Which function is equivalent to f(x) =2x² - 8x + 3?
g(x) = 2(x - 4)² - 13
g(x) = 2(x - 4)² + 19
g(x) = 2(x - 2)² + 11
g(x) = 2(x - 2)² - 5

Option C

For x = 1.5 we get f(x) = -2

Solution:

Given function is:

[tex]f(x) = 3.4x - 7.1[/tex]

We have to find the value of "x" so that f(x) = -2

Substitute f(x) = -2 in given function

[tex]-2 = 3.4x - 7.1[/tex]

Solve for "x" by moving the constants to one side and variables to other side

[tex]3.4x = -2 + 7.1\\\\3.4x = 5.1\\\\ \text{Divide both the sides of equation by 3.4 }\\\\x = \frac{5.1}{3.4}\\\\x = 1.5[/tex]

For x = 1.5 we get f(x) = -2

We can verify by substituting x = 1.5 in given function

[tex]f(1.5) = 3.4(1.5) - 7.1\\\\f(1.5) =5.1-7.1\\\\f(1.5) = -2[/tex]

Thus for x = 1.5 we get f(x) = -2

Answer:

33%

Step-by-step explanation:

hope this helps :)

Answer:

it is 33% thank you

Step-by-step explanation:

hope this helps ,':) XD

Answer:

The range is the resulting y-values we get after substituting all the possible x-values.

For the given function : [tex]f(x) = \frac{3}{4x} -4[/tex]

See the attached figure.

The zeros of the denominator at x = 0

The domain is: (-∞,0)∪(0,∞)

The range of the function is the domain of the inverse function of f(x)

y = 3/(4x) - 4

y + 4 = 3/(4x)

4x = 3/(y+4)

[tex]x=\frac{3}{4(y+4)}[/tex]

The zeros of the inverse function:

4(y+4) = 0

y + 4 = 0

y = -4

∴ The range is (-∞,-4)∪(-4,∞)

So, the answer is {y | y > –4} ∪ {y | y < – 4}

=========================================

Note: If the given function is : [tex]f(x) = \frac{3}{4} x-4[/tex]

It will be first degree polynomial function.

Both of the domain and the range = all real numbers R

Answer:

D.Train A by a factor of 1.1

Step-by-step explanation:

[tex](f+g)(x) \text{ is equal to } x^2+x-8[/tex]

Solution:

Given that the functions are:

[tex]f(x) = x-8\\\\g(x)=x^2[/tex]

We have to find the value of (f + g)(x)

By operations on functions, we know that,

(f + g)(x) = f (x) + g(x)

Thus (f + g)(x) can be found by adding both the given functions

[tex](f + g)(x) = f (x) + g(x)\\\\(f + g)(x) = x - 8 + x^2\\\\(f + g)(x) = x^2+x-8[/tex]

Thus (f + g)(x) is equal to [tex]x^2+x-8[/tex]

Answer:

X=4

Step-by-step explanation:

The angle CA equals 4. The angle AB are equal to the angle CA therfore, the outcome of x=4.

Final answer:

To find how long it takes Miguel to drive 469 miles at the same rate he drove 737 miles, simply divide the distance by his speed. In this case, it would take him 7 hours.

Explanation:

To find the time it would take Miguel to drive 469 miles at the same rate:

Therefore, it would take Miguel 7 hours to drive 469 miles at the same rate.

The total cost which includes tip, food cost without tax and sales tax for the considered situation is 19.63 bucks approximately.

Suppose the value of which a thing is expressed in percentage is "a'

Suppose the percent that considered thing is of "a" is b%

Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).

Thus, that thing in number is

[tex]\dfrac{a}{100} \times b[/tex]

For this case, we're specified that:

Pizza cost = 15.95 +7% of tax on 15.95 bucks

Tip  = 15%  of pizza cost

Total cost = Pizza cost + tip

7% of 15.95 is: [tex]\dfrac{15.95}{100} \times 7 = 1.1165[/tex] bucks

Thus, pizza cost = The  (15.95 + 1.1165) = 17.0665

Tip price = 15% of 17.0665 = [tex]\dfrac{17.0665}{100} \times 15 \approx 2.56[/tex] bucks.

Thus, total cost ≈ 17.0665 + 2.56 ≈ 19.63 bucks

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Answer:

  no

Step-by-step explanation:

If you mean

  27^4 - 9^5·3^9 = -1161730026

it has no factors of 5, so cannot be divisible by 25.

__

If you mean ...

  (27^4 -9^5)/3^9 = ((3^3)^4 -(3^2)^5)/3^9 = 3^10(3^2 -1)/3^9 = 3(9-1) = 24

it is not divisible by 25, either.

Answer:

[tex]3^9(25)[/tex]

Step-by-step explanation:

Let's rewrite all values with a base of 3:

[tex]27^4 = (3^3)^4 = 3^{12}\\\\\\9^5 = (3^2)^5 = 3^{10}\\\\\\3^9 = 3^9[/tex]

Now, let's factor the equation:  [tex]3^{12} -3^{10} + 3^{9}[/tex]

[tex]\\3^{12} -3^{10} + 3^{9}\\\\= 3^9(3^3 - 3 + 1)\\\\= 3^9(27 - 2)\\\\= 3^9(25)[/tex]

Your answer is    [tex]3^9(25)[/tex]

To prove MN = 2KL we can use the Multiplication Property of Equality and SAS Similarity Theorem.

In terms of geometry, the triangle is a three-sided polygon with three edges and three vertices. The triangle's interior angles add up to 180°.

It is given that:

K is the midpoint of MJ.

L is the midpoint of NJ.

It is required to prove: MN = 2KL

From the diagram and table given in the picture:

1. K is MJ's midway. L is where NJ splits in half. ~ Given

2. MK, KJ, and NL, LJ: Midpoint Definition

3. Segment Congruence Postulate: MK=KJ and NL=LJ

4. Segment Addition Postulate: MJ = MK + KJ and NJ = NL + LJ

5. Substitution Property of Equality: MJ = 2KJ, NJ = 2LJ

6. The Division Property of Equality: MJ/KJ = NJ/LJ = 2

7. The Reflexive Property of J

8. The SAS Similarity Theorem, JMN, and JKL

9. Corresponding parts of identical triangles have a proportional relationship (MN/KL = MJ/KJ).

10. Substitution: MN/KL = 2

11. The Multiplication Property of Equality: MN = 2KL

Thus, to prove MN = 2KL we can use the Multiplication Property of Equality and SAS Similarity Theorem.

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Answer:

there were 12 pencils in each packet

Answer:

-add 8 and 40

-divide by 4

-not sure

-12

Step-by-step explanation:

Answer:

D:100

Step-by-step explanation:

20x5 cm.

Actual distance between two points is 100 miles

Distance between two points = 20 cm

Scale factor = 1cm = 5 mile

Actual distance between two points

Actual distance between two points = 20 × 5

Actual distance between two points = 100 miles

So, Option "D" is the correct answer to the following question.

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Answer: 4/25

Step-by-step explanation:

16% = 16/100 both can be divided by 4 so 16/4= 4, and 100/4=25. So 16%=4/25

Answer:

4 / 25

Step-by-step explanation:

The question is simplying request you simplify 16/100 to it's lowest form.

From the question,

The Carbohydrates recommended contents = 16/100

To Simplify this to the lowest form, we die de through by 4.

= (16/4) / (100/4)

= 4 / 25

Answer:

about 324 times.

Step-by-step explanation:

2400/7

342.857142857

Answer:

Step-by-step explanation:

In order to graph [tex]y\geq 2[/tex], we first need to graph y = 2.

y = 2 is a straight line which will be parallel to the x-axis.

We need to graph [tex]y \geq 2[/tex].

3, 4, 5......> 2. That is, all these values satisfies [tex]y \geq 2[/tex].

Hence, the will be the area towards the points y = 3 / 4 / 5 / ......

Data collection is the process of gathering and measuring information on variables of interest. strawberry yoghurt makes up less than 1/3 of their sales

Data collection is the process of gathering and measuring information on variables of interest, in an established systematic fashion that enables one to answer stated research questions, test hypotheses, and evaluate outcomes.

The data collection component of research is common to all fields of study including physical and social sciences, humanities, business, etc. While methods vary by discipline, the emphasis on ensuring accurate and honest collection remains the same.

In the first graph, the strawberry yogurt is a little larger than 1/4. Second, the yogurt increases instead of decreases n the first six months. And third, the store actually sold a little less than 3,000 yogurts in November than in August.

Hence  strawberry yoghurt makes up less than 1/3 of their sales

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The question deals with interpreting graphical data from a frozen yogurt store, analyzing statistical data to determine independence of variables, and understanding sales and cost curves in relation to profit in a business case.

The student is asking about interpreting graphs related to customer purchase behavior from a frozen yogurt store and analyzing statistical data in various situations. For instance, when analyzing whether the geographic location is independent of favorite ice cream flavors or discussing the relationship between store temperature and energy consumption, understanding and interpreting graphical data is crucial. In terms of sales and costs for a raspberry farm, understanding the graph where the total cost curve intersects the vertical axis indicates fixed costs, and the upward slope shows variable costs in relation to revenue, which identifies profit maximization points. These analyses are part of mathematical statistics, which is used to making informed decisions in a business context.

Answer:

41 (d)

Step-by-step explanation:

The maximum number of pages for which the time to print at Jerry's Print Shop is less than at Joe's Print Shop is 14.

This question deals with comparing two linear equations [tex]t1 = 45 + 5p[/tex] for Joe's Print Shop and t2 = 30 + 6p for Jerry's Print Shop. To determine the maximum number of pages (p) where Jerry's shop is quicker than Joe's, we need to find the value of p where t2 < t1.

Setting the two equations equal to each other, we get:

[tex]45 + 5p = 30 + 6p,[/tex]

Solving this equation, we find that p = 15.

However, p=15 is when the time at both shops is the same. Since we want the number of pages for which Jerry’s is less than Joe's, we should choose the next value lower, which is p=14.

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Answer:

The number of games Sydney played is 5 and the number of rides she went on is 8.

Step-by-step explanation:

Given:

Sydney is going to a carnival that has games and rides. Each game costs $1.25 and  each ride costs $2.25. Sydney spent $24.25 altogether at the carnival and the number  of rides she went on is 3 more than the number of games she played.

Now, to find the number of games Sydney played and the number of rides she went on.

Let the number of games she played be [tex]x.[/tex]

As given, the number  of rides she went on is 3 more than the number of games she played.

So, the number of rides be [tex]x+3.[/tex]

Each game costs $1.25 and  each ride costs $2.25. Sydney spent $24.25 altogether at the carnival.

According to question:

[tex]1.25x+2.25(x+3)=24.25[/tex]

[tex]1.25x+2.25x+6.75=24.25[/tex]

[tex]3.50x+6.75=24.25[/tex]

Subtracting both sides by 6.75 we get:

[tex]3.50x=17.50[/tex]

Dividing both sides by 3.50 we get:

[tex]x=5.[/tex]

Number of games = 5.

So, number of rides:

[tex]x+3\\=5+3\\=8.[/tex]

Therefore, the number of games Sydney played is 5 and the number of rides she went on is 8.

Answer:

D

14,1

x1  y1                     18,17

                            x2  y2  

17-1     =16/12

18-4

Answer:

b.

She did not keep the order of the points the same in the numerator and the denominator.

Step-by-step explanation:

Answer:

0.0173913043

Step-by-step explanation:

I used a calculator

Answer:

18

Step-by-step explanation:

Solve for  x  by simplifying both sides of the equation, then isolating the variable.

Answer:

18

Step-by-step explanation:

1/3x=6

x=6/(1/3)

x=(6/1)(3/1)

x=18/1

x=18

Answer:

Step-by-step explanation:

72%

Answer: 72%

Step by Step Explanation:

1. We assume, that the number 25 is 100% - because it's the output value of the task.

2. We assume, that x is the value we are looking for.

3. If 100% equals 25, so we can write it down as 100%=25.

4. We know, that x% equals 18 of the output value, so we can write it down as x%=18.

5. Now we have two simple equations:

1) 100%=25

2) x%=18

where left sides of both of them have the same units, and both right sides have the same units, so we can do something like that:

100%/x%=25/18

6. Now we just have to solve the simple equation, and we will get the solution we are looking for.

7. Solution for 18 is what percent of 25

100%/x%=25/18

(100/x)*x=(25/18)*x       - we multiply both sides of the equation by x

100=1.38888888889*x       - we divide both sides of the equation by (1.38888888889) to get x

100/1.38888888889=x

72=x

x=72

now we have:

18 is 72% of 25

Answer:

n = -36

Step-by-step explanation:

Let the number be n.

Then n/3 + 11 = -1

Solve for n/3, and then for n:

Subtract 11 from both sides, obtaining

n/3 = -12

Multiplying both sides by 3 yields:

n = -36

The required number that Mo thought of is -36.

A number is determined that Mo is thinking of a number. 11 more than 1/3 of the number is -1.  

in mathematics it is used to decode the statement into mathematical expression to evaluate problems.

Let the number be x and this number is 11 more than 1/3 of that number equal to -1.

⇒ 1/3(x)+11= -1
    1/3(x) = -12
     x = -36

Thus, the required number that Mo thought of is -36.

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The length of side CD is 11.

To find the length of side CD, we can use the distance formula, which is as follows:

distance = √((x2 - x1)^2 + (y2 - y1)^2)

where (x1, y1) and (x2, y2) are the coordinates of the two points.

In this case, the coordinates of the two points are (-4, -5) and (-4, 6). Substituting these coordinates into the distance formula, we get:

distance = √(((-4) - (-4))^2 + ((6) - (-5))^2)

distance = √(0^2 + 11^2)

distance = √121

distance = 11

Therefore, the length of side CD is 11.

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800 dentists recommended Flash toothpaste

Solution:

Given that, magazine as states that 4 out of 7 dentists prefer flash toothpaste

1400 dentists were surveyed

To find: Number of dentists recommended falsh toothpaste

Let "x" be the number of dentists recommended falsh toothpaste

Then, we can say,

4 out of 7 equals x out of 1400

[tex]\rightarrow \frac{4}{7} = x \times 1400\\\\\rightarrow x = \frac{4}{7} \times 1400\\\\\rightarrow x = 800[/tex]

Thus 800 dentists recommended Flash toothpaste

Good evening

Answer:

Step-by-step

let c be the total number of cartoons

Cost of purchase = 50c

total sale price = 100(c-15)

profit = total sale price - cost of purchase    

        = 100(c-15) - 50c = 2250 cents

Then (100c-50c) - 1500 = 2250

then 50c = 3750

Then c = 3750/50 = 75

:)

Answer:

Step-by-step explanation:

form.

2 1/2divide2 1/6

= 5/2 ÷ 13/6

= 5/2 × 6/13

= (5×3)/13

= 15/13

= 1 2/13

Answer:

1 2/13.

Step-by-step explanation:

2 1/2 / 2 1/6

= 5/2 / 13/6

= 5/2 * 6/13

= 30/26

= 15/13

= 1 2/13

=

The speed in running is 10 mph and speed in biking is 16 mph

Solution:

Given that, Cruz is training to compete in a triathlon

He left his house at 6:00 and ran until 7:30

Time taken for running = 1.5 hours

Then he rode his bike until 9:45

7: 30 to 9: 45 is biking time

Time taken for biking = 2.25 hours

He covered a total distance of 51 miles

Total distance = 51 miles

Let "x" be the speed in running

His speed when biking was 1.6 times his speed when running

Speed in biking = 1.6x

Total distance = distance in running + distance in biking

The distance is given by formula:

[tex]distance = speed \times time[/tex]

Therefore,

[tex]Total\ Distance = x \times 1.5 + 1.6x \times 2.25\\\\51 = 1.5x + 3.6x\\\\5.1x = 51\\\\x = 10[/tex]

Thus speed in running is 10 miles per hour

Speed in biking = 1.6x = 1.6(10) = 16

Thus speed in running is 10 mph and speed in biking is 16 mph

Answer:

1/5 and 2/10

Step-by-step explanation: