 = x^2 + 2ax + a^2[/tex],

Therefore, [tex]x^2 + 2ax[/tex] can be written as

[tex]x^2 + 2ax = (x + a)^2 - a^2[/tex]

Further, we try to write the g(x) in the vertex form it can be written as,

[tex]\begin{aligned}g(x) &= 4x^2 + 40x\\\\ &= 4[x^2 + 10x]\\\\ &= 4[(x + 5)^2 - 5^2]\\\\ &= 4(x + 5)^2 - 100\\\end{aligned}[/tex]

Hence, the vertex form of the function g(x)=40x-4x² is g(x) = 4(x + 5)² - 100, where the vertex lies at (-5, -100).

Learn more about Parabola:

https://brainly.com/question/8495268

Answer:

5 times a number subtracted from another number divided by 3.

Step-by-step explanation:

Answer: 2016 in^2

Step-by-step explanation:

3) Let's start with the taller rectangular prism. The height is 24", the width is 12", and the length is 12". The smaller rectangular prism is actually a cube because the height, width, and length are all 12". Just as a refresher, the surface area of an object is only the area of each outside face. For rectangular prisms, the surface area is 2(lh+wh+lw) (l=length, h=height, w=width). And for cubes, the surface area is 6s^2, where s is the side. 2(12*24+12*24+12*12) is equal to 1440 inches squared, however, half of one face is covered. This is the longest face shaded in dark green: 24" times 12", but because only half is showing, it is 24*12 divided by 2. This is equal to 144"; and you must subtract this from the entire surface area to account for that covered space. 1440-144 is 1296 inches squared. The cube is (12*12)(6) which is 864. But one whole side is covered, meaning you need to subtract 144 to have the surface area be 720 inches squared. 1296 plus 720 is 2016 inches squared. Decounting the half a side from the prism and one full side from the cube, there are only 10 and a half sides shown.

Hope this helps :)

Answer:

Step-by-step explanation:

Simplify the following (12+7)-(2-23)

(12 + 7) - (2 - 23) =

19 - (-21) =

19 + 21 =

40

Answer:

-5.5

Step-by-step explanation:

Answer:

-5. 9

Step-by-step explanation:

[tex] \sqrt[3]{ - 205} = - 5.8963...... = approximately - 5.9[/tex]