Systems of equations

factor x2 − 2xy − 10y2 is (x+2y)(x−5y) .

A polynomial is an expression made up of indeterminates and coefficients that only uses addition, subtraction, multiplication, and positive-integer powers of variables. x2 4x + 7 is an example of a polynomial with a single indeterminate x.

Therefore,

phrase reordering

x2−10y2−2xy

Rearrange 10y2 and 2xY.

x2−2xy−10y2

Subtract 3 from 3xy.

x2−2(xy)−10y2

Write 2as 2 plus 5 x2+(25)(xy)10y2 instead.

The distributive property should be used.

x2+2(xy)−5(xy)−10y2

Delete any extra parentheses.

x2+2xy−5(xy)−10y2

Delete any extra parentheses.

x2+2xy−5xy−10y2

For a polynomial of the form ax2+bx+c, rewrite the middle term as a sum of two terms whose product is a⋅ c=1⋅−10=−10 and whose sum is b=−2

Put the first and last two terms together.

(x2+2xy)

−5xy−10y2

Subtract each group's GCF, or greatest common factor.

x(x+2y)−5y(x+2y)

Remove the polynomial's x+2y largest common factor to factor it.

(x+2y)(x−5y)

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In this problem the total price (p) will be equal to the price per kilogram (p) times the number of kilograms of food (k) so the equation will be:

To detremine the ordered pairs that represent the system of inequalities given, from the choices given, the corredct ordered pairs are:

(x, y) ==> (-6, 3), (-4, 2), (-6, 6), (-4, 0)

Answer: x = -1/2 and x = -3

Given the following quadratic function

The solution of the above quadratic function is x = -1/2 and x = -3

The total distance from Washington DC to Dulles airport is 15 miles

The total cost of the cab ride is $25. 50

The cabbie charges $1.50 per mile for the entire trip

Let T be the total cost of the entire trip

Let x represents the number of miles traveled

Let y be the flat rate of the cab ride

Total cost = flat rate + charge per trip x number of miles covered

Mathematically,

T = y + 1.5 * x

T = y + 1.5x

Where, 1.5 is the charge per trip.

The equation becomes

T = y + 1.5x

B

To calculate the flat rate of the cab ride?

The total cost = $25.50

Charges per mile = $1.5

Total number of miles = 15

Substitute the above values into the equation

25.50 = y + 1.5 x 15

25.50 = y + 22.5

Make y the subject of the formula

y = 25.50 - 22.5

Y = $3

The flat rate of the cab ride is $3

C

How much does it cos

The fraction of cookies left for Suzanne will be equal to 2/5 of the total number of cookies.

In Mathematics, fractions are represented as a numerical value, which defines a part of a whole. Example -  5/9. Here, (5) is called numerator and (9) is called denominator.

Given is Melinda who ate 3/5 of the cookies and left the rest for Suzanne.

Assume that the fraction of cookies left for Suzanne is represented by [x].

Fraction of cookies ate by Melinda = [y] = 3/5

The sum of the fractions representing the cookies eaten by both Suzanne and Melinda will be equal to 1. Mathematically -

x + y = 1

x + 3/5 = 1

x = 1 - 3/5

x = (5 - 3)/5

x = 2/5

Therefore, the fraction of cookies left for Suzanne will be equal to 2/5 of the total number of cookies.

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Answer:

Symmetric Property

Step-by-step explanation:

In order to calculate the volume of a cylinder, we can use the formula below:

If the base diameter is 6 in and the height is 8 in, we have:

Therefore the volume is 226.2 in³.

7

400 ÷ 64 = 6.25

This doesnt mean its 7 because if u multiply

6 x 64 =384

Multiply 64 x 7 it gives you 448 which means she has enough to go on the trip

The y-intercept of the equation y = 3x − 2 is (0, -2).

y-intercept

In Mathematics, an intercept is a point on the y-axis, through which the slope of the line passes. It is the y-coordinate of a point where a straight line or a curve intersects the y-axis. This is represented when we write the equation for a line, y = mx + c, where m is slope and c is the y-intercept.

Equation of a line

The standard form of equation of a line is ax + by + c = 0. Here a, b, are the coefficients, x, y are the variables, and c is the constant term. It is an equation of degree one, with variables x and y. The values of x and y represent the coordinates of the point on the line represented in the coordinate plane.

Given that lies on the graph of the equation y = 3x − 2.

We know that

In an equation of line

y = mx + c

m = slope of a line

c = y intercept

So therefore in given equation of line the y intercept is (0, -2).

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Consider that the general form of a line can be written as follow:

y = mx + b

where m is the slope and b the y-intercept.

Take into account that if two lines are parallel, then, the slopes of the line are equal. Based on the given equations, you can notice that the slopes are different, m1 = 2 and m2= -3.

Two lines are perpendicular if:

m1 = -1/m2

you can notice, based on the given equations that m1 is not equal to -1/m2, that is, 2 ≠ -1/(-3).

Hence, the lines are neither perpendicular nor parallel

1) ∠4 ≅∠1

Vertically opposite angle

2) ∠4 ≅∠5

Alternate angle

An angle is a figure in plane geometry that is created by two rays or lines that have a shared endpoint. The Latin word "angulus," which meaning "corner," is the source of the English term "angle." The shared terminus of two rays is known as the vertex, and the two rays are referred to as sides of an angle.

An acute angle is one that is smaller than 90 degrees. Right Angle: An angle with a 90 degree exactness. More than 90 degrees but less than 180 degrees is referred to as an obtuse angle. A straight angle is one that has a 180 degree angle. An angle that is more than 180 degrees but less than 360 degrees is called a reflex angle.

Given Data

∠1 ≅∠5

1) ∠4 ≅∠1

Vertically opposite angle

2) ∠4 ≅∠5

Alternate angle

3) p ║r

When a transversal cuts two lines so that the accompanying angles are congruent, the lines are said to be parallel. When a transversal cuts two lines so that their opposing interior angles coincide, the lines are said to be parallel.

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14 ounces of peppers ---------- 7 ounces of onions

wee need satisfy always this equivalence

B. satisfy the equivalence

2 ounces of peppers ---------- 1 ounce of onions

D. satisfy the equivalence

1 ounce of peppers ---------- 0.5 ounces of onions

we always need to have the relations 2:1

the correct statements are B and D

Answer:

Step-by-step explanation:

degree 6 -- triple root, double root, single root

leading coefficient is negative -- it opens downward

3 distinct roots

3 relative extrema

Price = 72.87

The markup is 30% or 30/100 = 0.3

Let's find the markup of the price:

The retail price, or selling price, is the price + markup.

Thus, retail price is:

Answers:

When the overdraft occurred, the balance was -48.31.

Major Takeaways. When your account balance drops below zero, you have an overdraft. If you have overdraft protection, your bank may permit a negative balance on your account or may provide one-time exceptions, but they may charge you for each transaction. Bank clients are required by federal regulations to choose to participate in overdraft protection schemes.

Let x represent the balance at the time the account entered overdraft.

He consistently made deposits totaling $30.84 a week in order to return to a positive balance.

Amount deposited per week = $30.84

Amount deposited 3 weeks =  30.84 × 3 = 92.52

Now amount in account after 3 weeks =x+ 92.52

We are given that After 3 weeks, he had $44.21 in the account.

So,x+92.52=44.21

x=44.21-92.52

x=-48.31

Hence The balance when the account went into overdraft was -48.31

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Let's say that the two objects have 5 centimeters and 7 centimeters of diameter.

The circumference of a circle is defined as

Where d is the diameter. Using the measures above, we have

Tucker is painting his pool deck over the weekend. The area of the deck is 76 1/2 square meters. He paints 2/3 of the deck before stopping to eat lunch. How many square meters does Tucker have left to paint after lunch?

Write your answer as a whole number, fraction, or mixed number. Simplify any fractions.

we have that

total area=76 1/2 m2

Convert to an improper fraction

76 1/2=76+1/2=153/2 m2

1-(2/3)=1/3

Multiply the total area by 1/3

(153/2)*(1/3)=51/2=25.5 m2 ------> 25 1/2 m2

To solve this question we are going to need to define an equation with the data that the problem gives us

The first part (rate of growth) shows us a derivate, this is equal to 9 square root of t or:

where P is the population size and t is the time in days

Now we need the population after 7 days, so we need the P(t) formula, which means that we need the integration

First, we send the dt to the other side to have something to integrate

Solving

We know that P(0)=600 so

Now we replace the t by 7

Answer: 711

Let x be the total of students in their Junior Year.

So, 84% of x =378

84% = 0.84

0.84x=378 (divided by 0.84)

x= 450 students.

The ones that chose not to take spanish will be:

450-378=72

72 students chose not to take spanish in their junior year.

Two lines are 2linese intersect to form linear pairs with equal measures one angle measures 2x other measure 11y+2. x is 45 and y is 8.

The sum of a linear pair of angles is 180 degrees.

Now, we are given two pieces of information. We will use these to develop equations and then solve the equations simultaneously.

First, we know that the two angles are equal, therefore:

2x = 11y+2-------.> equation 1

Second, we know that the two angles form a linear pair of angles, therefore:

2x +11y+2 = 180 -------.> equation 2

Substitute by equation 1 in equation 2:

2x +2x = 180

4x       = 180

        x =  45

Substitute with the value of x in equation 1 to get y as follows:

2x = 11y+2

2 (45) -2 = 11y

         88 = 11y

         y = 8

Therefore:

the first angle = 2x = 2(45) = 90 degrees

the second angle = 11(8)+2 = 90 degrees

The two angles are equal and their sum is 180 .

Line pairs of angles occur when two lines intersect at a single point. Angles are considered linear if they are adjacent after the intersection of these two lines. The sum of the angles of a linear pair is always 180°. Such angles are also called supplementary angles.

If there is a pair of adjacent angles, the pair is a linear pair if the sum of the two angles (their measures) is 180°. Thus, linear pairs of angles always add up to 180°.

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Answer:

Yes

Step-by-step explanation:

Any number divided by 1 equals itself. This rule tells us simply that if we have a number divided by 1, our answer will equal that number regardless of what that number is.

Hope this helps you

Tell me if I'm wrong

The equation to show the change in temperature between 9 a.m. and noon is given as d = x - y.

An equation contains two mathematical expressions that state that they are equal or equivalent.

We use the equation mark (=) to show that two expressions possess equality.

Air temperature at 9 a.m., y  -5.8 degrees Celsius

Air temperature at noon, x = -1.6 degrees Celsius

Change in temperature, d = 4.2 degrees Celsius (-1.6 - -5.8)

The equation to show the change is d = x - y, where d is the change in temperature, x is the final temperature, and y is the initial temperature.

Thus, based on the equation, the temperature increased by 4.2 degrees Celsium from the earlier -5.8 degrees Celsius to result in a final temperature of -1.6 degrees Celsius at noon.

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The formula for the expected value from an event is given as;

From the table given, we can obtain the expected value of winning as;

Therefore, the expected value of winning is $5.2

a) We can see that an increase in the number of employees (x) also leads to an increase in the number of products produced monthly, thus we can say that there is a positive correlation between the number of employees in the plant and the number of products produced monthly.

A positive correlation occurs when one variable increases with respect to another variable.

b) The function that best fits.

Let's first Find the rate of change(slope).

Take the points;

(x1, y1) ==> (0, 120)

(x2, y2) ==> (10, 200)

Use the slope formula:

We have:

Use the form:

y = mx + b

Where m is the slope and b is the y-intercept

We have:

y = 8x + b

Substitue 0 for x and 120 for y, to solve for b.

120 = 8(0) + b

120 = b

Thus, we have the function:

y = 8x + 120

f(x) = 8x + 120

c) The slope, m is = 8

The slope indicates that the avearge rate of change between both variables is 8.

The y-intercept can be said to be the point where the line of the plot crosses the y-axis. This means when the number of employees are is zero, the number of products will be 120.

It can also be called the constant value.

Answer:

1) 6000/30=200

2)5820/28=207.9 (1dp)

Step-by-step explanation:

A polynomial function is a function that only employs non-negative integer powers or only positive integer exponents of a variable in an equation such as the quadratic equation, cubic equation, etc. For instance, the exponent of the polynomial 2x+5 is 1.

 A polynomial equation in standard form before attempting to solve it. Factor it, then set each variable factor to zero after it has reached zero. The original equations' answers are the solutions to the derived equations. Factoring cannot always be used to solve polynomial equations.

The variable t in the formula b(t) stands for the number of years following 2008. This function's range of application is. More over 258.7 wouldn't make sense as a range. The function's graph is continuously drawn at all times.

Explanation:

Since 2008, the provided function b(t) displays the bobcat population in Northern Arizona. The number of years following 2008 is therefore represented by the variable t.

The domain of this function is because t stands for the number of years after 2008, which can be either positive or zero.(0,∞)

Provided that the given function is a quadratic function with a negative coefficient, it is a descending parabola. There is no meaning in the range above the vertex's y-coordinate.

Vertex function is (4.2,258.7)

This is polynomial function so the graph of the function always continuous

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Given:

Lan pays,

A semiannual premium of ​$650 for automobile​ insurance.

A monthly premium of ​$150 for health​ insurance.

An annual premium of ​$350 for life insurance.

To find:

The monthly expense.

Explanation:

According to the problem,

The amount paid for automobile​ insurance per year will be,

The amount paid for health​ insurance per year will be,

The amount paid for life insurance per year will be,

The total expenses in a year are,

So, the monthly expense is,

Therefore, the monthly expense is $287.50.

Final answer:

The monthly expense is $287.50.

For the value of c = 0,c=1 then A is not invertible

For given matrix  A is invertible if  c≠ 0 and c≠ 1

[tex]Given \ $A=\left[\begin{array}{ll}1 & 1 \\ c & c^2\end{array}\right]$ \\A matrix $A$ is invertible if $|A|={det}(A) \neq 0$.\\Now consider $|A|={det}(A)=0$.[/tex]

[tex]$$\begin{aligned}&\Rightarrow\left|\begin{array}{ll}1 & 1 \\c & c^2\end{array}\right|=0 \\&\qquad \quad \text { If } A=\left[\begin{array}{ll}a & b \\c & d\end{array}\right] \text { then }|A|={det}(A)=a d-b c\end{aligned}$$[/tex][tex]$$\begin{aligned}&\Rightarrow c^2-c=0 \\&\Rightarrow c(c-1)=0 \\&\Rightarrow c=0, c=1\end{aligned}$If $c=0$ or $c=1$ then \A \is \\not \ invertible. \\$\therefore$ Given matrix $A$ is invertible iff $c \neq 0$ and $c \neq 1$. \\ie Given marix $A$ is invertible for $c \in \mathbb{R}-\{0,1\}$.[/tex]

Matrix, a collection of numbers arranged in rows and columns forming a rectangular array. The number is called the elements or entries of the matrix. Matrices have wide applications in engineering, physics, economics and statistics, as well as in various areas of mathematics. Matrices also have important applications in computer graphics, where they have been used to represent image rotations and other transformations.

Different types of matrices are

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5^3 = 5x5x5 = 125

6^2 = 6x6 = 36

2^7 = 2x2x2x2x2x2x2 = 128

From least to greatest

36 - 125- 128

6^2- 5^3 - 2^7