If cos x= sin(20 + x)° and 0° < x < 90°, what is the value of x

To simplify the expressions and arrange them based on the coefficient of n², combine like terms and perform necessary operations. The expressions, in increasing order, are: 3n + 2, 2n³ - n² + 2n, -5n³ + 6n² - n + 5, and 6n³ - n² + n - 6.

To simplify each expression and arrange them in increasing order based on the coefficient of n², we need to combine like terms and perform any necessary operations. Let's go through each expression:

Arranging them in increasing order based on the coefficient of n², we have:

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Step-by-step explanation:

As Dave's sister baked 3 dozen pies.

So, total number of pies = 3 × 12 = 36

Number of pies = 3×12 = 36

Pies which contained chocolate = 1/3×36 = 12

Pies which contained marshmallows = 1/4×36 = 9

Pies which contained cayenne = 1/6×36 = 6

Pies contained soy nut = 1/12×36 = 3

So,

Pies that had none of these ingredients = 36 - (12+9+6+3)

                                                                   = 36 - 30

                                                                    = 6 pies

So, total 6 pieces are left  that had none of these ingredients.

i.e. 1, 2, 3, 4, 5, 6

Therefore,

Keywords: smallest possible number

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She baked 36 pies. Of these

1/3*36=12 contained chocolate

1/4*36=9 contained marshmallows

1/636=6 contained cayenne

1/12*36=3 contained salted soy nuts.

In order to make the number of pies with none of these ingredients as small as possible, Dave's sister should put all of these ingredients in different pies so that only one of the ingredients is in any pie. If she does this, then 12+9+6+3=30 of the pies will have one of these ingredients. The other 6 pies will have none of these ingredients. At least 6 pies have none of these ingredients.

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Answer:

[tex]12\sqrt{2}\ cm[/tex]

Step-by-step explanation:

step 1

Find the length side of the square

we know that

The area of a square is equal to

[tex]A=b^{2}[/tex]

where

b is the length side

we have

[tex]A=144\ cm^2[/tex]

substitute in the formula of area

[tex]144=b^{2}[/tex]

solve for b

square root both sides

[tex]b=12\ cm[/tex]

step 2

Find the length of the diagonal

Applying the Pythagorean Theorem

[tex]d^2=b^2+b^2[/tex]

see the attached figure to better understand the problem

substitute the given values

[tex]d^2=12^2+12^2[/tex]

[tex]d^2=288[/tex]

square root both sides

[tex]d=\sqrt{288}\ cm[/tex]

simplify

[tex]d=12\sqrt{2}\ cm[/tex]

Answer:

The system is

[tex]x+2y \leq -8[/tex]

[tex]y> 2x[/tex]

Step-by-step explanation:

Part 1

Find the equation of the first inequality

we know that

The first line is a solid line with negative slope passing through the points (-6,-1) and (0,-4)

The slope is equal to

[tex]m=(-4+1)/(0+6)\\m=-0.5[/tex]

The equation of the solid line in slope intercept form is

[tex]y=-0.5x-4[/tex]

Everything below the line is shaded

so

The inequality is

[tex]y \leq -0.5x-4[/tex]

Convert to standard form

Adds 0.5x both sides

[tex]0.5x+y \leq -4[/tex]

Multiply by 2 both sides

[tex]x+2y \leq -8[/tex] -----> First inequality

Part 2

Find the equation of the second inequality

we know that

The second line is a dashed line with positive slope passing through the points (-2,-4) and (0,0)

This line represent a proportional relationship, because the line passes through the origin

The slope is equal to the constant of proportionality

[tex]k=(-4)/(-2)=2[/tex]

The equation of the dashed line is

[tex]y=2x[/tex]

Everything to the left of the line is shade

so

The inequality is

[tex]y> 2x[/tex] -----> Second inequality

see the attached figure to better understand the problem

The system of inequalities represented by the given graph is y > 2x and x + 2y ≤ –8.

The system of inequalities represented by the given graph is:

We can determine the equations of the lines using the given points:

Line 1: y = mx + b, where m is the slope and b is the y-intercept. Using the points (–6, –1) and (0, –4), we can calculate the slope: m = (–4 – (–1)) / (0 – (–6)) = –3 / 6 = –1/2. Thus the equation of Line 1 is y = –(1/2)x – 3.

Line 2: Using the points (–2, –4) and (0, 0), we can calculate the slope: m = (0 – (–4)) / (0 – (–2)) = 4 / 2 = 2. Thus the equation of Line 2 is y = 2x – 4.

By looking at the graph, we can see that everything below Line 1 (shaded area) satisfies y > 2x, while everything below or on Line 2 (including the line itself) satisfies x + 2y ≤ –8.

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Answer:

The Amount paid after 8 years is $72611.76

Step-by-step explanation:

Given as :

The principal mortgage = p = $31,200

The rate of interest = r = 10.7%  compounded quarterly

The time period of mortgage = t = 8 years

Let The Amount paid after 8 years = $A

Now, According to question

From Compounded Interest method

Amount = Principal × [tex](1+\dfrac{\textrm rate}{4\times 100})^{\textrm 4\times time}[/tex]

Or, A = p × [tex](1+\dfrac{\textrm r}{4\times 100})^{\textrm 4\times t}[/tex]

Or, A = $31,200 × [tex](1+\dfrac{\textrm 10.7}{4\times 100})^{\textrm 4\times 8}[/tex]

Or, A = $31,200 × [tex](1.02675)^{32}[/tex]

Or, A = $31,200 × 2.3273

∴ A = $72611.76

So, The Amount paid after 8 years = A = $72611.76

Hence, The Amount paid after 8 years is $72611.76  Answer

Answer: [tex]QR=4.04[/tex]

Step-by-step explanation:

For this exercise you must use the followinG Trigonometric Identity:

[tex]tan\alpha=\frac{opposite}{adjacent}[/tex]

In this case, given the right triangle PQR, you can identify that:

[tex]\alpha=60\°\\opposite=PR=7.0\\adjacent=QR[/tex]

Then, the  next step is to substitute those values into [tex]tan\alpha=\frac{opposite}{adjacent}[/tex]:

[tex]tan(60\°)=\frac{7.0}{QR}[/tex]

And the final step is to solve for "QR" in order to find its value.

So you get that this is:

[tex](QR)(tan(60\°))=7.0\\\\QR=\frac{7.0}{tan(60\°)}\\\\QR=4.04[/tex]

Answer:

30% of them preferred hab juice.

Step-by-step explanation:

Given:

A survey of all beings on planet Tott found that 12 beings preferred hab juice to all other juices.

40 beings were surveyed altogether.

Now, to find percent of them preferred hab juice.

Total beings surveyed = 40.

Number of beings preferred hab juice = 12.

So, to get the percent:

[tex]\frac{Total\ beings\ surveyed}{Number\ of\ beings\ preferred\ hab\ juice} \times 100.[/tex]

[tex]=\frac{12}{40} \times 100[/tex]

[tex]=0.3\times 100[/tex]

[tex]=30\%.[/tex]

Therefore, 30% of them preferred hab juice.

The answer is y = 5x.

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Answer:

y=5x

Step-by-step explanation:

I did the test

Answer:

Hypothesis is: Intersection happens at a point

Step-by-step explanation:

A hypothesis in science is a suggested explanation of something that has a consequence or leads to an occurrence.  Usually it will be written in the form of an "if and then" statement.

Such statement explains what would occur, or follow if the possibility enunciated in the "if" part of the statement happens.

In this case the hypothesis is that if there is intersection of lines, it has to occur at a point. Therefore the closest to that statement among the options given in the problem is the last one: "Intersection happens at a point"

Answer:

Two Line Intersect

Step-by-step explanation:

I got it right on the test :)

Answer:

see explanation

Step-by-step explanation:

The n th term of a geometric sequence is

[tex]a_{n}[/tex] = a[tex](r)^{n-1}[/tex]

where a is the first term and r the common ratio

Both a and r have to be found

Given a₃ = - 2, then

ar² = - 2 → (1)

Given a₇ = - 32, then

a[tex]r^{6}[/tex] = - 32 → (2)

Divide (2) by (1)

[tex]\frac{ar^6}{ar^2}[/tex] = [tex]\frac{-32}{-2}[/tex], that is

[tex]r^{4}[/tex] = 16 ( take the fourth root of both sides )

r = 2 ← common ratio

Substitute r = 2 into (1)

a × 2² = - 2, that is

4a = - 2 ( divide both sides by 4 )

a = - [tex]\frac{1}{2}[/tex] ← first term

Hence

[tex]a_{n}[/tex] = - [tex]\frac{1}{2}[/tex][tex](2)^{n-1}[/tex] ← explicit formula

and

[tex]a_{10}[/tex] = - [tex]\frac{1}{2}[/tex] × [tex]2^{9}[/tex] = - 0.5 × 512 = - 256

Answer:

The cost of one lime is $0.65

Step-by-step explanation:

Let

x ---> the cost of one lemon

y ---> the cost of one lime

we know that

Mickey

[tex]5x+3y=3.70[/tex] ----> equation A

Minnie

[tex]15x+4y=7.85[/tex] ---> equation B

Solve the system by elimination

Multiply by -3 both sides equation A

[tex]-3(5x+3y)=-3(3.70)[/tex]

[tex]-15x-9y=-11.10[/tex] ----> equation C

Adds equation C and equation B

[tex]-15x-9y=-11.10\\15x+4y=7.85\\--------\\-9y+4y=-11.10+7.85\\-5y=-3.25\\y=0.65[/tex]

therefore

The cost of one lime is $0.65

Answer:

A

Step-by-step explanation:

A limacon curve passes trough the point [tex]\left(\dfrac{\pi}{2},0\right)[/tex], this means when [tex]\theta =\dfrac{\pi}{2},[/tex] the distance [tex]r=0.[/tex]

Note that

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

so, if [tex]r=a+b\sin \theta,[/tex]

then

[tex]r\left(\dfrac{\pi}{2}\right)=a+b=0\\ \\a=-b[/tex]

The only option which shows a = -b is option A.

Answer:

b

Step-by-step explanation:

The area of the semicircle if the radius is 2 in terms of π is 2π.

Area of a circle = πr²

Where,

r = radius

A semicircle is half of a circle.

So,

Area of a semicircle = ½πr²

If r = 2

Area of a semicircle = ½ × π × 2²

= ½ × Π × 4

= 4/2π

= 2π

Hence, the area of the semicircle is 2π.

Read more on area of semicircle:

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[tex]

x^2-1 < 18 \\

x^2 < 19 \\

x < \sqrt{19}

[/tex]

Hope this helps.

Answer:

The periodic interest rate is 1.62 %

Step-by-step explanation:

Given:

Annual percentage rate  = 19.66%

Time period  = 30 days

To Find:

Periodic interest rate  =?

Solution:

The periodic interest rate r is calculated using the following formula:

r = (1 + \frac{i}{m})^{\frac{m}{n}} - 1

Where,

i = nominal annual rate

n = number of payments per year i.e., 12 for monthly payment, 1 for yearly payment and so on.

m = number of compounding periods per year

The period interest rate per payment is integral to the calculation of annuity instruments including loans and investments.

Now substituting the values we get

[tex]r = (1 + \frac{19.66}{12})^{\frac{12}{12}} - 1[/tex]

[tex]r = (1 + \frac{19.66}{12})^1 - 1[/tex]

r = (1 +1.638 ) - 1

r = (2.638 ) - 1

r = 1.638 %

Answer:

26 is the number

Step-by-step explanation:

12/13 x = 24

Multiply by 13 on both sides

12x = 24 * 13

12x = 312

Simplify

x = 26

26

Hope this helps :)

Answer:

Marla didn't use the right steps to complete the square. Maria made a mistake in step 1, she put 8x instead of -2x

Step-by-step explanation:

we have

[tex]-4x^{2}+8x-25[/tex]

This is a vertical parabola open downward

The vertex is a maximum

Find the vertex

step 1

Factor the leading coefficient -4

[tex]-4(x^{2}-2x)-25[/tex]

step 2

Complete the square

[tex]-4(x^{2}-2x+1-1)-25[/tex]

step 3

[tex]-4(x^{2}-2x+1)-25+4[/tex]

[tex]-4(x^{2}-2x+1)-21[/tex]

step 4

Rewrite as perfect squares

[tex]-4(x-1)^{2}-21[/tex]

the vertex is the point (1,-21)

so

The maximum value of the quadratic equation is (1,-21)

therefore

Marla didn't use the right steps to complete the square. Maria made a mistake in step 1, she put 8x instead of -2x

Marla correctly completed the square for the expression −4x2+8x−25, arriving at the simplified form −4(x+4)2 + 39 to find the minimum value.

To find the minimum value of the quadratic expression −4x2+8x−25, Marla completed the square. Her steps are as follows:

Marla used the correct steps to complete the square, which simplifies to −4(x+4)2 + 39.

Answer:

(Q.1) No solution

(Q.2) True

(Q.3)  x = 4 - 2y

(Q.4) True

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

Step-by-step explanation:

(Q.1) As shown in the first attached figure.

By graphing.   x + 2y = 8   &   x + 2y = -4

The two lines are parallel, there is no intersection points between the lines.

So, there is no solution to the system of equations.

Also, we should note the parallel lines have the same slope

to find it make the equation similar to y = mx + c where m is the slope

at this situation m = -1/2

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

(Q.2) As shown in the second attached figure.

By graphing the system of inequalities  y> -3x+2  &  y<2x+1

The Shaded area represents the solution of the system of inequalities

And the point (4,2) is inside the shaded area

So, The ordered pair (4,2) is a solution to the system of inequalities.

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

(Q.3) solving the system { x+2y=4  &  2x+2y=6 } by substitution

From the first equation x + 2y = 4

we will find x in terms of y then plug it into the second equation

So, x + 2y = 4 ⇒  x = 4 - 2y

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

(Q.4) As shown in the third attached figure.

By graphing.   2x + 4y = 8  &  x + 2y = 6

The two lines are parallel, there is no intersection points between the lines.

So, there is no solution to the system of equations.

Also, we should note the parallel lines have the same slope

to find it make the equation similar to y = mx + c where m is the slope

at this situation m = -1/2

Answer:

see explanation

Step-by-step explanation:

To graph the line, we require 2 points

Find the intercepts, that is where the graph crosses the x and y axes

To find the x- intercept let y = 0 in the equation and solve for x

x - 3 = 0 ( add 3 to both sides )

x = 3 ⇒ (3, 0 ) ← x- intercept

To find the y- intercept let x = 0 in the equation and solve for y

- y - 3 = 0 ( add 3 to both sides )

- y = 3 ( multiply both sides by - 1 )

y = - 3 ⇒ (0, - 3 ) ← y- intercept

Plot the points (3, 0) and (0, - 3) and draw a straight line through them

Note that [tex]10^a\cdot10^b=10^{a+b}[/tex] or more general form, [tex]a^b\cdot a^c=a^{b+c}[/tex].

[tex]10^5\cdot6\cdot10^4=\boxed{6\cdot10^9}[/tex]

Hope this helps.

Answer:

-0.42

Step-by-step explanation:

To match the world record, the runner needs a time difference for the fourth lap that brings the total time difference from all laps to zero. This time difference is calculated based on the sum of time differences of the first three laps.

This question is asking about the time difference that the runner needs for the fourth lap in order to match the world record.

Assuming that the total time difference after the first three laps is provided in the table, what you'll do is add these three time differences to get the total difference for the first three laps.

Let's say, for instance, the total after three laps is +15 seconds. Since a positive number means the runner is behind the world record holder's time, we want the fourth lap to compensate for that and bring the total time difference to zero to match the world record. Therefore, the runner will need a -15 seconds time difference on the fourth lap.

Remember that a negative number means the runner ran the lap faster than the world record holder.

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Step-by-step explanation:

2x+y = 5 (divided by 2)

If x= 0, y=5

If x= 1, y=3

If x=-1, y=7

So, coordinate points are (0,5),(1,3),(1,7) and so on.

Continue above explanation.

After , draw a graph on x,y axis .

Answer: I used a graphing calculator.

Step-by-step explanation:

Answer:

A would be best

Step-by-step explanation:

200 km is roughly 124.2 miles

200 m is about 0.12 miles

200 cm and 200 mm is way too small to be distances between cities because 200 cm is like 78.7 inches

200 mm is like 7.8 inches

124.2 miles or 200 km would be a reasonable distances between two cities.

Answer:

A. 200km is your answer

Step-by-step explanation:

Answer:

$431.36 is budgeted for rent.

Step-by-step explanation:

Given:

Madison’s monthly salary is $1348.

Her budget for rent is 32% of salary.

Now, to find the amount budgeted for rent.

So, salary = $1348.

And, budget for rent = 32% of $1348.

Thus, the budgeted for rent is:

[tex]32\%\ of\ \$1348.[/tex]

[tex]=\frac{32}{100} \times 1348[/tex]

[tex]=0.32\times 1348[/tex]

[tex]=\$431.36.[/tex]

Therefore, $431.36 is budgeted for rent.

Answer:

y = -5x -8

Explanation:

Find b in equation y = mx + b

Insert numbers to find b

-3 = -5· -1 + b

Step 1: Simplify both sides of the equation.

−3=(−5)(−1)+b

−3=5+b

−3=b+5

Step 2: Flip the equation.

b+5=−3

Step 3: Subtract 5 from both sides.

b+5−5=−3−5

b=−8

Insert into equation

y = -5x - 8

Answer:

0.06

Step-by-step explanation:

If you round 0.566 to the nearest tenth it would be 0.06

pls rate and thank me

Answer:

To round 0.566 to the nearest tenth consider the hundredths' value of 0.566, which is 6 and equal or more than 5. Therefore, the tenths value of 0.566 increases by 1 to 6.

=0.6

Step-by-step explanation:

comment how this helps

Answer:

y+6=2(x+6)

Step-by-step explanation:

y-y1=m(x-x1)

y-(-6)=2(x-(-6))

y+6=2(x+6)

Answer:

$1.58

Step-by-step explanation:

1.50 multiplied by 1.05

answer is 1.575

rounded is 1.58

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Answer:

2.25

Step-by-step explanation:

just multiply .05 by 1.50 so that would be .075, so then add that by original price so 2.25. Don't Quote me on this its been awile.

Answer:

it's (-3,9 i hope in prey so

Step-by-step explanation:

Answer:

(- 2, - 5 )

Step-by-step explanation:

Note that y = 1 is a horizontal line passing through all points with a y- coordinate of 1

The point (- 2, 7 ) is 6 units above y = 1 (7 - 1 = 6 ), thus

The reflection is 6 units below y = 1, (1 - 6 = - 5 ), hence

P(- 2, 7 ) → P'(- 2, - 5 )

Answer:

Triangle

Step-by-step explanation:

cross section through the cone perpendicular will be a triangle with the base of the cone's base diameter.