Find the area of the triangle.

Answer:

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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.

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

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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°

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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

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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.

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The standard form for a circle is (x - h)2 + (y - k)2 = r2, where (h, k) is the center and r is the radius. Since the radius is not given, we need to plug in the information given.  Since the center is at the origin, this is the point (0, 0).  Since another point on the circle is (6, 8), that is the (x, y) value.  So let's plug it into the equation:

(8 - 0)2 + (8 - 0)2 = r2  --> 82 + 82 = r2 --> 100 = r2  --> 10 = r.

Since r = 10 and the center is (0, 0), the standard form equation of this circle is (x - 0)2 + (y - 0)2 = 102 or just x2 + y2 = 100.

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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

On solving the provided question, we can say that - there are 120 distinct pizza topping combinations that may be created if the maximum number of toppings is 3.

Regardless of the sequence in which the items were chosen, a mathematical approach known as a combination may be used to calculate the number of alternative arrangements within a collection of objects. Any order can be chosen by a combination. Combinations in mathematics are ways to choose elements from a collection, and the order in which they are chosen is irrelevant. Let's say we have a trio of numbers: P, Q, and R. The amount of possible combinations for two integers from each set is determined by combinations.

Given: Six toppings in all.

There are three toppings to choose from.

Additionally, if topping repetition is prohibited, the number of viable combinations is equal to 6 × 5 x 4. [We select one out of six first, then one out of the remaining five, then one out of four, and finally we multiply the options for three toppings]

= 120

As a result, there are 120 distinct pizza topping combinations that may be created if the maximum number of toppings is 3.

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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)

Answer:

4

Step-by-step explanation:

√64 = 8

√4 = 2

8/2 = 4

Answer:4

Step-by-step explanation:

[tex]\sqrt{64[/tex] = 8

[tex]\sqrt{4[/tex]  = 2

8÷2=4

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

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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

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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.

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Answer:

Step-by-step explanation:

f(x) = 8 sin [2(x+3)] + 9

x = 8 sin [2(y+3)] + 9

isolate y [tex](f^{-1}(x))[/tex]:

x/8 - 9 = sin[2(y+3)]

[tex]sin^{-1}(\frac{x}{8} - 9) = 2(y+3)[/tex]

                     =  2y + 6

[tex]sin^{-1}(\frac{x}{8} - 9) = 2y + 6\\sin^{-1}(\frac{x}{8} - 9) - 6 = 2y\\\frac{sin^{-1}(\frac{x}{8} - 9) - 6}{2} = y[/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).

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:

x = 20

y = 70

Step-by-step explanation:

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

[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]

Answer:

C - 52.50

Step-by-step explanation:

49 Euros To dollars

Answer:

C) 52.50

Step-by-step explanation:

[tex]\frac{15}{14}[/tex] = [tex]\frac{x}{49}[/tex]  Cross multiply and solve for x

14x = 15(49)

14x = 735  Divide both sides by 14

[tex]\frac{14x}{14}[/tex] = [tex]\frac{735}{14}[/tex]

x = 52.50

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 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

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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

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

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

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After 7 hours, the population of bacteria is obtained as 418544.

Some of the rules of exponents are as follows,

The product of two exponents having the same power is equal to the power of their base multiplied.

The product of two exponents having the same base is equal to the sum of the powers of different exponents to the same base.

The initial population of bacteria is given as 37000.

And, the doubling time is 2 hours.

Then, the formula for the population of bacteria at t hour can be given as,

P(t) = P₀ × [tex]2^{t/2}[/tex] where P₀ is the initial population.

Substitute t = 7 and P₀ = 37000 to get,

P(7) = 37000 × [tex]2^{7/2}[/tex]

⇒ P(7) = 418544

Hence, the population of bacteria after 7 hours is 418544.

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Answer:

Step-by-step explanation:

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.

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:

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%