Caroline rewrote a quadratic equation in vertex form by completing the square, but her work has errors.
f(x)
-2x² + 12x15
-2(x² - 6x) — 15
-2(x² - 6x + 9) - 9 - 15
-2(x - 3)²9 - 15
-2(x - 3)² - 24
Identify the first error in her work.

The sum of the given arithmetic series  5+6+7+ . . . . . . +11 is 56.

Suppose we are given an arithmetic series:

   a(1) + a(2) + a(3) + a(4) + .... + a(n)

Then, each term of the series follow the general formula:

a(n) = a(1) + (n-1) . d

Where:

a(n) = nth term

a(1) = first term

d = common difference = a(n) - a(n-1)

We are given:

        5+6+7+ . . . . . . +11

Parameters we get from this series:

a(1) = 5

d = 6 - 5 = 1

a(n) = 11

We need to find n that results in a(n) = 11

Substitute a(n) = 11, a(1) = 5, and d = 1:

a(n) = a(1) + (n-1) . d

11 = 5 + (n-1) . 1

11 = n + 4

n = 7

The sum of the first n terms of an arithmetic series is:

S(n) = n/2 [ a(1) + a(n) ]

S(7) = 7/2 (5 + 11)

       = 7 . 8 = 56

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Answer:

That is wrong it is not $938 its $322

Step-by-step explanation:

Answer:

Just graph, first one Y int: 2 and X is rise over run 1 and 2

Step-by-step explanation:

Answer:

try it's your self i am sure you can do it.

Step-by-step explanation:

Let's go together

Using the Pythagorean Theorem, it is found that:

a) The hypotenuse is of 9.49 cm.

b) The new area of the triangle is of 30 cm².

The Pythagorean Theorem relates the length of the legs [tex]l_1[/tex] and [tex]l_2[/tex] of a right triangle with the length of the hypotenuse h, according to the following equation:

[tex]h^2 = l_1^2 + l_2^2[/tex]

For this problem, the sides are given as follows:

3 cm and 9 cm.

Hence the hypotenuse is given by:

h² = 3² + 9²

h = sqrt(3² + 9²)

h = 9.49 cm.

The hypotenuse is of 9.49 cm.

The area of a right triangle of sides a and b is given by half the multiplication of the sides, as follows:

A = 0.5ab.

For this problem, we have that:

Then:

A = 0.5 x 5 x 12 = 30 cm².

The new area of the triangle is of 30 cm².

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Answer:

Step-by-step explanation:

5×(3+6)²-62=

5×9²-62=

5×81-62=

405-62=

343

Answer:

16/1071

Step-by-step explanation:

The average is the given by summing all the numbers and deciding by how many numbers you have

So, the answer is given by:

(-1/12 + 4/17 - 3/28) / 3 which yields to 16/1071

The congruency can also be tested by three postulates shown in the lesson: ASA (angle-side-angle), SAS (side-angle-side), and SSS (side-side-side). The first one claims that triangles are congruent if two angles and one side (between the angles) of one triangle are equal to two angles and one side of another triangle.

If two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the triangles are congruent.

A ∠ ≅ ∠ .

Vertical Angles Theorem: ...

Indicator marks for sides and angles in a triangle diagram. Indicator marks are used to show whether two or more sides are congruent (equal in measure).

Thus, because all right angles are congruent. Since vertical angles are congruent by the vertical angles theorem.

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Answer:

Step-by-step explanation:

hi

Simplification of each sum or difference of the given equation [tex]\frac{(5y+2)}{(xy^{2} )}+ \frac{(2x-4)}{4xy}[/tex] is equal to [tex]\frac{(xy+8y+4)}{2xy^{2} }[/tex] .Restriction on the variables is given by x≠0 , y≠0 .

As given in the question,

Given equation is [tex]\frac{(5y+2)}{(xy^{2} )}+ \frac{(2x-4)}{4xy}[/tex]

Simplify the given equation by taking the least common multiple,

[tex]\frac{(5y+2)}{(xy^{2} )}+ \frac{(2x-4)}{4xy}\\\\\\= \frac{20y +8+2xy-4y}{4xy^{2}}\\ \\\\= \frac{2xy+16y+8}{4xy^{2}}\\ \\\\= \frac{xy+8y+4}{2xy^{2}}[/tex]

Restriction on the variables are x≠0 , y≠0.

Therefore, simplification of each sum or difference of the given equation [tex]\frac{(5y+2)}{(xy^{2} )}+ \frac{(2x-4)}{4xy}[/tex] is equal to [tex]\frac{(xy+8y+4)}{2xy^{2} }[/tex] .Restriction on the variables is given by x≠0 , y≠0 .

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a. an inequality to find the number of monthly calls for which Plan 1 is more economical than Plan 2 is : 19 +0.04x >23

b. the meaning of the answer to part a is : Cost of Plan 2 > Cost of Plan 1

c.  the number of monthly calls x  is x > 100

What is inequality ?

In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. It is used most often to compare two numbers on the number line by their size.

Plan 1: $23 per month for unlimited calls

Plan 2: $19 per month + $0.04 per call

Let the number of calls be x

a. 19 +0.04x >23

0.04x >4

x > 100

b. If Plan 1 should be more economical, then the above inequality represents that cost of plan 2 should be more than plan 1. therefore, the plan 2 is greater than plan 1.

On solving the above inequality, we get over 100 calls should be made  so that Plan 1 is more economical than Plan 2.

c. x > 100

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Answer:

why did the teacher give an exam

According to the given statement The sum of pair of vectors are  =  (-16 , -28).

The operation of combining two or even more vectors into a vector sum is known as vector addition. The rule for addition and multiplication of two or more vectors is given by the so-called parallelogram law. When two vectors are placed head to tail, the vector total is determined by drawing this same vector from of the free tail towards the free head.

Given two vectors are:

a =(6,-31)

b = (-22,3)

The vector sum is,

M = (a1 + b1, a2 + b2)

   = (Mx, My).

Substitution of the value we  get:

M = (6 + (-22), (-31) + (3))

   = (-16 , -28)

The sum of pair of vectors are  =  (-16 , -28).

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1) Factorizing the expression x⁶ - 729 is; (x + 3)(x - 3)(x⁴ + 9x² + 81)

2) Solving the equation 2x² + 16x – 11 = -7 by completing the square is; x = -4 + √18 or -4 - √18

3) Factorizing x⁴ – 5x² – 36 over the complex numbers is; (x + 3i)(x - 3i)(x + 2)(x - 2)

1) We are given the expression; x⁶ - 729

It can also be written as;

(x²)³ - 9³

Now, from factorization of algebra, we  know that;

a³ - b³ = (a - b)(a² + ab + b²)

Thus;

(x²)³ - 9³ = (x² - 9)((x²)² + 9x² + 9²)

= (x² - 9)(x⁴ + 9x² + 81)

= (x + 3)(x - 3)(x⁴ + 9x² + 81)

2) We want to solve the equation 2x² + 16x – 11 = -7 by completing the square.

Add 7 to both sides to get;

2x² + 16x – 11 + 7 = -7 + 7

2x² + 16x – 4 = 0

Divide through by 2 to get;

x² + 8x – 2 = 0

Add 2 to both sides to get;

x² + 8x = 2

Take half of the x term and square it and then add the result to both sides to get;

x² + 8x + 16 = 2 + 16

Rewrite the perfect square on the left to get;

(x + 4)² = 18

Take square root of both sides to get;

x + 4 = ±√18

Subtract 4 from both sides to get;

x = -4 ± √18

x = -4 + √18 or -4 - √18

3) We want to factorize x⁴ – 5x² – 36

Using the difference of squares identity, we know that;

a² - b² = (a + b)(a - b)

Thus;

x⁴ – 5x² – 36 = (x² + 9)(x² - 4)

Now, (x² + 9) factored over the complex numbers gives;

(x² + 9) = (x + 3i)(x - 3i)

Thus;

x⁴ – 5x² – 36 = (x + 3i)(x - 3i)(x + 2)(x - 2)

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The simplification of each or difference of the given expression [tex]\frac{y}{(2y+4)}-\frac{3}{y+2}[/tex]  is equal to (y-6) /2(y+2). Restriction on the variables is given by y ≠ -2.

As given in the question,

Given expression [tex]\frac{y}{(2y+4)}-\frac{3}{y+2}[/tex]

Simplify the given expression by taking the least common multiple

[tex]\frac{y}{(2y+4)}-\frac{3}{y+2}\\\\\\= \frac{y}{2(y+2)}-\frac{3}{y+2}\\\\= \frac{y-6}{2(y+2)}[/tex]

Restriction on the variables is given by y ≠ -2.

Therefore, the simplification of each or difference of the given expression [tex]\frac{y}{(2y+4)}-\frac{3}{y+2}[/tex]  is equal to (y-6) /2(y+2). Restriction on the variables is given by y ≠ -2.

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The correct answer would be option 2 and 3:

We have to sove the problem by carefully trying to understand the statements

x = largest angle

y =  next largest angle

z = smallest.

1. For the first statement: The measure of the largest angle is 40 degrees less than the sum of the measure of the other two angles.

largest angle < y + z

This would be represented as

x = y + z - 40

2. The largest angle is twice the smaller angle minus 30 degrees.

This is represented as

2 times of smallest = 2 * z = 2z

minus 30 degrees = 2z - 30

Hence the solutions to the question from the option that we have would be the options

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Answer:

2) x=2z−30

3) x=y+z−40

Step-by-step explanation:

Answer:

I think its -y

Step-by-step explanation:

Answer:

x is my answer

Step-by-step explanation:

i don't know sorry

The geometric mean of 3√5/4 and 5√5/4 is 5√3/4.

Geometric mean, like arithmetic mean, is a kind of average and a measure of central tendency.

To solve for the geometric mean, we multiply the numbers together and then take a square root (for two numbers), cube root (for three numbers) etc. In other words, geometric mean is the nth root of the product of n values.

The formula for the geometric mean is given by:

GM = n√x1 x2 . . . xn

Solving for the geometric mean between 3√5/4 and 5√5/4 using the formula:

GM = n√x1 x2 . . . xn

where n = 2, x1 = 3√5/4, and x2 = 5√5/4

GM = √(3√5/4)(5√5/4)

GM = √(75/16)

GM = 5√3/4

Hence, the geometric mean of 3√5/4 and 5√5/4 is 5√3/4.

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The equation of the circle that passes through the point (-6 , 0) and has a center located at the origin is x^2 + y^2 = 36.

Using the distance formula, get the radius of the circle by solving for the distance between the center and the point (-6 , 0).

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

radius = √(-6 - 0)^2 + (0 - 0)^2

radius= √36

radius = 6

The standard form of the equation of the circle is given by (x - h)^2 + (y - k)^2 = r^2, where (h , k) is the location of the center and r is the radius of the circle.

Given the radius and center of the circle, substitute these values to the standard form of the equation of the circle.

(x - h)^2 + (y - k)^2 = r^2

where (h , k) = (0 , 0)

r = 6

(x - 0)^2 + (y - 0)^2 = 6^2

x^2 + y^2 = 36

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The following set of numbers, 11, 60, and 61, can be the measures of the sides of a right triangle.

A triangle is a polygon with three sides and three vertices.

To know if a set of number is a valid measure of the sides of a triangle, it must follow the Triangle Inequality Theorem which states that the sum of any two sides must be greater than the third side, such that a + b > c, a + c > b, and b + c > a.

let a = 11, b = 60, and c = 61

a + b > c     11 + 60 > 61     71 > 61     True

a + c > b     11 + 61 > 60     72 > 60     True

b + c > a     60 + 61 > 11     121 > 11     True

To know what type of triangle based on the length of its side:

1. Take the sum of the squares of the two smaller sides.

11^2 + 60^2 = 3721

2. Compare it to the square of the largest side.

61^2 = 3721

3721 = 3721

If the sum of the squares of the 2 is larger than the square of the 3rd, it is an acute triangle.

if they are equal, it is a right triangle.

if they are smaller, then it is an obtuse triangle.

Hence, 11, 60, and 61 can be the measure of the sides of a right triangle.

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The ordered pairs of the given relation r on the set t is ungrouped data.

The data you initially collect from an experiment or study is known as ungrouped data. The data is unsorted, unclassified, or otherwise grouped; it is therefore considered to be raw. A list of numbers is an ungrouped piece of data.

Ungrouped data is a distribution type where each piece of information is presented in its rawest form. For instance, a batsman's five most recent scores are 45, 34, 2, 77, and 80.

Raw data is another name for ungrouped data.

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The probability, expressed as a percentage rounded to a nearest tenth, that Victoro chooses a green jelly then a red one is 0.1.

A combination is a preference of all or part of a group of objects, regardless of their order of selection.

You can choose the items in just about any order in combinations. Permutations and combinations are often confused.

Now, as per the given question;

The total number of red jelly beans in a bag is 7.

The total number of yellow jelly beans in a bag is 11.

The total number of green jelly beans in a bag is 13.

Thus, the total number of jelly beans in a bag is;

7 + 11 + 13 = 31.

First, Victoro picks the green one;

Thus, the probability of picking a green jelly out of total 13 green jellys is;

¹³C₁/ ³¹C₁ = 13/31

Now, as the second jelly picked by Victoro is red which is without replacement.

Thus, the probability for getting a red jelly out of total 30 left jellys is;

⁷C₁/ ³⁰C₁ = 7/30

Therefore, the total probability that Victoro picks a green one and then a red one is ;

= 13/31×7/30

= 91/930

= 0.097

= 0.10 (rounded to the nearest tenth)

Therefore, the probability of getting the red jelly after the green jelly is 0.10.

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Answer:

0

Step-by-step explanation:14 subtracted by 14 is 0

Using it's concept, the average rate of change of the function in the intervals is given by:

a. 1.

b. -5/3.

c. -1.

d. 4.

e. -3.

f. 0.

The average rate of change of a function is given by the change in the output divided by the change in the input. Hence, over an interval [a,b], the rate is given as follows:

[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]

For item a, we have that:

Hence the rate is:

r = (1 - 0)/(-2 - (-3)) = 1.

For item b, we have that:

Hence the rate is:

r = (-4 - 1)/(1 - (-2)) = -5/3.

For item c, we have that:

Hence the rate is:

r = (-4 - (-3))/(1 - 0) = -1.

For item d, we have that:

Hence the rate is:

r = (-0 - (-4))/(2 - 1) = 4.

For item e, we have that:

Hence the rate is:

r = (-3 - 0)/(0 - (-1)) = -3.

For item f, we have that:

Hence the rate is:

r = (0 - 0)/(2 - (-1)) = 0.

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Answer:

Recurring Decimal

Recurring Decimal, also called as repeating decimal, is a decimal number only that consists of digits repeating after a fixed interval after the decimal. For example, 46.374374374..., 5173.838383... etc. Decimals can be classified into different categories depending upon what type of digits occur after the decimal point, whether the digits are repeating, non-repeating, end, or unending (infinite digits after the decimal point).

Examples are

0.6666666666,

1.456456456

Step-by-step explanation:

Set as brainliest

The expression that represents the difference between the student's guess and the actual number of marbles will be 1206 - 2m.

When there are 1206 marbles in a jar and a student makes a guess of m marbles. The expression for the guesses will be:

= 2 × m

= 2m

The expression that represents the difference between the student's guess and the actual number of marbles will be:

= 1206 - 2m

= 2(603 - m)

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For this, we need to make ratios(unit per unit, in this case, red paint per white paint).

Sydney's Mix - [tex]\frac{7 red}{4 white}[/tex]

Maria's Mix - [tex]\frac{5 red}{3 white}[/tex]

Both of these fractions are improper, so you can make mixed fractions and then find their common denominators:

Sydney's Mix - 1[tex]\frac{3}{4}[/tex] = 1[tex]\frac{9}{12}[/tex]

Maria's Mix - 1[tex]\frac{2}{3}[/tex] = 1[tex]\frac{8}{12}[/tex]

Therefore, they do not have the same shade of pink because 1[tex]\frac{9}{12}[/tex] [tex]\neq[/tex] 1[tex]\frac{8}{12}[/tex] :)