The steps to derive the quadratic formula are shown below:


I need help pls

Step 1 ax2 + bx + c = 0
Step 2 ax2 + bx = − c
Step 3 x2 + b over a times x equals negative c over a
Step 4 x2 + b over a times x plus b squared over 4 times a squared equals negative c over a plus b squared over 4 times a squared
Step 5 x2 + b over a times x plus b squared over 4 times a squared equals negative 4 multiplied by a multiplied by c, all over 4 multiplied by a squared plus b squared over 4 times a squared
Step 6


Provide the next step to derive the quadratic formula. (1 point)

x plus b over 2 times a equals plus or minus b squared minus 4 times a times c all over the square root of 4 times a squared

x plus b over 2 times a equals plus or minus b minus 2 times a times c all over square root of 2 times a

x plus b over 2 times a equals plus or minus the square root of the quantity b squared minus 4 times a times c all over the square root of 4 times a squared

x plus b over 2 times a equals plus or minus the square root of the quantity b squared minus 4 times a times c all over the square root of 2 times a

The minimum surface area for the rectangular container is [tex]588cm^{2}[/tex].

A solid object's surface area is a measurement of the overall space that the object's surface takes up.  Compared to the definition of the arc length of a one-dimensional curve or the definition of the surface area for polyhedra (i.e., objects with flat polygonal faces), where the surface area is equal to the sum of the areas of its faces, the mathematical definition of surface area in the presence of curved surfaces is much more complex.

Let s be the side of the square base and h be the height.

Surface Area=[tex]s^{2}+4sh[/tex]

Volume=[tex]s^{2}h[/tex]

According to the question,

[tex]s^{2}h=1372\\ h=\frac{1372}{s^{2} }[/tex]

So, surface area=[tex]s^{2} +4s(\frac{1372}{s^{2} })[/tex]

                          =[tex]s^{2}+\frac{5488}{s}[/tex]

Differentiate with respect to s,

Surface area=[tex]2s-\frac{5488}{s^{2} }[/tex]

Now, [tex]2s-\frac{5488}{s^{2} }=0[/tex]

[tex]2s=\frac{5488}{s^{2} } \\2s^{3}=5488\\ s^{3}=2744\\ s=14[/tex]

Find the value of h from the volume.

[tex]14*14*h=1372\\h=\frac{1372}{14*14}\\ h=7[/tex]

Thus, the minimum surface area=[tex]14^{2}+4*14*7[/tex]

                                                      =[tex]588cm^{2}[/tex]

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The graph that corresponds to the proportional relationship M = 3n is graph vs.

A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:

y = kx

In which k is the constant of proportionality.

In this problem, the relationship is:

M = 3n.

Considering that the montant is the vertical axis, the graph is composed by points (n, 3n), that is, the vertical axis is triple the horizontal axis, having points (100, 300), (200, 600) and so on, the graph is graph vs.

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The volume of the modified globe would be 523.3 cubic inches (Option 3)

What is the volume of the globe with modified dimensions?

Information Given

The current diameter of the globe = 20 inches

We know that the radius of a sphere (globe) is half its diameter.

⇒ The radius of the globe = 10 inches

If the dimensions of the globe were reduced by half, the new diameter would be, [tex]\frac{20}{2} = 10[/tex] inches.

⇒ New radius of the globe, [tex]r = 10[/tex] inches

Calculating the Volume of the Modified Globe

The volume of a sphere (globe) is given by,

[tex]V = \frac{4}{3} \pi r^{3}[/tex]

Here, [tex]r[/tex] is the new radius of the globe.

∴ The volume of the new globe would be,

[tex]V = \frac{4}{3} \pi (5)^{3}[/tex]

Use [tex]\pi =3.14[/tex]

⇒ [tex]V = \frac{4}{3} (3.14) (5)^{3}[/tex]

⇒ [tex]V = 523.333..[/tex] cubic inches

Rounding off the result to the nearest tenth, we get,

[tex]V = 523.3[/tex] cubic inches

Thus, if the dimensions of the globe were reduced by half, its volume would be 523.3 cubic inches.

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Using the z-distribution, the 99% confidence interval of the population mean number of days it takes to find a job is (35.38, 44.62).

The confidence interval is:

[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]

In which:

In this problem, we have a 99% confidence level, hence[tex]\alpha = 0.99[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.99}{2} = 0.995[/tex], so the critical value is z = 2.575.

The other parameters are:

[tex]\overline{x} = 40, \sigma = 10, n = 31[/tex]

Hence the bounds of the interval are:

[tex]\overline{x} - z\frac{\sigma}{\sqrt{n}} = 40 - 2.575\frac{10}{\sqrt{31}} = 35.38[/tex]

[tex]\overline{x} + z\frac{\sigma}{\sqrt{n}} = 40 + 2.575\frac{10}{\sqrt{31}} = 44.62[/tex]

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Using supplementary angles, it is found that the measure of angle x is of 65º.

Angles are called supplementary if the sum of their measures is of 180º.

In this problem, angles x, 25, and 90º are supplementary, hence:

x + 25 + 90 = 180

x = 180 - (25 + 90)

x = 65º.

The measure of angle x is of 65º.

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The inverse function of f(x) = 6x + 4 is f^-1(x) = (x - 4)/6

The function is given as:

f(x) = 6x + 4

Rewrite as:

y = 6x + 4

Swap x and y

x = 6y + 4

Subtract 4 from both sides

6y = x - 4

Divide through by 6

y = (x - 4)/6

Rewrite as:

f^-1(x) = (x - 4)/6

Hence, the inverse function of f(x) = 6x + 4 is f^-1(x) = (x - 4)/6

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Answer:

https://brainly.com/question/14172055?referrer=searchResults

Step-by-step explanation:

Your question has already been answered.

Here is the link to the answer:

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Hope this helps!

If not, I am sorry.

The volume of the trough is V(w) = w³ + 20w² - 429w and the rate of change of the volume over a width of 38 inches to 53 inches is 4695 in³/in

An equation is an expression that shows the relationship between two or more variables and numbers.

Let w represent the width, hence:

length = w + 33, height = w - 13

Volume (V) = w(w + 33)(w - 13) = w³ + 20w² - 429w

V(w) = w³ + 20w² - 429w

Rate of change = dV/dw = 3w² + 40w - 429

When w = 38, dV/dw = 3(38)² + 40(38) - 429 = 5423

When w = 53, dV/dw = 3(53)² + 40(53) - 429 = 10118

Rate = 10118 - 5423 = 4695 in³/in

The volume of the trough is V(w) = w³ + 20w² - 429w and the rate of change of the volume over a width of 38 inches to 53 inches is 4695 in³/in

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Hello !

[tex]\begin{cases} 5x+3y - 35&=0 \\ 3x - 4y &= - 8 \end{cases}[/tex]

[tex]\Leftrightarrow\begin{cases} 5x+3y &=35 \\ 3x - 4y &= - 8 \end{cases}[/tex]

[tex]\Leftrightarrow AX = B [/tex]

With

[tex]A=\left[\begin{array}{ccc}5&3\\3& - 4\end{array}\right] [/tex]

[tex]X=\left[\begin{array}{ccc}x\\y\\\end{array}\right] [/tex]

[tex]B=\left[\begin{array}{ccc}35\\ - 8\\\end{array}\right] [/tex]

The solution is given by [tex]X=A^{-1}B[/tex].

[tex]X= {\left[\begin{array}{ccc}5&3\\3& - 4\end{array}\right] }^{ - 1} \left[\begin{array}{ccc}35\\ - 8\\\end{array}\right] [/tex]

[tex]X=\left[\begin{array}{ccc}4\\ 5\\\end{array}\right] [/tex]

The point of intersection between the lines is (4;5).

Have a nice day

Answer:

Point of intersection (4,5)

Step-by-step explanation:

5x + 3y - 35 = 0

3x - 4y = -8

 ⇒ 5x + 3y = 35

     3x - 4y = -8

  Matrix A will be formed by the coefficient of x and y. Matrix B will be formed by the constants.

[tex]\sf A = \left[\begin{array}{cc}5&3\\3&-4\end{array}\right][/tex]

[tex]\sf B = \left[\begin{array}{c}35&-8\end{array}\right][/tex]

AX = B

 [tex]\sf X =A^{-1}B[/tex]

[tex]Now ,\ we \ have \ to \ find \ A^{-1}[/tex],

Find the workout in the document attached.

Answer:

1. to c.

2. to d.

3. to a.

4. to b.

Step-by-step explanation:

These answers should be right.

Hope this helps!

The matching of the polynomials to their correct names are:

a. h(x) = 15x+2 is a linear binomial

b. j(x)=x²-3x³ + 9x²  is a  Quartic trinomial

c. f(x)= 3x² - 5x+7 is a Quadratic trinomial

d. 8(x)=-5x³ is a Cubic monomial

A polynomial is an expression having more than one algebraic terms.

1) A quadratic trinomial is a polynomial that is defined as a quadratic expression with all three terms in the form of ax² + bx + c, where a, b, and c are numbers and not a 0.

2) A cubic monomial is defined as a a monomial that has a degree of 3.

3) Linear binomial is defined as a polynomial with two terms whose variable has degree 1. For example, 4x − 5 or 3x + 12 are both linear binomials.

4) A quartic trinomial is defined as a polynomial with three terms having the highest degree 4

Thus:

a. h(x) = 15x+2 is a linear binomial

b. j(x)=x²-3x³ + 9x²  is a  Quartic trinomial

c. f(x)= 3x² - 5x+7 is a Quadratic trinomial

d. 8(x)=-5x³ is a Cubic monomial

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1. Lines a and b are parallel by the converse of alternate interior angles theorem

2. l║m by the converse of consecutive interior angles theorem.

Given that the interior angles, ∠3 ≅ ∠7, according to the converse of alternate interior angles theorem, the lines they are found on, lines a and b would be parallel.

1. Lines a and b are parallel.

Given that the interior angles, m∠5 + m∠12 = 180, according to the converse of consecutive interior angles theorem, the lines they are found on, lines l and m would be parallel.

2. Lines l and m are parallel.

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Answer:

x<3

Step-by-step explanation:

3x - 4 < 17 - 4x

So, the -4 shall cross to the other side and replace the -4x which will now take the place of where the -4 used to be and the signs of both digits will change to a positive (+)

Remember the inequality sign (<) shall not change

so now the equation shall appear like this;

3x + 4x < 17 + 4

add both sides and it will appear like this;

7x < 21

simplify both sides by 7 and you'll get

x < 3

Yolanda’s error during the calculation of the volume is that A. Yolanda should have found the volume by multiplying 8 by Two-thirds.

It should be noted that the volume of a sphere is simply 4/3πr³.

In this case, the sphere and a cylinder have the same radius and height and the volume of the cylinder is 8 meters cubed.

Based on the information given, Yolanda’s error during the calculation of the volume is that she should have found the volume by multiplying 8 by two-thirds.

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[tex]\angle FHD=74^{\circ}[/tex] (alternate segment theorem)

[tex]x=77^{\circ}[/tex] (angles in a triangle add to 180 degrees)

The products of the two polynomials (x² + x – 2) and (4x² – 8x) is 4x⁴ - 4x³ - 16x² + 16x

An equation is an expression that shows the relationship between two or more variables and numbers.

The products of the two polynomials (x² + x – 2) and (4x² – 8x) is:

= 4x⁴ - 8x³ + 4x³ - 8x² - 8x² + 16x

= 4x⁴ - 4x³ - 16x² + 16x

The products of the two polynomials (x² + x – 2) and (4x² – 8x) is 4x⁴ - 4x³ - 16x² + 16x

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Answer:

D

Step-by-step explanation:

This result is true by De Moivre's theorem.

The expected value of x is 10.

It is given that the number of dice that are showing an even number is a binomial random variable with n = 4, and p = 1/2 (because half the faces on the die are even and half are odd).

The expected value of this random variable is n*p = 4*1/2 = 2.

The number of points is simply 5 times this random variable, and by the rules of expected value, E(C*Y) = C*E(Y), where C is a constant and Y is a random variable.

Thus E(X) = 5*2 = 10.

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The equation with infinitely many solutions is:

9x + 80 - 1x = 8*(x + 10)

An equation has infinitely many solutions when the dependence on x vanishes.

If you look at the third equation, we get:

9x + 80 - 1x = 8*(x + 10)

If we simplify the left side and expand the right side, we get:

8x + 80 = 8x + 80

So we have the exact same thing in both sides, this means that the equation is true for any value of x, so the equation has infinite solutions.

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Answer:

4 legs from the bed and 4 from the chair im guessing since not all have 4

Hope This Help

Answer:

4 legs from the bed and 4 from the chair

Step-by-step explanation:

im a math wizard fr

The width is 1 meter.

Given,

Jarom is working for a landscaping company and is responsible for building the stone border around a rectangular pond.The pond measures 6 meters by 15 meters. The manager told Jarom that the budget only allowed enough stone for 46 square meters

Let the border be width  = x

then the area of the border will be

2(6x) + 2(15x) +4x2 = 46

= 12x +30x+ 4x2 = 46

= 4x2 + 42x - 46 = 0

=> x =( -42 +- √42² +4*4*46)/8

x =1 , x = -11.5

since the width is 1 meter.

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Answer:

[tex]y = \dfrac{1}{2}x-4[/tex]

Step-by-step explanation:

       [tex]\sf slope = m =\dfrac{1}{2}\\\\Point (2, -3) ; x_1 = 2 \ \& y_1 = -3\\\\\boxed{\bf y - y_1 =m(x -x_1)}[/tex]

         [tex]\sf y - [-3] = \dfrac{1}{2}(x - 2)\\\\y + 3 = \dfrac{1}{2}x - 2*\dfrac{1}{2}\\\\y + 3 = \dfrac{1}{2}x-1\\\\[/tex]

                [tex]\sf y = \dfrac{1}{2}x - 1 - 3\\\\ y =\dfrac{1}{2}x-4[/tex]

Answer:

(2x - 5)(3x + 1)

Step-by-step explanation:

6x² - 13x - 5

ax² + bx + c

ac = 6 × (-5) = -30

-30 = -15 × 2

-13 = -15 + 2

6x² - 13x - 5 =

= 6x² - 15x + 2x - 5

= 3x(2x - 5) + 1(2x - 5)

= (2x - 5)(3x + 1)

Answer: its a.) (2x-5)(3x+1)

Step-by-step explanation:

6x² - 13x - 5ax² + bx + cac = 6 × (-5) = -30-30 = -15 × 2-13 = -15 + 26x² - 13x - 5 == 6x² - 15x + 2x - 5= 3x(2x - 5) + 1(2x - 5)= (2x - 5)(3x + 1)

and got it right on the test review.

Answer:

4th option

Step-by-step explanation:

L = larger softball and S = smaller softball ,then

L + S = 80 → (1) ← equation based on number of softballs ordered

2.75L + 3.25S = 245 → (2) ← equation based on cost

subtract S from both sides in (1)

L = 80 - S → (3)

substitute L = 80 - S into (2)

2.75(80 - S) + 3.25S = 245 ← distribute parenthesis and simplify left side

220 - 2.75S + 3.25S = 245

220 + 0.5S = 245 ( subtract 220 from both sides )

0.5S = 25 ( divide both sides by 0.5 )

S = 50

substitute S = 50 into (3)

L = 80 - 50 = 30

50 small softballs and 30 large softballs were ordered

Answer:

the 4th answer option

Step-by-step explanation:

L, S are the number of balls of that size.

so, L + S = 80. as we order a total of 80 balls.

then each large ball costs $2.75. and each small ball costs $3.25.

so, the total price is

2.75L + 3.25S = 245

as we order balls in total for $245.

so, this set of 2 equations with 2 variables allows us to find the solution.

one defines the total number of balls, and one defines the total amount of money spent by using the individual prices for each type of ball.

the advantage of variables is that we can define the rising and dependencies before we have to calculate any of them specifically.

and once we have all of them defined, then we can start solving the numbers.

If the function is f(x)=35.5x+6 and snowfall in inches are 53,42,55,63,58,47 then the income received will be $1887.5,$1497,$1958.5,$2242.5,$2065$1674.5.

Given Snowfall received during the years:53,42,55,63,58,47 and f(x)=35.5x+6

We have to find the income in dollars received if f(x) shows the income.

Function is a relationship between variables and it have each value of y for each value of x.

To find the income we have to just put the values of x=53,42,55,63,58,47one by one and we will get income.

f(53)=35.5*53+6=1887.5

f(42)=35.5*42+6=1497

f(55)=35.5*55+6=1958.5

f(63)=35.5*63+6=2242.5

f(58)=35.5*58+6=2065

f(47)=35.5847+6=1674.5

Hence the income for snowfall 53,42,55,63,58,47 inches are 1887.5,1497,1958.5,2242.5,2065,2674.5.

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The statement which best describes the translation from the graph y= 6x² to the graph of y = 6(x+1)² is; The translation represents a unit shift rightward.

The translation involved in the transformation of the graph as given in the task content represents a rightward shift of the graph y = 6x² by 1 unit.

On this note, it follows that the translation involved between the two graphs is; a unit shift to the right.

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Answer:

Step-by-step explanation:

one unit to the right

Answer:

d - the minimum value of d is 5 more than the maximum value of c

Step-by-step explanation:

we can see from the graph that d has a minimum value

that value is at (-1, 2) and the minimum is 2

for c the vertex is where the graph reflects itself

that point is (-4, -3) and the maximum is -3

that means that the minimum value of d is 5 more than the maximum value of c because 2 - (-3) = 5

Answer:

I am not sure how that works but from the way it look and adding it up it comes to 66.6 but I was thinking around 75 - 85

Step-by-step explanation:

Answer:

○ The distance between a and b on the number line is 0.47 units.

Explanation:

The first statement is not true because the distance between a and b on the number line is not 0.47.

Distance between a and b = 5.25 - (-5.72)

                                             = 10.97

• The second statement is true because the sum of a and b is negative:

Sum = a + b

        = -5.72 + 5.25

        = -0.47

• The third statement is true because the quotient of a and -b is:

a ÷ -b

⇒ -5.72 ÷ -5.25

⇒ 1

And the quotient of -a and b is:

-a ÷ b

⇒ -(-5.72) ÷ 5.25

⇒ 1

This shows that the quotients are the same.

• The fourth statement is true because the product of a and -b:

a × -b

⇒ -5.72 × -(5.25)

⇒ 30.03 ,

is positive.