sometimes a change of variable can be used to convert a differential equation into a separable equation. one common change of variable technique is as follows. consider a differential equation of the form , where , and are constants. use the change of variable to rewrite the differential equation as a separable equation of the form . solve the initial value problem (a) help (formulas) (b) help (formulas)

The new points of the trapezoid are P'(4, -8), Q'(8, -8), R'(8, 4) and S'(-8, 4)

An equation is an expression relating two or more numbers and variables.

Dilation is the increase or decrease in size of a figure by a scale factor. The rule for dilation is:

(x, y) ⇒ (kx, ky)

The vertices of the trapezoid is P(1, -2), Q(2, -2), R(2, 1) and S(-2, 1)

If the trapezoid is dilated by a scale factor of 4 about the origin, the new points are:

P'(4, -8), Q'(8, -8), R'(8, 4) and S'(-8, 4)

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Answer:

the third one

Step-by-step explanation:

an open circle means it does not include that number. therefore, it needs to be x is less than -2. a closed circle means it includes that number. therefore, x is greater than or equal to 4

a) The Corresponding minimum UGPA = 3.70

b) The range of middle 50% values will be: (3.28, 3.52).

What is the z-score?

A z-score (also known as a standard score) is a measure of how many standard deviations an individual data point is from the mean of a distribution. A z-score is calculated by subtracting the population mean from an individual data point, and then dividing that number by the population standard deviation.

a) z score corresponding to top 5% area = 1.645

Hence,

Corresponding minimum UGPA = 3.40 + 1.645*0.18 = 3.70

b) z score corresponding to middle 50% area = -0.67, 0.67

Hence,

The range of middle 50% values will be:

(3.40 - 0.67*0.18, 3.40 + 0.67*0.18)

(3.28, 3.52)

Hence,

a) The Corresponding minimum UGPA = 3.70

b) The range of middle 50% values will be: (3.28, 3.52).

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Therefore , the solution of the given problem of function comes out to be g(x) is given by g(x) = (x-4)² + 6

The study of numbers, their variations, mathematics and the regional tissue, structures, and both their actual and imagined locations, is known as mathematics. A function is a mathematical representation of the relationship between a set of inputs, each of which has an associated output. A function is a group of inputs that, when combined, result in a single, recognized output for each input. Each function is given a city, town, or scope, which is frequently referred to as a realm.

Here,

Given the graph of the original function f(x), whose vertex is at (0, 0), and indeed the graph of the translating function g(x), whose vertex is at (0, 0), (5, 2).

Be aware that the translated function's vertex is 2 units higher and 5 units to the right of the f graph's graph (x).

The function f(x) is then translated 5 units toward the right и 2 units up to arrive at g(x).

Recall that provided a function, f(x), is characterized as a parabola with a vertex at (h, k).

=> f(x) = (x-h)² + k

The outcome of translating a unit to the right with b unit up is

=>f'(x) = (x-h-a)² + k + b

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Answer:

Out of all possible choices you've shown, I'd say the best answer would be C

Step-by-step explanation:

The journal entries required on February 28, 2021, for Selkirk Company to accrue interest and to record the discounting are as follows:

Debit Interest Receivable $225

Credit Interest Revenue $225

Debit Cash $15,048

Debit Interest Expense $177

Credit Note Receivable $15,000

Credit Interest Receivable $225

When a note receivable is discounted, the following steps are followed:

February 28, 2021

Interest Receivable $225 Interest Revenue $225

Cash $15,048 Interest Expense $177 Note Receivable $15,000 Interest Receivable $225

Note receivable = $15,000

Interest = 9%

Maturity period = 6 months (Jan 1, 2021, to July 1, 2021) or 180 days

Discount date = February 28, 2021

Maturity value = $15,675 ($15,000 + $15,000 x 9% x 6/12)

Discount = $627 ($15,675 x 12% x 120/360)

Proceeds = $15,048 ($15,675 - $627)

Accrued interest = $225 ($15,000 x 9% x 60/360)

Note's carrying value on February 28, 2021, = $15,225 ($15,000 + $225)

Interest expense = $177 ($15,048 - $15,225)

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The shape that results from a plane passing through a cone that is perpendicular to the base is a B. Circle

A circle intersects a cone when a plane passes through it perpendicular to the base. This is due to the plane cutting through the cone's circular cross-section at a 90-degree angle to the base of the cone.

As a result, if the plane were to be slanted or angled, the intersection would have the shape of an ellipse, which is a circle that has been flattened.

This is due to the fact that an ellipse is the shape created when a plane crosses a cone at an angle other than perpendicular to the base.

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Answer: 1. 7a 2. 5r 3. 8y+4 4. 12m-7 5. 7u+5 6. 8q+6 7. 3w+5x 8. 4j + 4k 9. 5d+6

Step-by-step explanation: Add the coefficients of the terms with same variables. ex. 5a+4a+7... 5a and 4a have same variable which is a so add the 5 and 4 and you get 9a and the 7 doesn't match so leave it out and you get 9a + 7

Answer:

1) 7a

2) 5r

3) 8y +4

4) 12m-7

5) 7u+5

6) 8q+6

7) 3w+5x

8) 4j +4k

9) 5d+6

Step-by-step explanation:

you just add or subtract the number with the same letter after it (if there is no letter just leave it as is, unless there are two or more numbers with no letter after, then add or subtract as normal)

Answer: It will take 7 more years for George’s sister to be taller than him.

Step-by-step explanation:

Answer:

Step-by-step explanation:

7 years

Answer:

it's a function

Step-by-step explanation:

to test if it's a function or not you do the vertical line test if it intersects the function at more than one point then it's not a function,, but here in the given function when you do the vertical test it'll only intersect it at one point so it's a function

Answer:

[tex]j = \dfrac{9}{2} = 4,5 \\\\\\k = 2[/tex]

Step-by-step explanation:

I am working on the assumption that the figure shown is a parallelogram, otherwise my answer will not be valid

The diagonals of a parallelogram bisect each other

In the above figure, the top left-bottom right diagonal is bisected by the top right  - bottom-left diagonal

This means

[tex]3j = 5j - 9[/tex]

Subtract 5j from both sides:

[tex]3j - 5j = -9[/tex]

[tex]-2j = -9[/tex]

[tex]j = \dfrac{-9}{-2} = \dfrac{9}{2} = 4,5 \\[/tex]
I am not sure if you want it in fraction or decimal

Similarly

[tex]k + 10 = 6k\\\\[/tex]

Subtract k from both sides:
[tex]10 = 6k-k\\\\\\10 = 5k\\\\\\\textrm{Switching sides,}\\5k = 10\\\\k = \dfrac{10}{5} = 2\\\\[/tex]

The equation formed by the sentence is 9b - 7 = 8.

What is equation ?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.

A mathematical expression with an equals sign is referred to as an equation. Algebra is widely used in equations. When performing calculations but unsure of the precise amount, algebra is used.

Let the variable be b

By the given sentence we get the equation

9b - 7 = 8

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Angles in parallel lines are formed when two parallel lines intersect with another line known as a transversal. So here ∠y is 40° and ∠z is 140°.

We know that sum of angles over a straight line is 180°

So here ∠x + 140° = 180°

So ∠x = 180 - 140

Therefore ∠x = 40°

So in this figure ∠x = ∠y , Since they are corresponding angles are equal.

Therefore ∠y = 40°

So ∠z will be 140° . Since ∠y = 40° its opposite angle will also be 40°.

So ∠z + 40° = 180°

Therefore ∠z = 140°

So the angles ∠y = 40° and ∠z = 140°.

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The integral[tex]∫20(45t^3-34t^2+25t)dt[/tex] can be evaluated by using the power rule of integration, which states that the derivative of x^n is [tex]nx^(n-1)[/tex]. This rule can be applied to each term of the integral separately.

The first step is to integrate [tex]∫20(45t^3-34t^2+25t)dt[/tex] with respect to t. By using the power rule, we can find the antiderivative of each term inside the parentheses:

[tex]∫45t^3 dt = (45/4)t^4 + C[/tex]  (the antiderivative of 45t^3 is (45/4)t∧4)

[tex]∫34t^2 dt = (34/3)t^3 + C[/tex] (the antiderivative of 34t^2 is (34/3)t∧3)

[tex]∫25t dt = (25/2)t^2 + C[/tex] (the antiderivative of 25t is (25/2)t∧2)

Now, we can substitute these results back into the original integral:

[tex]20(∫45t^3 dt - ∫34t^2 dt + ∫25t dt) = 20((45/4)t^4 + (34/3)t^3 + (25/2)t^2) + C= 20(15t^4-11t^3+25t^2) + C[/tex]

So, the evaluated integral for [tex]∫20(45t^3-34t^2+25t)dt[/tex] is [tex]20(15t^4-11t^3+25t^2) + C.[/tex]

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Answer: x = -8/3

Step-by-step explanation:

7 = 3(5+x)

3(5+x)=7

apply the distributive property

15+3x=7

rearrange the variables to  the left side of the equation

3x=7-15

3x=-8

divide on both sides

x=-8/3

Answer:

x = -8/3

Step-by-step explanation:

Now we have to,

→ Find the required value of x.

The equation is,

→ 7 = 3(5 + x)

Then the value of x will be,

→ 7 = 3(5 + x)

→ 7 = 3(5) + 3(x)

→ 7 = 15 + 3x

→ 7 - 15 = 3x

→ -8 = 3x

→ 3x = -8

→ [ x = -8/3 ]

Hence, the value of x is -8/3.

Answer:

7 and 40

Step-by-step explanation:

for you to get the next number you have to add 7 to that number...then add 1 to the number you have gotten then continue like that

eg: to get 8 you had to add 7 to 1 now to get the next number add 1 to 8 to get 9 then add 7 to 9 to get 16 then continue like that

Answer:

Rectangle, parallelogram, trapezoid, quadrilateral

Step-by-step explanation:

because the properties of the rhomboid(that is what it is called) match with those different shapes listed above

The indices for the directions are indicated by the two vectors in the following sketch - [1 0 0] and [ 2 0 3].

Miller Indices of Direction Vector:

The Miller indices of direction are rationalized components of the direction vectors taken in all crystallographic directions. They are indicated by [[u v w ]]. They are always defined as the smallest integers, so if they occur in fractional or decimal form, we need to convert them into the smallest integral value by algebraic manipulation.

The indices of direction 1.

Let the length of direction 1 along the x-axis be X units. The length of the vectors along the y and z axes is 0.

[ X 0 0 ]

⇒ [tex]\left[\begin{array}{ccc}0&0&0\\X'&X'&X'\\\end{array}\right][/tex]

Divide each length by X to convert it into the smallest integer.

⇒ [1 0 0]

And, this is the Miller indices of the direction vector 1.

So, the Miller indices of the direction vector 1 are [ 1 0 0].

Direction 2

The indices of direction 2.

Let the length of direction 2 along the x-axis be X units. The length of the vector along the y and z axes are 0.

[ 0.2 0 0.3 ]

⇒[ 2 0 3 ]

Multiply each fractional length by 10 to convert it into the smallest integer.

So, the Miller indices of the direction vector 2 are [ 2 0 3].

Therefore, The indices for the directions are indicated by the two vectors in the following sketch - [1 0 0] and [ 2 0 3].

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The average rate of change from the sixth to the fourteenth hours indicates that, on average, 15 fewer pairs of shoes were sold every hour.

A line's slope determines how steep it is. A mathematical equation for the gradient is called "gradient overflow" (the change in y divided by the change in x). The slope is the ratio of the vertical change (rise) between two points to the horizontal change (run) between those same two spots. When a straight line's equation is written as y = mx + b, the slope-intercept form of an equation is employed to express it. The y-intercept is located at a location where the line's slope is m, b is b, and (0, b). For instance, the slope of the equation y = 3x - 7 and the y-intercept (0, 7).

given

slope = y2- y1 / x2 - x1

= -120/8  = -15

( 6 , 120 )

( 14 , 0 )

The average rate of change from the sixth to the fourteenth hours indicates that, on average, 15 fewer pairs of shoes were sold every hour.

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The solution to the system of equations for this problem is given as follows:

(11.59, 479).

The system of equations for this problem is defined as follows:

The solution for x is obtained when the two equations are equal, hence:

14.3x + 318 = 3.6x + 442

10.7x = 124

x = 124/10.7

x = 11.59.

Applying the substitution in any of the equations, the solution for y is obtained as follows:

y = 3.2(11.59) + 442

y = 479.

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The value of an irrational numbers are,

⇒ √28

⇒ √11

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The numbers are,

⇒ √100

⇒ √28

⇒ √11

⇒ 2.78⁻⁻⁻

Now, We know that;

An irrational number is a number that cannot be expressed as a fraction for any integers.

Hence, We get;

The correct value of an irrational numbers are,

⇒ √28

⇒ √11

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Upon solving the decimals, The expression which is equivalent to 0.125 are -12.5 ÷ 10²⇒ 0.125 and 1,250 ÷ 10⁴ ⇒ 0.125.

A decimal is a number that is divided into two parts: a whole and a fraction. Between integers, decimal numbers are used to express the numerical value of complete and partially whole quantities.

Decimal fractions and recurring (repeating or non-terminating, like) decimals are the three different sorts of decimals (a.k.a. converting a decimal into a fraction whose denominator is a power of ten).

1.25 ÷ 10       ⇒ 0.125

Upon solving the decimals,

12.5 ÷ 10²       ⇒ 0.125

0.125 ÷ 100    ⇒ 0.00125

1,250 ÷ 10⁴     ⇒ 0.125

12.5 ÷ 1           ⇒ 12.5

125 ÷ 1,000    ⇒ 0.0125

The expression which is equivalent to 0.125 are -

12.5 ÷ 10²       ⇒ 0.125

1,250 ÷ 10⁴     ⇒ 0.125

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Sawyer lives 12.7 km farther from the soccer field.

Jabar lives 5 miles from the soccer fields, Sawyer lives 12.7 km from the same soccer fields .

The person that lives farther form the soccer field can be calculated as follows;

Let's convert Jabar distance from the soccer field to km.

1 miles = 1.60934

5 miles = ?

cross multiply

distance of Jabar from the soccer field = 5 × 1.60934

distance of Jabar from the soccer field = 8.0467 km

Therefore, jabar lives 8.0467 km from the soccer field.

Hence, Sawyer lives 12.7 km farther from the soccer field.

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The measure of the smaller complementary angles is 40°

When two angles add up to 90°, we say they complement each other in terms of mathematics. Hence in geometry, complementary angles are defined as two angles whose sum is 90 degrees.

The larger angle = 50°

we shall represent the smaller angle with the letter x so that;

x + 50° = 90°

subtract 50° from both sides of the equation

x + 50° - 50° = 90° - 50°

x = 40°

Therefore, the smaller complementary angle has a measure of 40°.

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Answer:

Step-by-step explanation:

A typical geometric sequence can be represented as

c

0

a

,

c

0

a

2

,

⋯

,

c

0

a

k

and a typical arithmetic sequence as

c

0

a

,

c

0

a

+

Δ

,

c

0

a

+

2

Δ

,

⋯

,

c

0

a

+

k

Δ

Calling

c

0

a

as the first element for the geometric sequence we have

⎧

⎪

⎨

⎪

⎩

c

0

a

2

=

c

0

a

+

2

Δ

→

First and second of GS are  the first and third of a LS

c

0

a

+

3

Δ

=

10

→

The fourth term of the linear sequence is 10

5

c

0

a

+

10

Δ

=

60

→

The sum of its first five term is 60

Solving for

c

0

,

a

,

Δ

we obtain

c

0

=

64

3

,

a

=

3

4

,

Δ

=

−

2

and the first five elements for the arithmetic sequence are

{

16

,

14

,

12

,

10A typical geometric sequence can be represented as

c

0

a

,

c

0

a

2

,

⋯

,

c

0

a

k

and a typical arithmetic sequence as

c

0

a

,

c

0

a

+

Δ

,

c

0

a

+

2

Δ

,

⋯

,

c

0

a

+

k

Δ

Calling

c

0

a

as the first element for the geometric sequence we have

⎧

⎪

⎨

⎪

⎩

c

0

a

2

=

c

0

a

+

2

Δ

→

First and second of GS are  the first and third of a LS

c

0

a

+

3

Δ

=

10

→

The fourth term of the linear sequence is 10

5

c

0

a

+

10

Δ

=

60

→

The sum of its first five term is 60

Solving for

c

0

,

a

,

Δ

we obtain

c

0

=

64

3

,

a

=

3

4

,

Δ

=

−

2

and the first five elements for the arithmetic sequence are

{

16

,

14

,

12

,

10

Answer:

[tex]\frac{35}{12}[/tex]

Step-by-step Explanation:

The tangent of an acute angle in a right triangle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.

If Catarina’s boat has come untied and floated away on the lake. She is standing atop a cliff that is 35 feet above the water in a lake. Approximately the distance from the cliff is Catarina’s boat is : 63.6ft.

Distance can be defined as how far an object is from another object.

Now let find the distance:

AE/CD = BC/DE

Hence,

5.5/3.5 = 10/DE

Cross multiply

AE = 350/5.5

AE = 63.6ft

Therefore we can conclude that the distance is 63.6ft.

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The values of maximum and minimum values are  11i + 3 and √5+ 3 .

Function can be defined in which it relates an input to the output. Functions are relationships in mathematics where each input has a particular output. Functions are often used in science and mathematics. In this section, we will learn the definitions of functions, various kinds of functions, and properties, along with examples to help us understand.

Given,

The function is f(x) = √x+3.

We have to find the maximum and minimum values on the interval [-11,5]

So,

f'(x) = 1/2√x

As when,

f'(x) = 0

has no solution than,

f(-11)  =  √-11 + 3

= 11i + 3

f(5) = √5+ 3 .

Therefore, The values of maximum and minimum values are 11i + 3 and √5+ 3 .

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The area of the rectangle represented as the sum of cubes is x³ + 3³

An equation is an expression showing the relationship between numbers and variables.

The sum of cubes of a polynomial is in the form a³ + b³ while A the difference of cubes of a polynomial is a³ - b³

The area of rectangle = length * width

From the diagram, length = x² - 3x + 9; width = x + 3, hence:

The area of rectangle = length * width = (x² - 3x + 9)(x + 3)

Area = x³ - 3x² + 9x + 3x² - 9x + 27 = x³ + 27

Area = x³ + 3³

The area of the rectangle is x³ + 3³

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