an expression that equals to 6/5

Answer:

[tex]y=-2(sin(2x))-7[/tex]

Step-by-step explanation:

1. Approach

Given information:

What conclusions can be made about this function:

Therefore, one has the following information figured out:

[tex]y=-n(sin(ax))+b[/tex]

Now one has to find the following information:

2. Midline

The midlines can simply be defined as a line that goes through a sinusoidal function, cutting the function in half. This is represented by the constant (b). One is given that point (0, -7) is where the graph intersects the midline. The (y-coordinate) of this point is the midline. Therefore, the midline is the following:

y = -7

2. Amplitude

The amplitude is represented by the coefficient (n). It can simply be defined by the distance from the midline to point of maximum (the highest part of a sinusoidal function) or point of minimum (lowest point on the function). Since the function reaches a point of minimum after intercepting the (y-axis) at its midlines, the amplitude is a negative coefficient. One can find the absolute value of the amplitude by finding the difference of the (y-coordinate) of the point of minimum (or maximum) and the absolute value of the midline.

point of minimum: [tex](\frac{\pi}{4},9)[/tex]

midline: [tex]y=-7[/tex]

Amplitude: 9 - |-7| = 9 - 7 = 2

3. Period

The period of a sinusoidal function is the amount of time it takes to reach the same point on the wave. In essence, if one were to select any point on the sinusoidal function, and draw a line going to the right, how long would it take for that line to reach a point on the function that is identical to the point at which it started. This can be found by taking the difference of the (x- coordinate) of the intersection point of the midline, and the (x-coordinate) of the point of minimum, and multiplying it by (4).

point of minimum: [tex](\frac{\pi}{4},9)[/tex]

midline intersection: [tex](0, -7)[/tex]

Period: [tex]4(\frac{\pi}{4}-0)=4(\frac{\pi}{4})=\pi[/tex]

However, in order to input this into the function in place of the variable (a), one has to divide this number by ([tex]2\pi[/tex]).

[tex]a=\frac{2\pi}{\pi}=2[/tex]

4. Assemble the function

One now has the following solutions to the variables:

[tex]n =-16\\a=2\\b=-7\\[/tex]

Substitute these values into the function:

[tex]y=-2(sin(2x))-7[/tex]

Answer:

108°

Step-by-step explanation:

The sum of angles on a straight line is 180°

Therefore:

x + 72° = 180°

x = 180° - 72°

x = 108°

Therefore, the value of x is 108°

Answer:

There are 43200 minutes in a 30-day month.

Step-by-step explanation:

We know that:

60 minutes = 1 hour

24 hours = 1 day

Thus to determine the minutes in a 30-day month, let us first determine the number of hours in the month.

   30

x  24

_______

  120

 60

_______

 720 hours

The 30-day month has a total of 720 hours.

So that the number of minutes that make up 720 hours can be determined by;

    720

 x   60

_______

   000

4320

_______

43200

Therefore, there are 43200 minutes in a 30-day month.

Answer:

3 sqrt(5) meters

Step-by-step explanation:

This is a right triangle so we can use the Pythagorean theorem.

a^2 +b^2 = c^2 where a and b are the legs and c is the hypotenuse

3^2+6^2 = c^2

9+36 = c^2

45 = c^2

Taking the square root

sqrt(45) = sqrt(c^2)

sqrt(9*5) = c

sqrt(9) sqrt(5) =c

3sqrt(5) = c

[tex]\boxed{\large{\bold{\blue{ANSWER~:) }}}}[/tex]

Ross walked 3 m east and 6 m north.

so her path is a right angle triangle path.

we know that,

in a right angle triangle, According to the Pythagorean theorom,

[tex]\boxed{\sf{l^2+b^2=h^2 }}[/tex]

where

he is [tex]\sf{3\sqrt{5} }[/tex] far from the starting point

Answer:

75

Step-by-step explanation:

5 miles-8km

x miles-120 km

x=120×5÷8

x=75 (miles)

Answer:

s

Step-by-step explanation:

since 5 miles is the same as 8 kilometers,how many miles is 120 kilometers..use ratio and proportion

5miles:8kilometers

x. :120kilometers

8x/8=600/8

x=75miles

I hope this helps

Notice that the prime factorization of [tex]20^{20}[/tex] and [tex]10^{10}[/tex] are [tex]2^{40}\cdot5^{20}[/tex] and [tex]2^{10}\cdot5^{10}[/tex], respectively. also, notice that both of their prime factorizations contain only 2 and 5.

Let the divisor of 20^20 that is a multiple of 10^10 be:

[tex]2^y\cdot5^x\cdot2^{10}\cdot5^{10}\\=2^{10+y}\cdot5^{10+x}[/tex]

where y and x are positive integers.

We can have y equal to 0, 1, 2, ... 30 before the exponent of 2 exceeds 40, and we can have x equal to 0, 1, 2, ... 10 before the exponent of 5 exceeds 20.

That is 11*31= 341 numbers in total.

There are (40+1)(20+1)=861 factors in 20^20, which means that the final answer is:

[tex]\boxed{\frac{341}{861}}[/tex]

also are you, by any chance, the same guest who posted the same question in web2.0?

Answer:

The vertices of ABCD:

A ( - 3, 1 )

B ( 4 , - 3 )

C ( 1, 3 )

D ( - 1 , 4 )

∴ ( 4 x,  4 y ):

A ` ( - 12, 4 )

B ` ( 16, - 12 )

C ` ( 4, 12 )

D ` ( - 4 , 16 )

Step-by-step explanation: I hope this helps! ™(*/ω＼*)

Answer:

5y-3y+12+12=18

2y = 18 - 24

y = -6/2

y = -3

[tex]\huge\textsf{Hey there!}[/tex]

[tex]\large\textsf{5y + 12 - 3y + 12 = 18}\\\\\large\text{COMBINE the LIKE TERMS}\\\\\large\textsf{(5y - 3y) + (12 + 12) = 18}\\\\\large\text{NEW EQUATION: \textsf{2y + 24 = 18}}\\\\\large\text{SUBTRACT 24 to BOTH SIDES}\\\\\large\textsf{2y + 24 - 24 = 18 + 24}\\\\\large\text{Cancel out: \textsf{24 - 24} because it gives you 0}\\\\\large\text{Keep: \textsf{18 - 24} because it helps solve it helps solve for y}\\\\\large\textsf{18 - 24 = \bf -6}[/tex]

[tex]\large\text{NEW EQUATION: \textsf{2y = -6}}\\\\\large\text{DIVIDE 2 to BOTH SIDES}\\\\\mathsf{\dfrac{2y}{2y}=\dfrac{-6}{2}}\\\\\large\text{Cancel out: }\mathsf{\dfrac{2}{2}}\large\text{ because it gives you 1}\\\\\large\text{KEEP: }\mathsf{\dfrac{-6}{2}}\large\text{ because it gives you the y-value}\\\\\large\textsf{y = }\mathsf{\dfrac{-6}{2}}\\\\\mathsf{\dfrac{-6}{2}= \bf -3}\\\\\\\\\\\boxed{\boxed{\huge\textsf{Answer: y = \bf -3}}}\huge\checkmark[/tex]

[tex]\huge\textsf{Good luck on your assignment \& enjoy your day!}\\\\\\\\\\\\\\\\\frak{Amphitrite1040:)}[/tex]

Answer:

129

Step-by-step explanation:

Since,

AD = BC

AD = 3x + 24

BC = 4x - 11

3x + 24 = 4x - 11

4x - 11 = 3x + 24

4x - 3x = 24 + 11

x = 35

BC = 4x - 11

= 4 ( 35 ) - 11

= 140 - 11

BC = 129

Answer:

[tex]AB=BC[/tex]

[tex]3x+24=4x-11[/tex]

[tex]3x-4x=-11-24[/tex]

[tex]x=35[/tex]

[tex]BC=4\times 35-1[/tex]

[tex]=140-11[/tex]

[tex]=129[/tex]

--------------------------

Hope it helps..

Have a great day!!

Answer:

156

Step-by-step explanation:

Answer: The expression would look like 2x+(25+3y).

Step-by-step explanation:

Let the number be x

2x+(25+3y)

The algebraic expression will be [tex]2x+(25+3y)[/tex] .

Expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

We have,

A number [tex]x[/tex]

Number [tex]y[/tex],

The sum of twice the number [tex]x[/tex] and [tex]25[/tex] more than [tex]3[/tex] times the number [tex]y[/tex] ,

So,

According to the question,

sum of twice the number [tex]x[/tex] [tex]=2x[/tex]

And,

ore than [tex]3[/tex] times the number [tex]y[/tex] [tex]=25+3y[/tex]

Now,

The whole  algebraic expression,

[tex]2x+25+3y[/tex]

Hence, we can say that the algebraic expression will be [tex]2x+(25+3y)[/tex] .

To know more about expression click here

https://brainly.com/question/953809

#SPJ3

Answer:

x = 2sqrt(2)

y = 2sqrt(6)

Step-by-step explanation:

The ratio of the lengths of the sides of a 30-60-90 triangle is

1 : sqrt(3) : 2

x = 0.5 * 4 sqrt(2) = 2sqrt(2)

y = x * sqrt(3) = 2sqrt(6)

Answer:

[tex]x=3\\[/tex]

Step-by-step explanation:

Note that because BD is an angle bisector, then angle XBD and angle DXY are equal. Also note that BYD and BXD are equal because they are both right angles. Also, by the transaitive property, BD = BD. Therefore, it can be concluded that BXD is congruent to BYD.

Therefore, we must solve [tex]5x+4=19 \Longrightarrow 5x = 15 \Longrightarrow x=3[/tex].

Answer:

smaller figure/larger figure = 3/12 = ¼

Step-by-step explanation:

Scale factor = Smaller figure side length / corresponding side length of the larger figure.

Length of a side of the smaller figure = 3

Corresponding Length of a side of the larger figure = 12

Scale factor = smaller figure/larger figure = 3/12 = 1/4

Answer:

11

Step-by-step explanation:

first you sum the ratios

1+2=3

[tex] \frac{2}{3} \times x = 22 \\ 2x = 66 \\ x = 33 \\ this \: mean \: that \: we \: have \: 33 \: \\ students[/tex]

since boys are 22 , all we have to do is to subtract 22 from 33 the answer would be 11

therefore we have 11 girls.

Answer:

its 11

Step-by-step explanation:

Answer:

1 : 2 : 1

Step-by-step explanation:

2:4:2

Divide each  term by 2

2/2:4/2:2/2

1 : 2 : 1

Answer:

Surface Area = 3,543.7 cm²

Step-by-step explanation:

Surface area of the cylinder = 2πr(h + r)

Where,

radius (r) = 12 cm

height (h) = 35 cm

Plug in the values into the surface area formula

S.A = 2*π*12(35 + 12)

S.A = 24π(47)

S.A = 3,543.71651 cm²

≈ 3,543.7 cm² (approximated to the nearest tenth)

f(x) -> - f(x): Relflection across x-axis

-f(x) -> -f(x-4): Vertical Translation right 4 units

Answer:

360

Step-by-step explanation:

The formula for the sum of an infinite geometric series is a₁/(1-r), where a₁ represents the first value and r represents the ratio. We can plug in our values here to get

a₁/(1-r) = 240/(1-1/3)

= 240 / (2/3)

= (240/1) / (2/3)

= (240/1) * (3/2)

= 360

Answer:

444 pot soils

Step-by-step explanation:

Answer:

0033

Step-by-step explanation:

.033 of a whole number so its .033

Answer:

A. System C simplifies to 2x - 3y = 4 and 4x - y = 54 by dividing the second equation by three (3).

B. Systems A and C have the same solutions.

C. Systems A and B have different solutions.

Step-by-step explanation:

Given the following system of equations;

System A

2x - 3y = 4  .....equation 1

4x - y = 18  .......equation 2

We would solve the above equations using the elimination method;

Multiplying eqn 1 by 2;

2*(2x) - 2*(3y) = 4*2

4x - 6y = 8  ...... equation 3

Subtracting eqn 2 from eqn 3;

(4x - 4x) + (-6y - (-y)) = 8 - 18

0 + (-6y + y) = -10

-5y = -10

5y = 10

[tex] y = \frac {10}{5} [/tex]

y = 2

To find the value of x;

2x - 3y = 4

2x - 3(2) = 4

2x - 6 = 4

2x = 4 + 6

2x = 10

[tex] x = \frac {10}{2} [/tex]

x = 5

Solutions (x, y) = (5, 2)

System B

3x - 4y = 5  ..... equation 1

y = 5x + 3  ..... equation 2

We would solve the equations using substitution method;

Substituting eqn 2 into eqn 1, we have;

3x - 4(5x + 3) = 5

3x - 20x - 12 = 5

-17x - 12 = 5

-17x = 12 + 5

-17x = 17

[tex] x = \frac {-17}{17} [/tex]

x = -1

To find the value of y;

y = 5x + 3

y = 5(-1) + 3

y = -5 + 3

y = -2

Solutions (x, y) = (-1, -2)

System C

2x - 3y = 4  ..... equation 1

12x - 3y = 54  ...... equation 2

We would solve the above equations using the elimination method;

Subtracting eqn 2 from eqn 1;

(2x - 12x) + (-3y -(-3y)) = 4 - 54

-10x + (-3y + 3y) = -50

-10x + 0 = -50

-10x = -50

10x = 50

[tex] x = \frac {50}{10} [/tex]

x = 5

To find the value of y;

2x - 3y = 4

2(5) - 3y = 4

10 - 3y = 4

3y = 10 - 4

3y = 6

[tex] y = \frac {6}{3} [/tex]

y = 2

Solutions (x, y) = (5, 2)

Answer:

peter will get 225

Answer:

C. 5+ 1.50x is less than or equal to 25

Step-by-step explanation:

Maya has 25 dollars to spend, and it cost 5 to get in. Each ride will cost her 1.50, so she has to spend up to or less than 25 on the entry fee and each ride.

Answer:169

Step-by-step explanation:13 x 13 = 169

You would take the larger side of the pen (13) or else it wouldn’t fit if you chose 10.

Answer:

6(k+2) -8

Step-by-step explanation:

Start with k

k

Add 2

(k+2)

Multiply by 6

6(k+2)

Then subtract 8

6(k+2) -8

6(k+2)-8 is a required answer.

Answer:

Solution given:

Start with k.

add 2

multiply by six

subtract by 8

9514 1404 393

Answer:

  10.8 miles

Step-by-step explanation:

The distance between (-3, -4) and (3, 5) can be found using the distance formula.

  d = √((x2 -x1)^2 +(y2 -y1)^2)

  d = √((3 -(-3))^2 +(5 -(-4))^2) = √(6^2 +9^2) = √117

  d ≈ 10.8

It is about 10.8 miles from the mall to the park.

Answer:

2. Candle dimensions: x = 6.3 cm                   h  = 6.29 cm

A (min) = 373.49 cm²

3. Cylindrical oven dimensions:  x  = 0.54 m   h = 0.55 m

A (min)= 1.4747 m²

Step-by-step explanation:

2.A   The volume V of the cylindrical candle is 785 cm³

V = π*x²*h                x is the radius of the base and h the heigh of the cylinder

The surface area A is area of the base   π*x² . plus lateral area 2*π*r*h

then .   A  = π*x²  + 2*π*x*h .             h = V/π*x²

A as a function of x . is

A(x)  = π*x²  + 2*π*x*785/π*x²

A(x) =  π*x²  + 1570/x

Taking derivatives on both sides of the equation we get:

A' (x) = 2*π*x - 1570/x²

A'(x) = 0 .   2*π*x - 1570/x² = 0 .       2*π*x³  =  1570

x³ = 250

x = 6.3 cm .              and .            h  = 785/π*x² .  h = 785/124.63

h  = 6.29 cm

Then dimensions of the cylindrical candle:

x = 6.3 cm                   h  = 6.29 cm

A (min) =  3.14 * (6.3)²  + 6.28*6.3*6.29

A (min) = 124.63  + 248.86

A (min) = 373.49 cm²

3. For a cylindrical oven    V = 0.512    h =  0.512/ π*x²

Following the same procedure

A(x)  = π*x²  + 2*π*x*0.512/π*x² .A(x)  = π*x²  + 1024/x

A'(x) = 2* π*x - 1.024/x²

A'(x) =0 .                2* π*x - 1.024/x² =0 .       2* π*x³ . = 1.024

x³ = 0.512/π .            x³ = 0.163

x  = 0.54 m     h  = 0.512/π*x² .            h = 0.55 m

A(min) = 3.14*(0.54)²  +  1024/x

A(min)= 0.9156 + 0.5591

A (min)= 1.4747 m²