SIMPLIFIED Uplift Summer Algebra 1 Final Assessment - Copy12 of 2012 of 20 ItemsQuestionColton solves -30=6(x-1) by dividing both sides by 6 first. Kaylee solves the same equation by using the Distributive Property first on the right side of the equation. Who is correct?

ANSWER

EXPLANATION

First we have to find the partial products by multiplying each term of the first polynomial by each term of the second polynomial:

Now the second term of the second polynomial:

And now we just have to add these partial products:

we have

solve for d

therefore

From the information given, the entrance to a state park costs $5 per vehicle, plus $2 per person in the vehicle. Given that 4 people entered the one vehicle, the amount that would be paid for the vehicle is $5. Sinec it is $2 per person, the amount for 4 persons would be 2 * 4 = 8

Thus, the total cost would be

5 + 8 = $13

Answer:

10 (duh)

Step-by-step explanation:

Solve the following system of equations;

The answer is 0 = 24, which is not possible.

Hence, the system of equations has NO SOLUTION

You have to determine the solution of the equation system by looking at the graph.

For any equation system there are three possible scenarions, that the system has "no solution", that the system has "infinite solutions" and that the system has "one solution"

Looking at the graph you can determine which situation if:

- both lines are parallel, they never meet, which indicates that the system has no solution.

- both lines are superimposed, i.e. they seem as if there is only one line, the system has infinite solutions.

- both lines cross at one point, this indicates that the system has only one solution and the solution will be the point where the lines intersect.

In the given graph, the lines cross at one point, which means that the system has one solution. To determine said solution you have to read the x and y coordinates of the point in the grid.

The lines meet at x=4 and y=2, which means that the solution of this system is a

Answer:

A. as x→∞, y→∞ as x→−∞, y→−∞

Explanation:

Given the function:

In order to determine the end behavior of f(x), we use the leading coefficient test.

When using the Leading coefficient test, the following rule applies:

• When the ,degree is odd and the leading coefficient is positive,, the graph falls to the left and rises to the right.

• When the ,degree is odd and the leading coefficient is negative,, the graph rises to the left and falls to the right.

• When the ,degree is even and the leading coefficient is positive,, the graph rises to the left and right.

• When the ,degree is even and the leading coefficient is negative,, the graph falls to the left and right.

From the function, f(x):

• The degree of the polynomial = 3 (Odd)

• The leading coefficient is 2 (Positive)

Thus, using the 1st rule of the 4 given above, we have that as x→∞, y→∞ as x→−∞, y→−∞.

The correct option is A.

Explanation

We can round to the nearest hundreds of thousands below.

Answer:

Zoo D: 200,000

Zoo E: 900,000

Zoo F: 400,000

Answer: 80

Step-by-step explanation:

= 72/90

= 72/0.9

= 80

The value of x is 50 for which line l is parallel to line m and the angles are equal by the properties of parallel lines that is vertically opposite angles are equal.

Two lines (in the same plane) are said to be parallel if they never collide, regardless matter how far they are extended on either side. Parallel lines travel parallel to each other, like train tracks. Parallel lines in geometry are two lines in the same plane that are at equal distance from each other but never intersect. They can be both horizontal and vertical in orientation. Parallel lines can be found in everyday life, such as zebra crossings, notepad lines, and railway tracks.

Here,

Since l ⇵ m,

Vertically opposite angles are equal by the properties of parallel lines.

2x-5=95

2x=100

x=50

The value of x is 50, which means that line l is parallel to line m and the angles are equal according to the property of parallel lines, which states that vertically opposing angles are equal.

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First, we need to find the midpoint. We can find it using the following equations:

Where:

So:

Now, we need to find the slope of the line segment:

Since it is the line of the perpendicular bisector:

Using the point-slope equation:

Answer:

a)

Given:

The equation is,

The objective is to sketch the graph of the equation.

Since, the highest degree of the equation is 1, it could be a straight line. The general equation of straight line is,

Here, m represents the slope of the equation and c represents the y intercept. Then comparing the both equations,

Substitute, y = 0 in the given equation.

Thus, at y = 0, the value of x = 5.

Using the coordinates (5,0) and y intercept c = 7, the graph will be,

Hence, the required graph is obtained,

Given the functions:

Let's determine the transformation that occurred from f(x) to g(x).

Apply the transformation rules for functions.

After a shift d units to theupwards, we have:

Thus, from the given translation, we can see that the function f(x) is translated 4 units to get the function g(x).

The meaning of;

In algebra, when there is an unknown number it is generally represented by a letter (such as x,y,z etc.)

The letters x in x/4 represents an unkown number.

So, x/4 represent the unknown number x divided by 4.

For example; if x=20, then;

The domain of a function is the set of values where the function is defined (values of x where y is defined).

The range of a function are the values of the function where is defined (values of y).

For the given function:

Domain: values of n {6,-8, 4, 2}

Range: values of k(n)

n= 6

n=-8

n=4

n=2

Then, the range is: {-16, 26, -10, -4}

Given

To draw 64ft long house using a 8 inch scale.

Explanation:

Since the unit of inch is smaller than the unit of feet.

Then, by using the 8inches long scale.

Consider, 1 inch is equal to 8ft.

That implies,

Hence,

Recall that the slope-intercept form of the line equation is of the form y=mx+b, where m is the slope and b is the y-intercept.

To transform the equation 10=-2y-x into the slope-intercept form we should apply algebraic operations so we isolate the y on one side of the equation.

Let's add x on both sides, we get

Now, lets divide by -2 on both sides, we get

we see that this now has the slope-intercept form, where the slope is m=(-1/2) and b=-5

The perimeter of a polygon is given by the sum of the length of its sides. For the polygon in the picture we have the following side lengths:

Then their sum is:

We can group like terms. Like terms are terms multiplied by the same power of x. In this case we have two groups of like terms: constants and terms multiplied by x. Then we group them:

We can use the distributive property in the terms with x. For example:

We use this and we also add the constants so we get:

Then the answer is that the perimeter of the figure is 18x+44.

The correct options are : x = 1.5, side length is 1.6, and side length is 3.9.

We are given a triangle. The vertices of the triangle are P, Q, and R. The lengths of the sides PQ, QR, and RP are "x + 0.1", "x + 2.4", and "3x - 0.6". The triangle is an isosceles triangle. The lengths of the sides RP and QR are equal to each other. So, we can form an equation and find the value of the variable "x".

RP = QR

3x - 0.6 = x + 2.4

2x = 3

x = 1.5

The length of the side PQ is x + 0.1 = 1.5 + 0.1 = 1.6. The length of the side QR is x + 2.4 = 1.5 + 2.4 = 3.9. The length of the side RP is 3x - 0.6 = 3(1.5) - 0.6 = 3.9.

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The sum of 4 consecutive integers is 254. What is the value of the greatest integer?

Let

x -----> the first integeer

x+1 ----> second integer

x+2----> third integer

x+3 ----> fourth integer

we have that

x+(x+1)+(x+2)+(x+3)=254

solve for x

4x+6=254

4x=254-6

4x=248

x=62

therefore

the greatest integer is x+3

so

62+3=65

Given equation:

Let's solve the question to identify the type of solution.

Using factorization method:

The solution is thus

Hence, there is one solution and it is real.

Answer: 1 real (Option B)

Answer:

7.05%

Explanation:

Mr Bernard taxable income = $68,000

Amount paid as social security tax on earnings = $4,794

Let the social security tax rate = x

This gives:

Next, solve for x:

The social security tax rate for that year (to the nearest hundredth of a percent) is 7.05%.

The boxplot that shows points that Dwight scored in each game has a minimum value of 1 point and a maximum value of 20 points.

The box plot that shows the points that Ron scored in each game, has a minimum value of 4, and a maximum value of 18 points.

The values below the minimum point and above the maximum point of the data set can be considered "outliers", i.e. atypical observations, and the probability if them being observed is very low.

Ron's box plot goes from 4 to 18 points, it is very unlikely for him to score less than 3 points or above 18, both scores would be considered "outliers" for him.

But, Dwigth's box plot goes from 1 to 20, which means that "scoring less than 3 on a game" or "scoring more than 18 on a game" are more possible situations for him.

So Dwight is more likely to score more than 18 points on a game and he is also more likely to have a very bad game and score less than 3 points.

There is no mistake in Chase solving steps.

An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values. In a equation say : ax + b, [a] is called coefficient of [x] and [b] is independent of [x] and hence is called constant.

We have a equation :

(1/3)(g - 3) = 3

We can write -

(1/3)(g - 3) = 3

We can write -

g - 3 = 3 x 3

g - 3 = 9

g = 12

Therefore, there is no mistake in Chase solving steps.

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The formula for finding the area of the unshaded segment is given as

Given the following parameters,

π = 3.14

θ = 80°

r = 5 cm

Substituting,

To find the area of the shaded portion, we would subtract the area of the unshaded segment from the area of the circle.

Area of circle = πr²

Therefore,

The area of the shaded region = 78.5 - 5.1 = 73.4 cm²

aₙ = 1/2(5/2-4√2)(1-√2)ⁿ+1/2(5/2+4√2)(1+√2)ⁿ-n-5/2 is the solution of aₙ -2aₙ₋₁ + aₙ₋₂ = 2n + 1

Recurrence relation is an equation according to which the nth term of a sequence of numbers is equal to some combination of the previous terms

aₙ -2aₙ₋₁ + aₙ₋₂ = 2n + 1

Homogenous case,

aₙ -2aₙ₋₁ + aₙ₋₂ with characteristic t²-2t-1=0

t=1

aₙ=C₁.(1-√2)ⁿ+C₂.(1+√2)ⁿ

Special case, Since non homogenous part is 2n+1

Let aₙ=pn+q, then

aₙ -aₙ₋₁ + aₙ₋₂=2n+1

pn+q-2(p(n-1)+q)-p(n-2)-q=2n+1

-2pn+qp-2q=2n+1

p=-1 and q=4p-1/2=-5/2

Combine both cases, aₙ = C₁(1-√2)ⁿ+C₂((1+√2)ⁿ-n-5/2

Substitute a₁=7 and a₂=19

a₁ = C₁(1-√2)+C₂((1+√2)-1-5/2

a₁ = C₁(1-√2)+C₂((1+√2)-7/2=7

(C₁+C₂)+(C₂-C₁)√2)=21/2..(1)

a₂ = C₁(1-√2)²+C₂((1+√2)²-2-5/2

= C₁(1-√2)²+C₂((1+√2)²-9/2=19

3(C₁+C₂)+2(C₂-C₁)√2)=97/2..(2)

By solving 1 and 2 we get

C₁=1/2(5/2-4√2)

C2=1/2(5/2+4√2)

aₙ = 1/2(5/2-4√2)(1-√2)ⁿ+1/2(5/2+4√2)(1+√2)ⁿ-n-5/2

Hence, aₙ = 1/2(5/2-4√2)(1-√2)ⁿ+1/2(5/2+4√2)(1+√2)ⁿ-n-5/2 is the solution of aₙ -2aₙ₋₁ + aₙ₋₂ = 2n + 1

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Write a function with vertical asymptote x=4, horizontal asymptote y=1, y intercept at (0,2).

A possible function can be express as:

Let's prove that this function fulfils our conditions. Let's start with the y-intercept, we know that this happens when x=0, then we have:

Hence the y-intercept is at (0,2).

Now, we know that a rational function has horizontal asymptote y=b if:

Let's find these limits:

and:

This means that we have a horizontal asymptote y=1 as we wanted.

Now, a rational function has vertical asymptote at x=a if:

to determine the value of a we need to look where the function is not defined, that is, the values which make the denominator zero, in this case we have:

Then we need to find the limits:

Now, if we approach the value x=4 from the left we notice that as x gets closer to 4 the function gets bigger and bigger, for example:

if we follow this procedure, we conclude that:

Similarly, if we approach x=4 from the right the function gets smaller and smaller, for example:

Then we can conclude that:

Hence, we conclude that the function we proposed has a vertical asymptote x=4 like we wanted.

the properties we gave can be seen in the following graph: