what is the first word

Answer:

$2520

Step-by-step explanation:

→ Work out the area of the drive way

18 m × 4 m= 72 m²

→ Multiply the area by the cost per square metre

72 m² × $35 = $2520

The cost of paving a driveway that is 18m long and 4 m wide, if the paving costs $35 per square metre is $2520.

To calculate the cost of paving the driveway, you need to find the total area of the driveway and then multiply it by the cost per square meter.

The total area of the driveway can be calculated using the formula:

Area = length × width.

Given that the driveway is 18 meters long and 4 meters wide, the area would be:

Area = 18m × 4m

Area = 72 square meters.

Now,  find the cost of paving the driveway by multiplying the area by the cost per square meter:

Cost = Area × Cost per square meter

Cost = 72 square meters × $35/square meter

Cost = $2520.

So, the cost of paying the driveway would be $2520.

To learn more on Area click:

https://brainly.com/question/20693059

#SPJ4

The rectangle which should go in position I is rectangle A.

We are given that;

The rectangles A,B,C and D with numbers

Now,

To take the same the number of side

If we take A on 1 place

F will be on second place

And  B will be on 4th place

Therefore, by algebra the answer will be rectangle A.

More about the Algebra link is given below.

brainly.com/question/953809

#SPJ1

Answer:

B

Step-by-step explanation:

The equation of the line would be y = (-3/4)x + 5.

What is the slope-point form of the line?

For the line having slope "m" and the point (x1, y1) the equation of the line passing through the point (x1, y1) having slope 'm' would be

                      y - y1 = m(x - x1)

The given equation is \(y=-\frac{3}{4}x-17\)

The required line is parallel to the given line.

and we know that the slopes of the parallel lines are equal so the slope of the required line would be m = -3/4

And the required line passes through (8, -1)

so by using slope - point form of the line,

      y - (-1) = (-3/4)(x - 8)

      y + 1 = (-3/4)x - (-3/4)8

       y + 1 = (-3/4)x + 24/4

       y = (-3/4)x + (12/2 - 1)

       y = (-3/4)x + 5

Hence, the equation of the line would be y = (-3/4)x + 5.

To learn more about slope - point form of the line, visit:

https://brainly.com/question/24907633

#SPJ1

a. the factors of equation is \(f(x)=(x-1)(x-10)(2x-3)\)

b. the factors of equation is \(f(x)=(x-1)(x^2+x+4)\)

A polynomial is an expression consisting of variables and coefficients that involves only the operations of addition, subtraction, and multiplication, with non-negative integer exponents.

a. Given function,

\(f(x)=2x^3 -25x^2 + 53x - 30\)

By using trial and error method, put values of x =1, x= 10, and x= 3/2 are satisfied values for above function,

\(f(x)=(x-1)(x-10)(2x-3)\)

therefore, the factors of equation is (x-1) (x-10) (2x-3)

b. Given function,

\(f(x)=x^3 +3x - 4\)

Similarly using trial and error method,

\(f(x)=(x-1)(x^2+x+4)\)

therefore, the factors of equation is (x-1) (x² + x + 4)

To know more about expression, visit:

https://brainly.com/question/1859113

#SPJ1

Factor of given polynomials are a. (x-1)(x-10)(2x-3), b. (x-1)(x² + x + 4) .

In mathematics, a polynomial is an expression that consists of variables and coefficients, combined using the operations of addition, subtraction, and multiplication, but not division by a variable. The variables in a polynomial can only have non-negative integer exponents.

Polynomials can have different degrees, which is the highest power of the variable in the expression. For example, the polynomial 3x² - 5x + 2 is a quadratic polynomial, since its highest power of x is 2. If the degree of a polynomial is n, then it has at most n roots, which are the values of x that make the polynomial equal to zero.

Polynomials are used in many areas of mathematics and science, including algebra, calculus, physics, and engineering. They are used to model and analyze many different types of phenomena, such as motion, population growth, and electrical circuits.

Polynomials can also be added, subtracted, and multiplied together to form new polynomials. Additionally, polynomials can be factored, which involves breaking them down into simpler polynomials that multiply together to give the original polynomial.

a) f(x)= 2x³ - 25x² + 53x - 30
⇒(x-1)(x-10)(2x-3)

b) f(x)= x³ + 3x - 4
⇒(x-1)(x² + x + 4)

To know more about factor visit:

https://brainly.com/question/26354419

#SPJ1  

The complete question is:

Answer:

The values of \(r_{2}\) and \(\alpha_{2}\) are 2 and 150º.

Step-by-step explanation:

The complete statement is:

Find \(\alpha_{2}\) and \(r_{2}\) such that  \(\sin \theta - \sqrt{3}\cdot \cos \theta = r_{2}\cdot \cos (\theta - \alpha_{2})\).

We proceed to use the following trigonometric identity:

\(\cos (\theta - \alpha_{2}) = \cos \theta \cdot \cos \alpha_{2} +\sin \theta \cdot \sin \alpha_{2}\) (1)

\(\sin \theta -\sqrt{3}\cdot \cos \theta = r_{2}\cdot \cos \theta \cdot \cos \alpha_{2}+r_{2}\cdot \sin \theta \cdot \sin \alpha_{2}\)

By direct comparison we derive these expressions:

\(r_{2}\cdot \sin \alpha_{2} = 1\) (2)

\(r_{2}\cdot \cos \alpha_{2} = -\sqrt{3}\) (3)

By dividing (2) by (3), we have the following formula:

\(\tan \alpha_{2} = -\frac{1}{\sqrt{3}}\)

\(\tan \alpha_{2} = -\frac{\sqrt{3}}{3}\)

The tangent function is negative at second and fourth quadrants. That is:

\(\alpha_{2} = \tan^{-1} \left(-\frac{\sqrt{3}}{3} \right)\)

There are at least two solutions:

\(\alpha_{2,1} = 150^{\circ}\), \(\alpha_{2,2} = 330^{\circ}\)

And the value of \(r_{2}\):

\(r_{2}^{2}\cdot \sin^{2}\alpha_{2} + r_{2}^{2}\cdot \cos^{2}\alpha_{2} = 4\)

\(r_{2}^{2} = 4\)

\(r_{2} = 2\)

The values of \(r_{2}\) and \(\alpha_{2}\) are 2 and 150º.

Answer:

13

Step-by-step explanation:

1+1=2

1+2=3

2+3=5

3+5=8

8+blank=21

21-8=13

Answer:

13

1+1=2+3=5+8=13+21=...

Answer:

71

Step-by-step explanation:

2n-1=141

2n=142

n=71

Answer:

speed=24km/h or 6.67m/s

Step-by-step explanation:

Given data:

time taken = t =43 hours

distance covered = d = 1032 km

to find:

speed of the ship = v =?

solution:

as we know that speed is defined as the distance covered by an object in unit time.Formula

speed = distance covered /time taken

speed = 1032km/43hours

speed =24km/h or in international system of units the answer is 6.67m/s

The number of schedules that are possible, considering each case and the Fundamental Counting Theorem, is given as follows:

a) No restrictions: 3,628,800.

b) Last two games against the same team: 362,880.

The Fundamental Counting Principle states that if there are n independent trials, each with \(n_1, n_2, \cdots, n_n\) possible results, the total number of outcomes is calculated by the multiplication of the factorials as presented as follows:

\(N = n_1 \times n_2 \times \cdots \times n_n\)

Teams play each other only once during the season, hence, if there are no restrictions, the parameters are given as follows:

\(n_1 = 10, n_2 = 9, \cdots, n_{10} = 1\)

Hence the number of schedules is:

N = 10! = 10 x 9 x 8 x ... x 1 = 3,628,800.

If the last game is fixed, then the remaining games are an arrangements from 9 games, and thus the number of schedules is:

N = 9! = 362,880.

More can be learned about the Fundamental Counting Theorem at https://brainly.com/question/15878751

#SPJ1

Answer:

terminal point is at (0, -1) and sin 0 = -1

Step-by-step explanation:

In a unit circle the radius of the circle is 1 so

- we know the points where the circle intersects the x-axis and y-axis as a (x , y) coordinates.

(1, 0) where we start on the positive x-axis and where angle is 0°

(0, 1) where we go counterclockwise and where angle is 90°

(-1, 0) where we go continue counterclockwise and where angle is 180°

(0, -1) where we stop in our problem because the angle is 270°

-we also know that x= cos O and y= sin O so the coordinates (x, y) are really

(cos O, sinO)

Given:

        0 = 270°

    sin 0 = sin 270°

sin 270°  =  -1

The terminal point is at (0, -1) and sin 0 = -1

Consider the function f: Z → S defined as f(x) = 2x for every integer x ∈ Z. This function maps each integer to its corresponding even integer. For example, f(1) = 2, f(-1) = -2, and so on. To show that f is a bijection, we need to prove that it's both injective (one-to-one) and surjective (onto).
1. Injective: If f(x1) = f(x2), then 2x1 = 2x2. Dividing both sides by 2, we get x1 = x2. Thus, f is injective.
2. Surjective: For any even integer y ∈ S, there exists an integer x ∈ Z such that f(x) = y. Since y is even, y = 2x for some x ∈ Z. Thus, f(x) = 2x = y, and f is surjective.

To prove that set s, which is the set of even integers, is epicardial with set z, we need to show that there exists a one-to-one correspondence between the two sets.
We can define a function f: z → s as f(x) = 2x. This function maps each integer in z to its corresponding even integer in s.

To show that f is one-to-one, we need to show that if f(x) = f(y), then x = y. Suppose f(x) = f(y). This means that 2x = 2y, which implies that x = y. Therefore, f is one-to-one.

To show that f is onto, we need to show that for every element y in s, there exists an element x in z such that f(x) = y. Since y is an even integer, we can write it as y = 2x for some integer x. Therefore, f(x) = y, and f is onto.

Since f is one-to-one and onto, it is a bijection, which means that there exists a one-to-one correspondence between sets s and z. Therefore, s is epicardial with z.

Learn more about Function:

brainly.com/question/12431044

#SPJ11

Answer:

.363

Step-by-step explanation:

I believe that the answer is .363, I didn't round anything

Answer:

The answer is letter C.

I hope it help

The symbol ∠ is used to denote an angle. The symbol m ∠ is sometimes used to denote the measure of an angle.

x = 15

∠H = 82

∠I = 49

∠G = 49

Note that side HG and side HI are congruent ( indicated by the little dashed line ) which means that their opposite angles are congruent ( ∠I and ∠G to be more specific. )

Angles in a triangle add up to equal 180°

Hence, 3x + 37 + 2 ( 4x - 11 ) = 180 ( note that the 2 in 2(4x - 11) came from angles I and G being congruent )

We now solve for x

3x + 37 + 2 ( 4x - 11 ) = 180

step 1 distribute the 2 to the 4x and -11

2 + 4x = 8x

-11 * 2 = -22

we now have 3x + 37 + 8x -22 = 180

step 2 combine like terms

3x + 8x = 11x

37 - 22 = 15

we now have 11x + 15 = 180

step 3 subtract 15 from each side

15 - 15 cancels out

180 - 15 = 165

we now have 11x = 165

step 4 divide each side by 11

11x / 11 = x

165 / 11 = 15

we're left with x = 15

Our final step is to find the measures of ∠G, ∠H and ∠I

We can do this by simply replacing x with 15 in their given expression

∠H = 3x + 37

* substitute 15 with x *

3 ( 15 ) + 37

3 * 15 = 45

45 + 37 = 82

Hence, ∠H = 82

∠I = 4x - 11

* substitute x with 15 *

4(15) - 11

4 * 15 = 60

60 - 11 = 49

Hence, ∠I = 49

Like stated previously ∠G and ∠I are congruent

Hence, ∠G = 49

To learn more about Angle refer to:

https://brainly.com/question/28420303

#SPJ1

Answer:

Angle 1- 36

Angle 2- 90

Angle 3- 54

Angle 4- 36
Angle 5- 90

Angle 6- 54

Angle 7- 128

Angle 8- 54

Angle 9- 128

Angle 10- 54

Angle 11- 36

Angle 12- 144

Angle 13- 36
Angle 14- 144

Lets simplify

\(\\ \sf\longmapsto \dfrac{x}{3}=-7.\dfrac{x}{3}\)

\(\\ \sf\longmapsto \dfrac{x}{3}=\dfrac{-7x}{3}\)

\(\\ \sf\longmapsto -7\)

Hence its not a fraction

Answer: 5.7

Step-by-step explanation: Add up the numbers 12.5+5.7+18.2 and subtract by 30.7 to get 5.7

Answer:

=6

Step-by-step explanation:

It will take 56 days for the lilypad to cover the entire pond. On day 28, the lilypad covers 1/2 of the pond, as we saw earlier.

The lilypad doubles in size each day, which means that if it covers a certain fraction of the pond on day n, it will cover twice that fraction on day n+1. In other words, if the lilypad covers 1/2^k of the pond on day k, then it will cover 1/2^(k-1) of the pond on day k+1.

If we let n be the number of days it takes for the lilypad to cover the entire pond, then we can say that on day n-28, the lilypad covers 1/2 of the pond (since on day n-28, the lilypad will be half the size of what it is on day n). Therefore, we want to solve for n-28 when the lilypad covers the entire pond, which is equivalent to the lilypad doubling in size 28 times:

1/2 * 2^28 = 2^(28-n+28)

Simplifying, we get:

2^(n-28) = 2^28

Taking the logarithm base 2 of both sides, we get:

n-28 = 28

Solving for n, we get:

n = 56

Therefore, it will take 56 days for the lilypad to cover the entire pond. On day 28, the lilypad covers 1/2 of the pond, as we saw earlier.

Learn more about "Fraction" : https://brainly.com/question/30154928

#SPJ11

Answer:

it would be 10 soccer balls

Step-by-step explanation:

10 every week if it was constant (because they could've sold more one week then less the next) but the genuine answer is 10 soccer balls :)

Using visual interpretation of the plot trend, the scatter plot shows positive correlation.

A positive correlation is depicted by a positive slope or trend line on a scatter plot. The trend of the scatter plot slopes upward which establishes a positive association.

If the slope is otherwise negative, such that the trend line slopes downward, then we have a negative association or relationship.

Therefore, the scatter plot shows positive relationship.

Learn more on scatter plot:https://brainly.com/question/6592115

#SPJ1

Answer:

i think it is d and b

Step-by-step explanation:

Answer:

-8

Step-by-step explanation:

Create this equation into a y=mx+b form

8x-3y=24

-8x       -8x           -8 to solve for -3y

-3y=-8x+24

----    ---   ---              divide by -3 to leave y by itself

-3      -3   -3

y= 8

    --- x-8

     3

y intercept is -8

Answer: −8

Step-by-step explanation:

Subtract 8x from both sides of the equation.

−3y=24−8x

Divide each term by −3 and simplify.

y=8x/3−8

Reorder terms.

y=8/3x−8

Y-INTERCEPT = -8

The mood of the categorical syllogism in example 2 is AIO.

In your example, we have the following premises and conclusion:

1. Major Premise: No dogmatists are scholars who encourage free thinking.
2. Minor Premise: Some theologians are scholars who encourage free thinking.
3. Conclusion: Some theologians are not dogmatists.

The major premise in example 2 is an A proposition (All S are not P). The minor premise in example 2 is an I proposition (Some S are P). The conclusion in example 2 is an O proposition (Some S are not P).

To learn more about premises, refer here:

https://brainly.com/question/29699382#

#SPJ11

I hope this help you

The blocks in this design are c. the four different litters. The pigs within each litter were grouped together as a block, and the three dietary supplements were randomly assigned to the two pigs within each block.

This helps control for any variation between litters that could affect the results of the feed trial. The 24 identical pens are not the blocks in this design, but rather the units where the treatments were applied.

A litter is defined as the live birth of several young at once in an animal from the same mother and typically from the same pair of parents, especially three to eight young. The term is most frequently used to refer to the offspring of mammals, although it can also refer to any animal that bears numerous offspring.

Learn more about blocks here brainly.com/question/23780656

#SPJ4

Answer:

Student 2 only

Step-by-step explanation:

Given that:

The written antiderivatives formulas by the students for k sin (kx), where  k > 1 are:

Student 1 : \(\int (k \ sin (kx)) \ dx= k^2 \ cos (kx) + C\)

Student 2: \(\int (k \ sin (kx) ) \ dx = - cos (kx) + C\)

The student that wrote the correct anti-derivate formula is Student 2 only.

This is because:

Suppose:

\(I = \int (k \sin (kx) ) \ dx\) where; k > 1

This implies that:

\(I = \int (k \sin (kx) ) \ dx\)

\(I =k \bigg ( \dfrac{-cos (kx)}{k} \bigg) + C\)   because \(\int sin (ax) \ dx = \dfrac{-cos (ax)}{a}+C\)

here;

C = constant of the integration

∴

I = - cos (kx) + C  which aligns with the answer given by student 2 only.