What is the equation of a line that is parallel to the line y= x+2? (Sorry I forgot to add multiple choice the first time.)

a) y- 2x= 3
b) 2x+ y= -2
c) x+y= 5
d) y- x= -1​

Answer:

-4-10-(-9)

= -4-10+9

= -4+(-10)+9

= -14+9

= -5

\(f(x)=x^2-5x+6\)

↝ f(4) equals to substituting x = 4 in the equation.

Thus,

\(f(4)=4^2-5(4)+6\\f(4)=16-20+6\\f(4)=22-20\\f(4)=2\)

Therefore, f(4) = 2

Answer:

2

Step-by-step explanation:

f(4) = 4^2-5(4) + 6

     = 2

For any price of h and k = -12, the system x + 3y = h and -4x + ky = -9 will haven't any answer.

To determine the values of h and okay for which the device of equations has no answer, we want to locate the situations underneath which the equations are inconsistent or parallel.

The given system of equations is:

Equation 1: x + 3y = h

Equation 2: -4x + ky = -9

For the gadget to haven't any answer, the lines represented with the aid of these equations should be parallel and in no way intersect. In different phrases, the slopes of the traces need to be equal, but the y-intercepts should be specific.

Let's first discover the slopes of the traces. The slope-intercept form of Equation 1 is y = (-1/3)x + (h/3), wherein the slope is -1/3. The slope-intercept shape of Equation 2 is y = (4/k)x - (9/k), wherein the slope is 4/k.

For the strains to be parallel, the slopes should be equal. Therefore, we have the condition: -1/3 = 4/k.

To locate the values of h and okay for which the gadget has no answer, we need to locate the values of h that satisfy the situation -1/3 = 4/k.

Solving this equation for ok, we've got:

-1/3 = 4/k

-1 = 12/k

k = -12

Substituting k = -12 returned into the equation -1/3 = 4/k, we've:

-1/3 = 4/(-12)

-1/3 = -1/3

Since the equation holds real for any value of h, there aren't any restrictions at the price of h.

Therefore, for any price of h and k = -12, the system x + 3y = h and -4x + ky = -9 will haven't any answer.

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The system of equations has no solution when k is equal to 12. The value of h can be any real number.

To determine the values of h and f for which the system has no solution, we need to analyze the coefficients of the variables and the constants in the equations.

The given system of equations is:

x + 3y = h

-4x + ky = -9

We can rewrite the second equation as:

-4x + ky = -9

Dividing both sides of the equation by -4, we get:

x - (k/4)y = 9/4

Comparing the coefficients of x and y in the two equations, we can see that the slopes of the lines represented by the equations are different when k is not equal to 12.

Therefore, for the system to have no solution, k must be equal to 12.

As for the value of h, it can be any real number since it does not affect the slopes of the lines.

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Answer:

Step-by-step explanation:

Area = 4(6+12)/2 = 36 sq cm

Answer:

36cm²

Step-by-step explanation:

Hey There!

So the first thing we need to do is find the area of a trapezoid formula

\(A = \frac{a +b}{2} h\)

a = base 1

b = base 2

h = hypotenuse

Now we just plug in the values and get

\(A = \frac{6+12}{2} 4\)

6+12=18

\(\frac{18}{2} = 9\)

9x4=36

So the area of the trapezoid is 36 cm ²

Answer:

-4x is equivalent to 19x-23x.

Step-by-step explanation:

19x and 23x are like terms because they both end in a "x."

We can add or subtract like terms, so 19x-23x just becomes (19-23)x.

(19-23)x = (-4)x = -4x

Let me know if this helps!

Answer: $310,000

Step-by-step explanation:

In 40 additional years, the amount she made less than her college counterparts was;

= 10,000 * 40

= $400,000

She however made $90,000 more than them as they went to college;

= 400,000 - 90,000

= $310,000

The long-term financial cost was $310,000.

Answer:

8

Step-by-step explanation:

fist take y2-y1 to get 16 that do x2-x1 to get 2 the do 16 divided by to to get 8

The largest area that can be enclosed if 88 feet of fencing material is available is 484 feet².

Given, a barn has a perimeter of 88 feet.

Now, the perimeter of the rectangle i.e. Barn is 88 feet.

Perimeter = 2(l + b)

88 = 2(l + b)

l + b = 44

b = 44 - l

Now, area = l × b

Area = l × (44 - l)

Area = 44l - l²

On differentiating both the sides, we get

A' = 44 - 2l

On putting A' = 0

44 - 2l = 0

l = 22

Now, for l = 22 the area will be the largest.

if l = 22

then, 22 + b = 44

b = 22

So, the largest area will be 22×22 = 484

Hence, the largest area that can be enclosed if 88 feet of fencing material is available is 484 feet².

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Answer:

this is confusing

Step-by-step explanation:

Answer:

\(f'(x)= \frac{13}{(2x+3)^2}\\\)

Step-by-step explanation:

\(f(x)= \frac{3x-2}{2x+3} \\\)

\(f'(x)=\frac{dy}{dx} = \frac{d}{dx}(\frac{3x-2}{2x+3})\\ f'(x)= \frac{(2x+3)\frac{d}{dx}(3x-2)-(3x-2)\frac{d}{dx}(2x+3) }{(2x+3)^{2} } \\f'(x)= \frac{(2x+3)(3)-(3x-2)(2)}{(2x+3)^{2} } \\\)

\(f'(x)= \frac{6x+9-6x+4}{(2x+3)^{2} }\\ f'(x)= \frac{13}{(2x+3)^2}\\\)

Answer:

To find out how much the TV is worth now, we need to apply the depreciation rate of 9% to the original price for 8 months:

First, let's calculate the value after the first month:

Value after 1 month = $2740 - (9% of $2740) = $2501.40

Now, let's calculate the value after 2 months:

Value after 2 months = $2501.40 - (9% of $2501.40) = $2275.80

We can continue this process for 8 months to find the current value:

Value after 3 months = $2071.67

Value after 4 months = $1888.81

Value after 5 months = $1725.10

Value after 6 months = $1579.92

Value after 7 months = $1452.16

Value after 8 months = $1339.53

Therefore, the TV is worth $1,339.53 now.

If new mobile device has a value of $256.25 and its value changes by \(22\frac{1}{2}\)% each year, then the value of phone after two years is $153.76

The value of new mobile device = $256.25

The percentage of value change =  \(22\frac{1}{2}\)%

Convert the mixed fraction to decimal form

\(22\frac{1}{2}\)% = 22.5%

After one year mobile value = 256 - (256×22.5/100)

= 256-57.6

= $198.4

After two year the mobile value = 198.4-(198.4×22.5/100)

= 198.4-44.64

= $153.76

Hence, if new mobile device has a value of $256.25 and its value changes by \(22\frac{1}{2}\)% each year, then the value of phone after two years is $153.76

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Based on the dotplots, it can be concluded that the number of snacks grabbed for class A has less variability than the number of snacks grabbed for class B.

The dotplots show the number of snacks grabbed by students in two statistic classes. To determine the variability of the number of snacks grabbed in each class, we can analyze the spread of the data displayed in the dotplots.

In class A, with 32 students, the dotplot shows a relatively narrow spread of data. The dots are concentrated in a smaller range, indicating less variability in the number of snacks grabbed by the students. This suggests that the students in class A have a similar behavior when it comes to grabbing snacks with one hand.

In class B, with 34 students, the dotplot displays a wider spread of data. The dots are more scattered and distributed over a larger range, indicating higher variability in the number of snacks grabbed by the students. This suggests that the students in class B have a wider range of behaviors when it comes to grabbing snacks with one hand, with some students grabbing more snacks and others grabbing fewer snacks.

Overall, based on the dotplots, we can conclude that the number of snacks grabbed for class A has less variability compared to the number of snacks grabbed for class B.

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The birth weight of newborns, measured in grams, is an example of quantitative data. So the option a is correct.

In the given question,

The birth weight of newborns, measured in grams, is an example of .

a. quantitative data

b. either categorical or quantitative data

c. neither categorical nor quantitative data

d. categorical data

The quantitative data means data that is explain in the subjective ways. It is  also explain quantity, amount and range.

Categorical data is a body of knowledge that is organised into categories. For instance, the data obtained when an organisation or agency tries to collect the biodata of its employees is referred to as categorical data.

The birth weight of newborns measured in grams, is an example of quantitative data.

Birth weight is quantitative because it can take on multiple numerical values. So the option a is correct.

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The statement "x ∈ {x}" is true. The statement "{x} ⊆ {x}" is true. The statement "{x} ∈ {x}" is false. The statement "{x} ∈ {{x}}" is true.

a) The statement is true because an element x can be a member of a set that contains only itself. In this case, the set {x} contains the element x.

b) The statement is true because every element in {x} is also in {x}. Since both sets are identical, {x} is a subset of itself.

c) The statement is false because a set cannot be an element of itself. In this case, {x} is a set, and it cannot be an element of the same set.

d) The statement is true because the set {{x}} contains the set {x} as its only element. Therefore, {x} is an element of the set {{x}}.

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Answer:

1/2

Step-by-step explanation:

(1,1) (2,3)

you have to do the difference of the x axis and y axis then divid them by each other

In the given list of numbers (56, 25, 26, 28, 81, 93, 92, 85, 99, 87), when the Partition function is called with the range from 5 to 9, the pivot chosen is 93. The low partition consists of the numbers less than or equal to the pivot.

Quicksort is a sorting algorithm that involves partitioning the list around a pivot and recursively sorting the resulting sublists. In this case, the given list of numbers is (56, 25, 26, 28, 81, 93, 92, 85, 99, 87).

When the Partition function is called with the range from 5 to 9, the pivot is chosen as the element at the midpoint of that range. So, the midpoint of the range from 5 to 9 is (5 + 9) / 2 = 7. Therefore, the pivot chosen is the 7th element of the list, which is 93.

The low partition consists of the numbers less than or equal to the pivot. In this case, the numbers less than or equal to 93 are 56, 25, 26, 28, 81, and 92.

Hence, the pivot is 93, and the low partition consists of the numbers 56, 25, 26, 28, 81, and 92.

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Total number of seats that remain unsold are 168.

What is statistics?

The branch of mathematics dealing with data collection, organization, analysis, interpretation and presentation.

Let's start by defining some variables to represent the unknowns in the problem:

From the problem, we know that:

We also know that the total revenue collected is $34,650:

27x + 45y = 34650

Now we can substitute y = 0.5x from the second equation into the third equation and simplify:

27x + 45(0.5x) = 34650

27x + 22.5x = 34650

49.5x = 34650

x = 700

So there were 700 $30-seats and 350 $50-seats.

The number of sold $30-seats is 0.9(30x) = 567, and the number of sold $50-seats is 0.9(50y) = 315.

Therefore, the total number of seats sold is 882, and the number of unsold seats is:

1050 - 882 = 168

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Three different ways are cos (2θ) = cos²θ - sin²θ, 2cos²θ - 1 = cos (2θ) and cos (2θ) = 1 - 2sin²θ.

The double-angle formula for cosine can be expressed in three different ways:

cos (2θ) = cos²θ - sin²θ

2cos²θ - 1 = cos (2θ)

cos (2θ) = 1 - 2sin²θ

These formulas allow us to find the cosine of twice a given angle θ in terms of the sine and cosine of the original angle θ. These formulas are useful in solving trigonometry problems and proving other trigonometric identities.

Therefore, three different ways are cos (2θ) = cos²θ - sin²θ, 2cos²θ - 1 = cos (2θ) and cos (2θ) = 1 - 2sin²θ.

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Answer:

\(4\sqrt{10}\)

Step-by-step explanation:

Answer:

y = 5/3

x = 8/3

Steps:

y = x - 1

2x + y = 7

Substitute y = x-1

(2x + x - 1 = 7)

Simplify: 3x - 1 = 7

Isolate x: 3x - 1 = 7:  x=8/3

Plug the valuse of x into the other equation (y = x- 1):    y = 8/3 - 1

8/3 - 1 = 5/3

y = 5/3

y = 5/3, x = 8/3

12 terms are in an arithmetic sequence.

What comprises an arithmetic series?

A group of integers that are arranged in a particular order and share a difference between each term is known as an arithmetic sequence.

            For instance, the common difference between the numbers 3, 9, 15, 21, and 27 in mathematics is 6. The term "arithmetic progression" can refer to an arithmetic sequence.

a = 6,

d = -3,

last term, l = -45

a + (n - 1)*d

45 = a + (n - 1)d

45 = 6 + (n -1)-3

45 - 6 = -3(n - 1)

39 = -3(n - 1)

-3(n - 1) = 39

n - 1 = -39/3

n - 1 = -13

n = -13 + 1

n = - 12

There are 12 terms.

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Answer:

10

Step-by-step explanation:

ans is 10

because 2×5 is 10

Answer:

2x5= 10

Step-by-step explanation:

5, 10,15,20

five 2 times is 10

Answer:

Essentially, integers are any full number so no decimals.

Explanation:

Altough it could be -34, 0, 14, etc but not 5.3. so as long as nothing is in the decimal place, its an integer

I hope this helps, have a blessed day!

The distance between A and B is √40.

We know the coordinates of the two points A and B.

We will use the distance formula to find the distance between A and B.

Distance Formula:

d = √(x2 - x1)² + (y2 - y1)²,

where (x1, y1) and (x2, y2) are the coordinates of the two points.

Given, the coordinates of points A and B as

A = (-7, 9)B = (-5, 3)

Using the distance formula,

d = √(x2 - x1)² + (y2 - y1)²

Substituting the values of x1, x2, y1, y2,

d = √(-5 - (-7))² + (3 - 9)²

= √2² + (-6)²

= √4 + 36

= √40

Therefore, the distance between A and B is √40, which is approximately equal to 6.3 (rounded to the nearest tenth).

d = √40 ≈ 6.3

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The value of the integral ∫√x/(x - 4) dx from 9 to 16 is 3.022

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

∫√x/(x - 4) dx from 9 to 16

The above expression can be integrated using integration by parts method

When integrated, we have

∫√x/(x - 4) dx = 2(√x - ln(√x + 2) + ln(|√x - 2|))

Recall that the x values are from 9 to 16

This means that

∫√x/(x - 4) dx = 2(√16 - ln(√16 + 2) + ln(|√16 - 2|)) - 2(√9 - ln(√9 + 2) + ln(|√9 - 2|))

So, we have

∫√x/(x - 4) dx = 2(4 - ln(4 + 2) + ln(|4 - 2|)) - 2(3 - ln(3 + 2) + ln(|3 - 2|))

Solving further, we get

∫√x/(x - 4) dx = 2(4 - ln(6) + ln(2)) - 2(3 - ln(5) + ln(1))

Evaluate

∫√x/(x - 4) dx = 3.022

Hence, the value of the integral is 3.022

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Answer:

x = 21

Step-by-step explanation:

given : angle a = 75

we need to find the value of x.

To find the value of x.

we know that it is a straight angle so the sum of angles on a line will be 180

3x + 2x + a = 180

5x + 75 = 180

5x = 180 - 75

5x = 105

x = 105/5

x = 21

Answer: x equals to 21 AAs I calculated it

Step-by-step explanation:

Answer:

the final option

Step-by-step explanation:

the negative sign causes a reflection, the +6 in the parentheses cases a 6 unit shift left and the +3 causes a 3 unit shift up