Find all values of x in the interval [0, 2π] that satisfy the equation. (Enter your answers as a comma-separated list.)
6 sin2(x) = 3

Answer:

David is 55 years old

Morgan is 23 years old

__________________________________________________________

Step-by-step explanation:

Let the age of David = x years

Let the age of Morgan = y years

We are Given:

The sum of David and Morgan's age is 78

7 years ago, David's age was 3 times Morgan's age

__________________________________________________________

Making the equations:

from the first statement, the sum of their ages is 78

So, we can write it as:

x + y = 78

from the second statement,7 years ago, David's age was 3 times Morgan's age

David's age 7 years ago = (x - 7)

Morgan's age 7 years ago = (y-7)

So, we can write the equation as:

(x - 7) = 3(y - 7)

which can be simplified to:

x = 3y - 14

__________________________________________________________

Solving the equations:

We have the 2 equations:

from the first equation, we can say that:

x = 78 - y

Using this value in the second equation:

x = 3y - 14

78 - y=  3y - 14                                                             [since x = 78 - y]

78 + 14 = 4y

4y = 92

y = 23

Using this value in the first equation:

x + y = 78

x + 23 = 78                                                                  [since y = 23]

x = 55

__________________________________________________________

The Age of David and Morgan:

Since we assigned x to the age of David:

David is 55 years old

We assigned y to the age of Morgan. So,

Morgan is 23 years old

Answer:

12 pi or 37.7units

Step-by-step explanation:

the perimeter is 4 semicircles which is 2 full circles. the formula for circumference of a circle (perimeter) is diameter times pi. the diameter given is 6 so you do 6 pi times 2 full circles which is 12 pi or 37.7 units

Answer:

12pi is ur correct answer

Answer:

A. Horizontal and slope is 0

B. Horizontal and slope is 0

C. Vertical and slope is undefined

D. Vertical and slope is undefined

Step-by-step explanation:

Answer:

1 /25

Step-by-step explanation:

percent means  

out of 100

⇒

4

%

=

4

100

as a fraction

To simplify the fraction we require to find a  

common factor

to both 4 and 100 and reduce the fraction by dividing. The common factors are 2 and 4 . Choose the largest, that is 4

⇒

4

100

=

4

÷

4

100

÷

4

=

1

25

This calculation is usually set out using  

cancelling

4

100

=

4

1

100

25

=

1

25

←

in simplest form

A fraction is in  

simplest form

when no other factor but 1 will divide into the numerator/denominator.

Answer:

The amount invested in the mutual fund that earned 5% was $1000.

The amount invested in the mutual fund that earned 3% was $1100.

Step-by-step explanation:

Let the amount invested in the mutual fund that was earned 5% be x and the amount invested in the mutual fund that earned 3% be y.

Statement 1: [tex]\frac{5}{100}[/tex]X+[tex]\frac{3}{100}[/tex]y = 83

Statement 2: x+y = 2100

I'll use the elimination method:

Statement 1 × 20: x+[tex]\frac{60}{100}[/tex]y = 1660

Minus Statement 1 × 20 from Statement 2: x+y-x-[tex]\frac{60}{100}[/tex]y = 2100-1660

[tex]\frac{40}{100}[/tex]y = 440

y = [tex]\frac{100}{40}[/tex]×440

  = 1100

x = 2100-1100

  = 1000

Answer:

Step-by-step explanation:

there are a couple ways to find slope

1. Rise over Run Method:

for this method, you use basic counting

to do this, you count the number of x spaces it takes the line to get from one y space to the next

for your line, the run is 3 because it takes 3 x spaces to get from one whole number to the next on the y spaces

you would say the rise is -1 because the line is going down, and it takes 3 x spaces to get the next pot that is on a y-axis increment

so we know the rise is -1 and the run is 3

if you put this into rise/run format, you get 1/-3

so -1/3 is you slope

2. Using the Coordinates

in this line, you see two points

the points are 1. (-1, -1), and 2. (2, -2)

using the coordinates means that you use a formula: [tex]\frac{y_{2}-y_{1} }{x_{2} -x_{1} }[/tex]

the y2 is the y value of the second coordinate (-2), the y1 is the y value of the first coordinate (-1)

the x2 is the x value of the second coordinate (2), the x1 is the x value of the  first coordinate (-1)

if you plug these it you get: -2 - (-1) / 2 - (-1)

this can be simplified to -2 + 1 / 2 + 1

and simplified again to -1/3

Qhat ever method you use, you should get the same answer. Using both methods is a good way to check your work.

Answer && Step-by-step explanation:

Simple plug and chug

we know a+b == 6 so replace the set as 6 so:

2(6)+6/6+(6)^2-2

12+1+36-2

49-2

==47

Answer:

Length = 7 ft

Breadth = 7 ft

Step-by-step explanation:

Let lenght of rectangle be x

and breadth be y

Area = [tex]49\ \text{ft}^2[/tex]

[tex]xy=49\\\Rightarrow x=\dfrac{49}{y}[/tex]

Permiter of a rectangle is given by

[tex]P=2(x+y)\\\Rightarrow P=2x+2y\\\Rightarrow P=2\times\dfrac{49}{y}+2y\\\Rightarrow P=\dfrac{98}{y}+2y[/tex]

Differentiating with respect to y we get

[tex]\dfrac{dP}{dy}=-\dfrac{98}{y^2}+2[/tex]

Equating with zero

[tex]0=-\dfrac{98}{y^2}+2\\\Rightarrow -2=-\dfrac{98}{y^2}\\\Rightarrow y^2=\dfrac{98}{2}\\\Rightarrow y^2=49\\\Rightarrow y=7[/tex]

Double derivative of the equation

[tex]\dfrac{d^2P}{dy^2}=2\dfrac{98}{y^3}\\\Rightarrow \dfrac{d^2P}{dy^2}=\dfrac{196}{y^3}>0[/tex]

So the value of y is minimum at 7.

[tex]x=\dfrac{49}{y}=\dfrac{49}{7}\\\Rightarrow x=7[/tex]

Hence, [tex]x=7,y=7[/tex]

The mimimum length and breadth of the rectangle is both 7 ft.

Answer:

Changes

Step-by-step explanation:

#teamtrees #WAP (Water And Plant)

Answer:

♡ let's kill this love! ♡

you should definitely get "the album."

it has a very good rating and its great ☆

stan blackpink for clear skin, have a great day!

-madi/madeline

✧･ﾟ: *✧･ﾟ:･ﾟ✧*:･ﾟ✧･ﾟ: *✧･ﾟ:･ﾟ✧*:･ﾟ✧

Step-by-step explanation:

Answer:

S10 = 320

Step-by-step explanation:

The formula for calculating the sum of the nth term of an AP is expressed as

Sn = n/2(2a+(n-1)d))

Given

a = 4

d = 5

n = 10

S10 =10/2{2(5)+(10-1)5}

S10 =5{10+9(6)}

S10 =5{10+54}

S10 = 5(64)

S10 = 320

Hence the sum of the first ten terms of the sequence is 320

Slope (m)= y\x= 9/2 = 4.5

your equation for the line is

y=4.5x+3.5

Answer:

some dumb mod deleted my answer because i didnt show work. Who cares about the work everyone just wants the answers.

55.) A.9 B. 29

57.) SAS

Step-by-step explanation:

Answer:

347 + 645 = 992

Step-by-step explanation:

 347

+645

 922

Answer:

[tex]\frac{d}{2} - 120[/tex]

Step-by-step explanation:

You work backwards:

Half of d dollars is d/2. Then you take 120 less than that, which means you are subtracting.

Answer:

1/2d-120

Step-by-step explanation:

Alright.

d=amount of money

1/2d=half of the amount of money

1/2d-120=half of the money minus 120

Answer:

∠1 = 124 degrees

Step-by-step explanation:

Vertical angles are always congruent

So ∠1  = ∠2

Answer:

Supplement of m∠1 = 56°

Step-by-step explanation:

Since both angles are vertical, they both equal to each other.

m∠2 = m∠1

        = 124°

To find the supplement of m∠1, we need to remember that supplementary angles add up to 180°.

Supplement of m∠1 = 180°-124°

                                 = 56°

Answer:

X=8, Y=9

Step-by-step explanation:

9/6=1.5

12/1.5=8

6*1.5=9

PLS GIVE BRAINLIEST

Answer:

25%

Step-by-step explanation:

8/32= 25%

Answer:

Step-by-step explanation:

Onehundred twenty-million-fivehundred forty thousand

Answer:

the answer is a your welcome

Answer:

3(x+6) =2

3x+18 =2

3x=2-18

3x=16

x=16/3

x=5.33333333

Answer:

A) Maximum for dosage is 0.11

B) maximum blood pressure = 1.625

Step-by-step explanation:

We are given the function;

B(x) = 395x² - 2370x³

To find maximum, we will find the derivative of the function and equate to zero.

B'(x) = 790x - 7110x²

Equating to zero gives;

790x - 7110x² = 0

790x = 7110x²

Dividing both sides by x gives;

790 = 7110x

x = 790/7110

x = 0.11

This falls in between the range of 0 <= x <= 0.16 given to us.

Therefore x = 0.11 is a maximum

Plugging this into B(x) = 395x² - 2370x³ gives;

B(0.11) = 395(0.11)² - 2370(0.11)³

B(0.11) = 1.625

Thus;

Maximum dosage is 0.11

maximum blood pressure = 1.625

Answer:

-4/7-5/7-6/7-3/14 ascending order

Answer:

The sorted inputs in order from least to greatest is:

-6/7 < -5/7 < -3/14 < 4/7

Step-by-step explanation:

Given

-5/7, -3/14, 4/7, -6/7​

The least common denominator (LCD) is: 14

Rewriting as equivalent fractions with the LCD:

-5/7            -3/14            4/7          -6/7

-10/14          -3/14           8/14          -12/14

Sorting this table by the numerators of the equivalent fractions in order from least to greatest:

-6/7                -5/7              -3/14              4/7

-12/14     <      -10/14     <      -3/14        <   8/14

Therefore, the sorted inputs in order from least to greatest is:

-6/7 < -5/7 < -3/14 < 4/7

Answer:

x<4.7

Step-by-step explanation:

2(x-2)+8.6<14

2x-4+8.6<14

2x=4.6<14

2x<14-4.6

2x<9.4

_____

x<4.7

                                mom said its my turn to be brainliest answer ;0

                                also, help me on my math hw maybe ?

Answer: x < 4.7

Step-by-step explanation:

Answer

35

Step-by-step explanation:

4.55/.13=35. Also, Heidi could do 35x13. I hope this helps!

Answer:

Right

Step-by-step explanation:

20 boxes minus 9 boxes

Answer: x=-1

Step-by-step explanation:

Answer:

0.35%

Step-by-step explanation:

Answer:

65

Step-by-step explanation:

I think. hope this hepls

Answer:

There are 1600 residents.

Step-by-step explanation:

0.2 times x = 320  divide by 0.2

x = 1600