A portion of the Quadratic Formula proof is shown. Fill in the missing reason.


Statements Reasons
ax2 + bx + c = 0 Given
ax2 + bx = −c Subtract c from both sides of the equation
x squared plus b over a times x equals negative c over a Divide both sides of the equation by a
x squared plus b over a times x plus the quantity b over 2 times a squared equals negative c over a plus the quantity b over 2 times a squared Complete the square and add the quantity b over 2 times a squared to both sides
x squared plus b over a times x plus the quantity b over 2 times a squared equals negative c over a plus b squared over 4 times a squared Square the quantity b over 2 times a on the right side of the equation
x squared plus b over a times x plus the quantity b over 2 times a end quantity squared equals negative 4 times a times c over 4 times a squared plus b squared over 4 times a squared Find a common denominator on the right side of the equation
x squared plus b over a times x plus the quantity b over 2 times a squared equals b squared minus 4 times a times c all over 4 times a squared Add the fractions together on the right side of the equation
quantity x plus b over 2 times a end quantity squared equals b squared minus 4 times a times c all over 4 times a squared ?
Rewrite the perfect square trinomial as a binomial squared on the left side of the equation
Take the square root of both sides of the equation
Multiply both sides of the equation by 2
Square the left side of the equation

Answer:

B

Step-by-step explanation:

using Pythagoras' identity in the right triangle

the square on the hypotenuse is equal to the sum of the squares on the other 2 sides , then

(x + 1)² + (x + 3)² = (x + 5)² ← expand all factors using FOIL

x² + 2x + 1 + x² + 6x + 9 = x² + 10x + 25 , that is

2x² + 8x + 10 = x² + 10x + 25 ← subtract x² + 10x + 25 from both sides

x² - 2x - 15 = 0 ← in standard form

(x - 5)(x + 3) = 0 ← in factored form

equate each factor to zero and solve for x

x - 5 = 0 ⇒ x = 5

x + 3 = 0 ⇒ x = - 3

however, x > 0 , then x = 5

Answer:

B. 5

Step-by-step explanation:

[tex] \sf{C = \sqrt{ A {}^{2} + B {}^{2} }}[/tex]

[tex]\sf{x + 5 = \sqrt{ {(x + 3)}^{2} + {(x + 1)}^{2} }}[/tex]

[tex]\sf{x + 5 = \sqrt{ {(x {}^{2} + 6x + 9)} + {(x {}^{2} + 2x + 1)}}}[/tex]

[tex]\sf{x + 5 = \sqrt{ {(2x {}^{2} + 8x + 10)}}}[/tex]

[tex]\sf{(x + 5) {}^{2} = { {2x {}^{2} + 8x + 10}}}[/tex]

[tex]\sf{ {x}^{2} + 10x + 25= { {2x {}^{2} + 8x + 10}}}[/tex]

[tex]\sf{0= { {2x {}^{2} \red{ { - x}^{2} } + 8x \red{ - 10x} + 10 \red{ - 25}}}}[/tex]

[tex]\sf{0= x^{2} } - 2x { - 15}[/tex]

[tex]\sf{0= x^{2} } - 2x { - 15}[/tex]

[tex]\sf{0= (x - 5)(x + 3)}[/tex]

[tex] \sf{x_{1} - 5 = 0 }[/tex]

[tex] \sf{x_{1} = 0 + 5 }[/tex]

[tex] \sf{x_{1} = \boxed{5 }}[/tex]

[tex] \sf{x_{2} + 3 = 0 }[/tex]

[tex] \sf{x_{2} = 0 - 3 }[/tex]

[tex] \sf{x_{2} = \boxed{- 3 }}[/tex]

Option B. 5

Answer:

D. 2730

Step-by-step explanation:

I just had this question on FLVS yesterday.
you use factorials for this:

15!/12!

15*14*13*12!/12!

15*14*13

2730

Number of ways in which 3 positions can be filled are 2730.

The number of ways in which objects from a set may be selected, generally without replacements, to form subsets. This selection of subset is called permutation when order of selection is a factor.

If n things taken r at a time and n!  = n × (n-1) × (n-2) × (n-3)..........3 × 2 × 1

⇒Permutation,

                              [tex]P(n,r) =\frac{n!}{(n-r)!}[/tex]

Now it is given that number of candidates, n = 15

and number of position, r = 3

Hence number of ways positions can be filled-

                           [tex]P(n,r) =\frac{15!}{(15-3)!}[/tex]

⇒                         [tex]P(15,3) =\frac{15!}{12!}[/tex]

⇒                         P(15,3) =  (15 × 14 × 13)12!/12!

⇒                         P(15,3) =  (15 × 14 × 13)

⇒                         P(15,3) =  2730

∴ Number of ways in which 3 positions can be filled are 2730.

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(a) The gradient is [tex]\frac{40}{5}=\boxed{8}[/tex], and represents the cost of buying one book in dollars.

(b) Draw the line through (0,0) and (20, 130).

(c) Since the gradient of the line representing company B is less (6.5 vs 8), it is better to buy books from company B because they are cheaper.

The statements about the function that are true include:

g(0) = 0

g(1) = -1

g(-1) = 1

From the information, the points include:

(x1, y1) = (-2, 2, 5).

(x2, y2) = (0, 0)

(x3, y3) = (2, 3, 5).

It should be noted that (x2, y2) implies that g(0) = 0. In this case, the statements about the function that are true include g(0) = 0, g(1) = -1, and g(-1) = 1. This is illustrated in ten graph.

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Answer: the answer is b, d, and e.

g(0) = 0

g(1) = 1

g(-1) = 1

Step-by-step explanation:

A coordinate system in geometry is a system that employs one or more integers, or coordinates, to define the position. The correct option is D.

A coordinate system in geometry is a system that employs one or more integers, or coordinates, to define the position of points or other geometric components on a manifold such as Euclidean space.

For a function to be even, the graph of the function should be such that it should be symmetrical about the x-axis. Therefore, the points of the graph will be the opposite.

The 7 points of option D can be plotted as shown below, which is symmetrical about the X-axis. Hence, the correct option is D.

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The number of teams that can be made is 10.

In order to determine the number of teams he can make, divide the number of friends by the total number of people that must be in the team. Division is the process of grouping a number into equal parts using another number.

31 / 3 = 10 remainder 1

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Answer:this is all I could find

Step-by-step explanation:

The additive inverse of the polynomial is 6x³-4x²+4x.

Given The polynomial is -6x³+4x²-4x.

A polynomial is an expression that solely uses the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables. It consists of indeterminates and coefficients.

The number that results in zero when a number is added to it is said to be a number's additive inverse. The opposite, a shift in the sign, and negation are other names for this number.

The given polynomial is -6x³+4x²-4x.

To find the additive inverse of the polynomial, multiply the polynomial with minus sign, we get

-(-6x³+4x²-4x)=6x³-4x²+4x.

Hence, the additive inverse of the polynomial -6x³+4x²-4x is 6x³-4x²+4x.

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Answer:

[tex]y = \frac{17}{15}x + \frac{16}{15}[/tex]

Step-by-step explanation:

So the slope-intercept form is given as: y=mx+b where m is the slope and b is the y-intercept (since if you plug in 0 as x, mx will be 0 leaving only b). You can calculate the slope with the slope formula: [tex]slope=\frac{y_2-y_1}{x_2-x_1}[/tex] which is essentially [tex]\frac{rise}{run}[/tex]. So for this example (-8, -8) will be ([tex]x_1, y_1[/tex]) and (7, 9) will be ([tex]x_2, y_2[/tex]).

Plug values into equation:

[tex]\frac{9 - (-8)}{7 - (-8)}[/tex]

cancel out negatives

[tex]\frac{9+8}{7+8}\\[/tex]

Simplify

[tex]\frac{17}{15}[/tex]

The fraction is in the most simplified form unless you want to have a mixed fraction, otherwise you can't do anything else to the fraction.

so now we have the slope we have one part of the equation: [tex]y=\frac{17}{15}x + b[/tex], but now we need to solve for b. This can be done by using either of the points and plugging in x and y, but for this example I'll use (7, 9).

Plug in (7, 9) as (x, y)

[tex]9 = \frac{17}{15}(7) + b[/tex]

Multiply

[tex]9 = \frac{119}{15}+b[/tex]

Subtract

[tex]9-\frac{119}{15}=b[/tex]

Rewrite 9 as a fraction

[tex]\frac{135}{15} - \frac{119}{15} = b[/tex]

Subtract numerators

[tex]\frac{16}{15} = b[/tex]

now we have both pieces of information

[tex]y = \frac{17}{15}x + \frac{16}{15}[/tex]

Answer:

14641

Step-by-step explanation:

[tex]formular \: for \: the \: digits \: in \: each \\ row \: of \: a \: pascal \: triangle \: is \: = 11 {}^{n} \\ row \: 0 = \: 11 {}^{0} = 1 \: \\ row \: 1 \: = 11 {}^{1} = 11 \\ row \: \: 2 \: = 11 {}^{2} = 121 \\ row \: 3 = \: 11 {}^{3} = 1331 \\ row \: 4 = 11 {}^{4} = 14641 \\ therefore \: the \: fourth \: row \: is \: 14641[/tex]

The locus of the point represented by the equation y = 3•x + 2, indicates that the point (1, 5) is on the locus of the point.

The distance from the x-axis is the y-value

The distance from the y-axis is the x-value

Therefore;

The equation of the locus of the point is presented as follows;

When x = 1, y = 3 × 1 + 2 = 5

When x = 1, y= 5

Therefore;

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The dimensions i.e. length and width of the deck in the drawing is 8 and 6.4 inches respectively.

Given that the length of the previous deck = 15 feet

The width of the previous deck = 12 feet

Since the new deck will add 5 feet to the length and 4 feet to the width,

The length of the new deck = 15 + 5 = 20 feet

The width of the new deck = 12 + 4 = 16 feet

Also given that a drawing of the new deck uses a scale of 1 inch = 2.5 feet.

So, The length of the deck in the drawing = 20/2.5 inches = 8 inches

The width of the deck in the drawing = 16/2.5 inches = 6.4 inches

Therefore, the dimensions i.e. length and width of the deck in the drawing is 8 and 6.4 inches respectively.

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The proportion that solves for the distance between D and E is  x/15 = 6/9

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

Triangle ABC and CDE are similar triangles, hence the ratio of their corresponding sides are in the same proportion.

Hence:

x/15 = 6/9

The proportion that solves for the distance between D and E is  x/15 = 6/9

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Answer:

The equation for the line which passes through the points given as (a, b) and (a, b+1), is x=a, which represents a vertical line.

Step-by-step explanation:

It is given that a line passes through the points whose coordinates are (a, b) and (a, b+1).

It is asked to find the linear equation which passes through the given points.

To do so, first determine the slope of the given line using the coordinates and the formula for the slope. Accordingly, proceed to find the equation of the given line.

Step 1 of 2

Determine the slope of the line.

The points through which the line passes are given as (a, b) and (a, b+1). Next, the formula for the slope is given as,

[tex]$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$[/tex]

Substitute b+1&b for [tex]$y_{2}$[/tex] and [tex]$y_{1}$[/tex] respectively, and a&a for [tex]$x_{2}$[/tex] and [tex]$x_{1}$[/tex] respectively in the above formula. Then simplify to get the slope as follows,

[tex]m=\frac{b+1-b}{a-a}$\\ $m=\frac{1}{0}$[/tex]

b+1. So the equation of the line cannot be found using the general point-slope form equation.

Step 2 of 2

Write the equation of the line.

So, by definition, the line that passes through the given points is a vertical line. Now, as its x- coordinate is a, so the equation of the line is given as x=a.

Required probability is 0.8990

Given that,

p = 0.44

1 - p = 0.56

n = 736

[tex]\mu_\hat{p}} = p = 0.44\\\sigma_\hat{p}} = \frac{p*(1-p)}{n} = \sqrt(\frac{0.44*0.56)}{736} ) =[/tex]0.01830

Converting Normal distribution to standard normal because  A normal distribution is determined by two parameters the mean and the variance. A normal distribution with a mean of 0 and a standard deviation of 1 is called a standard normal distribution. Hence it's easy to work with standard normal distribution.

P(0.14<[tex]\hat{p}[/tex]<0.47) =  P((0.41-0.44)/0.01830) < [tex]\frac{\hat{p} - \mu _{\hat{p}} }{\sigma _{\hat{p}} }[/tex]<(0.47-0.44)/0.01830

Using normal algebra we get:

= P(-1.64 < z < 1.64)

= P(z < 1.64) - P(z < -1.64)

= 0.9495 - 0.0505

= 0.8990

Thus, required probability is 0.8990

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Answer:

1.  A(-8,3) B(-8,-2) C(-4,-2)

2. A'(8,3) B'(8,-2) C'(4,-2)

3. A"(-12,1.5) B"(-12,-3) C"(-6,-3)

4. they give you the coordinates, haha. Just graph and connect the dots.

5. Coordinates of ABC: A(-8,3) B(-8,-2) C(-4,-2)

   Coordinates of A'''B'''C''': A'''(-3,10) B'''(-3,5) C'''(1,5)

The correct coordinates for a 90 degree rotation is: A''''(3,8) B''''(-2,8) C''''(-2,4)

Most of these are formulas so I hope you have this memorized in preparation for tests! Good luck!

Answer:

Step-by-step explanation:

Both triangles are similar by SAS property,

that means corresponding sides are proportional,so,

5/6 = 15/N

= 6/5 = N/15

N = (6×15)/5

N = 6×3

N = 18

The system of linear inequalities which satisfy the region R are:

Mathematically, the standard equation of a straight line is given by y = mx + b.

In order to determine the system of linear inequalities that satisfy the region R, we would identify the points through which the lines passes through.

For the broken line, we have:

y-intercept = 3.

x-intercept = -3.

Points (x, y) = (0, 3) and (-3, 0).

Since the line is broken (not equal to), the inequality is given by:

y < x - 3.

For the other line, we have:

y-intercept = 5.

x-intercept = -5/2.

Points (x, y) = (0, 5) and (-5/2, 0).

(x/-5/2) + y/5 ≤ 1

-2x + y ≤ 5

y ≤ -2x + 5

For the line passing through the origin, we have:

y - x ≥ 0

y ≥ x.

In conclusion, the system of linear inequalities which satisfy the region R are:

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Answer: [tex]|f(x)-8| < 0.03[/tex]

The number b is b > -5/9

The statement is given as:

a number b times 18 is greater than -10

This can be represented as:

b * 18 > -10

Divide both sides by 18

b > -10/18

Simplify

b > -5/9

Hence, the number b is b > -5/9

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Answer:

The answer is a since non of the other answer would go throught that point

Hope This Helps!!!

Answer:

c.) 6 1/2

Step-by-step explanation:

Volume = length × width × height

2 1/6 × 1 1/5 × 2 1/2

13/6 × 6/5 × 5/2

13/5 × 5/2

13/2 = 6 1/2

Based on the given texts in the table about the graph of the function, the true statements are:

The function, 4x - 15 shows that 15 is the y-intercept which means that the graph will cross the y-axis at (0,15).

The point of discontinuity is x = - 2 and we see this with the gap created at x < -2 and -2 ≤ x ≤ 4.

The graph is indeed increasing over the interval (4, ∞o) because any value of x that is greater than 4 will increase f(x) = [tex]3^x^-^4[/tex].

The domain of the function is also all real numbers as it begins at negative infinity and ends at infinity, (-∞, ∞).

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The approximate solution of the above equation is: 55/15 (Option A). This is solved using the quartic formula, not quadratic equation.

The quartic formula has up to four various solutions including real and imaginary numbers. Read on for more explanation.

First we restate the above equation:

x²-3x+2= √(x-2) + 2

Next we remove square roots

[tex]x^{4}[/tex] - 6x³ + 9x² = x - 2

Add two to both sides

→ [tex]x^{4}[/tex] - 6x³ + 9x²+2 = x - 2 +2

→  [tex]x^{4}[/tex] - 6x³ + 9x²+2 = x

Subtract X from both sides

→  [tex]x^{4}[/tex] - 6x³ + 9x²+2 -x = x -x

→  [tex]x^{4}[/tex] - 6x³ + 9x²+2 - x= 0

Using the Quartic formula to solve the fourth order equation:
a[tex]x^{4}[/tex] + bx³ + cx² + dx + e

The resolution of x is given as:

x = 2.691085, 3.346753

Because the fraction nearest to 3.4 is 55/16

hence, the correct answer is Option A.

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Answer:

30000 milliliters

0.03 liters

Step-by-step explanation:

The volume of the box is 2.5 x 3.0 x 4.0 = 30 cc

There are 1000 ml in 1 cc so 30cc = 30 x 1000 = 30000 ml

There are 1000 cc in 1 liter so 30 cc = 30/1000 = 0.03 liters

The volume of the box is 30 mL or 0.03 L.

Volume is a metric magnitude that is defined as the extension in three dimensions of a region of space. Volume is defined as the amount of space occupied by the object or figure in three-dimensional space. Volume is measured in cubic units.

The volume of this prism depends on its three dimensions and is calculated as the multiplication of these dimensions,

Volume= Dimension 1× Dimension 2× Dimension 3

The volume of the box = 2.5 x 3.0 x 4.0 = 30 cc

There are 1000 ml in 1 cc so 30cc = 30 x 1000 = 30000 ml

There are 1000 cc in 1 liter so 30 cc = 30/1000 = 0.03 liters

Hence, the volume of the box is 30 mL or 0.03 L.

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Answer:

6 StartRoot 3 EndRoot units

Step-by-step explanation:

The longest possible integer length of the third side of the triangle is 6 < x < 28

The sum of any two sides must be greater than the third side for a triangle to exist

let the third side be x

x + 11 > 17 and x + 17 > 11 and 11 + 17 > x

x > 6 and x > - 6 and x < 28

The longest possible integer length of the third side of the triangle is 6 < x < 28

The length of the 3 sides of a triangle needs to always be among (however no longer the same) the sum and the difference of the opposite two sides. As an example, take the instance of two, 6, and seven. and. consequently, the third side period should be extra than 4 and less than 8.

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Answer:

27

Step-by-step explanation:

Let the third side length be s. Then, by the Triangle Inequality, we know that s satisfies the inequalities

[tex]s + 11 & > 17, \\ s + 17 & > 11, \\ 11 + 17 & > s.[/tex]

[tex]\begin{align*} s + 11 & > 17, \\ s + 17 & > 11, \\ 11 + 17 & > s.\end{align*}[/tex]

The first two inequalities hold as long as s > 6 and the third holds if s < 28. The largest possible integer s that satisfies all of these is 27.

Answer:

Check the first box, third box and fifth box

Explanation:

1st box:

Rewrite the fraction: 48

- ----

17

Check equivalency: True

Answer: True

2nd box:

Check equivalency: False

Answer: False

3rd box:

Convert the improper fraction into a mixed number:

2 × 17 + 14

- -----------------

17

Calculate the product or quotient: 34 + 14

- -----------

17

Calculate the sum or difference: 48

- ----

17

Check equivalency: True

Answer: True

4th box:

Rewrite the fraction: 17

----

48

Check equivalency: False

Answer: False

5th box:

Rewrite the fraction: 48

- ----

17

Check equivalency: True

Answer: True

I hope this helps!