Select the correct answer.
What is the domain of y= cos (x)

a.2pie
b. [-1,1]
c. (-infinity, infinity)
d. [0,infinity)

The expression a⁷- a is divisible by 7 if a is an integer.

Given that,

7 divides a^7−a

To find that if a is an integer, then 7 divides a^7 -a or a⁷- a is divisible by the number 7

We can write, where k is an integer

a^7−a=7k

a(a^6−1)=7k

Now if a=k then

a^6−1=7

a^6=8

and a=±1.414 so a^7−a=9.898

If a is not equal to k then

a(a^6−1)=a(a^3+1)(a^3−1)=7k

since a(a+1)(a−1) is the not product of 3 consecutive integers, the expression is divisible by 7.

Hence, The expression a⁷- a is divisible by 7 if a is an integer.

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The greatest number of rectangles 6cm×4cm that can be cut from a metal that measure 16cm×20cm is 13 rectangles.

A rectangle is a plane shape that has pair of opposite sides equala and parallel.

To calculate the greatest number of rectangles, we use the formula below.

Formula:

Where:

Ferom  the question,

Given:

Substitute these values into equation 1

Hence, the greatest number of rectangles is 13 rectangles.

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Out of all the given situations, all are fair gambles,

Any gamble is considered to be a fair gamble if the expectation of it is 0. Here, gamble means any situation which has a probabilistic uncertainty attached to it.

The expectation of any game is

E(X) = ∑xp(x)

In the first case

The probability to get a had or tails on flipping a coin is 1/2

Hence the expectation will be

E(X) = 0.5 X 10  +  0.5 X (-10)

= 5 - 5

= 0

Hence this is a fair gamble

In the next gamble, two coins are tosses

The probability to get 2 head is 1/4

The probability to get 2 tails is 1/4

The probability to get one head and one tail is 1/2

Hence,

E(X) = 0.25 X 10  +  0.25 X (-10)  +  0.5 X 0

= 2.5 - 2.5

= 0

Hence this too is a fair gamble

Here,it is given that

Probability              Gain

0.5                            $100

0.25                       - $200

0.25                           $0

Therefore,

E(X) = 0.5 X 100  +  0.25 X (-200)  +  0.25 X 0

= 50  - 50

= 0

Hence, all are fair gambles.

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Correct Question

which of the following is a fair gamble?

one coin toss: win $10 if heads, lose $10 if tails.

two coin tosses: win $10 if two heads, lose $10 if two tails, and no change of wealth otherwise.

a game in which you win $100 with a probability of 50%, lose $200 with a probability of 25%, and gain nothing with a probability of 25%.

all of the above are fair gambles.

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The distance around the bases in meters will be 27.432 meters.

How many meters are in 1 feet?

In one feet there are 0.3048 meters.

Given is a baseball field measures 90 feet between each base.

Distance between each base in feet = [d] = 90 feet

The distance between each base in meters will be -

D [meters] = 90 x 1 ft

D [meters] = 90 x 0.3048 meters

D [meters] = 27.432 meters

Therefore, the distance around the bases in meters will be 27.432 meters.

The equation of the graph is a straight line written in slope-intercept form as y = -33.3x + 450. When Misty travelled for 9 hours, he drove 150.3 miles.

The general equation of a straight line is y = mx + c, where m is the slope of the line and c is the y-intercept. It is the most common form of the equation of a straight line that is used in geometry. The equation of a straight line can be written in different forms such as point-slope form, slope-intercept form, general form, standard form, etc. A straight line is a two-dimensional geometrical entity that extends on both its ends till infinity.

The equation of a straight line is a mathematical equation that gives the relation between the coordinate points lying on that straight line. It can be written in different forms and tells the slope, x-intercept, and y-intercept of the line. The most commonly used forms of the equation of straight line are y = mx + c and ax + by = c. Some other forms are point-slope form, slope-intercept form, general form, standard form, etc. Let us go through the formula for the equation of a straight line

13: The equation of graph in slope-intercept form

But for this case, we will represent our equation using point-slope formula which is y = mx + c

Let's find the slope of the line.

To do this, we will pick any two points and solve for the slope.

A = (0, 450), B = (6, 250)

The equation of slope of a line is given as

m = y₂ - y₁ / x₂ - x₁

m = 250 - 450 / 6 - 0

m = -200/6

m = -33.3

The y-intercept is the point which the line touches the y-axis or y-plane and in this case, the y-intercept is 450.

The equation of the line is y = -33.3x + 450

14: If he has been travelling for 9 hours, how many miles left ?

Using the equation y = -33.3x + 450; put x = 9

y = -33.3(9) + 450

y = 150.3 miles

Misty has 150.3 miles left.

15: If there are 50 miles in the trip left, how many hours has Misty travelled.

Using the equation y = -33.3x + 450

50 = -33.3x + 450

-400 = -33.3x

x = 12 hours

Misty has approximately travelled 12 hours.

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Using x only once in the inequality, the inequality expression is 8 > x > 2

The mathematical statement is given as

8 is greater than x, and x is greater than 2.

In mathematical expressions, greater than can be represented as >

So, we have the following representations

8 > x, and x > 2

Next, we combine the inequality expressions

This becomes

8 > x > 2

Hence, the inequality expression is 8 > x > 2

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The transformation rule used to transform Triangle PQR to P'Q'R' is; (x, y) → (⁵/₂x, ⁵/₂y)

We are told that the triangle P'Q'R' has been transformed from triangle PQR.

Now, the coordinates of triangle PQR are;

P(-1, 1)

Q(2, 0)

R(-1, -2)

The coordinates of the transformed triangle P'Q'R' are;

P(-5/2, 5/2)

Q(5, 0)

R(-5/2, -5)

Thus, this is clear that the transformation rule used is;

(x, y) → (⁵/₂x, ⁵/₂y)

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The answers are:

Q1 = x < -1

Q2 = x ≤ 2

Q3 = x > -2

Q4 = x > 0

Code = 4776

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal = ≤

Greater than and equal = ≥

We have,

Solve for x.

3 < -5x + 2x

3 < -3x

Divide both sides by 3.

1 < -x

Change sign.

x < -1

18 ≥ 5x  + 4x

18 ≥ 9x

Divide both sides by 9.

2 ≥ x

-6x - 16 < 2x

Add 16 on both sides.

-6x < 2x + 16
Subtract 2x on both sides.

-6x - 2x < 16

-8x < 16

Divide both sides by 8.

-x < 2

Change sign.

x > -2

(1/2)x - 4 > -4

1/2x > -4 + 4

1/2x > 0

x > 0

Code = 4776

Thus,

The answers are:

Q1 = x < -1

Q2 = x ≤ 2

Q3 = x > -2

Q4 = x > 0

Code = 4776

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The total cookies she baked altogether is 28 cookies

A word problem is a math problem written out as a short story or scenario. Basically, it describes a realistic problem and asks you to imagine how you would solve it using math.

Half of the cookies is placed on the table, 6 is eaten by my dog, half is eaten by my brother and I ate the last 4, the means my brother ate 4 cookies too.

Therefore the total cookies put on the plate is 6+4+4= 14cookies

half of all the cookies were put in the plate,

therefore the total cookies made is 14×2= 28cookies.

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The image of the given point after the translation will be (-5,1).

The given point is (0,2).

We have to find out the image of the given point after a translation left 5 units and up to 1 units.

Since it is given that there is a translation left 5 units, starting from point (0,2), the image will be on the negative side of x-axis at point 3.

Similarly, it is given that there is also a translation up to 1 units. This implies starting from point (0,2), the image will be on the positive side of y-axis at point 1.

So, the image of the given point after the translation will be (-3,1).

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Answer:

-6n-4+3<17

-6n-1<17

-6n<17+1

-6n<18

DIVIDE BOTH SIDE WITH THE COEFFICIENT OF n WHICH IS (-6)

-6n =18

-6 -6

n= -3

Answer:

Step-by-step explanation:

1.3

10/13=1.3

Answer:

[tex]\boxed{\sf \boxed{\sf x=\cfrac{13}{10}}\:or\: \boxed{\sf x=1.3}}[/tex]

Step-by-step explanation:

[tex]\sf 10x= 13[/tex]

Divide both sides by 10:-

[tex]\sf \cfrac{10x}{10}=\cfrac{13}{10}[/tex]

Simplify:-

[tex]\sf x=\cfrac{13}{10}[/tex]

____________________

Hope this helps!

Have a great day!

The amount to be invested today in order to have $600 in 20 years is $189.66.

When an account pays interest that is compounded quarterly, it means that both the amount invested and the interest that has already been earned increases in value four times in a year.

In order to determine the amount to be invested today, determine the present value of $600.

The formula for calculating present value:

P = FV / [(1 + r)^nm]

Where:

P = 600 / [(1.0145)^80] = $189.66

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Answer: it is 200

Step-by-step explanation:

The standard form of the equation y = -2/3 x - 1 is 2x + 3y = -3.

The standard form for linear equations in two variables is Ax + By = C. Where,

The equation is represented in slope intercept form. So, let' represent it in standard form.

Therefore,

y = - 2 / 3 x - 1

add 2 / 3 x to both sides of the equation

y = - 2 / 3 x - 1

y + 2 / 3 x  = - 2 / 3 x + 2 / 3 x - 1

y + 2 / 3 x  = - 1

Let's multiply all through by 3 to eliminate the fraction

y + 2 / 3 x  = - 1

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

Therefore, the standard form equation is 2x + 3y = -3

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The required simplified solution of the given subtraction is 16/25. Option D is correct.

Given that,
To Subtract. and determine the lower terms,

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Given expression,
= 47/50 - 3/10
= [47 - 3×5] / 50
= [47 - 15] /50
= 32 / 50
= 16 / 25

The required simplified solution of the given subtraction is 16/25. Option D is correct.

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Answer:

d) 16/25

Step-by-step explanation:

The problem is,

→ (47/50) - (3/10)

Let's solve the problem,

→ (47/50) - (3/10)

→ (47/50) - (15/50)

→ (47 - 15)/50

→ 32/50

→ (32 ÷ 2)/(50 ÷ 2)

→ 16/25

Hence, answer is 16/25.

The measure of the smallest angle of the quadrilateral is  60° .

In the question ,

it is given that ,

the angle measure of the quadrilateral are in the ratio 4 : 5 : 6 : 9 .

So , the measure of the largest angle is = 9x

and the measure of the smallest angle is = 4x .

we know that the sum of the measure of all the angles of the quadrilateral is 360° .

that means ,

4x + 5x + 6x + 9x = 360°

24x = 360

dividing both sides by 24 ,

x = 360/24

x = 15 .

the smallest angle is = 4(15) = 60°

Therefore ,  The measure of the smallest angle of the quadrilateral is  60° .

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Answer:1712

Step-by-step explanation:  is 1712

The amount Heidi earned in commission is $30 and the amount store made from her sale is $720.

We will solve the given problem using percentages.

We are given the following;

A salesperson at a jewelry store eams 4% commission each week.

Last week, Heidi sold $750 worth of jewelry.

We need to find the amount Heidi earned in commission and the amount store made from her sale.

Let us find the amount Heidi earned in commission;

$750 * 4% = 750 * 4 / 100 = 7.5 * 4 = 30

So, Heidi earned $30 from the commission.

Let us find the amount store made from her sale;

The amount store earns

= The total amount of sales - commission of Heidi

= $750 - $30

= $720

So, the store earns $720.

Thus, the amount Heidi earned in commission is $30 and the amount store made from her sale is $720.

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The height of the sunflower after 9 weeks is 52 inches and the function that represent the height of the sunflower after w weeks = 25 + 3w weeks.

Sophia planted a tiny sunflower in her backyard at the start of spring.

When she planted the sunflower,

The height of the sunflower = Initial height of the sunflower = 25 inches.

Now, The sunflower then began to grow at a rate of 3 inches per week.

Thus, the growth rate of the sunflower = 3 inches/week

The growth in 9 weeks = 3*9 = 27 inches,

The height of the sunflower after 9 weeks = initial height + growth = 25 +27 = 52 inches.

The growth in w week = 3w inches,

The height of the sunflower after w weeks = initial height + growth = 25 + 3w inches.

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Answer:

*Note: Perimeter is equal to the sum of all side lengths

1.   3cm + 3cm + 5cm + 4cm = 6cm + 9cm = 15cm

2.   3.5cm + 3cm + 3.5cm + 3.5cm + 3cm + 3.5cm

      = 6cm + 7cm + 7cm = 6cm + 14cm = 20cm

3.   2cm + 3cm + 3cm + 3cm + 5cm + 6cm = 5cm + 6cm + 11cm

      = 11cm + 11cm = 22cm

7.   9cm + 9cm + 9cm = 27cm

8.   Perimeter of a rectangle = 2 times the length plus 2 times the width

     P = 2(60m) + 2(48m) = 120m + 96m = 216m

9.   1 roll of 16m of wire = $3,214

     216m/16m = 13.5 rolls of wire

     13.5 rolls($3,214) = $43,389

Answer:

3. line XZ is congruent to line XZ | reflexive property
4. triangle WXZ is congruent to triangle YZX | HL (i think)
5. angle WXZ is congruent to angle YXZ | CPCTC

Step-by-step explanation:

Solving each pair of expression shows that

(1/5)^2 + 1 ≠ 2 * 12 / 25

( 1 + 1/4 )^2 = 2 - 7/16

Putting equals sign implies that the the expression in left hand side of the equation is equal to the expression on the right hand side

If they are not equal the sigh to be used is not not equal to

(1/5)^2 + 1 & 2 * 12 / 25

1/25 + 1 & 24/25

26/25 ≠ 24/25

( 1 + 1/4 )^2 & 2 - 7/16

(5/4)^2 & 25/16

25/16 = 25/16

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Answer:

add 54 to the numerator and 61 to the denominator because after you add it the fraction, it should be 60/90: simplified to 2/3 if you divide the numerator and denominator by 30.

The number that must be added to the numerator and denominator is 40.

A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.

Example: 1/2, 1/3 is a fraction.

We have,

Fraction = 6/29

The new fraction = 2/3

Now,

(6 + x)/(29 + x) = 2/3

3(6 + x) = 2(29 + x)

18 + 3x = 58 + 2x

3x - 2x = 58 - 18

x = 40

Thus,

The number x is 40.

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The side lengths of the fence he can build with the greatest area inside are of:

75 yards and 75 yards.

Considering a rectangle of length l and width w, we have that the area and the perimeter of the rectangle are given as follows:

A farmer has 300 yards of fencing, hence the perimeter is:

P = 300.

Then:

2(l + w) = 300

l + w = 150

l = 150 - w.

Then the equation giving the area of the fence is:

A = lw

A = w(150 - w)

A = -w² + 150w.

Which is a quadratic equation with coefficients given by:

a = -1, b = 150.

The width that will give the highest possible area is the x-coordinate of the vertex, hence:

w = -150/(2(-1)) = 75 yards.

The length is of:

l = 150 - w = 150 - 75 = 75 yards.

Which means that the third option is correct.

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If the average annual stock return is 11. 3%, the average holds a portfolio of $8600 worth 30 years.

It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.

The usage of percentages is widespread and diverse. For instance, numerous data in the media, bank interest rates, retail discounts, and inflation rates are all reported as percentages. For comprehending the financial elements of daily life, percentages are crucial.

It is given that, the average annual stock return is 11. 3% and you begin your investment portfolio with $2,000,

Suppose the amount he earns in one year is x,

x=  11. 3%. of $2,000

x=220

The portfolio be worth 30 years if the average holds are,

=220 × 30

=$ 6600

The net cost is the sum of the return and the initial investment,

=$ 6600 + $ 2000

=$8600

Thus, if the average annual stock return is 11. 3%, the average holds a portfolio of $8600 worth 30 years.

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Answer:

(-1,3)

Step-by-step explanation:

x+4y=11

 -4y.  -4y

x=11-4y

3(11-4y)+5y=12

33-12y+5y=12

33-7y=12

-33.    -33

-7y=-21

/-7.  /-7

y=3

x+4(3)=11

x+12=11

-12.  -12

x=-1

Hopes this helps please mark brainliest

Answer:

x= −1 and y= 3

Step-by-step explanation:

Step One: Rewrite Equations

x+ 4y = 11

3x +5y = 12

Step Two: Solve x +4y = 11 for x:

x +4y = 11

x +4y + −4y = 11 + −4y (Add -4y to both sides)

x = −4y +11

Step Three: Substitute −4y +11 for x in 3x +5y = 12:

3x +5y = 12

3(−4y +11) +5y = 12

−7y +33 = 12 (Simplify both sides of the equation)

−7y +33 +−33 = 12 +−33(Add -33 to both sides)

−7y = −21

(-7y/-7) = (-21/-7) (Divide both sides by -7)

y = 3

I sincerely hope this helped you, good luck on your assignment!

Answer:no image I can’t see on mobile

Step-by-step explanation:

h

Answer:

the correct answer is -32+43

Step-by-step explanation:

I just know

Answer:

If m angle EFD = 75°, then m angle JAB = ??

C

B

A

1.

2.

The valid conclusion about statement A and statement B is "If Figure A is a parallelogram, then Figure A’s angles sum to 360°".

The correct answer option is option D.

A conditional statement can be defined a statement that is written in the form “If A then B,” where A and B are sentences.

For this conditional statement:

Sentence A is called the hypothesis

Sentence B is called the conclusion.

Hypothesis: This is an assumption taken to be true for the purpose of argument or investigation.

Conclusion: This is the proposition that follows as a necessary consequence of the premises in an argument or syllogism.

Hence, “If A then B” means that B must be true whenever A is true.

Therefore, if a figure is a parallelogram, then it is a quadrilateral; If a figure is a quadrilateral, then its angles sum to 360°.

It can be concluded that if a figure is a parallelogram, then it's angles must sum to 360°.

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