Vincent is completing his math homework about the process of Completing the Square to solve quadratic equations. His work is shown below.
solve: x²-3x+7=0

step 1: x²-3x = -7
step 2: x²-3x+9=-7 +9
step 3: (x-3)² = 2
step 4: X-3= = √2
x=3 = √2

Did Vincent make a mistake as he solved the quadratic using Completing the Square? If so, in what
step did he first make a mistake? (Step numbers are labeled in blue on the left)

A diagram is provided, on which R S T U's perimeter is 72 and R V's is 16, RT= 32  and UV ≈ 8.2.

A diagram is provided, on which R S T U's perimeter is 72 and R V's is 16.

Finding R T and U V is our goal.

First, let's assume that the figure RSTU is a rhombus since its perimeter and one-half of a diagonal's length are both provided. RT is the result of adding the segments RV and VT.

RT=RV + VT

We are informed that the RV is sixteen. If RV and VT are congruent, then V T equals 16. So:

R T = 16 + 16 = 32

In order to determine the UV length, we must first determine the RU length. Since a rhombus's sides are the same length, we can divide its perimeter by four to determine

RU= Perimeter/ 4

If we simplify and replace Perimeter with 72, we get:

RU = 72 / 4

RU =18

Since UB is a member of the right triangle RUV created by the intersection of the diagonals, we can now use the Pythagorean theorem to determine its length. So:

U V²+ R V² =  RU²

If R V = 16 and R U = 18, we obtain:

U V² + 16 ²= 18²

By way of summary, we have:

U V² + 256 = 324

U V² + 256 − 256 = 324 − 256

√ UV = √ 68

UV = 8.2462

UV ≈ 8.2

Our recommendations are as follows:

RT= 32

UV ≈ 8.2.

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According to the BODMAS rule, the first step to solve the given expression is to solve the bracket.

Children can use the acronym BODMAS to help them remember the right order to carry out mathematical operations while solving problems.

B-Brackets, O-Orders (powers/exponents or roots), D-Division, M-Multiplication, A-Addition, and S-Subtraction are all abbreviated as BODMAS.

So, we have the expression: 3(3½ ÷ 3)-4

The next step would be according to the BODMAS rule.

In the BODMAS rule the letter B stand for brackets.

Hence, the first step will be to solve the bracket.

Therefore, according to the BODMAS rule, the first step to solve the given expression is to solve the bracket.

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The answer will be in the picture provided below!

Whereas students from single parent or two parent homes make up 54% of new students, these students eventually go on to complete their college studies..

By dividing the value by the entire value and multiplying the result by 100, one can compute the percentage. The formula for calculating percentage is (value/total value)100%.When a piece of a whole is stated as a percentage, it is not a fraction but rather a number between 0 and 100. There are three percentages: 100% for everything, 50% for half of it, and 0% for the remaining portion.

calculation

25% of new students come from one-parent households, which equals 0.25;

75% of new students come from two-parent households, which is 0.75.

42% of incoming students from homes with only one parent go on to complete their college studies = 0. 42

58 percent of incoming students who come from two-parent households go on to complete their education =0.58

= 0.25 * 0.42 + 0.75 * 0.58 = 0.54 = 54%.

Whereas students from single parent or two parent homes make up 54% of new students, these students eventually go on to complete their college studies..

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Solving the given equation, we calculate the value of x to be 10.369

An equation is a mathematical statement that shows that two expressions are equal. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.

Simplification is the process of reducing an expression or equation to its simplest form by applying the rules of algebra. Simplifying procedures is one way to achieve uniformity in work efforts, expenses, and time. It reduces diversity and variety that is pointless, harmful, or unnecessary.

By isolating the variable x and using calculator, we find the answer = 10.369.

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Answer:

5 6/7 or C option

Step-by-step explanation:

5 6/7 is equal to 5.857 and rounded it is 6

While all the others round to 5

Hopes this helps please mark brainliest

We know that Martin earn $81 last week by raking 27 bags using simple mathematical operations.

A mathematical expression known as an "operation" in mathematics is one that transforms zero or even more input data into a precisely specified actual output.

The number of arithmetic determines the difficulty of the operation.

The four basic operations in arithmetic are addition, subtraction, multiplication, and division, according to the majority of people.

So, money was earned by raking 27 bags.

Martin earns $15 for raking 5 bags.

The amount earned by raking 1 bag:

15/5 = $3

Now, the amount earned by raking 27 bags:

27 * 3 = $81

Therefore, we know that Martin earn $81 last week by raking 27 bags using simple mathematical operations.

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One hose can fill a small swimming pool in 75 minutes. Two hoses will fill the pool in 30 minutes when working together.

Given, the volume ( the space occupied by an solid object)  per minute

Smaller hose fills  the pool in 75 minutes. (1/75)

A larger one can fill the pool in 50 minutes. (1/50)

So, together they will fill = (1/ 75 ) + (1/50) , the lcm of 75 and 50 is 150

                                            =  (2/150) + (3/150)  

                                            =  5/150

                                            = 1/30 or 30 minutes

So, we can say that the two hoses will fill the pool in 30 minutes when working together.

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it is the 1st graph.

Graph A.

The inverse of the given relation  {(5, 1), (4, -3), (3, -1)} is  {(1, 5), (-3, 4), (-1, 3).

The inverse of a relation is a relation obtained by interchanging or swapping the elements or coordinates of each ordered pair in the relation.

The ordered pair (x, y) of f(x) becomes (y, x) of f⁻¹(x).

Given, A relation in form of a set of ordered pairs {(5, 1), (4, -3), (3, -1)} let this be f(x).

∴ The ordered pair of f⁻¹(x) will be {(1, 5), (-3, 4), (-1, 3).

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Answer:4f+3t=7.95  2f+10t=9.50

Step-by-step explanation:

Let the cost of fudge be f and taffy be t.

Chris bought 4 pieces of fudge and 3 pieces of taffy for a total of $7.95

 4 f + 3 t = 7.95

Samantha bought 2 pieces of fudge and 10 pieces of taffy for a total of $9.50

 2 f + 10 t = 9.5

Answer: √345600

Step-by-step explanation:

1st step: 10*6√96

2nd step: 60√96

3rd step:240√6

4th step (convert to radical form): √345600

there's your answer

Answer: B

Step-by-step explanation:

Multiply matrices

AB = [ 4    5 ]       x    [   3   ]

        [ 8    7 ]             [   9   ]

4 x 3 + 5 x 9 = 12 + 45 = 57

8 x 3 + 7 x 9 = 24 + 63 = 87

[ 57 ]

[ 87 ]

Answer: No

A correlation is a relationship between two variables that tend to move in the same direction. Therefore, a positive correlation will describe two variables that increase together. However, correlation does not always equal causation, and in this case, this conclusion cannot be made. A more probable explanation is that there is some third variable causing an increase in population, so more people are buying more cars, not the other way around.

Answer: 16 glasses of milk

Step-by-step explanation: To find how many glasses can be filled with milk, we must know that this is a division problem. So, we divide 12 by 3/4 to get 16. When dividing, the answer will be greater than the number it is being divided by, because the reciprocal will be found, and it will be greater when multiplied. I hope this helped. Please mark brainliest (If can)

1.22ft is the length, in feet, of the model.

What is arithmetic?

Arithmetic is an elementary a part of arithmetic that consists of the study of the properties of the normal operations on numbers—addition, subtraction, multiplication, division, involution, and extraction of roots.

Main Body:

Length of Clark house = 30.5 ft

Dimensions of the model were 1/25 the dimension of Clark's actual home.

so , we can write as -

Write and solve an equation of ratios:

 1          x

---- = ----------

25      30.5 ft

Then 30.5 ft = 25 x, and x = 1.22 ft, or 14.64 inches.

Hence 1.22ft is the length, in feet, of the model.

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Hello,

The slope-intercept form of a linear equation is:

y = mx + b

where m is the slope of the line and b is the y-intercept, which is the point where the line crosses the y-axis.

To write the equation of the line with slope m = -1 that passes through the point (4, 5), you can use the point-slope form of a linear equation, which is:

y - y1 = m(x - x1)

where (x1, y1) is a point on the line and m is the slope of the line. Plugging in the values, we get:

y - 5 = -1(x - 4)

This simplifies to:

y - 5 = -x + 4

Finally, we can rearrange the terms to put the equation in slope-intercept form:

y = -x + 9

This is the equation of the line with slope m = -1 that passes through the point (4, 5).

---

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Happy Holidays!

The A ∩ B ∩ C = {0}, if  A = {1,3,5,7,9,11}, B = {2,4,6,8,12} and C = {5,10,15,20}.

Any group of objects (elements) in mathematics and logic, whether they are mathematical (such as numbers and functions), is referred to as a set.

Given:

Set A = {1,3,5,7,9,11},

B = {2,4,6,8,12},

C = {5,10,15,20}

Calculate the A ∩ B ∩ C by the formula given below,

A ∩ B ∩ C = {0}

As there is nothing common between sets A, B, and C.

Therefore, A ∩ B ∩ C = {0}.

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Answer:

Length (L) = 50 m

Step-by-step explanation:

Given information,

→ 400 m long fencing wire is required to surround square flower garden 2 times.

Now the fence taken for 1 time,

→ 400 ÷ 2

→ 200 m

Formula we use,

→ P = 4 × L

[Perimeter of square]

Then the length of the garden is,

→ P = 4 × L

→ 200 = 4L

→ 4L = 200

→ L = 200/4

→ [ L = 50 m ]

Hence, length of garden is 50 m.

Answer:

122.5

Step-by-step explanation:

first you divide 70/4 =17.5 then you multiply 17.5 by 7 and get 122.5

Based on the given rate, which is  4-ounce serving of applesauce has 70 Calories the Calorie level of 7 ounces of applesauce is 122.5 calories

The number of calories in 7 ounces of applesauce is solved by comparing the how many 4 ounce is in 7 ounce

The amount of 4 ounce in 7 ounce = 7 ounce / 4 ounce

The amount of 4 ounce in 7 ounce = 1.75 ounce

Then the equivalent amount of calories is solved by multiplication

The number of calories in 7 ounces of applesauce  = 1.75 * 70 calories

= 122.5 calories

The number of calories in 7 ounces of applesauce is 122.5

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The required product of the given product numeral is -1536. Option C is correct.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,

Here,
=  (−16)(−4)(−24)
= 64(-24)
= -1536

Thus, the required product of the given product numeral is -1536. Option C is correct.

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Answer:

18

Step-by-step explanation:

for the first one, 2(5+1)+10=22

for the second one, 2(6+4)+10=30

using the same concept, 2(3+1)+10=18

?=18

im not sure if im right or not lol

Answer:

79.2Million?

Step-by-step explanation:

hope this helps

By evaluating the function in x = -2, we will get:

f(-2) = -2

To do that, we need to evaluate the given linear equation:

f(x) = -x - 4

We want to find f(-2), so we need to evaluate the linear equation in x = -2, this means that we just need to replace the variable by the corresponding number.

Then we will get:

f(-2) = -(-2) - 4

f(-2) = +2 - 4

f(-2) = -2

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The coordinates of the centroid of triangle DEF with the vertices (0,4) (6,6), and (2,2) is calculated as: (8/3, 4).

The formula for finding the coordinates of the centroid of a triangle is given as:

C(x, y) = [tex]( \frac{(x1+x2+x3)}{3}, ( \frac{(y1+y2+y3)}{3})[/tex].

Given the vertices of triangle DEF as follows:

D (0, 4) = [tex](x_1, y_1)[/tex]

E (6, 6) = [tex](x_2, y_2)[/tex]

F (2, 2) = [tex](x_3, y_3)[/tex]

Substitute the values into the centroid formula to find the coordinates:

C(x, y) = [(0 + 6 + 2)/3, (4 + 6 + 2)/3]

C(x, y) = (8/3, 12/3)

C(x, y) = (8/3, 4)

Therefore, the centroid has the coordinates that are calculated as: (8/3, 4).

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WXYZ to JKLM

JM is equal to 9, ZW is 13.5, JK is 12, and WX is 18.

To obtain the coordinates of the other shape, multiply the original shape by the scale factor

What is the scale factor?

The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller). For instance, we can increase the size of a rectangle with sides of 2 cm and 4 cm by multiplying each side by, let's say, 2.

13.5 / 9 = 1.5

9 * 1.5 = 13.5 \s12 * 1.5 = 18

You have a scale factor of 1.5. (because if u multiply 1.5 by the original shape, u get the new shape)

JKLM ~ WXYZ

So  JK ~  WX

So the scale factor  =  WX / JK

Scale Factor   =  18 / 12 =   3 / 2    =   1.5

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The value of a for system ax + 12y = −6, 2x − 6y = 4 having no solution is a = -4.

Equation: A statement that two variable or integer expressions are equal. In essence, equations are questions, and the motivation for the development of mathematics has been the systematic search for the answers to these questions.

Given:

ax + 12y = −6

2x − 6y = 4

Calculate the value of a by using the condition of no solution of the system given below,

[tex]a_1 / a_2 = b_1 / b_2 \neq c_1/c_2[/tex]

So, a₁ / a₂ = b₁ / b₂

a / 2 = 12 / (-6)

a / 2 =  - 2

a = -4

And -4 / 2 ≠ -6 / 4

Therefore, the value of a for system ax + 12y = −6, 2x − 6y = 4 having no solution is a = -4.

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Answer:630

Step-by-step explanation:

Answer:

Step-by-step explanation:

For an equation or function be linear, it should be in the form:

Y= mX +b

then

a) YES Linear

b) NO linear

c) YES Linear

d) NO linear