Shashi has a rectangular garden. The length of the garden is 4 feet less than twice the width. The area of the garden is 448 square feet. What is the length of the garden?

The sounds of music are related to trigonometric functions because trigonometry is used in measuring the level of the pitch of a sound wave or musical note.

It should be noted trigonometry is important for measuring pitch level. The notes are measured in Hertz.

A sound wave's amplitude relates to the change in the pressure that's caused by the wave measured at a specific location.

The sound is perceived as louder when the amplitude increases.

Pieces of music often have repetitive choruses or bars, similar to patterns. In mathematics, we look for patterns to interpret and predict the unknown. Music uses the same techniques. If you look at a piece of music, artists look at the notes they see to find the rare (high or low) and uncommon notes.

In this way, the notes are related. Relationships are important in mathematics and create an interesting link between music and mathematics.

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To prove that △DFE ~ △GFH by the SSS similarity theorem, the correct answer is; Option C: HF is 4 units and GH is 2 units

The SSS Similarity theorem states that two triangles are similar If all the three sides of one of the triangles are in same proportion to the three sides of the other triangle.

Since triangle DFE is similar to triangle GHF as seen in the attached diagram, then we can say that;

DF/GF = DE/GH

20/5 = 8/GH

GH = 2 units

Also:

EF/HF = DF/GF

(12 + HF)/HF = 20/5

HF = 4 units

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Answer:

3/2

Step-by-step explanation:

comparing the straight line with ax + bx + c = 0,

we get a = 3 and b = -2

we know,

slope of line = -a/b

= -3/-2

= 3/2

Hope it helped

Answer:

x = -2

Step-by-step explanation:

1. Square both sides
x^2 +3x + 6 = x^2
2. Subtract x^2 from both sides
3x + 6 = 0
3. Subtract 6 from both sides and divide by 3
x = -2

Answer:

The number of computers that must be surveyed is 1681.

Step-by-step explanation:

The formula to find the sample size is given by:-

[tex]n=p(1-p)(\frac{\frac{z_{\alpha } }{2} }{E} )^{2}[/tex]

where p = prior population proportion,

[tex]\frac{z_{\alpha }}{2}[/tex]= Two-tailed z-value for ∝

E= Margin of error.

As per the given, we have

Confidence level :

1 - ∝ = 0.90

⇒∝= 1 - 0.90= 0.10

Two -tailed z-value for ∝= 0.10 : [tex]\frac{z_{\alpha }}{2}[/tex] = 1.64

E= 2%=0.02

We assume that nothing is known about the percentage of computers with new operating systems.

Let us take p=0.5  [we take p= 0.5 if the prior estimate of proportion is unknown.]

The required sample size will be:-

[tex]n= 0.5(1-0.5)(\frac{1.64}{0.02} )^{2}[/tex]

=> [tex]0.25(82)^{2}[/tex]

=> 1681

Hence, the number of the computer must be surveyed = 1681

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Answer:

[tex]\circledast \ \ f\circ f\left( x\right) = x[/tex]

[tex]\circledast \ \ g\circ g\left( x\right) =4x - 21[/tex]

Step-by-step explanation:

[tex]f(x)=\frac{5}{2x}[/tex]

g(x) = 2x - 7

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

[tex]f\circ f\left( x\right) =\frac{5}{2\left( f\left( x\right) \right) }[/tex]

             [tex]=\frac{5}{2\left( \frac{5}{2x} \right) }[/tex]

             [tex]=\frac{5}{\left( \frac{5}{x} \right) }[/tex]

             [tex]=5\times\frac{x}{5}[/tex]

             [tex]=x[/tex]

_____________

[tex]g\circ g\left( x\right) =2(g(x)) - 7[/tex]

            = 2(2x - 7) - 7

           = 4x - 14 - 7

           = 4x - 23

The value of the variable x is 30° and the value of the variable y is 10°.

The missing diagram is attached below.

The angle is the distance between the intersecting lines or surfaces.

Corresponding angle – If two lines are parallel, then the third line. The corresponding angles are equal angles.

Vertically opposite angle – When two lines intersect, then their opposite angles are equal.

Linear angle – If the total of two angles is 180 degrees, they are said to be linear angles.

If angle ∠1 = 105°, angle ∠12 = (3x + 15)°, and angle ∠7 = (8y-5)°.

∠1 = ∠5 = ∠9 = 105° (corresponding angles)

∠1 = ∠4 = 105° (Vertical opposite angles)

∠1 + ∠2 = 180° (linear angle)

       ∠2 = 75°

∠2 = ∠3 = 75° (Vertical opposite angles)

∠3 = ∠8 = ∠12 = 75° (corresponding angles)

Then the value of x and y will be

   ∠9 = ∠12

   ∠1 = ∠12

105° = (3x + 15)°

  3x = 90°

    x = 30°

∠6 = ∠7

75° = (8y – 5)°

8y = 80°

  y = 10°

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Answer:

To solve this quadratic equation, take the square root of both sides.

Since the left side is a perfect square, it will just be reduced to:

4y - 3

For the constant on the right side, the positive and negative roots must be considered.

√72 = ±6√2

Equating the two:

4y - 3 = ±6√2

4y = 3 ± 6√2

y = (3 ± 6√2)/4

y = (3 + 6√2) / 4 = 2.87

and

y = (3 - 6√2) / 4 = -1.37

The function s = f(w) = 12 + 4w represents the relationship between the number of stamps (s) and the number of weeks (w) option (A) is correct.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have:

Neil started a stamp collection with 12 stamps. Every week, he adds 4 more stamps to the collection.

The number of stamps is s and the number of weeks is w.

s = f(w) = 12 + 4w

Because Every week, he adds 4 more stamps to the collection

Thus, the function s = f(w) = 12 + 4w represents the relationship between the number of stamps (s) and the number of weeks (w) option (A) is correct.

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sinusoidal curve equation 29 sin ([tex]\pi[/tex]/9 x)-49

Given the graph of a sinusoidal function, we can write its equation in the form y = A·sin(B(x - C)) + D using the following steps. D: To find D, take the average of a local maximum and minimum of the sinusoid. y=D is the "midline," or the line around which the sinusoid is centered.

In the state of Michigan, the lowest average temperature of the year is in January and is about 20 °F.

The highest monthly average temperature occurs in July at 78 °F

Assume the period is 12 months and January is at the origin of the graph of this function.

sinusoidal curve equation that models the data y

Then, Graph the curve using x = 0 for January, and x = 11 for December, so that x = 12 will be the start of the next year, or end of the period.

So, using the property of sinusoidal curve equation we have

=29 sin ([tex]\pi[/tex]/9 x)-49

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Answer:

To find the slope:

[tex]\frac{(y_{1} - y_{2})}{(x_{1} - x_{2})} =\frac{(-3-(-4))}{(-5-0)} =\frac{1}{-5}[/tex]

Hope it helps!

umm....... I think it was exactly 2 head

There are [tex]\binom62=15[/tex] ways of selecting any two fruit from the basket, where

[tex]\dbinom nk = \dfrac{n!}{k!(n-k)!}[/tex]

is the so-called binomial coefficient.

If the baby picks out [tex]k[/tex] oranges, where [tex]k\in\{0,1,2\}[/tex], it can do so in

[tex]\dbinom 3k \dbinom3{2-k} = \dfrac{3!}{k!} \dfrac{3!}{(2-k)! (1 + k)!}[/tex]

ways.

Then the PMF (probability mass function) of [tex]X[/tex] is

[tex]P(X=x) = \begin{cases} \dfrac{\binom30 \binom32}{\binom62} = \dfrac3{15} & \text{if }x=0 \\\\ \dfrac{\binom31 \binom31}{\binom62} = \dfrac9{15} & \text{if }x = 1 \\\\ \dfrac{\binom32 \binom30}{\binom62} = \dfrac3{15} & \text{if }x=2 \\\\ 0 &\text{otherwise}\end{cases}[/tex]

Answer:

1)x+1

2)x-1

3)x+1,R-1

Step-by-step explanation:

please mark me as brainlest

0.70 -0.50 = 0.20 cent mark up

0.20/0.50 = 0.40 = 40% markup

The company needs 41 labels on average, each minute.

The perimeter of a circle (circumference): 2 π radius

Replacing with the values given:

C = 2 (3.14) 2 = 12.56 cm

So, the area of one label is:

Area of a rectangle: length x width = 12.56 x 7 = 87.92 cm sq.

Now, the number of label be n

87.92 x n = 3612.64 cm2

n = 3612.64 / 87.92

n = 41.09

Hence, The company needs 41 labels on average, each minute.

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Answer:

[tex]\left[\begin{array}{}0&\\1&\\-2&\\1&\end{array}\right][/tex]  t in R   Correct option (B)

Step-by-step explanation:

Orthogonal vectors : We say that 2 vectors are orthogonal if they are perpendicular to each other. i.e. the dot product of the two vectors is zero.

Dot product : The dot product of two vectors is equal to the sum of the products of the individual components of the two vectors.

for the given vector (a, b, c, d) to be orthogonal its dot product with each vector must be 0

therefore (1, 2, 1, 0).(a, b, c, d) = 0

                        a + 2b+ c+ 0    = 0    -------- (i)

similarly   (1, -1, 1, 3 ).(a, b, c, d) = 0

                        a - b + c + 3d    = 0   -------- (ii)

                 (2, -1, 0, 1).(a, b, c, d) = 0

                        2a - b + 0 + d   = 0 ---------- (iii)

subtracting equation (i) from (ii)

a - b + c + 3d - a - 2b - c - 0 = 0

                               -3b + 3d = 0

                                           b = d

substituting  b = d in (iii)

                       2a + b + 0 + b = 0

                                 2a + 2b = 0

                                           a = 0

substituting a = 0 , b = d in (i)

                       0 + 2d + c + 0 = 0

                                          c   = -2d

thus for any t ∈ R, vector(0, t, -2t, t)  will make the given set orthogonal

the above vector can also be written as (0, 1, -2, 1)

therefor option B is correct

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39 hours;  she works per week if the paramedic maintains a time card for hours she works on the rescue squad.

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We have:

A paramedic maintains a time card for the hours she works on the rescue squad shown in the table:

We can write a mixed fraction in a fraction:

6 1/2 = 13/2

8 1/2  = 33/2

7 3/4 = 31/4

8 1/12 = 97/12

8 5/12 = 101/12

Adding all the fractions:

[tex]=\rm \dfrac{13}{2}+\dfrac{33}{4}+\dfrac{31}{4}+\dfrac{97}{12}+\dfrac{101}{12}[/tex]

[tex]=\dfrac{13}{2}+\dfrac{64}{4}+\dfrac{97}{12}+\dfrac{101}{12}[/tex]

[tex]=\dfrac{13}{2}+\dfrac{64}{4}+\dfrac{198}{12}[/tex]

[tex]=\dfrac{13}{2}+\dfrac{64}{4}+\dfrac{33}{2}[/tex]

[tex]=23+\dfrac{64}{4}[/tex]

= 39 hours

Thus, 39 hours;  she works per week if the paramedic maintains a time card for hours she works on the rescue squad.

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An equation is formed of two equal expressions. The medals won by country A, country B, and country C is 79, 26, and 11, respectively.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Let the number of medals won by country A, country B, and country C be represented by A, B, and C, respectively. Now, the given conditions can be written as,

1.) The top three countries country A, country B, and country C won a total of 120 medals.

A + B + C = 120

2.) Country B won 11 more medals than country C

B = C + 11

3.) Country A won 38 more medals than the total amount won by the other two.

A = B + C + 38

A - 38 = B + C

Substitute the value of B+C form the last equation to the first equation,

A + A - 38 = 120

A = 79

Now, Substitue the value of A and B(from second equation)  in the first equation,

79 + C + 11 + C = 120

C = 15

Now, substitute the value of C in the second equation,

B = C + 11

B = 15 + 11

B = 26

Hence, the medals won by country A, country B, and country C is 79, 26, and 11, respectively.

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Answer:

simple interest is $281(nearest whole number)

Step-by-step explanation:

S. I=PXTXR

100

P=$6609

T=5

R=8.5 or 85/10

S. I=6609X5X85

100X10

=280.8825

=281

The amount of interest after 3 years will be $15.

The complete question is given below.

You loaned a friend $100 and will charge him 5% annual simple interest when he pay it back. What is the amount of interest after 3 years?

Simple interest is the concept that is used in many companies such as banking, finance, automobile, and so on.

The interest is given as

I = (P × R × T) / 100

Where, P is the initial amount, R is simple interest rate, and T is the time.

We have

P = $100

R = 5%

T = 3 years

Then the interest will be

I = (100 × 5 × 3) / 100

I = $15

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Answer:

11. always

12. always

13. always

14. never

15. never

16. always

17. always

18. sometimes

19. sometimes

20. never

Step-by-step explanation:

11. A line can be defined by at least two points

12. A plane can be defined by at least three points

13. If two planes intersect, then they form a line at the intersection.

14. If two lines intersect, then they form a point at the intersection (not a segment).

15. A line does not have any endpoints (infinite in both ways).

16. If two planes are not parallel they will always intersect.

17. If two lines are not parallel they will always intersect.

18. Two points are sometimes collinear. It depends on where they are.

19. Two points are sometimes coplanar. It depends on where they are.

20. Ray MN and NM are not the same ray because the end points are different.

Polynomial is an expression that consists of indeterminates(variable) and coefficients. The possible formula for P(x) is x⁵ - 2x⁴ - 4x³ + 8x².

Polynomial is an expression that consists of indeterminates(variable) and coefficient, it involves mathematical operations such as addition, subtraction, multiplication, etc, and non-negative integer exponentials.

Given the roots of the polynomial, therefore, the following details can be written as,

Therefore, the polynomial will become,

P(x) = (x-2)²(x-0)²(x+2)¹

      = (x²+4-4x) (x)² (x+2)

       = (x²+4-4x) (x³+2x²)

       = x⁵ + 2x⁴ + 4x³ + 8x² - 4x⁴ -8x³

       = x⁵ - 2x⁴ - 4x³ + 8x²

Hence, the possible formula for P(x) is x⁵ - 2x⁴ - 4x³ + 8x².

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Answer:

22

Step-by-step explanation:

Is easy just multiple

Answer:

usually at the login screen it gives you an option to reset your password if you forgot, it will appear in blue as "forgot password?" or "trouble logging in?"

I assume you meant [tex]f(x)=100(0.7)^{x}[/tex]. The graph is shown in the image below.

Answer:

Graph A. On a coordinate plane, a curve approaches y = 0 in quadrant 1 and curves up into quadrant 2. It goes through (2, 49) and (0, 100).

Step-by-step explanation:

Edge