Solve the equation below. Only 1 term should be entered in each blank space.


Begin by reducing the fraction on the left by the greatest common factor and entering the new denominator

Since the terms on the left side of the equation are all divisible by that denominator, simplify the left side of the equation

To prove that Sin (A-B) = sinAcos B - Cos Asin B, we can use the angle subtraction formula for sine:

Sin (A-B) = Sin A Cos B - Cos A Sin B

This formula is derived from the identity:

Sin (A-B) = Sin A Cos B - Cos A Sin B

which can be derived by using the double angle identities for sine and cosine:

Sin (2A) = 2 Sin A Cos A

Cos (2A) = Cos^2 A - Sin^2 A = 2 Cos^2 A - 1 = 1 - 2 Sin^2 A

Substituting these identities into the identity above, we get:

Sin (A-B) = Sin A Cos B - Cos A Sin B

Angle subtraction formulas is otherwise known as angle subtraction identities. This angle subtraction formulas permit us to find the exact values of less common trigonometric angles by expressing the less common angle as the difference of two common angles. For example, 15 degrees = 45 degrees - 30 degrees.

Therefore, Sin (A-B) = sinAcos B - Cos Asin B.

learn more about angle subtraction formulas: https://brainly.com/question/17000026

#SPJ1

Answer:

86

Explanation:

3² × (2³ + 4) - 22

9 × (8 + 4) - 22

9 × 12 - 22

108 - 22

86

Answer:

x = 20

y = 70

Step-by-step explanation:

It's rather difficult to explain since nothing is labeled but those are the answers

The measure of ∠A is 29.

What is an angle?

An angle is a figure in plane geometry that is created by two rays or lines that have a shared endpoint. The Latin word "angulus," which meaning "corner," is the source of the English term "angle." The shared terminus of two rays is known as the vertex, and the two rays are referred to as sides of an angle.

Given that,

m∠A = (2x−13)° and m∠B = (2x+ 7)° and ∠A and ∠B are complementary angles.

Therefore

m∠A + m∠B = 90°

(2x−13)° + (2x+ 7)° = 90°

4x + 6 =90

Subtract 6 from both sides:

4x = 84

Divide both sides by 4:

x = 21

Putting x = 21 in m∠A = (2x−13)°:

m∠A = (2 × 21−13)°

m∠A = 29°

To learn more about complementary angles, click on below link:

https://brainly.com/question/18589026

#SPJ1

Step-by-step explanation:

f(x) = 3(x - 5) + 8

f-1(x) = -1(3(x - 5) + 8)

= -3(x - 5) - 8

= -3x + 15 -8

= -3x + 7

Answer:

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

The charge of $55 with error margin of  ± 1.3 results in the least value of $(55 - 1.3) = $53.7 and greatest value of $(55 + 1.3) = $56.3.

If 1000 people signed up for the service, then the least total amount is:

Correct choice is B.

[tex]5x+10y=25[/tex]

Add -10y to both sides:

[tex]5x+10y+-10y=25+-10y[/tex]

[tex]5x=-10y+25[/tex]

Divide both sides by 5:

[tex]\dfrac{5x}{5} =\dfrac{-10y+25}{5}[/tex]

[tex]\fbox{y = -2y + 5}[/tex]

The function h(x) = (f.g)(x) would be x² + 10x + 24.

What are composite functions?

A composite function is generally a function that is written inside another function. The composition of a function is done by substituting one function into another function. For example, f [g (x)] is the composite function of f (x) and g (x). The composite function f [g (x)] is read as “f of g of x”.

To find h(x) = (f.g)(x), we need to find the composition of the functions f(x) and g(x).

The composition of two functions f(x) and g(x) is denoted by (f.g)(x) and is defined as (f.g)(x) = f(g(x)).

In this case, we have:

h(x) = (f.g)(x) = f(g(x)) = f(x + 5)

Substituting x + 5 for g(x) in the equation for f(x), we get:

h(x) = (f.g)(x) = f(x + 5) = (x + 5)² - 1

Simplifying this expression, we get:

h(x) = (f.g)(x) = x² + 10x + 24

Hence, the function h(x) = (f.g)(x) would be x² + 10x + 24.

To learn more about the composite functions, visit:

https://brainly.com/question/10687170

#SPJ1

An item is regularly priced at, 1.98$ is discounted from the regular price.

A percentage is a portion of a whole expressed as a number between 0 and 100 rather than as a fraction. All of something is 100 percent, half of it is fifty percent, none of something is zero percent. To determine a percentage, you divide the portion of the whole by the whole itself and multiply by 100.

Given that,

First, change the percentage into decimal:

Let us assume,

Sale of regular price = 1%

1% = 1/100 = 0.01

Assume, item regular price is = 2$

Multiply 2 with 0.01:

2 * 0.01 = 0.02

Note that this number 0.02 (0.01 of 2) is the amount off from the original price (2). Subtract 2 from 0.02

2 - 0.02 = 1.98

Therefore,

An item is regularly priced at, 1.98$ is discounted from the regular price.

To learn more about Regular price problems visit :

brainly.com/question/11848736

#SPJ4

Answer:

22

Step-by-step explanation:

Corresponding sides of similar triangles are proportional.

[tex]\frac{3x+2}{5x-4}=\frac{15}{20}=\frac{3}{4} \\ \\ 12x+8=15x-12 \\ \\ 3x=20 \\ \\ \therefore SP=20+2=22[/tex]

The solution is Option D.

The minimum number of trips of buses to carry 420 people is 5 trips

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is given as

The number of people the tour bus can carry = 72 people

The total number of people who want to go sightseeing = 420 people

So , the equation will be

The number of trips of bus to carry 420 people =  total number of people who want to go sightseeing / number of people the tour bus can carry

Substituting the values in the equation , we get

The number of trips of bus to carry 420 people = 420/72

The number of trips of bus to carry 420 people = 5.8

The number of trips of bus to carry 420 people = 5 buses

Therefore , the minimum number of buses is 5 buses

Hence , The minimum number of trips of buses to carry 420 people is 5 trips

To learn more about equations click :

https://brainly.com/question/19297665

#SPJ1

Answer: 22( w + 2 ) =77 and the amount of the water bottle would be 1.50

Step-by-step explanation: i dont know what to write??

the maximum altitude attained by the rocket is 300 ft (rounded to the nearest foot) with time.

To find the maximum altitude attained by the rocket, we need to find the vertex of the function h(t). We can do this by taking the derivative of the function and setting it equal to 0.

h'(t) = -32t + 300

Setting h'(t) = 0, we get

-32t + 300 = 0

32t = 300

t = 300/32

hence the time t ≈ 9.375

Now, we can substitute the value of t in the original equation h(t) to get the maximum altitude attained by the rocket.

h(9.375) = -16(9.375)2 + 300(9.375)

h(9.375) = 300 ft

Therefore, the maximum altitude attained by the rocket is 300 ft (rounded to the nearest foot).

The complete question is :

flight of a rocket the altitude in feet attained by a model rocket t time seconds into flight is given by the function h(t). find the maximum altitude (in ft) attained by the rocket. (round your answer to the nearest foot.) h(t)= -16t2 + 300t

Learn more about time here

https://brainly.com/question/28050940

#SPJ4

The point difference between Huskies and Bobcats are 3 x + 4.

Given data :

Difference = Huskies - Bobcats

Hence,

( 5x - 3 ) - ( 2x - 7 )

= 5x - 3 - 2x + 7

= 3x + 4

Learn more about algebra refer to :

https://brainly.com/question/22399890

#SPJ1

68,887 is the sum of the sequence (7+21+63...) to the 9th term.

That is, the sequence (as far as we are given) has a common ratio r=3, between successive terms. The initial term  a= 7 and we are interested in the sum to N = 9 terms.

and the sum of the 9th term is

[a^n = a( 1 - r^N)/1 - r ]

=[7 ( 1 - 3^9 )/ 1 - 3 ]

=7 ( 1 - 19683) / -2

= - 137,774 / -2

= 68,887

9th term = 68,887

To know more about the sequence

https://brainly.com/question/21961097

two thirds of a number b which is no more than 12, is b ≤ 18

What is inequality ?

In mathematics, an inequality represents the connection between two values in an imbalanced algebraic statement. A sign of inequality can be used to show that one of the two variables is larger than, greater than or equal to, less than, or equal to another value.

According to question

two thirds of a number b = (2/3)b

Given two thirds of number b is no more than 12

⇒   (2/3)b ≤ 12

⇒   2b ≤ 12*3

⇒   b ≤ (12*3)/2

⇒   b ≤ 36/2

⇒   b ≤ 18

hence the number b whose 2/3 is no more than 12 is, b ≤ 18

To learn more about Inequality , check out

https://brainly.com/question/28823603

#SPJ1

The area of the composite shape is 292.96 in² and the perimeter of the composite shape is 65.12 inches

The quantity of surface contained within a semicircle's perimeter is known to as its area.

The formula for the Area of a half circle with a Radius (r) is given by  

            Area of Half circle = πr²/2

The formula for the perimeter of a half circle with a radius (r) is given by

           Perimeter of Half circle = πr

Here we have

A picture of a Rectangle with a half circle

Dimensions of Rectangle = 16 in × 12 in

=> Area of rectangle = 16 in × 12 in = 192 in²

=> Perimeter of rectangle shape = 12 + 16 + 12 = 40 inches

[ Here we only take one side of the rectangle since one of the sides is connected with a Half circle ]

The radius of half circle = 8 inch

=> Area of Half circle = π(8)² = (3.14)(64)/2 = 100.96 in²

=> Perimeter of Half circle = πr =(3.14)(8) = 25.12 in

Area of the composite shape

= Ractangle's Area + Half circle's Area

= 192 in² + 100.96 in²

= 292.96 in²

The perimeter of the composite shape

= Ractangle perimeter + Half circle perimeter

= 40 inches + 25.12 inches

= 65.12 inches

Therefore,

The area of the composite shape is 292.96 in² and the perimeter of the composite shape is 65.12 inches

Learn more about Half circles at

https://brainly.com/question/23157566

#SPJ1

Answer:

25x^2√(2x)

Step-by-step explanation:

2√(50x^5) + 5x√(18x^3) =

2√((2*25) * x^(4+1)) + 5x√((2*9) * x^(2+1)) =

2√(2 * 5^2 * x^4 * x^1) + 5x√(2 * 3^2 * x^2 * x^1) =

5*2√(2 * 1 * x^(2^2) * x) + 3*5x√(2 * 1 * x^2 * x) =

10√(2 * x^(2^2) * x) + 15*x*x√(2 * 1 * x) =

10√(2x * (x^2)^2) + 15*x^2√(2x) =

10x^2√(2x) + 15x^2√(2x) = 25x^2√(2x)

[tex]3y= -6x+1[/tex] for y

Divide both sides by 3:

[tex]\dfrac{3y}{3} =\dfrac{-6x+1}{3}[/tex]

[tex]\fbox{y = $-2x+\dfrac{1}{3} $}[/tex]

62/87,21

y = x + 5

3x + y = 25

Substitute x + 5 for y in the second equation.

Substitute the solution for x into either equation to find y.

The solution is (5, 10).

The LCM of the given pairs are 10, 15,12,30,6,24,20,18, and 63 respectively.

The least common multiple (LCM) of two numbers is the lowest possible number that can be divisible by both numbers.

There are 9 pairs, so let's name them using the letters A to I.

The LCM of the first pair A (2, 5) is 10.

The LCM of the pair B (3, 15) is 1*3*5 = 15.

The LCM of the pair C (6, 12) is 3*2*1*2 = 12.

The LCM of the pair D (3, 15) is 2*3*1*5 = 30.

The LCM of the pair E (2, 3) is 1*3*2 = 6.

The LCM of the pair F (8, 24) is 2*2*2*1*3 = 24.

The LCM of the pair G (4, 10) is 2*2*5 = 20.

The LCM of the pair H (6, 9) is 3*2*3 = 18.

The LCM of the pair I (7, 9) is 7*9 = 63.

Hence, 10,15,12,30,6,24,20,18,63 are the LCM of the given pairs.

To learn more about LCM, use the link given below:

https://brainly.com/question/20739723

#SPJ1

Answer:

photo?

Step-by-step explanation:

The simple interest implies that Lonzo owes $1513.5

The given variables can be represented as:

Loan amount P = $1500

Rate of interest, R = 1.2%

Time to pay back the loan, t = 9 months i.e. 0.75 year

The amount from a simple interest can be calculated using:

A = P(1 + RT)

Substitute the known values in the above equation, so, we have the following representation

A = 1500 * (1 + 1.2% * 0.75)

Evaluate

A = 1513.5

Hence, the amount owed is $1513.5

Read more about simple interest at:

https://brainly.com/question/20690803

#SPJ1

Since the line is linear, the sum of the angles should be 180 degrees

x + 28 + 73 = 180

x = 180 - 28 - 73

x = 79 degrees

Hope this helped :)

Answer:

Negative seven and seven sixteenths

Step-by-step explanation:

2⅛ x (-7) x 5/10

= 17/8 x (-7) x 1/2

= - 119/16

= - 7 7/16

To find the difference in the number of items produced by the two plants, we can subtract the production level of the second plant from that of the first plant. This gives us:

Therefore, the first plant produces [tex]5x + 22[/tex] more items daily than the second plant.

It will take 5 minutes before the stadium is half empty

Given that:

Over 92,000 fans pack the stadium to watch the Tigers play

The fans leave at a rate of 10% per minute

The number of fans that leave per minute will be:

10% of  92,000 = 10/100 × 92, 000 = 9,200

The stadium will be fully empty  in:

time = 92,000/9,200 = 10 minutes

The stadium will be half empty  in:

time = 10 minutes / 2 = 5 minutes

Learn more about rate and time on:

https://brainly.com/question/17146782

#SPJ1

Answer:

  equilateral

Step-by-step explanation:

You want to know if the given triangle with angles marked (2x)°, (2x)°, and (3x-30)° is equilateral, isosceles, or neither.

On the face of it, the triangle is at least isosceles, as two angles are marked identically as (2x)°.

When we apply the angle sum theorem, we find ...

  (2x)° +(2x)° +(3x -30)° = 180°

  7x -30 = 180

  7x = 210

  x = 30

  2x = 2(30) = 60

  3x -30 = 3(30) -30 = 60

All of the angles have the same measure, 60°, so the triangle is equilateral.

Answer:

Step-by-step explanation:

2x + 2x + 3x - 30 = 180

7x = 210

x = 210 : 7

x = 30

2 x 30 = 60°

3 x 30 - 30 = 60

3 equal angles = equilateral triangle

Answer:

20% decrease

Step-by-step explanation:

[tex]\frac{75-60}{75}[/tex]

[tex]\frac{15}{75}[/tex] = .2  to make a percent, multiply by 100 = 20%

Answer:

She walked 1.508 miles

Step-by-step explanation:

In 1 hour, Marta can walk 2.9 miles

In 0.52 hours, she can walk 2.9 x 0.52 = 1.508 miles