Sorting Quadratic Function Discriminants
Warm-Up
Determine the number and type of zeros of the quadratic function based on the value of the discriminant.
discriminant = 0
2 Real Number Solutions 1 Real Number Solution
discriminant = -36
discriminant = 3
discriminant = 2
discriminant = 100
discriminant =-4
Intro
0 Real Number Solutions
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Concept:

Parallel planes are planes in the same three-dimensional space that never meet.

Parallel Lines or parallel Segments are always the same distance apart, they will never meet.

skew lines are two lines that do not intersect and are not parallel.

Question: Name a plane parallel to plane PQR:

Answer: plane JKL

Question: Name a segment parallel to segment KP:

Answer: segment OJ

Question: Name a segment that is skew to OJ

Answer: segment SR

Answer:

Step-by-step explanation:

in x²+y²+2gx+2fy+c=0

center=(-g,-f)

radius=√((-g)²+(-f)²-c)

if center is not changed ,then c will change .

Here only coefficients of  E will change.

Answer:

C

Step-by-step explanation:

Because it isn't a negative number so it should have a closed circle with a line going to 11 and on. Hoped this helped. ;)

Answer:

C

Step-by-step explanation:

Answer:

ab is opposite to the letterac

Answer:

(3a - 4 )^2

Step-by-step explanation:

(9a^2-24a+16)=(3a - 4 )^2

Therefore the length of each side of the square is (3a - 4 )^2

Answer:

Part A: (3a - 4)^2

Part B: (5a + 6b)(5a - 6b)

Step-by-step explanation:

Part A:

It looks like this is the square of a binomial. Now we check it.

9a^2 is the square of 3a.

16 is the square of 4 and of -4.

Check the middle term:

2 * 3a * 4 = 24a

2 * 3a * (-4) = -24a

Since we get -24a when we use 4, the second term of the binomial is 4.

Answer:

9a^2 - 24a + 16 = (3a - 4)^2

Part B:

25a^2 − 36b^2

This is a two-term polynomial. The two terms are perfect squares and there is a subtraction sign between them, so this is the difference of two squares. The difference of two squares factors into the product of a sum and a difference.

25a^2 is the square of 5a.

36b^2 is the square of 6b.

25a^2 − 36b^2 = (5a + 6b)(5a - 6b)

Answer:

5. x = 3, y = 3

Step-by-step explanation:

5. cos45 = y/(3√2)

y = 3

sin45 = x/(3√2)

x = 3

The population of Springfield in 2046, given the growth rate, can be found to be  251, 940 people

When given the starting population, and the population growth rate, the growth in population can be found by the formula:

= Starting population x ( 1 + population growth rate ) ^ number of years

The number of years would be:
= 2046 - 2019

= 27 years

The population in 2046 would be:

= 202, 628 x ( 1 + 0.81 % ) ²⁷

= 251, 940 people

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The per-unit reactance of the transformer is 0.0444 pu.

To calculate the per-unit reactance of the transformer, we need to use the following formula:

Xpu = X / (Vbas\(e^2\) / Sbase)

where X is the reactance in ohms, Vbase is the base voltage in volts, and Sbase is the base power in volt-amperes.

In this case, the rated power of the transformer is 5 kVA, and the rated voltage on the high side is 400V. Therefore, the base power and base voltage are:

Sbase = 5 kVA

Vbase = 400V

The reactance of the transformer referred to the low voltage side is given as 2Ω. To convert this to per-unit, we substitute the values in the formula:

Xpu = 2Ω / (300\(V^2\) / 5 kVA)

Xpu = 0.0444 pu

Therefore, the per-unit reactance of the transformer is 0.0444 pu.

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Based on the given responses, the student who factored 20x^6 = (2x)(10x^5) correctly is Andrei. Therefore, the correct answer is (Choice A) Andrei.

Among the given responses, the student who factored 20x^6 = 20, x to the power of 6 correctly is Andrei. Andrei's factorization is (2x)(10x^5), which correctly represents the original term 20x^6. Therefore, the correct answer is (Choice A) Andrei.

Amit's factorization is (4x^3)(5x^3), which is incorrect because it breaks down the term into two factors with the same exponent, while the original term has an exponent of 6.

Andrew's factorization is (20x^2)(x^3), which is also incorrect as it does not accurately represent the original term 20x^6.

Hence, the only student who correctly factored 20x^6 = 20, x to the power of 6 is Andrei.

The right answer is A. Andrei who factored 20x^6 = (2x)(10x^5) correctly.

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Explanation is\(^{}\) in a file

bit.\(^{}\)ly/3gVQKw3

The answers are:

27. P(6) = 0.2 , 28. P(even number) = 0.6 , 29. P(6) = 1/10 , 30. P(even number) = 5/10 = 0.5

The experimental probability of getting a 6 is 0.2, because 2 out of 50 displays were 6s.

The experimental probability of getting an even number is 0.6, because 30 out of 50 displays were even numbers.

The theoretical probability of getting a 6 is 1/10, because there is 1 chance out of 10 that the calculator will display a 6.

The theoretical probability of getting an even number is 5/10, because there are 5 chances out of 10 that the calculator will display an even number.

As you can see, the experimental probabilities are close to the theoretical probabilities. This is because the calculator was programmed to randomly display a digit from 0 to 9, so the results should be evenly distributed. However, there is always some chance of variation, so the experimental probabilities may not be exactly equal to the theoretical probabilities.

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Answer: y=3x

Step-by-step explanation:

The equation can be found by finding the slope of the given line. Visually, this can be found by counting the distance between two points. From (1,3) and (2,6), the line "rises" 3 units and "runs" 1 unit to the right. Since slope is calculated as rise over run, this gives us 3/1, or just 3 for slope. In slope-intercept form, this becomes y=3x.

Just to note, we know it is not negative because of the direction of the slope. Visually, if the slope "moves" in the direction of upwards and to the left, it will be positive. This can be calculated more accurately using the slope formula (y2-y1/x2-x1)

Answer:

A triangle with sides 7, 23, and 25 is not a right triangle.

Step-by-step explanation:

Answer:

8 2/3

Step-by-step explanation:

The solution to the given problem is:f(x) = 2√2 + 4g(x) = -2cos(3π/8) + 4h(x) = 4√2 + 3j(x) = -2√2 - 2.To find the solution for the given problem, we need to evaluate each of the following functions at x = π/16:

\(f(x) = 4cos(2x - π/4) + 4g(x) = -2cos(2x + π/4) + 4h(x) = -4cos(4x - π) + 3j(x) = 4cos(4x + π) - 2\)

To evaluate the given functions, we substitute the value of x = π/16 in each of the functions:

f(x) = 4cos(2x - π/4) + 4= 4cos[2(π/16) - π/4] + 4= 4cos(π/8 - π/4) + 4= 4cos(-π/8) + 4= 4cos(π/8) + 4= 4(√2/2) + 4= 2√2 + 4g(x) = -2cos(2x + π/4) + 4= -2cos[2(π/16) + π/4] + 4= -2cos(π/8 + π/4) + 4= -2cos(3π/8) + 4h(x) = -4cos(4x - π) + 3= -4cos[4(π/16) - π] + 3= -4cos(π/4 - π) + 3= -4cos(-3π/4) + 3= 4√2 + 3j(x) = 4cos(4x + π) - 2= 4cos[4(π/16) + π] - 2= 4cos(5π/4) - 2= -2√2 - 2.

Therefore, the solution to the given problem is:f(x) = 2√2 + 4g(x) = -2cos(3π/8) + 4h(x) = 4√2 + 3j(x) = -2√2 - 2.

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The set of prime numbers greater than 11 with the cardinality of 5 is {13, 17, 19, 23, 29}

From the question, we have the following parametes that can be used in our computation:

Set = prime numbers

Cardinality = 5

The cardinality implies that the number of elements in the set is 5

5 prime numbers greater than 11 are 13, 17, 19, 23, 29

Hence, the set is {13, 17, 19, 23, 29}

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Answer:

%62.5

Step-by-step explanation:

Im pretty sure you jsut divide 5/8 and then multiply by 100 to get a percent

5/8=.625

.625*100=62.5

%62.5

Answer:

y + 5 = 3y - 1

2y = 6, so y = 3

4x - 2 = x + 10

3x = 12, so x = 4

Answer:

x = -3  or x = 3  or x = 6

Step-by-step explanation:

x3 – 6x2 – 9x + 54 = 0

There is no common factor to factor out. There are 4 terms. We try factoring by grouping. Factor a common factor out of the first two terms. Factor a common factor out of the last two terms.

x^2(x - 6) - 9(x - 6) = 0

x - 6 is a common factor, so we factor it out.

(x^2 - 9)(x - 6) = 0

x^2 - 9 is the difference of 2 squares, so we factor it.

(x + 3)(x - 3)(x - 6) = 0

x + 3 = 0  or  x - 3 = 0  or x - 6 = 0

x = -3  or x = 3  or x = 6

Answer:

x=6     x=3   x=-3

Step-by-step explanation:

x^3 – 6x^2 – 9x + 54 = 0

Factor by grouping

x^3 – 6x^2     – 9x + 54 = 0

x^2(x-6)    -9(x-6 ) =0

Factor out x-6

(x-6)(x^2 -9) =0

Notice x^2 -9 is the difference of squares

(x-6)(x-3)(x+3) = 0

Using the zero product property

x-6 =0    x-3 =0   x+3 =0

x=6     x=3   x=-3

Answer:

Yes, x = 1/2 is a solution

Step-by-step explanation:

To see if it is a solution, plug it into the equation:

3(x + 1) = 3x + 3

3(0.5 + 1) = 3(0.5) + 3

3(1.5) = 1.5 + 3

4.5 = 4.5

Since this is true, x = 1/2 is a solution of the equation.

Answer:

your answer is -120

Step-By-Step Explanation:

2(-3)^3 - 9(-3)^2 -5(-3)

2 (-27) - 9(9) +15

-54 -81 +15

-135 +15

-120

i hope this helps :)

Answer: -120

Hope this helps :)

Answer:

D. Division Property of Equality

Step-by-step explanation:

Given that \( 8D = 56 \), to find the value of D, the property of equality that needs to be applied here would be the one that would make both sides equal by performing the same operation on both sides of the equation.

Thus:

Applying the the Division Property of Equality, we would divide both sides by 8.

\( \frac{8D}{8} = \frac{56}{8} \)

\( D = 7 \)

This will leave you with D standing alone. Of which value is 7.

The equation will be t = 3s where t is total cost and s is number of snow cones. this can be find out be relationship of number of snow cones and total cost in table .

In given table :

Number of snow cones               Total cost

2                                                      6

6                                                      12

5                                                      15

From above table, we can relate

1st case :
number of snow cones = 2 and total cost = 6

i.e. 3 times of number of cones.

2nd case:

number of cones = 4 and total cost = 12

i.e. 3 times the number of cones.

3rd case :

number of cones = 5 and total cost = 15

i.e. 3 times the number of cones.

So, we see same pattern is repeated in all.

Then equation will be t = 3s where t = total cost , s = number of snow cones.

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The yearly taxable income of the officer and government servant are solved where

a) Taxable income of officer = Rs 5,25,000

b) Taxable income of government servant = Rs 0

Given data ,

To calculate the taxable income, we need to subtract the deductible expenses from the total income. In this case, the deductible expense is the life insurance premium.

For the officer:

Yearly income: Rs 5,50,000

Life insurance premium: Rs 25,000

Taxable income = Yearly income - Life insurance premium

Taxable income = Rs 5,50,000 - Rs 25,000

Taxable income = Rs 5,25,000

Therefore, the officer's taxable income is Rs 5,25,000.

For the government servant:

Monthly income: Rs 77,280

Festival expenses (one month's salary): Rs 77,280

Taxable income = Monthly income - Festival expenses

Taxable income = Rs 77,280 - Rs 77,280

Taxable income = Rs 0

Hence , the taxable income for the government servant is Rs 0, as the festival expenses are equal to one month's salary

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Based on the above table , the fastest growing listed occupation for those without a college degree is Gaming and sports book writers and runners.

Therefore option A is correct.

The college degree is described as a qualification awarded to students after completing the requirements for a specific course of study of which the two most common types of degrees are the Bachelor of Arts and Bachelor of Science.

With reference to the table, the occupations that do not require a college degree are:

We were able to conclude that Based on the above table , the fastest growing listed occupation for those without a college degree is Gaming and sports book writers and runners with a rate of 24.6%.

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The expression 8x + 4y is not equivalent to 4(2x + 1). Therefore, 8x + 4y = 4(2x + y)

Two expressions are said to be equivalent if they have the same value irrespective of the value of the variable(s) in them.

Equivalent expressions are expressions that have similar value or worth but do not look the same.

Let's determine whether the expression 8x + 4y is equivalent to 4(2x + 1).

Let's factorise to know whether the expressions are equivalent.

Therefore, using the common factors,

8x + 4y = 4(2x + y)

Hence, the expression are not equivalent .

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Answer:

$889.94 after six years

Step-by-step explanation:

The equation is I=P(1-r)^t so after six years it would be worth $889.94. Every year the value depreciates by $4,130.