The radius of the circle below is 21 mm.
Calculate the area of the circle.
Give your answer in mm² to 1 d. p.
21 mm

Rewritten the Expression Using Logical AND Parentheses as "(X > 0) AND (X < 10)"

A logical operator is a symbol or keyword used in a programming language to perform a logical operation on one or more values.

The expression "0 < X < 10" is often misinterpreted as a range for a single variable X.

However, in most programming languages, this expression is considered an error because it does not explicitly state the logical relationship between the two inequalities.

To correct the expression, we use the logical operator AND to connect the two inequalities. The resulting expression, "(X > 0) AND (X < 10)", states that a variable X is within the desired range if it is greater than 0 and less than 10. The parentheses are used to make the expression clearer and to ensure that the logical operation is applied to the correct values.

Hence, "(X > 0) AND (X < 10)"

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The pair of transformations that could map ABC to A’B’C’, such that the triangles are similar but not congruent are dilation and rotation

Resizing an item uses a transition called Dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. Dilation transformations ensure that the shape will stay the same and that corresponding angles will be congruent

Given data ,

Let the triangle be represented as ΔABC

Let the dilated triangle be represented as ΔA'B'C'

Let the dilation scale factor be represented as k

Now , when a triangle is dilated by a scale factor of k , there is a change in the shape of the triangle

After a dilation , the triangle will enlarge or compress by a factor k , but it will be similar to the parent triangle

Now , when the triangle is rotated , it only changes the initial coordinates of A , B and C

Hence , the transformations are dilation and rotation

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Answer: The derivative of f(x) = 4x^3 - 5x^2 + 7x - 10 is given by f'(x) = 12x^2 - 10x + 7.

Step-by-step explanation:

Answer:

177°

Step-by-step explanation:

A sector is the area between two radi.

We are given the perimeter of the sector as 21.4cm and the radius 4.2cm. Subtracting two radi from the perimeter will give us the arc of the sector as 13.

As we know, the formula for the length of an arc is: length of arc = ∅/360 × πd. Diameter is double the radius so in this case it's 8.4; so filling in the blanks our new formula is: 13 = ∅/360 × 8.4π.

We are trying to find ∅ which is the degree of the sector. So from this formula we can rearrange it by dividing 8.4π on both sides of the equation giving ¹³/8.4π = ∅/360; from here we multiply 360 on both sides and therefore getting ∅ on its own therefore allowing us to equate it.

Plug that all into a calculator and you get 177.3440794 so you can round it down to 177°

I saw this question a few minutes ago but spent a bit of time calculating it...sorry :)

So, using a heater with a heating output of 5900 kJ/min, it will take roughly 9.05 hours to heat the water in the hot tub from 65°F to 104°F.

When the temperature rises, atoms and molecules move faster and collide, creating thermal energy (also known as heat energy). Thermal energy is the energy that results from the heated substance's temperature.

Calculate the square footage or square metres of your room. The room's dimensions are then multiplied by its width, height, and length. Then double this amount by 6. For BTUs or 0.0606 for kW, respectively. 

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The number which correctly represents the decimal 0.6 as a whole number is; 1.

It follows from the task content that the number which correctly represents the number 0.6 as a whole number is to be determined.

Since the given number is 0.6. It follows that the closest whole number can be determined by rounding off to th nearest whole number.

Hence, by rounding off; we have; 1.

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The equation x = √-x + 6 cannot have any real solutions, because taking the square root of a negative number is not a real number. So the answer is none of the options listed.

In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical phrase with two equal sides separated by an equal sign is called an equation. Linear equations are classified into three types: point-slope, standard, and slope-intercept. Identity equations and conditional equations are the two types of equations. An identity holds true for all possible values of the variables. A conditional equation is valid only for certain values of the variables. An equation consists of two expressions joined by an equals sign ("=").

Here,

The equation x = √-x + 6 cannot have any real solutions, because taking the square root of a negative number is not a real number.

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The analisis and interpretation of functions, its domain and its range, indicates the following conclusions:

Case 2 - a) Domain: - 15 ≤ x < 15, b) Range: - 200 ≤ y < 400, c) f(0) = 100, d) f(x) = 0, when x = - 5.

Case 3 - g(1) = 6, g(x) = 1 when x = - 2, g(x) = 2 when x = 0 or x = 4.

In this question we must answer two exercises on functions. In the second case we have the representation of a function on Cartesian plane, whose domain is the set of all values on horizontal axis and range is for vertical axis.

By direct inspection, we find the following information:

a) Domain

- 15 ≤ x < 15

b) Range

- 200 ≤ y < 400

c) f(0) = 100

d) f(x) = 0, when x = - 5

The third case includes a table with domain and range of a functions, this must be interpreted to fill the following blanks:

g(1) = 6

g(x) = 1 when x = - 2

g(x) = 2 when x = 0 or x = 4

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The answer to the "different" question is: 32

The answer to the "same" question is: 2

The probabilities are;

(a) 0.5648

(b) 0.3497

(c) 0.0855

The possibility of an event in time is known as probability in mathematics. How frequently does the incidence occur over the course of a specific time period, in plain English?

Given:

A table shows the smoking habits of college students.

a) If a student is chosen at random, the probability of getting someone who is a woman or a heavy smoker is,

= P(woman) + P(heavy smoker) - P(a woman and a heavy smoker)

= 213/386 + 10/386 - 5/386

= 0.5648 to 4 decimal places.

b) If two students are chosen at random without replacement, the probability of getting both who are non-smokers and a man is,

= P(non smoker and man)

= 135/386

= 0.34974093264

= 0.3497

c) If a student is chosen at random, the probability of getting someone who is a regular smoker given the person is a woman is,

= P( regular smoker and a woman)

= 33/386

= 0.08549222797

= 0.0855

Therefore, 0.0855 is the probability.

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The time it would take for the rock to reach the ground is given as follows:

3.19 seconds.

The quadratic equation that models a projectile's height is given as follows:

y = -9.81t² + v(0)t + h(0).

In which:

The parameters for this problem are given as follows:

v(0) = 0, h(0) = 100.

The rock reaches the ground when y = 0, hence:

9.81t² = 100

t = sqrt(100/9.81)

t = 3.19 seconds.

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Answer:

(3, - 4 )

Step-by-step explanation:

under a reflection in the x- axis

a point (x, y ) → (x, - y ) , then

(- 3, 4 ) → (- 3, - 4 )

under a reflection in the y- axis

a point (x, y ) → (- x, y ) , then

(- 3, - 4 ) → (3, - 4 )

Answer: 4 hours

Step-by-step explanation: y int = 120, slope = 30

For the given triangle the value of z = 1, y = 6, and x = 4.75.

One of the earliest areas of mathematics is geometry, along with arithmetic. It is concerned with spatial characteristics like the separation, shape, size, and relative placement of objects.

The value of x,y, and z will be calculated by the property states that the ratio of the median line passing from the centroid of the triangle is divided into the ratio of 1: 2.

The value of x,

( 2x - 6 ) / 7 = 1 / 2

2 ( 2x - 6 ) = 7

4x - 12 = 7

4x = 19

x = 19 / 4

The value of y,

3 / y = 1 / 2

y = 3 x 2

y = 6

The value of z,

2z / 4 = 1 / 2

4z = 4

z = 1

Therefore, the values are z = 1, y = 6, and x = 4.75.

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Answer:

15

Step-by-step explanation:

The distance can't be negative.

20-5=15

The value of x from the given kite is 254.

In Euclidean geometry, a kite is a quadrilateral whose four sides can be grouped into two pairs of equal-length sides that are adjacent to each other.

Given that, m∠N=53°, ∠T=67° and m∠F=(1/2 x-8)°

In kite the two angles are equal where the unequal sides meet.

So, m∠W=m∠F=(1/2 x-8)°

Now, m∠N+m∠T+m∠W+m∠F=360°

53°+67°+(1/2 x-8)°+(1/2 x-8)°=360°

120+x-16=360

x=360-104

x=254

Therefore, the value of x is 254.

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The end behavior of f(x) = -x^4 + x^2 - x + 1 is that it approaches negative infinity as x approaches both positive and negative infinity.

The end behavior of a function refers to the limiting behavior of the function as x approaches positive infinity and negative infinity.

For the function f(x) = -x^4 + x^2 - x + 1, as x approaches positive infinity, the x^4 term dominates, and the value of the function approaches negative infinity.

As x approaches negative infinity, the x^4 term again dominates and the value of the function approaches negative infinity.

Therefore, the end behavior of f(x) = -x^4 + x^2 - x + 1 is that it approaches negative infinity as x approaches both positive and negative infinity.

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Answer:

two plus two equals five

Step-by-step explanation:

Answer: In an 8-hour day, the factory produces 32 tables. In 1 day, the factory produces 32 tables.

In 3 days, the factory will produce 3 days * 32 tables per day = 96 tables.

Step-by-step explanation:

The solution to the given values by reducing them to their lowest term is 7m/h

The reduction of the given values to the lowest term possible can be achieved by using the long division process. So, we set up the division problem in a long division format.

5 || 35

Divide 35 by 5 . Place this digit in the quotient on top of the division symbol.

     7

5 || 35

Multiply the newest quotient digit (7) by the divisor 5.

     7

5 || 35

     35

Subtract 35 from 35.

     7

5 || 35

     35

       0

The result of the division to the lowest term possible is 7 m/h.

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Answer:

(b) four units below the xy-plane (in the negative z-direction).

Step-by-step explanation:

here's your answer for your questions

The option c yields the greatest balance after 8 years.

The formula for compounding Interest

n times a year :

[tex]A=P(1+\frac{r}{100n})^{nt}\\[/tex]

(a)

Investing $20,000 implies P=20000 and t=8,

interest is compounded daily, which means that n=365 r is given as 6%.

Substitute these values in the formula to get find balance after 8 years,

[tex]20000(1+\frac{6}{100*365})^{365*8}=$ $ 32320.21[/tex]

(b)

$ 30,000 after eight years, is the final balance. Because there is no time left to invest it,

(c)

We get $8000, which we can invest for 8 years,

and we will get $20,000 after 4 years which we can invest for 4 years.

final balance on the $ 8000 invested for 8 years can be found using the formula substitute p=8000, t=8 and r=6%, n=365.

[tex]8000(1+\frac{6}{100*365})^{365*8}=12928.09$[/tex]

final balance on the $ 20,000 invested for 4 years can be found using the formula P=20,000, t=4, and r=6, and n=365.

= 25424.58.

Under the option c, the final balance is 12928.09+25424.58=38352.57

(d)

under this option, we get $ 9000, which we can invest for 8 years.

we will again get 9000 after 4 years, which we can invest for four year,

we will again get

9000 after 8 years, for which we have not invested.

final balance on the 8000 invested for 8 years can be found using above formula p=9000, t=8 and r=6

=14544.1$

final balance of 9000 invest for four years is = 11441.02

total final balance = 34985.12$

Option c yields the greatest balance after 8 years.

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Answer: sorry downbad for points god bless

Step-by-step explanation:

Answer:

-a^2+7a

Step-by-step explanation:

Answer: Y-axis

Step-by-step explanation:

It is reflected across the y-axis , which cam be seem as it goes up

Answer: It's the Y-Axis

Step-by-step explanation:

the green triangle and the orange triangle are flipped from left and right, that means its on the y axis. if it was up and down it would be x axis.

Answer:

Step-by-step explanation:

If Martha needs 28 strawberries for every 4 smoothies she makes, then she needs 7 strawberries per smoothie.

a) For two distinct real roots: x > 0 or x > m

b) For two distinct real roots: x > 0 or x > 2m

c) For two distinct real roots: x > 0 or x > 4

This is based on the quadratic equation.

Only non-negative integer powers of x are present in the quadratic equation, making it a polynomial equation. In actuality, the Latin word quadratus, which means square, is the root of the term quadratic. The quadratic equation has the generic form ax² + bx + c = 0. where x is an unknowable variable and a, b, and c are mathematical coefficients.

a) Quadratic equation: x² - 4x + m = 0

The discriminant: Δ = b² - 4ac

Δ = (2x)² - 4.x.(m)

Δ = 4x² - 4mx

Δ = 4x (x - m)

For two distinct real roots: Δ > 0

4x (x - m) > 0

x > 0 or x > m

For two real roots: Δ ≥ 0

4x (x - m) ≥ 0

x ≥ 0 or x ≥ m

For a repeated root: Δ = 0

4x (x - m) = 0

x = 0 or x = m

(b) Quadratic equation: mx² + 3x + 2 = 0

The discriminant: Δ = b² - 4ac

Δ = (3x)² - 4.mx.(2)

Δ = 4x² - 8mx

Δ = 4x (x - 2m)

For two distinct real roots: Δ > 0

4x (x - 2m) > 0

x > 0 or x > 2m

For two real roots: Δ ≥ 0

4x (x - 2m) ≥ 0

x ≥ 0 or x ≥ 2m

For a repeated root: Δ = 0

4x (x - 2m) = 0

x = 0 or x = 2m

(c) Quadratic equation: x² - mx + 1 = 0

The discriminant: Δ = b² - 4ac

Δ = (x)² - 4.x.(1)

Δ = x² - 4x

Δ = x (x - 4)

For two distinct real roots: Δ > 0

x (x - 4) > 0

x > 0 or x > 4

For two real roots: Δ ≥ 0

x (x - 4) ≥ 0

x ≥ 0 or x ≥ 4

For a repeated root: Δ = 0

x (x - 4) = 0

x = 0 or x = 4

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