[tex] \sf \huge{ question \hookleftarrow}[/tex]If [tex] \alpha \: and \: \beta [/tex] are roots of a equation " ax + by + c ", then find the value of the following in terms of a , b and c ~ [tex] \boxed{ \boxed{ \sf \sqrt{ \alpha} + \sqrt{ \beta } = \: ?}}[/tex]

[tex]\underline{\bf{Given \:equation:-}}[/tex] [tex]\\ \sf{:}\dashrightarrow ax^2+by+c=0[/tex][tex]\sf Let\:roots\;of\:the\: equation\:be\:\alpha\:and\beta.[/tex][tex]\sf We\:know,[/tex][tex]\boxed{\sf sum\:of\:roots=\alpha+\beta=\dfrac{-b}{a}}[/tex][tex]\boxed{\sf Product\:of\:roots=\alpha\beta=\dfrac{c}{a}}[/tex][tex]\underline{\large{\bf Identities\:used:-}}[/tex][tex]\boxed{\sf (a+b)^2=a^2+2ab+b^2}[/tex][tex]\boxed{\sf (a)^2=a}[/tex][tex]\boxed{\sf \sqrt{a}\sqrt{b}=\sqrt{ab}}[/tex][tex]\boxed{\sf \sqrt{\sqrt{a}}=a}[/tex][tex]\underline{\bf Final\: Solution:-}[/tex] [tex]\\ \sf{:}\dashrightarrow \sqrt{\alpha}+\sqrt{\beta}[/tex][tex]\bull\sf Apply\: Squares[/tex] [tex]\\ \sf{:}\dashrightarrow (\sqrt{\alpha}+\sqrt{\beta})^2= (\sqrt{\alpha})^2+2\sqrt{\alpha}\sqrt{\beta}+(\sqrt{\beta})^2[/tex] [tex]\\ \sf{:}\dashrightarrow (\sqrt{\alpha}+\sqrt{\beta})^2 \alpha+\beta+2\sqrt{\alpha\beta}[/tex][tex]\bull\sf Put\:values[/tex] [tex]\\ \sf{:}\dashrightarrow (\sqrt{\alpha}+\sqrt{\beta})^2=\dfrac{-b}{a}+2\sqrt{\dfrac{c}{a}}[/tex] [tex]\\ \sf{:}\dashrightarrow \sqrt{\alpha}+\sqrt{\beta}=\sqrt{\dfrac{-b}{a}+2\sqrt{\dfrac{c}{a}}}[/tex][tex]\bull\sf Simplify[/tex] [tex]\\ \sf{:}\dashrightarrow \underline{\boxed{\bf {\sqrt{\boldsymbol{\alpha}}+\sqrt{\boldsymbol{\beta}}=\sqrt{\dfrac{-b}{a}}+\sqrt{2}\dfrac{c}{a}}}}[/tex][tex]\underline{\bf More\: simplification:-}[/tex] [tex]\\ \sf{:}\dashrightarrow \sqrt{\alpha}+\sqrt{\beta}=\dfrac{\sqrt{-b}}{\sqrt{a}}+\dfrac{c\sqrt{2}}{a}[/tex] [tex]\\ \sf{:}\dashrightarrow \sqrt{\alpha}+\sqrt{\beta}=\dfrac{\sqrt{a}\sqrt{-b}+c\sqrt{2}}{a}[/tex][tex]\underline{\Large{\bf Simplified\: Answer:-}}[/tex] [tex]\\ \sf{:}\dashrightarrow\underline{\boxed{\bf{ \sqrt{\boldsymbol{\alpha}}+\sqrt{\boldsymbol{\beta}}=\dfrac{\sqrt{-ab}+c\sqrt{2}}{a}}}}[/tex]

The value [tex]\sqrt{\alpha } +\sqrt{\beta }[/tex] in terms of a, b and c is [tex]\sqrt{{(\frac{b}{a})^2 } +2\sqrt{\frac{c}{a} } } \\[/tex]Roots of a quadratic equationGiven the quadratic equation ax + bx + c, the sum and product of the roots are expressed as:[tex]\alpha +\beta =-\frac{b}{a} [/tex][tex]\alpha \beta =\frac{c}{a} [/tex]Get the value of the radical expression [tex]\sqrt{\alpha } +\sqrt{\beta } [/tex]Taking the square of the expression will give:[tex](\sqrt{\alpha } +\sqrt{\beta } )^2=(\sqrt{\alpha } )^2+(\sqrt{\beta } )^2+2\sqrt{\alpha \beta} [/tex]Take the square root of both sides:[tex]\sqrt{(\sqrt{\alpha } +\sqrt{\beta } )^2} =\sqrt{(\sqrt{\alpha } )^2+(\sqrt{\beta } )^2+2\sqrt{\alpha \beta} } \\\sqrt{\alpha } +\sqrt{\beta }=\sqrt{{(\alpha }+{\beta} )+2\sqrt{\alpha \beta} } \\[/tex]Substitute the product and the sum values into the expression to have:[tex]\sqrt{\alpha } +\sqrt{\beta }=\sqrt{{(-\frac{b}{a})^2 } +2\sqrt{\frac{c}{a} } } \\\sqrt{\alpha } +\sqrt{\beta }=\sqrt{{(\frac{b}{a})^2 } +2\sqrt{\frac{c}{a} } } \\[/tex]Hence the value [tex]\sqrt{\alpha } +\sqrt{\beta }[/tex] in terms of a, b and c is [tex]\sqrt{{(\frac{b}{a})^2 } +2\sqrt{\frac{c}{a} } } \\[/tex]Learn more on the roots of equation here: https://brainly.com/question/25841119

Mathematics High School

$ \sf \huge{ question \hookleftarrow}$

If $ \alpha \: and \: \beta $ are roots of a equation " ax² + by + c ", then find the value of the following in terms of a , b and c ~

$ \boxed{ \boxed{ \sf \sqrt{ \alpha} + \sqrt{ \beta } = \: ?}}$

Answers

Answer 1

$\underline{\bf{Given \:equation:-}}$

$\\ \sf{:}\dashrightarrow ax^2+by+c=0$

$\sf Let\:roots\;of\:the\: equation\:be\:\alpha\:and\beta.$

$\sf We\:know,$

$\boxed{\sf sum\:of\:roots=\alpha+\beta=\dfrac{-b}{a}}$

$\boxed{\sf Product\:of\:roots=\alpha\beta=\dfrac{c}{a}}$

$\underline{\large{\bf Identities\:used:-}}$

$\boxed{\sf (a+b)^2=a^2+2ab+b^2}$

$\boxed{\sf (√a)^2=a}$

$\boxed{\sf \sqrt{a}\sqrt{b}=\sqrt{ab}}$

$\boxed{\sf \sqrt{\sqrt{a}}=a}$

$\underline{\bf Final\: Solution:-}$

$\\ \sf{:}\dashrightarrow \sqrt{\alpha}+\sqrt{\beta}$

$\bull\sf Apply\: Squares$

$\\ \sf{:}\dashrightarrow (\sqrt{\alpha}+\sqrt{\beta})^2= (\sqrt{\alpha})^2+2\sqrt{\alpha}\sqrt{\beta}+(\sqrt{\beta})^2$

$\\ \sf{:}\dashrightarrow (\sqrt{\alpha}+\sqrt{\beta})^2 \alpha+\beta+2\sqrt{\alpha\beta}$

$\bull\sf Put\:values$

$\\ \sf{:}\dashrightarrow (\sqrt{\alpha}+\sqrt{\beta})^2=\dfrac{-b}{a}+2\sqrt{\dfrac{c}{a}}$

$\\ \sf{:}\dashrightarrow \sqrt{\alpha}+\sqrt{\beta}=\sqrt{\dfrac{-b}{a}+2\sqrt{\dfrac{c}{a}}}$

$\bull\sf Simplify$

$\\ \sf{:}\dashrightarrow \underline{\boxed{\bf {\sqrt{\boldsymbol{\alpha}}+\sqrt{\boldsymbol{\beta}}=\sqrt{\dfrac{-b}{a}}+\sqrt{2}\dfrac{c}{a}}}}$

$\underline{\bf More\: simplification:-}$

$\\ \sf{:}\dashrightarrow \sqrt{\alpha}+\sqrt{\beta}=\dfrac{\sqrt{-b}}{\sqrt{a}}+\dfrac{c\sqrt{2}}{a}$

$\\ \sf{:}\dashrightarrow \sqrt{\alpha}+\sqrt{\beta}=\dfrac{\sqrt{a}\sqrt{-b}+c\sqrt{2}}{a}$

$\underline{\Large{\bf Simplified\: Answer:-}}$

$\\ \sf{:}\dashrightarrow\underline{\boxed{\bf{ \sqrt{\boldsymbol{\alpha}}+\sqrt{\boldsymbol{\beta}}=\dfrac{\sqrt{-ab}+c\sqrt{2}}{a}}}}$

Answer 2

The value $\sqrt{\alpha } +\sqrt{\beta }$ in terms of a, b and c is $\sqrt{{(\frac{b}{a})^2 } +2\sqrt{\frac{c}{a} } } \\$

Roots of a quadratic equation

Given the quadratic equation ax² + bx + c, the sum and product of the roots are expressed as:

$\alpha +\beta =-\frac{b}{a} $$\alpha \beta =\frac{c}{a} $

Get the value of the radical expression $\sqrt{\alpha } +\sqrt{\beta } $

Taking the square of the expression will give:

$(\sqrt{\alpha } +\sqrt{\beta } )^2=(\sqrt{\alpha } )^2+(\sqrt{\beta } )^2+2\sqrt{\alpha \beta} $

Take the square root of both sides:

$\sqrt{(\sqrt{\alpha } +\sqrt{\beta } )^2} =\sqrt{(\sqrt{\alpha } )^2+(\sqrt{\beta } )^2+2\sqrt{\alpha \beta} } \\ \sqrt{\alpha } +\sqrt{\beta }=\sqrt{{(\alpha }+{\beta} )+2\sqrt{\alpha \beta} } \\$

Substitute the product and the sum values into the expression to have:

$\sqrt{\alpha } +\sqrt{\beta }=\sqrt{{(-\frac{b}{a})^2 } +2\sqrt{\frac{c}{a} } } \\\sqrt{\alpha } +\sqrt{\beta }=\sqrt{{(\frac{b}{a})^2 } +2\sqrt{\frac{c}{a} } } \\$

Hence the value $\sqrt{\alpha } +\sqrt{\beta }$ in terms of a, b and c is $\sqrt{{(\frac{b}{a})^2 } +2\sqrt{\frac{c}{a} } } \\$

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Related Questions

PLEASE HELP ME ASAP PLEASE.

Answers

Answer:

See below

Step-by-step explanation:

g (h(6)) :

h (6) = 3 ( 6^2) + 2 = 110

then g (110) = sqrt (110)

h (g(5))

g(5) = sqrt 5

then h( sqrt5) = 3 ( sqrt5)^2 + 2 = 17

What is the value of the expression h-20 when h = 60

Answers

40 (b) because 60-20=40

Ryan invested \$4,800$4,800 in an account in the year 1990, and the value has been growing exponentially at a constant rate. The value of the account reached \$6,300$6,300 in the year 1998. Determine the value of the account, to the nearest dollar, in the year 2007.

Answers

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?

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

Q3) (25p) Solve the following 0-1 integer programming model problem by implicit enumeration. Maximize 2x1 −x2 −x3

Subject to
2x1+3x2−x3 ≤4
2x2 +x3 ≥2
3x1 + 3x2 + 3x3 ≥6
x1 ,x2 ,x 3 ∈{0,1}

Answers

The 0-1 integer programming problem is solved using implicit enumeration to maximize the objective function 2x1 - x2 - x3, subject to three constraints. The optimal solution to the 0-1 integer programming problem is x1 = 0, x2 = 1, and x3 = 1, with a maximum objective function value of 1.

The optimal solution is found by systematically evaluating all possible combinations of binary values for the decision variables x1, x2, and x3 and selecting the one that yields the highest objective function value.
To solve the 0-1 integer programming problem using implicit enumeration, we systematically evaluate all possible combinations of binary values for the decision variables x1, x2, and x3. In this case, there are only eight possible combinations since each variable can take on either 0 or 1. We calculate the objective function value for each combination and select the one that maximizes the objective function.
The first constraint, 2x1 + 3x2 - x3 ≤ 4, represents an upper limit on the sum of the decision variables weighted by their coefficients. We check each combination of x1, x2, and x3 to ensure that this constraint is satisfied.
The second constraint, 2x2 + x3 ≥ 2, represents a lower limit on the sum of the decision variables weighted by their coefficients. Again, we check each combination of x1, x2, and x3 to ensure that this constraint is met.
The third constraint, 3x1 + 3x2 + 3x3 ≥ 6, imposes a lower limit on the sum of the decision variables weighted by their coefficients. We evaluate each combination of x1, x2, and x3 to verify that this constraint is satisfied.
By evaluating all eight combinations and calculating the objective function value for each, we determine that the optimal solution occurs when x1 = 0, x2 = 1, and x3 = 1. This combination yields the maximum objective function value of 1. Therefore, the solution to the 0-1 integer programming problem, maximizing 2x1 - x2 - x3, subject to the given constraints, is achieved when x1 = 0, x2 = 1, and x3 = 1, resulting in an objective function value of 1.

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1.Find the area of a trapezium with parallel sides of
length 15 cm & 7 cm. The perpendicular distance
between the parallel sides is 6.8 cm.

Answers

Answer:

The area of the trapezium is $74.8\ cm^2$

Step-by-step explanation:

Area of a trapezium:

$\displaystyle A=\frac{b1+b2}{2}h$

This formula is valid if b1 and b2 are parallel and h is perpendicular to both.

Since the trapezium given in the problem satisfies those conditions, we use the formula with:

b1=15 cm

b2=7 cm

h=6.8 cm

$\displaystyle A=\frac{15+7}{2}\cdot 6.8$

$A=74.8\ cm^2$

The area of the trapezium is $74.8\ cm^2$

2. Solve 4(3c + 10) < 12c + 40.
use photo for Choices

Answers

Answer:

no solution

Step-by-step explanation:

4 (3c + 10) < 12c + 4012c +40 < 12c +4012c- 12c < 40 -40 0 < 0

Left and right sides are equal so no solution

Answer:No solution

Step-by-step explanation: I got it right on the test :)

Use the function f(x) to answer the questions: f(x)=4x^2-7x-15 Part A: what are the x-intercepts of the graph of f(x)? Show your work(2 points) Part b: Is the vertex of the graph of f(x) going to be maximum or minimum? What are the coordinates of the vertex? Justify your answer and show your work (3 points) Part c what are the steps you would use to graph f(x)? Justify that you can use the answer obtained in part a and part b to draw the graph. (5 points)

Answers

Answer:

(Hope this helps can I pls have brainlist (crown)☺️)

Step-by-step explanation:

To find the x-intercept, substitute in 0 for y and solve for x .To find the y-intercept, substitute in 0 for x and solve for y .

x-intercept(s): ( $-\frac{5}{4}$ , 0 )

y-intercept(s): ( 0 , − 15 )

Vertex: y = 4 ( x - $\frac{7}{8}$ )^2 $\frac{289}{16}$

Graph in pic

Use the function f(x) to answer the questions: f(x)=4x^2-7x-15 Part A: what are the x-intercepts of the

for students who earned a score of 20 or lower on the quiz, the cumulative frequency is and the relative cumulative frequency is . a.) 16; 32% b.) 9; 18% c.) 38; 76% d.) 29; 58%

Answers

The cumulative frequency and relative cumulative frequency for students who earned a score of 20 or lower on the quiz is 29; 58%. (option d)

Cumulative frequency refers to the running total of frequencies, or the sum of frequencies up to a certain point. In this case, the cumulative frequency is the number of students who scored 20 or lower on the quiz.

Relative cumulative frequency, on the other hand, expresses the cumulative frequency as a percentage of the total number of students in the sample. To find the relative cumulative frequency, we divide the cumulative frequency by the total number of students and multiply by 100.

Therefore, for students who scored 20 or lower on the quiz, the cumulative frequency is 29 and the relative cumulative frequency is 58% (29/50 * 100).

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Answer: 38, 76%

Step-by-step explanation:

Recall that for cumulative frequency we add up all the values that fall above or below a given bin of data. So, if we want all scores less than 20 it should be the first four bins with a total of:

8 plus 8 plus 13 plus 9 equals 38

To get the relative frequency we take the total in the bins for scores of 20 and lower divided by the total of all bins:

38 over 50 equals 0.76 equals 76 percent sign

x - 3 < 4

graph the inequality

Answers

Answer: See the image below.

When you mix two colors of paint in equivalent ratios, the resulting color is always the same.

Use the table below to help you answer the following question.
How many cups of yellow paint should you mix with 1 cup of blue paint to make the same shade of green?

Answers

can i see the table

the weights of steers in a herd are distributed normally. the variance is 90,000 and the mean steer weight is 1200lbs. find the probability that the weight of a randomly selected steer is between 1379 and 1590lbs. round your answer to four decimal places.

Answers

The probability that the weight of a randomly selected steer is between 1379 and 1590lbs is P(1.39 < z < 1.80) = P(z < 1.80) - P(z < 1.39)

Let X the random variable that represent the weights of a population, and for this case we know the distribution for X is given by:

X~N (1379,1590)

Where we know u = 1200 and a = $\sqrt{90000}$ = 300

we need probability of

P (1379 < X < 1590)

now we can solve this using z = x-u/a

by using the above formula we get:

1590-1200/300 = P(1.39 < z < 1.8)

And we can find this probability using the normal standard table with this difference:

P(1.39 < z < 1.80) =

P(z < 1.80) - P(z < 1.39)

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4. Solve: 8−2n−6n=−16
A. n=11
B. n=9
C. n=10
D. n=3

Answers

Answer:

D. n=3

Step-by-step explanation:

8-2n-6n= –16

Take 8 to the other side

-2n-6n= -16-8

Solve them

-8n = -24

Take -8 to the other side

$n \: = \frac{ - 24}{ - 8} $

n = 3

$\huge\text{Hey there!}$

$\huge\textbf{Equation:}$

$\mathbf{8 - 2n - 6n = -16}$

$\huge\textbf{Solving for the answer:}$

$\mathbf{8 - 2n - 6n = -16}$

$\huge\textbf{Combine the like terms:}$

$\mathbf{(-2n - 6n) + 8 = -16}$

$\mathbf{-2n - 6n + 8 = -16}$

$\mathbf{-8n + 8 = -16}$

$\huge\textbf{Subtract \boxed{\bf 8} to both sides:}$

$\mathbf{-8n + 8 - 8 = -16 - 8}$

$\huge\textbf{Simplify it:}$

$\mathbf{-8n = -16 - 8}$

$\mathbf{-8n = -24}$

$\huge\textbf{Divide \boxed{\bf -8} to both sides:}$

$\mathbf{\dfrac{-8n}{-8} = \dfrac{-24}{-8}}$

$\huge\textbf{Simplify it:}$

$\mathbf{n = \dfrac{-24}{-8}}$

$\mathbf{n = -24 \div -8}$

$\mathbf{n = 3}$

$\huge\textbf{Therefore, your answer should be:}$

$\huge\boxed{\textsf{Option D. \boxed{\frak{n = 3}}}}\huge\checkmark$

$\huge\text{Good luck on your assignment \& enjoy your day!}$

~$\frak{Amphitrite1040:)}$

please help making brainliest if correct

Answers

Answer:

I'm very sure this is using SAS.

Answer:

SAS is the correct answer

Determine whether each number is an integer, a rational number that is not an integer, or an irrational number. pls help very urgent

Answers

Integer: 12

Irrational numbers: -2√10 and √20

Rational numbers: 17/4, 0.25, and -77/11.

What are integers?

Any positive or negative number without fractions or decimal places is known as an integer, often known as a "round number" or "whole number."

Given:

There are rational and irrational numbers in the image.

The numbers can be written in the form of p/q, where q is never zero is rational numbers.

And rest of the numbers are irrational numbers.

So, the solutions are given in the image below.

√144 = 12

0.25 = 25/100 = 1/4

Therefore, the solutions are given in the image below.

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If the change in y equals 10 and the change in x equals -5, then

the slope of the curve is positive.
the slope of the curve is negative.
the curve must be a straight line.
the slope cannot be calculated without more information.

Answers

Perhaps positive if the outcome equals positive since y = 10.

Randomly select a painted rock from a bag containing 4 purple rocks, 3 green rocks, 3 orange rocks, and 2 blue rocks.

Answers

Answer:

i got a orange

Step-by-step explanation:

I would choose blue rocks bestie

A high school has 1,300 students, 320 of which are seniors. An administrator surveys 50 seniors and finds that 18 seniors plan to attend community college the year after they graduate. What is the population

Answers

The population of seniors who plan to attend community college is; 115.

Population and Sample size

According to the task content;

It follows that the 50 senior students were surveyed and only 18 wanted to attend community college.

On this note, the number of seniors who want to attend community college among the 320 seniors is;

(18/50) × 320

= 115.2.

On this note, it follows that the number of seniors who want to attend community college is; 115 seniors.

Answers

Answer:

9 weeks

Step-by-step explanation:

50+ (30x9)=320

8 weeks because $50+$30 is $80. $80-$320 is $240.split $240 into 8 separate payments of $30

what is the range of the function f(x)=-8x+13 when the domain is (-2,0,3)?

Answers

Answer:

The complete set of domain (x) and range values (y) is given by:

x y

-2 39

0 13

3 11

Step-by-step explanation:

Considering the function

$f(x)=-8x+13$

As we know that the range of a function consists of the entire set of all possible resulting values of the dependent variable commanly called y or f(x), once we have substituted the domain.

Now

As the x values are -2, 0, and 3. So, the domain interval is (-2,0,3).

Putting x = -2 in f(x) to determine the range for the value x = -2

$f(x)=-8x+13$

$f(-2)=-8(-2)+13=16+13=39$

Putting x = 0 in f(x) determine the range for the value x = 0

$f(x)=-8x+13$

$f(0)=-8(0)+13=0+13=13$

Putting x = 0 in f(x) determine the range for the value x = 3

$f(x)=-8x+13$

$f(3)=-8(3)+13=-24+13=11$

Therefore, the complete set of domain (x) and range values (y) is given by:

x y

-2 39

0 13

3 11

Hanson has 38 pieces of candy. He gives away c of the pieces. Write an expression that
shows the number of pieces of candy Hanson has left.

Answers

Answer:

38-c

Step-by-step explanation:

We know that the answer is 38-c because any piece of candy that Hanson gives away will be subtracted from the amount that he started out with.

A general formula for a parabola is y2=4px. what is the value of p in the equation y2=−4x?

Answers

The value of p is -1 in the given equation of of parabola.

What is a parabola?

A parabola is an approximately U-shaped, mirror-symmetrical planar curve. It corresponds to a number of seemingly unrelated mathematical descriptions, all of which can be shown to define the same curves. One way to describe a parabola is with a point called focus and a line called the directrix.

Equation for a Parabola

The general formula or the equation for representing a parabola is given by,

y² = 4px

Here, (h,k) being the vertex of the parabola,

y = a(x-h)² + k

x = b(y-k)² + h

The focus of this parabola is given by (p, 0).

The directrix of the parabola is the line drawn perpendicular to the y-axis and traversing the point (-p, 0). The directrix is parallel to the parabola's axis.

What is the value of p in the equation for parabola?

The given equation is,

y² = -4x

Comparing this equation with the general formula of the parabola, we get,

p = -1

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Please help!! The question is negative 2 over 3 multiplied by ( negative 1 over 4 )

Answers

Hi!

So, we are given the following:

$-\frac{2}{3}$ × $\frac{-1}{4}$

The exact form solution to the given equation would be:

$\frac{1}{6}$

Hope this helps!

Combinations and Separations of Functions

Answers

Answer:

Step-by-step explanation:

The intersection of the domains of both functions is all real x greater than or equal to 2.

The domain of the given function h(x) = f(x) - g(x) is x ≥ 2.

A function is a mathematical expression written in terms of one or more than one variables.

There are given two functions, f(x) and g(x).

From the given graph, it is evident that the domain of the function f(x) is x ≥ 2.

Also, from the same graph, it is evident that the domain of the function f(x) is x ≥ -1.

The function h(x) is the difference between the functions f(x) and g(x).

Therefore,

domain of h(x) = domain of f(x) ∩ domain of g(x)

= {x | x ≥ 2} ∩ {x | x ≥ -1}

= {x | x ≥ 2}

Therefore, the domain of the function h(x) is [2, ∞).

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Evaluate the equation (-3/2)^4

Answers

Answer:

$-81/16$

Step-by-step explanation:

$(-3/2)^4$

Apply exponent to numerator and denominator.

$-3^4/2^4$

Solve for exponent.

$-81/16$

diana had 41 stickers she put them in 7 equal groups she put as many possible in each group she gave the leftover stickers to her sister how many stickers did diana give to her sister

Answers

6 number of stickers diana given to her sister.

What is Division?

A division is a process of splitting a specific amount into equal parts.

Diana had 41 stickers and she put them in 7 equal groups. To find out how many stickers she put in each group, we can divide 41 by 7:

41 ÷ 7 = 5 with a remainder of 6

This means that Diana put 5 stickers in each of the 7 groups, and she had 6 stickers leftover.

She gave the leftover stickers to her sister, so she gave her sister 6 stickers.

Hence, 6 number of stickers diana given to her sister.

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If a test statistic has been found to be statistically significant at the .05 level, the probability of getting this result by chance alone is

Answers

A test statistic found to be statistically significant at the .05 level means that the probability of obtaining that result by chance alone is 5% or less.

If a test statistic has been found to be statistically significant at the .05 level, the probability of getting this result by chance alone is 5% or less.

1. When conducting hypothesis testing, a significance level (also known as alpha) is chosen, typically .05.
2. If the test statistic falls in the critical region, which is determined based on the significance level, we reject the null hypothesis.
3. The probability of obtaining a test statistic as extreme as the one observed, assuming the null hypothesis is true, is the p-value. If the p-value is less than the significance level, we reject the null hypothesis, indicating statistical significance.

In conclusion, a test statistic found to be statistically significant at the .05 level means that the probability of obtaining that result by chance alone is 5% or less.

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Consider a situation in which p(x) = and p(y) = . if p(x and y) is = , which best describes the events?

Answers

The correct option is (A) P(X) × P(Y) = P(X ∩ Y)

What is probability and example?

Probability = the number of ways of achieving success. the total number of possible outcomes. For example, the probability of flipping a coin and it being heads is ½, because there is 1 way of getting a head and the total number of possible outcomes is 2 (a head or tail). We write P(heads) = ½ .

We are given to consider a situation in which X and Y are two events such that

P(X) = 4/5, P(Y) = 1/4, P(X ∩ Y) = 1/5

We are to select the statement that best describes the events X and Y

We know that

any two events A and B are said to be independent if

P(A) × P(B) = P (A ∩ B)

We have, for events X and Y,

P(X) × P(Y) = 4/5 × 1/4 = 1/5 = P (X ∩ Y)

P(X) × P(Y) = P(X ∩ Y)

Thus, X and Y are independent because P(X) × P(Y) = P(X ∩ Y)

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The complete question is -

Consider a situation in which P(X) = 4/5 and P(Y) = 1/4. If P(X and Y) is = 1/5, which best describes the events?

They are independent because P(X) x P(Y) = P(X and Y).

They are independent because P(X) + P(Y) = P(X and Y).

They are dependent because P(X) x P(Y) = P(X and Y).

They are dependent because P(X) + P(Y) = P(X and Y).

Answer: a

Step-by-step explanation:

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Sarah took the advertising department from her company on a round trip to meet with a potential client. Including Sarah a total of 10 people took the trip. She was able to purchase coach tickets for 240$ and first class tickets for 1090$ She used her total budget for airfare for the trip, which was 6650$. How many first class tickets did she buy? How many coach tickets did she buy?

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Answer:

Step-by-step explanation:

Class tickets she brought was 109 and coach tickets was 24

Ms. dulaney teaches 7 classes a day. each class has 23 students. after school she coaches the girls track team. there are 47 students on the track team that do not have a class with ms. dulaney. how many different students does ms. dulaney work with each day?

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Ms. Dulaney works with 208 different students. each day.

It is given that Ms. Dulaney taught 7 classes each day that had 2 students each.

We also know that after school, Ms. Dulaney coached the girl's track team. The girl's track team had 47 such students that did not have a class with Ms. Dulaney.

Here, we need to find the number of different students Ms. Dulaney worked with.

Therefore the different students she works with will be

Total no. of students she teaches in class + no. of students in the track team that do not have a class with Ms. Dulaney

= No. of students in each class X no. of classes + 47

= 23 X 7 + 47

= 161 + 47

= 208 students

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Can someone please help me ASAP?? It’s due today!! I will give brainliest If It’s correct.

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The correct option that indicates how Christa sliced the rectangular pyramid is the second option.

Christa sliced the pyramid perpendicular to its base through two edges.

What is a rectangular pyramid?

A rectangular pyramid is a pyramid with a rectangular base and four triangular faces.

The height of the cross section indicates that the location where Christa sliced the shape is lower than the apex of the pyramid.

The trapezoid shape of the cross section of the pyramid indicates that the top and base of the cross section are parallel, indicating that Christa sliced the pyramid parallel to a side of the base of the pyramid, such that it intersects two of the edges of the pyramid

The correct option is therefore the second option;

Christa sliced the pyramid perpendicular to its base through two edges

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\( \sf \huge{ question \hookleftarrow}\)If \( \alpha \: and \: \beta \) are roots of a equation " ax² + by + c ", then find the value of the following in terms of a , b and c ~ \( \boxed{ \boxed{ \sf \sqrt{ \alpha} + \sqrt{ \beta } = \: ?}}\)​

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\( \sf \huge{ question \hookleftarrow}\)

If \( \alpha \: and \: \beta \) are roots of a equation " ax² + by + c ", then find the value of the following in terms of a , b and c ~

\( \boxed{ \boxed{ \sf \sqrt{ \alpha} + \sqrt{ \beta } = \: ?}}\)