Carlos graphed the system of equations that can be used to solve x cubed minus 2 x squared 5 x minus 6 = negative 4 x squared 14 x 12. On a coordinate plane, 2 functions are shown. The functions intersect at (negative 3, negative 66), (negative 2, negative 32), and (3, 18) What are the roots of the polynomial equation? –3, –2, 3 –3, 2 18, 32 18, 32, 66

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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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:

24/1

Step-by-step explanation:

[tex] \frac{2400}{ \\ 100} [/tex]

and u get 24/1

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.

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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:

86

Explanation:

3² × (2³ + 4) - 22

9 × (8 + 4) - 22

9 × 12 - 22

108 - 22

86

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]

[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:

  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 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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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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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

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[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]

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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AB is congruent to CD.AB = CD =[tex]\sqrt{14} units[/tex] (proved)

In coordinate geometry, we use the distance formula to find the distance between two coordinates in a straight line. It represented D.

Let's consider two points on a coordinate plane given as A and B (x₂, y₂).

D = [tex]\sqrt{(x2 -x 1)^2 + (y2 - y1)^2}[/tex]

Given:

The coordinates of the given quadrilateral are,

A(1, 5), B(6, 1), C(−2, 8), D(−6, 3).

According to the question we need to determine AB = CD.

By using the distance formula of coordinate geometry.

[tex]\sqrt{(x2 -x 1)^2 + (y2 - y1)^2}[/tex]

Distance between A and B,

[tex]AB =\sqrt{(6 - 1)^2 + (5-1)^2 } \\AB = \sqrt{5^2 + 4^2} \\AB = \sqrt{25 + 16} \\AB = \sqrt{41} units[/tex]        .......(1)

Distance between C and D,

[tex]CD =\sqrt{(-6 -(-2))^2 + (3-8)^2 } \\CD = \sqrt{(-4)^2 + (-5)^2} \\CD = \sqrt{16 + 25} \\CD = \sqrt{41} units[/tex].......(2)

From equation (1) and (2) we find that

AB = CD =[tex]\sqrt{14} units[/tex]

Hence, AB is congruent to CD.AB = CD =[tex]\sqrt{14} units[/tex] (proved).

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The only true given statement about debtors and creditors is; C. Debtors receive loans as capital from creditors.

Debtors are defined as the party from whom we have to receive the payment in the form of cash or any negotiable instrument.This means an asset for the firm.

Meanwhile, the creditors are defined as the party to which we will pay in the future agreed date in the form of cash or any negotiable instrument. This means liability for a firm.

A) This is not true because creditors don't receive  loans from consumers as capital. This is the role of debtors.

B) This is not correct because it is not true that every debtor is guaranteed a loan.

C) This is true as defined earlier on the role of debtors and creditors.

D) This is not true because different creditors have different lending rates as the case may be.

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The required life is any living thing that has the property to be born, grow and end of the life cycle is life.

Any object that has characteristics of life is called living a being.

Here,

Life can be defined as the ability for growth, response to encouragements, metabolism, energy vitality and reproduction are characteristics that set life apart from matter that lacks biological activities, such as signaling and self-sustaining processes.

Thus, the required life is any living thing that has the property to be born, grow and end the life cycle is life.

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Answer:

photo?

Step-by-step explanation:

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 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

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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)

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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Answer: 15/16 hour

Step-by-step explanation:

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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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 equations a + 4 = 14 and a = 6 - 4 are not equivalent.

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.

From the information, a - 4 = 14

Therefore a = 14 + 4

a = 18.

a + 4 = 6

a = 6 - 4.

a = 2

They are not equivalent.

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a - 4 = 14

a + 4 = 6

Are these 2 equivalent.

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.

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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??

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.