Work out a)4/5-1/5 b)9/11+5/11 c)3/4+1/8

x ∈ ( -π/2 + 2kπ ; π/2 + 2kπ) ; k ∈ Z

The domain of f(x)=ln(cosx) =  x ∈ ( -π/2 + 2kπ ; π/2 + 2kπ) ; k ∈ Z

Given function,

            f(x)=ln(cosx)

When cos(x) is positive, the domain is.

(cos(x)) > 0

since,

cos0 = 1

cos π/2 = 0

cos π = -1

cos 3π/2 = 0

cos 2π = 1

cos 3π/2 = 0

The values of cos(x) are then between -1 and 1.

That is domain of  f(x)=ln(cos x)

= cos x ∈ (0;1] -> x ∈ ( -π/2 + 2kπ ; π/2 + 2kπ) ; k ∈ Z

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The answer of the expression is 3 -4 and the sum is -1

Given,

In the figure, given a number line.

And, write an addition expression represented by number line. Then find the sum.

Now, According to the question:

To solve for an expression is:

Calculate the principle based on the number line .

We can figure out the formula .

= 3 - 4

[Moving to the right is positive and moving to the left is negative ]

To find the sum:

3 - 4 = -1

According to the figure , the end point of the movement is -1 and the answer is correct.

Hence, The answer of the expression is 3 -4 and the sum is -1

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Mix of paintings to obtain 20 cups of paint

there are 3X cups of yellow

there are 2Y cups of red

then find X and Y such that

3X + 2Y = 20

One possible solution is X = 2 Y= 7

2 cups yellow, and 7 cups red

Triangle is a right triangle because has a 90° angle

then we can use trigonometric ratios to find sides

if I use sine

whre alpha is the reference angle, O the opposite side to the angle and h the hypotenuse of the triangle

using 60° as reference angle

then solve for x

the value of side x is 6 units

If I use cosine

where alpha is the reference angle, a the adjacent side to the references angle and H the hypotenyse of the triangle

using 60° as reference angle

then solve for y

the value of side x is 2root3 units

Not true, true, true, true, true, true, true, not true, true, true

See explanation below

From the diagram, we noticed a change in lengths when all four vertex was dragged.

This means the 4 sides will not always be the same (congruent).

Not always true: The four sides are congruent

From both diagrams. we found the opposite sides are the same (congruent)

Always true: The opposite sides are congruent

Since they opposite sides arecongruent, this also means the opposite sides are parallel

Always true: opposite sides are parallel

All four angles from both diagrams are equal (congruent)

Always true: all four angles are congruent

SInce all four angles areequal, then the angles opposite each other will also be equal.

Always true: opposite angles are congruent

The diagonals of both shapes bisect each other. Hence, they are congruent.

Always true: Diagonals are congruent

Always true: diagonals bisect each other

Diagonals of a square (the shapethat has all sides equal ) intersect at a right right angle.

Diagonals of a rectangle ( the shape with opposite sides equal) don ot intersect at right angle.

Not always true: Diagonals intersect at a right angle

The interior angles were split by the two diagonals in both shapes.

Always true: Diagonals bisect interior angles

The sum of angles in a quadrilateral is equal to 360°

Both shapes are quadrilaterals. Hence, the sumof their angles is 360°.

Always true: sum of all angles equal 360°

The total cost of a CD player is $58.52

The equation which represents Jessica's income is 1900+50n.

Jessica's total income after selling 28 copies of History is Fun is $3300

Base salary of Jessica = $1900

The additional income per copy of History is Fun = $50

Let p represent her total pay (in dollars), and let n represent the number of copies of History is Fun she sells:

Formulating the equation we get the following:

Jessica's total pay = Base salary + Additional income per copy of History is Fun*Number of copies sold by Jessica

= 1900 + 50*n

Income, when she sells 28 copies of History, is Fun:

= 1900 + 50*28

= 1900 + 1400

= $3300

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ANSWER

y = 1.5 or 3/2

EXPLANATION

We are given that:

y = 3 when x = 2

From the question, we know that y and x have a proportional relationship.

This means that y and x change at the same rate:

=> y = kx

where k = constant of proportionality

y is 3 when x is 2:

3 = k * 2

=> k = 3/2 = 1.5

Therefore, when x = 1:

y = 1.5 * 1

y = 1.5 or 3/2

Answer:

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

Vertex form of quadratic equation:

Convert the given expression into vertex form by completing the square:

Answer:

[tex]f(x)=\left(x+\dfrac{1}{2}\right)^2+\dfrac{3}{4}[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{5.6 cm}\underline{Vertex form of a quadratic equation}\\\\$y=a(x-h)^2+k$\\\\where:\\ \phantom{ww}$\bullet$ $(h,k)$ is the vertex. \\ \phantom{ww}$\bullet$ $a$ is some constant.\\\end{minipage}}[/tex]

To find the vertex form of the given function, complete the square.

Given function:

[tex]f(x)=x^2+x+1[/tex]

Add and subtract the square of half the coefficient of the term in x:

[tex]\implies f(x)=x^2+x+\left(\dfrac{1}{2}\right)^2+1-\left(\dfrac{1}{2}\right)^2[/tex]

[tex]\implies f(x)=x^2+x+\dfrac{1}{4}+1-\dfrac{1}{4}[/tex]

[tex]\implies f(x)=x^2+x+\dfrac{1}{4}+\dfrac{3}{4}[/tex]

Factor the perfect square trinomial formed by the first three terms:

[tex]\implies f(x)=\left(x+\dfrac{1}{2}\right)^2+\dfrac{3}{4}[/tex]

Given: The following

To Determine: The number of edges

Solution:

The Euler's formula is given as

F + V = E + 2,

where F is the number of faces,

V the number of vertices, and

E the number of edges.

Substitute the given into the formula

Hence, the number of edges possessed by the polyhedron is 15

Let n be the smallest integer of the 3, then since all the numbers have to be even numbers, the other two numbers are of the form:

Since the sum of the numbers has to be 78, we can set the following equation:

Simplifying the above equation we get:

Answer:

Answer: -25

Step-by-step explanation: 8 - x = 17 ~ x=-9                         6*(-9)-22=-25

As shown in the figure :

The sum of the central angles = 360

so,

Solve the equation for x :

So, the answer is : x = 81

Answer:

100 ×10 =1000

Step-by-step explanation:

10% of 1000 is 100 that's the final answer if am wrong let me know

Given data:

The time taken by Amy is A=30 min.

The expression for the time taken by Julian is,

Substitute the given values in the above expression.

Thus, the time taken by Julian is 48 minutes.

The number is 6.

What is a number?

A number is a mathematical entity that may be used to count, measure, and name things. The natural numbers 1, 2, 3, 4, and so on are the original instances. Number words can be used to represent numbers in language. Individual numbers can be represented more generically by symbols known as numerals; for example, "5" is a numeral that represents the number five. Because only a small number of symbols can be memorized, fundamental numerals are often structured in a numeral system, which is a systematic method of representing any number. The most prevalent numeral system is the Hindu-Arabic numeral system, which allows any number to be represented using a combination of 10 fundamental numeric symbols known as digits.

Let the number be n.

Then according to que, n + (5+n) = 17

or, 2n = 17 - 5

or, n = 12/2 = 6

Hence the number is 6.

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Answer:

there is no solution because there aren't any nubmer of X to get linear equation

3X-3X= 12-7

0=5

there aren't solutions so it will be 0

Answer:

700 ml of Solution B was used

Step-by-step explanation:

Whenever we have unknowns the first thing to do is to represent the unknowns using variables, set up equations using given information and solve equations for the unknowns

Here the unknowns are volume of solution A and volume of solution B

Set up our variables as follows

Let x = volume of solution A used for mixing in ml

Let y = volume of solution B used for mixing in ml

We are given that volume of A used is 400 ml less than volume of B used

In math terms this can be represented as
y - x = 400

Or,

- x + y = 400       [1]

We are given the percentages of alcohol in A and B respectively
Since A contains 12% alcohol, the actual volume of alcohol in A
= 12% of  x ml

= 0.12x               (12% = 12/100 = 0.12)

Similarly alcohol by volume in B
= 0.20x

Total alcohol by volume if x of A and y of B are mixed is
0.12x + 0.20y

and we are given that this quantity is 176 ml

So we set up our second equation as
0.12x + 0.20y = 176      [2]

Using both equations we eliminate either the x or y terms to arrive at an equation involving only the other term.

Since the question asks us to determine only the volume of Solution B used, we should eliminate x term from both equations to get a single equation involving only the y term

Let's review the equations:
- x + y = 400    [1]

0.12x + 0.20y = 176  [2]

Make the coefficients of x the same :
Multiply [1] by 0.12

=> -0.12x + 0.12y = = 0.12 x 400
=> 0.12x + 0.12y = 48  [3]

Add [2] and [3] to eliminate the x term

     0.12x + 0.20y   =  176
+
     -0.12x + 0.12y    =   48

-----------------------------------------
          0x    + 0.32 y =  224

=> 0,32y = 224

Divide both sides by 0.32
==> 0.32y/0.32 = 224/0.32

==> y = 700

So 700 ml of Solution B was used

If we wanted to find volume of solution A used, subtract 400 from 700 to get 300 ml of A

The inequality for the given statement is  [tex]f-\frac{4}{7} \leq -\frac{9}{11}[/tex] .

By definition, any monotonically growing function can be applied to both sides of an inequality without destroying the relationship between the two (provided that both expressions are in the domain of that function).

The inequality for the given statement is  [tex]f-\frac{4}{7} \leq -\frac{9}{11}[/tex] .

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Answer:

the answer is D.

Answer:

600

Step-by-step explanation:

[tex]R(1)=400 \\ \\ R(2)=1000 \\ \\ R(2)-R(1)=600[/tex]

The mixed fraction can be 3 2/3 and the improper fraction would be 11/3 for the same mixed fraction.

A mixed fraction is one that is represented by its quotient and remainder. 2 1/3, for example, is a mixed fraction in which 2 is the quotient and 1 is the remainder. A mixed fraction is thus the product of a whole number and a proper fraction.

An improper fraction is one in which the numerator (top number) exceeds or equals the denominator (bottom number). Fractions like 651/14 are "incorrect." They are simply another way to write a mixed number.

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Let's define,

X := Total minutes it takes to fill the plane (with fuel)

Then,

Solving it for X, we get

This means that the vehicle takes 1 h 2 min to fill the plane. If the fuelling finished at 10:35, it began at

9:33.

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data:

polynomials

Step 02:

applications of polynomials:

The polynomials can be represented graphically, and are used in many economics and engineering problems. In economics they appear, for example, to model markets, showing how prices vary over time; how raising or lowering the price of a product affects its sales; or also in the calculation of taxes.

In forestry engineering, for example, we need geometry to calculate areas, but also polynomials in problems such as calculating how many trees we need to replant after having cut down an area of a forest.

Other uses of polynomials are the calculation of the trajectory of projectiles (they are parabolic trajectories), or in the calculation of orbits of satellites or rockets.

That is the full solution.

In order to find the minimum distance, first let's write a map with all positions and distances:

Now, let's write the total distance for the paths she can choose:

Therefore the minimum distance is 26 miles.

Answer:

Slope = 0.25

Step-by-step explanation:

m= -3 / -12 = -1 / -4 = 0.25

distance between x's = 12

distance between y's = 3

hope this helped thank you!

For any given angle in a right triangle that is not the 90° angle its sine is given by the quotient between its opposite side and the hypotenuse. For triangle ABC the hypotenuse is BC and the opposite side to theta is AB. Then the sine of this angle is given by the following equation:

Then the answer is the third option, 4/5.

Answer: [tex]9x^8 6^{9x/2}+\ln(6^{4.5}) \cdot 6^{4.5x}[/tex]

Step-by-step explanation:

[tex]w=\sqrt{(x^2 6^x)^9}=(x^2 6^x)^{9/2}=x^9 6^{9x/2}\\\\[/tex]

Using the product rule,

[tex]\frac{dw}{dx}=6^{9x/2}\frac{d}{dx} (x^9)+x^9 \frac{d}{dx}(6^{9x/2})\\\\=9x^8 6^{9x/2}+\ln(6^{4.5}) \cdot 6^{4.5x}[/tex]

Answer: -33

Step-by-step explanation: I guess he had like debt to pay lol but he would've had to have -33 dollars and added $84 to get a total of $51

Given that the radius r of a circle is written as a function of the area A with the following equation:

The domain of the above function is the area A of the circle.

This is because, in this context, the area is an independent and unique variable.

A is the input value.