In triangle DEF, PQ is the midsegment, FInd the the value X
A. 8.5
B. 17.5
C. 8
D. 4

Answer & step-by-step explanation:

Stationary points are the points where the first derivative is equal to zero.

Let's calculate it using the power rule (exponent comes forward, decrease exponent by 1) and the fact that the derivative is a linear operation (that is [tex]D[a\ f(x) + b\ g(x)] = a Df(x) + b Dg(x)[/tex])

The first derivative is then

[tex]y' = \frac13 (3x^2) - \frac12 (2x) -6 = x^2-x-6 = (x+2)(x-3)[/tex]

Note that the last passage is not strictly needed, but it's really helpful to find stationary points, when in this next passage we set it equal to zero. Alternatively, you can use the quadratic formula if you can pull the factors out of your head right away.

[tex]y'=0 \rightarrow (x+2)(x-3) = 0 \implies x=-2 || x=3[/tex]

These two point could be maxima, minima, or inflection points. To check them you can either see how the sign of the first derivative goes, or check the sign of the second derivative, as you're required.

The rules states that if the second derivative evaluated in that point is negative we have a maximum, if it's positive we have a minimum, and if we have a zero we keep derivating until we get a non-zero  value.

In our case, the second derivative we get by calculating the derivative again and we get [tex]y'' = 2x-1[/tex] . Evaluating it at both points we get

[tex]y''(-2) = 2(-2)-1 = -5\\y''(3) = 2(3) -1 = 5[/tex]

so -2 is a maximum and 3 is a minimum.

Answer:

[tex]\left( 3, -\dfrac{13}{2} \right) \textsf{minimum}[/tex]

[tex]\left( -2, -\dfrac{43}{3} \right)\textsf{maximum}[/tex]

Step-by-step explanation:

To find the stationary points, differentiate, set to zero, and solve for x.  Input found values of x into original equation to find y-coordinates.

[tex]y=\dfrac13x^3-\dfrac12x^2-6x+7[/tex]

[tex]\implies \dfrac{dy}{dx}=3\cdot \dfrac13x^{(3-1)}-2 \cdot \dfrac12x^{(2-1)}-6x^{(1-1)}+7\cdot0[/tex]

[tex]\implies \dfrac{dy}{dx}=x^2-x-6[/tex]

[tex]\dfrac{dy}{dx}=0[/tex]

[tex]\implies x^2-x-6=0[/tex]

[tex]\implies (x-3)(x+2)=0[/tex]

[tex]\implies x=3, x=-2[/tex]

[tex]\textsf{at }x=3: y=\dfrac13(3)^3-\dfrac12(3)^2-6(3)+7=-\dfrac{13}{2}[/tex]

[tex]\textsf{at }x=-2: y=\dfrac13(-2)^3-\dfrac12(-2)^2-6(-2)+7=\dfrac{43}{3}[/tex]

To determine the nature of each point, differentiate again, input found values of x into the second derivative. If positive then minimum point, if negative then maximum point.

[tex]\dfrac{d^2y}{dx^2}=2 \cdot x^{(2-1)}-x^{(1-1)}-6 \cdot0[/tex]

[tex]\implies \dfrac{d^2y}{dx^2}=2x-1[/tex]

[tex]\textsf{at }x=3:\dfrac{d^2y}{dx^2}=2(3)-1=5 > 0\implies \textsf{minimum}[/tex]

[tex]\textsf{at }x=-2:\dfrac{d^2y}{dx^2}=2(-2)-1=-5 < 0\implies \textsf{maximum}[/tex]

Answer:

35 million

Step-by-step explanation:

20000000×70%=35million

Compounding is a process where the interest is credited to the initial amount and interest, on the whole, is charged again. The correct option is D, 38 millon.

Compounding is a process where the interest is credited to the initial amount and interest, on the whole, is charged again. and this continues for t period of time.

It is given by the formula,

A = P(1+r)ⁿ

where, A is the value after n period of time, P is the initial amount, and,

r is the rate of increment or decrement.

Given that On the first day of a song's release, it had 20 million streams. Also, the number of streams increases by 10% per day. Therefore, it can be said that the number of streams is compounding. Thus, the number of streams on the seventh day will be,

Number of streams = 20 (1+0.10)⁷ million

                                 = 20 × 1.9487 million

                                 = 38.974 million

                                 = 38 million

Hence, the number of streams there will be on the seventh day is 38 million.

Learn more about Compounding:

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Answer:

3w-4.5

Step-by-step explanation:

im pretty sure this is right. good luck

Solution:

Given:

Substitute the values into the equation:

Simplify the numerator and the denominator:

Simplify the fraction:

Correct option is B.

Answer:

[tex][-\frac{1023}{4} ][/tex]

Step-by-step explanation:

[tex]\frac{x^6-x}{4y}[/tex]

x = -4

y = 4

Replace all the variables with the corresponding values given:

[tex]\frac{-4^6-(-4)}{4(4)}[/tex]

Now solve,

-4 to the power of 6 is equal to -4096

[tex]\frac{-4096-(-4)}{4(4)}[/tex]

we see that we are subtracting a negative number, meaning that it'll cancel out and turn into an addition sign. Therefore:

[tex]-4096 + 4[/tex]

[tex]-4092[/tex]

[tex]\frac{-4092}{4(4)}[/tex]

4(4) is equal to 16

[tex]\frac{-4092}{16}[/tex]

When divided, you'll get a mixed fraction of [tex]-255\frac{3}{4}[/tex]

To turn into an improper fraction, simply multiply the whole number by the denominator, then add the numerator to the result.

[tex]-255 * 4 + 3[/tex]

[tex][-\frac{1023}{4} ][/tex]

Answer:

look below

Step-by-step explanation:

Lets round the 0.59562 first

0.59562 rounded to the nearest hundreth (because thats how cents go) rounds up to .60

there is 100 cents in a dollar

there is 13 dollars

13 * 100 is 1300

1300 + 60

1360 cents

Answer:

The lines intersect at 90°

Step-by-step explanation:

If two lines are perpendicular, they intersect to form right angles.

Right angle = 90°

Line is different from line segment or a ray. The given lines MR and XY are best described by: Option A: The lines intersect at a 90° angle.

To get to know about intersection of MR and XY, we need to know what a line is.

If they are not parallel (having 0 degree angle between each other) and not coincident (not lying over each other), then those two lines always intersect.

Since the considered lines MR and XY are said to be perpendicular (having 90° angle between them, thus, they will intersect each other).

Therefore, the given lines MR and XY are best described by: Option A: The lines intersect at a 90° angle.

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Answer:

The statement "Every real number is also rational" is FALSE.

Step-by-step explanation:

Natural numbers, Whole numbers, Rational numbers and Irrational numbers are all real. Imaginary and Complex numbers are not Real (yes, this is an actual math thing.)

So you may have an Irrational number such as pi or sqroot(7) that are Real but not Rational. This proves the statement is FALSE. (counter-example)

Answer:

1.57

Step-by-step explanation:

2000/8=250      250/160.67= 1.56

Answer:

33=h-8

Step-by-step explanation:

33= h-8                                              add 8 on both sides to solve for h

+8           +8

41= h                                                   The hawks won 41 games.

A correct conclusion that can be reached is that: D) The Vikings averaged more points at home games, but were more consistent when playing on the road.

An arithmetic average is also referred to as mean and it can be defined as a ratio of the sum of the total number in a data set (population) to the frequency of the data set.

This ultimately implies that, an average score is a mean score and it can be calculated by dividing the total number of scores obtained by the total number of Vikings players.

In conclusion, we can reasonably infer and logically deduce that Walker Vikings were more consistent when playing on the road, but averaged more points at home games.

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Answer:

x = 17

Step-by-step explanation:

5x - 18 and 4x + 45 are adjacent angles on as straight line and sum to 180° , so

5x - 18 + 4x + 45 = 180 , that is

9x + 27 = 180 ( subtract 27 from both sides )

9x = 153 ( divide both sides by 9 )

x = 17

Answer: x=5

Step-by-step explanation:

divide both sides by the numeric factor on the left side, then that will give the answer for x

Answer: Velocity is a vector, so it has a magnitude and direction.

Speed is its magnitude, which is obtained from

|〈-3, 4〉 m/s| = √((-3 m/s)² + (4 m/s)²) = √(25 m²/s²) = 5 m/s

Its direction is an angle θ made with the positive horizontal axis, satisfying

tan(θ) = (4 m/s) / (-3 m/s) = -4/3   →   θ = arctan(-4/3) + 180°n

where n is any integer. Now you have to consider that the x coordinate is negative and the y coordinate is positive, so 〈-3, 4〉 points into the second quadrant, and we get an angle there for n = 1 of about

θ ≈ 126.87°

Alternatively, you can use the vector 〈1, 0〉 in place of the axis, then compute the angle by relating it to the dot product, so θ is such that

〈-3, 4〉 • 〈1, 0〉 = |〈-3, 4〉| |〈1, 0〉| cos(θ)

(-3)•1 + 4•0 = √((-3)² + 4²) • √(1² + 0²) cos(θ)

-3/5 = cos(θ)   →   θ = arccos(-3/5) + 360°n

where again, n is any integer, and we get the same solution θ ≈ 126.87° in the second quadrant when n = 0.

Step-by-step explanation:

Answer:

0.00907

Step-by-step explanation:

Answer:

0.00907

Step-by-step explanation:

Answer:

about 4,400 times

Step-by-step explanation:

its simple

Answer:

One tank holds 45 gallons and the other holds 19.5 gallons.

Step-by-step explanation:

Answer:

x^222/7

Step-by-step explanation:

Equation at the end of step 3:                x74

 ((78 • x73) • ———) • x75

               79

STEP 4 :Multiplying exponential expressions : 4.1    x147 multiplied by x75 = x(147 + 75) = x222

Answer: 57=-10z+7 Answer: z=-- -

Step-by-step explanation: 57=-10z+7 Answer: z=-- -

Answer:

[tex] - 3 \leqslant x < 2[/tex]

Step-by-step explanation:

the black dot on -3 represents less than equal to X and the white dot on 2 represents X is less than 2

Answer:

Step-by-step explanation:

To find the lengths, we use the Pythagorean theorem, which states (a^2)+(b^2)=(c^2) where c^2 is the hypotenuse, length opposite of the right angle. For the first set of coordinates J and K, we find the horizontal and vertical differences between them to represent sides a and b. Which would be a horizontal length of 8 and a vertical length of 3.

(8^2)+(3^2)=c^2

73=c^2

c=square root of 73

(I've added a picture of a graph I drew below)

I would suggest you draw graphs of the points and use the Pythagorean theorem to conceptualize it, but I'll list the rest of the measurements below.

MN:

Vertical length between 2 and -3 = 5

Horizontal length between 7 and 1 = 6

(6^2)+(5^2)=c^2

36+25=c^2

61=c^2

c= square root of 61

PQ:

Vertical length between -6 and -2 = 4

Horizontal length between -8 and -3 = 5

(5^2)+(4^2)=c^2

25+16=c^2

41=c^2

c= square root of 41

As for the "checking all the statements" part, none of them are true because none of the lengths are equal.

Hope this helps! (Sorry for being so late)

Answer:

The width would be 8.

Hope this helps!! PLEASEEE give Brainlist!!

Answer: 8:14

Step-by-step explanation:

Your answer would be 8:14, as Steven answered 8 questions incorrectly along with the total number of problems being 14 when you add his correct answers with his incorrect ones: "6+8"

Solution:

Note that:

Simplify the LHS, then use cross multiplication to solve for n.

Answer:

n = 15

Step-by-step explanation:

[tex]\dfrac{1}{5}n=3[/tex]

Multiply both sides by 5:

[tex]\implies n = 3 \times 5 = 15[/tex]

Answer:

4/3

Step-by-step explanation:

reduce the fraction by a factor of 6

pretty sure you mean write 24/18 in simplest form so that's the answer

Hope this helps! :)

Answer:

I'm sorry but where's the picture

Answer:

i think the answer would be 4c + 6m = 100, 8c + 12m = 200

Step-by-step explanation:

Answer:

c = 2

Step-by-step explanation:

2c – 4 = 3(4 – 2c)

Expand brackets:

⇒ 2c – 4 = 12 - 6c

Add 6c to both sides:

⇒ 8c – 4 = 12

Add 4 to both sides:

⇒ 8c = 16

Divide both sides by 8:

⇒ c = 2

Answer:

c = 2

Step-by-step explanation:

First expand 3(4-2c):

3×4=12

3×-2c=-6c

Now our equation is :

2c-4 = 12-6c

Add 4 to both sides:

2c-4+4=12-6c+4

Simplify:

2c = -6c+16

Add 6c to both sides:

2c+6c = -6c+16+16

Simplify:

8c=16

Divide both sides by 8:

8c÷8 = 16÷8

c = 2

Answer:

0.875=7/8

Step-by-step explanation:

to answer it, You'll need to change 7/8 to 7÷8

Answer:

7.675

Step-by-step explanation:

please mark brainliest

Answer:

4.725 or 18.175

Step-by-step explanation:

If its 7x27/40 its 4.725

                or

if its 727/40 its 18.175

That means that the maximum number of fruit cans is 16 and the maximum number of vegetable cans is 6.

Hope that helps!

The answer is... the max for fruit cans is 16 fruit cans, and for vegetables is 6.