Determine the discriminant for the quadratic equation -3=x2+4x+1. Based on the discriminant value, how many real number
solutions does the equation have?
Discriminant = b2-4ac
0
1
2
o 12
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Answer:

Option 1

Step-by-step explanation:

3x - 7y = -7y + 3x

They have simply been moved to opposite ends of the equation.

Answer: 25

               2

Step-by-step explanation:

900 - 400 = 500 = 25

  50 - 10 =     40=    2        

Answer: C

Step-by-step explanation: Hope this help :D

The time take to fill the pool will be 494 hours.

Inlet pipe fills in  38 hours = 1 pool

Inlet pipe fills in 1 hours = 1/38

Drain pipe empty in 39 hours = 1 pool

Drain pipe empty in 1 hour = 1/39

If both pipes are opened together then in pool fills in 1 hour =  1/38 - 1/39

= 1/1482

Therefore, 1/1482 fills in 1 hour.

. Therefore, 1/3 will be:

= 1/3 × 1482

= 494 hours.

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The biker needs to travel 45 km more to complete his journey.

Given that, a biker traveled 2/5 of the road on the first day, then traveled 5 kilometers less on the next day, which is equal to 3/8 of the road, we need to find how much he need to cover more,

Let the total distance of the road be x,
So,

2x/5 - 5 = 3x/8

2x/5 - 3x/8 = 5

Solving for x,

Multiply by 40 to both sides,

16x-15x = 200

x = 200

Therefore, the total distance of the road is 200 km.

Since, he travelled =

200 (2/5) = 80 km + 200 (3/8) = 75 km = 155 km

Therefore, he needs to travel 200-155 = 45 km more.

Hence, the biker needs to travel 45 km more to complete his journey.

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Answer:

The Answer is 2000$..........

The point (-√2,1) can also be represented as (√3, 5.18) in polar coordinates.

To find the polar coordinates of the rectangular coordinates (-√2,1), we can use the following formulas:

r = √(x² + y²)

θ = tan^⁻1(y/x)

Plugging in the given values of (-√2,1), we get:

r = √((-√2)² + 1²) = √(2 + 1) = √3

θ = tan^⁻1(1/(-√2)) ≈ 2.0344 radians

Note that since the point (-√2,1) is in the second quadrant, we need to add π to the value of θ obtained from the inverse tangent in order to obtain an angle in the interval [0,2π). Thus, we have:

θ ≈ 2.0344 + π ≈ 5.1779 radians

Rounding to 2 decimal places as needed, we get the polar coordinates of (-√2,1) as (r,θ) ≈ (√3, 5.18).

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Answer:

there is no image

Step-by-step explanation:

Answer:

S = 2π(3^2) + 2π(3)(8.2) = 67.2π = 211 cm^3

The average weight of a male Florida panther rounded to the nearest whole number is 53 kg

What is average?

The middle number, which is determined by dividing the sum of all the numbers by the total number of numbers, is the average value in mathematics. When determining the average for a set of data, we add up all the values and divide this sum by the total number of values.

Average weight = 52.6 kg

52.6

The number after decimal point is 6 which is more than 5.

So add  1 to the 52, we get 53

Thus, the average weight of a male Florida panther rounded to the nearest whole number is 53 kg

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Answer:

Step-by-step explanation:

Answer:

3x² - 14x + 15

Step-by-step explanation:

Step 1: Write expression

(x - 3)(3x - 5)

Step 2: FOIL

3x² - 5x - 9x + 15

Step 3: Combine like terms

3x² - 14x + 15

The person is approximately 8.43 miles from home, and they need to walk in the direction of approximately 26.6 degrees east of north to head directly home.

To determine the distance from home, we can use the concept of vector addition. The person walks 4 miles west, which can be represented as a vector (-4, 0) in a coordinate plane. Then, they walk 5 miles southwest, which can be represented as a vector (-3.54, -3.54) since southwest is a combination of west and south. Adding these two vectors together gives us (-7.54, -3.54).

To find the magnitude or distance from home, we use the Pythagorean theorem. The distance is given by sqrt((-7.54)^2 + (-3.54)^2) = 8.43 miles (approximately).

To determine the direction to head directly home, we need to find the angle between the vector (-7.54, -3.54) and the positive x-axis. We can use trigonometry to find this angle. The tangent of the angle is given by the ratio of the y-coordinate to the x-coordinate, which is -3.54 / -7.54. Taking the inverse tangent of this value gives us approximately 26.6 degrees.

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Answer:

The answer is D

Step-by-step explanation:

The length AC in the kite is 8.7 cm.

A kite is a quadrilateral that has two pairs of consecutive equal sides and

perpendicular diagonals. Therefore, let's find the length AC in the kite.

Hence, using Pythagoras's theorem, let's find CE.

Therefore,

7² - 4² = CE²

CE = √49 - 16

CE = √33

CE = √33

Let's find AE as follows:

5²- 4² = AE²

AE = √25 - 16

AE = √9

AE = 3 units

Therefore,

AC = √33 + 3

AC = 5.74456264654 + 3

AC = 8.74456264654

AC = 8.7 units

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A.= \($\left( -4,\frac{5\pi}{4}\right)\,\, \left( 4,\frac{-7\pi}{4}\right)\),  B = \($\left( 4,\frac{3\pi}{4}\right)\,\, \left( -4,\frac{-\pi}{4}\right)\),

C=\($\left( -4,\frac{\pi}{4}\right)\,\, \left( 4,\frac{5\pi}{4}\right)\),  D = \($\left( -4,\frac{3\pi}{4}\right)\,\, \left( 4,\frac{7\pi}{4}\right)\)

\($\left( -4,\frac{5\pi}{4}\right) = \left( 4,\frac{5\pi}{4}+\pi = 2\pi + \pi/4\right )\,\,, \left( 4,\frac{-7\pi}{4}\right) =\left( 4,\frac{-7\pi}{4}+2\pi = \pi/4\right)\)

\($\left( 4,\frac{3\pi}{4}\right)\,\, , \,\left( -4,\frac{-\pi}{4}\right) = \left(4,\frac{-\pi}{4}+\pi = 3\pi/4\right)\)

\($\left( -4,\frac{\pi}{4}\right)=\left( 4,\frac{\pi}{4}+\pi = 5\pi/4\right)\,\, ,\,\left( 4,\frac{5\pi}{4}\right)\)

\($\left( -4,\frac{3\pi}{4}\right)=\left ( 4,\frac{3\pi}{4}+\pi = 7\pi/4 \right)\,,\, \left( 4,\frac{7\pi}{4}\right)\)

When \(r\geq 0\) and \(0\leq \theta < 2\pi\), we call the polar coordinates \((r,\theta)\) standard polar coordinates. To convert any given coordinates to standard coordinates 1. if r<0 then replace r with |r| and \(\theta\) with \(\theta + \pi\). 2. Now if \(\theta < 0 \textrm{ or }\theta\geq 2\pi\), we add a suitable multiple of \(2\pi \textrm{ to }\theta\) to bring it inside [0,\(2\pi\)) interval.

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Using implicit differentiation dy/dx = -(2x + y)/(x + 2y) and d2y/dx² = -2(x² - 3xy - y²)/(x + 2y)³.

Implicit differentiation is the process of differentiating an equation in which it is not easy or possible to express y explicitly in terms of x.

Given the equation x² + xy + y² = 5,

we can differentiate both sides with respect to x using the chain rule as follows:

2x + (x(dy/dx) + y) + 2y(dy/dx) = 0

Simplifying this equation yields:

(x + 2y)dy/dx = -(2x + y)

Hence, dy/dx = -(2x + y)/(x + 2y)

Next, we need to find d^2y/dx^2 by differentiating the expression for dy/dx obtained above with respect to x, using the quotient rule.

That is:

d/dx(dy/dx) = d/dx[-(2x + y)/(x + 2y)](x + 2y)d^2y/dx² - (2x + y)(d/dx(x + 2y))

= -(2x + y)(d/dx(x + 2y)) + (x + 2y)(d/dx(2x + y))

Simplifying this equation yields:

d2y/dx² = -2(x² - 3xy - y²)/(x + 2y)³

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Given:

Sol:.

11 x 7 + 11 x 4 is the expression of the total area as the sum of the areas of

each room.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

11 (7 + 4)

Using the property of multiplication over addition.

11 x 7 + 11 x 4

Thus,

11 x 7 + 11 x 4.

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Answer:

Range = [-129, 136]

Step-by-step explanation:

If this is not the answer you are looking for, please comment

Answer:

265°

Step-by-step explanation:

from -129° to 0° is 129°

from 0° to 136° there is 136°

you add this numbers together and get an answer, so 129°+136°= 265°

Answer:

16

Step-by-step explanation:

\(50 - 34 = 16\)

Answer:

16

Step-by-step explanation:

a) The deepest that the diver went is of: 432 yards deep.

b) It took 12 minutes for the diver to return to the surface.

c) After one minute, the diver was 132 yards deep.

The quadratic function modeling the diver's height after x seconds is given as follows:

d(x) = 12x² - 144x.

The coefficients are given as follows:

a = 12, b = -144, c = 0.

The x-coordinate of the vertex is given as follows:

x = -b/2a

x = 144/24

x = 6.

Item a:

As a > 0, in item a, the minimum height is given as follows:

d(6) = 12(6)² - 144(6)

d(6) = -432 feet.

Item b:

The roots of the function, in item b, are obtained as follows:

12x² - 144x = 0

12x(x - 12) = 0

Hence:

12 - 0 = 12, hence it took 12 minutes for the diver to return to the surface.

Item c:

After one minute, the depth of the diver, in item c, is given as follows:

d(1) = 12(1)² - 144

d(1) = -132 yards.

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We have the following:

The formula for the area of the circle is as follows

replacing:

Therefore the area of the circle is 33.17 square yards.

A 95% confidence that the true proportion of adults who regularly snore is between 0.682 and 0.818.

What is random sample ?

A random sample is a subset of a larger population that is chosen in such a way that every member of the population has an equal chance of being selected. In other words, a random sample is a sample that is chosen at random from the population, without any bias or preference for certain members of the population.

Random sampling is an important technique used in statistics and other fields that deal with large populations. By taking a random sample of the population, statisticians can make inferences about the entire population with a high degree of confidence, without having to survey or study every individual in the population. This is because a random sample is more likely to be representative of the population as a whole, and therefore the statistics derived from the sample are more likely to accurately reflect the characteristics of the population.

According to the question:
To calculate the 95% confidence interval for the proportion of adults who regularly snore, we can use the formula:

\(CI = p \± z\sqrt{p(1-p)/n}\)

where:

CI is the confidence interval

p is the sample proportion (in this case, 0.75 or 75%)

z is the critical value from the standard normal distribution for the desired level of confidence (in this case, 95%, which corresponds to a z-value of 1.96)

n is the sample size (250 adults in this case)

Substituting the given values, we get:

p = 0.75

z = 1.96

n = 250

Plugging these values into the formula, we get:

\(CI = 0.75 \± 1.96\sqrt{0.75(1-0.75)/250}\)

Simplifying and solving for the upper and lower bounds of the confidence interval, we get:

CI = 0.75 ± 0.068

CI = (0.682, 0.818)

Therefore, we can say with 95% confidence that the true proportion of adults who regularly snore is between 0.682 and 0.818.

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Answer: 15.3 cm

Step-by-step explanation:

The actual length of the line in question is 1.53km.

The scale is 10 cm to 1 km.

You can therefore use direct proportion to solve this.

Assume the length on the drawing is x:

10cm  :   1km

x cm  :   1.53 km

Cross multiply:

x = 15.3 cm

Answer:

The answer is 0.372 because you jus dividing it by 10 jus like 0.372 x 10= 3.72 you jus putting the 0 first when dividing .

Step-by-step explanation:

Answer:

c

Step-by-step explanation: