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Answer:

Step-by-step explanation:

x² - 3x - 1 = 0

a = 1, b = -3, c = -1

x₁ = (3 + sqrt(-3² - 4(1(-1))))/(2(1))

x₁ = (3 + sqrt(9 + 4))/2

x₁ = (3 + sqrt(13))/2

x₁ = 3.302...

x₂ = (3 - sqrt(-3² - 4(1(-1))))/(2(1))

x₂ = (3 - sqrt(9 + 4))/2

x₂ = (3 - sqrt(13))/2

x₂ = -0.302...

The mixed numbers that have 12 as the LCD are 2 11/12 and 6 4/5. All other fractions do not have 12 as the denominator and are not equivalent.

Mixed numbers consist of a whole number and a fractional part. To add or subtract mixed numbers, the fractions must have the same denominator (the bottom number of the fraction).

The LCD (lowest common denominator) is the smallest number that all of the denominators can be divided into evenly. In this case, the LCD is 12.

2 11/12 and 6 4/5 both have 12 as the denominator. The denominator of 11/12 can be divided by 11 and 12, so it is the same as 12/12. The denominator of 4/5 can be divided by 4 and 12, so it is the same as 48/12 (4 x 12 = 48). Therefore, both fractions have the same denominator.

The other fractions do not have 12 as their denominator. 3 1/7 can be divided by 3, 7, and 12, so it is the same as 21/12 (3 x 7 = 21). 5 3/4 can be divided by 4, 5, and 12, so it is the same as 60/12 (4 x 5 = 60). 8 38/47 can be divided by 8, 47, and 12, so it is the same as 376/12 (8 x 47 = 376). Since none of these fractions are equal to 12/12, they are not equivalent to the other two fractions.

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Question :

Which mixed numbers have 12 as the LCD (lowest common denominator)?

2 11/12

3 1/7

5 3/4

6 4/5

8 38/47

Answer:

  (d)  523.3 in³

Step-by-step explanation:

The radius of the sphere is 10 in/2 = 5 in. The volume is given by ...

  V = (4/3)πr³

  V = (4/3)(3.14)(5 in)³ = 4·3.14·125/3 in³ ≈ 523.3 in³

The number of sea stars is 64.

What is a ratio?

Comparing two amounts of the same units and determining the ratio tells us how much of one quantity is in the other.

In general, a: b, which can be interpreted as "a is to b," is used to denote a ratio between two quantities, let's say "a" and "b."

This ratio is expressed in fraction form as a/b. We utilize the same method for further simplifying a ratio as we use for further simplifying a fraction.

According to the question,

Ratio of sea stars to wolf eels = 4:5

Number of rock fish= 5/8 (Number of sea stars)

Number of wolf eels - Number of rock fish = 40

Using the given information, we get,

Number of sea stars = 8/5 (Number of rock fish)

On simplification,

Number of wolf eels = 80

So, number of sea stars = (4/5)*80

                                          = 64

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Answer:

7 2/3 + 7 2/3 = 14 4/3 = 15 1/3

Step-by-step explanation:

Answer:

7+7= 14 than 2/3+2/3= 4/3= 15 1/3

Step-by-step explanation:

Answer: All real numbers

Step-by-step explanation:

I assume you meant \(y=5.3^x\).

In this case, the domain is the set of real numbers, as is with most standard exponential functions.

\(▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪\)

Let's solve for e :

value of " e " = -2

\(\\ \sf\longmapsto 9e-7=7e-11\)

\(\\ \sf\longmapsto 9e-7e=-11+7\)

\(\\ \sf\longmapsto 2e=-4\)

\(\\ \sf\longmapsto e=\dfrac{-4}{2}\)

\(\\ \sf\longmapsto e=-2\)

The correct trigonometric substitution for evaluating integral ∫√(x² + 64) dx is option B. x = 8 tan θ.

To evaluate the integral ∫√(x² + 64) dx using trigonometric substitution, use the substitution x = 8 tan θ.

Let's go through the steps to see how this substitution leads us to the solution:

1. Substitute x = 8 tan θ.

This implies dx = 8 sec² θ dθ.

2. Substitute the expression for x and dx in the integral:

∫√(x² + 64) dx becomes ∫√((8 tan θ)² + 64) * 8 sec² θ dθ.

3. Simplify the expression:

∫√(64 tan² θ + 64) * 8 sec² θ dθ = ∫√(64(sec² θ - 1)) * 8 sec² θ dθ.

4. Further simplify:

∫√(64sec² θ - 64) * 8 sec² θ dθ = ∫√(64sec² θ) * 8 sec² θ dθ.

5. Simplify the expression inside the square root:

∫8sec θ * 8 sec² θ dθ = ∫64sec³ θ dθ.

6. Integrate with respect to θ:

∫64sec³ θ dθ = 64∫sec³ θ dθ.

Now, this integral can be evaluated using standard trigonometric integral identities or integration techniques. However, it's worth noting that the original integral did not involve the variable θ, so we would eventually need to convert the result back to x by substituting x = 8 tan θ.

The correct answer is B. x = 8 tan θ.

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The sum (A+B)(x) and difference (A-B)(x) of two quadratic functions A(x) and B(x) were found, along with their values for x=5, vertices, intercepts, and where they are increasing/decreasing.

To find (A+B)(x), we simply add the two functions:

(A+B)(x) = A(x) + B(x) = (\(-0.25x^2+20x\)) + (\(-0.19x^2+15.2x\)) = \(-0.44x^2\) + 35.2x

To find (A-B)(x), we simply subtract B(x) from A(x):

(A-B)(x) = A(x) - B(x) = (\(-0.25x^2+20x\)) - (\(-0.19x^2+15.2x\)) = \(-0.06x^2\) + 4.8x

When x=5, we can evaluate each expression:

(A+B)(5) = \(-0.44(5)^2\) + 35.2(5) = 60

(A-B)(5) = \(-0.06(5)^2\) + 4.8(5) = 12

To find the vertices and intercepts of the functions A(x) and B(x), we can use the vertex and intercept formulas for quadratic functions:

For A(x):

Vertex = (-b/2a, f(-b/2a)) = (-20/-0.5, A(20/-0.5)) = (40, 400)

x-intercepts: 0 = \(-0.25x^2\) + 20x, so x = 0 or x = 80

y-intercept: A(0) = 0

For B(x):

Vertex = (-b/2a, f(-b/2a)) = (-15.2/-0.38, B(15.2/-0.38)) = (40, 304)

x-intercepts: 0 = \(-0.19x^2\) + 15.2x, so x = 0 or x = 80

y-intercept: B(0) = 0

Both functions are decreasing for x < 40, and increasing for x > 40. The vertex (40, 400) is the maximum point for A(x), and the vertex (40, 304) is the maximum point for B(x).

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Answer:

B, Associative property for multiplication

Step-by-step explanation:

Commutative property means the numbers can be multiplied in any order, so the (5 x 3) x 2 could be written as 3 x 5 x 2 and would be the same.

Associative property deals more with groupings of terms/numbers. Since the order of the numbers stayed the same, and the parentheses are moved, this is an example of the associative property.

Answer:

s = 3

Step-by-step explanation:

Solving

Answer:

-140

Step-by-step explanation:

Answer:

Step-by-step explanation:

The segment sum theorem tells you the whole is the sum of the parts. That can be used to write an equation for y.

  RS +ST = RT

  (5y +5) +(4y +8) = 67

Simplifying, we get ...

  9y +13 = 67

  9y = 54 . . . . . . . . subtract 13

  y = 6 . . . . . . . . . divide by 9

RS = 5y +5 = 5·6 +5 = 35

ST = 4y +8 = 4·6 +8 = 32

The values of interest are ...

Answer:

≈ 404.6666667

Step-by-step explanation:

70 - 8 ÷ 6 + 8 x 42

70 - 1.33333333 + 8 x 42

70 - 1.33333333 + 336

68.6666667 + 336

404.6666667

Answer:

257890 is the function of the equation

Step-by-step explanation:

mark me BRAINLIEST

a) There are no values of x for which h'(x) is undefined.

b) The critical numbers of h(x) = sin²(x) + cos(x) in the domain 0 < x < 2π are x = kπ, x = π/3 + 2πn, and x = 5π/3 + 2πn, where k and n are integers.

a) To find the values of c for which h'(c) = 0 or is undefined, we first need to find the derivative of h(x):

h'(x) = 2sin(x)cos(x) - sin(x)

Now we can set h'(x) equal to 0 and solve for x:

2sin(x)cos(x) - sin(x) = 0

sin(x)(2cos(x) - 1) = 0

This equation is satisfied when sin(x) = 0 or 2cos(x) - 1 = 0. The first equation has solutions x = kπ, where k is an integer. The second equation has solutions x = π/3 + 2πn or x = 5π/3 + 2πn, where n is an integer.

Next, we need to check if there are any values of x for which h'(x) is undefined. Since h'(x) is a combination of sin(x) and cos(x), it is defined for all values of x in the given domain.

b) The critical numbers of h(x) are the values of x at which h'(x) = 0 or h'(x) is undefined. From part (a), we have the solutions x = kπ, x = π/3 + 2πn, and x = 5π/3 + 2πn, where k and n are integers. These are the critical numbers of h(x) in the given domain.

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Answer:

the anser of this question for a is 17

Step-by-step explanation:

all sides are the same

When factoring a polynomial in the form ax2 + bx + c, where a, b, and c are positive real numbers, the signs in the binomials should be both positive

Quadratic equations are second-order polynomial equations and they have the form y = ax^2 + bx + c or y = a(x - h)^2 + k

The form of the polynomial is given as:

ax2 + bx + c

Where a, b, and c are positive real numbers.

Since a, b, and c are positive real numbers. then the form of the expansion would be:

ax2 + bx + c = (dx + e)(fx + g)

Take for instance, we have the following quadratic equation

x^2 + 6x +  8

Expand the equation

x^2 + 6x +  8 = x^2 + 4x + 2x +  8

Factorize the equation

x^2 + 6x +  8 = (x + 2)(x + 4)

Hence, the signs in the binomials should be both positive

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The required linear speed of a point on its surface is 75 meters per second.

The linear speed of a point on the surface of a rotating shaft can be found using the formula,

v = πdN

where,
v is the linear speed in meters per second,
d is the diameter of the shaft in meters,
N is the rotational speed in revolutions per second.

Here,

In this case, the diameter of the shaft is 16mm, which is equal to 0.016 meters. The rotational speed is 1500 revolutions per second. Substituting these values into the formula gives:

v = πdN
v = π x 0.016 x 1500
v = 75.36 meters per second

Rounding to the nearest meter per second, the linear speed is 75 meters per second.

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Answer:

The bias is they only picked men to test the new medication on to see if it was ready for the general public to use.

Step-by-step explanation:

The measure of other two sides of triangle is12cm and 17cm.

What is a triangle?

A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes.

In Euclidean geometry, any three points that are not collinear produce a singular triangle and a singular plane. In other words, every triangle is contained in a plane, and there is only one plane that contains that triangle.

If all of geometry is the Euclidean plane, then all triangles are enclosed in a single plane, however in higher-dimensional Euclidean spaces, this is no longer the case. Except when otherwise specified, this article discusses triangles in Euclidean geometry, namely the Euclidean plane.

here it is given in the question

the base of the triangle is 10cm.

then the value of other two side is 12cm and 17cm.

Hence, The measure of other two sides of triangle is12cm and 17cm.

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Answer:

625 and 5375

Step-by-step explanation:

X percent on 5

Y percent on 13

0.05X + 0.13Y = 730

X+Y = 6000

5X + 13Y = 73000

X = 6000 - Y

5 (6000 -Y) +13Y = 73000

30000 - 5Y +13Y= 73000

8Y = 43000

Y = 5375

X = 625

The amount of $625 is invested at 5%, and $5375 is invested at 13% when a total of $6000 is invested.

The formula for calculating simple interest is:

Interest = (Principal × Rate × Time)/100

Given that

The total amount invested is $6000.

The total annual interest = $730

Consider,

The amount invested at 5% is  "x" dollars,

The amounts invested at 13% as "6000 - x" doll

The equation formed according to the question is :

Interest from 5% investment + Interest from 13% investment = $730

0.05x+0.13(6000−x)=730

This can be simplified as:

0.05x + 780- 0.13x = 730

780 -730 = 0.13x - 0.05x

50 = 0.08x

Divide both sides by 0.08 to get the value of x

x = 50/0.08

x = 625

So, $625 is invested at 5%.

The amount invested at 13% is calculated by subtracting  $625 from the total amount.

Amount invested at 13% = $6000 - $625

                                         = $5375

Therefore, $625 is invested at 5%, and $5375 is invested at 13%.

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Answer:

gftfyuoppoiu7644wqqettuiopouytrewesdffhjklju

Step-by-step explanation:

gffggghhhjjklliigg

Step-by-step explanation:

can u translate to English please, if not I can't understand

The correct form of the regression line is \(\log time = 0.699 + 0.500\cdot \log length\) (Correct choice: D).

According to the information presented in the figure, we know the following function:

Hence, the correct form of the regression line is:

\(\log time = 0.699 + 0.500\cdot \log length\) (Correct choice: D)

The correct form of the regression line is \(\log time = 0.699 + 0.500\cdot \log length\) (Correct choice: D).

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Answer:

D: logTime=0.699 + 0.500

Step-by-step explanation:

0.699 is the x value which can be found in data under Coef and Constant. The y value can be found under coef and log(length)

Answer:

so im not sure it can either be 33, 1.5 or 49.5

Step-by-step explanation:

It is recommended that you visit your courses on D2L frequently, ideally at least once a day, to stay up-to-date with any new announcements or assignments posted by your instructor. This will help you stay on track with your coursework and prevent you from falling behind. Additionally, regular visits to your courses can help you participate in discussions with your peers and ask questions if you are unsure about any of the material. It's important to remember that online learning requires a high level of self-discipline and responsibility, so making a habit of checking in on your courses regularly can contribute to your overall success in the class.

Answer:

x = 9

Step-by-step explanation:

given two secants to a circle from an external point , then

the product of the measures of one secant's external part and that entire secant is equal to the product of the measures of the other secant's external part and that entire secant , that is

x(x + 21) = 10(10 + 17) ← distribute parenthesis

x² + 21x = 10 × 27 = 270 ( subtract 270 from both sides )

x² + 21x - 270 = 0 ← in standard form

(x + 30)(x - 9) = 0 ← in factored form

equate each factor to zero and solve for x

x + 30 = 0 ⇒ x = - 30

x - 9 = 0 ⇒ x = 9

however, x > 0 , then x = 9

Answer:

2

Step-by-step explanation:

The equation has 2 terms in it which means 2 is the answer.

As per the concept of system of linear equations, the maximum revenue of this basket ball match is $3.4

Linear equation:

Linear equation refers the one variable is an equation in which there is only one variable present. And it is of the form Ax + B = 0, where A and B are any two real numbers and x is an unknown variable that has only one solution.

Given,

A baseball team plays in a stadium that holds 66000 spectators. With the ticket price at $10 the average attendance has been 28000. When the price dropped to $7, the average attendance rose to 33000. Assume that attendance is linearly related to ticket price.

Here we need to find the ticket price would maximize revenue.

In order to find the ticket price for the maximum revenue,

We have to identify the details from the given question,

Total seating capacity = 66,000

When ticket price $10 then the attendance 28,000

When ticket price $7 then the attendance 33,000

Let us consider the x be the maximum revenue ticket price.

Now, to solve this we have to find the slope for the equation,

That is,

=> m = (33000 - 28000)/(7 - 10)

=> m = 5000/-3

=>  m = -5000/3

=> m = 1666.6

Then the revenue equation is written as,

=> y = (10 - x) * (28,000 + 1666.6x)

=> y = 280000-11334x-1666.6x²

If we plot the this function into the graph, then we get the graph like the following.

Therefore, the solution of the graph is 3.4.

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