use the discriminant to determine how many and what kind of solutions the quadratic equation 3x2 4x=-5 has

The equations of the lines parallel and perpendicular to the lines f (y = 2), ang g (y = 2·x - 1), with the parallel lines passing through the point P(-2, -1), and the perpendicular line passing through the point Q(3, -2) are;

A. The equation of the line parallel to the line f and passing through the point P is; y = -1

B. Equation of the parallel line to g and passing through P is; y = 2·x + 3

C. Equation of the line perpendicular to f passing through P is; x = 3

D. The equation of the line perpendicular to g and which passes through P is y = -0.5·x - 0.5

Perpendicular lines are lines that intersect forming (right angles) an angle of 90°.

The equation that represents the line f is y = 2

The equation that represents the line y = 2·x - 1

A. The slope of a line parallel to another line are the same, therefore;

The equation of the line parallel to the line y = 2, has a slope which is the coefficient of x of 0.

The line f is parallel to the x-axis

The equation that is parallel to line f and passes through the point P(-2, -1)  therefore has the same y-value as the point P of -1 and an x-value of 0, the equation is therefore;

B. The slope of the line g, y = 2·x - 1 is 2

The slope of the graph of the equation of the line that is parallel to the line g, is also 2

The equation of the line parallel to the line g and passing through the point (-2, -1) is; y - (-1) = 2·(x - (-2)) = 2·x + 4

y + 1 = 2·x + 4

y = 2·x + 4 - 1 = 2·x + 3

The equation of the line parallel to the line g and passing through the point P(-2, -1) is therefore;

C. The line f is parallel to the x-axis, therefore, the line perpendicular to the line f is perpendicular to the x-axis or parallel to the y-axis

The equation of the line perpendicular to the line f and passing through the point Q(3, -2), is therefore;

D. The slope of the line perpendicular to the line g, has a slope that is the negative inverse of the slope of the line g

The slope of the line g is 2, therefore, the slope of the perpendicular line is -1/2

The equation of the perpendicular line to the line of the equation g and passing through the point Q(3, -2) in point-slope form is therefore;

y - (-2) = (-1/2)·(x - 3) = -x/2 + 3/2

y = -x/2 + 3/2 - 2 = -x/2 - 1/2 = -0.5·x - 0.5

y = -0.5·x - 0.5

Learn more about parallel and perpendicular lines here:

https://brainly.com/question/29632338

#SPJ1

The distance between the two lines from the graph is 1 unit.

To represent a straight line on a graph consider two points namely x and y intercepts of the line. To find x-intercept put y = 0 and for y-intercept put x = 0. Then draw a line passing through these two points.

The given equations are as below,

y = x - 1

And,

y = 2x - 4

They can be drawn on a graph as follows,

From the graph the distance between two lines can be calculated as the difference between their x-intercepts as,

2 - 1 = 1 unit.

Hence, the distance between the two lines is given as 1 unit.

To know more about straight line equation click on,

brainly.com/question/21627259

#SPJ1

We can rewrite the circle equation as:

(x - 1)^2 + y^2 = 9

Then the two true statements are:

"The center of the circle lies on the x-axis"

" The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9."

Remember that a general circle equation with a center (a, b) and radius R is:

(x - a)^2 + (y - b)^2 = R^2

Here the equation is:

x^2 + y^2- 2 x - 8 = 0

We can rewrite this as:

(x^2 - 2x) + y^2 = 8

Adding and subtracting 1 in the left side we can complete squares:

(x^2 - 2x + 1) - 1 + y^2 = 8

(x - 1)^2 + y^2 = 9

Tha is our equation, so the center is (1, 0) and the radius is 3 units.

Then the true statements are:

"The center of the circle lies on the x-axis"

" The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9."

Learn more about circle equations:

https://brainly.com/question/1559324

#SPJ1

The equation that can be used to determine the pounds of laundry the customer brought in to be washed and folded that month is;

D. 0.53x + 26.00 = 37.66

We are given that;

Monthly service fee for Lundromat = $26

They wash and fold clothes at $0.53 per pound  for those customers with a laundry service.

Now, we are told that a customer paid $37.66 total for the month.

If the number of pounds of clothes is denoted as x, then it means that the equation for this will be;

0.53x + 26.00 = 37.66

Read more about Linear equation word problem at; https://brainly.com/question/21405634

#SPJ1

If the exterior angle is of 90º, it's adjacent interior angle will also be of 90º

What is exterior angle property of triangle?

According to the exterior angle theorem, the exterior angle that results from stretching a triangle's side is equal to the sum of the dimensions of the triangle's two opposed interior angles. The theorem can be used to determine a triangle's unknown angle's measurement. We must first determine the triangle's exterior angle and then its two remote inner angles in order to apply the theorem.

Using the concept of supplementary angles, it is found that the measure of an exterior angle of a triangle is equal to the measure of it's adjacent interior angle if both measure 90º.

Two angles are called supplementary if their measures add to 180º.

The exterior angle of a triangle is supplementary to it's adjacent interior angle.

Thus, if the exterior angle is of 90º, it's adjacent interior angle will also be of 90º.

Learn more about exterior angle property of triangle link below

https://brainly.com/question/14256482

#SPJ1

Answer:

Step-by-step explanation:

12.1

Answer:

8 [tex]\frac{1}{10}[/tex]

Step-by-step explanation:

[tex]\frac{17}{20}[/tex] = [tex]\frac{34}{40}[/tex] Multiplied the numerator and denominator by 2

[tex]\frac{1}{2}[/tex] = [tex]\frac{20}{40}[/tex]  Multiplied the numerator and denominator by 20

[tex]\frac{3}{4}[/tex] = [tex]\frac{30}{40}[/tex]  Multiplied the numerator and denominator by 10

2 + 3 + 1 [tex]\frac{34}{40}[/tex] + [tex]\frac{20}{40}[/tex] + [tex]\frac{30}{40}[/tex]

6 [tex]\frac{84}{40}[/tex]  This can be written

6 + [tex]\frac{40}{40}[/tex] + [tex]\frac{40}{40}[/tex] + [tex]\frac{4}{40}[/tex]  another name for [tex]\frac{40}{40}[/tex] is 1

6 + 1 + 1 +[tex]\frac{4}{40}[/tex]

8[tex]\frac{4}{40}[/tex]  Divide the numerator and denominator by 4 to simplify

8 [tex]\frac{1}{10}[/tex]

Answer:

$97

Step-by-step explanation:

In the collection, there are 11 nickels and 23 dimes. If each nickel is replaced with a quarter, the value of the collection becomes $5.05. So, C is correct. By writing them in the system of equations, we get the required value.

The given units are nickels, dimes, and quarters. Their conversion into dollars is as follows:

1 nickel = $0.05

1 dime = $0.10

1 quarter = $0.25

Given a collection of nickels and dimes is worth $2.85.

And there are 34 coins in the collection.

So, consider the number of nickel coins = n and the number of dime coins = d.

Then, the equation for the given collection is

n + d = 34...(1)

0.05n + 0.10d = 2.85...(2)

On simplifying (2), we get

5n + 10d = 2.85 × 100

⇒ 5n + 10d = 285

From (1), n = 34 - d, we get

5(34 - d) + 10d = 285

⇒ 170 - 5d + 10d = 285

⇒ 5d = 285 - 170 = 115

∴ d = 115/5 = 23

Thus, the number of dime coins is 23.

So, from (1), we get n + 23 = 34 ⇒ n = 34 - 23 = 11

∴ n = 11

Thus, the number of nickel coins is 11.

If each nickel coin in the collection is replaced with a quarter, then the value of the collection is

q + d = 34 and 0.25q + 0.10d = Y

Here q = 11; d = 23

So, we get

0.25(11) + 0.10(23) = Y

⇒ 2.75 + 2.3 = Y

⇒ 5.05 = Y

∴ Y = $5.05

The value of the new collection becomes $5.05.

Learn more about equations at the following link:

https://brainly.com/question/22688504

#SPJ1

The Sum of the first six terms of the progression is 14706

What is Geometric Progression?

A geometric progression, also known as a geometric sequence, is a non-zero numerical series in which each term after the first is determined by multiplying the preceding one by a fixed, non-zero value known as the common ratio.

Solution:

On carefully observing

We can state that, the Common Ratio is -7

Sum(n) = a([tex]r^{n}[/tex] - 1) / r - 1

Sum(6) = -1 (-7^6 - 1) / -7-1

Sum(6) = -1(117648)/-8

Sum(6) = 14706

To learn more about Geometric Progression from the given link

https://brainly.com/question/24643676

#SPJ1

Answer: 18 inches

Step-by-step explanation:

A triangle with three equivalent angles, because of the properties of triangles, would also be an equilateral triangle. This means each side length is 6 inches. 6+6+6=18 inches.

Answer:10

Step-by-step explanation:

Answer:

$37.50

Step-by-step explanation:

75% of $50:

0.75x50=$37.50

the probability that a person picked at random from the group is a male or female is fit to climb Mount Shasta is  0.472 (or in percent near 47.2%).

The probability is computed by dividing the total number of possible outcomes by the number of possible ways the event might occur. Probability and odds are two distinct ideas. Odds are calculated by dividing the likelihood of an event by the likelihood that it won't.

Classical: (equally probable outcomes) (equally probable outcomes) Let S be the sample space (the collection of all unique outcomes that might occur).

Subjective Probability. Definition of Relative Frequency.

1. Determine the number of male climbers:

200 men - 100%

x men - 12 %

. Of the 60 people in California who are physically capable of climbing Mount Shasta, 24 are men, leaving 36 women.

 The likelihood that a guy will be selected at random from the group is

 The likelihood that a random member of the group is physically capable of climbing Mount Shasta is: 0.472

 0.472 (or, in percentage terms, close to 47.2%).

To learn more about probability click the following link:-

https://brainly.com/question/1748262

#SPJ1

The component that is missing from the biologist's process is: c. The biologist did not randomly assign the each of the bats to the treatment groups.

When we carry out a research study that has  created groups that you want to study, then the differences between and within groups can be thoroughly checked to make sure that they are not systematic when subjects are randomly assigned to groups.

Therefore this random assignment of subjects, gives the researcher the confidence that groups are the same in terms of variables, and any differences can be confidently allocated to experimental treatments.

Therefore, we can conclude that the component that is missing from the biologist's process is given in option C because the biologist did not randomly assign the each of the bats to the treatment groups.

Read more about Randomization at; https://brainly.com/question/24466382

#SPJ1

The equation of the circle in general form is x² + y² - 2 · x - 2 · y - 8 = 0.

In this problem we need to derive the equation of a circle that contains three points: (x₁, y₁) = (- 2, 2), (x₂, y₂) = (2, 4), (x₃, y₃) = (4, 0). The general form of the equation of the circle is a second order polynomial of the form:

x² + y² + B · x + C · y + D = 0

Where B, C, D are real coefficients.

First, use the points to generate a system of linear equations:

- 2 · B + 2 · C + D = - 8

2 · B + 4 · C + D = - 20

4 · B + D = - 16

Second, resolve the system by means of numerical methods:

(B, C, D) = (- 2, - 2, - 8)

Third, write the general form of the equation is:

x² + y² - 2 · x - 2 · y - 8 = 0

To learn more on equations of the circle: https://brainly.com/question/23799314

#SPJ1

Answer:

-3x^2--20x+(y-8)=0

Answer:

To find the sum of the two fractions, we first need to express them in a common denominator. Since the denominators of the two fractions are different, we will need to find the least common multiple (LCM) of the two denominators.

The LCM of 4 and 5 is 20, so we can express the two fractions in terms of 20 as follows:

-3 1/4 = -3 5/20

-4 2/5 = -4 8/20

Now that the two fractions have a common denominator, we can add them by adding the numerators and keeping the denominator the same:

(-3 5/20) + (-4 8/20) = (-3 + -4) 13/20 = -7 13/20

Therefore, the sum of the two fractions is -7 13/20.

The sum of −3 1/4 + (−4 2/5) is 7.65

Mixed fractions are type of a fraction which includes a whole number and a fraction.

So, any improper fraction can be written as a mixed fraction. Quotient will be the whole number and in the fractional part, numerator is the remainder and denominator will be the divisor.

[−(3 1/4)] + [−(4 2/5)] = [-(13/4)] + [-(22/5)]

When cross multiplying, we will get

-(13/4 + 22/5) = -(65 + 88)/20 = -153/20 = 7.65

Hence, the sum of −3 1/4 + (−4 2/5) is 7.65.

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

So, if you find this answer helpful, please mark as brainliest! It will support my account and everything.

The measurement of ∠RPQ is 20°.

What is the meaning of extended point?

A polygon's extended side or sideline in plane geometry is the line that contains one of the polygon's sides. Several situations call for the extension of a side.

Given that,

In ΔPQR, the side PR is extended to the point S.

The measurement of ∠RPQ is (x+12)°, ∠QRS is (7x+8)°, and ∠PQR is (3x+20)°.

We know that, the exterior angle of triangle is equal to the sum of opposite interior angles.

Therefore,

∠QRS = ∠RPQ + ∠PQR

Putting the value of ∠QRS, ∠RPQ, ∠PQR in the above equation:

(7x+8)° = (x+12)° + (3x+20)°

7x + 8 = 4x + 32

Subtract 4x from both sides:

3x  + 8 = 32

Subtract 8 from both sides:

3x = 24

Divide both sides by 3:

x = 8

Putting x = 8 in ∠RPQ = (x+12)°

∠RPQ = (8+12)° = 20°

To learn more about exterior angle, click on below link:

https://brainly.com/question/22073609

#SPJ1

The probability that Lamar and Lawrence finish their jobs within 5 minutes of each other on a randomly selected day is 0.2892

Consider the time for the Lamar to finish the job as x and the time for the Lawrence to finish the job as x

Consider the random variable x-y

x-y normal with mean = 105 - 98

= 7

Similarly the variance of the random variable x-y

= 105 + 225

= 325

The standard deviation = [tex]\sqrt{325}[/tex]

= 18.03

Here we have to find the probability that Lamar and Lawrence  finish their jobs within 5 minutes of each other on a randomly selected day

P(|x-y|<5) = P(-5<U<5)

Now we have to convert to standard normal variate Z

Then the it will be

(-5-7)/18.03 = -0.67

(5-7) / (18.03)= 0.11

The probability of the given condition will be

P(-0.67<Z<0.11) = 0.2454 + 0.0438

Add the terms

= 0.2892

Therefore, the probability is 0.2892

The complete question is:

Lamar and Lawrence run a two-person lawn-care service. they have been caring for Mr. Johnson's very large lawn for several years, and they have found that the time it takes Lamar to mow the lawn itself is approximately normally distributed with a mean of 105 minutes and a standard deviation of 10 minutes. meanwhile, the time it takes for Lawrence to use the edger and string trimmer to attend to details is also normally distributed with a mean of 98 minutes and a standard deviation of 15 minutes. they prefer to finish their jobs within 5 minutes of each other. what is the probability that this happens, assuming their finish times are independent?

Learn more about probability here

brainly.com/question/11234923

#SPJ4

The simplified expression for its perimeter and area are 8x and 4x².

What is the square's perimeter?

What is a square area?

Area of square = a²

= (2x)²

= 4x²

Area of square = 4x²

Perimeter of square = 4*a

= 4 * 2x

= 8x

Perimeter of square = 8x

Hence, the simplified expression for its perimeter and area are 8x and 4x².

To know more about square check the below link:

https://brainly.com/question/25092270

#SPJ1

Answer:

50

Step-by-step explanation:

To determine the length of time it takes for all three moons to return to the same position, you need to find the least common multiple (LCM) of the three time periods.

The LCM of 25 days, 30 days, and 20 days is the smallest number that is a multiple of all three of these numbers. You can find the LCM by listing the multiples of each number and finding the smallest number that is a multiple of all three:

25 days: 25, 50, 75, 100, 125, 150, 175, 200, 225, 250, ...

30 days: 30, 60, 90, 120, 150, 180, 210, 240, 270, 300, ...

20 days: 20, 40, 60, 80, 100, 120, 140, 160, 180, 200, ...

The LCM of 25, 30, and 20 is 60 days, so it will take 60 days for the three moons to be in the same position again. Therefore, the correct answer is (c) 300 days.

learn more from here:

https://brainly.com/question/16709756

Answer:

Acute Scalene Triangle  

Step-by-step explanation:

Look at all three angles of the triangle they are all acute. In addition, all of the angles on the triangle are different making it scalene.

Answer:

Yes, there is. It's called a regular 52-gon.

For the given log function, the value of y is 8.

An exponent is a logarithm. In logarithmic form, any exponential expression can be rewritten.

Here given, log function :

Log 5 + Log y = Log 40

Can be also written as,

Log y = Log 40 - Log 5  => (eq1)

Based on log property we know that,

Log m - Log n = Log

That is,

Log 40 - Log 5 = Log

Also be written as,

Log 40 - Log 5 = Log 8   => (eq2)

By solving eq1 and eq2, we get,

Log y = Log 8

∴  y = 8

Therefore, The value of will be y = 8

Hence by solving  Log 5 + Log y = Log 40 , the value of y is 8.

To learn more about logarithmic function refer to :

https://brainly.com/question/13473114

#SPJ4

Value of y is 8.

What is a logarithmic equation?

The logarithm is exponentiation's opposite function in mathematics. This indicates that the exponent to which b must be raised in order to obtain a number x is the logarithm of x to the base b. For instance, because 1000 is equal to 10³, its logarithm in base 10 is 3, or log₁₀ (1000) = 3. When there is no possibility of mistake or when the base is irrelevant, as in big O notation, the logarithm of x to base a is written as logₐ (x), logₐ x, or even without the explicit base, log x.

Given, the equation is log5 + logy = log40

log 40 can be written as log (5*8)

According to the logarithmic equation of log ab = log a + log b

Thus log 40 = log 5 + log 8

Now, the expression becomes

log5 + logy = log 5 + log 8

⇒ log y = log 8

⇒ y = 8

Thus, value of y is 8.

To learn more about logarithmic equations refer to :

brainly.com/question/13473114

#SPJ4

Answer:

The percent discount is 17.3%.

The answer to this question would be 5 by 9.

The lowest temperature in January is -10°C if the lowest temperature in January is less than -6°C.

A scaled way of measuring how hot or how chilly something is a living body's normal level of heat production; see thermometer. a condition of extreme body heat with an average oral temperature of 98.6°F. The ideas of hotness and coolness are expressed numerically as a physical value called temperature.

The calibration of thermometers involves employing a variety of temperature scales with clearly defined reference points and thermometric materials. The Celsius scale (°C), formerly known as centigrade, with the unit symbol °C, is the most commonly used scale, followed by the Fahrenheit scale (°F) and the Kelvin scale (K), which is mostly used for scientific purposes. One of the seven base units in the International System of Units is the kelvin (SI).

Given,

Less than 6° was the lowest temperature recorded in January.

The lowest temperature in January will be=?

It is -10°C.

Therefore, the lowest temperature in January is -10°C.

To know more about temperature, visit:

https://brainly.com/question/28463594

#SPJ1

The angle between the ladder and the ground is - 0.075 rad/s.

Pythagoras' theorem is a essential relation in Euclidean geometry among the 3 facets of a proper triangle. It states that the region of the rectangular whose aspect is the hypotenuse (the aspect contrary the proper angle) is identical to the sum of the regions of the squares on the alternative  facets.

cosθ = x/10

On differentiating the above equation,

- sinθdθ/dt = (1/10)dx/dt

dθ/dt = -(1/10)dx/dt/sinθ

sinθ = y/10

= √(100 - 36)/10

= 0.8; dθ/dt

= -(1/10)·0.6 ft/s/0.8

= - 0.075 rad/s

To learn more about triangle check the link below:

https://brainly.com/question/17335144

#SPJ4