2) 5x2 - 11x - 42 = 0
Quadratic formula

The correct option for the given question is c) lim x→a¯ f(x) = f(a) when the function f(x) is said to have jump discontinuity at a point x=a.

Jump continuity is a concept in calculus that describes the behaviour of a function at a specific point where the function jumps from one value to another value without any intermediate values. In other words, a function is considered jump continuous at a point if the function approaches a finite limit from both the left and right sides of that point, but the function values on the left and right sides of the point are not equal.

According to the given information:

The correct notation for the left-hand limit as x approaches a from the left side is lim x→a¯, where the horizontal line above the "a" indicates approaching from the left side.

The statement "lim x→a¯ f(x) = f(a)" means that the limit of f(x) as x approaches a from the left side is equal to the value of f(a) at x = a. This indicates that the function f(x) has a jump discontinuity at x = a, where the function jumps from one value to another value at that specific point.

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The straight-line distance between Akira's house and Cooper's house is 6.13 kilometers (rounded to the nearest tenth)

Given that,To get from home to his friend Akira's house, Jaden would have to walk 2.8 kilometers due east.The straight-line distance between Akira's house and Cooper's house is given by the distance between two points in a coordinate plane. Let the home be the origin (0, 0) of the coordinate plane and Akira's house be represented by the point (2.8, 4.7). Similarly, let Cooper's house be represented by the point (8.3, 7.4).The distance formula between the two points (2.8, 4.7) and (8.3, 7.4) is given by:distance = √[(8.3 - 2.8)² + (7.4 - 4.7)²]= √[5.5² + 2.7²]= √(30.25 + 7.29)= √37.54= 6.13 km (rounded to the nearest tenth)

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Answer:

43°

Step-by-step explanation:

supplementary angles sum to 180° , then

second angle + 137° = 180° ( subtract 137° from both sides )

second angle = 43°

Answer:

Step-by-step explanation:

Answer:

If no time is spent on homework, the test grade is approximately 72.

Step-by-step explanation:

The y-intercept of the line can be interpreted if no time is spent on homework, the test grade is approximately 72.

A graph can be described as a pictorial representation of data. A graph is made up of a x-axis and a y-axis.  The y-intercept is the point where the line crosses the y-axis. The y-intercept is the value of the data set when x is zero.

If x is zero, y = 0 + 72

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Answer: linear



Step-by-step explanation:

-Hope this helps :D

Let the present age of student be x

Present of teacher will be 4x

After 20 years,

Age of student = x + 20

Age of teacher = 4x + 20

According to the given condition after 20 years,

x + 20 = (4x + 20)/2

x + 20 = 2x + 10

2x - x = 20 - 10

x = 10

So student's present age is 10 years while teacher's is 4 x 10 i.e 40 years.

Hope This Helps You!

The cost of one plate is $4.30 and the cost of one cup is $2.00.

Let's assume the cost of one plate is p dollars and the cost of one cup is c dollars.

From the given information, we can set up two equations based on the total costs:

Equation 1: 5p + 4c = 26.30 (since 5 plates and 4 cups cost $26.30)

Equation 2: 6p + 5c = 32.00 (since 6 plates and 5 cups cost $32.00)

We have a system of two equations with two unknowns. We can solve this system of equations using various methods, such as substitution or elimination. Let's use the elimination method.

Multiply Equation 1 by 5 and Equation 2 by 4 to eliminate the variable "c" when we add the equations together:

25p + 20c = 131.50 (5 times Equation 1)

24p + 20c = 128.00 (4 times Equation 2)

Subtract Equation 2 from Equation 1:

25p - 24p = 131.50 - 128.00

p = 3.50

Now, substitute the value of p into Equation 1 to find the value of c:

5(3.50) + 4c = 26.30

17.50 + 4c = 26.30

4c = 26.30 - 17.50

4c = 8.80

c = 2.20

Therefore, the cost of one plate is $3.50 and the cost of one cup is $2.20.

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Area of rectangular prism: Base x Height.

so 3x1/3x2/5=0.4 0r 2/5

The inverse function:  \(f^{-1} (x) =\) \((\frac{x -5}{5} )^{2} -13\)

The inverse is defined on the domain x < 5 and x ≥ -13 for the original function, which means that the range of the original function is y ≥ 5.

A function is a relationship that exists between two sets of numbers, with each input from the first set, known as the domain, corresponding to only one output from the second set, known as the range.

Given function is;   \(f(x) = 5\sqrt{(x + 13)} + 5\)

To find the inverse of the given function, we first replace f(x) with y:

⇒  \(y = 5\sqrt{(x + 13)} + 5\)

Subtract 5 from both sides:

⇒ \(y -5 = 5\sqrt{(x + 13)}\)

⇒ \(\frac{(y -5)}{5} = \sqrt{(x + 13)}\)

⇒ \((\frac{y -5}{5} )^{2} = x + 13\)

⇒ \((\frac{y -5}{5} )^{2} -13 = x\)

Now we have x in terms of y, so we can replace x with f⁻¹(x) and y with x to get the inverse function:

f⁻¹(x) = \((\frac{x -5}{5} )^{2} -13\)

The domain of the inverse function is x ≥ 5, because this is the range of the original function, and we were given that the inverse is defined on the domain x < 5. However, we must also exclude the value x = 5, because the denominator of the fraction \((\frac{x -5}{5} )^{2}\) becomes zero at this value. Therefore, the domain of f⁻¹(x) is x > 5.

We were given that x ≥ -13 for the original function, which means that the range of the original function is y ≥ 5. Therefore, the domain of the inverse function becomes the range of the original function, and the range of the inverse function becomes the domain of the original function.

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Answer:

9.6

Step-by-step explanation:

As YZ is parallel to VX, then ΔWYZ ≅ ΔWVX

⇒ WX : WV = WZ : ZX

⇒ 5.6 : (5.6 + 8.4) : 6.4 : (6.4 + J)

\(\implies \dfrac{5.6}{5.6+8.4}=\dfrac{6.4}{6.4+J}x^{2}\)

\(\implies 5.6(6.4 + J)=6.4 (5.6+8.4)\)

\(\implies 35.84+5.6J=89.6\)

\(\implies 5.6J=53.76\)

\(\implies J=9.6\)

Ab=3.14xRadious to the power of 2

then to the area of the rectange you do B x H = YOUR ANSWER

Answer:

1

Step-by-step explanation:

\(( { \sec}^{2} \theta - 1)( { \csc}^{2} \theta - 1) \\ \\ = { \tan}^{2} \theta. { \cot}^{2} \theta \\ \\ = 1\)

Answer:

C: w > y

D: w > x

E: x + y = w

Answer:

-1.33333 < x

Step-by-step explanation:

subtract 5 from both sides

get -4<3x

divde 3 by both sides

-1.33< x

Hi, there!

 _______

The first step is:

» Subtract both sides by 5

\(\sf{-4 < 3x}\)

Now divide each term by 3:

\(\sf{-\dfrac{4}{3} < x}\)

We can flip it over:

\(\sf{x > -\dfrac{4}{3}}\)

Hope the answer - and explanation - made sense,

happy studying!!

Answer:

Step-by-step explanation:

-16t² + 96t = 0

divide by -16

t² - 6t = 0

t(t - 6) = 0

so either

t = 0 (the ball gets wh*acked)

or

t - 6 = 0

t = 6 s  when the ball hits assumed level ground again.

Answer:

Step-by-step explanation:

-16t² + 96t = 0

divide by -16

t² - 6t = 0

t(t - 6) = 0

so either

t = 0 (the ball gets wh*acked)

or

t - 6 = 0

t = 6 s  when the ball hits assumed level ground again.

Answer: Half of them are even and half of them are odd.

Step-by-step explanation:

The even numbers are 6, 12, 18, 24, and 30. An even number is defined as a number that is divisible by 2, meaning it has no remainder when divided by 2. For example, 6 divided by 2 equals 3 with no remainder, so 6 is even.

The odd numbers are 3, 9, 15, 21, and 27. An odd number is defined as a number that is not divisible by 2, meaning it has a remainder of 1 when divided by 2. For example, 9 divided by 2 equals 4 with a remainder of 1, so 9 is odd.

Therefore, out of the given numbers, half of them are even and half of them are odd.

________________________________________________________

Answer:

the answer is A

I followed the point slope formula and added in the x and y values

\(\huge{\textbf{\textsf{{\color{pink}{An}}{\red{sw}}{\orange{er}} {\color{yellow}{:}}}}}\)

D. 400 sq units

The surface area of the right prism given below is 432 square units.

The area of a three dimensional object on it's outer surface is called the surface area of the object.

Given a right prism.

The right prism consists of three rectangular faces and two triangular faces.

Area of a triangular face = 1/2 × 8 × 6 = 24

Area of two triangular faces = 2 × 24 = 48 square units

Area of rectangular faces = (10 × 16) + (8 × 16) + (6 × 16)

                                          = 384 square units

Total area of the prism = 48 square units + 384 square units

                                      = 432 square units

Hence the total area of the prism is 432 square units.

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Answer:

24 1/4 * 7 = 169 3/4

The boat will arrive at the other port at 12:45 p.m.

To determine the time the boat arrives at the other port, we can use the formula:

Time = Distance / Speed

Given:

Distance = 80 km

Speed = 32 km/h

Calculate the time it takes for the boat to travel the given distance:

Time = Distance / Speed

Time = 80 km / 32 km/h

Time = 2.5 hours

Convert the time to minutes:

Since the time is given in hours, we need to convert it to minutes.

1 hour = 60 minutes

2.5 hours = 2.5 * 60 = 150 minutes

Add the calculated time to the departure time:

The boat leaves the port at 10:15 a.m. We need to add 150 minutes to this time to find the arrival time.

10:15 a.m. + 150 minutes = 12:45 p.m.

Therefore,​ the boat will arrive at the other port at 12:45 p.m.

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The missing statement is the quadratic formula and the correct option therefore is the third option;

The quadratic formula is used to find the solution of a quadratic equation. The quadratic formula is; \(x = \frac{-b\pm\sqrt{b^2-4\cdot a\cdot c} }{2\cdot a}\)

The statements and reasons can be presented algebraically as follows;

Statements \({}\)                                          Reasons

\(x^2+\frac{b}{a}\cdot x+(\frac{b}{2\cdot a} )^2 = -\frac{4\cdot a\cdot c}{4\cdot a^2}+ \frac{b^2}{4\cdot a^2}\)        Find a common denominator on the

                                                            right side of the equation

\(x^2 + \frac{b}{a} \cdot x+(\frac{b}{2\cdot a} )^2 = \frac{b^2-4\cdot a \cdot c}{4\cdot a^2}\)                 Add the fractions together on the

                                                     \({}\)        right side of the equation

\((x +\frac{b}{2\cdot a} )^2 = \frac{b^2 - 4\cdot a \cdot c}{4\cdot a^2}\)                             Rewrite the perfect squared equation

                                                      \({}\)      to the left side of the equation as a

                                                        \({}\)    binomial squared

\(x + \frac{b}{2\cdot a} = \pm\sqrt{\frac{b^2 - 4\cdot a \cdot c}{4\cdot a^2} }\)                   Take the square root of both sides of  the

                                                    \({}\) equation

\(\underline{x = \frac{-b\pm\sqrt{b^2 - 4\cdot a \cdot c} }{2\cdot a}}\)                                 Simplify the right side of the equation    

The correct option is therefore;

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Answer:

A

Step-by-step explanation:

i took the test

have a great day :) .!

Answer:

Step-by-step explanation:

Let x be the number of miles you and your friend travel.We know that the cost of the bus ride is 60 cents per mile, so the total cost of the trip is 60 * x.This can be written as an equation as follows:Cost = 60 * xOr, more simply:Cost = 60xThis equation represents the relationship between the number of miles you and your friend travel and the cost of the trip. As the number of miles increases, the cost of the trip also increases at a rate of 60 cents per mile.

Answer:

f(x) has not x^2 term.

Step-by-step explanation:

Linear function is in the form of y=mx+b

In the linear function y=mx+b there is a constant term b

There is also an x term.

m is the slope of f(x). The value of 'm' can be any number.

If we have x^2 term in f(x) then it is quadratic function.

Linear function must always have x with exponent 1

True option is f(x) has not x^2 term.

Answer:

B) 4,700

Step-by-step explanation:

6000 - 4000 = 2000

2000 in 15 year, find how much for each year

2000/ 15 = 133.3333333

133.3333333 estimated = 133

133 approximately for each year

1975 to 1980 is five years

133 x 5 = 665

4000 + 665 = 4665

4665 rounded the the nearest hundred

4700

The function that would have the greatest value at x = 16 include the following: B. y = x² - 17x + 182.

In Mathematics and Geometry, a function is a mathematical equation which defines and represents the relationship that exists between two or more variables such as an ordered pair in tables or relations.

In this exercise, we would determine the corresponding output value for this function of y based on the x-value (x = 16) in simplified form as follows;

\(y = 10^{16}\)

y = 10,000,000,000,000,000.

y = x² - 17x + 182

y = 16² - 17(16) + 182

y = 256 - 272 + 182

y = 166.

\(y = 1.17^x\\\\y = 1.17^{16}\)

y = 12.330304108137675851908392069373.

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Answer:

780

Step-by-step explanation:

In this example we will call Original Price = y

72%=0.72

218.40=0.72*y

1-0.72=0.28

218.4÷0.28=780