8 divided by 2 (2+2). 1 or 16

Answer:

7x ( - x + 5 )

Step-by-step explanation:

- 7x² = 7x × - x

35x = 7x × 5

- 7x² + 35x = 7x ( - x + 5 )

Answer:

20 rational. 5/6 rational. square root of 20 is irrational. d is irrational

Step-by-step explanation:

bc its an integer.  5/6 can be written in p/q form, where p and q are integers and q is a non-zero number.  not a whole number. its a non terminating number

Answer:

m+g≤40

12m+14g≥250

Step-by-step explanation:

The sum of hours spent mowing (m) and hours spent panting (g) per week must be no more than 40 (that is, less than or equal to 40):

m+g≤40

The amount of money made by mowing is the amount of hours spent mowing multiplied by the amount of money paid per hour: 12m

The amount of money made by planting is the amount of hours spent planting multiplied by the amount of money paid per hour: 14g

The sum of the money from mowing (12m) and from planting (14g) must be at least $250 (that is, equal to or more than 250):

12m+14g≥250

Answer: 2.5 inches

Step-by-step explanation: 17 1/2 divided by 7

Answer:

(1, -2)

Step-by-step explanation:

There are two ways:

1. You can find the answe by looking at where the lines intercept

2. Plug in each answer into the locations they're supposed to be in, for example, (1, 2) x=1 and y=2, and if the end result it 0=0 its correct.

Hope that helped!

Answer:

x=1 4/3

Step-by-step explanation:

The equation which describes the relationship between the side length and shaded area of the quilt is y=0.5x²

Side length, x = 1,3,4,5,8

Shaded Area, y = 0.5, 4.5, 8, 12.5, 32

The relationship can be modeled as a quadratic function. Using a graphing calculator for the quadratic function written in the form y = ax² + bx + c

a = 0.5 ; b = 0 ; c = 0

Therefore, the quadratic function can be written as y = 0.5x²

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Answer:

f(x) = x³ - 4x + 6

f'(x) = 3x² - 4

a) f'(2) = 3(2²) - 4 = 12 - 4 = 8

6 = 8(2) + b

6 = 16 + b

b = -10

y = 8x - 10

b) 3x² - 4 = 0

3x² = 4, so x = ±2/√3 = ±(2/3)√3

= ±1.1547

f(-(2/3)√3) = 9.0792

f((2/3)√3) = 2.9208

c) 3x² - 4 = 8

3x² = 12

x² = 4, so x = ±2

f(-2) = (-2)³ - 4(-2) + 6 = -8 + 8 + 6 = 6

6 = -2(8) + b

6 = -16 + b

b = 22

y = 8x + 22

f(2) = 6

y = 8x - 10

The equation perpendicular to the tangent is y = -1/8x + 25/4

-The smallest slope on the curve is 2.92

The curve has the smallest slope at the point (1.15, 2.92)

The equations at tangent points are y = 8x + 16 and  y = 8x - 16

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

y = x³ - 4x + 6

Differentiate

So, we have

f'(x) = 3x² - 4

The point is (2, 6)

So, we have

f'(2) = 3(2)² - 4

f'(2) = 8

The slope of the perpendicular line is

Slope = -1/8

So, we have

y = -1/8(x - 2) + 6

y = -1/8x + 25/4

We have

f'(x) = 3x² - 4

Set to 0

3x² - 4 = 0

Solve for x

x = √[4/3]

x = 1.15

So, we have

Smallest slope = (√[4/3])³ - 4(√[4/3]) + 6

Smallest slope = 2.92

So, the smallest slope is 2.92 at (1.15, 2.92)

Here, we set f'(x) to 8

3x² - 4 = 8

Solve for x

x = ±2

Calculate y at x = ±2

y = (-2)³ - 4(-2) + 6 = 6: (-2, 0)

y = (2)³ - 4(2) + 6 = 6: (2, 0)

The equations at these points are

y = 8x + 16

y = 8x - 16

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(i) The first term (a) is 24 and the common difference (d) is -2.

(ii) The sum of the progression is 2520.

i) Finding the first term and common difference:

Given that the number of terms in the arithmetic progression is 40 and the last term is -54, we can use the formula for the nth term of an arithmetic progression to find the first term (a) and the common difference (d).

The nth term formula is: An = a + (n-1)d

Using the given information, we can substitute the values:

-54 = a + (40-1)d

-54 = a + 39d

We also know that the sum of the first 15 terms added to the sum of the first 30 terms is zero:

S15 + S30 = 0

The sum of the first n terms of an arithmetic progression can be calculated using the formula:

Sn = (n/2)(2a + (n-1)d)

Substituting the values for S15 and S30:

[(15/2)(2a + (15-1)d)] + [(30/2)(2a + (30-1)d)] = 0

Simplifying the equation:

15(2a + 14d) + 30(2a + 29d) = 0

30a + 210d + 60a + 870d = 0

90a + 1080d = 0

a + 12d = 0

a = -12d

Substituting this value into the equation -54 = a + 39d:

-54 = -12d + 39d

-54 = 27d

d = -2

Now we can find the value of a by substituting d = -2 into the equation a = -12d:

a = -12(-2)

a = 24

Therefore, the first term (a) is 24 and the common difference (d) is -2.

ii) Finding the sum of the progression:

The sum of the first n terms of an arithmetic progression can be calculated using the formula:

Sn = (n/2)(2a + (n-1)d)

Substituting the values:

S40 = (40/2)(2(24) + (40-1)(-2))

S40 = 20(48 - 39(-2))

S40 = 20(48 + 78)

S40 = 20(126)

S40 = 2520

Therefore, the sum of the arithmetic progression is 2520.

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a) On Monday, the total number of muffins that the baker makes is, proportionately, 90.

b) On Tuesday, the number of blueberry muffins that the baker makes is 24, which is 40% of 60.

Proportion is the equation of two ratios.

Proportional values are depicted as fractions, decimals, or percentages.

Monday:

The percentage of blueberry muffins to the total number of muffins made daily = 40%

The number of blueberry muffins the baker makes = 36

40% = 36

Proportionately, 100% = 90 (36 ÷ 0.4)

Thus, the total number of muffins that the baker makes on Monday = 90.

Tuesday:

The total number of muffins made = 60

The number of blueberry muffins = 24 (60 x 0.4)

Thus, proportionately, on Tuesday, the number of blueberry muffins, which represents 40% of 60, is 24.

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The number of blueberry muffins that a baker makes each day is 40% of the total number of muffins she makes.

Answer:

1384.7

Step-by-step explanation:

42/2     21^2x3.14=1384.74

Hope this Helps :)

a) The opposite of the numbers 3, 7.5, and -2(2/3) will be 0.33, 0.133, and -0.375.

b) The sum of the given number and its opposite will be 7.928.

It is defined as the numbers in all real numbers which cannot be represented as rational numbers, in other words, the irrational number cannot be expressed in the form of p/q form.

A rational number is a sort of real number that has the form p/q and does not equal zero.

The given number is as,

3, 7.5, and -2(2/3)

a)

The opposite number is obtained as 1 by dividing the given number,

⇒ 1 / 3 = 0.33

⇒ 1 / 7.5 = 0.133

⇒ 1 / -2(2/3) = -0.375

b)

The sum of the given number and its opposite is,

= 3+0.33 + 7.5 + 0.133+ (-2(2/3) ) + (-0.375)

= 7.928

Thus, the opposite of the numbers 3, 7.5, and -2(2/3) will be 0.33, 0.133, and -0.375.and the sum of the given number and its opposite will be 7.928.

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Let \(e\) and \(r\) be the number of elves and reindeers, respectively.

We know that:

\(r+e=14\) (so far 14 of them have arrived)

\(4r+2e = 38\)(each reindeer has 4 legs and each elf has two)

If we multiply the first equation by 2 we have \(2r+2e=28\), and if we subtract this equation from the second we have \(2r=10\) which implies \(r=5\).

So, there are 5 reindeers and 9 elves (remember that they have to sum up to 14).

The number of reindeers is 5 and the number of elves is 9.

Two equations can be derived from the equation:

e + r = 14 equation 1

2e + 4r = 38 equation 2

Where:

e = number of elves at the meeting

r = number of reindeers at the meeting

In order to determine the value of r, multiply equation 1 by 2.

2e + 2r = 28 equation 3

Subtract equation 3 from 2

2r = 10

Divide both sides of the equation by 2

r = 5

To solve for e substitute for r in equation 1

5 + e = 14

e = 14 - 5

e = 9

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The correct statement regarding the inverse function of f(x) = 4x^4 is given as follows:

\(f^{-1}(x) = \pm \left(\frac{x}{4}\right)^{\frac{1}{4}}\); f^(-1)(x) is not a function.

The function in this problem is defined as follows:

f(x) = 4x^4.

To obtain the inverse of a function y = f(x), first the variables y and x are exchanged, as follows:

x = 4y^4.

Isolating the variable y, we have that:

y^4 = (x/4).

The inverse operation of the fourth power is the fourth root, hence:

\(y = \pm \sqrt[4]{\frac{x}{4}}\)

\(f^{-1}(x) = \pm \sqrt[4]{\frac{x}{4}}\)

\(f^{-1}(x) = \pm \left(\frac{x}{4}\right)^{\frac{1}{4}}\)

The plus/minus symbol means that for each input of x, the inverse function gives two outputs, meaning that there are multiple outputs mapped to each input, and thus the inverse is not a function.

This means that the second statement is correct.

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Answer:

55/4

Step-by-step explanation:

The method is: Find the increase and find the ratio of the increase and the old price.

The percentage increase is 20%

A percentage is defined as the ratio that can be expressed as a fraction of 100.

The method below shows how you would calculate the % increase.

First step: Find the increase:

increase = 480 - 400 = $80

Second step: Find the ratio of the increase and the old price and multiply by 100 to express in percentage:

80/400 * 100 = 20%

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Answer:

8(3+4p)

Step-by-step explanation:

8 goes into 24 and 32, so it can be factored out:

\(24+32p=8(3+4p)\)

Answer:

8(3 + 4p)

Step-by-step explanation:

Factor 24 + 32p

First, factor out the GCF. In this case, the GCF is 8, and we have

8(3 + 4p)

We can't factor anymore so the answer is 8(3 + 4p)

\(~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-3}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{8}~,~\stackrel{y_2}{-6})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{(~~8 - (-3)~~)^2 + (~~-6 - 0~~)^2} \implies d=\sqrt{(8 +3)^2 + (-6)^2} \\\\\\ d=\sqrt{( 11 )^2 + ( -6 )^2} \implies d=\sqrt{ 121 + 36 } \implies d=\sqrt{ 157 }\)

The 2 : 5 scaled version of the deck Sam plans to build and the dimensions of the original deck indicates;

Part A; Base length of the new deck = 7.2 feet

Height of the new deck = 2.8 feet

Part B; The area of the original deck is 63 square feet

The area of the new deck is 10.08 square feet

Part C; The ratio of the areas is the square of the scale factor

A scale factor is a number or factor that is used to enlarge or reduce the dimensions a shape or size of a figure.

The base length of the triangular deck = 18 feet

The height of the triangular deck = 7 feet

The scale factor for the scaled version Sam intends to build = 2 : 5

Part A; The dimensions of the new deck are;

Base length of the new deck using the the 2 : 5 ratio is; (2/5) × 18 = 7.2 feet

The height of the new deck = (2/5) × 7 = 2.8 feet

Part B; The area of the original deck = (1/2) × 18 × 7 = 63 square feet

Area of the new dec = (1/2) × 7.2 × 2.8 = 10.08 square feet

Part C; The ratio of the areas is; 10.08/63

Ratio of the area = 10.08/63 = 4/25 = 4 : 25

The scale factor is; 2 : 5

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The comparisons that are true are 11. -5 < 0 12. 9 > -8 14. 55 > -75 15. -32 < -24 16. 89 > 73 17. -58 < -51  19. 17 < 23  20. 18 > -36 and that is not true are 13. -7 = -7 (not true) 18. -32 > 4 (not true)

To make each statement true, write < or >. We need to compare two values for each statement to determine whether it is true or false.

To indicate that the first value is less than the second value, write <.

Alternatively, to indicate that the first value is greater than the second value, write >.

Below are the comparisons: 11. -5 < 0 12. 9 > -8 13. -7 > -7 14. 55 > -75 15. -32 < -24 16. 89 > 73 17. -58 < -51 18. -32 > 4 19. 17 > 23 20. 18 > -36

To determine the direction of inequality, we need to compare the values.

We used inequality signs such as > (greater than) or < (less than) to indicate which value is larger or smaller than the other.

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The correct question would be as

Write > or < to make each statement true.

11. -5 0

12. 9 -8

13. -7 7

14. 55 -75

15. -32 -24

16. 89 73

17. -58 -51

18. -32 4

19. 17 23

20. 18 -36​

Answer:

(120,122), (150,152), (200,202), (210,212)

Step-by-step explanation:

just add two to the number of students

Step-by-step explanation:

Let (15 + x) and (22 + x) be the future ages of the brothers.

We have (15 + x)(22 + x) = 330 + 37x + x² = 408

Therefore x² + 37x = 78 and x = 2.

Hence the answer is 2 years later.

The recursive formula of the function is P(n + 1) = 3 + Pn while the explicit formula  is P(n) = 6 + 3(n -1)

The given parameters are

Po = 6

P1 = 9

From the question, we understand that the number of cars follows a linear model

This means that the common difference is

d = P1 - Po

So, we have

d = 9 - 6

Evaluate

d = 3

The recursive formula  is

P(n + 1) = d + Pn

So, we have

P(n + 1) = 3 + Pn

From the question, we understand that the number of cars follows a linear model

This means that the common difference is

d = 9 - 6

Evaluate

d = 3

The explicit formula  is

P(n) = Po + (n -1) * d

So, we have

P(n) = 6 + (n -1) * 3

Evaluate

P(n) = 6 + 3(n -1)

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Answer:

x=-9/7

Step-by-step explanation:

Answer:-12(x - 3) - (2x - 6) = 60

= -12 OJHORZHOEHFOSDHSKDKCDEZIAIFDNSQDKFFFFFFFFFFFFZIDJAZIFJOIJF

Step-by-step explanation:

EFKJNDOIDNOIEFJOAIZFOUJFNJBVJFNVJNZJCN

The given question is incomplete as the graph is missing.

But, considering a line graph, the following parameters can be represented on the x-axis and y-axis:

X-Axis                                                     Y-Axis

Year                                                         Population

Time                                                         Number of employees hired

Identical items purchased                      Total cost in dollars    

What does the blank observed line represent in each graph?  

The blank observed line represents the time. A line graph is basically used to connect the quantitative values over the different time intervals. The change in values over time is easier to estimate, by the help of the line graph. For example: in a graph showing the year on the x-axis and the population on the y-axis, the blank line represents the change in population over the years, the increase or decrease or the rate of change.  

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Answer:

b

Step-by-step explanation:

(a) In 1365 different ways the 4 computers can be chosen.

(b) The probability that exactly one of the computers will be defective, is 44/91.

(c) The probability that at least one of the computers selected is defective is 69/91.

(a) We have to determine in how many different ways the 4 computers can be chosen.

The probability of  computers can be chosen = \(^{15}C_4\)

The probability of  computers can be chosen = 1365 ways

(b)  We have to determine the probability that exactly one of the computers will be defective.

The probability that exactly one of the computers will be defective = \(\frac{^{4}C_{1}\times ^{11}C_{3}}{^{15}C_{4}}\)

The probability that exactly one of the computers will be defective = 660/1365

The probability that exactly one of the computers will be defective = 44/91

(c)  We have to determine the probability that at least one of the computers selected is defective.

Probability that none of the computers is defective = \(\frac{^{11}C_{4}}{^{15}C_{4}}\)

Probability that none of the computers is defective = 330/1365

Probability that none of the computers is defective = 22/91

Probability that at least 1 is defective = 1 - Probability that none of the computers is defective

Probability that at least 1 is defective = 1 - 22/91

Probability that at least 1 is defective = 69/91

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Answer:

The constant of proportionality is k=1/4

Step-by-step explanation:

For the equation y=kx, y varies directly with x with the constant of proportionality k. Therefore, k=1/4 is the answer.

Factor 2 is 4x greater, Factor 3 is 9x greater and Factor 5 is 25x greater and  the pattern in part A is Factor square.

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

A cylinder is formed by 2 circles and a rectangle in the middle. That's why surface area is given by circumference of a circle, which is the length of the rectangle times height of the rectangle, i.e.:

A = 2.π.r.h

A cylinder of radius r and height h has area:

A₁= 2πrh

If multiply both dimensions by a factor of 2:

A₂= 8πrh

Comparing A₁ to A₂ :

A₁/A₂=4

Doubling radius and height creates a surface area of a cylinder 4 times greater.

By factor 3:

A₃=18πrh

Comparing areas:

A₃/A₁=9

Multiplying by 3, gives an area 9 times bigger.

By factor 5:

A₅=50πrh

Comparing A₅ to A₁

A₅/A₁=25

The new area is 25 times greater.

We can notice the increase in area is factor².

For example, when multiplied by a factor of 3, the new area is 9 times greater.

Hence, Factor 2 is 4x greater, Factor 3 is 9x greater and Factor 5 is 25x greater and  the pattern in part A is Factor square.

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