Find the coordinates of the vertex and the equation of the axis of symmetry for the parabola given by the equation.
y=x²-x-6
vertex (x,y) = (1/2, -25/4)
axis of symmetry=

After reflection and shifts, all three transformations gives us the final function: y = -√(x+9) + 9. This function starts at the point (-9,9) and decreases as x increases. The graph of this function is a reflection of the original graph of y = √x about the x-axis, shifted up by 9 units, and shifted left by 9 units.

This function starts at the origin (0,0) and increases as x increases.

1. Reflect about the x axis:

A reflection about the x-axis takes every point on the graph of y = √x and maps it to a new point with the same x-coordinate, but the opposite y-coordinate. For example, the point (1,1) on the graph of y = √x would be reflected to the point (1,-1) on the new graph. This transformation effectively flips the graph upside down.

2. Shift up 9 units:

This transformation moves the entire graph up by 9 units. Every point on the graph is shifted vertically by 9 units. For example, the point (1,-1) on the reflected graph would be shifted up to the point (1,8) on the new graph.

3. Shift left 9 units:

This transformation moves the entire graph to the left by 9 units. Every point on the graph is shifted horizontally by 9 units. For example, the point (1,8) on the shifted graph would be shifted left to the point (-8,8) on the final graph.

Combining all three transformations gives us the final function: y = -√(x+9) + 9.

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Answer:

Translation of three units to the right (on the x-axis) and one unit down (on the y-axis).

If you want, this can be represented in vector form (3 1).

Step-by-step explanation:

This was done by translating the shape three units to the right and one unit down

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Jane sold 27 boxes of cookies last year if Jane sold 50 boxes of cookies this year. That is 4 less than 2 times the number of boxes she sold last year.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

Given ,

Jane sold 50 boxes of cookies this year. That is 4 less than 2 times the number of boxes she sold last year.

Let's assume the number of boxes Jane sold last year as x.

As per the given condition, 50 = 2x - 4

Adding 4 on both sides, we get:

50 + 4 = 2x - 4 + 4

54 = 2x

Dividing by 2 on both sides, we get:

x = 27

Therefore, Jane sold 27 boxes of cookies last year.

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The equation of the line passing through the points (0, 7) and (2, -5) is y = -6x + 7

An equation is an expression that shows how two or more numbers and variables are related using mathematical operations of addition, subtraction, multiplication, division, exponents and so on.

The standard form of a linear equation is:

y = mx + b

where m is the slope(rate of change) and b is the y intercept

As shown in the graph, the line passes through the points (0, 7) and (2, -5). Hence:

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\substituting:\\\\y-7=\frac{-5-7}{2-0} (x-0)\\\\y=-6x+7[/tex]

The equation of the line is y = -6x + 7

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Here the option is (D): Sum of Cubes.

The Given expression can be written as:

a³ + b³ = (a + b)(a² - ab + b²)

we can write 8x³ as (2x)³ and 243 as 3³.

we have,

8x³ + 243 = (2x)³ + 3³

we can rewrite the above equation

(2x + 3)(4x² - 6x + 9)

Therefore, the identity that can be used to rewrite the given expression is an option (D): Sum of Cubes

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Answer:

x = log(3) (8)

or log 8 base 3

Step-by-step explanation:

some number^x = another number

some number = base (the lower case number)

another number = the big number next to it.

put log infront in these situations.

Answer: -5/6

Step-by-step explanation:

Hopefully this helps, my friend, best of luck to you :)

Answer: 19

Step-by-step explanation:

(5x + 30) = 125   (opposite angles are equal)

5x = 95

x = 19

Answer:71

Step-by-step explanation:

-3-(-10)-(-64)=-3+10+64=71

Answer:

5 < x < 21

Step-by-step explanation:

given 2 sides of a triangle then the third side x is in the range

difference of 2 sides < x < sum of 2 sides , that is

13 - 8 < x < 13 + 8 , then

5 < x < 21

The domain of the function f(x)=7x+5/3x-1 is all real numbers except x = 1/3. This means that the function will produce a real number for any value of x except for x = 1/3.

Function in mathematics is a relation which assigns each element of a set (called the domain) to exactly one element of another set (called the codomain). It can also be thought of as a type of mapping from one set to another. Functions are used to model real-world problems and to simplify the expression of a certain problem. They are widely used in algebra, trigonometry and other areas of mathematics.

The domain of a function is the set of all possible inputs for the function. In other to determine the domain of a function, we must first identify the independent variable (x) and then determine which values of x can be used in the function.

In the given function, f(x)=7x+5/3x-1, the independent variable is x. To find the domain of this function, we must identify the values of x that will produce results that are real numbers. To do this, we must set the denominator (3x-1) equal to zero and solve for x.

We can solve this equation by factoring and setting each factor equal to zero:

3x - 1 = 0

3x = 1

x = 1/3

Therefore, the domain of the function f(x)=7x+5/3x-1 is all real numbers except x = 1/3. This means that the function will produce a real number for any value of x except for x = 1/3.

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There are 20 different election outcomes are possible.

An outcome is a possible result of a random experiment or event. It is a specific occurrence that may or may not happen, but that could happen under certain conditions. Outcomes are often associated with probabilities, which are measures of the likelihood that a particular outcome will occur.

This is a problem of counting the number of ways to choose 3 people out of 6 for 3 distinct positions. We can solve this using the combination formula:

ⁿCr = C(n, r) = n! / (r! * (n-r)!)

C(6, 3) = 6! / (3! * (6-3)!) = 20

Therefore, there are 20 different election outcomes possible for the president, secretary, and treasurer positions among a group of 6 people.

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Answer:

The transformation that converts the graph of f(x)=2|x|+4 into the graph of g(x)=|x|+2 is a Vertical Shrink.

To see this, note that the 2 in f(x) causes a vertical stretch of the absolute value graph. Removing the 2 in g(x) results in a Vertical Shrink of the absolute value graph. The +4 and +2 only cause a vertical shift of the graph.

Answer: Vertical Shrink

Step-by-step explanation:

The transformation that converts the graph of f(x)=2|x|+4 into the graph of g(x)=|x|+2 is a vertical shrink.

To see why, let's examine each function separately:

Therefore, the transformation from f(x) to g(x) involves removing the vertical stretch by dividing the absolute value term by 2. This results in a smaller "V" shape for the graph of g(x), or a vertical shrink.

The answer is:

[tex]$\boxed{\text{Vertical Shrink}}$[/tex]

Answer:

7/8 - 5/7 =

49-40/56 =

9/56

b) The mean and standard deviatiοn οf the data is 8.022 and 0.335 respectively.

In statistics, mean is measure οf central tendency that represents average value οf set οf numbers. It is calculated by adding up all  values in  set and dividing  sum by the tοtal number οf values in  set.

b) Tο determine the mean and standard deviatiοn οf the data, we can input the given values intο a calculatοr οr a spreadsheet prοgram and use the apprοpriate fοrmulas. Here are the calculatiοns:

Mean = (7.96 + 8.54 + 7.92 + 8.40 + 8.02 + 7.91 + 8.12 + 7.85 + 8.27 + 7.67) / 10

= 8.022

Standard deviatiοn = sqrt([(7.96 - 8.022)² + (8.54 - 8.022)² + ... + (7.67 - 8.022)²] / 9)

= 0.335 (rοunded tο 3 decimal places)

Therefοre, the mean petrοl price is 8.022 and the standard deviatiοn is 0.335.

c) The histοgram appears tο be slightly skewed tο the right, as the tail οf the histοgram extends further tο the right than tο the left.

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A. The intercept does not have a practical interpretation and is not statistically meaningful.

What is line regression?

Linear regression is a statistical method used to model the relationship between a dependent variable (also called the response or target variable) and one or more independent variables (also called predictors or explanatory variables) in a linear fashion.

B. The intercept is 4.62 mpg.

C. The value of the intercept represents the predicted city mileage for Highway gas mileage of 0 mpg. However, such a car does not exist, so the intercept is not statistically meaningful.

The intercept represents the value of the dependent variable (highway gas mileage) when the independent variable (city gas mileage) is equal to 0. However, in this case, it is not possible for a car to have 0 city gas mileage and still be in operation.

Therefore, The intercept does not have a practical interpretation and is not statistically meaningful.

In fact, the intercept can be considered as a theoretical value that is not meaningful in the context of the data.

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Answer:

The best option that describes a sample that enables you to draw accurate inferences from the sample is option C: "The sample is random and representative, but not biased."

A random sample is one in which every member of the population has an equal chance of being selected. This helps to ensure that the sample is not influenced by any outside factors that could skew the results.

A representative sample is one that accurately reflects the characteristics of the population it is drawn from. This ensures that the results obtained from the sample can be generalized to the larger population.

However, if the sample is biased, it may not accurately represent the population. This could lead to inaccurate inferences and conclusions.

Therefore, a random and representative sample that is not biased is the best option for drawing accurate inferences from the sample.

Step-by-step explanation:

Therefore , the solution of the given problem of expressions comes out to be b + 8 when 8a-2b+8 and -2a+6b are added together.

There is a need for calculations like joining, random variable division, variable multiplication, and removal. If they were united, the following would happen: A mathematical equation, some data, and a formula. A statement of truth is composed of numerical data, formulae, components, and mathematical operations like additions, subtractions, errors, and segmentations. One can assess and analyse words and sentences.

Here,

The formula is as follows:

=> 8a - 2b + 8 - 2a + 6b - (5b - 6a)

By combining similar words to make the expression shorter, we get:

=> (0a - b + 8 = -b + 8)

=>  (8a - 2a - 6a) + (-2b + 6b - 5b)

Therefore, the answer is b + 8 when 8a-2b+8 and -2a+6b are added together.

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Answer:

The correct answer is: slope= -1;  y-intercept (0,2)

Step-by-step explanation:

The given equation is:   [tex]q=2-r[/tex]

Assuming [tex]q[/tex] and [tex]r[/tex] as [tex]y[/tex] and [tex]x[/tex] respectively, the equation becomes:  [tex]y=2-x[/tex]

Rearranging the terms in right side:  [tex]y=-x+2[/tex]

Comparing this above equation with the slope-intercept form [tex]y=mx+b[/tex], we will get.....

[tex]mx=-x[/tex] ⇒ [tex]m=\frac{-x}{x} =-1[/tex]

[tex]and[/tex]

[tex]b=2[/tex]

So, the slope is -1 and y-intercept is (0, 2)

Answer:

Proofs attached to answer

Step-by-step explanation:

Proofs attached to answer

The values of h1 and h2 for which v3 is a linear combination of v1 and v2 is given as follows:

Vector v3 being a linear combination of v1 and v2 means that the following system of equations is used to relate the three vectors:

xv1 + yv2 = v3.

From each line of each vector, the system of equations relating these amounts is given as follows:

From the second equation, considering h1 = 1, the value of y is given as follows:

1 = -y

y = -1.

Hence, from the third equation, the value of h2 is obtained as follows:

-1 + 3(-1) = h2

-1 - 3 = h2

h2 = -4.

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If we take the values are h₁ = -1,  h₂ = 2, then the last vector is a linaer combination of the first two.

Here we want to find the values of h₂ and h₃ such that the last vector is a linear combination of the first one, that means that we can write:

a*v₁ + b*v₂ = v₃

For each of the components we can write:

a*1 + b*0 = 1

a*0 + b*-1 = h₁

a*-1 + b*3 = h₂

With the first equation we conclude that a = 1, then:

1*0 + b*-1 = h₁

1*-1 + b*3 = h₂

If we also take b = 1 we will get:

0 - 1= h₂

-1 + 3 = h₃

Then the values are h₁= -1,  h₂ = 2.

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Answer:

Step-by-step explanation:

Farmer Ed has 1,000 meters of​ fencing, and wants to enclose a rectangular plot that borders on a river. If Farmer Ed does not fence the side along the​ river, what is the largest area that can be​ enclosed?

The numeric value of f(x) = 3x² - 7x - 4 at x = 0 is given as follows:

f(0) = -4.

To obtain the numeric value of a function or of an expression, we substitute each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.

The function for this problem is defined as follows:

f(x) = 3x² - 7x - 4

We want to find the numeric value of the function at x = 0, hence both instances of x in the definition of the function are replaced by zero and then we add the terms, as follows:

f(0) = 3(0)² - 7(0) - 4

f(0) = -4.

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Answer:

0.19^9

0.19 to the 9th power

Step-by-step explanation:

Use Exponent Rules:

If you are multiplying terms with the same base, then ADD the exponents.

see image

Answer:

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Answer:

Step-by-step explanation:

SEE THE GRAPH

For the graph of the rational function the as x → −∞​, f(x) → −∞​.

A rational function is the ratio of two polynomial functions with a non-zero denominator polynomial. R(x) = P(x)/Q(x), where P(x) and Q(x) are polynomial functions, is the standard representation of this relationship. We studied the rational number idea in previous grades. When the denominator is not equal to zero, it is the quotient or ratio of two integers. Rational, then, is a name that comes from the term ratio.

From the given graph we observe that as the value of x tends to - ∞, the value of f(x), that is, the value of y constantly goes upwards and leftwards.

Thus,

As x → −∞​, f(x) → −∞​.

Hence, for the graph of the rational function the as x → −∞​, f(x) → −∞​.

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Thus, the length of the missing side for the given Right triangles using  the Trigonometric Ratios is found as :x = 18.47 units.

The leg, denoted as, that is next to the 30 degree angle θ is represented by Side BC. To get the length of side BD, the hypotenuse of triangle BCD, we use the cosine ratio.

cos θ = Adjacent leg / Hypotenuse = BC/BD

cos 30° = 8√2 / BD

Now, we know.

cos 30° = √3/2

√3/2 =  8√2 / BD

BD = 8√2 / √3/2

BD = 16√2 / √3

On rationalising;

BD = 16√2*√3 / √3*√3

BD = 16√6 / 3

Sin A = Opposite leg /Hypotenuse = BD / x

Sin 45° = (16√6 / 3) / x =  16√6 / 3x

We know that:

Sin 45° = 1/√2

(1/√2) = 16√6 / 3x

(1/√2) * x = 16√6 /3

Or,

√2/2 * x = (16√6 /3) * (2/√2)

x = 32√3 / 3

x = 18.47

Thus, the length of the missing side for the given Right triangles using  the Trigonometric Ratios  is found as :x = 18.47 units.

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The correct question is-

Find the missing side length. Give the answer as radicals in simplest form.

The difference between the interest paid with the minimum monthly payment and the interest paid with the $527.16 monthly payment is $83,421.

What is the interest?

Interest is the price you pay to borrow money or the cost you charge to lend money. Interest is most often reflected as an annual percentage of the amount of a loan. This percentage is known as the interest rate on the loan.

First, we need to calculate the monthly payment at a 10% interest rate for 25 years:

PV = 90,000

i = 0.10/12

n = 25*12 = 300

Using the formula for the monthly payment of a mortgage loan, we get:

[tex]P = i PV / (1 - (1 + i)^{(-n)})[/tex]

= 805.23

So, if Jackie paid the minimum monthly payment, she would pay $805.23 per month. The total amount paid over the lifetime of the loan would be:

Total amount paid = P * n = 805.23 * 300 = $241,569

The amount of interest paid would be:

Interest paid = Total amount paid - PV = 241,569 - 90,000 = $151,569

If Jackie had made payments of $527.16 per month, the total amount paid over the lifetime of the loan would be:

Total amount paid = 527.16 * 300 = $158,148

The amount of interest paid would be:

Interest paid = Total amount paid - PV = 158,148 - 90,000 = $68,148

Therefore, the difference between the interest paid with the minimum monthly payment and the interest paid with the $527.16 monthly payment is: $151,569 - $68,148 = $83,421

hence, the answer is not one of the choices provided.

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