Y intercept and slope

Answer:
3(y^2 + 1) + 2(y+4)

Step-by-step explanation:

2y^2 + 8.9 + 6y - 8.6 - 4y + y^2
= 2y^2 + y^2 + 6y - 4y + 8.9 - 8.6
= 3y^2 + 2y + 8(9-6)
= 3y^2 + 2y + 24
= 3y^2 + 2y + 3.2.2.2
= 3(y^2 + 1) + 2(y+4)

The length of AB in the line segment is 21 units.

A line segment is bounded by two distinct points on a line. In other words, a line segment is a part of a line that connects two points which are considered to be its endpoints.

Therefore, let's find the length AB, in the line segment AC.

Hence,

AC = AB + BC

AC = 23

AB = 2x + 7

BC = 3x - 19

Therefore,

23 = 2x + 7 + 3x - 19

23 = 5x  - 12

23 + 12 = 5x

35 = 5x

divide both sides by 5

x = 35 / 5

x = 7

Therefore,

AB = 2x + 7 = 2(7) + 7 = 14 + 7 = 21

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1) Note that in the problem above, the complete table is given as:

Team Number:     1             2      3           4           5

Best Jump (ft)       20.6    21.5    20.9      19.4        20.2

2) If Best Jump is denoted as y and Team number as x then, Best Jump is the Range while Team Number is the Domain.

3) For each element of the domain, there is a corresponding element of the range. So this relation is a function.

Domain and range are crucial characteristics that aid in the definition of a relationship. The domain is a collection of input values.

The independent variable represents these values, which are graphed on the axis of a coordinate graph. A function's range is its collection of output values.

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The equation of rational function is (c) g(x) = (2x + 4)/(x + 1).

Each element of X receives exactly one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given that,

The function g(x).

The graph of a function never touches the x = 1 line

At x = -1 there will be a vertical asymptote.

At x = -2 there will be a horizontal asymptote.

The equation of the function g(x) will be:

g(x) = (2x + 4)/(x + 1)

The equation of rational function is g(x) = (2x + 4)/(x + 1)

Therefore,  g(x) = (2x + 4)/(x + 1) is correct.

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Answer:

X > -20

Step-by-step explanation:

-10 - 9/2 x < 80

Move 10 to the other side

- 9/2 x < 80 + 10

Simplify

-9/2 x < 90

-9 x < 180

x > -20

(We switch the inequality sign if we are dividing with negatives)

The values of A and B are 2 and 4 respectively.

Given is the equation as -

(x + A)² - 3 = x² + 4x + B

We can write the given equation as -

(x + A)² - 3 = x² + 4x + B

x² + A² + 2Ax = x² + 4x + B

A² + 2Ax = 4x + B

A² + 2Ax = B + 4x

Equating both sides, we get -

A² = B

and

2A = 4

A = 2

Then B will be equivalent to 4.

B = 4

Therefore, the values of A and B are 2 and 4 respectively.

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Answer: $272

Step-by-step explanation: you would multiply 250 * 0.022 = 5.5

then you would multiply 5.5 * 4 = 22 then you would add 22 + 250 = 272

Answer:

A sample of helium was compressed at 35 °C from a volume of 0.5 L

to 0.25 L where the pressure is 500 mmHg. What was the original pressure?

Step-by-step explanation:

Answer:

y-int = 0

slope = -1

equation: y = -x

Step-by-step explanation:

The line crosses the y-axis at y = 0, so the y-intercept is 0.

Go from (0, 0) to (-1, 1).

slope = m = rise/run = 1/(-1) = -1

y = mx + b

y = -x

y-int = 0

slope = -1

equation: y = -x

P(1.6,-2.9) are the coordinates of circumcentre of the triangle

The circumcenter of a triangle is the point where the perpendicular bisectors of the sides of that particular triangle intersect.

Let L(3,−6), M(5,−3), N(8,−6) be the vertices of the given △LMN.

Let P(x,y) be the circumcentre of △LMN. Then,

PL = PM = PN

Also, PL² = PM² = PN²

PL² = PM²

(x-3)² + (y-(-6))² = (x-5)² + (y-(-3))²

(x-3)² + (y+6)² = (x-5)² + (y+3)²

x²-6x+9 + y²+12y+36 = x²-10x+25 + y²+6y+9

4x + 6y = -11   ---- (1)

Also, PM² = PN²

(x-5)² + (y-(-3))² = (x-8)² + (y-(-6))²

(x-5)² + (y+3)² = (x-8)² + (y+6)²

x²-10x+25 + y²+6y+9 = x²-16x+64 + y²+12y+36

6x - 6y = 27   ---- (2)

Solve (1) and (2) simultaneously by elimination:

6 × (4x + 6x = -11)

4 × (6x - 6y = 27)

24x + 36y = -66

24x - 24y = 108

subtract:

         60y = -174

         y = -174/60

         y = -2.9

Put y = -2.9 into (1):

4x + 6x = -11

4x + 6(-2.9) = -11

4x - 17.4 = -11

4x = 6.4

x = 1.6

Thus, the coordinates of the circumcentre of △LMN are P(1.6, -2.9)

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Answer:

102200

Step-by-step explanation:

564+458= 1022

1 decagram=100 decigram

So multiply the sum by 100

1022*100=102200

The value of the numerical expression 5² + 7 - 3 + 4 will be 33.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

The expression is given below.

⇒ 5² + 7 - 3 + 4

Simplify the expression, then we have

⇒ 5² + 7 - 3 + 4

⇒ 25 + 7 - 3 + 4

⇒ 36 - 3

⇒ 33

The value of the numerical expression 5² + 7 - 3 + 4 will be 33.

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Answer:

highest 77 and lowest is 4

Answer:

x > -4

Step-by-step explanation:

This is solved just like as if it was an equation. Its a two-step equation (inequality) The only thing that's different is with an inequality, it is imperative that you flip the inequality symbol if you multiply or divide by a negative number.

Here, we'll subtract 4 from both sides. Then divide by -3 on both sides. Flip! the < to a >.

see image.

x > -4.

[tex]4-3x < 16[/tex]

[tex]4-3x-4 < 16-4\\ \\-3x < 12[/tex]

[tex]\frac{-3x}{-3} < \frac{12}{-3} \\ \\x > -4[/tex]

Important. See that we switched the inequality symbol from "<" to ">", and this is because the symbol of the coefficient of variable "x" changed from negative to positive when it was divided by "-3". This rule will always be true, any time the symbol of the variable changed, the inequality symbol changes.

If x >-4 is the correct answer, then substituting x by "-4" in the inequation should make the inequation return the same value on both sides of the inequality symbol (>).

[tex]4-3(-4) > 16\\ \\4-(-12) > 16\\ \\4+12 > 16\\ \\16 > 16[/tex]

That's correct! x > -4 is the correct answer.

Answer:

a and c are both congruent to each other i just learned about rhombuses the other day so if a and c are congruent then b and d are congruent too

Answer:

To determine which loan will have a higher balance at the time of repayment, we need to calculate the balance of each loan after the interest has been compounded over the repayment period.

The unsubsidized Stafford Loan has an annual interest rate of 3.85% and a grace period of six months from the time of graduation. This means that the loan will accrue interest for a total of 12 months - 6 months = 6 months.

The balance of the unsubsidized Stafford Loan at the time of repayment can be calculated using the following formula:

Balance = Principal * (1 + Interest rate / Number of compounding periods per year)^(Number of compounding periods)

Plugging in the given values, we have:

Balance = $10,958 * (1 + 0.0385 / 12)^(6) = $10,958 * (1.003125)^(6) = $11,283.16

The PLUS loan has an annual interest rate of 4.15% and a balance of $11,421.51 at the time of repayment.

The balance of the PLUS loan at the time of repayment can be calculated using the same formula:

Balance = $11,421.51 * (1 + 0.0415 / 12)^(6) = $11,421.51 * (1.003479)^(6) = $11,973.54

Therefore, the PLUS loan will have a higher balance at the time of repayment, by $11,973.54 - $11,283.16 = $690.38.

Step-by-step explanation:

Answer:

-1

Step-by-step explanation:

Night: -4
Morning: -4 + 3 = -1

Answer:

Step-by-step explanation:

So Rahquez is traveling 20 mph, and Francesca is traveling 25 mph in opposite direction.

Acceleration is the rate of change of velocity of an object. It is a vector quantity that has both magnitude and direction. Mathematically, it is the derivative of velocity with respect to time. In simpler terms, it is the change in speed or direction of an object over time. If an object is speeding up, it is said to have a positive acceleration, while if it is slowing down, it has a negative acceleration.

Velocity is a vector quantity that describes the rate of change of an object's position. It has both magnitude and direction. The magnitude of velocity is the speed of an object, which is the distance covered per unit of time. The direction of velocity is the direction of the motion of an object. The standard unit of velocity is meters per second (m/s) or miles per hour (mph).

Let's call Rahquez's speed "R" and Francesca's speed "F". We know from the problem that:

F = R + 5 (Francesca is traveling 5 mph faster than Rahquez)

We also know that after 3 hours they are 105 miles apart, so we can set up an equation using distance = speed x time:

105 = (R + F) * 3

Now we can substitute the first equation into the second equation:

105 = (R + (R + 5)) * 3

Simplifying and solving for R, we get:

R = 20 mph

So Rahquez is traveling 20 mph, and Francesca is traveling 25 mph (since F = R + 5).

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The number of weeks w is given by the equation w = 6 weeks

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Let the number of weeks be represented as w

The prints cost $108 plus any add-ons she wants to purchase

The amount saved by Latisha per week = $ 18

So , the total amount saved by Latisha for w weeks = 18w

Now , the equation will be

18w = 108   be equation (1)

On simplifying the equation , we get

Divide both sides of the equation by 18 , we get

w = 108 / 18

w = 6 weeks

Therefore , the value of w is 6

Hence , the number of weeks is 6 weeks

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Answer: y = 2x-8

Step-by-step explanation:

Let's try to determine by substitution method. Starting from the first equation:

y = 2x-8

2·0-8 = -8

2·1-8 = -6

2·3-8 = -2

2·4-8 = 0

The first equation satisfies the conditions of the table.

Answer:

The area of the new triangle would be A = (1/2) * 30ft * 40ft = (1/2) * 1200ft^2 = 600ft^2

Step-by-step explanation:

To increase the size of a triangle by a scale factor of 10/3, you can multiply each side length of the triangle by 10/3.

The new dimensions of the triangle would be (10/3) * 9ft = 30ft and (10/3) * 12ft = 40ft.

The area of a triangle is given by the formula A = (1/2) * b * h, where b is the length of the base and h is the height of the triangle.

Using the new dimensions of the triangle, the area of the new triangle would be A = (1/2) * 30ft * 40ft = (1/2) * 1200ft^2 = 600ft^2.

The function f(x) = -x-3.

A relation between a collection of inputs and outputs is known as a function. A function is a connection between inputs in which each input is connected to precisely one output. Each function has a range, co-domain, and domain.

Given function:

f(x)+3f(-x) = 2x+6.

Let the function is an even function.

So, f(-x) = f(x)

To solve for f(x):

Substituting the property of an even function,

f(x) - 3f(x) = 2x + 6

-2f(x) = 2x + 6

f(x) = -x-3

Therefore, f(x) = -x-3 is the function.

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The product of 5 and 14 using the distributive property is 70.

Multiplication of two numbers is defined as the addition of one of the number repeatedly until the times of the other number.

a × b means that a is added to itself b times or b is added to itself a times.

For three numbers a, b and c, Distributive property states that,

a (b + c) = a b + a c

We have to find the product 5 × 14 using distributive property.

5 × 14 = 5 (12 + 2)

Using distributive property,

5 × 14 = (5 × 12) + (5 × 2)

          = 60 + 10

          = 70

Hence using distributive property, we can find the product of 5 and 14 as 70.

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A rational function is the algebraic expression y = 2 / x. (Correct choice: A)

Rational functions are algebraic expressions, whose form is described below:

R(x) = P(x) / Q(x)

Where:

Please notice that Q(x) must be a polynomial whose grade is greater than zero.

Polynomials are algebraic expressions of the form:

P(x) = ∑ cₙ · xⁿ, for n = {0, 1, 2, 3, ..., n, ..., m}, where m is the grade of the polynomial.

Therefore, by direct inspection, we conclude that algebraic expression y = 2 / x is a rational expression.

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Answer:

45 cars

Step-by-step explanation:

115+365+(55*5) = 755

755 - 485 =270

270/6 = 45

False, the function f(x)=[tex]-3x^3 + x^2 +2x[/tex] does not rises as x grows very small.

First, we need to know that functions are described as laws, expressions or rules that are used to show the relationship between two variables in an equation.

These variables are known as;

The function f(x) =[tex]-3x^3 + x^2 + 2x[/tex]  does not rise as x grows very small. When x approaches negative infinity, the dominant term is [tex]-3x^3[/tex], which becomes increasingly negative.

Therefore, the function decreases as x grows very small in the negative direction.

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Check the picture below.

Answer:

I hope this helps. Do let me know if you have any doubts and wish me luck I have my maths exams tomorrow!