DE bisects AB at C. if AC=8x-3 and CB=4x+57. find the value of X and find the length of AC and CB

Answer:

Step-by-step explanation:

To find g[f(2)], we need to evaluate the composite function g[f(2)] by first finding f(2) and then substituting the result into g(x).

Let's start by finding f(2):

f(x) = 2x² - 3x

f(2) = 2(2)² - 3(2)

= 2(4) - 6

= 8 - 6

= 2

Now that we have the value of f(2) as 2, we can substitute it into g(x):

g(x) = 5x - 1

g[f(2)] = g(2)

= 5(2) - 1

= 10 - 1

= 9

Therefore, g[f(2)] is equal to 9.

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Answer:

\(2.\bar{81}mm\)

Step-by-step explanation:

First the formula for find the are of a trapezoid is:

\(A = \frac{h(a+b)}{2}\)

Where \(a\) is the top, \(h\) the height and \(b\) the base measures.

Then we need to know what is the base (\(b\)), for that isolate \(b\) from the equation

\(2A = h(a+b)\\\frac{2A}{h} = a+b\\\frac{2A}{h} - a = b\)

Then in the new equation replace the given values:

\(A = 65mm^2\\a = 9mm\\h = 11mm\)

\(\frac{2 \cdot 65mm^2}{11mm} -9mm = b\\\frac{130mm^2}{11mm} -9mm = b\\11.\bar{81}mm -9mm = b\\2.\bar{81}mm = b\)

So the final answer is \(2.\bar{81}mm\)

Answer:

The answer is 5n-2 so the 3rd choice.

Answer: 5n-2

Step-by-step explanation:

2 less than: means to put -2 at the end

product of 5 and a number: means that you're multiplying 5 and n (5n

So, you end up with C. 5n-2

Hope this helps!!

The average charge on arginine at pH 9.20 is +1.

Arginine is an amino acid that contains multiple ionizable groups, including the amino group (-NH2), the carboxyl group (-COOH), and the guanidino group (-NH-C(NH2)2). The average charge on arginine depends on the pKa values of these groups and the pH of the solution.

At pH 9.20, which is alkaline or basic, the carboxyl group (-COOH) and the guanidino group (-NH-C(NH2)2) will be deprotonated and carry a negative charge, while the amino group (-NH2) will be protonated and carry a positive charge.

The pKa values of the ionizable groups in arginine are approximately as follows:

Carboxyl group: pKa ~ 2.17

Amino group: pKa ~ 9.00

Guanidino group: pKa ~ 12.48

To determine the average charge on arginine at pH 9.20, we need to consider the ionization states of these groups. Since the pH is greater than the pKa of the carboxyl group and the guanidino group, these groups will be deprotonated and carry a negative charge. The amino group will be protonated and carry a positive charge.

Therefore, at pH 9.20, the average charge on arginine is +1. This means that, on average, arginine will have a net positive charge of +1 under these conditions.

At pH 9.20, the average charge on arginine is +1. This indicates that, on average, arginine will carry a net positive charge of +1 in a solution with this pH.

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Answer:

4th option

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

(x + 4)² + (y + 5)² = 64 ← is in standard form

with h = - 4, k = - 5 and r = \(\sqrt{64}\) = 8

centre = (- 4, - 5) and r = 8

The Coordinate of A is (0, 1) and the equation of the graph with B coordinate is ¹/₂^(ˣ) - (¹/₂)x

The equation of the accompanying graph is;

f(x) = aˣ

1) We want to write the coordinate of A. Thus;

f(0) = a⁰ = 1

Thus;

Coordinate of A = (0, 1)

2) The way we can tell that: 0 < a < 1 is; From figure number and inverse functions.

3) If B is the point (4, ¹/₁₆), then;

f(4) = a⁴ = ¹/₁₆

a = ⁴√(¹/₁₆)

a = ¹/₂

4) The equation of the graph with B coordinate is;

y - ax

⇒ ¹/₂^(ˣ) - (¹/₂)x

5) To get the coordinates of the point of intersection of the two graphs is;

¹/₂^(ˣ) - (¹/₂)x = ¹/₂^(ˣ)

⇒ (¹/₂)x = 0

x = 0

Thus, the coordinate of the intersection is; (0, 0)

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The simplified version of (sec a - cosec a) / (sec a + cosec a)  is cosec 2a(cosec 2a - 2) / (sec²a - cosec²a).

The study of correlations between triangles' side lengths and angles is known as trigonometry. The field was created in the Hellenistic era in the third century BC as a result of the use of geometry in astronomical research.

Given:

(sec a - cosec a) / (sec a + cosec a)

Multiply the numerator and denominator by (sec a - cosec a)

(sec a - cosec a) / (sec a + cosec a)  × (sec a - cosec a)

(sec²a + cosec²a -2sec a cosec a) / (sec²a - cosec²a)

As we know,

\(sec^2a + cosec^2a = sec^2a \ cosec^2a\)

sec² a cosec² a - 2sec a cosec a /  (sec²a - cosec²a)

sec a cosec a (sec a cosec a - 2) / (sec²a - cosec²a)

cosec 2a(cosec 2a - 2) / (sec²a - cosec²a)

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Answer:

8 >_ 3 +x

Step-by-step explanation:

X = 5 and any numbers below 5

Answer:

8 ( > or equal to) n + 3

Step-by-step explanation:

I hope this helps :)

Answer:

y=4x-23

Step-by-step explanation:

y+3=4(x-5)

y+3=4x-20

y=4x-20-3

y=4x-23

Answer: The average rate of change of Jack's investment from the third year to the fifth year is $6.43

Step-by-step explanation:

The function that defines the value of his investment after x years,

Putting the value of x as 3 and 5, we can get the value of his investment after 3 years and 5 years respectively.

Symbolab is an online math tool that offers a wide range of math-related services, including a derivative calculator. The derivative calculator provided by Symbolab is a free tool that allows users to calculate the derivative of a given function with respect to a variable.

To use the Symbolab derivative calculator, you simply need to enter the function you want to differentiate and choose the variable with respect to which you want to differentiate the function. The calculator will then provide you with the derivative of the function in a step-by-step format, including the derivative rules used at each step.

The Symbolab derivative calculator supports a wide range of functions, including trigonometric functions, exponential functions, logarithmic functions, and more. It also supports partial derivatives and implicit differentiation.

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Answer:

x=1, y=-2

Step-by-step explanation:

\( - 4x + 2 = 6x - 8\)

\(2 = 10x - 8\)

\(10 = 10x\)

\(x = 1\)

\( - 4(1) + 2 = - 2\)

and

\(6(1) - 8 = - 2\)

so

\(y = - 2\)

Answer:

B. 314.9 m2

Step-by-step explanation:

The function in variable w giving the cost C (in dollars) of constructing the box is C(w) = 30w² + 270/w. The result is obtained by using the formula of volume and area of the box.

We have a rectangular storage container without a lid.

The formula of volume of the box is

V = l × w × h

Where

So, the height is

10 = 2w × w × h

10 = 2w² × h

h = 10/2w²

h = 5/w²

To find the total cost, calculate the area of base and sides of the box!

See the picture in the attachment!

The base area is

A₁ = 2w × w = 2w² m²

The sides area is

A₂ = 2(2wh + wh)

A₂ = 2(3wh)

A₂ = 6wh

A₂ = 6w(5/w²)

A₂ = 30/w m²

The total cost is

C = $15(2w²) + $9(30/w)

C = $30w² + $270/w

The function of the total cost is

C(w) = 30w² + 270/w

Hence, the function of constructing the box is C(w) = 30w² + 270/w.

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Answer:

i don't know

Step-by-step explanation:

maybe x=something happend

1/x

Here we have two vectors a and b such that a=⟨2,1,−2⟩ and b=⟨3,2,4⟩

(a) Vector 3a-4b have components: ⟨-6, -5, -22⟩

(b) There exists a unit vector in the direction of a is ⟨2/3, 1/3, -2/3⟩.

Given that a and b are two vectors:

a= ⟨2,1,−2⟩

b= ⟨3,2,4⟩

(a) To find the components of vector 3a−4b. Firstly, multiply the components of vector b by 4 :

b=⟨3,2,4⟩

4·b = 4·⟨3,2,4⟩

4b= ⟨12,8,16⟩

Now, multiply components of vector a by 3

a=⟨2,1,−2⟩

3·a=3·⟨2,1,−2⟩

3a=⟨6,3,-6⟩

By subtracting vector 4b from vector 3a we obtain,

3a-4b= ⟨6,3,-6⟩ - ⟨12,8,16⟩

3a-4b= ⟨-6,-5,-22⟩

Therefore, the value of the vector 3a-4b= ⟨-6,-5,-22⟩

(b) To find a unit vector in the direction of vector a

a=⟨2,1,−2⟩

Vector's magnitude formula:

\(|A| =\sqrt{x^2+y^2+z^2}\)

where \(A= x\hat{i}+y\hat{j}+z\hat{k}\)      

Using the formula to obtain |a|

\(|a|=\sqrt{(2)^2+(1)^2+(-2)^2}\)

Solving the above equation,

\(|a|=\sqrt{4+1+4}\)

\(|a|=\sqrt{9}\)

|a| = 3

The unit vector in the direction of vector a,

\(\hat{a}=\frac{a}{|a|}\)

\(\hat{a}=\frac{(2,1,-2)}{3}\)

\(\hat{a}=(\frac{2}{3}+\frac{1}{3}-\frac{2}{3})\)

Therefore, the unit vector in the direction of vector a is ⟨2/3, 1/3, -2/3⟩.

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Answer:

y= -1+5x

Step-by-step explanation:

Answer:

4:5

Step-by-step explanation:

I don't see the table but since it is 4 out of every 5 stickers are purple, the ratio would be 4:5, 4/5, or 4 to 5. It doesn't really matter, because all of these mean the same thing.

Tell me if I'm wrong :)

Answer:

T6 = 1 944

Step-by-step explanation:

Tn = a\(r^{n-1}\)

T6 = \(8(3)^{6-1}\)

T6 = 1 944

The coordinates of the midpoint M of segment JK are (-0. 3). The distance between the endpoints of JK is sqrt(104) or approximately 10.198.

To find the coordinates of the midpoint M of segment JK, we can use the midpoint formula, which states that the x-coordinate of the midpoint is the average of the x-coordinates of the endpoints and the y-coordinate of the midpoint is the average of the y-coordinates of the endpoints. So, for segment JK with endpoints J(3, -6) and K(-3, 2), the x-coordinate of the midpoint is (-3+3)/2 = 0 and the y-coordinate of the midpoint is (-6+2)/2 = -2. Therefore, the coordinates of the midpoint M are (0, -2).

To find the distance between the endpoints of JK, we can use the distance formula, which states that the distance between two points with coordinates (x1, y1) and (x2, y2) is given by the square root of [(x2-x1)^2 + (y2-y1)^2]. So for segment JK with endpoints J(3, -6) and K(-3, 2), the distance is sqrt[(-3-3)^2 + (2-(-6))^2] = sqrt[36 + 64] = sqrt(100) = 10. Therefore, the distance between the endpoints of JK is approximately 10.198.

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The person can make 60 trips.

Let us say that A indicates the major sea Islands and B indicates the major lakes. Taking both the cases as events, we will use multiplication principle. Based on the information, the event A occurs in m ways and the event B will occur in n ways. So, the two events will occur in m×n ways.

Thus, A × B = 5 × 12

Performing multiplication on Right Hand Side of the equation to find the number of trips

Total number of trips = 60

Hence, there are 60 trips that could be made.

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The equation of the line tangent to the curve at the point corresponding to the given value of t.

x = t²-23 and y = t³ + t, at t = 5 is

38x - 5y + 574 = 0

Given, a curve with the points represented by

x = t²-23 and y = t³ + t, at t = 5

we have to find an equation of the line tangent to the curve at the given point on the curve.

so, the given point is (x , y) = (5² - 23 , 5³ + 5)

(x , y) = (2 , 130)

Now, the slope of the curve at that point be,

dy/dx = (3t² + 1)/(2t)

dy/dx = 76/10

Now, on using the slope-intercept form, we get

(y - 130)/(x - 2) = 38/5

5(y - 130) = 38(x - 2)

5y - 650 = 38x - 76

38x - 5y + 574 = 0

Hence, the equation of the line tangent to the curve at the point corresponding to the given value of t.

x = t²-23 and y = t³ + t, at t = 5 is

38x - 5y + 574 = 0

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Answer:

a) 2*(x+4)

b) 1/4*x + 1/3*x

Answer:

a) 2(x+4)

b) 7x/12

Step-by-step explanation:

a) Sum of x and 4 is (x+4). Since the number is doubled,

2 * (x+4) = 2(x+4)

b) One fourth of a number x is x/4 and one third of the number is x/3.

Adding these two:

x/4 + x/3

The LCM of 4 and 3 is 12 and so,

(4x + 3x)/12

= 7x/12

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Step-by-step explanation:

total weight = 81 + 97+69+75+74+96+86+53 = 613kg

2 people will have to wait

Answer:

25

Step-by-step explanation:

un carro tiene 4 ruedas, entonces divide 100 por 4

100÷4=25

Pick out the largest and the smallest integers from -3, -7, -42, 0, 5, 38, 11, -1, 15, -99

largest: 38

smallest: -99

On solving the provided question, we can say that 1 degree = 3600 arc seconds and 1 degree = 60 arc minutes.

A 160 degree angle is measured in arc minutes, often known as arcmin, arcmin, arcmin, or arc minutes (represented by the sign '). One minute is equal to 121600 revolutions, or one degree, hence one degree equals 1360 revolutions (or one complete revolution). A degree, also known as a complete angle of arc, angle of arc, or angle of arc, is a unit of measurement for plane angles in which a full rotation equals 360 degrees. A degree is sometimes referred to as an arc degree if it has an arc of 60 minutes. Since there are 360 degrees in a circle, an arc's angles make up 1/360 of its circumference.

1 degree = 3600 arc seconds

1 degree = 60 arc minutes

A. 2 degree 18'36 = 2 + 18/60 + 36 / 2600 = 231 / 100 degree

B. 36 ′ 18 ′′ = 36/60 + 18/2600 = 121 / 200 degree

C. 7 degrees 59′ 59′′ = 7 + 59 / 60 + 59 / 3600 = 28799 / 3600 degree

D. 1' = 1/60 degree

F. 1" = 1/3600 degree

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Sum of two opposite angles in a Cyclic Quadiratral is 180°

\(\\ \sf\longmapsto 110+<CDE=180\)

\(\\ \sf\longmapsto <CDE=180-110\)

\(\\ \sf\longmapsto <CDE=70°\)

Answer:

let <CDE be x:

\({ \tt{110 \degree + x = 180\degree}} \\ \\ { \tt{x = 180 \degree - 110 \degree}} \\ \\ { \tt{x = 70 \degree}}\)

Answer:

The length of the arc is the answer.