Clean Machine is Middletown's premier house cleaning service. The company used 2,920 gallons of soap last year, and 35% less this year. How many gallons of soap did the company use this year?

The trigonometric function cosine is use to find value of x

The given triangle is a right angled triangle.

The opposite side of angle 35 degrees is x

The hypotenuse of the triangle is 15

We know that cosine function is a ratio of adjacent side and hypotenuse

Cos∠x= adjacent side / hypotenuse

Plug in the values of adjacent side and hypotenuse and the angle

Cos 35 = x/15

Apply cross multiplication

x=cos 35(15)

Hence, the trigonometric function cosine is used to find the value of x.

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Answer:

i am learning about this too!!! heres the answer:

Step-by-step explanation:

reflection translation and rotation

tip:look at Mr. Colin Dodds geometric Shapes song

it helped me memorize this perfectly!!!

Step-by-step explanation:

for what question ?

just in case, always remember Pythagoras

c² = a² + b²

with c being the Hypotenuse, a and b are the legs.

then there is the law of sine

a/sin(A) = b/sin(B) = c/sin(C)

a,b,c being the sides opposite of the A, B, C angles.

and as always : the sum of all angles in a triangle is always 180°.

1.

a)

angle A = 180 - 90 - 35 = 55°

a/sin(55) = 15/sin(90) = 15

a = 15×sin(55) = 12.28728066... m

b)

angle A = 180 - 90 - 25 = 65°

250/sin(65) = b/sin(90) = b = 275.8444797...

2.

a)

remember the trigonometric triangle with the up/down leg being sine (multiplied by the circle radius, which is the Hypotenuse of the triangle), and the left/ right leg being cosine (again multiplied by the Hypotenuse).

5 = 12×sin(x)

sin(x) = 5/12 = 0.416666666...

x = 24.62431835...°

b)

the same principle as for a), just now we need cosine.

12 = 15×cos(x)

cos(x) = 12/15 = 4/5 = 0.8

x = 36.86989765...°

3.

AB² = 125² + 65² = 15625 + 4225 = 19850

AB = sqrt(19850) = 140.890028... cm

angel C = 90°

125/sin(B) = 65/sin(A) = 140.890028.../sin(90)

sin(B) = 125/140.890028... = 0.887216801...

angle B = 62.52556837...°

angle A = 180 - 90 - 62.52556837... = 27.47443163...°

If circle with center N with m∠MNP=124 ∘ and MN=13,  the area of sector MNP is approximately equal to 194.86 square units.

To find the area of a sector of a circle, we need to use the formula:

Area of sector = (central angle/360°) x πr²

Where r is the radius of the circle.

In this problem, we know that the central angle m∠MNP is 124° and MN, which is also the radius of the circle, is 13. So we can substitute these values into the formula:

Area of sector = (124/360) x π(13)²

Area of sector ≈ 194.86

Therefore, the area of sector MNP is approximately equal to 194.86 square units.

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Answer:

For a heptagon or other polygon to be classified as convex, the interior angles must total less than 180°. Any ordinary heptagon could be classified as a convex heptagon.

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Have a GREAT day!!!

Answer:

  0.00000002119188

Step-by-step explanation:

If you enter this number into a spreadsheet (with a single E), you can set the display format to show you the value in standard form. The exponent (E) of -8 indicates the most-significant digit (2) is in the 8th place to the right of the decimal point:

  = 2.119188×10^-8

  = 0.00000002119188

a. Length of GK = \(\sqrt{34}\)  and Length of adjacent to GK = \(\sqrt{34}\)

b. Slope of GK = \(\frac{5}{3}\) and Slope of adjacent to RS =  \(-\frac{3}{5}\)

c. The parallelogram GHJK is Square.

A quadrilateral with two sets of parallel sides is referred to as a parallelogram. As a result, a parallelogram's opposite sides are parallel and congruent in length, and its opposite angles are similarly congruent.

Given in figure GHJK, the vertices are G(-3, 6), H(2, 3), J(-1, -2), K(-6, 1)

a. Length of line = \(\sqrt{({x_{2}-x_{1})^{2} } + ({y_{2}-y_{1})^{2}}\)

for points G(-3, 6) and K(-6, 1)

Length of GK = \(\sqrt{(-6+3)^{2} + (1-6)^{2} }\) = \(\sqrt{34}\)

Length of GK = \(\sqrt{34}\)

Length of adjacent side (GH, KJ) to GK =  \(\sqrt{(2+3)^{2} + (3-6)^{2} }\) = \(\sqrt{34}\)

Length of adjacent to GK = \(\sqrt{34}\)

b. \(Slope = \frac{(y_{2} -y_{1})}{(x_{2} -x_{1})}\)

Slope of GK = \(\frac{(1 - 6)}{(-6 + 3)}\) = \(\frac{5}{3}\)

Slope of GK = \(\frac{5}{3}\)

Slope of adjacent side to GK = \(\frac{3-6}{2+3}\) = \(-\frac{3}{5}\)

Slope of adjacent to RS =  \(-\frac{3}{5}\)

c. All sides are equals to \(\sqrt{34}\)

So, length of diagonal GJ = \(\sqrt{({-3+1))^{2} } + ({6+2})^{2}} = \sqrt{68}\)

and length of diagonal HK = \(\sqrt{({2+6))^{2} } + ({3-1})^{2}} = \sqrt{68}\)

All sides and diagonals are equal then parallelogram GHJK is Square.

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Answer:

48 minutes

Step-by-step explanation:

Answer:

1106

Step-by-step explanation:

PEMDAS [the order of operations]

M[ultiplication] comes before S[ubtraction], so we should multiply first:

26 × 43 = 1118

Now, we can subtract:

1118 - 12 = 1106

you can write this equation as:

(26 × 43) - 12

if that makes more sense to you

hope this helps!! :)

The coordinate of point R after the rotation is determined as = ( - 4, 7).

option A.

A rotation is a transformation that turns the figure in either a clockwise or counterclockwise direction.

You can turn a figure 90°, a quarter turn, either clockwise or counterclockwise. When you spin the figure exactly halfway, you have rotated it 180°. Turning it all the way around rotates the figure 360°.

When a figure is rotated 180 degrees, each point of the figure is moved to a new position that is exactly opposite its original position with respect to a fixed center of rotation.

The initial coordinate of point R = ( 4, 7),

The new coordinate of point R after the rotation = ( - 4, 7)

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The expression that represents the perimeter of the rectangle is 30h - 2

The dimensions of the rectangle are given as:

Length = 7h + 3

Width = 8h - 4

The perimeter of the rectangle is given as:

P = 2 * (Length + Width)

Substitute the known values in the above equation

P =2 * (7h + 3 + 8h - 4)

Evaluate the like terms

P = 2 * (15h - 1)

Evaluate the product

P = 30h - 2

Hence, the expression that represents the perimeter of the rectangle is 30h - 2

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Answer:

459.54

Step-by-step explanation:

46(9.99)

=459.54

Answer:

$159.89

Step-by-step explanation:

36 hours + 10 hours = 46

14.99 * 10 = 149.9

(36 hours) $9.99 + (overtime pay) $149.9 = (Total money) $159.89

$9.99 + $149.9 = $159.89

$159.89

A. The margin of error for a 99% confidence interval is $$2,320.75.

B. The confidence interval for the mean starting salary of college graduates who have taken a statistics course is CI = $42,462.25 to $47,103.75

PART A.

The margin of error (ME) is determined using the formula:

ME= z ∗ σ/√n

where:

z is the z-score for the desired confidence level

σ is the population standard deviation

n is the sample size

For a 99% confidence level, the z-score is 2.576. The population standard deviation is $10,272, and the sample size is 130.

Substituting these values into the formula, we have:

ME =  2.576 ∗ 10272/√130

ME = $2,320.75

PART B

The confidence interval (CI) is determined using the formula:

CI = \(\bar{x}\) ± ME

where:

\(\bar{x}\) is the sample mean

ME is the margin of error

The sample mean is $44,783, and the margin of error is $2,320.75.

Substituting the values into the formula, we get:

CI= 44783 ± 2320.75

CI = $42,462.25 to $47,103.75

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Answer:

3(x+13)

Step-by-step explanation:

use the distributive property to multiply -3 by

3x -5

12x -9x + 15 + 24

then

combine 12x and -9x to get 3

add 15 + 24 to get 39

Answer:

i think it's 40 I don't know.

Step-by-step explanation:

(:

The two sides and two top angles are identical so the two bottom halves are the same

18 -2r = 4R

Add 2r to both sides

18 = 6r

Divide both sides by 6

R = 3

The answer is A. 3

Answer:

-90

Step-by-step explanation:

Answer:

  C:  y = -(x +3)² -1

Step-by-step explanation:

You want the vertex-form equation of the parabola with vertex (-3, -1) and opening downward.

For vertex (h, k), the vertex form equation of a parabola is ...

  y = a(x -h)² +k

Given that (h, k) = (-3, -1), the equation will have the form ...

  y = a(x -(-3))² + (-1)

  y = a(x +3)² -1 . . . . . . . . . . matches choice C

The value of 'a' will be negative when the parabola opens downward. Here, its value is -1.

  y = -(x +3)² -1

__

Additional comment

Once you identify the left-shift of 3 units as resulting in an equation with (x +3)² as a component, you can make the appropriate answer choice without considering anything else. Of course, the fact that the curve opens downward immediately eliminates choices A and B.

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Complete

Find the integral of  \(f(x) =  16sin^2 (x ) cos(x) dx\)

Answer:

The solution is    \(\frac{16}{3} sin^{3}x + c\)

Step-by-step explanation:

So

   \(Let \  u  =  sin(x)\)

=>  \(\frac{du}{dx}  =  cos (x)\)

=>   \(du  =  cos(x)dx\)

So

   \(\int\limits {16sin^2 (x ) cos(x) dx} \, \equiv \int\limits {16u^2  du}\)

=>  \(\int\limits {16u^2  du} = 16 [\frac{u^3}{3} ] + c\)

Now substituting sin(x) for u  

      \(\frac{16}{3} u^3 + c  =  \frac{16}{3} sin^{3}x + c\)

So the  integral of  \(f(x) =  16sin^2 (x ) cos(x) dx\)  is

      \(\frac{16}{3} sin^{3}x + c\)

Answer:

-2/4

Step-by-step explanation:

-4/5 × 10/16

= 2/-4

= -2/4

Answer:

first you correct like terns

Answer:

-3x-2y

Step-by-step explanation:

(-6x+3y)-(-3x+5y)

-6x+3x+3y-5y

-3x-2y

Answer:

$34.99

Step-by-step explanation:

49.99 - 14.997=

34.99

Answer:

the answer is 34.99

if you want me to explain i will ")

Answer:

Step-by-step explanation:

First, you could factor 2 out of the whole thing.  The result would be 2(x^2-4x-45). Now we find the factors of 45 which are 1, 45, 5, 9, 15, 3. We have to find the pair that adds up to 4, and multiply to get 45. After some guess and check, we can find that 5 and 9 are those numbers. Now we have to get the right signs. Since the result is a negative number for -8k, and -90, the number that is a negative must be less than the other negative. -9<-5, so the answer would be 2(x-9)(x+5)

Step-by-step explanation:

7 x7+3-2(-7) (618)

=7 x7+3-2(-4326)

=-4341

Answer:

Step-by-step explanation:

Comment

The sum of the digits is 13.

The first digit is 2

The last digit is 0 or 5

Can it be zero?

2 + _ + 0  = 13

2 + 0  _ x = 13                  Subtract 2 from both sides

2 - 2 + 0 + x = 13 - 2        Combine

x = 11

No there is no such thing as a digit is value is 11. So the last digit is 5

2 + __ + 5 = 13

7 + x = 13                          Subtract 7 from both sides

7-7 + x = 13 - 7                 Combine

x = 6

The middle number is 6

Answer: I am 265

Answer:

A). thickness are correct

The service charge rate are: Help desks $50 per call, Network center $75 per device monitored, Electronic mail $10 per user or per e-mail account, Local voice support $14 per phone extension.

a. Service charge rate

Service charge rate=Budgeted cost/ Budgeted activity base quantity

Help desks:

Service charge rate=$160,000/3,200 calls

Service charge rate=$50 per call

Network center:

Service charge rate=$735,000/9,800 devices

Service charge rate=$75 per device monitored

Electronic mail:

Service charge rate=$100,000/10,000 accounts

Service charge rate=$10 per user or per e-mail account

Local voice support:

Service charge rate=$124,600/8,900 phone extensions

Service charge rate=$14 per phone extension

b.  Help desk charge

Help desk charge =(Number of employees times × Percentage of office employees× Percentage with a computer ×Number of calls)× Service charge rate

Help desk charge:

(5,200 employee×25%×96%×1.5)× $50 per call

=$93,600

Network center charge:

[(5,200 employee×25%×96%)+ 600]× $75 per device

=$138,600

Electronic mail:

(5,200 employee×25%×96%×100)×$10 per user or per e-mail account

=$12,480

Local voice support:

(5,200 employee×25%)× $14 per phone extension

=$18,200

Therefore the service charge rate are: Help desks $50 per call, Network center $75 per device monitored, Electronic mail $10 per user or per e-mail account, Local voice support $14 per phone extension.

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By using trigonometric functions, the value of \(\sin \text{x}^\circ\) is \(\frac{\text{a}}{\text{b}}\).

Trigonometric functions are also known as Circular Functions can be simply defined as the functions of an angle of a triangle. It means that the relationship between the angles and sides of a triangle are given by these trig functions. The basic trigonometric functions are sine, cosine, tangent, cotangent, secant and cosecant.

Given

\(\sin \text{x}^\circ= \ ?\)

\(\tan \text{x}^\circ=\dfrac{\text{a}}{4}\)

\(\cos \text{x}^\circ=\dfrac{4}{\text{b}}\)

Formula to find \(\sin \text{x}^\circ\)

\(\sin \text{x}^\circ=\dfrac{\text{Opposite}}{\text{Hypotenuse}}\)

\(\rightarrow\sin \text{x}^\circ=\bold{\dfrac{a}{b}}\)

Therefore, by using trigonometric functions, the value of \(\sin \text{x}^\circ\) is \(\frac{\text{a}}{\text{b}}\).

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To convert kilometers to miles, we need to divide the number of kilometers by the conversion factor of 1.6.

So, the distance to the gas station in miles is:

36 km ÷ 1.6 km/mi = 22.5 mi

Therefore, the gas station is 22.5 miles away.

Answer:

22.5 miles

Step-by-step explanation: