x^2-8x+5=25 solve by completeing the square

Answer: Order of operations

Step-by-step explanation:

Plug in 3 for x so...

y = -2(3)² + 12(3) - 15

Don't forget the order of operations, exponents go first

y = -2(9) + 12(3) - 15

Then multiply

y = -18 + 36 - 15

Simplify

y = 3

Jug A has a vοlume οf 400 ml and jug B has a vοlume οf 400 ml.

An equatiοn in twο variables is an equatiοn that invοlves twο variables, typically x and y, and relates them with cοnstants and mathematical οperatiοns such as additiοn, subtractiοn, multiplicatiοn, and divisiοn.

Let's represent the vοlume οf jug A by x and the vοlume οf jug B by y.

We knοw that the cοmbined vοlume οf the twο jugs is 800 ml:

x + y = 800 (equatiοn 1)

We alsο knοw that after pοuring water frοm jug A tο jug B, there is 200 ml οf water remaining in jug A. This means that jug B cοntains x ml οf water:

y = x (equatiοn 2)

We can substitute equatiοn 2 intο equatiοn 1 tο eliminate y:

x + y = 800

x + x = 800

2x = 800

x = 400

Nοw that we knοw that the vοlume οf jug A is 400 ml, we can use equatiοn 2 tο find the vοlume οf jug B:

y = x

y = 400

Therefοre, the vοlume οf jug B is alsο 400 ml.

Hence, jug A has a vοlume οf 400 ml and jug B has a vοlume οf 400 ml.

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I apologize, but it seems that the question is incomplete or has not been properly formatted. Please provide the full question and any additional details or context so that I can accurately and effectively answer it. Thank you.

Answer:

The students would be paying a low amount of $5.60. The 30% discount takes off $2.40 of the original price, so the discount is worth $2.40

It is possible for each of the six quadratic equations to have at least one real root.

This is because the discriminant of a quadratic equation determines the nature of its roots. The discriminant is given by the formula: D = b² - 4ac.

If D > 0, the equation has two distinct real roots.
If D = 0, the equation has one real root (a double root).
If D < 0, the equation has no real roots (two complex roots).

In each of the six equations, the coefficients a, b, and c are non-zero real numbers. This means that the discriminant can be positive, zero, or negative, depending on the values of a, b, and c. Therefore, it is possible for each of the six equations to have at least one real root.

For example, consider the equation ax² + bx + c = 0. If b² > 4ac, then the equation has two distinct real roots. If b² = 4ac, then the equation has one real root (a double root). If b² < 4ac, then the equation has no real roots (two complex roots).

Similarly, the other five equations can also have at least one real root, depending on the values of the coefficients a, b, and c.

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Answer:

The correct answers are:

As x approaches positive infinity, f(x) approaches positive infinity.

As x approaches negative infinity, f(x) approaches 0.

Step-by-step explanation:

By the fundamental theorem of algebra, it has exactly 4 complex roots, counting multiplicities.

A function is a mathematical rule that assigns a unique output value for each input value. It is a set of ordered pairs where the first element is the input and the second element is the output.

The given function is a polynomial of degree 4. Therefore, by the fundamental theorem of algebra, it has exactly 4 complex roots, counting multiplicities.

However, we do not know if these roots are all real or if some of them are complex. To determine this, we would need to use techniques such as factoring, synthetic division, or the quadratic formula to solve for the roots of the polynomial.

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Answer:

$156.45

Step-by-step explanation:

Swing set $745

21/100 x $745 = 156.45

Answer:

d. Insured banks pay a premium on the money insured. The FDIC's reserve fund comes from premiums paid by insured banks. The premiums are paid based on the amount of deposits held by the bank and the level of risk the bank poses to the FDIC's insurance fund.

The estimated height of the child at delivery is represented by the y-intercept, which is 72.66.

We may use linear regression to construct an equation that represents the link between this child's height and age. The line of best fit for the supplied data is determined by linear regression, which can be written as:

Age (years) + b * m * Height (cm)

where m denotes the line's slope and b its y-intercept.

The equation that most closely matches the above data can be determined using a calculator or spreadsheet software as follows:

Age (years) + 72.66 Height (cm) = 6.087

Thus, the height of the youngster increases by roughly 6.087 centimetres for every year that their age rises. The estimated height of the infant at delivery is represented by the y-intercept, which is 72.66.

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Using the addition method the solution to the system is (x,y) = (14/3, 7/3) and using the substitution method the solution to the system is (x,y) = (7,7).

Using the addition method, we can rearrange the equations so that one of the variables cancels out:

y=2x-7  ->  -2x + y = -7
y=4x-21  ->  -4x + y = -21

Now, we can add the two equations together to eliminate the y variable:

-2x + y = -7
-4x + y = -21
______________
-6x = -28

Next, we can solve for x:

x = 28/6 = 14/3

Now, we can substitute this value of x back into one of the original equations to find y:

y = 2x - 7 = 2(14/3) - 7 = 28/3 - 21/3 = 7/3

So the solution to the system is (x,y) = (14/3, 7/3).

Using the substitution method, we can substitute one equation into the other to eliminate one of the variables. For example, we can substitute the first equation, y=2x-7, into the second equation, y=4x-21:

2x-7 = 4x-21

Next, we can rearrange the equation to solve for x:

2x = 14
x = 7

Now, we can substitute this value of x back into one of the original equations to find y:

y = 2x - 7 = 2(7) - 7 = 7

So the solution to the system is (x,y) = (7,7).

In conclusion, we can solve the system y=2x-7 and y=4x-21 using either the addition method or the substitution method to find the solution (x,y).

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Answer:

14

Step-by-step explanation:

The number of pounds of peaches sold is given as follows:

65 pounds, option 2.

The amount is obtained solving a system of equations, for which the variables are given as follows:

She sold a total of 165 pounds, hence:

x + y = 165

x = 165 - y.

She made $337.50, hence:

1.75x + 2.5y = 337.50.

Replacing the first equation into the second, the value of y is obtained as follows:

1.75(165 - y) + 2.5y = 337.50

0.75y = 48.75

y = 48.75/0.75

y = 65 pounds.

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We can write the perimeter of the equilateral triangle as -

P = 13x - 19.

Given is a equilateral triangle.

We can write the perimeter of a equilateral triangle as -

Perimeter = (2x + 3) + (4x - 5) + (7x - 17)

Perimeter = 2x + 4x + 7x + 3 - 5 - 17

Perimeter = 13x - 19

Therefore, we can write the perimeter of the equilateral triangle as -

P = 13x - 19.

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Answer:

To find the total price, we need to add the tip and tax to the total bill amount.

First, we need to find the amount of the tip. To do this, we will multiply the total bill by 22% (or 0.22):

$45.65 x 0.22 = $10.04

This means the tip amount is $10.04.

Next, we need to find the amount of tax. To do this, we will multiply the total bill by 5% (or 0.05):

$45.65 x 0.05 = $2.28

This means the tax amount is $2.28.

Finally, we can find the total price by adding the total bill, tip, and tax together:

$45.65 + $10.04 + $2.28 = $57.97

Therefore, the total price is $57.97.

Ian’s mom sang him S songs. Then his sister sang him two times as many as his mom had. If Ian listened to nine songs in all, Ian's mom sanghim twIan’s mom sang him S songs. Then his sister sang him two times as many as his mom had. If Ian listened to nine songs in all, Ian's mom sango times as many as his mom had. If Ian listened to nine songs in all, Ian's mom sang _____songs.

Answer:

110° and 215°

Step-by-step explanation:

the bearing of one point to another is the measure of the clockwise angle from the north line N at the point C to the point D , that is

(a)

bearing of D from C is 110° ( purple shaded angle )

(b)

the bearing of D from C is 215° ( blue shaded angle )

Answer:

answer is sus.

Step-by-step explanation:

sus is the correct answer to your problrm. hope this helps!

Using the definition of a parallelogram in Euclid's first book, we can say that a non-perpendicular, unequal, non-bisecting diagonal produces either a trapezium or a rhombus if the opposite angles are equal, then it is a rhombus, and if the opposite angles are unequal, then it is a trapezium.

To use Euclid's first book to prove what specific quadrilaterals are produced by non-perpendicular, unequal, non-bisecting diagonals, start by considering Euclid's definitions of a parallelogram, a trapezium, and a rhombus.

In Euclid's first book, a parallelogram is defined as a quadrilateral which has two pairs of equal and parallel sides, while a trapezium is defined as a quadrilateral which has two pairs of opposite sides parallel, but with the other two sides unequal and non-parallel.

Finally, a rhombus is defined as a quadrilateral (parallelogram) which has all four sides equal, and with the opposite angles equal.

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The transformations that are occurring between each of the function are given as follows:

f(x) = 14(x - 3) + 1 and g(x) = 7(x + 2) + 1: vertical compression by a factor of 1/2 and shift left 5 units.

f(x) = 6(x + 2) - 3 and g(x) = 8(x - 3) + 6: vertical stretch by a factor of 4/3, shift right 5 units and shift up 9 units.

f(x) = 3(x - 1) + 2/3 and g(x) = 3(3 - x) - 2/3: reflection over the y-axis, shift left 2 units and shift up 4/3 units.

f(x) = 1/3(x + 2) - 4 and g(x) = 1/3(-x - 2) + 6: reflection over the y-axis and shift up 10 units.

f(x) = 4/3(x - 2/3) + 1/3 and g(x) = 2/3(2/3 - x) = reflection over the y-axis, shift down of 1/3 units and vertical stretch by a factor of 2.

The curve of the graph "moves to the left/right/up/down," "it expands or compresses," or "it reflects" when a function is changed.

The transformation rules are defined as follows:

x -> x + a: shift left a unit.

x -> x - a: shift right a unit.

y -> y + a: shift up a unit.

y -> y - a: shift down a unit.

y -> ky, k > 1: vertical stretching by k times.

Vertical compression by a factor of k is achieved by y -> ky, k 1, horizontal compression by a factor of k is achieved by x -> kx, k > 1, and vertical stretch by a factor of k is achieved by x -> kx, k 1.

x -> -x: reflection over the y-axis.

y -> -y: reflection over the x-axis.

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Answer:

To evaluate the function when x = 3, we substitute 3 for x in the given function f(x) = 5x + 2:

f(3) = 5(3) + 2

f(3) = 15 + 2

f(3) = 17

Therefore, when x = 3, the value of the function f(x) = 5x + 2 is 17.

So, the correct answer is option D, 7 is incorrect because 5*3+2 = 17.

The Answers given are incorrect this is because the correct answer is 5.7

f(x) = 5x + 2

f(3)=5(3)+2

3f=15+2

3f=17

3f÷3=17÷3

f=5.66666666667

=5.7

Other fractions could represent the part of the beads on the bracelet that will be green are : 1/3, 2/6, 3/9, 4/12.

A fraction represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one-half, eight-fifths, three-quarters.

here, we have,

The maximum number of beads the bracelet can have  = 12 beads

The fraction of green beads in the bracelet = 1/3

⇒ 1 bead in every 3 bead is GREEN.

⇒The minimum number of total beads = Number of (green+ Other) bead                                                           = 2 + 1  = 3

Now, the possible number of total beads the bracelet can have is

3, 4, 5 , 6, 7, 8, 9 ,10, 11 and 12.

If there are total 3 beads, the fraction representing the green bead  = 1/3

If there are total 6( =3 +3) beads, the fraction representing the green bead  

= 1 green bead in first 3 beads +  1  green bead in next 3 beads

=   2 green beads in total 6 beads

=   2/6

If there are total 9( = 3 +3 +3) beads, the fraction representing the green bead  = 3/9

If there are total 12( = 3 +  3 +3 +3) beads, the fraction representing the green bead  = 4/12

Hence, other fractions could represent the part of the beads on the bracelet that will be green are :1/3, 2/6, 3/9, 4/12.

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Axj = bj, j=1,…,r.

To show that AX = B if and only if Axj = bj, j=1,…,r, we can start by recognizing that AX is an m×r matrix and B is an m×r matrix. Since the dimensions of these two matrices are the same, they are equal if and only if each corresponding element is equal.

Therefore, we can conclude that AX = B if and only if each corresponding element of AX is equal to its corresponding element in B. Mathematically, this is expressed as Axj = bj, j=1,…,r.

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The answer: no real solutions to this equation

To solve the equation, we need to find a common denominator for all of the fractions on the left side of the equation. The common denominator will be (y-2)(y-3), so we will multiply each fraction by the appropriate factor to get the common denominator.

[tex]y/y -2y+ 4/y-3 = 4/ y2-5y+6[/tex]

[tex]y(y-3)/(y-2)(y-3) - 2y(y-2)/(y-2)(y-3) + 4(y-2)/(y-2)(y-3) = 4/(y-2)(y-3)[/tex]

Now we can combine the fractions on the left side of the equation:

[tex](y2-3y-2y2+4y+4y-8)/(y-2)(y-3) = 4/(y-2)(y-3)[/tex]

Simplifying the numerator on the left side gives us:

[tex](-y2+5y-8)/(y-2)(y-3) = 4/(y-2)(y-3)[/tex]

Now we can cross-multiply and simplify:

[tex](-y2+5y-8) = 4[/tex]

[tex]-y2+5y-12 = 0[/tex]

To solve this equation, we can use the quadratic formula:

[tex]y=\left(-5\pm \sqrt{52-4\left(-1\right)\left(-12\right)}\right)[/tex]

[tex]y=\left(-5\pm \sqrt{25-48}\right)[/tex]

[tex]y=\left(-5\pm \sqrt{-23}\right)[/tex]

Since the square root of a negative number is not a real number, there are no real solutions to this equation. Therefore, the answer is no solution.

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The value of the expression is approximately -102.8571.

A set of guidelines known as the order of operations establishes the order in which mathematical operations should be carried out. Mathematical computations are carried out consistently and accurately by following the correct order of operations. Without a set order of operations, it would be possible for individuals to incorrectly and erroneously understand mathematical equations.

The given expression is:

6 x 7 - 3 x 96 / 2 + 86 / 7 x 354 / 21

= 42 - 288 / 2 + 86 / 49 x 354 / 21

= 42 - 144 + 4 x 354 / 21

= -102.8571

Hence, the value of the expression is approximately -102.8571.

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Answer:

Step-by-step explanation:

Im not sure I can't see the picture.

Answer: Hence, the width of the path is 4 meters.

First we should find the area of the pool. Our width is 14 and our length is 18. In order to find the area, we must multiply these two numbers. 14 times 18 is 252. This means that the area of the pool is 252.

Since we know that one side of the pool is 18 and one side is 14, we can write out the equation below.

572= (18+2x)(14+2x)

The first thing we should do is combine like-terms.Our equation would now be as below.

x^2+16-80=0

Next we would take our quadratic equation- x=-b+-√b2-4ac/2a and fill it in with the numbers that we had in the first equation, our equation would be like below.  A=1   B=16   C=-80

x=-16+-√16^2-4* 1 * -80 /2 * 1

When then simplify our equation leaving us with x=-16+-√16^2-4*1(-80)/2 * 1, which broken down is x=-16+-√+-24/2.

Lastly we must subtract and add to receive our two answers.

One side is 4 and the other is -20. Since the width of the walk cannot not be a negative number, we know that the width of the path is 4 meters.

Hence, the width of the path is 4 meters.

I hope this helped & Good Luck <3!!!

Answer:

x = -6

Step-by-step explanation:

-4 + 2x = 4x+8

-4-8 = 4x - 2x

-12 = 2x

x = -6

Answer:

x = - 6

Step-by-step explanation:

Hope this helps! <33

The minimum value of f(x) over the interval [3,5] is -512 and the maximum value is 225.

To find the minimum and maximum values of the function f(x) = x^(4) - 32 x^(2) over the interval [3,5], we can use the following steps:

1. Find the first derivative of the function: f'(x) = 4x^(3) - 64x
2. Set the first derivative equal to zero to find the critical points: 4x^(3) - 64x = 0
3. Solve for x to find the critical points: x = 0, x = 4√2, x = -4√2
4. Check the value of the function at the critical points and at the endpoints of the interval to find the minimum and maximum values.
5. The minimum value occurs at x = 4√2, where f(4√2) = (4√2)^(4) - 32(4√2)^(2) = -512
6. The maximum value occurs at x = 5, where f(5) = 5^(4) - 32(5)^(2) = 225
7. Therefore, the minimum value is -512 and the maximum value is 225.

The least value of f(x) over the interval [3,5] is -512 and the largest value is 225.

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On sοlving the given trigοnοmetric expressiοn using the trigοnοmetric identity, we fοund that it is equal tο tan (π/35).

Mathematical expressiοns cοnsist οf at least twο numbers οr variables, at least οne maths οperatiοn, and a statement. It's pοssible tο multiply, divide, add, οr subtract with this mathematical οperatiοn. A finite cοmbinatiοn οf symbοls that are well-fοrmed in accοrdance with cοntext-dependent principles is referred tο as an expressiοn οr mathematical expressiοn.

There are twο sοrts οf expressiοns in mathematics: numerical expressiοns, which οnly cοntain numbers, and algebraic expressiοns, which alsο include variables. Expressiοns can be categοrised as arithmetic/numerical expressiοns, fractiοnal expressiοns, οr algebraic expressiοns depending οn the terms they cοntain.

The given trigοnοmetric expressiοn is:

[tex]\frac{tan (3\pi /7) - tan (2\pi /5)}{1+tan (3\pi /7) tan (2\pi /5)}[/tex]

tan (a-b) = sin(a-b)  / cοs (a-b)

    = (sin a cοs b - cοs a sin b) / (cοs a cοs b + sin a sin b)

  Dividing the numeratοr and denοminatοr by (cοs a cοs b), we get,

tan (a-b) = (tan (a) - tan (b)) / (1+tan a tan b)

This expressiοn is similar tο the given expressiοn.

Cοmparing,

a = 3π/7

b = 2π/5

[tex]\frac{tan (3\pi /7) - tan (2\pi /5)}{1+tan (3\pi /7) tan (2\pi /5)}[/tex]  = tan( 3π/7 - 2π/5) = tan (π/35)

Therefοre on solving the given trigonοmetric expression using the trigonοmetric identity, we found that it is equal tο tan (π/35).

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