If sin x = -1/2, and 270° < x < 360°, what is cos(x - 30°)?

Answer:

y = - 6x + 5

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = [tex]\frac{1}{6}[/tex] x + 3 ← is in slope- intercept form

with slope m = [tex]\frac{1}{6}[/tex]

Given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{1}{6} }[/tex] = - 6, hence

y = - 6x + c ← is the partial equation of the perpendicular line.

To find c substitute (- 3, 23) into the partial equation

23 = 18 + c ⇒ c = 23 - 18 = 5

y = - 6x + 5 ← equation of perpendicular line

Answer:

A.2sinxcosx

Step-by-step explanation:

We know the trig identity

Sin (2a) = 2 sin a cos a

sin (2x) = 2 sin x cos x

Answer:

2sinxcosx

Step-by-step explanation:

A P E X

Answer:

[tex]x_1 = 9[/tex] and [tex]x_2 = 11[/tex].

Step-by-step explanation:

Start by adding 1 to both sides of this equation.

[tex](x - 10)^{2} = 1[/tex].

The square of what number or numbers will lead to the number "1"? It turns out that not only [tex]1^{2} = 1[/tex], but [tex](-1)^{2}= 1[/tex] as well. In other words, the value [tex](x - 10)[/tex] can be either 1 or -1. Either way, the equation is still going to hold. That's the reason why there are two solutions to this equation.

Consider the case when [tex]x - 10 = 1[/tex]. Add 10 to both sides of the equation. [tex]x = 11[/tex].

Now, consider the case when [tex]x - 10 = -1[/tex]. Again, add 10 to both sides of the equation, [tex]x = 9[/tex].

Order the two solutions in an increasing order:

Answer:

If the width of the rectangle is x than the length is 4x because 4x*x is 4x^2

Step-by-step explanation:

To find the inverse of a function switch the place of y (aka f(x) ) with x. Then solve for y.

Original equation:

y = 2x + 17

Switched:

x = 2y + 17

Solve for y by isolating it:

x - 17 = 2y + 17 - 17

x - 17 = 2y

(x - 17)/2 = 2y/2

[tex]\frac{1}{2}x-\frac{17}{2}= y[/tex]

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

=$2739.81

Step-by-step explanation:

To find the total amount if the interest is compounded, we use the compound interest formula.

A=P(1+R/100)ⁿ

A is the amount, P- principal, is the invested amount R is the % interest rate, n is the number if periods.

If compounded semi-annually, it means we have two periods in 1 year

The rate is also divided by 2

Thus 25 years have (25×2) = 50 periods.

A= 750(1+5.25/200)⁵⁰

=750(1.02625)⁵⁰

=$2739.81

Answer:

10sqrt3+22

Step-by-step explanation:

Ok, let us imagine it as a sort of rectangle split upon its diagonal.

Using that, we can Pythag it out,

11^2+b^2=14^2

121+b^2=196

b^2=75

b=sqrt75

b=5sqrt3

Ok, using this info, we find the perimeter,

5sqrt3+5sqrt3+11+11

10sqrt3+22

The answer is 10sqrt3+22

The answer is:

The perimeter of the rectangle is equal to 39.32".

[tex]Perimeter=39.32in[/tex]

Since we are working with a rectangle, we can use the Pythagorean theorem to find the missing side of the rectangle and calculate its perimeter. We must remember that we can divide a rectangle into two equal right triangles.

According to the Pythagorean Theorem, we have:

[tex]a^{2}=b^{2}+c^{2}[/tex]

Where:

a, represents the hypotenuse of the triangle which is equal to the diagonal of the given rectangle (14")

b and c are the other sides of the triangle.

Now, let be "a" 14" and "b" 11"

So, solving we have:

[tex]a^{2}=b^{2}+c^{2}[/tex]

[tex]14^{2}=11^{2}+c^{2}[/tex]

[tex]14^{2}-11^{2}=c^{2}[/tex]

[tex]14^{2}-11^{2}=c^{2}\\\\c=\sqrt{14^{2} -11^{2} }=\sqrt{196-121}=\sqrt{75}=8.66in[/tex]

Now, that we already know the the missing side of the rectangle, we can calculate the perimeter using the following formula:

[tex]Perimeter=2base+2length\\\\Perimeter=2*11in+2*8.66in=22in+17.32in=39.32n[/tex]

Hence, we have that the perimeter of the rectangle is equal to 39.32".

Have a nice day!

Answer:

The correct option is A.

Step-by-step explanation:

We need to find the cheapest per month over all.

Assume a month has 30 days.

In option A:

Rent = 11.95 a day

Monthly rent = 11.95 × 30 = 358.5

Total renting amount is 358.5.

In option B:

Lease = 149.00 a month 3180 due at signing

Total amount = 149 + 3180 = 3329

Total leasing amount is 3329.

In option C:

Buying = 16,000

In option D:

Finance = 389.00 /month

The cheapest amount for a month is 358.5 .Therefore the correct option is A.

Answer: renting a car

Step-by-step explanation:

Answer:

270

Step-by-step explanation:

base area=18

18*15=270

The volume of the triangular prism is equal to [tex]270[/tex] cu. units.

" Volume is defined as the total space occupied by a three-dimensional object."

Formula used

Volume of a triangular prism = Area of the base × height

Area of the base [tex]= \frac{1}{2} \times base \times height[/tex]

According to the question,

Given dimensions,

Base of triangle [tex]= 9 units[/tex]

Height of the triangle [tex]=4 units[/tex]

Height of the triangular prism [tex]= 15 units[/tex]

Substitute the value in the formula to get the area of the base we have,

Area of the base [tex]= \frac{1}{2}\times 9\times 4[/tex]

                             [tex]= 18 square units[/tex]

Volume of a triangular prism [tex]= 18 \times 15[/tex]

                                                  [tex]= 270 cu.units[/tex]

Hence, the volume of the triangular prism is equal to [tex]270[/tex] cu. units.

Learn more about volume here

https://brainly.com/question/1578538

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Answer:

it must be 9

Step-by-step explanation:

it is a simple division.

To isolate the variable terms on one side and the constant terms on the other side of the equation 3x - 5 = -2 + 10, add 2 to both sides, simplify to 3x - 3 = 10, then add 3 to both sides to get the final simplified equation 3x = 13.

The equation 3x - 5 = -2 + 10 needs to be rearranged to isolate the variable terms on one side and the constant terms on the other. To do this, follow these steps:

Now, we have successfully isolated the variable terms (3x) on one side of the equation and the constant terms (13) on the other side.

Answer:

a) The length of the diagonal is 17.71 feet

b)  The area of the trapezoid is 123.14 feet²

Step-by-step explanation:

* Lets explain how to solve the problem

- Look to the attached figure

- ABCD is an isosceles trapezoid

∵ DC is the longer base with length 18 feet

∵ AD and BC are the two non-parallel sides with length 8 feet

∵ ∠ ADC and ∠ BCD are the bases angles with measure 75°

- AE and BF are ⊥ DC

# In Δ BFC

∵ m∠BFC = 90° ⇒ BF ⊥ CD

∵ m∠C = 75°

∵ BC = 8

∵ sin∠C = BF/BC

∴ sin(75) = BF/8 ⇒ multiply both sides by 8

∴ BF = 8 × sin(75) = 7.73

∵ cos∠C = CF/BC

∴ cos(75) = CF/8 ⇒ multiply both sides by 8

∴ CF = 8 × cos(75) = 2.07

# In Δ BFD

∵ m∠BFD = 90°

∵ DF = CD - CF

∴ DF = 18 - 2.07 = 15.93

∵ BD = √[(DF)² + (BF)²] ⇒ Pythagoras Theorem

∴ BD = √[(15.93)² + (7.73)²] = 17.71

a)

∵ BD is the diagonal of the trapezoid

* The length of the diagonal is 17.71 feet

b)

- The area of any trapezoid is A = 1/2 (b1 + b2) × h, where b1 and b2

  are the barallel bases and h is the height between the two bases

∵ b1 is CD

∴ b1 = 18

∵ b2 is AB

∵ AB = CD - (CF + DE)

∵ ABCD is an isosceles trapezoid

∴ CF = DE

∴ AB = 18 - (2.07 + 2.07) = 13.86

- BF is the perpendicular between AB and CD

∴ BF = h

∴ h = 7.73

∵ A = 1/2 (18 + 13.86) × 7.73 = 123.14

* The area of the trapezoid is 123.14 feet²

[tex]\bf r=2sec(\theta )\qquad \begin{cases} x=rcos(\theta )\\ \frac{x}{r}=cos(\theta ) \end{cases}\qquad \implies r=2\cdot \cfrac{1}{cos(\theta )}\implies r=\cfrac{2}{~~\frac{x}{r}~~} \\\\\\ r=\cfrac{\frac{2}{1}}{~~\frac{x}{r}~~}\implies r=\cfrac{2r}{x}\implies x=\cfrac{2~~\begin{matrix} r \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{~~\begin{matrix} r \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\implies x=2[/tex]

Final answer:

The notation h(40)=1820 means that the function h produces an output of 1820 when the input is 40, although additional context is needed to determine what h represents specifically in this scenario.

Explanation:

The expression h(40)=1820 typically means that a function h is being evaluated at the input value of 40, and the output is 1820. This could represent a variety of contexts, such as the height of a rocket in meters at 40 seconds after launch, the amount of money saved after 40 weeks, or any other situation described by a function where the variable h depends on the number 40. Without additional context, it's impossible to say precisely what 1820 refers to, but it is the result of the function h when the input is 40.

The restriction on the domain of the function [tex]f(x) = {x + 5}/{x - 2}.[/tex] is that x cannot be equal to 2, since it would make the denominator zero, which is undefined in real numbers.

The student is asking to identify the restrictions on the domain of the function [tex]f(x) = {x + 5}/{x - 2}.[/tex] The domain of a function includes all the values that x can take for which the function is defined. In the case of a rational function, any values that make the denominator zero must be excluded from the domain since division by zero is undefined.

In this function, the denominator is x - 2. Therefore, the value that makes the denominator zero is x = 2. To identify the restrictions on the domain of [tex]f(x) = {x + 5}/{x - 2}.[/tex] we set the denominator equal to zero and solve for x:

Hence, the only restriction on the domain of this function is that x cannot be 2. So the domain of f(x) is all real numbers except x = 2.

Irrational numbers cannot be expressed as a fraction or ratio of two integers and have decimal representations that go on forever without repeating.

Irrational numbers are numbers that cannot be expressed as a fraction or ratio of two integers. They are decimal numbers that go on forever without repeating. Examples of irrational numbers include π, √2, and √3. These numbers cannot be expressed as a simple fraction or as a terminating or repeating decimal.

Answer:

1. Dispersion: how data is distributed

2. Inter quartile range:the difference between the largest and smallest of the middle 50% of the data set

3. Lower Quartile:the median of the lower half of the data set; a value which 25% of the data set falls below

4. Outlier:a data value that is far from the others

5. Percentile: a value below which a certain percentage of the data set falls; the median is the 50th percentile.

6. Range:the difference between the largest and smallest of the numbers in a set

7. Upper Quartile:the median of the upper half of the data set; a value which 75% of the data set falls below

Final answer:

In statistics, 'dispersion' refers to the distribution of data, the 'inter-quartile range' is the spread of the middle 50% of data, 'lower quartile' (Q1) is the value below which 25% of data falls, an 'outlier' is a data point far from the others, 'percentile' is a value below a certain percentage of data, 'range' is the difference between the largest and smallest data values, and 'upper quartile' (Q3) is the value below which 75% of the data falls.

Explanation:

To correctly match the terms to their definitions from the provided options:

Dispersion is matched to 'how data is distributed.'

Inter-quartile range (IQR) is 'the difference between the largest and smallest of the middle 50% of the data set.'

Lower quartile (also known as the first quartile or Q1) is 'the median of the lower half of the data set; a value which 25% of the data set falls below.'

Outlier is 'a data value that is far from the others.'

Percentile is 'a value below which a certain percentage of the data set falls; the median is the 50th percentile.'

Range is 'the difference between the largest and smallest of the numbers in a set.'

Upper quartile (also known as the third quartile or Q3) is 'the median of the upper half of the data set; a value which 75% of the data set falls below.'

Answer:

This is the definition of rational number.

These include: Integers, Terminating Decimals, Repeating Decimals, or Proper, Improper, and Mixed Fractions where each part is an integer.  

Step-by-step explanation:

This is the definition of rational number.

Here are some examples of rational number:

-3  (negative integers are included because they can be rewritten; here -3=-3/1)

5 (positive integers are included because they can be rewritten; here 5=5/1)

0 (neutral integers are included also because 0/4 or 0/1 are still 0)

5/3 (impropert fractions where top and bottom are integers; this is already written in the form required)

1   2/3  (mixed fractions because they can rewritten as improper fractions with top and bottom as integers; example here this 5/3)

2/5  (proper fractions where top and bottom are integers; this is already written in the form required)

.55555555555...=[tex]. \overline{5}[/tex] (repeating decimals; example this one can be written as 5/9)

.23 (terminating decimals; example this can be written as 23/100 )

Answer:

3x+10

Step-by-step explanation:

( - x + 12) - (  - 4x + 2)

Distribute the minus sign

( - x + 12) + 4x - 2

Combine like terms

3x +10

Answer:

800 milliliters

Step-by-step explanation:

we know that

To find out the total amount Kelly drank, add the amount of coffee and the amount of yogurt and convert the result to milliliters.

so

0.5+0.3=0.8 liters

Remember that

1 liter= 1,000 milliliters

so

0.8 liters=0.8*1,000=800 milliliters

Answer:

800 mL

Step-by-step explanation:

Because we know that

1 liter equals 1000 milliliters

So 0.5+0.3=0.8

0.8 Liters=0.8*1,000 ML

[tex]\bf a^3b^{-2}c^{-1}d\implies \cfrac{a^3d}{b^2c}\qquad \begin{cases} a=2\\ b=4\\ c=10\\ d=15 \end{cases}\implies \cfrac{2^3\cdot 15}{4^2\cdot 10}\implies \cfrac{120}{160}\implies \cfrac{3}{4}[/tex]

Answer:

Scalene Triangle

Step-by-step explanation:

By definition, scalene triangles have 3 sides of unequal length.

FYI,

Right Triangle : triangle with one of the angles = 90°

Isosceles Triangles: Triangle with 2 sides of the same length.

Equilateral triangle: Triangle with 3 sides of the same length.

Answer:

29.1 cm

Step-by-step explanation:

Circumference of a circle is:

C = 2πr

Given that C = 183 cm:

183 = 2πr

r = 183 / (2π)

r ≈ 29.1 cm

Answer:

45.55 m to the nearest hundredth.

Step-by-step explanation:

tan 26 = opposite / adjacent side = h / 90   where h = height of the dam - Scarlett's height.

The height of the dam =

y = 90 tan 26

= 43.895 m

Now we need to add Scarlett's height  

= 45.55 m.

Answer:

grg

Step-by-step explanation:

rgg

Answer:

B

Step-by-step explanation:

The solution to a system of equations given graphically is at the point of intersection of the 2 lines, that is

Solution = (1, 5 ) → B

[tex]\huge{\boxed{\text{(1, 5)}}}[/tex]

All you need to do is find where the intersection of the lines is located.

Count how many units to the right. [tex]1[/tex] This is our [tex]x[/tex] value.

Count how many units up. [tex]5[/tex] This is our [tex]y[/tex] value.

Answer:

z = 5/3 or 1 2/3

Step-by-step explanation:

2/3·z=10/9

Multiply each side by 3/2

3/2*2/3·z=10/9*3/2

z = 30/18

We can simplify by dividing the top and bottom by 6

z = 5/3

Changing to a mixed number

z =1 2/3

Answer:

1⅔ [OR 5⁄3]

Step-by-step explanation:

2 × ? = 10

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

3 × ? = 9

That would be 1⅔.

I am joyous to assist you anytime.

[tex]\bf sin(y)+cos(y)+tan(y)sin(y)=sec(y)+cos(y)tan(y) \\\\[-0.35em] ~\dotfill\\\\ sin(y)+cos(y)+tan(y)sin(y)\implies sin(y)+cos(y)+\cfrac{sin(y)}{cos(y)}\cdot sin(y) \\\\\\ sin(y)+cos(y)+\cfrac{sin^2(y)}{cos(y)}\implies \stackrel{\textit{using the LCD of cos(y)}}{\cfrac{sin(y)cos(y)+cos^2(y)+sin^2(y)}{cos(y)}} \\\\\\ \cfrac{sin(y)cos(y)+\stackrel{cos^2(y)+sin^2(y)}{1}}{cos(y)}\implies \cfrac{sin(y)cos(y)+1}{cos(y)} \\\\\\ \cfrac{sin(y)}{cos(y)}\cdot cos(y)+\cfrac{1}{cos(y)}\implies tan(y)cos(y)+sec(y)[/tex]

Answer:

Proof is in the explanation.

Step-by-step explanation:

I'm going to use mathematical induction.

That means we are going to show:

1) For n=3 the expression given is a multiple of 6. (We started at n=3 because it says n>2.)

2) If the base cases check out, then we are going to assume (n-2)(n-1)(2n-3) is a multiple of 6, then show ([n+1]-2)([n+1]-1)(2[n+1]-3) is also a multiple of 6.

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

Proof:

Base case (n=3):

(3-2)(3-1)(2*3-3)

1(2)(6-3)

2(3)

6

6 is a multiple of 6 since 6(1)=6.

After the base case (for all natural numbers greater than 2):

Assume there is integer k such that:

6k=(n-2)(n-1)(2n-3).

We are going to show 6m=([n+1]-2)([n+1]-1)(2[n+1]-3) where m is a integer.

([n+1]-2)([n+1]-1)(2[n+1]-3)

(n-1)(n)(2n-1)

(n-2+1)(n)(2n-1)

(n-2)(n)(2n-1)+1(n)(2n-1)

(n)(n-2)(2n-1)+1(n)(2n-1)

(n-1+1)(n-2)(2n-1)+1(n)(2n-1)

(n-1)(n-2)(2n-1)+1(n-2)(2n-1)+1(n)(2n-1)

(2n-1)(n-2)(n-1)+1(n-2)(2n-1)+1(n)(2n-1)

(2n-3+2)(n-2)(n-1)+1(n-2)(2n-1)+1(n)(2n-1)

(2n-3)(n-2)(n-1)+2(n-2)(n-1)+1(n-2)(2n-1)+1(n)(2n-1)

6k+2(n-2)(n-1)+1(n-2)(2n-1)+1(n)(2n-1)

6k+2(n^2-3n+2)+1(2n^2-5n+2)+2n^2-n

6k+6n^2-12n+6

6(k+n^2-2n+1)

where k+n^2-2n+1 since integers are closed under addition and multiplication (referring to the n^2, the n*n part).

Since we have found an integer m, k+n^2-2n+1, such that

6m=([n+1]-2)([n+1]-1)(2[n+1]-3)

then we have shown for all integers greater than 2 we have that

(n-2)(n-1)(2n-3) is divisible by 6.

//

again, bearing in mind that standard form for a linear equation means

• all coefficients must be integers, no fractions

• only the constant on the right-hand-side

• all variables on the left-hand-side, sorted

• "x" must not have a negative coefficient

[tex]\bf (\stackrel{x_1}{3}~,~\stackrel{y_1}{-2})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{2}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{2-(-2)}{6-3}\implies \cfrac{2+2}{6-3}\implies \cfrac{4}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-(-2)=\cfrac{4}{3}(x-3)\implies y+2=\cfrac{4}{3}x-4 \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf y=\cfrac{4}{3}x-6\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{3}}{3(y)=3\left( \cfrac{4}{3}x-6 \right)}\implies 3y=4x-18 \\\\\\ -4x+3y=-18\implies \stackrel{\textit{standard form}}{4x-3y=18}[/tex]