Simplify the expression.
2+2 4+3
O 6
o 7
o 21
067

Yall help this is worth 30 points

The solutions to the equation 1x² - 16x = 20 are x = 8 + 2√21 and x = 8 - 2√21.

To solve the quadratic equation 1x² - 16x = 20, we need to rearrange it into the standard form ax² + bx + c = 0. Let's simplify the equation step by step:

1x² - 16x = 20

First, move all terms to one side of the equation:

1x² - 16x - 20 = 0

Now we have a quadratic equation in the standard form. To solve it, we can use factoring, completing the square, or the quadratic formula. In this case, factoring may not be straightforward, so let's use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

For our equation, a = 1, b = -16, and c = -20. Substituting these values into the quadratic formula:

x = (-(-16) ± √((-16)² - 4(1)(-20))) / (2(1))

Simplifying further:

x = (16 ± √(256 + 80)) / 2

x = (16 ± √336) / 2

x = (16 ± √(16 * 21)) / 2

x = (16 ± 4√21) / 2

Simplifying:

x = 8 ± 2√21

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Answer: \(\frac{2(-\pi^5) }{5} + 18 + C\) , I hope this is right. Im kind of new to integral calculus

Step-by-step explanation:

You essentially want to split this integral into two parts, because its a piecewise function. The conditions on the right side basically say for when x is less than and when x is greater than 0. So, we should split this integral at 0.

The first function says that -pi is less than 0, so change the upper boundary to 0. This make the definite integral bounded at -pi to 0. But now, we have to take the anti derivative of 2x^4 using the reverse power rule. Add one to the power, then divide by the new power. So the new function is \(\frac{2x^5}{5}\) defined at lower boundary -pi and upper boundary of 0. Use the fundamental theorem of calculus to solve the integral. You get \(\frac{2(-\pi ^5)}{5} - \frac{2(0^5)}{5} = \frac{2(-\pi^5) }{5}\). You want to add the 2nd integral to this, so lets go solve that.

Now for this integral, we have the conditions that pi is greater than 0. So 0 will be in the lower boundary this time and pi will be in the upper. Basically apply the same thing from the first integral. Do anti derivative and use fund. theorem of calculus. the anti-derivative of sinx is -cosx. You can take this 9 out because its a constant that is scaling -cosx. So now 9 is on the outside of the integral and you have the definite integral of -cosx with the boundaries of 0 and pi. Plug in pi to get -1, then multiply that by the negative sign to get postive 1. Now let's plug in the lower boundary, 0. Cosine of 0 is 1, then we are multiplying by the negative sign to get -1. Subtract 1 and -1 to get postive 2. Finally multiply that by the 9 from before to get 18

Final Answer finally:

\(\frac{2(-\pi^5) }{5} + 18\)

OH, do not forget the C. This took me 30 minutes of constant typing so hopefully Im right

The total volume of the air space of spherical ball is A = 12.265625 inches³

Given data ,

Since each tennis ball has a diameter of 2.5 inches, the radius of each ball is 1.25 inches.

The air space around the balls can be thought of as a cylinder with a height equal to the diameter of one ball and a radius equal to the radius of one ball.

The height of the cylinder is 2.5 inches, and the radius is 1.25 inches.

The formula for the volume of a cylinder is:

V = πr²h

V = ( 3.14 ) ( 1.25 )² ( 7.5 )

V = 36.796875 inches³

where V is the volume, r is the radius, and h is the height.

So, the volume of the one ball is:

V₁ = ( 4/3 )π(1.25)³

V₁ = 8.177083 inches³

The total volume of three balls is = volume of 3 spherical balls

V₂ = 3V₁ = 3(8.177083) ≈ 24.53125 cubic inches

Therefore, the total volume of the air space around the three tennis balls is approximately A = 36.796875 inches³ - 24.53125 inches³

A = 12.265625 inches³

Hence , the volume of air space is A = 12.265625 inches³

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Answer:

Easy. The smaller is x/2.

Step-by-step explanation:

2 times is larger, so larger divided by 2 is the smaller.

An example of a function that models a linear relationship between two quantities, x and y is y = mx + b

We need to use the equation of a straight line, which is commonly expressed in slope-intercept form as:

y = mx + b

In this function, x represents the independent variable, m is the slope of the line, and b is the y-intercept. To use this function, we simply plug in the values of x, m, and b that correspond to the specific relationship we are modeling.

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Answer:

d) 1/12

Step-by-step explanation:

Answer:

100

Step-by-step explanation:diego died

Step-by-step explanation:

well, the combination of all set elements.

FYI : if some elements appear in both sets, we only use these once for the result set (this is not the case here, but it might be in other questions).

the combination of both sets is then

{b, c, d, e, g, h}

a. C = 5.00 + 0.75t

b. It will cost Elaine $23.00 to park her car for a full 24 hours at the parking lot.

(a) To represent Elaine's total parking cost, C, in dollars for t hours, we can use the following equation:

C = 5.00 + 0.75t

In this equation, the constant term 5.00 represents the flat fee for parking, and the term 0.75t represents the additional cost per hour based on the number of hours (t) the car is parked. By adding the flat fee to the hourly cost, we get the total parking cost for t hours.

(b) To find out how much it will cost Elaine to park her car for a full 24 hours, we can substitute t = 24 into the equation:

C = 5.00 + 0.75 * 24

Calculating this expression, we get:

C = 5.00 + 18.00

C = 23.00

Therefore, it will cost Elaine $23.00 to park her car for a full 24 hours at the parking lot.

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Answer:

1/4

Step-by-step explanation:

Answer:

0.056

Step-by-step explanation:

I used my calculator, not much work to show :)

Answer:

The answer for 0.7 x 0.08 is 0.056.

Explantion:

I am smart like that.

I am built different.

Answer:

4 5/8

Step-by-step explanation:

Rewriting our equation with parts separated

=4+12+18

Solving the fraction parts

12+18=?

Find the LCD of 1/2 and 1/8 and rewrite to solve with the equivalent fractions.

LCD = 8

48+18=58

Combining the whole and fraction parts

4+58=458

Answer:

Step-by-step explanation:

so, i might be wrong but i hope this helps.

The slope will be the same for a straight line no matter which two points you pick as you know. All you need to do is to calculate the difference in the y coordinates of the 2 points and divide that by the difference of the x coordinates of the points(rise over run). That will give you the slope.

Answer:

A) \(x=-1\pm\sqrt{\frac{13}{6}}\)

Step-by-step explanation:

\(\displaystyle x=\frac{-12\pm\sqrt{12^2-4(6)(-7)}}{2(6)}\\\\x=\frac{-12\pm\sqrt{144+168}}{12}\\\\x=\frac{-12\pm\sqrt{312}}{12}\\\\x=\frac{-12\pm2\sqrt{78}}{12}\\\\x=-1\pm\frac{\sqrt{78}}{6}\\\\x=-1\pm\sqrt{\frac{78}{36}}\\\\x=-1\pm\sqrt{\frac{13}{6}}\)

Answer:

general ledger

Step-by-step explanation:

     "Not independent" means that the situation is dependent. It is not relying on something else, or something else will not change the outcome. Independent means the situation is isolated, it is independent.

A jar contains green marbles and orange marbles. A green marble is selected followed by an orange marble, at random, without replacement.

Not independent

-> Since the marbles are not being replaced, this isn't independent

A coin is flipped three times.

Independent

A bag contains nickels and dimes. A nickel is selected followed by a dime, at random, with replacement.

Independent

-> Because there is replacement, this is independent

A number cube is rolled twice.

Independent

14. The trigonometric equation (sin47°/cos43°)² + (cos43°/sin47°)² - 4cos²45° = 4

15. In the trigonometric equation 2(cos²θ - sin²θ) = 1, θ = 15°

A trigonometric equation is an equation that contains a trigonometric ration.

14. To find the value of (sin47°/cos43°)² + (cos43°/sin47°)² - 4cos²45°, we proceed as follows

Since we have the trigonometric equation (sin47°/cos43°)² + (cos43°/sin47°)² - 4cos²45°,

We know that sin47° = sin(90 - 43°) = cos43°. So, substituting this into the equation, we have that

(sin47°/cos43°)² + (cos43°/sin47°)² - 4cos²45° = (cos43°/cos43°)² + (cos43°/cos43°)² - 4cos²45°

= 1² + 1² - 4cos²45°

We know that cos45° = 1/√2. So, we have

1² + 1² - 4cos²45° = 1² + 1² - 4(1/√2)²

= 1 + 1 + 4/2

= 2 + 2

= 4

So, (sin47°/cos43°)² + (cos43°/sin47°)² - 4cos²45° = 4

15. If 2(cos²θ - sin²θ) = 1 and θ is a positive acute angle, we need to find the value of θ. We proceed as follows

Since we have the trigonometric equation 2(cos²θ - sin²θ) = 1

We know that cos2θ = cos²θ - sin²θ. so, substituting this into the equation, we have that

2(cos²θ - sin²θ) = 1

2(cos2θ) = 1

cos2θ = 1/2

Taking inverse cosine, we have that

2θ = cos⁻¹(1/2)

2θ = 30°

θ = 30°/2

θ = 15°

So, θ = 15°

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Answer:

QUESTION:

If you throw a six-sided number cube. then how many times will I get a 7

ANSWER:

This is a tricked question. You will never roll a 7 on a six-sided numbered cube unless you have 2 dice.

Step-by-step explanation:

Hope that this helps you out! :)      

If you have any questions please put them in the comment section below this answer.      

Have a great rest of your day/night!      

Please thank me on my profile if this answer has helped you.

Therefore , the solution of the given problem of area comes out to be

r = 8.

The term "area" describes the amount of space occupied by a 2D form or surface. We use cm2 or m2 as our units for measuring area. A shape's area is determined by dividing its length by its breadth.

Here,

A 90 degree sector occupies 1/4 of a circle, which has 360 degrees. Consequently, the area of the whole circle can be written as

Sector Size/Sector Area = Circle Area/360

16 ft2/90 = n/360

(360) (16 ft2)/90 = n

(4)(16 ft2) = n

The total size of the circle is n = 64 ft2.

Since Area of a Circle equals r2,

∏r2 = 64

r2 = 64/∏

r = √(64/∏)

We multiply by / to get by rationalizing the denominator.

r = √(64∏)/√(∏2) Then using the denominator's square root, we can obtain the solution of

r = √(64∏)/∏

r = 8

Therefore , the solution of the given problem of area comes out to be

r = 8.

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Answer: D

Step-by-step explanation:

To determine which ordered pair is a solution to the inequality, we can substitute the values of x and y into the inequality and check if it is true.

Let's start with ordered pair A (80, 6):

1/4x ≤ 7/3y + 2

1/4(80) ≤ 7/3(6) + 2

20 ≤ 14 + 2

20 ≤ 16

This is not true, so ordered pair A is not a solution to the inequality.

Now let's try ordered pair B (48, 9):

1/4x ≤ 7/3y + 2

1/4(48) ≤ 7/3(9) + 2

12 ≤ 21 + 2

12 ≤ 23

This is also not true, so ordered pair B is not a solution to the inequality.

Next, let's try ordered pair C (40, 3):

1/4x ≤ 7/3y + 2

1/4(40) ≤ 7/3(3) + 2

10 ≤ 7 + 2

10 ≤ 9

This is false, so option C is not a solution to the inequality.

Finally, we have option D: (2, -6)

1/4(2) ≤ 7/3(-6) + 2

1/2 ≤ -14 + 2

1/2 ≤ -12

This is true, so option D is a solution to the inequality.

Therefore, the answer is D: (2, -6).

Given:

The equation is

\((x-2)=-(x-2)\)

Isabel says that the given equation has no  solution because a number can never be equal to its opposite.

To find:

Isabel's mistake.

Solution:

Her reason "a number can never be equal to its opposite" is not correct.

Zero is a number that can be equal to its opposite.

So, the given equation has solution for which LHS=RHS=0.

We have,

\((x-2)=-(x-2)\)

\(x-2=-(x)-(-2)\)

\(x-2=-x+2\)

Add x and 2 on both sides.

\(x-2+x+2=-x+2+x+2\)

\(2x=4\)

Divide both sides by 2.

\(x=\dfrac{4}{2}\)

\(x=2\)

So, the given equation has a solution x=2.

Answer:

hewo

Step-by-step explanation:

well you need to multiply 1/4*114 and that should give you your answer

which would be 28.5

7. m<2 = 138° based on the definition of vertical angles.

8. m<3 is supplementary to angle 8

9. The measure of angle 2 = 50°

10. The value of x = 20

A supplementary angle is a pair of angles whose sum is equal to 180 degrees. In other words, two angles are supplementary if they add up to a straight angle.

For example, if one angle measures 70 degrees, its supplement would be 180 - 70 = 110 degrees.

7. m<2 = 138° (reason: vertical angles are equal).

8. m<3 is supplementary to angle 8 because angle 3 and 5 are supplementary, and angle 5 is congruent to angle 8.

9. 5x + 55 = 2x + 100 (corresponding angles are equal)

Find x:

5x - 2x = -55 + 100

3x = 45

x = 15

m<2 = 180 - (5x + 55) (linear pair is equal to 180 degrees)

Plug in the value of x

m<2 = 180 - (5(15) + 55)

m<2 = 180 - 130

m<2 = 50°

10. 45 + 5x + 35 = 180 (supplementary angles)

5x + 80 = 180

5x = 180 - 80

5x = 100

x = 20

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(a) A vector in the null space of A has 6 entries in it.

(b) A vector in the row space of A has 7 entries in it.

(c) A vector in the column space of A has 7 entries in it.

(a) A vector in the null space of A has 6 entries in it, which is the number of columns of A. This is because a vector in the null space of A is a solution to the equation Ax = 0, where x is a column vector with the same number of entries as there are columns in A.

(b) A vector in the row space of A has 7 entries in it, which is the number of rows of A. This is because the row space of A is the span of the row vectors of A, and each row vector has the same number of entries as there are columns in A.

(c) A vector in the column space of A has 7 entries in it, which is the number of rows of A. This is because the column space of A is the span of the column vectors of A, and each column vector has the same number of entries as there are rows in A.

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The given question is incomplete, the complete question is:

Suppose that A is a 7 x 6 matrix. !!! entries in it.

(a) A vector in the null space of A has ____ entries in it

(b) A vector in the row space of A has _______entries in it.  

(c) A vector in the column space of A has_____ entries in it

Answer:

a

Step-by-step explanation:

The ordered pairs (-1, -6), (2, -18), (0, 0), and (-4, -12) do not correspond to the intervals where the graph of f(x) is decreasing. The pairs (1, -2) and (-3, -18) are the correct ones.

To determine where the graph of f(x) is decreasing, we need to examine the intervals where the function's derivative is negative. The derivative of f(x) is given by f'(x) = -3x^2 - 8x + 3.

Now, let's evaluate f'(x) for each of the given x-values:

f'(-1) = -3(-1)^2 - 8(-1) + 3 = -3 + 8 + 3 = 8

f'(2) = -3(2)^2 - 8(2) + 3 = -12 - 16 + 3 = -25

f'(0) = -3(0)^2 - 8(0) + 3 = 3

f'(1) = -3(1)^2 - 8(1) + 3 = -3 - 8 + 3 = -8

f'(-3) = -3(-3)^2 - 8(-3) + 3 = -27 + 24 + 3 = 0

f'(-4) = -3(-4)^2 - 8(-4) + 3 = -48 + 32 + 3 = -13

From the values above, we can determine the intervals where f(x) is decreasing:

f(x) is decreasing for x in the interval (-∞, -3).

f(x) is decreasing for x in the interval (1, 2).

Now let's check the ordered pairs in the table:

(-1, -6): Not in a decreasing interval.

(2, -18): Not in a decreasing interval.

(0, 0): Not in a decreasing interval.

(1, -2): In a decreasing interval.

(-3, -18): In a decreasing interval.

(-4, -12): Not in a decreasing interval.

Therefore, the ordered pairs (-1, -6), (2, -18), (0, 0), and (-4, -12) are not located in the intervals where the graph of f(x) is decreasing. The correct answer is: (1, -2), (-3, -18).

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Note the complete and the correct question is

Q- Consider the function below, which has a relative minimum located at (-3, -18) and a relative maximum located at 1/3, 14/27).

\(f(x) = -x^3 - 4x^2 + 3x\).

Select all ordered pairs in the table which are located where the graph of f(x) is decreasing: Ordered pairs: (-1, -6), (2, -18), (0, 0),(1 , -2), (-3 , -18), (-4. , -12)

Answer:

Kinda cheesy:)

Step-by-step explanation:

If you what to give 2 friends candy and all you have is 8 pieces of candy, each friend will get 4 pieces of candy.

Answer:

9π cm - exact value

28.26 cm - approximate value

Step-by-step explanation:

C = πd =9π cm - exact value

or

C=9π≈ 28.26 cm - approximate value

Answer:-4 + -6 = -10

Step-by-step explanation: