12x-4
————
2

Simplify

The average rate of change of the function over the interval is -6

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

The graph

The interval is given as

From x = 2 to x = 4

The function is a quadratic function

This means that it does not have a constant average rate of change

So, we have

f(2) = -3

f(4) = -15

Next, we have

Rate = (-15 + 3)/(4 - 2)

Evaluate

Rate = -6

Hence, the rate is -6

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To find the discount on $215 worth of merchandise with a 15% discount, you can use the following steps:

1. Calculate the discount amount as a percentage of the original price:

discount amount = original price x discount rate

discount amount = $215 x 0.15

discount amount = $32.25

2. Subtract the discount amount from the original price to find the sale price:

sale price = original price - discount amount

sale price = $215 - $32.25

sale price = $182.75

Therefore, the discount on $215 worth of merchandise with a 15% discount is $32.25. The sale price after the discount is $182.75.

Answer:

112.5

Step-by-step explanation:I got it right on the assignment no joke. I don't answer questions for the points but to help people out there who have no clue on what to do.

Answer:

x=-1

Step-by-step explanation:

4x+35x-15=9x-45
39x-15=9x-45
39x-9x=-45+15
30=+-30
x=-1

Answer:

\( \sf \: x = - 1\)

Step-by-step explanation:

Given equation,

→ 4x + 5(7x - 3) = 9(x - 5)

Now the value of x will be,

→ 4x + 5(7x - 3) = 9(x - 5)

→ 4x + 35x - 15 = 9x - 45

→ 39x - 15 = 9x - 45

→ 39x - 9x = -45 + 15

→ 30x = -30

→ x = -30 ÷ 30

→ [ x = -1 ]

Hence, the value of x is -1.

The correct answer is March, as it was the month in which the average number of hours worked by the website designers was closest to 50 hours.

A month is a unit of time typically consisting of 30 or 31 days. It is used for measuring periods of time, for example, when we say something happened "a month ago". Months are used in both the Gregorian calendar and the Julian calendar.

This data was gathered from a survey of website designers, which was conducted to determine the average number of hours each month that these professionals spent working.

In January, the average number of hours worked was 46.5. In February, it was 48.8. However, in March, the average number of hours worked was 49.4, which was the closest to 50 hours. This was followed by April, in which the average was 49.7.

Overall, it can be concluded that March was the month in which the average number of hours worked by website designers was closest to 50 hours. This is important data for website designers, as it allows them to understand the amount of time they should be spending on their work in order to be successful. It also helps employers gauge the workload of their website designers and ensure they are providing an adequate amount of work.

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Answer:

Min: 1

Q1: 2
Median: 7
Q3: 9
Max: 11.5

Step-by-step explanation:

The five bars of the box plot correspond (from left-to-right) to the numbers in the five-number summary.

The first bar represents the minimum, which in this case is 1.

The second bar represents the first quartile (Q1), which in this case is 2.

The third bar represents the median, which in this case is 7.

The fourth bar represents the third quartile (Q3), which in this case is 9.

And the fifth bar represents the maximum, which in this case is 11.5.

Answer:

Min: 1

Q1: 2

Median: 7

Q3: 9

Max: 11.5

Step-by-step explanation:

I hope it helps:)

The two column proof showing that  ΔWXZ ≅ ΔYXZ is as shown below

From the given triangle, we see that;

Given: WX ≅ XY, XZ bisects WXY

Prove: ΔWXZ ≅ ΔYXZ

The two column proof for the above is as follows;

Statement 1;  WX ≅ XY, XZ bisects 2

Reason 1; Given

Statement 2: ∠WXZ ≅ YXZ

Reason 2; Angle bisector

Statement 3; XZ ≅ XZ

Reason 3: Reflexive property of congruence

Statement 4:  ΔWXZ  ≅ ΔYXZ

Reason 4:  SAS Congruence Postulate

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1. The equation that represents distance Jamie will run in kilometers (d) at a rate of r kilometers per hour is d = 0.5r

2. The distance Jamie will run if he chooses a rate of 8 kilometers per hour is 4 Km

Speed is the distance travelled per unit. Mathematically, it can be expressed as:

Speed = distance / time

with the above formula, we give the various answers to questions. Details below

Speed = distance / time

r = d / 0.5

Cross multiply

d = r × 0.5

d = 0.5r

Thus, the equation to determine the distance travelled is d = 0.5r

Using the equation d = 0.5r, we can determine the distance travelled at a rate of 8 Km/h as illustrated below:

d = 0.5r

d = 0.5 × 8

d = 4 Km

Thus, the distance travelled at a rate of 8 Km/h in 1/2 hour is 4 km

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Based on the limited information provided, it is not possible to definitively determine the type of economy in Country A. More specific details and factors would be necessary to make a conclusive determination.

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

To find the quotient of z₁ by z₂ in trigonometric form, we'll express both complex numbers in trigonometric form and then divide them.

Let's represent z₁ in trigonometric form as z₁ = r₁(cosθ₁ + isinθ₁), where r₁ is the magnitude of z₁ and θ₁ is the argument of z₁.

We have:

z₁ = 7(cos(577°) + i sin(577°))

Now, let's represent z₂ in trigonometric form as z₂ = r₂(cosθ₂ + isinθ₂), where r₂ is the magnitude of z₂ and θ₂ is the argument of z₂.

From the given information, we have:

z₂ = 21(cos(-7°) + i sin(-77°))

To find the quotient, we divide z₁ by z₂:

z₁ / z₂ = (r₁/r₂) * [cos(θ₁ - θ₂) + i sin(θ₁ - θ₂)]

Substituting the given values, we have:

z₁ / z₂ = (7/21) * [cos(577° - (-7°)) + i sin(577° - (-7°))]

= (7/21) * [cos(584°) + i sin(584°)]

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

Option C, 21(cos(-7°) + i sin(-77°)), is not the correct answer as it does not represent the quotient of z₁ by z₂.

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By applying the features of polynomials, the quadratic function g(x) = (1/5) · x² - 2 · x + 21/5 passes through the points (x₁, y₁) = (-8, 33), (x₂, y₂) = (2, 1) and (x₃, y₃) = (8, 1).

Polynomials are algebraic expressions of the form \(\sum \limits_{i=0}^{n} c_{i}\cdot x^{i}\), where \(c_{i}\) is the i-th coefficient of the polynomial and n is the grade of the polynomial. In addition, we know that polynomials have n + 1 coefficients.

In the case of quadratic functions, the grade is 2 and the function have three coefficients. Hence, we need three distinct points to determine all the coefficients of a quadratic function.

(x₁, y₁) = (-8, 33)

64 · a - 8 · b + c = 33     (1)

(x₂, y₂) = (2, 1)

4 · a + 2 · b + c = 1     (2)

(x₃, y₃) = (8, 1)

64 · a + 8 · b + c = 1     (3)

Then, we find the solution of this system of linear equations:

a = 1/5, b = -2, c = 21/5

By applying the features of polynomials, the quadratic function g(x) = (1/5) · x² - 2 · x + 21/5 passes through the points (x₁, y₁) = (-8, 33), (x₂, y₂) = (2, 1) and (x₃, y₃) = (8, 1).

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Step-by-step explanation:

x=7 (given)

2x=14 (divide)

2x+5-5=19-5 (subtraction property of equality)

2x/2=14/2 (divide)

2x + 5=19 (division property of equality)

the length of th diagonal is 10√2

side length = 10 inches

We need an illustration to solve the question:

Using pythagoras' theorem:

Hypotenuse² = opposite² + adjacent²

hypotenuse = diagonal

opposite = 10 in, adjacent = 10 in

diagonal² = 10² + 10²

diagonal² = 100 + 100

diagonal² = 200

diagonal = √200

diagonal = 10√2

Hence, the length of th diagonal is 10√2

Using linear function you would need to cross the bridge 30 times for the costs of the two toll options to be the same.

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Rewriting 4 x 3/6 as the product of a unit fraction and a whole number is: 12 * 1/6

The parameters are given as:

Number - 4

Fraction - 3/6

The following steps can be used to determine the product as the product of a whole number and a unit fraction:

Step 1 - Remember the whole number are those numbers that involve all positive integers and zero.

Step 2 - Also remember that the unit fraction is nothing but a fraction whose numerator is 1.

Step 3 - Write the given expression.

4 * 3/6

Step 4 - Convert the given fraction into a unit fraction by multiplying 4 by 3 in the above expression.

4 * 3 * 1/6

Step 5 - Simplify the above expression.

12 * 1/6

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Interpreting the situation, it is found that Marjorie will have 240 left after paying her penalty.

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

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If a number is divisible by 4 and 7, the number must have at least six factors. What are they?

we know that

(4)(7)=(2^2)(7)=28

so

the factors are

1

2

2^2=4

7

2(7)=14

4(7)=28

therefore

the answer is

Answer:

70,79

Step-by-step explanation:

jwhsbsvevshwksksnbs

Answer:

A b and c

Step-by-step explanation:

D might be true but i am not sure

Answer:

192 times

Step-by-step explanation:

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75

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176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200  - 31 times

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351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375

376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400  - 71 times

401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425

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476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500  - 91 times

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626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650

651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675

676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700  - 131 times

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751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775

776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800  - 151 times

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851 852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 870 871 872 873 874 875

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951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975

976 977 978 979 980 981 982 983 984 985 986 987 988 989 990 991 992 993 994 995 996 997 998 999 1000  - 192 times

The given statement is true.

Step-by-step explanation:

The order of the numbers doesn't matter, so we'll use combinations instead of permutations.  The number of combinations is:

₄₅C₈ = 215,553,195

So the probability of a ticket having the winning combination is 1 / 215,553,195.

The expected value to the state is:

E(X) = 10,000 (1) ($2) + 10,000 (1 / 215,553,195) (-$1,000,000)

E(X) = $19954

The expected value to you is:

E(X) = 10,000 (1) (-$2) + 10,000 (1 / 215,553,195) ($1,000,000)

E(X) = -$19954

The total distance travelled by the body is 48 meters

According to the question we have been given an equation of the position of  a body moving along x-axis as

                    s = t³ - 12t² + 36t

where,    s = distance in meters

             t = time in seconds

We need to find the total distance traveled by the body from t=0s to t=4s

The formula for the total distance is given as :

            S = |s(1) - s(0)| + |s(2) - s(1)| + |s(3) - s(2)| + |s(4) - s(3)|

Now we will find out the distance travelled in time 0s to 4s

when t = 0s ,  s = (0)³ - 12(0)² + 36*0

                         = 0m

         t = 1s ,  s = (1)³ - 12(1)² + 36*1

                         =  25m

         t = 2s ,  s = (2)³ - 12(2)² + 36*2

                         =  32m

         t = 3s , s = (3)³ - 12(3)² + 36*3

                         = 27m

         t = 4s , s = (4)³ - 12(4)² + 36*4

                         = 16m

Putting the required values in the above formula we get ,

  S = |25-0|+|32-25|+|27-32|+|16-27|

  S = 25 + 7 + 5 + 11 meters

   S = 48 meters

Hence the total distance travelled by the body is 48 meters

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Therefore , the solution of the given problem of area comes out to be

r = 8.

The term "area" describes the amount of space occupied by a 2D form or surface. We use cm2 or m2 as our units for measuring area. A shape's area is determined by dividing its length by its breadth.

Here,

A 90 degree sector occupies 1/4 of a circle, which has 360 degrees. Consequently, the area of the whole circle can be written as

Sector Size/Sector Area = Circle Area/360

16 ft2/90 = n/360

(360) (16 ft2)/90 = n

(4)(16 ft2) = n

The total size of the circle is n = 64 ft2.

Since Area of a Circle equals r2,

∏r2 = 64

r2 = 64/∏

r = √(64/∏)

We multiply by / to get by rationalizing the denominator.

r = √(64∏)/√(∏2) Then using the denominator's square root, we can obtain the solution of

r = √(64∏)/∏

r = 8

Therefore , the solution of the given problem of area comes out to be

r = 8.

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Answer:

6.6

Step-by-step explanation:

40/6=6.6

We can represent the elevation of Death Valley as 282 feet above sea level, using the absolute value to convert the negative value to a positive integer.

One way to use absolute value to represent the elevation of Death Valley as a positive integer is to take the absolute value of the negative elevation. Absolute value is a mathematical function that returns the magnitude of a number without considering its sign.

In this case, the elevation of Death Valley is -282 feet, but the absolute value of -282 is 282. Therefore, we can represent the elevation of Death Valley as 282 feet above sea level, using the absolute value to convert the negative value to a positive integer.

that this representation does not change the actual elevation of Death Valley, but it is a way to express the same information using a positive integer.

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