Find the sum of the arithmetic sequence. 5, 7, 9, 11, ..., 23

The change in the cube's surface area is -180 m^2/min when the edge length is 3 m. This is found by differentiating the surface area with respect to time and substituting the given values.

The subject of the question is related to rates of change in the context of the geometry of a cube. To address this problem, we use the formula for a cube's surface area, which is given by A = 6x^2, where x represents the length of an edge. If x changes with respect to time, we denote this change as dx/dt, which is given as -5m/min. You want to find how quickly the surface area, A, changes when x = 3.

First, let us differentiate the surface area A with respect to time t. By the chain rule of differentiation, dA/dt = dA/dx * dx/dt. Given A = 6x^2, dA/dx = 12x. substituting x=3 and dx/dt=-5, we find that dA/dt = 12*3*-5, which equals -180m^2/min.

Therefore, the change in the cube's surface area is -180 m^2/min when the edge length is 3 m.

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SSS similarity theorem states: If the corresponding sides of two triangles are proportional, then the two triangles are similar.

You have two isosceles triangle, then if

[tex]\dfrac{44}{20}=\dfrac{x}{35},\\ \\x=\dfrac{44\cdot 35}{20}=11\cdot 7=77,[/tex]

two isosceles triangles will be similar by SSS theorem.

Answer: correct choice is C.

The value of x that will make the triangles similar by SSS similarity theorem is;

x = 77.

We are told that the 2 triangles are similar by SSS theorem.

Now, SSS means Side - Side -Side and it is a congruence theorem which states that the 3 corresponding sides of two triangles have same ratio, then we can say that the two triangles are congruent by SSS theorem

Thus, in our 2 given triangles ,applying the SSS postulate gives;

x/35 = 44/20

Applying the multiplication property of equality, let us multiply both sides by 35 to get;

x = (44 * 35)/20

x = 77

Thus, in conclusion the value of x that will make the triangles similar by SSS similarity theorem is 77.

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​x² - 5x - 24 = 0

First, we have to solve the quadratic equation and find the two values of x that fit the equation.​

[tex]x = \frac{5+- \sqrt{5^{2} + 4*1*24 } }{2*1} = \frac{5+- \sqrt{25 + 96} }{2} = \frac{5+- \sqrt{121} }{2} = \frac{5+-11}{2} [/tex]​

There are two values of x that fit:​

x₁ = (5+11)/2 = 16/2 = 8​

x₂ = (5-11)/2 = -6/2 = -3​

Now I can restate the original equation in terms of a product of factors, with this product being equal to zero:​

(x - x₁) * (x - x₂) = 0​

ANSWER ​(x-8) * (x+3) = 0

Now I can solve each factor by setting each one equal to zero and solving the resulting linear equations:​

x - 8 = 0 or x + 3 = 0​

x = 8 or x = -3​

We can check that these two values are the solution to the original quadratic equation.​

x² - 5x - 24 = 0​

​First value

​8² -5*8 -24 = 0

64 - 40 -24 = 0​

0 = 0 ¡Checked!​

Second value​

(-3)² -5(-3) -24 = 0​

9 + 15 -24 = 0​

0 = 0 ¡Checked!​

​Hope this helps!

​[tex]\textit{\textbf{Spymore}}[/tex]​​​

Answer:

(x+3)(x-8)=0

Step-by-step explanation:

To find the number of batches of pasta, convert the amount of flour per batch to an improper fraction, create an equation based on the total flour used, and solve for the number of batches, which is 16.

To solve for b, the number of batches of pasta the chef makes during the week using a total of 86 pounds of flour:

First, convert the amounts of each flour from mixed numbers to improper fractions:

1 5/8 pounds = 13/8 pounds

Now add the two amounts together to get the total flour used per batch:

(15/4) + (13/8) = 30/8 + 13/8 = 43/8 pounds per batch

The equation to solve for b is:

(43/8) * b = 86

To find b:

b = 86 / (43/8)

Multiply both sides by the reciprocal of 43/8:

b = 86 * (8/43)

b = (86 * 8) / 43

Calculate the value of b:

b = 688 / 43

b = 16

Final answer:

CPCTC stands for Corresponding Parts of Congruent Triangles are Congruent and can only be used after proving triangles are congruent. It helps in confirming that corresponding parts of congruent triangles are congruent.

Explanation:

CPCTC stands for Corresponding Parts of Congruent Triangles are Congruent. It can only be used after you prove triangles are congruent. When two triangles are proven congruent, CPCTC allows you to show that corresponding parts like angles and sides are congruent as well.

Answer:  the correct option is (C) x - 1.

Step-by-step explanation:  We are given to select the correct binomial that is a factor of the following trinomial :

[tex]T=4x^2+20x-24~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

To select the factor, we need to factorize expression (i). To factorize, we need two integers with sum 20 and product -96.

From (i), we have

[tex]T\\\\=4x^2+20x-24\\\\=4x^2+24x-4x-24\\\\=4x(x+6)-4(x+6)\\\\=(x+6)(4x-4)\\\\=4(x+6)(x-1).[/tex]

So, the factors of the given trinomial are 4, (x + 6) and (x - 1).

Since 4 and ( x + 6) are not in the options, so (x - 1),  is the correct binomial.

Thus, (C) is the correct option.

Answer:

Inverse of y = [tex]f^{-1}(x)[/tex] = [tex]\sqrt{100 -x}[/tex].

Step-by-step explanation:

Given  : f(x) = y = 100 - x²

To find : Find inverse.

Solution : We have given that :

f(x) = y = 100 - x²

Step1) : Replace every x with a y and replace every y with an x .

x = 100 - y².

Step 2): Solve for y

On subtracting 100 from both sides

x - 100 = -y²

On multiplying both side by -1

100 -x = y²

Taking square root both sides and switching sides

y = ± [tex]\sqrt{100-x}[/tex].

Step3 ) : Replace y with [tex]f^{-1}(x)[/tex].

[tex]f^{-1}(x)[/tex] = ± [tex]\sqrt{100-x}[/tex].

Therefore, inverse of y = [tex]f^{-1}(x)[/tex] = ± [tex]\sqrt{100-x}[/tex].

Answer:

A on edge

Step-by-step explanation:

We can see here that to guarantee that no two adjacent rooms are the same color, a minimum of four colors is generally needed.

To determine the minimum number of colors needed to paint each room in a way that no two adjacent rooms have the same color, we can use a coloring algorithm known as the "Four Color Theorem." According to this theorem, it is possible to color any map on a plane using at most four colors, ensuring that no two adjacent regions have the same color.

Applying this concept to the rooms, we can conclude that a minimum of four colors is needed to satisfy the given condition. By using these four colors, we can ensure that no two adjacent rooms share the same color.

Tom weighed 122 pounds at the end of the year.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Tom weighed 110 pounds at the beginning of the year.

Pounds gained in June = 13

Pounds lost in August = 5

Pounds gained in November = 4

Now,

Total pounds at the end of the year.

= 110 + 13 - 5 + 4

= 110 + 17 - 5

= 110 + 12

= 122 pounds

Thus,

122 pounds at the end of the year.

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Answer:

Hence, the length of the radius of a circle with center at origin is 17 units.

Step-by-step explanation:

" We know that radius of  a circle is any line segment joining center to any point on the circle ".

We have to find the length of the radius of a circle with a center at the origin i.e. (0,0) and a point on the circle at 8 + 15i i.e. at (8,15).

( Since any complex number of the form z=x+iy has a point in the coordinate plane as:  (x,y) ).

Hence , we have to find the distance between the point (0,0) and (8,15).

The distance between two points (a,b) and (c,d) is given by:

[tex]\sqrt{(a-c)^2+(b-d)^2}[/tex]

Here (a,b)=(0,0) and (c,d)=(8,15)

Hence distance between (0,0) and (8,15) is:

[tex]\sqrt{(0-8)^2+(0-15)^2\\} \\=\sqrt{(8)^2+(15)^2\\} \\=\sqrt{64+225}\\ \\=\sqrt{289}\\ \\=17[/tex]

Hence, the length of the radius of a circle with center at origin is 17 units.

Answer: 17

Step-by-step explanation: the length of the radius of a circle with center at origin is 17 units.

Answer:

Step-by-step explanation:

B

f(x) = -1/5(3)ˣ⁻¹ formula can  be used to describe the sequence.

The given sequence is -3, 3/5, -3/25, 3/125, -3/625

We can observe that each term alternates between negative and positive.

Additionally, the denominator of each term is increasing by a power of 5, while the numerator alternates between -3 and 3.

The formula f(x) = -1/5(3)ˣ⁻¹, fits this pattern.

By plugging in the values of x = 1, 2, 3, 4, and so on, the formula generates the corresponding terms of the sequence:

f(1) = -1/5(3)¹⁻¹= -3/5

f(2) = -1/5(3)²⁻¹ = 3/25

f(3) = -1/5(3)³⁻¹ = -3/125

f(4) = -1/5(3)⁴⁻¹ = 3/625

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Answer with explanation:

1.⇒ The given equation is

  5x-2y=3

For one solution ,you should write linear equation in such a way

ax+by=c, such that

  [tex]\frac{5}{a}\neq \frac{-2}{b}\neq \frac{3}{c}[/tex]

So, the linear equation will be

→3x+4y=8

You can write many more by yourself.

2.⇒Exactly two solutions

The two lines intersect at only one point.So,there are no such lines which has two point of Intersection.

3.⇒No solutions

It means the two lines will never intersect.

 For no solution ,you should write equation of line in such a way

ax+by=c, such that

  [tex]\frac{5}{a}=\frac{-2}{b}\neq \frac{3}{c}[/tex]

So, the linear equation will be

→10x -4y=15

You can write many more by yourself.

4.⇒Infinitely many solutions

For Infinite number of solution ,you should write linear equation in such a way

ax+by=c, such that

  [tex]\frac{5}{a}=\frac{-2}{b}=\frac{3}{c}[/tex]

→10x-4y=6

Final answer:

To find the whale's average speed per hour, divide the total distance of 184 miles by the time of 6 hours, resulting in an average speed of approximately 30.67 miles per hour.

Explanation:

The question asks for the speed of a whale per hour based on a certain distance traveled over a period of time. To calculate the speed of the whale, we can use the formula:

Speed = Distance ÷ Time

In this case, the whale traveled 184 miles in 6 hours. Using the formula, we divide 184 miles by 6 hours:

Speed = 184 miles ÷ 6 hours = 30.67 miles per hour

So, the whale swam at an average speed of about 30.67 miles per hour.