1. Perform the indicated operations.
(8x2 - 16x - 9) - (14x² - 17x + 9)
r 1 Assessment FINAL Version
-6x²+x-18
6x² - x
6x²+x+18
-6x²-x-18

The distance between the two given points X(-3,3) and Z(4,4) in the given cartesian plane is XZ = √50 = 7.07 units.

As per the question statement, we are supposed to calculate the distance between the two given points X(-3,3) and Z(4,4) in the given cartesian plane. We know that the distance between any two points in the plane is given by:

d=√((x2 – x1)² + (y2 – y1)²), where "d" is the distance between the points (x1,y1) and (x2,y2). Using this formula to find the distance between the two given points X(-3,3) and Z(4,4).

XZ = √((4 +3)² + (4 – 3)²)

XZ = √((7)²+ (1)²)

XZ = √(50)

XZ = 7.07 units

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Remember that the coordinates are written in the form (x,y). Plot the points with the given coordinates: A(1,6), B(1,1) and C(5,1):

Draw a right triangle using the same measures for the legs in order to construct ΔDEF, as described below:

The slope point form is

m is the slope

x1, y1 are the coordinates of a point on the line

The slope of the line is -1

m = -1

point (-5, -4) lies on the line

x1 = -5 and y1 = -4

Let us substitute them in the form above

Remember (-)(-) = (+)

The equation of the line in the slope-point form is y + 4 = -1(x + 5)

Answer:

y2-y1 x2-x1

Step-by-step explanation:

-5-(-1)

--------

0-(-2)

-4

---

2

-2

----

1

The radius(r) of the wheel is;

The perimeter(P) of the wheel is given by the formula below:

The distance travelled by Ivan is 165m.

So, the number(n) of times the wheel is:

Hence, the correct answer is 47.8

The profit of the store is represented by the quadratic formula:

Where

P is the profit

x is the number of videos rented

The coefficients of the parabola are:

a= -1 (coefficient of the quadratic term)

b= 90 (coefficient of the x-term)

c=52 (constant)

The value of a is negative, which indicates that the parabola opens downwards and that its maximum value is represented by the vertex.

To determine the maximum profit, you have to determine the coordinates of the vertex.

First, calculate the x-coordinate of the vertex, to do so you have to use the following formula:

Replace it with the values of the coefficients a=-1 and b=90

Second, replace x=45 in the equation to determine the y-coordinate of the vertex:

The y-coordinate of the vertex represents the maximum profit.

So the maximum profit is $2077, the correct option is option A.

The probability that a player dealt with four hearts = 0

Probability is defined as the prediction of the occurrence of an event in a stated set.

This can be expressed in proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.

From the question given, the 6 sets include the following;

9, 10, jack, queen, king and ace.

There are no hearts given in the set of the event that occurred, therefore, the probability that a player dealt with four hearts = 0.

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option (c) is correct.

An expression is a set of numbers or variables combined using the operations + , – , × or ÷ . Arithmetic expression that contains only numbers and mathematical operators and algebraic expression that contains variables, numbers and mathematical operators.

Given that,

An expression

1/2bh + 4

There are two terms in the first term b and h are variables and its coefficient is [tex]\frac{1}{2}[/tex] .

In the second term only 4 is a constant term.

It means this expression has two.

(a)  Teemu said, "[tex]\frac{-1}{2}[/tex] is a coefficient"

In the first term [tex]\frac{1}{2}[/tex] is a coefficient of b and h.

(b)  Sammy said, "The entire expression is the sum of 4 terms."

No this expression has only two terms.

Hence, Neither student is correct.

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Answer: Only teemu

Step-by-step explanation: Because 1/2 is the numerical factor in a product involving variables and although sammy said it is the sum of 4 terms, there is 2 in the expression.

Answer:Its d(x)=1/4f(x)+9, mate

Step-by-step explanation:I just guessed and got it correct lol, also its "1/4" as a fraction

The given equation is

First, we subtract 6 on each side.

Then, we divide the inequality by 4.

We will determine how to evaluate the side length of a square given its area.

A square is a four sided 2D planar figure with all its sides at right angles and equal in magnitude as follows:

The side a square are all equal and will be denoted by a variable as follows:

We will now express the Area of the square in terms of its side length using the basic definition as follows:

We will now express the above in terms of the side length variable ( x ) as follows:

We are given that Natasha's garden has the following area:

Now we will equate the result of area of a square with the side length ( x ) terms as follows:

Evaluate(solve) the above the equation for the variable ( x ) by taking a square root on both sides of the equation as follows:

For practical sense, the variable ( x ) denotes the magnitude of the side length of the square which can not be negative. Hence, we have only solution for the side length ( x ) as follows:

Step 1

From the question, Hailey reads 48 pages of a book

Blake reads half as many as Hailey.

Hence Blake reads;

The answer will be together they read;

Answer; Option C

SOLUTION

The given question is

Simplify the expression

The difference of two cubes is given as

Hence the given expression becomes

This gives

Using the concept of volume, 700 milliliters of Solution B was used.

Each thing in three dimensions takes up some space. The volume of this area is what is being measured. The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.

When dealing with unknowns, the first step is to represent the unknowns using variables, draw up equations based on the available data, and then solve those equations to account for the unknowns.

Volumes of solutions A and B are here which is unknown.

Put these factors in place for us

Let x = the amount of solution A that was mixed in milliliters.

Let y= the amount of solution B that was mixed in milliliters.

The amount of volume utilized for A is 400 ml less than the amount used

for B.

This can be expressed mathematically as y - x = 400.

Or,

- x + y = 400 [1]

The ratios of alcohol in A and B are provided to us.

A contains 12% alcohol, hence its real alcohol content is 12% of x ml.

= 0.12x (12% = 12/100 = 0.12)

Similar to A, B has an alcohol content of 0.20x.

If x of A and y of B are combined, the total alcohol by volume is 0.12x + 0.20y.

and it is said that this amount is 176 ml.

Our second equation is therefore set up as 0.12x + 0.20y = 176 [2].

We create an equation containing only the other term by using both equations and removing either the x or y terms.

We should remove the x term from both equations to create a single equation that just contains the y term because the question only asks us to compute the volume of Solution B that was used.

Review the equations now:

- x + y = 400 [1]

0.12x + 0.20y = 176 [2]

x's coefficients should all be the same:

Increase [1] by 0.12

=> -0.12x + 0.12y =

= 0.12 x 400

=> 0.12x + 0.12y = 48 [3]

By adding [2] and [3], the x word is removed.

0.12x + 0.20y = 176+( -0.12x) + 0.12y = 48

0x + 0.32 y = 224

=> 0,32y = 224

Subtract 0.32 from both sides to get[tex]\frac{0.32y}{0.32}[/tex] = [tex]\frac{224}{0.32}[/tex]

==> y = 700

Therefore, 700 cc of Solution B was utilized.

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For the given points, vector in component form equals -6i^ - 7j^ and its magnitude is 9.22

A quantity or phenomena with independent qualities for both magnitude and direction is called a vector. The term can also refer to a quantity's mathematical or geometrical representation. Velocity, momentum, force, electromagnetic fields, and weight are a few examples of vectors in nature.

Examples of vectors include displacement, velocity, acceleration, force, and others that show both the direction and the size of a quantity. Vector: The displacement is -4 feet, while the velocity is -40 miles per hour. Negative displacement and velocity indicate that the object is travelling counterclockwise.

Vector in component form -

(-4 -2)i^ + (-2-5)j^

= -6i^ - 7j^

Magnitude of the vector equals =

√(-6)² + (-7)² = √85 = 9.22

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Complete Question -

Vector w has its initial point at (2, 5) and its terminal point at (-4, -2). Write the vector in component form and find its magnitude.

The segment RS has a length of 9 units

From the question, the partition of the line segment is given as

RS : ST : TU = 1 : 1 : 4

Where the endpoints of the line segments are R and U

This means that the length RS can be calculated using the following equation

Length RS = Ratio of RS/Sum of the ratios x The length of RU

Substitute the known values in the above equation

So, we have

Length RS = 1/(1 + 1 + 4) x 54

Evaluate the sum

Length RS = 1/6 x 54

Evaluate the products

Length RS = 9

Hence, the length of the segment RS is 9 units

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Step 1: We have the following expression:

Step 2: Fon finding the equivalent expression, we have to factoring the polynomial, this way:

Step 3: Now we have to find two integer numbers that the result of adding them is - 7 and the result of multipliying them is 12

First number: -4

Second number: -3

Therefore, we have now:

2 (x - 4) (x - 3)

Step 4

Explanation

We are given the following information:

• Amount at the beginning of an investment = $5500

• Percent decrease = 24.6%

We want to determine the decreased amount in dollars and the amount in his account at the end of the year.

We can determine the decreased amount with the formula below:

Therefore, the decreased amount can be calculated as:

Hence, the decreased amount is $1353.

At the end of last year, the amount left in his account can be calculated as follows:

Hence, the year-end amount is $4147.

Explanations:

Given the following parameters

An initial deposit of Gerard is "d" dollars

For the savings with 5% interest, the interest on "d" dollars will be expressed as;

Get the total savings plus interest in the first account

Hence the $1.05d will be in the first savings account if Gerard's initial deposit were d dollars

For the other account:

Initial deposit = "d" dollars

Interest = $100

Since the interest will be added to the first deposit, hence;

In Tabulated form:

Assuming Ken gets the same percentage as usuall in these 5 times, we can calculated how many times he did get on base by calculating 60% of 5.

To do this we transform 60% into decimal my dropping the percentage sign and dividing it by 100 and then we multiply the decimal by 5:

So, Ken got on base 3 times.

1)  The Linear equation that models the average price of a new home is;

y = -800x + 294000.

2) The prediction of the average price of a new hom in the year 2014 is; $256000

We are told that the average price in the year 2004 was $294000

We are told that y is the average price in a home in the year x, where x = 0 represents the year 2004. Thus, this means that the y-intercept is $294000.

Since the line must pass through the points (0, 294000) and (7, 288400), it means that;

Slope = (288400 - 294000)/(7 - 0)

Slope = -5600/7

Slope = -800

Now, we know that the general formula for equation in slope intercept form is; y = mx + c

where; m is slope and c is y-intercept.

Thus;

1) Linear equation is; y = -800x + 294000.

2) For the average price of a new home in the year 2014, this means that x = 2014 - 2004 = 10 years

Thus;

y = -800(10) + 294000

y = $256000

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The area of the circle is given as:

plugging the value given we have that:

Now, the circumference is given as:

where d is the diameter of the circle. The diameter is twice the raidues, hence the diameter is 38, therefore the circumference is:

Therefore the circumference is 38pi

Given the function

To find the inverse, we must recall that the domain of the function becomes the range of the inverse function and vice-versa.

We are already given the domain of f, all the real numbers equal or greater than zero.

The domain of the function is exactly the same because x squared is always positive or zero, thus the domain and range of the inverse should be x≥0.

Once we find the inverse function, we'll use this concept.

Step 1: Substitute f(x) for y:

Step 2: Swap the variables:

Step 3: Solve for y:

But as said above, the range of this function cannot include the negative numbers, thus the inverse function is:

The quadratic equation that has roots √3 + 1 / 2 and √3 - 1 / 2 and a leading coefficient of 9 is y = 9 · x² - 18√3 · x + 99 / 4.

In this problem we must determine the quadratic equation such that its roots are √3 + 1 / 2 and √3 - 1 / 2 and whose leading coefficient is equal to 9. This can be found by substituting on factor form:

y = a · (x - r₁) · (x - r₂)

Where:

If we know that r₁ = √3 + 1 / 2, r₂ = √3 - 1 / 2 and a = 9, then the quadratic equation is:

y = 9 · (x - √3 - 1 / 2) · (x - √3 + 1 / 2)

y = 9 · [x² - (√3 - 1 / 2) · x - (√3 + 1 / 2) · x + 3 - 1 / 4]

y = 9 · (x² - 2√3 · x + 11 / 4)

y = 9 · x² - 18√3 · x + 99 / 4

The quadratic equation is y = 9 · x² - 18√3 · x + 99 / 4.

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Given:

an equation is given as y = -8.

Find:

we have to find an equation parallel to the given equation and passing through (-6, -7).

Explanation:

Compare the given equation with y = mx + b,

we find that slope ,m = 0 ,

the equation of the line passing through (-6,-7) is

y - (-7) = m( x - (-6))

y + 7 = 0(x + 6)

y + 7 = 0

y = -7

Therefore, y = -7 is an equation which is parallel to y = -8 and passing through ( -6, -7).

The graph of both y = -8 and its parallel equation y = -7 which passes through (-6, -7) is given as below

Red line represents the equation y = -8

and blue line represents the equation y = -7 passes through the point (-6,-7).

Therefore, the equation of the line parallel to y = -8 and passing through (-6,-7) is y = -7.

Using linear functions, it is found that:

a) The expression to convert from Fahrenheit to Celsius is: y = 5x/9 - 160/9.

b) The inverse expression is: y = 9x/5 + 32.

The slope-intercept representation of a linear function is given as follows:

y = mx + b

The coefficients of the function are described as follows:

For the conversion of Fahrenheit to Celsius, we have two points, as follows:

(32,0), (68, 20).

When the input increases by 36, the output increases by 20, hence the slope is calculated as follows:

m = 20/36 = 5/9

Hence:

y = 5/9x + b.

When x = 32, y = 0, hence the intercept b is calculated as follows:

0 = 5/9(32) + b

b = -5 x 32/9

b = -160/9

Hence the equation is:

y = 5/9x - 160/9.

To find the inverse expression, we exchange x and y and then isolate y, as follows:

x = 5/9y - 160/9.

5/9y = x + 160/9

5y = 9x + 160

y = 9x/5 + 32.

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Each senior citizen ticket costs $7.

One child's ticket costs $14.

Describe algebra.

Algebra is one of the numerous subfields of mathematics. The study of mathematical symbols and the rules for employing them in formulas is commonly referred to as algebra, which runs across almost all of mathematics.

S represents the senior citizen ticket cost.

C is the child's ticket cost.

Price is expressed as USD per ticket.

8S + 15C = 266

8S + 8C = 168

Subtract both equations now to get rid of S

8S + 15C = 266

8S + 8C = 168

———————————-

7C = 98

C = 98/7

C = $14

Changing the value of C in the first

8S + 15(14) = 266

8S + 210 = 266

8S = 266 - 210

8S = 56

S = 56 / 8

S = $7

Hence, $7 is the price for senior citizen

And, $14 is the price for child

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The number of cans is proportional to the number of days, because each day it uses 2 c

we get that the final price of a 16-ounce smoothie is:

$4.94