Help me in the second question please

The square root expression with it's correct simplified radical can be matched as follow:

√45 =  3√5

√200 = 10√2

√80 = 4√5

√24 = 2√6

A simplified radical is a radical expression in which the radicand (the expression inside the square root symbol) has been simplified as much as possible. For example, the simplified form of √8 is 2√2.

√45 = √(9*5) = √9 * √5 = 3  * √5  =  3√5

√200 = √(100*2) = √100 * √2 = 10 * √2  =  10√2

√80 = √(16*5) = √16 * √5 = 4 * √5  =  4√5

√24 = √(4*6) = √4 * √6 = 2 * √6  =  2√6

Thus, match the square root expression with it's correct simplified radical accordingly.

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Answer:

Step-by-step explanation:

You want the value of x that makes f(x) = 60, when f(x) is the exponential function with an initial value of 100 and a decay factor of 0.95.

The form of an exponential function is ...

  f(x) = (initial value) · (decay factor)^x

For the given initial value and decay factor, the function is ...

  f(x) = 100 (0.95^x)

Solving for x, we find ...

  f(x)/100 = 0.95^x

  log(f(x)/100) = x·log(0.95)

  x = log(f(x)/100)/log(0.95)

For f(x) = 60, the value of x is about ...

  x = log(60/100)/log(0.95) ≈ 9.959

The value of x is about 9.959.

The error made by the student in the exponential function, y = 48,000(1.03)^x is that the function represented an exponential growth rather than an exponential decay.

An exponential function is written in the form y = abˣ.

In the exponential function, the exponent, x is a variable.

Annual decreasing rate of the fish population = 3% or 0.03

Original population = 48,000

Let the number of years = x

Exponential function: 48,000 (1 - 0.03)^x

= 48,000(0.97)^x

Thus, to represent an exponential decay, the exponential function should have been written as y = 48,000(0.97)^x.

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Answer:

2826 sqft

Step-by-step explanation:

π r² = 900π =2826

If all 4 posts are painted, 44 square feet must be painted.

We know that the formula for the surface area of the cylinder is:

A = 2πrh + 2πr²

Here, the dimensions of the each cylindrical post:

the diameter d = 1 foot and the height is 3 feet high.

So, the radius r = 0.5 ft and height h = 3 ft

Let us assume that the surface area of one post be A₁

Using above formula of surface area of cylinder,

A₁ =  2πr(h + r)

A₁ =  2 × π × 0.5 × (3 + 0.5)

A₁ =  2 × 3.14 × 0.5 × (3.5)

A₁ =  10.99

A₁ ≈ 11 sq.ft.

So, the total surface area of  4 cylindrical posts would be,

A = 4 × A₁

A = 4 × 11

A = 44 sq.ft.

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The description is that a unit increment in the number of sweatshirt will cause a $6.50 increment in the total charges

From the question, we have the following parameters that can be used in our computation:

Using the above as a guide, we have the following:

Slope = 6.50

This means that a unit increment in the number of sweatshirt will cause a $6.50 increment in the total charges

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The option that is not a way by which minerals are being formed is decrystallization. That is option B

Minerals are organic substances that are form through the following ways;

Decrystallization is not a way through which minerals are formed because it is just the break down of solid or crystal structures.

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Complete question:

Which of the following is not a method by which minerals form?. a. crystallization. b. decrystallization. c. water evaporation from a solution. d. cooling of magma or lava

The image vertices of D′ if the preimage is rotated 90° counterclockwise is: A. D′(−2, −4).

In Geometry, the rotation of a point 90° about the center (origin) in a counterclockwise (anticlockwise) direction would produce a point that has these coordinates (-y, x).

By applying a rotation of 90° counterclockwise to the vertices for D, the coordinates of the vertices of the image point D' are as follows:

(x, y)                               →            (-y, x)

Ordered pair D  = (-4, 2) → Ordered pair D' = (-2, -4)

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The equation of the new graph is f(x) = 9^(x - 2)

From the question, we have the following parameters that can be used in our computation:

f(x) = 9^x

Also, we have

shifted 2 units to the right,

This is represented as

(x, y) = (x - 2, y)

Substitute the known values in the above equation, so, we have the following representation

f(x) = 9^(x - 2)

Hence, the function is f(x) = 9^(x - 2)

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Answer:

using the equation of the straight line we solve

You can estimate that the used cars Mr. Ford reviewed were worth roughly $2,200 less now than when they were new, had an average price of around $22,000 when new, and typically lose $2,200 of value per year. (option 1, 2, 3)

To calculate this, you can substitute the x-values from the table into the equation and solve for y. For example, when x is 3,

which is the price of the car when it was 3 years old. This same formula can be used to calculate the price of the car at other age values and shows that the car loses an average of $2,200 of value per year. At 5 years old, the equation would be

which is the average value of the used car at that age.

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Complete Question:

Mr. Ford wants to better understand the value of used cars over time. He reviewed some used-car ads and recorded the relationship between age and price in a table. Finally, he calculated a line of best fit. Used cars Age in years (x) 3 6 4 2 6

Price (y) $15,000 $8,000 $12,000 $5,000 $19,000 $10,000

The equation for the line of best fit is y = -2,200x + 22,000.

Based on the equation, what estimates can you make about the used cars Mr. Ford reviewed?

Select all that apply.

For the given height function h(t)= -16t²+88t the rocket is in the air for 5.5 seconds.

Height of the launched rocket is equal to :

h(t)= -16t²+88t

Time is represented by 't' in seconds after launch

'h' represents the height of the rocket.

For how long time rocket is in the air :

h(t) = 0

⇒  -16t²+88t = 0

⇒ t ( -16t+88 ) = 0

⇒ t = 0 or ( -16t+88 ) = 0

value of time 't' cannot be equal to zero.

This implies ( -16t+88 ) = 0

⇒16t = 88

⇒ t = 88 / 16

⇒ t = 5.5 seconds

Therefore, the time for which rocket is in the air as per given height function is equal to 5.5 seconds.

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Answer: 12/35 units sqr

Step-by-step explanation: Multiply both values to find area and put proper units.

Answer:

Step-by-step explanation:

The area of a rectangle is given by the formula: area = length x width.

For a rectangle with length 4/7 and width 3/5, the area can be calculated as follows:

area = 4/7 x 3/5

= 12/35

So, the area of the rectangle with length 4/7 and width 3/5 is 12/35 square units.

Answer:

EG/HJ=GF/JI or EG/HJ=FE/IH

Step-by-step explanation:

Given

AngleF=AngleI

AngleE=AngleH

Therefore triangles EGF AND HJI are similar by Angle-Angle Similarity Theorem

So

EG/HJ=GF/JI=FE/IH as they are the corresponding sides of a similar triangle

Answer:

$ 4564.32

Step-by-step explanation:

APR=2%, monthly interest rate, i=2%/12=0.02/12

Monthly payment, A=250

After 18 monnth, n=18 months,

the balance. Pis therefore

P = A((1+i)^n-1)/i

=250((1+0.02/12)^18-1)/(0.02/12)

=$ 4564.32

Given that x, y, z are different and satisfy the equations:

x^3 + x^2 - x = 0

y^3 + y^2 - y = 0

z^3 + z^2 - z = 0

We can multiply the first equation by y, the second by z, and the third by x to obtain:

x^3y + x^2y - xy = 0

y^3z + y^2z - yz = 0

z^3x + z^2x - zx = 0

Adding these three equations together, we get:

x^3y + x^2y - xy + y^3z + y^2z - yz + z^3x + z^2x - zx = 0

Expanding and simplifying, we find that:

x^2y + xy^2 + y^2z + yz^2 + z^2x + zx^2 - xy - yz - zx = 0

Now, we use the fact that x, y, and z are roots of the equations given above to simplify the expression further:

x^2 - x + y^2 - y + z^2 - z = 0

We can also write this as:

(x - 1)(x + 1) + (y - 1)(y + 1) + (z - 1)(z + 1) = 0

This expression can be factorized as:

(x - 1)(x + 1)(y - 1)(y + 1)(z - 1)(z + 1) = 0

Since x, y, and z are all different, we have that:

(x - 1)(x + 1) ≠ 0

(y - 1)(y + 1) ≠ 0

(z - 1)(z + 1) ≠ 0

Therefore, we have:

(x - 1)(x + 1)(y - 1)(y + 1)(z - 1)(z + 1) = (x - 1)(x + 1)(y - 1)(y + 1)(z - 1)(z + 1) = 0

So, we can conclude that:

xyz = -1

And,

1 + xyz = 0

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The smallest possible value for a term in the five-term arithmetic sequence is 1.The sum of a five-term arithmetic sequence is given as 100 and all terms are positive integers. Let's call the first term "a" and the common difference "d".

The five terms can be represented as a, a + d, a + 2d, a + 3d, and a + 4d. The sum of these five terms is 100, which can be represented as:

a + (a + d) + (a + 2d) + (a + 3d) + (a + 4d) = 100

Simplifying the expression, we get:

5a + 10d = 100

Dividing both sides by 5, we get:

a + 2d = 20

Since all terms are positive integers, it follows that "a" and "d" must also be positive integers. The smallest possible value for "a" is 1, and the smallest possible value for "d" is 1. Substituting these values into the expression for "a + 2d" yields:

1 + 2 * 1 = 3

Thus, the smallest possible value for a term in the five-term arithmetic sequence is 1.

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Answer:

Step-by-step explanation:

To find the missing side lengths in the given right triangles, use trigonometric ratios.

[tex]\boxed{\begin{minipage}{9.4 cm}\underline{Trigonometric ratios} \\\\$\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}[/tex]

From inspection of the first triangle ABC, we have been given the angle, the side opposite the angle and the side adjacent the angle.

Therefore, to calculate the length of the adjacent side, x, substitute the values into the tangent ratio:

[tex]\implies \tan 18^{\circ}=\dfrac{15}{x}[/tex]

[tex]\implies x\tan 18^{\circ}=15[/tex]

[tex]\implies x=\dfrac{15}{\tan 18^{\circ}}[/tex]

[tex]\implies x=46.165253...[/tex]

[tex]\implies x=46.2\;\;\sf(nearest\;tenth)[/tex]

----------------------------------------------------------------------------------------

Triangle LMN is a right triangle. Interior angles of a triangle sum to 180°.

Therefore, as m∠M = 50° and m∠MLN = 90°, then m∠MNL = 40°.

As KN is perpendicular to NM and m∠MNL = 40° then m∠KNL = 50°.

As KL is parallel to NM, then m∠K = 90°.  Therefore, m∠KLN = 40°.

(Refer to the attached diagram).

For right triangle LMN, we have been given the angle (∠M) and the side adjacent to the angle (LM). To find an expression for the length of the side opposite the angle (LN), use the tangent ratio:

[tex]\implies \tan 50^{\circ}=\dfrac{LN}{45}[/tex]

[tex]\implies LN=45\tan 50^{\circ}[/tex]

LN is the hypotenuse of right triangle KLN.

If we use ∠KNL as θ, then side KN is adjacent to the angle.

Therefore, to find the KN use the cosine ratio:

[tex]\implies \cos 50^{\circ}=\dfrac{KN}{LN}[/tex]

[tex]\implies \cos 50^{\circ}=\dfrac{KN}{45\tan 50^{\circ}}[/tex]

[tex]\implies KN=45\tan 50^{\circ}\cos 50^{\circ}[/tex]

[tex]\implies KN=34.471999...[/tex]

[tex]\implies KN=34.5\;\; \sf (nearest\;tenth)[/tex]

As KL is the side opposite ∠KNL, to find KL use the sine ratio:

[tex]\implies \sin 50^{\circ}=\dfrac{KL}{LN}[/tex]

[tex]\implies \sin50^{\circ}=\dfrac{KL}{45\tan 50^{\circ}}[/tex]

[tex]\implies KL=45\tan 50^{\circ}\sin50^{\circ}[/tex]

[tex]\implies KL=41.0821297...[/tex]

[tex]\implies KL=41.1\;\;\sf (nearest\;tenth)[/tex]

----------------------------------------------------------------------------------------

From inspection of the second triangle ABC, we have been given the angle, the side adjacent the angle and the hypotenuse.

Therefore, to calculate the length of the adjacent side, x, substitute the values into the cosine ratio:

[tex]\implies \cos 70^{\circ}=\dfrac{x}{46}[/tex]

[tex]\implies x=46\cos 70^{\circ}[/tex]

[tex]\implies x=15.732926...[/tex]

[tex]\implies x=15.7\;\;\sf(nearest\;tenth)[/tex]

The z statistic that is associated with the class's average is 1.25.

In the given question the population of all standardized ex scores has a mean of 500 and a standard deviation of 100 . Twenty-five students in a professor's class take the ex , and their average score is 525.

We have to find z statistic that is associated with the class's average.

n = 25

μ = 500

σ = 100

[tex]\bar X[/tex] = 525

Then ,

z statistic = [tex]\frac{\bar{X} - \mu}{\frac{\sigma}{\sqrt n} }[/tex]

putting the value in the formula:

z statistic = (525-500)/(100/\sqrt 25)

z statistic = (25)/(100/5)

z statistic = (25)/(20)

z statistic = 1.25

Therefore,

The z statistic that is associated with the class's average is 1.25.

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Step-by-step explanation:

Seeing the question, I assume there are answer choices, but I'll give all possible answers below.

A ratio is pretty much a fraction, that's about it. It's asking the ratio of undergraduate to graduate, which creates

[tex] \frac{undergraduate}{graduate} [/tex]

Now we plug in those numbers in the correct spots

[tex] \frac{8500}{3500} [/tex]

Now to simplify. Since both of these numbers end in 0, there a little truck you can do to automatically make it smaller, and that's getting rid of all the 0s on the end. That makes it...

[tex] \frac{85}{35} [/tex]

To continue simplifying

[tex] \frac{8500}{3500} = \frac{85}{35} = \frac{17}{7} [/tex]

Answer:

40%

Step-by-step explanation:

32 out of 80 as a percentage it is 40%

The surface area of the right triangular prism with legs of 5 centimeters and 12 centimeters, a hypotenuse of 13 centimeters, and a height of 2 centimeters is 108 square centimeters.

Surface area refers to the total area of the surface of a three-dimensional object. When it comes to a right triangular prism, the surface area includes the area of all six faces.

Let's call the height of the triangular prism "h" and label the legs of the triangle "a" and "b". Using these values, we can find the area of the base of the triangular prism. The area of a right triangle is equal to 1/2 times the product of the legs, so the area of the base is

=> (1/2) * a * b = (1/2) * 5 * 12 = 30 square centimeters.

Next, we need to find the surface area of each of the three lateral faces. Each of these faces is a rectangle, so we can find the area by multiplying the height of the prism by the length of one of the sides of the triangle base.

The length of one side of the triangle base is equal to the hypotenuse, which is 13 centimeters. So, the surface area of each of the three lateral faces is

=> h * 13 = 2 * 13 = 26 square centimeters.

Finally, we can find the total surface area by adding the surface area of the base and the surface area of the three lateral faces.

The surface area of the base is 30 square centimeters, and the surface area of each lateral face is 26 square centimeters, so the total surface area is

=> 30 + 3 * 26 = 30 + 78 = 108 square centimeters.

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Using a trigonometric relation we will see that the value of x is 81.2°

We can see that we have a right triangle, and the angle x is the one that is on the top vertex.

We can use any trigonometric relation to find the value of x, for example we can use:

sin(x) = (opposite cathetus)/(hypotenuse)

Where we can see that:

opposite cathetus = 84

hypotenuse = 85

Then we will get:

sin(x) = 84/85

x = Asin(84/85) = 81.2°

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Answer:

17.2%

Step-by-step explanation:

In the first hour:

The farmer sells 8% of the total chickens:

         [tex]= \frac{8}{100}[/tex]×[tex]250[/tex]

         = 20 chickens

Therefore, the number of chickens left are:

= (250 - 20) chickens

= 230 chickens

In the second hour:

The farmer sells 10% of the chickens left:

= [tex]\frac{10}{100}[/tex]×[tex]230[/tex]

= 23 chicken

∴ The total number of chickens sold in the two hours = (20 + 23) chickens

                                                                                      = 43 chickens

43 has to be expressed as a percentage of the original number (i.e. 250)

Percentage = [tex]\frac{Number Of Chickens Sold}{Total Number Of Chickens}[/tex]×[tex]100[/tex]%

                    = [tex]\frac{43}{250}[/tex]×[tex]100[/tex]%

                    = 17.2%

Answer: 16

Step-by-step explanation:

      The geometric number between 7 and 28 is 16. Geometric numbers are the numbers you get by multiplying by a factor. If we multiply by 2 for this common geometric sequence, we get 16:

1 * 2 = 2, 2 * 2 = 4, 4 * 2 = 8, 8 * 2 = 16,16 * 2 = 32, etc.

         7 < 16 < 28

KLMN is a trapezoid where KL=MN and m∠1=m∠2 . It is also given that LM:KN = 8/9 and PKLMN=132.The midsegment is 34 units long.

The trapezoidal shape KLMN, where KL = MN.

m∠1=m∠2

Moreover, LM/KN = 8/9

Additionally, KLMN's perimeter is 132 units.

The midsegment's size (KM).

We can see that in the above case, KM is a transversal in relation to the parallel lines LM and KN. which implies,

∠KML=∠MKN

∠1=∠2

Two base angles are clearly equal. So, KLM and KMN are isosceles triangles.

Using the side ratios of two triangles as an example,

= KL: LM: MN: KN

= 8 : 8 : 8 : 9

The ratio units add out to 8 + 8 + 8 + 9 = 33. Consequently, each ratio's value is,

=[tex]\frac{perimeter}{33} \\\\\frac{132}{33} \\\\=4[/tex]

The segment LM's length is thus,

LM=8×4=32

Additionally, section KN's length is

KN=9×4=36

Taking the average of LM and KN as, one can then determine the length of the midsegment KM.

[tex]KM=\frac{LM+KN}{2} \\\\\\KM=\frac{32+36}{2}[/tex]

KE=34

As a result, the midsegment is 34 units long.

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Samantha used 120 grams of 25% sugar syrup.

An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given that, Samantha mixes some amount of 25% sugar syrup with x grams of 10% sugar syrup. The result is 120 grams of 15% sugar syrup.

Let Samantha used y grams of 25% sugar syrup.

Then, she used (120 - y) grams of 10% sugar syrup.

We know that the final concentration of sugar syrup is 15%, which means that 15% of the total 120 grams of the syrup is sugar.

This can be expressed as:

0.15 x (y + (120 - y)) = 0.15 x 120

Expanding and simplifying the equation, we get:

0.15y + 0.15 x 120 - 0.15y = 18

0.15 x 120 = 18

Solving for y, we get:

y = 120 x 18 / (0.15 x 120)

= 120 x 18 / 18

= 120.

Hence, Samantha used 120 grams of 25% sugar syrup.

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Answer:

work hard you can get it

Step-by-step explanation:

lol

Length of AD is, 2.5 inches

Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.

Given that;

Values are,

AB = 18 inches,

AE = 5 inches,

CE = 6 inches,

Let the length of ED = x

Now, By the figure,

⇒ ΔABD ≈ ΔECD

Hence, By definition of proportional we get;

⇒ AB / AD = EC / ED

⇒ AB / (AE + ED) = EC / ED

⇒ 18 / (5 + x) = 6 / x

⇒ 3x = 5 + x

⇒ 3x - x  =5

⇒ 2x = 5

⇒ x = 2.5 inches

Thus, Length of AD is, 2.5 inches

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we add row 1 to row 3 to get the final matrix = [3, 0, 3; 1, 1, 1; 0, 0, 0]. Thus, the new matrix is obtained by applying the given row operations in the given order.

Let A be a given matrix.

Row Operation 1: Exchange row 1 and row 2.

Row Operation 2: Multiply row 1 by 3.

Row Operation 3: Add row 1 to row 3.

Then,

= [ 3, 0, 3; 1, 1, 1; 0, 0, 0 ]

We can obtain the matrix by applying the row operations in the given order. First, we exchange row 1 and row 2 to obtain the matrix [1, 1, 1; 3, 0, 3; 0, 0, 0]. Then we multiply row 1 by 3 to get [3, 0, 3; 1, 1, 1; 0, 0, 0]. Finally, we add row 1 to row 3 to get the final matrix = [3, 0, 3; 1, 1, 1; 0, 0, 0]. Thus, the new matrix is obtained by applying the given row operations in the given order.

The complete question is :

Suppose [tex]$\begin{bmatrix}4 & -2 & 3 \\2 & 3 & 1 \\5 & 1 & -2\end{bmatrix}$[/tex] is an matrix that can be obtained from [tex]$\begin{bmatrix}1 & 2 & 3 \\3 & 2 & 1 \\2 & 5 & -2\end{bmatrix}$[/tex]using the row operations (in the given order) [tex]$R_1 \leftrightarrow R_2, R_2 - 3R_1, R_3 - 5R_1$[/tex]

What is [tex]$\begin{bmatrix}1 & 2 & 3 \\3 & 2 & 1 \\2 & 5 & -2\end{bmatrix}$[/tex]?

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