What does the quadratic function f(x)=x^2-10x+9 look like when it is rewritten in the form f(x) = a (x-h) + k

The error is identified in C. In step 2, he confused the multiplication and addition signs.

Calvin's error can be described as follows:

In step 2, he distributed the -2/3 instead of the 5.

The correct expression in step 2 should be (-2/3) * (5 + 1/6) instead of (-2/3 + 5) * (-2/3 + 1/3).

Calvin mistakenly distributed the -2/3 across the addition instead of distributing it to the whole term, which led to an incorrect expression.

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Questiion

Calvin evaluated -2/3 x 5 1/6 using the steps below.

Step 1: -2/3 x (5 + 1/6)

Step 2: (-2/3 + 5)x(-2/3 + 1/3)

Step 3: 4 1/3 x -1/3

Step 4: -2 1/6

Which describes Calvin’s error?

In step 1, he incorrectly broke up 5 1/6.

In step 2, he distributed the -2/3 instead of the 5.

In step 2, he confused the multiplication and addition signs.

In step 3, he computed the addition and multiplication incorrectly.

You run 0.5 miles every 3 minutes => 1 mile every 6 minutes. Your friend runs 2 miles every 14 minutes => 1 mile every 7 minutes. You run a whole number of miles every number of minutes that is a multiple of 6. Your freind runs a whole number of miles every number of minutes that is a multiple of 7 Then the least possible number of miles that you both run to end at the same time is the least common factor of 7 and 6 minutes. This is 7 * 6 = 42 minutes. You will have run 42 min / (6 miles/min) = 7 miles, and your friend will have run 42 min / (7 miles/min) = 6 miles

The number of minutes would she take to run 9 miles will be 66 minutes.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

Speed is defined as the length traveled by a particle or entity in an hour. It is a scale parameter. It is the ratio of length to duration.

We know that the speed formula

Speed = Distance/Time

Rita runs 6 miles in 44 minutes. The speed is given as,

Speed = 6 / 44

Speed = 0.13636 miles per minute

The number of minutes would she take to run 9 miles will be given as,

0.13636 = 9 / T

T = 66 minutes

The number of minutes would she take to run 9 miles will be 66 minutes.

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Answer:

Odds against it being striped = 2/3 =0.6667 = 66.67 %

Explanation:

  Total number of billiard balls = 12

  Total number of solid colored balls = 8

  Total number of striped colored balls = 4

  Probability of an outcome = Number of favorable outcome/ Total number of outcome.

   Here total number of outcomes = Total number of billiard balls =  12

   Number of favorable outcomes =Total number of striped colored balls = 4

   Probability of ball being striped = 4/12 = 1/3 =0.333 =33.33 %

 So odds in favor of being striped = 1/3

 Odds against it being striped = 1-1/3 = 2/3 =0.6667 = 66.67 %

The odds against selecting a striped ball from a rack of 12 billiard balls with 4 striped balls is 2 to 1.

In this problem, we are trying to calculate the odds against selecting a striped ball. The total number of balls is 12. Among these, balls numbered 9 through 12, that is exactly 4 balls, have stripes. Hence, we have 8 solid-colored balls and 4 striped balls.

The odds against an event is calculated as the ratio of the number of unsuccessful outcomes to the successful outcomes. In this scenario, an unsuccessful outcome is drawing a striped ball. Hence, the number of unsuccessful outcomes is the number of solid-colored balls which is 8. So, the odds against selecting a striped ball is 8 to 4 or 2 to 1.

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No : the lines have unequal slopes

Parallel lines have equal slopes

calculate the slope( m) of each line using the gradient formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 7, 2) and (x₂, y₂ ) = (7, - 6 )

m = [tex]\frac{-6-2}{7+7}[/tex] = [tex]\frac{-8}{14}[/tex] = - [tex]\frac{4}{7}[/tex]

slope of other line using

(x₁, y₁ ) = (- 1, - 5 ) and (x₂, y₂ ) = (- 3, - 1 )

m = [tex]\frac{-1+5}{-3+1}[/tex] = [tex]\frac{4}{-2}[/tex] = - 2

lines are not parallel since slopes are unequal

The lines are not parallel since the slopes of the two lines are unequal.

The slope is the ratio of the vertical changes to the horizontal changes between two points of the line.

Given that the line passes through points p(-7,2) and q(7,-6) parallel to the line through points r9-1,-5) and S(-3,-1)

To calculate the slope( m) of each line using the gradient formula;

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 7, 2) and (x₂, y₂ ) = (7, - 6 )

m =  (-6 - 2)/(7+7) = -8/14

m = -4/7

Now the slope of other line using the same formula;

(x₁, y₁ ) = (- 1, - 5 ) and (x₂, y₂ ) = (- 3, - 1 )

m = (-1, +5)/ (-3, +1) = 4/-2 =  - 2

Hence, the lines are not parallel since the slopes of the two lines are unequal.

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Answer:

Step-by-step explanation:

8 filters = $39.92

1 filter = 39.92 : 8 = $4.99

6 filters = 6 × 4.99 = $29.94

We are given domain of the function: 1 ≤ x ≤ 5.

Range:  0 ≤ f(x) ≤ 15.

Also included order pairs  (1,4) and (5,15).

First order pair has domain 1, and second order pair has domain 5.

Both are included in domain of the given function.

Also, first order pair has range 4, and second order pair has range 15.

Both are included in range of the given function.

Option  C. (3,8)  has domain 3 and range 8 within the function.

But if we see option D. (5,10) also withing the function but we already given  (5,15), that is range for domain 5 is 15.

Answer:

D for plato users

Step-by-step explanation:

Answer: The upper right corner choice

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

The idea is that you graph y = x+3 but only when x < 0 (which is everything to the left of the y axis). This line goes through (-3,0) and (0,3). Note the open hole at x = 0 to indicate "do not include this point"

At the same time, you will also graph y = 2x but only if x is 0 or larger. The endpoint here is (0,0) which is a closed circle telling us to include this endpoint. Another point on this line is (1,2).

Tyler ate the most because if you find the least common denominator between all four of the fractions, which would be 8, Connor would've eaten 2/8 of a pizza, Brandon 2/8, Tyler 6/8, and Audrey 4/8. At the end Tyler ate the most since 6/8 is greater than 4/8 and 2/8. So your answer should be D.

Answer:

average rate =  75- 35 / 6 - 2 = 40/4 = 10

Step-by-step explanation:

This is the same  value if you use other pairs of x and y

the answer is 10, hope this helps

If the triangle is rotated 270° counterclockwise about the origin, the coordinates of A will be at (1, -4)

Given a coordinate (x, y), if the coordinate is rotated 270° counterclockwise about the origin, the resulting coordinates will be at (y, -x)

For the triangle ABC with coordinates (4, 1), B(2, 3), and C(7, 5), if the triangle is rotated 270° counterclockwise about the origin, the resulting coordinate of A will be at:

A' = (1, -4)

If the triangle is rotated 270° counterclockwise about the origin, the coordinates of A will be at (1, -4)

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You haven't provided any value, but I can tell you the solution set for the inequality.

First of all, expand both sides:

[tex] -3x+12 > 6x-6 [/tex]

Add 3x to both sides:

[tex] 12 > 9x-6 [/tex]

Add 6 to both sides:

[tex] 18 > 9x [/tex]

Which is of course equivalent to

[tex] 9x < 18 [/tex]

Divide both sides by 9

[tex] x < 2 [/tex]

So, every number smaller than 2 is part of the solution of this inequality.

$32.50 X .4 = $13, 32.5-13=19.5, 19.5 divided 2 =$9.75

Probability: [tex]\( \frac{111}{220} \)[/tex] or approximately 0.5045. Pita has about a 50.45% chance of drawing exactly £2.50.

To find the probability that Pita takes out exactly £2.50, we need to consider the different combinations of coins that would result in that amount.

First, let's calculate the total number of ways Pita can choose 3 coins out of 12:

[tex]\[ \text{Total number of ways} = \binom{12}{3} = \frac{12!}{3!(12-3)!} = \frac{12 \times 11 \times 10}{3 \times 2 \times 1} = 220 \][/tex]

Now, let's determine the combinations that would result in exactly £2.50. She can achieve this in two ways:

1. Selecting two 1 pound coins and one 50p coin.

2. Selecting five 50p coins.

For the first scenario, she can choose 2 out of the 3 1 pound coins and 1 out of the 9 50p coins. This can be calculated as:

[tex]\[ \binom{3}{2} \times \binom{9}{1} = \frac{3!}{2!(3-2)!} \times \frac{9!}{1!(9-1)!} = 3 \times 9 = 27 \][/tex]

For the second scenario, she can choose all 3 coins from the 9 50p coins:

[tex]\[ \binom{9}{3} = \frac{9!}{3!(9-3)!} = \frac{9 \times 8 \times 7}{3 \times 2 \times 1} = 84 \][/tex]

Now, let's add up these two possibilities to find the total number of favorable outcomes:

[tex]\[ \text{Total favorable outcomes} = 27 + 84 = 111 \][/tex]

Finally, we can calculate the probability:

[tex]\[ \text{Probability} = \frac{\text{Total favorable outcomes}}{\text{Total number of ways}} = \frac{111}{220} \][/tex]

[tex]\[ \text{Probability} \approx 0.5045 \][/tex]

So, the probability that Pita takes out exactly £2.50 is approximately 0.5045 or 50.45%.

The probability that Pita takes out exactly £2.50 when selecting 3 coins at random from her bag is approximately 42.27%.

To find the probability that Pita takes out exactly £2.50 when selecting 3 coins at random from her bag, we need to consider the different combinations of coins that would result in this amount.

Pita has 12 coins in total:

- 3 coins worth £1 each

- 9 coins worth 50p each

For a total of £2.50, she would need to select either:

1. Two £1 coins and one 50p coin, or

2. Five 50p coins

Let's calculate the probability for each case:

1. Probability of selecting two £1 coins and one 50p coin:

  - Probability of selecting a £1 coin on the first draw: [tex]\( \frac{3}{12} = \frac{1}{4} \)[/tex]

  - Probability of selecting another £1 coin on the second draw: [tex]\( \frac{2}{11} \)[/tex] (as there are 2 £1 coins left out of 11 total coins)

  - Probability of selecting a 50p coin on the third draw: [tex]\( \frac{9}{10} \)[/tex] (as there are 9 50p coins left out of 10 total coins)

  - Total probability for this case: [tex]\( \frac{1}{4} \times \frac{2}{11} \times \frac{9}{10} \)[/tex]

2. Probability of selecting five 50p coins:

  - Probability of selecting a 50p coin on the first draw: [tex]\( \frac{9}{12} = \frac{3}{4} \)[/tex]

  - Probability of selecting another 50p coin on the second draw: [tex]\( \frac{8}{11} \)[/tex] (as there are 8 50p coins left out of 11 total coins)

  - Probability of selecting another 50p coin on the third draw: [tex]\( \frac{7}{10} \)[/tex] (as there are 7 50p coins left out of 10 total coins)

  - Total probability for this case: [tex]\( \frac{3}{4} \times \frac{8}{11} \times \frac{7}{10} \)[/tex]

Now, we sum up the probabilities for both cases to find the total probability:

[tex]\[ \text{Total probability} = \left( \text{Probability of case 1} \right) + \left( \text{Probability of case 2} \right) \\\[ \text{Total probability} = \left( \frac{1}{4} \times \frac{2}{11} \times \frac{9}{10} \right) + \left( \frac{3}{4} \times \frac{8}{11} \times \frac{7}{10} \right) \][/tex]

Now, let's calculate these probabilities.

First, let's calculate the probability for case 1:

[tex]\[ \text{Probability of selecting two £1 coins and one 50p coin} \\\[ = \frac{1}{4} \times \frac{2}{11} \times \frac{9}{10} \\\[ = \frac{1}{4} \times \frac{18}{110} \\\[ = \frac{9}{220} \][/tex]

Now, let's calculate the probability for case 2:

[tex]\[ \text{Probability of selecting five 50p coins} \\\[ = \frac{3}{4} \times \frac{8}{11} \times \frac{7}{10} \\\[ = \frac{3}{4} \times \frac{56}{110} \\\[ = \frac{42}{110} \][/tex]

Now, let's sum up the probabilities for both cases to find the total probability:

[tex]\[ \text{Total probability} = \frac{9}{220} + \frac{42}{110} \][/tex]

Now, let's calculate the total probability.

[tex]\[ \text{Total probability} = \frac{9}{220} + \frac{42}{110} \][/tex]

First, let's find a common denominator for the fractions:

[tex]\[ \text{Total probability} = \frac{9}{220} + \frac{42 \times 2}{110 \times 2} \\\[ = \frac{9}{220} + \frac{84}{220} \][/tex]

Now, add the fractions:

[tex]\[ \text{Total probability} = \frac{9 + 84}{220} \\\[ = \frac{93}{220} \][/tex]

Now, let's simplify this fraction:

[tex]\[ \text{Total probability} = \frac{93}{220} \][/tex]

To express the probability as a decimal, we divide the numerator by the denominator:

[tex]\[ \text{Total probability} \approx \frac{93}{220} \approx 0.422727 \][/tex]

Now, let's express this probability as a percentage:

[tex]\[ \text{Total probability} \approx 0.422727 \times 100\% \approx 42.27\% \][/tex]

So, the probability that Pita takes out exactly £2.50 when selecting 3 coins at random from her bag is approximately 42.27%.

Answer: 32

Step-by-step explanation:

Red Blue Green

[tex]\frac{1}{4} * \frac{1}{4} * \frac{2}{4}[/tex]

= [tex]\frac{1}{4} * \frac{1}{4} * \frac{1}{2}[/tex]

= [tex]\frac{1}{32}[/tex]

Answer:

The answer is 1/32 ( i think this was D )

Step-by-step explanation:  

Its just 1/4 times 1/4 times 2/4 :)

A function is increasing if it "points upwards".

Think that you have two inputs [tex] x_1<x_2 [/tex] (think of them as being very close to each other). A function [tex] f [/tex] is increasing if

[tex] f(x_1)<f(x_2) [/tex]

So, smaller input, smaller output.

So:

So, the function is increasing in the third segment, which is delimited by

[tex] -2\leq x \leq 3 [/tex]

This question is based on the increasing function. Therefore,  the correct option is B, [tex]-2\leq x\leq 3[/tex] interval is the function in this graph increasing.

In this question, from the graph we have to observed that over what interval is the function in this graph increasing.

In general, a function is increasing, if graph pointed upwards.

If we have two points [tex]x_1[/tex] and [tex]x_2[/tex] then, we said that function f is increasing if,

[tex]f(x_1) =f(x_2)[/tex].

Therefore, from the given graph it is observed that:

In the first segment on the left, the function is decreasing: if you move with little steps rightwards, the output will get smaller and smaller (the function points to the right bottom).

In the second segment, the line is constant (it's horizontal). This means that even if you consider a larger input, the output remains constant.

In the third segment, the function is increasing. If you consider a larger input, the output will be larger as well: the function points to the top right.

In the fourth segment, the function is decreasing again.

Therefore,  the correct option is B, [tex]-2\leq x\leq 3[/tex] interval is the function in this graph increasing.

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[tex]\frac{90 + 87 + 72 + x}{4} = 88[/tex]

90 + 87 + 72 + x = 88(4)

             249 + x = 352

                        x = 103

Answer: 103

I hope the next exam has extra credit questions!

it is either 5 cm or its 4 cm

Answer:

Slope = 1/4. If the lines are parallel that means the have the same slope.

Answer:

y = -6x - 9

Step-by-step explanation:

Given 6x + y = 4, we borrow the form 6x + y = C to obtain a new line parallel to the given line.  Subst. -2 for x and 3 for y to find C:  6(-2) + 3 = C, or C = -9.

Thus, the desired equation is 6x + y = -9, or  y = -6x - 9.  

Check:  Does this line pass thru (-2,3)?  Is 3 = -6(-2) - 9 true?  Yes, it is.

under a reflection in the x- axis

a point (x, y) → (x, - y)

P( - 1, 0 ) → P'( - 1, 0 )

R(3, 1) → R'( 3, - 1 )

D( 3, - 2 ) → D'( 3, 2 )

Q(0, - 5 ) → Q'( 0,  5 )

U (0,5) P (-1,0) R (3,-1) D (3,2)

0

1

2

8

1+2=3

1+8=9

2+8=10

2+1+8=11

0 doesn't change the value of the sum, so we don't take into consideration subsets with 0 in it, except the subset with just 0 itself.

Therefore, there are 8 different sums.

The number of different sums we can obtain from the nonempty subsets of the set {2,0,1,8} is 12. This is because there are 15 nonempty subsets of the given set and the sums of these subsets range from 0 to 11.

In this problem, we are asked to calculate the total number of different sums we can obtain from nonempty subsets of the set {2,0,1,8}. We have four distinct integers in the set, hence there are 24 - 1 = 15 nonempty subsets (we subtract 1 to exclude the empty subset).

We can obtain different sums by adding the elements of these subsets. The lowest possible sum is 0 (for the subset {0}), the highest is 11 (for the subset {2,0,1,8}), and the other possible sums range in between these two with some sums being possible to achieve from multiple subsets. Thus, the result is 12 meaning there are 12 different sums we can obtain.

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Answer:

Olivia spent $97.25

Camille spent $175.10

Step-by-step explanation:

Let the amount spent by:

Olivia be x dollars

Camille be 2x - $19.40 dollars

x + 2x - $19.40 = $272.35

3x = $272.35 + $19.40

3x = $291.75

x = $97.25

To find the amount each girl spent, we can use variables to represent the unknown quantities and create a system of equations. By solving the system of equations, we find that Olivia spent $97.25 and Camille spent $175.10.

To solve this problem, let's use variables to represent the unknown quantities. Let x be the amount Olivia spent and y be the amount Camille spent. According to the problem, Camille spent 19.40 less than twice what Olivia spent, so we can write the equation y = 2x - 19.40. The total amount they spent is $272.35, so we can write another equation x + y = 272.35. We now have a system of equations that we can solve to find the values of x and y.

By substituting the value of y in the second equation with the expression for y from the first equation, we get x + (2x - 19.40) = 272.35. Simplifying this equation gives us 3x - 19.40 = 272.35. Adding 19.40 to both sides, we have 3x = 291.75. Dividing both sides by 3 gives us x = 97.25.

Now, we can substitute the value of x back into either of the original equations to find the value of y. Let's use the first equation y = 2x - 19.40. Plugging in x = 97.25, we get y = 2(97.25) - 19.40 = 194.50 - 19.40 = 175.10.

Therefore, Olivia spent $97.25 and Camille spent $175.10.

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x = -5 - it's the vertical line. Parallel line to vertical line is vertical.

Passes throught the point (1, 4) → x = 1, y = 4.

Therefore your answer x = 1.

Hey there!!

Basic formula :

... a² - b² = ( a + b ) ( a - b )

Equation given :

... 81x² - 25

... ( 9x )² - ( 5 )²

... ( 9x + 5 ) ( 9x - 5 )

Hope it helps!!

The expression 81x²-25 is a difference of squares that can be factored as (9x - 5)(9x + 5).

The given expression is 81x²-25, which is a difference of squares. The difference of squares is a special algebraic identity and it can be factored using the formula a²-b² = (a-b)(a+b). In this case, a is 9x and b is 5, because (9x)² = 81x² and 5² = 25. So, plug these values into the formula to get: 81x²-25 = (9x - 5)(9x + 5)

To factor 81x²-25, we can use the formula for the difference of squares: a² - b² = (a + b)(a - b). In this case, a is 9x and b is 5. So we have:

81x² - 25 = (9x + 5)(9x - 5)

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Answer:

-2.67,2.07,2.67,27/10

Step-by-step explanation:

40%

to calculate rate of discount,

[tex]\frac{discount}{original cost}[/tex] × 100%

discount = $60 - $36 = $24

[tex]\frac{24}{60}[/tex] × 100% = 40%

Answer:

it is 40%

Step-by-step explanation:

For a better understanding of the explanation given here please go through the two graphs provided in the two files attached.

In the first graph we have plotted all the given points from the question. The y-axis is the quantity and the x-axis is the price. As can be seen, as the price increases, the quantity decreases.

In the second graph, the line that connects all the given points is drawn. This line represents the "Demand" Line and is evaluated as follows:

We take any two points (in our case we took the first and the last points, that is, [tex](x_1,y_1)=(0,19)[/tex] and [tex](x_2,y_2)=(3,1)[/tex]) and we made use of the "point slope form" as:

[tex]\frac{y-y_1}{x-x_1}= \frac{y_2-y_1}{x_2-x_1}[/tex]

Thus, we got:

[tex]\frac{y-19}{x-0}= \frac{1-19}{3-0}= \frac{-18}{3}=-6[/tex]

[tex]y-19=-6x[/tex]

[tex]\therefore y=-6x+19[/tex]

Thus, the complete graph will be a straight line [tex]y=-6x+19[/tex] as shown in the second diagram.

First of all, you can sum the two terms involving g on the left hand side:

[tex] -6g + 3g + 12 > -18 \iff -3g + 12 > -18 [/tex]

Subtract 12 from both sides:

[tex] -3g > -30 [/tex]

Divide both sides by -3: note that since we're dividing by a negative number, we must invert the inequality sign:

[tex] g< 10 [/tex]

Final answer:

When solving the inequality, we combine like terms, subtract 12 from both sides, and divide by -3, reversing the inequality sign to find that g < 10, hence the correct answer is (c).

Explanation:

To solve the inequality -6g + 3g + 12 > -18, we first combine like terms to simplify the left side of the inequality:

Next, we subtract 12 from both sides of the inequality:

Now we divide by -3, remembering to reverse the inequality sign because we are dividing by a negative number:

Therefore, the correct answer is (c) g < 10.