Find the distance between points G and H

The differential equation is [tex]y=\frac{-7t^2+22t-7}{7t-22}[/tex]

We are given the Initial value problem:

y'=(t=y)²-1, y(3)=4

Substitute the value z=t+y

When t=3 and y=4 then z=3+4=7

y'=z²+1

Differentiate z w.r.t t

[tex]\frac{dz}{dt} =1+y'[/tex]

Then, we get [tex]z'=1+z'-1=z^2[/tex]

z⁻²dz=dt

Integrate on both sides:

-1/zdz=t+c

z=-1/t=c

Substitute t=3 and z=7

Then, we get

7=-1/3+c

21+7c=-1

7c=-1-21=-22

c=-22/7

Substitute the value of C then we get:

z=-1/t-22/7

z=-7/7t-22

y=z-t

y=-7/7t-22-t

y=-7-7t²+22t/7t-22

y=-7t²+22t-7/7t-22.

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Answer:

x² + y² - 4x - 6y - 3 = 0

Step-by-step explanation:

Formula for equation of circle when the radius r and centre (a,b) is given:

(x-a)² + (y-b)² = r²

(x-2)² + (y-3)² = 4²

Expanding the brackets;

x² - 4x + 4 + y² - 6x + 9 = 16

x² + y² - 4x - 6x + 4 + 9 = 16

x² + y² - 4x - 6x + 13 = 16

x² + y² - 4x - 6x + 13 - 16 = 0

x² + y² - 4x - 6x - 3 = 0 Ans.

Answer: (8*10) + (8*7)

Step-by-step explanation: This would be distributing the 8 to both numbers while still adding the two products

Answer: 136

Step-by-step explanation:

When you do distributive Property, you are multiplying everything right before the parenthesis, with everything inside the parenthesis.

8 x (10 + 7)

1. Multiply 8 by 10 to get 80

2. Multiply 8 by 7 to get 56

Now you have: (80 + 56)

3. Add the numbers

80 + 56 = 136

The value of y when x = 28 in the proportional relationship is 112.

Proportional relationships are relationships between two variables where their ratios are equivalent.

The value of y is directly proportional to the value of x. When x = 3.5, the value of y is 14.

Therefore, let's find the constant of proportionality.

y = kx

14  = 3.5k

divide both sides by 3.5

k = 14 / 3.5

k = 4

Let's find the value of y when x = 28.

Hence,

y = 4x

y = 4 × 28

Therefore,

y = 112

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Answer: The graph that represents a function is the parabola that opens to the left.

This can be determined by the following characteristics of the graph:

It is a parabola because it opens to the left and has a vertex on the y-axis.

It crosses the y-axis at (0, 3) and (0, negative 3), which means that it is symmetric about the y-axis, and also it crosses the x-axis at (9, 0) which means that it is a function.

A circle is not a function because, for any value of x, there are two different values of y that can be plotted on the graph (i.e. the point (5,0) and (-5,0) produce two different y values)

A straight line with a positive slope is not a function because, for any value of x, there is only one value of y that can be plotted on the graph.

So the parabola is the graph that represents a function.

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

Answer:

116 months

Step-by-step explanation:

A $659,000 property is depreciated for tax purposes by its owner with the straight-line depreciation method. The value of the building, y, after x months of use is given by:

y = 659,000 − 1800x

After how many months will the value of the building be $450,200?

y = 659,000 − 1800x

450,200 = 659,000 − 1800x

subtract 659,000 from both sides:

450,200 - 659,000 = 659,000 − 1800x - 659,000

-208,800 =  − 1800x

divide both sides by -1800:

-208,800/1800 =  − 1800x/1800

116= x

so:

x  = 116

Answer:

[tex]\bf x+23=64[/tex]

Step-by-step explanation:

you can try x+23=64

Let's solve it:-

[tex]\sf x+23=64[/tex]

Subtract 23 from both sides:-

[tex]\sf x+23-23=64-23[/tex]

[tex]\bf x=41[/tex]

__________________

Hope this's what you're looking for!

Have a great day!

Answer:

How about this:

290 / 8 * 2 - 31.5

Step-by-step explanation:

I dunno if that's hard enough, but there you go!

Answer:

9 and 4

Step-by-step explanation:

xy = 36

x+y = 13       or    13 - x = y    <====sub this into the first equation

x ( 13-x) = 36

-x^2 + 13x - 36 = 0  multiply the entire equation by -1  to make it easier solve

x^2 -13x+36 = 0     this factors to

(x -9)(x-4) = 0          showing x = 9 or 4     with y being 4 or 9

According to the solving the lengths of right angle triangle using Pythagorean theorem x = 6, y = 3

A fundamental relationship in Euclidean geometry between a right triangle's three sides is known as the Pythagorean theorem or Pythagoras' theorem. According to this rule, the area of the square with the hypotenuse side is equal to the sum of the areas of the squares with the other two sides.

The following is one way to perform the calculation. It may not be the best way.

c = b/cos(α)

= 6

a = √c2 - b2

= √62 - 5.192

= √9.0639

= 3.01063

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Answer:

The expression is a mathematical representation of an algebraic problem. The final form of the expression would be 75y -5 after combining like terms.

Here's the breakdown of the steps:

125y - 5 - 50y = (125-50)y -5 = 75y - 5

So the final simplified form of the expression is 75y -5.

Answer:

I think it’s D

Step-by-step explanation:

trust

On solving the provided question, we can say that  vertex form of the equation is in the form of y = a(x-h)^2 + k.

A vertex, or particular point, is a place where two or more lines or edges meet in a mathematical object. Angles, polygons, polyhedral, and graphs are where vertices are most frequently seen. Nodes and vertices in a graph are the same thing.

Recall that a parabola's General Form is y = ax2 + bx + c. The x-coordinate of the vertices, which is x = - b/2a, must first be discovered in order to find the vertex from this form. You will use this number to replace x in the parabola equation once you have determined the x-coordinate of the vertex.

a = -1/4 * (4 - 12) = -1

h = -b/(2a) = 12/(2(-1)) = -6

k = f(h) = -(-6)^2 + 12(-6) - 4 = 36

Therefore, the vertex form of the equation is y = -(x+6)^2 + 36.

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Answer:

The lowest temperature recorded is the furthest away from the average norm by 41.9 degrees.

Step-by-step explanation:

115-98.6= 16.4

98.6-56.7= 41.9

The equivalent expression of 2/5(s+20) is 2/5s+8 and expression (9+3)=12.

what are expressions?

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, nected by an operator in between. The mathematical operators can be of addition, subtraction, multiplication, or division. For example, x + y is an expression, where x and y are terms having an addition operator in between which math, there are two types of expressions, numerical  expressions - that contain only numbers; and algebraic expressions- that contain both numbers and variables.

e.g. A number is 6 more than half the other number, and the other number is x. This statement is written as x/2 + 6 in a mathematical expression. Mathematical expressions are used to solve complicated puzzles.

Now,

Given expression 2/5(s + 20)

Using distributive property

2/5s+2/5*20

2/5s+2*4

2/5s+8

and (9+3)=12

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Right question:-

Use the distributive property to write an equivalent expression for 2/5(s + 20). Then evaluate the expression (9+3).

The completed table with the values for composite functions in column 3, f(g(x)) and column 4, g(f(x))  included is presented as follows;

[tex]\begin{array}{|c|c|c|c|}f(x) & g(x) & f(g(x)) &g(f(x)) \\&&&\\x^2+1 &-2\cdot x + 5 &4\cdot x^2 -20\cdot x +26 & -2\cdot x^2+3 \\&&&\\2\cdot x^2 - 2\cdot x + 4 & x+3 & 2\cdot x^2 + 10\cdot x + 16& 2\cdot x^2 - 2\cdot x + 7 \\&&&\\ \sqrt{x-4} &2\cdot x^2+ 4 &x\cdot \sqrt{2} & 2\cdot x - 4 \\\end{matrix}[/tex]

f(g(x)) ≠ g(f(x)), because the operations and the order of operations in the functions are different

Composite functions are functions in which the input or argument are also functions.

The values of the composite functions based on the defined functions are found as follows;

f(x) = x² + 1, g(x) = -2·x + 5

Therefore; f(g(x)) is obtained by plugging in x = g(x) in f(x) as follows;

f(x) = x² + 1

f(g(x)) = (-2·x + 5)² + 1 = -2·x × (-2·x + 5) + 5 × (-2·x + 5) + 1

-2·x × (-2·x + 5) + 5 × (-2·x + 5) + 1 = 4·x² - 10·x - 10·x + 25 + 1

4·x² - 10·x - 10·x + 25 + 1  = 4·x² - 20·x + 26

When f(x) = x² + 1, and g(x) = -2·x + 5, f(g(x)) = 4·x² - 20·x + 26

g(f(x)) = is obtained by plugging in x = f(x) in g(x) as follows;

g(x) = -2·x + 5

f(x) = x² + 1

g(f(x)) = -2 × (x² + 1) + 5 = -2·x² - 2 + 5

g(f(x)) = -2·x² + 3

When f(x) = 2·x² - 2·x + 4, and g(x) = x + 3, we get;

f(g(x)) = 2×(x + 3)² - 2×(x + 3) + 4 = 2×(x² + 6·x + 9) - 2·x - 6 + 4

2×(x² + 6·x + 9) + 2·x + 6 + 4 = 2·x² + 10·x + 16

f(g(x)) = 2·x² + 10·x + 16

When f(x) = 2·x² - 2·x + 4, and g(x) = x + 3, f(g(x)) = 2·x² + 10·x + 16

g(f(x)) = is obtained by plugging in x = f(x) in g(x) as follows;

g(x) = x + 3

f(x) = 2·x² - 2·x + 4

g(f(x)) = 2·x² - 2·x + 4 + 3 = 2·x² - 2·x + 7

g(f(x)) = 2·x² - 2·x + 7

When f(x) = [tex]\sqrt{x - 4}[/tex], and g(x) = 2·x² + 4, we get;

f(g(x)) = [tex]\sqrt{2\cdot x^2 + 4 - 4} = x\cdot \sqrt{2}[/tex]

g(f(x)) = 2 × ([tex]\sqrt{x - 4}[/tex])² + 4 = 2 × (x - 4) + 4 = 2·x - 4

g(f(x)) = 2·x - 4

The values of the composite functions in column 3 and column 4 are included in the table in the first section of the response.

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Answer:

rawr :)

Step-by-step explanation:

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

∠RQS is 59.5 degrees as ∠RQS = ∠PQR.

Define angles.

An angled structure in geometry is composed of two rays that converge at the vertex, or core, of the angle. These rays are referred to as the angle's faces. Depending upon where they are situated, two beams may be able to form any angle within a plane. The intersection of two planes also produces an angle. Diahedral angles are the name for them. Light beams or lines that share the same endpoint in plane geometry can have a wide variety of shapes or angles. The English term "angle" derives from the Latin term "angulus," which meaning "horn." The intersection of the two rays is known as the vertex, or vertex of the angle.

Here,

QS cuts an angle. PQR, followed by ∠SQR = ∠ PQS and

∠PQS + ∠RQS = ∠PQR.

The equation then changes to

∠PQR = ∠PQS + ∠PQS

∠PQR = 2∠PQS

∠PQS equals ∠PQR/2

assuming∠ PQR = 119°

Replace in the resulting expression from the above;

∠PQS equals ∠PQR/2

∠PQS = 119/2

∠PQS = 59.5°

∠RQS is 59.5 degrees as ∠RQS = ∠PQR.

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

∠RQS is 59.5 degrees as ∠RQS = ∠PQR.

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Answer: To determine how many hours John needs to work to earn R750, you would need to know his hourly wage. If John earns R50 per hour, he would need to work 15 hours to earn R750 (R750 / R50/hour = 15 hours). If his hourly wage is different, the number of hours he needs to work will be different.

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

f(x)=2x-8

f(7)=2(7)-8

f(7)=6

Answer:

Step-by-step explanation:

f(7)=2x-8
f(7) = (2)(7)-8

f(7) = 14-8
f(7) = 6

The statement "She did not visit France and she did not visit Italy" using De Morgan's laws will be C. She did not cost France if a only if she did not visit Italy.

The complement of the product of all terms is equal to the complement of each term added together. Similarly, the product of the complements of each term equals the complement of the sum of all the terms.

The intersection of their complements is the complement of the union of two sets, and the union of their complements is the complement of the intersection of two sets.

In conclusion, the correct option is C.

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Therefore , the solution of the given problem of surface area comes out to be area of the shaded area equals 50.

The surface area of an object is an estimate of the entire amount of space it takes up. A three-dimensional shape surface area refers to the entire area surrounding it. The overall area of a muti shape is its surface area. The surface area of a cuboid can be calculated by adding the faces of each of its six rectangular sides. The following equation could be used to name the box's dimensions: Surface (SA) equals 2lh, 2lw, and 2hw. The surface area of a three-dimensional shape represents the overall area.

Here,

Square has an area of 100 a 2 = 100 a=10

QC=(1/2) AC=10/2=5,

BR=(1/2), and BD=10/2=5.

CD=AB=10=AC=BD

size of the triangle QCD is defined as: =(1/2)QCCD

= >(1/2)510=25.

size of the triangle ABR is =(1/2) ×AB×BR

=>( 1/2 ) ×10×5=25

Area of the darkened area equals area of square 2 area of triangles,

which is 100 (25+25)=50.

Area of the shaded area equals 50.

Therefore , the solution of the given problem of surface area comes out to be area of the shaded area equals 50.

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Answer: 12, 16, 20, and 320.

Step-by-step explanation:

The value of x can be solved as follows, take note of the numbers you will need to drag to complete the equations:

4x + 12x = 320 (segment addition postulate)

16x = 320 (combining like terms)

x = 20 (dividing both sides by 16)

We would end up with the value of x, which equals 20.

Numbers that we end up using are: 12, 16, 20, and 320.

The equivalent exponential expression for this problem is given as follows:

(2/x)² = 4/x².

The expression for this problem is defined as follows:

(2/x)².

We have a fraction that is squared, meaning that both the numerator and the denominator are squared, hence:

This means that the equivalent exponential expression for this problem is given as follows:

(2/x)² = 4/x².

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Answer:

Step-by-step explanation:

it depends on where each point is on each chart because they can't be blank

The quotient of the division (x^2-3x+5) divided (x-1) is x - 2 with a remainder of 3

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

(x^2-3x+5) divided (x-1)

Using the long division method of quotient, we have

x - 1 | x^2 - 3x + 5

The division steps are as follows

           x - 2

x - 1 | x^2 - 3x + 5

        x^2 - x

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

             -2x + 5

             -2x + 2

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

                         3

Hence, the quotient is x - 2

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Answer:

Step-by-step explanation: The formula for the line that intersects at (8,-5) and is parallel to line x+y = 8 is given by the algebraic expression y = -x +3.

What is Algebraic expression?

The concept of algebraic expressions is the use of letters or alphabets to represent numbers without providing their precise values.

Variables and constants can both be used in an algebraic expression.

A coefficient is any quantity that is added before a variable and then multiplied by it.

The Algebraic expression in this case is:

x + y = 8

which traverses points (8,-5)

Let's start by utilizing the point-intercept equation of line, which is provided by: to determine the slope of line m, that is parallel towards the line x + y = 8.

y = mx + c →(1)

x + y = 8

y = -x + 8

Comparing the aforementioned Algebraic expression to equation (1), we obtain

m = -1

The slope of the line parallel to the line x + y = 8 will now be the same, and it will be m = -1.

Let's use the point-slope equations of line to determine the linear equation now:

(y-y₁) = m(x-x₁)

Changing every value in the equation above to obtain the Algebraic expression for a line

(y-(-5)) = -1(x-8) (x-8)

(y+5) = -x+8

y + 5 = -x +8

y = -x +3

The formula for the line that intersects at (8,-5) and is parallel to line x+y = 8 is given by the algebraic expression y = -x +3

Answer:

-18

Step-by-step explanation:

The annual sales is 322,511.6 in 4 years.

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

Given that;

Record sales are increasing by 6% each year.

And, 260,090 records were sold this year.

Now, We have;

Record sales are increasing by 6% each year.

Hence, After 4 years;

The annual sales = 260,090 + 4 × 6% of 260,090

                           = 260,090 + 4 × 6/100 × 260,090

                           = 260,090 + 62,421.6

                           = 322,511.6

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Answer:328,358

Step-by-step explanation: