Please help, thanks. Simplify the radical

Answer:

Step-by-step explanation:

(a) and (b) see diagram

(c) you can see from the graph, the purple line hits the parabola twice which is y=6   or k=6

(d)  Solving simultaneously can mean to set equal

6x - x² = k                        >subtract k from both sides

6x - x² - k = 0                  >put in standard form

- x² + 6x - k = 0               >divide both sides by a -1

x² - 6x + k = 0

(e) The new equation is the same as the original equation just flipped (see image)

(f)  The discriminant is the part of the quadratic equation that is under the root. (not sure if they wanted the discriminant of new equation or orginal.  I chose new)

discriminant formula = b² - 4ac

equation:   x² - 6x + 6 = 0            a = 1      b=-6    c = 6

discriminant = b² - 4ac

discriminant= (-6)² - 4(1)(6)

discriminant = 36-24

discriminant = 12

Because the discriminant is positive, if you put it back in to the quadratic equation, you will get 2 real solutions.

Answer:

The answer is 1 inch per second

The answer of the average rate of change is f(x) = x² - 2x [-3, 4] f(x) = x² + 3x [-2, 3] f(x) = 3x - 8 [4, 5] f(x) = x² - 5 [-1, 1].

The average rate of change is the slope of the line formed by two points on a graph. The formula used to calculate the average rate of change is as follows:

Average rate of change = (f (b) - f (a)) / (b - a), where a and b are any two points on the interval.

The table below shows the average rate of change for each function on its respective interval:

Intervalsf(x) = x² + 3xf(x) = 3x - 8f(x) = x² - 2xf(x) = x² - 5[-2, 3]10-3[4, 5]3.3[−3, 4]23.5[−1, 1]-4

The intervals are arranged from the greatest to the least value based on their average rate of change.

f(x) = x² - 2x [-3, 4]: 23.5f(x) = x² + 3x [-2, 3]: 10f(x) = 3x - 8 [4, 5]: 3.3f(x) = x² - 5 [-1, 1]: -4

Therefore, the answer is f(x) = x² - 2x [-3, 4] f(x) = x² + 3x [-2, 3] f(x) = 3x - 8 [4, 5] f(x) = x² - 5 [-1, 1].

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The system of equations given by x - 5y = 4 and -2x + 10y = k has no unique solution for any value of k. It has a solution for all real values of k and infinitely many solutions for all real numbers k.

To determine the values of k for which the system of equations has a unique solution, no solution, or infinitely many solutions, let's analyze the given equations:

x - 5y = 4

-2x + 10y = k

We can observe that equation 2 is a scalar multiple of equation 1. Multiplying equation 1 by -2, we obtain:

-2(x - 5y) = -2(4)

2x - 10y = -8

Comparing this with equation 2, we see that both equations represent the same line. This implies that the system of equations has infinitely many solutions for any value of k, as both equations are equivalent and represent the same line.

Therefore, for part (a), there is no value of k that gives the system a unique solution. The correct choice is C: There is no value of k that will give the system a unique solution.

For part (b), since the system has infinitely many solutions for all values of k, the correct choice is C: The given system has a solution for all real values k.

For part (c), we have already determined that the system has infinitely many solutions for all values of k. Therefore, the correct choice is C: The given system has infinitely many solutions for all real numbers k.

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Using logical reasoning, we can say that (C) Kaylon is wrong because the shaded temperature is -° according to the given image.

In addition to formal deduction, two more categories of logical thinking are frequently distinguished: induction and abduction.

The following can be explained if one has a precondition or premise, a conclusion or logical consequence, and a rule or material conditional that indicates the conclusion given the precondition.

Mathematical logic and philosophical logic are frequently used to support the claim that "when it rains, objects outside become wet.

The grass is outside, therefore: when it rains, the grass gets wet."

A finding of the rule is supported by inductive reasoning.

So, according to the given, we can easily guess that Kaylon is wrong because the shaded temperature is -°.

Therefore, using logical reasoning, we can say that (C) Kaylon is wrong because the shaded temperature is -° according to the given image.

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The value of ACD of a trapezium is 26.56°.

Let ABCD be a trapezoid with BCǀǀAD and AB=BC=CD= ½ AD.

ACD can be determined by using the Pythagorean theorem or using the theorem of Pythagoras.

The theorem of Pythagoras states that if you draw a right-angled triangle with the hypotenuse as c and the legs a and b.

The sum of squares of the legs (a and b) equals the square of the hypotenuse (c).

Therefore, by using the Pythagorean theorem ; AC² = AB² + BC²

=> AC² = (1/2 AD)² + (1/2 AD)²

=> AC² = 1/4 AD² + 1/4 AD²

=> AC² = 1/2 AD².

Hence,AC² = 1/2 AD²

ACD is a right-angled triangle where AC is the hypotenuse.

Thus, using the theorem of Pythagoras, we can write: AD² = AC² + CD²

=> AD² = [√(1/2 AD²)]² + (AD/2)²

=> AD² = 1/2 AD² + 1/4 AD²

=> AD² = 3/4 AD²=> AD = √4/3 AD

Thus, ACD=ACD = tan¯¹(√1/2 AD²/AD/2) = tan¯¹(√2/4) = 26.56°

Therefore, ACD is 26.56°.

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Answer:

Its 6 cups of sugar per 4 cups  6:4 or 6/4

Step-by-step explanation:

if its 4 cups of flour to 6 cups of sugar and the question is  cups of sugar, per cup of flour then just reverse the numbers

Answer:

Step-by-step explanation:

A, B, D

Answer:

A,B,D

Step-by-step explanation:

Young people respond more favorably to literature that reflects their cultural customs, and this is because of the importance of cultural background in children’s reading development. Ethnic and cultural differences play an essential role in the children's reading development.

Children's cultural and ethnic background has a considerable impact on their learning, and thus the type of literature they respond to. Children tend to read more when they find that the stories and books reflect their cultural customs and identity. This enhances their literacy and reading skills, which in turn leads to an increased interest in reading and a better understanding of what they are reading.

Cultural diversity can help children become more empathetic and accepting of differences, and can help them to learn about new cultures. Therefore, it is crucial to provide children with access to a range of culturally diverse literature to help them understand the experiences of others. Children learn more effectively when they can make connections between what they are learning and their own experiences.

In conclusion, children's reading development is influenced by their ethnic and cultural background. Young people respond more favorably to literature that reflects their cultural customs, which can help them to become more empathetic and accepting of differences, as well as develop their literacy and reading skills. Therefore, it is essential to provide children with a range of culturally diverse literature to help them learn about new cultures and understand the experiences of others.

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Answer:

(-3) x (-3) x (-3) x (-3)

(-3)²

The value of her investment at the end of 7 years is $11804

The given parameters are

Principal, P = $5000

Rate, r = 4.5%

Time, t = 7 years

The value is then calculated as:

Value = P * P(1 + r)^t

So, we have:

Value = 5000 + 5000 * (1 + 4.5%)^7

Evaluate the expression

Value = 11804

Hence, the value of her investment at the end of 7 years is $11804

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Answer:

Area = 36 cm^2

Explanation:

The area of a parallelogram is the product of width and height

Now in our case w = 9 cm and h = 4cm; therefore, the area is

which is our answer!

a/b = c

The value of a.

a/b = c

or, a = c × b

or, a = bc

a = bc

The minimum (break-even) sales price that the company should charge per unit of the customized TK-15 for the special order is $30. To determine the break-even sales price per unit for the special order, we need to consider the additional costs incurred for customization and the lease of special equipment.

To determine the break-even sales price per unit for the special order, we need to consider the additional costs incurred for customization and the lease of special equipment.

The unit product cost of TK-15 is $20, which includes direct materials, direct labor, and manufacturing overhead. For the special order, additional direct materials cost of $6 per unit and additional direct labor cost of $4 per unit are required. This brings the total variable cost per unit to $20 + $6 + $4 = $30.

The fixed portion of manufacturing overhead does not change with the special order and is not relevant to the calculation of the break-even sales price.

In addition to the variable cost, the company incurs a lease cost of $80,000 for the special equipment. To determine the number of units needed to cover this cost, we divide the lease cost by the contribution margin per unit ($30 - $20 = $10) to get 8,000 units.

Since the special order is for 10,000 units, the fixed lease cost is covered within this quantity, and any additional units contribute towards covering the fixed manufacturing overhead and generating profit.

Therefore, the minimum (break-even) sales price that the company should charge per unit of the customized TK-15 for this special order is $30 (iii).

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Answer:

tenth- 49.1

Hundredth- 49.08

thousandsths- 49.076

ten-thousandths- 49.0758

well, from 1990 to 1998 is 8 years, and we know the amount went from $4800 to $6300, let's check for the rate of growth.

\(\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$6300\\ P=\textit{initial amount}\dotfill &\$4800\\ r=rate\to r\%\to \frac{r}{100}\\ t=\textit{years}\dotfill &8\\ \end{cases} \\\\\\ 6300=4800(1 + \frac{r}{100})^{8} \implies \cfrac{6300}{4800}=(1 + \frac{r}{100})^8\implies \cfrac{21}{16}=(1 + \frac{r}{100})^8\)

\(\sqrt[8]{\cfrac{21}{16}}=1 + \cfrac{r}{100}\implies \sqrt[8]{\cfrac{21}{16}}=\cfrac{100+r}{100} \\\\\\ 100\sqrt[8]{\cfrac{21}{16}}=100+r\implies 100\sqrt[8]{\cfrac{21}{16}}-100=r\implies \stackrel{\%}{3.46}\approx r\)

now, with an initial amount of $4800, up to 2007, namely 17 years later, how much will that be with a 3.46% rate?

\(\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &4800\\ r=rate\to 3.46\%\to \frac{3.46}{100}\dotfill &0.0346\\ t=years\dotfill &17\\ \end{cases} \\\\\\ A=4800(1 + 0.0346)^{17} \implies A=4800(1.0346)^{17}\implies A \approx 8558.02\)

Answer:

x = 138

Step-by-step explanation:

The exterior angle of a triangle is equal to the sum of the opposite interior angles

x = B+ C

x = 68+ 70

x =138

Answer:

138 degrees

Step-by-step explanation:

A triangle is made up of 180 degrees, it lists 2 values already, 68&70. when added that equals 138.

So 180-138 is 42 degrees, which would be the last angle within the triangle.

Since a line is also 180 degrees, its 180-42, which makes x 138 degrees

By using the change of base formula, 1.405684 is found to be the solution. Option 2 is the correct answer.

To solve the equation 3x+1 = 15 for x using the change of base formula, we need to first isolate the variable x. We can do this by subtracting 1 from both sides of the equation:

3x = 14

Then we can divide both sides by 3 to get x alone:

x = 14/3

Now we can use the change of base formula to express x in terms of logarithms. Let's use the base 10 logarithm:

log(14/3) = log(14) - log(3)

We can evaluate the logarithms using a calculator:

log(14) ≈ 1.146128

log(3) ≈ 0.477121

So we get:

log(14/3) ≈ 0.669007

Now we can use the given options to find the logarithm that is closest to 0.669007. We can do this by calculating the absolute value of the difference between each option and 0.669007, and choosing the option with the smallest absolute difference:

|log( y / b ) - 0.669007| ≈

-0.594316 : |(-0.594316) - 0.669007| ≈ 1.263323

1.405684 : |(1.405684) - 0.669007| ≈ 0.736677

1.464973 : |(1.464973) - 0.669007| ≈ 0.795966

3.469743 : |(3.469743) - 0.669007| ≈ 2.800736

Therefore, the option that is closest to 0.669007 is 1.405684. This means that:

log( y / b ) ≈ 1.405684

To find y/b, we can rewrite the equation as:

10^1.405684 ≈ y/b

Using a calculator, we get:

y/b ≈ 25.078

Therefore, the answer is approximately:

log(14/3) ≈ log(y/b) ≈ 1.405684

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Answer:

Graph is attached below with coordinated points of (3,3),  (-3,2),  (-2,-3),  (-3,-2),  (0, -4),  (-2,0),  (4,0), and (0,0)

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

The sample space for this experiment consists of 12 possible outcomes.

The sample space is a collection of all possible outcomes of an experiment.

There are three types of soups, two types of salads, and two types of sandwiches. Therefore, the sample space consists of 3x2x2 = 12 possible outcomes.

There could be a tomato soup, a spinach salad, and a turkey sandwich, which would be one possible outcome in the sample space. There could also be a minestrone soup, a Caesar salad, and a grilled cheese sandwich, which would be another possible outcome in the sample space.

Therefore, the sample space for this experiment consists of 12 possible outcomes, each of which is unique and representative of the customer's randomly chosen lunch.

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Answer:

8, 11, 14

Step-by-step explanation:

Answer:

Step-by-step explanation:

a=4

d=-1-(-4)=-1+4=3

\(a_{n}=a+(n-1)d\\a_{n}=-4+(n-1)3\\a_{n}=-4+3n-3\\a_{n}=-7+3n\)

x  y

1 -4

2 -1

3  2

4  5

5  8

6  11

7 14

(a) The function g(x) = -8\(x^2\) + 5x - 2 doesn't have two x-intercepts because ac > 0.

(b) The function h(x) = (-1/3)\(x^2\) + 3x doesn't have two x-intercepts because ac = 0.

(c) The function k(x) = 8\(x^2\) - 5x - 7 have two x-intercepts because ac < 0.

In the theorem, a, b, and c are real numbers.

Theorem - If f is a quadratic function of the form f(x) = a\(x^2\) + bx + c and ac < 0, then the function f has two x-intercepts.

(a) The function is g(x) = -8\(x^2\) + 5x - 2

On comparing the equation by f(x) = a\(x^2\) + bx + c, we get a = -8, b = 5 and c = -2.

To check the two x-intercepts, we put values in ac and compare with ac<0

ac = (-8)(-2)

ac = 16 > 0

As the value of ac is greater than 0. So we can say that it doesn't have two x-intercepts.

(b) The function is h(x) = (-1/3)\(x^2\) + 3x

On comparing the equation by f(x) = a\(x^2\) + bx + c, we get a = -1/3, b = 3 and c = 0.

To check the two x-intercepts, we put values in ac and compare with ac<0

ac = (-1/3)(0)

ac = 0 = 0

As the value of ac is equal to 0. So we can say that it doesn't have two x-intercepts.

(c) The function is k(x) = 8\(x^2\) - 5x - 7

On comparing the equation by f(x) = a\(x^2\) + bx + c, we get a = 8, b = -5 and c = -7.

To check the two x-intercepts, we put values in ac and compare with ac<0

ac = 8(-7)

ac = -56

ac < 0

As the value of ac is less than 0. So we can say that it have two x-intercepts.

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The number of hamburgers sold on Friday was 442.

Let us form the linear equation to find the number of burgers;

Let the cheeseburger be represented by x.

Since there were 67 more cheeseburgers sold than hamburgers. This means that hamburgers will be:

The number of hamburgers = x + 67.

Since the local hamburger shop sold a combined total of 817 hamburgers and cheeseburgers. This will be:

x + x + 67 = 817

2x + 67= 817

2x = 817 - 67

2x = 750

x = 750 / 2

x = 375

So, 375 cheeseburgers were sold on Friday.

Therefore, the number of hamburgers sold will be:

= 817 - 375

= 442

Thus, the number of hamburgers sold on Friday was 442.

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Answer:

Value of discriminant is 20

Step-by-step explanation:

Formula of discriminant is:

\(D=b^2-4ac\)

so our equation is

\(-4x^2+6x-1=0\)

where a = -4, b = 6 , c = -1

so our discriminant becomes,

\(D=b^2-4ac\\D=(6)^2-4(-4)(-1)\\D=36-16\\D=20\)

Since the discriminant is positive we have two distinct real number solutions or two distinct roots, and to solve the we just use the quadratic formula and get the two different values of x.

\(x_1=0.191\\x_2=1.309\)

I have attached a graph also to confirm your answer, you use an online graphing calculator to verify it as well.

Answer : The expression will be

( c - 7 ) / 3

Step-by-step explanation:

Let's say Adam has c pieces of candy

He took ten pieces for himself which means we can write this as c-7

He then divided this amount between his 3 children (c-7)/3