Enter the system represented on the graph below. Find and explain the meaning of the point of intersection of the lines.

Answer:

[tex]\dfrac{1}{x^2-8x+16}[/tex]

Step-by-step explanation:

The expression, written in full, looks like this:

[tex]\dfrac{x+3}{x^2-x-12}\cdot\dfrac{x-4}{x^2-8x+16}[/tex]

To simplify this expression, it would help us out a lot if we could factor the expressions in the denominators. Let's handle [tex]x^2-x-12[/tex] first:

[tex]x^2-x-12=\\=x^2-4x+3x-12\\=x(x-4)+3(x-4)\\=(x-4)(x+3)[/tex]

Next, we can factor [tex]x^2-8x+16[/tex]:

[tex]x^2-8x+16=\\=x^2-4x-4x+16\\=x(x-4)-4(x-4)\\=(x-4)(x-4)\\=(x-4)^2[/tex]

Substituting these back into our original expression, we get

[tex]\dfrac{x+3}{(x-4)(x+3)}\cdot\dfrac{x-4}{(x-4)^2}[/tex]

On the left, we can cancel an (x+3) in the numerator and denominator, and on the right, we can cancel an (x-4), simplifying the expression to

[tex]\dfrac{1}{x-4}\cdot\dfrac{1}{x-4}[/tex]

Multiplying the two together gives us the fraction

[tex]\dfrac{1\cdot1}{(x-4)\cdot(x-4)}=\dfrac{1}{(x-4)^2}[/tex]

Since [tex](x-4)^2=x^2-8x+16[/tex], we can rewrite this fraction in simplified form as

[tex]\dfrac{1}{x^2-8x+16}[/tex]

Answer:

It's A . 13 / (5√10)

Step-by-step explanation:

AD =   √(3^2 + 4^2) = √25

= 5 ( By the Pythagoras Theorem).

So sin 2α = 3/5 and cos 2α = 4/5.

m < B = α ( external angle of a triangle theorem)

and BD = AD = 5 (Isosceles triangle) and  BC = 4+5 = 9.

AB =  √(3^2 + 9^2) = √90 = 3√10

So sin α = 3 / 3√10 =  = 1 /√10  and cos α = 9 /3√10  = 3/√10.

Finally sin 3α = sin (2α + α) = sin 2α cos α + cos 2α sin α

=  3/5 * 3 / √10 +  4/5 *  1/√10

=  13/(5√10).

Answer:

Sorry i do not know the answer but...

Step-by-step explanation:

can u sub to Pewdiepie on YT.. Plz? Brofist

Answer:

Option d

Step-by-step explanation:

We need 2 fundamental data to solve this problem.

1.- Average number of clients attended in 1 hour.

2.- Time in which it is expected that a client will be attended.

They tell us that the average number of clients served in an hour is m = 8

They tell us to calculate the probability that the client will be seen in less than 15 minutes.

But the time t in the formula is given in hours.

Therefore we must write 15 minutes according to hours.

We know that [tex]1\ hour = 60 minutes[/tex].

So:

[tex]15\ minutes[\frac{1\ hour}{60\ minutes}] = 0.25\ hours[/tex].

Now we substitute in the formula [tex]m = 8[/tex] and [tex]t = 0.25[/tex] to find P.

[tex]P = 1 -e^{-mt}\\\\P = 1- e^{-(8)(0.25)}\\\\P = 1 - e^{-2}\\\\P = 0.8646\\\\P= 86\%[/tex]

Answer:

D edge

Step-by-step explanation:

Answer:

  A.  2

Step-by-step explanation:

There is a vertical asymptote where the denominator is zero. (x-2) is zero when x=2.

Answer:

The equation is that of ellipse withe angle of rotation 30° ⇒ answer (d)

Step-by-step explanation:

* Lets talk about the general form of the conic equations

- Ax² + Bxy + Cy² +D = 0 (center is the origin)

- A is the coefficient of x² , B is the coefficient of xy

 C is the coefficient of y² , D is the numerical term

* Now we will study how to know the type of the graph of this equation

- If A and C have different signs (different values)

∴ The equation is that of an ellipse

- If A and C have different signs (different values)

∴ The equation is on a hyperbola

* Now look at the equation:

 13x² + 6√3 xy + 7y² - 16 = 0

∵ A = 13 , B = 6√3 , C = 7 , D = -16

∵ A and C have same sign

∴ The equation is that of an ellipse

* Now lets find the angle of rotation by using the Rule:

- tan(2Ф) = B/(A - C) ⇒ Ф is the angle of rotation

- By using the value of A , B and C

∴ tan(2Ф) = 6√3/(13 - 7) = 6√3/6 = √3

∴ 2Ф = [tex]tan^{-1}\sqrt{3}=60[/tex]

∴ 2Ф = 60° ⇒ divide both sides by 2

∴ Ф = 30°

∴ The angle of rotation is 30°

∴ The equation is that of ellipse withe angle of rotation 30°

* The graph represent the ellipse

- The purple line represents the angle of rotation

Answer:

5 more minutes (total of 20 minutes per applicant)

Step-by-step explanation:

Divide an hour by 1/3 (60/3 = 20 minutes)

Divide an hour by 1/4 (60/4= 15 minutes)

By spending 1/3 of an hour (20 minutes) instead of 1/4 of an hour (15 minutes), she spent 5 more minutes meeting all applicants.

x = -21

explanation: a trick i used was just do -3 times 7 and get my answer -21. if you are unsure if the answer is right just check your work with a calculator. -21 divided by 7 is -3 so -21 is the value of x. please mark brainliest !!

1. The given curves intersect one another three times:

[tex]x^3=9x\implies x(x^2-9)=0\implies x=0,\pm3[/tex]

The area of the bounded region is

[tex]\displaystyle\int_{-3}^3|x^3-9x|\,\mathrm dx[/tex]

[tex]x^3-9x[/tex] is odd, but the absolute value makes it even. More formally,

[tex]|(-x)^3-9(-x)|=|-x^3+9x|=|x^3-9x|[/tex]

which means the integral is equivalent to

[tex]\displaystyle2\int_0^3|x^3-9x|\,\mathrm dx[/tex]

For [tex]0\le x\le 3[/tex], the definition of absolute value tells us that

[tex]|x^3-9x|=9x-x^3[/tex]

so the integral evaluates to

[tex]\displaystyle2\int_0^3(9x-x^3)\,\mathrm dx=\left(9x^2-\frac{x^4}2\right)\bigg|_{x=0}^{x=3}=\frac{81}2=40.5[/tex]

2. Using the disk method, the volume is given by the integral

[tex]\displaystyle\pi\int_0^\pi\sin^2(\sin x)\,\mathrm dx[/tex]

Use a calculator to get the result 1.219.

To find probability you can use proportions

What i would do is 6/10 since it cant be 7 and then cross multiply it by 1/10.

This should get you 60%

The probability of selecting a ball numbered less than 7 from an urn containing balls numbered 1 to 10 is 6 favorable outcomes out of 10 possible outcomes, which simplifies to 3/5 or 0.6.

The question is asking about the probability of selecting a ball with a number less than 7 from an urn with balls numbered from 1 to 10. To determine this probability, we count how many balls have numbers less than 7 which are 1, 2, 3, 4, 5, and 6. That gives us 6 balls. Since all balls are equally likely to be chosen, and there are 10 balls in total, the probability of drawing one with a number less than 7 is the number of favorable outcomes divided by the total number of outcomes.

Here is the calculation:

Therefore, the probability of drawing a ball with a number less than 7 is 6/10 which simplifies to 3/5 or 0.6.

Answer:

35 times

Step-by-step explanation:

The points Anita has remaining for a prize is  2580 - 480 = 2100 points

Since each time she earns 60 points, to get 2100 points, she needs to go:

[tex]\frac{2100}{60}=35[/tex] times

She needs to go 35 times

Answer:

35 times

Step-by-step explanation:

Answer:

The answer is hyperbola; 45° ⇒ answer (b)

Step-by-step explanation:

* At first lets talk about the general form of the conic equation

- Ax² + Bxy + Cy²  + Dx + Ey + F = 0

∵ B² - 4AC < 0 , if a conic exists, it will be either a circle or an ellipse.

∵ B² - 4AC = 0 , if a conic exists, it will be a parabola.

∵ B² - 4AC > 0 , if a conic exists, it will be a hyperbola.

* Now we will study our equation:

* 2xy - 9 = 0

∵ A = 0 , B = 2 , C = 0

∴ B² - 4 AC = (2)² - 4(0)(0) = 4 > 0

∴ B² - 4AC > 0

∴ The graph is hyperbola

* To find the angle of rotation use the rule:

- cot(2Ф) = (A - C)/B

∵ A = 0 , B = 2 , C = 0

∴ cot(2Ф) = 0/2 = 0

∴ 2Ф = 90°

∴ Ф = 45°

* The answer is hyperbola; with angle of rotation = 45°

Answer:

see explanation

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Rearrange x + 5y = 10 into this form

Subtract x from both sides

5y = - x + 10 ( divide all terms by 5 )

y = - [tex]\frac{1}{5}[/tex] x +2 ← in slope- intercept form

with slope m = - [tex]\frac{1}{5}[/tex]

• Parallel lines have equal slopes, hence

y = - [tex]\frac{1}{5}[/tex] x + c ← is the partial equation of the parallel line

To find c substitute (1, 3) into the partial equation

3 = - [tex]\frac{1}{5}[/tex] + c ⇒ c = [tex]\frac{16}{5}[/tex]

y = - [tex]\frac{1}{5}[/tex] x + [tex]\frac{16}{5}[/tex] ← equation of parallel line

Answer:

A) y = − 1 /5 x +  16/ 5

Step-by-step explanation:

Answer:

The length of BC = 28 units

Step-by-step explanation:

* In triangle ABC

∵ Angles B and C are congruent

∴ m∠B = m∠C

* In any triangle if two angles are equal in measure, then the triangle is isosceles means the two sides which opposite to the congruent angles are equal in length

∴ AB = AC

∵ AB = 4x - 7

∵ AC = 2x + 7

∴ 4x - 7 = 2x + 7 ⇒ collect like terms

∴ 4x - 2x = 7 + 7

∴ 2x = 14 ⇒ divide both sides by 2

∴ x = 14 ÷ 2 = 7

* Now we can find the length of BC

∵ The length of BC = 4x ⇒ substitute the value of x

∴ The length of BC = 4 × 7 = 28 units

To find the length of side BC of the triangle, you can use the fact that angle B and angle C are congruent. Set up an inequality using the lengths of side AB and side AC, and solve for x. Substitute x with an appropriate value to find the length of side BC.

To find the length of side BC of the triangle, we can use the fact that angle B and angle C are congruent. Let's represent the length of side AB as 4x - 7 and the length of side AC as 2x + 7. Since the sum of the lengths of the two smaller sides of a triangle must be larger than the length of the largest side, we can set up an inequality: 4x - 7 + 2x + 7 > 4x. Simplifying this inequality, we get 6x > 0, which tells us that x must be greater than 0.

Since side BC is labeled as 4x, we can substitute x with any positive value greater than 0. For example, if we let x = 1, then side BC would have a length of 4(1) = 4 units.

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ANSWER

a. A variable is an unknown number or value represented by a letter

EXPLANATION

In mathematics, we use letters to represent an unknown quantity or number.

For instance, we can use the letter , t, to represent time taken to cover a given distance.

We can use the letter , s, to represent displacement or distance covered by an object.

The letters that we use to represent the unknown values or numbers are called variables.

The correct answer is A.

A variable is a characteristic that can change in value across different instances. It can be represented by any letter and can be numerical or categorical. In mathematical contexts, it often represents an unknown value in an equation.

A variable, which can be represented by any letter, and not just 'x', is a characteristic that can vary in value across different instances. It could refer to different types of measurables such as a numerical variable like 'x' representing the number of points earned by a student or a categorical variable like 'y' representing someone's party affiliation. Variables in mathematical contexts are often used in equations to represent unknown values.

For example, if 'x' represents the number of children in a family, each different integer value of 'x'(0, 1, 2, 3, etc) specifies a unique family structure. Therefore, option A : 'A variable is an unknown number or value represented by a letter' is the correct choice.

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Answer:

a:  105.2 < µ < 112.8

b:  104.872 < µ < 113.128

c:  105.841 < µ < 112.159

d:  No, because n < 30

Step-by-step explanation:

For a - c, see attached photos for work.  There are 2 formulas to use.  The steps for constructing any confidence interval are the same, you will just use different numbers in the formula depending on what data is given to you.  

d:  With large sample sizes, the data often resembles normally distributed data, so we can still construct confidence intervals from the data.

Answer:

b

Step-by-step explanation:

Answer with step-by-step explanation:

We are given three different expressions and we are to write an equivalent exponential equation for them.

We know that the standard form of a logarithmic expression is given by:

[tex]y = log_a ( x )[/tex] which is equivalent to the exponential form  [tex]x = a ^ y[/tex].

1. [tex] log _ {10} (0.1) = -1 [/tex] ---> [tex]10^{-1}=0.1[/tex]

2. [tex] log _ {3} 9 = 2 [/tex] ---> [tex]3^2=9[/tex]

3. [tex] log _ 5 ( \frac { 1 } { \sqrt { 5 } } ) = -\frac { 1 } { 2 } [/tex] ---> [tex]5^{-\frac{1}{2} }=\frac{1}{\sqrt{5} }[/tex]

Answer: true :))

Step-by-step explanation:

Public relations is part of business and administrative support as it helps manage a business's image and relationship with the public. Meanwhile, bureaucracy plays a role in not only enforcing policies but also in policy formation.

Public relations is indeed a part of business and administrative support. Businesses use public relations to manage and protect their image and relationship with the public. It's a key component to business administration as it helps businesses improve their brand awareness, manage crises, and strengthen relationships with stakeholders.

The question about bureaucracy is a separate query and in this context, the statement is false. Bureaucracy is not only involved in enforcing policies to ensure people comply, but it is also involved in the process of policy formation. Through different departments and offices, information is gathered, policy proposals are developed and recommendations are made to decision-makers.

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Solve for x in the denominator  by setting it to zero:

(x+6) = 6

x = -6

Now using the given equation but replace the constant with c :

x^2 +8x +C

Replace x with -6:

(-6)^2 +8(-6) +c

36 - 48 +C = 0

-12 +c = 0

c = 12

The constant needs to be 12 in order for (x+6) to be a factor.

Answer:

13.76

Step-by-step explanation:

Area of the whole

The area of the whole = s^2 (the firgure is a square

s = 8

Area of the whole = 8^2 = 64

Area of the unshaded part

The 2 half circles = 1 whole circle

The radius of the 1/2 circle = 4 (eight has been cut in half)

Area of two half circles = 2* (pi r^2/2)

Area of two half circles = 2 * (pi 4^2/2)

area of two half circles =  16*pi

Area of the shaded area

Area of the shaded area = area of the whole - area of the unshaded area

Area of the shaded area = 64 - 16*pi

Area of the shaded area = 64 - 3.14*16 = 13.76

Answer:

57.82 gallons will be needed to fill the tank

Step-by-step explanation:

Final answer:

Leo's fish tank can hold approximately 57.8 gallons of water to the nearest tenth, calculated by finding the volume of the tank in cubic inches and then converting that to gallons using the conversion factor.

Explanation:

To calculate how many gallons of water can fill the fish tank to the nearest tenth, we need to find the volume of the tank in cubic inches and then convert that to gallons using the given conversion factor.

Step 1: Calculate the volume of the tank in cubic inches

The volume of the tank (V) is given by the formula V = length × width × height.

V = 24 in. (length) × 37 in. (width) × 15 in. (height) = 13,320 cubic inches.

Step 2: Convert cubic inches to gallons

Using the conversion factor 1 gallon = 230.4 cubic inches:

Number of gallons = Volume in cubic inches ÷ Conversion factor

Number of gallons = 13,320 in³ ÷ 230.4 in³/gal ≈ 57.8 gallons

Therefore, Leo's fish tank can hold approximately 57.8 gallons of water when filled to the top.

Answer: 1 hour and 15 minutes

Step-by-step explanation: When you multiply the 3 piano solos each for 5/12 of an hour you get 15/12 or 1 and 1/4. Then since 1/4 of an hour is 15 minutes, you will know that the answer is 1 hour and 15 minutes.

Answer:

The value of x is equal to [tex]5[/tex]

Step-by-step explanation:

we know that

The diameter divide the circle into two equal parts

In this problem

MO=NO

substitute the values

[tex]5x-7=18[/tex]

solve for x

Adds 7 both sides

[tex]5x=18+7[/tex]

[tex]5x=25[/tex]

Divide by 5 both sides

[tex]x=25/5=5[/tex]

Answer:

48

Step-by-step explanation:

divide 30 by 5/8

Answer: 48 cars washed yesterday.

Step-by-step explanation:

Given : An automatic car wash uses [tex]\dfrac{5}{8}[/tex] gallon of soap on each car that is washed.

Yesterday,the ,car wash used a total of 30 gallons of soap.

Then, the number of car washed yesterday is given by :-

[tex]30\div\dfrac{5}{8}\\\\=30\times\dfrac{8}{5}=48[/tex]

Hence, 48 cars washed yesterday.

Answer:576

Step-by-step explanation: For every year, Carter’s telephone bill will be $576. This is because is we know how much he is charged a month, we can take that number and multiply it by 12. We are multiplying it by 12 because there are 12 months in 1 year. Once we multiplied it that’s how we find out the cost for 1 year.

Have a great day,

Eric

Answer:

B

Step-by-step explanation:

An equivalent expression is an expression which is equal to 10k + 17 - 7j - 18 - 11k. You can expand or simplify an expression to make an equivalent expression. Combine like terms to form a new equivalent expression. Like terms are terms which have the same base or variable.

10k + 17 - 7j - 18 - 11k

10k -11k + 17 - 18 - 7j                Move to group like terms together.

-k - 1 - 7j

This is the same solution as B written in a different order.

Answer:

BBBBBBBBBBBBBBBBBBBBBBB

Step-by-step explanation:)

Answer:

In the morning, the packing rates per hour was 45. In the afternoon, the packing rates per hour was 40. The difference is 5.

Answer:

x = 4

Step-by-step explanation:

We are given a figure QRST which has two right angled triangles in it and we are to find the value of x.

To find x, we first need to find the side length of RT.

[tex]sin  60=\frac{2\sqrt{3} }{RT}[/tex]

[tex]RT = \frac{2\sqrt{3} }{sin 60}[/tex]

[tex] RT = 4 [/tex]

Now finding the value of x:

[tex] tan 45 = \frac { x } { 4 } [/tex]

[tex] x = tan 45 \times 4 [/tex]

x = 4

Answer:

The answer is parabola; (y')² - 8x' = 0 ⇒ answer (b)

Step-by-step explanation:

* At first lets talk about the general form of the conic equation

- Ax² + Bxy + Cy²  + Dx + Ey + F = 0

∵ B² - 4AC < 0 , if a conic exists, it will be either a circle or an ellipse.

∵ B² - 4AC = 0 , if a conic exists, it will be a parabola.

∵ B² - 4AC > 0 , if a conic exists, it will be a hyperbola.

* Now we will study our equation:

* x² - 8y = 0

∵ A = 1 , B = 0 , C =

∴ B² - 4AC = (0)² - 4(1)(0) = 0

∵ B² - 4AC = 0

∴ it will be a parabola.

∵ Ф = 90°

* The point (x , Y) will be (x' , y')

∵ x = x'cosФ - y'sinФ and y = x'sinФ + y'cosФ

∵ cos(90) = 0 and sin(90) = 1

∴ x = -y' and y = x'

* lets substitute x and y in the first equation

∴ (-y')² - 8(x') = 0

∴ (y')² - 8x' = 0

* We notice that the x' took the place of y and y' took the place of x

∴ The parabola rotated around the origin by 90°

∴ The equation of the parabola is (y')² - 8x' = 0

* The answer is parabola, with angle of rotation 90°

* The equation is (y')² - 8x' = 0

* Look to the graph

- The blue is x² - 8y = 0

- The green is (y')² - 8x' = 0

Answer:

the correct answer is D)

parabola

Answer:

x  =  0.0116096 ,  1.91705119

Step-by-step explanation:

I looked on a site to look this up.

Answer:

x = 0.92

Step-by-step explanation:

To solve this, we need first use the exponent rule of  [tex]e^{bc}=(e^b)^c[/tex]  on [tex]e^{2x}[/tex].  We can break it down to  [tex]e^{2x}=(e^x)^2[/tex]. We can now re-write as:

[tex]6(e^x)^{2}-13(e^x)-5=0[/tex]

This looks like a trinomial that we can middle term factorize by letting [tex]y=e^x[/tex]. Thus we can write and factorize and solve as shown below:

[tex]6(e^x)^{2}-13(e^x)-5=0\\6y^2-13y-5=0\\6y^2+2y-15y-5=0\\2y(3y+1)-5(3y+1)=0\\(2y-5)(3y+1)=0[/tex]

Thus, 2y-5 = 0 OR 3y+1 = 0

Solving we have  y = 5/2 and y = -1/3

Now bringing back the original variable of letting y = e^x, we have:

1. 5/2 = e^x, and

2. -1/3 = e^x

Solving 1:

[tex]\frac{5}{2}=e^x\\ln(\frac{5}{2})=ln(e^x)\\x=ln(\frac{5}{2})[/tex]

Solving 2:

We will have x = ln (-1/3) WHICH IS NOT POSSIBLE because ln is never negative.

So our answer is x = ln (5/2)

Rounding to nearest hundredth: x = 0.92