Solve the quadratic equation by completing the square. What are the missing pieces to the steps?​

Answer:

A family of functions is a group of functions that can all be derived from transforming a single function called the parent function. The parent function is the most basic function in the family of functions, the function from which all the other functions in the family can be derived.A family of functions is a group of functions that can all be derived from transforming a single function called the parent function. The parent function is the most basic function in the family of functions, the function from which all the other functions in the family can be derived.

Step-by-step explanation:

All of the functions within a family of functions can be derived from the parent function by taking the parent function's graph through various transformations.

These transformations include horizontal shifts, stretching or compressing vertically or horizontally, reflecting over the x or y axis, and vertical shifts.

Answer:

The parent function is the most basic.

Answer:

Option C.

Step-by-step explanation:

we know that

If two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

In this problem triangles HEF and EGE are similar  

because

[tex]EF/GF=HF/EF[/tex]

substitute the values

[tex]\frac{\sqrt{3}}{1}=\frac{3}{\sqrt{3}}\\ \\3=3[/tex]

Is true

The sides are proportional

and

∠HFE=∠GFE

∠EHF=∠GEF

∠HEF=∠EGF

The angles are congruent

The scale factor is equal to

[tex]EF/GF[/tex]

[tex]\frac{\sqrt{3}}{1}[/tex]

Answer:

Option C

Step-by-step explanation:

Two triangles are similar if they have at least 2 equal angles

Note that the HEF triangle has angles of 90 °, 60 ° and 30 °

Note that the EGF triangle has angles of 90 ° and 30 ° so the third angle must be 60 °

Then HEF and EGF are similar triangles.

By definition for similar triangles it is satisfied that if they have sides of length a, b, c and a ', b' c' then

[tex]\frac{a}{a'}=\frac{b}{b'}=\frac{c}{c'}=k[/tex]

Where the constant k is known as "scale factor"

In this case

[tex]\frac{HF}{EF}=\frac{HE}{EG}=\frac{FE}{GF}=k[/tex]

[tex]k=\frac{3}{\sqrt{3}}=\frac{2\sqrt{3}}{2}=\frac{\sqrt{3}}{1}=\sqrt{3}[/tex]

[tex]\frac{FE}{GF}=\frac{\sqrt{3}}{1}[/tex]

or

[tex]\sqrt{3}:1[/tex]

The answer is Option C

Answer:

[tex]X\leq -8[/tex]

This solution provides a step-by-step explanation to solve the inequality x – 1 ≤ -9, which results in the solution x ≤ -8. This solution indicates that all numbers x that are less than or equal to -8 will satisfy this inequality.

To solve the given inequality x – 1 ≤ – 9, you should first isolate the variable on one side of the inequality:

So, the solution to the inequality is x ≤ -8, which means all numbers x that are less than or equal to -8 will satisfy this inequality.

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Answer:

The sum of the geometric sequence is: -6665

Step-by-step explanation:

By looking at the geometric sequence, we can note that each term is multiplied by -6.

So, the fourth term is going to be: -216

The fifth term is going to be: 1296

The sixth term is going to be: -7776

The sum of the geometric sequence is: 1 - 6 + 36 - 216 + 1296 - 7776 = -6665

Answer:

slope = 0

Step-by-step explanation:

Calculate the slope m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 4, 3) and (x₂, y₂ ) = (5, 3)

m = [tex]\frac{3-3}{5+4}[/tex] = [tex]\frac{0}{9}[/tex] = 0

For this case we have the following function:

[tex]f (x) = - \sqrt {x + 3} -2[/tex]

By definition, the domain is given by all the values for which the function is defined.

The given function is no longer defined if the argument of the root is negative. So:

[tex]x + 3 \geq0\\x \geq-3[/tex]

Thus, the domain of the function is given by all the values of x greater than or equal to -3.

Domain: [-3, ∞)

Substituting the values of the domain, we find the range.

[tex]f (-3) = - \sqrt {-3 + 3} -2 = -2[/tex]

The function evaluated in ∞ gives -∞. So the range is given by:

(-∞, 2]

Answer:

Domain:  [-3, ∞)

Range: (-∞, 2]

The answer for this equation is C.

[tex]\bf \textit{Cofunction Identities} \\\\ sin\left(90^o-\theta\right)=cos(\theta) \qquad cos\left(90^o-\theta\right)=sin(\theta) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ cos(x)=\stackrel{90-56}{sin(\stackrel{\downarrow }{34^o})}\implies cos(\stackrel{\downarrow }{x})=sin(90^o-\stackrel{\downarrow }{56^o})\implies cos(56^o)[/tex]

There are 2 way to find value of x

cos x = sin 34°

First

Co-function identities

sin(90° -∅ ) =cos(∅)     cos(90 -∅) =sin(∅)

       90-56 ↓

cos(x)=sin(34°)⇒ cos (x) =sin(90°-56)⇒ cos(56°)

∴ value of x = 56°⇒ 0.5592

Second way to find  value x

x = cos-1(0.5592)

This is much simpler,

cos (90 - x)= sin x

So,

90 - 34 = 56

∴ x = 56

cos(56) = 0.5592

sin(34) = 0.5592.

A branch of mathematics that studies relationships between side lengths and angles of triangles.

Sin 34 degrees is the value of the sine trigonometric function for an angle equal to 34 degrees. The value of sin 34° is 0.5592

The value of cos 34

= 0.829

The value of cos 34° is equal to the x-coordinate (0.829).

∴ cos 34° = 0.829.

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Answer:

-3

Step-by-step explanation:

Consider the geometric sequence:

[tex]b_1=-2\\ \\b_2=6\\ \\b_3=-18\\ \\b_4=54\\ \\....[/tex]

Note that

[tex]b_2=b_1\cdot q\\ \\b_3=b_2\cdot q\\ \\b_4=b_3\cdot q\\ \\...[/tex]

So,

[tex]6=-2q\\ \\-18=6q\\ \\54=-18q\\ \\...[/tex]

From all of these equalities we can state that

[tex]q=-3[/tex]

Answer:

r = - 3

Step-by-step explanation:

The sequence is geometric if a common ratio r exists between consecutive terms.

6 ÷ - 2 = - 3

- 18 ÷ 6 = - 3

54 ÷ - 18 = -3

The sequence is geometric with common ratio r = - 3

Answer:

(b - 2)(3b + 7)

Step-by-step explanation:

Consider the factors of the product of the coefficient of the b² term and the constant term which sum to give the coefficient of the b- term

product = 3 × - 14 = - 42 and sum = + 1

The factors are - 6 and + 7

Use these factors to split the b- term

3b² - 6b + 7b - 14 ( factor the first/second and third/fourth terms )

= 3b(b - 2) + 7(b - 2) ← factor out (b - 2) from each term

= (b - 2)(3b + 7) ← in factored form

Answer: 107 degrees.

Step-by-step explanation:

A quadrilateral is defined as a 2-dimensional closed shape which has four sides and four vertices.

By definition the interior angles of a quadrilateral add up 360 degrees.

We know that this quadrilateral has 2 right angles (which are angles that measure 90 degrees) and we know that the measure of the third angle is 73 degrees.

Let be "x" the measure of the fourth angle.

Then you can write this expression:

[tex]360\°=90\°+90\°+73\°+x[/tex]

And finally solve for "x":

 [tex]360\°=253\°+x[/tex]

[tex]360\°-253\°=x[/tex]

[tex]x=107\°[/tex]

For this case we have that the variable "s" represents the quantity of slices for each pizza.

In total, 9 pizzas were purchased and 72 slices were obtained. Then we can raise the following equation:

[tex]9s = 72[/tex]

To know the amount of slices of each pizza we clear "s":

[tex]s = \frac {72} {9} = 8[/tex]

Answer:

[tex]9s = 72\\s = 8[/tex]

Answer:

x=3

Step-by-step explanation:

3/2x-5=5/6x-3

3/2x-5-5/6=5/6x-3-5/6x

2/3x-5=-3

2/3x-5+5=-3+5

2/3x=2

(3/2)*(2/3x)=(2)*(3/2)

x=3

Hope this helps a bit,

Flips

Answer:

f(3) = 64/3

Step-by-step explanation:

f(x)=1/3•4^x

Let x = 3

f(3) = 1/3* 4^3

    = 1/3 * 64

   = 64/3

Answer:

64/3 (APEX)

Step-by-step explanation:

Answer:

17.1

Step-by-step explanation:

1. Find the Mean

(25+40+35+25+40+60+75)/7 = 42.9

2.For each number, subtract the Mean and square the result.

(25-42.86)^2=319

(40-42.86)^2=8.2

(35-42.86)^2=61.8

(25-42.86)^2=319

(40-42.86)^2=8.2

(60-42.86)^2=293.8

(75-42.86)^2=1033

3. Find the Mean of those squared differences.

(319+8.2+61.8+319+8.2+293.8+1033)/7=291.9

4.Take the square root of that and this is what you want.

square root of 291.9 = 17.1

The standard deviation of the given data is 17.1

Standard deviation meaning in statistics is a measure of how much the data points vary from the mean or average. It is calculated as the square root of the variance, which is the average of the squared deviations of each data point from the mean.

Given is a data set, we need to find the standard deviation of the data set,

S = 25, 40, 35, 25, 40, 60, 75

Finding the mean =

(25+40+35+25+40+60+75)/7 = 42.86

Finding the variance =

(25-42.86)² = 319

(40-42.86)² = 8.2

(35-42.86)² = 61.8

(25-42.86)² = 319

(40-42.86)² = 8.2

(60-42.86)² = 293.8

(75-42.86)² = 1033

(319+8.2+61.8+319+8.2+293.8+1033)/7=291.9

Therefore, the standard deviation =

√291.9 = 17.1

Hence, the standard deviation of the given data is 17.1

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Answer:

Step-by-step explanation:

One

2/3 = 0.6666

4/5 = 0.8

5/6 = 0.8333

On a number line, the last 2 would be close to 1 and 4/5 would be closer to the center than 5/6.

2/3 is over half so it would be closest to the 1/2 point and the furthest left of the the points.

_____________________________|____________|___|_______

O                                                             2/3                   4/5   5/6

Two

What primes make up the number given

38: 2 * 19                

18: 3 *3 * 2

24:2*2 * 2 * 3

81: 3 * 3 * 3 * 3

Answer:

1730

Step-by-step explanation:

The exponential function is of the form

y = a × [tex]b^{n}[/tex]

where y is the insect population and n the number of weeks

a and b have to be found by using values from the table.

Using (0, 20), then

20 = a × [tex]b^{0}[/tex] ⇒ a = 20

Using (1, 30), then

30 = 20 × [tex]b^{1}[/tex] ⇒ b = [tex]\frac{30}{20}[/tex] = 1.5

Hence

y = 20 × [tex]1.5^{n}[/tex] ← exponential function

When n = 11

y = 20 × [tex]1.5^{11}[/tex] ≈ 1730 ( nearest whole number )

77.99+7.00+9.99=96.98

96.98 times 8.75% or 0.0875=8.48575 or 8.49                    8.49+96.98=$105.47

Answer:

c- shifted 3 units right and 4 units up

Step-by-step explanation:

In this problem, we have a quadrilateral named as ABCD. Recall that a quadrilateral is a two-dimensional shape having four sides. So, we need to identify what transformation has been performed to get A'B'C'D', which is the same quadrilateral shifted certain units right and up. So take one point, say, B, so how do we need to do to obtain point B'? well, we need to move that point 3 units right and 4 units up, but how can we know this? just count the number of squares you need to move from B to B' horizontally and vertically, which is in fact  3 units right and 4 units up.

Answer:  The correct option is

(c) shifted 3 units right and 4 units up

Step-by-step explanation:  We are given to select the correct steps that were applied o ABCD to obtain A'B'C'D' as shown in the figure.

From the graph, we note that

the co-ordinates of the vertices of quadrilateral ABCD are A(2, 3), B(4, 8), C(6, 8) and D(8, 3).

And, the co-ordinates of the vertices of quadrilateral A'B'C'D' are A'(5, 7), B'(7, 12), C'(9, 12) and D'(11, 7).

So, the transformations from the vertices of ABCD to the vertices of A'B'C'D' are as follows :

A(2, 3)    ⇒   A'(5, 7) = (2+3, 3+4),

B(4, 8)    ⇒   B'(7, 12) = (4+3, 8+4),

C(6, 8)    ⇒   C'(9, 12) = (6+3, 8+4),

D(8, 3)    ⇒   D'(11, 7) = (8+3, 3+4).

Therefore, the required rule of translation from ABCD to A'B'C'D' is

(x, y)  ⇒   (x+3, y+4). That is, 3 units right and 4 units up.

Thus, the required steps applied to ABCD to obtain A'B'C'D' are

Shifted 3 units right and 4 units up.

Option (c) is CORRECT.

Answer:

Third Option: $2.07

Step-by-step explanation:

Sales tax is the tax that is applied on the sales of goods by the government paid by the public. Here,

Given

Amount = $29.50

And

Sales tax rate = 7%

The formula for calculation of tax is:

Sales tax = Amount * tax rate

= 29.50 * 7/100

= 29.50*0.07

= 2.065

Rounding off will give

$2.07

So third option is correct ..

Answer:

$2.07

Step-by-step explanation:

Answer:

its b

Step-by-step explanation:

The height of the mat off the ground is 5√3 / 3 feet.

A triangle is a three-sided polygon with three edges and three vertices. A right triangle is a triangle in which one of its angles measures 90 degrees.

In order to determine he height of the mat, tan would be used.

Tan = opposite / adjacent

Tan 30 = opposite / 5

1 / √3 = opposite / 5 = 5

Opposite = 5√3 / 3 feet

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[tex]A=\pi r(r+l)\\r=4\\l=13\\\\A=\pi \cdot 4(4+13)=4\pi \cdot 17=68\pi[/tex]

The question appears to be about finding the surface area of a cone, but the provided information discusses a concave mirror instead, which is not relevant for the surface area calculation of a cone.

The question asks for the surface area of a right cone. However, the information provided pertains to the cross-sectional area of a concave mirror that is a quarter-section of a cylinder and not a cone. To find the surface area of a cone, one would use the formula A = πrs + πr^2 where r is the radius of the base and s is the slant height of the cone. In the given text, the radius of the mirror is mentioned to be 80.0 cm, and the insolation is 900 W/m².  This data seems to be mistakenly provided instead of the cone's dimensions and is irrelevant for calculating the surface area of a cone.

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The arithmetic expression (-7 + 31) minus (2) equals 22 when you apply the order of operations, which requires us to calculate expressions within parentheses first.

To solve this arithmetic problem, let's break down the expression into two parts, working within the parentheses first. The term inside the first set of parentheses is -7 + 31 which equals 24. The term inside the second set of parentheses appears to have missing or incorrect data.

If we ignore that, we have just (2). Now we subtract the second term (2) from the first term (24). Thus, the value of (-7 + 31) – (2) is 22.

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Answer:

16

Step-by-step explanation:

You need to multiply 4/5 * $20 = $16

Answer:

Step-by-step explanation:

Not sure

Answer:

a) $686

b) 17 weeks

Step-by-step explanation:

a) Set [tex]w=6[/tex], as Pablo has already saved for 6 weeks. Plug in the value and solve for [tex]A(6)[/tex].

[tex]A(w)=800-19w[/tex]

[tex]A(6)=800-19(6)[/tex]

[tex]A(6)=800-114[/tex]

[tex]A(6)=686[/tex]

Pablo still needs $686.

b) Set [tex]A(w)=477[/tex], as it is the "final amount" for that week.  Solve for [tex]w[/tex].

[tex]A(w)=800-19w[/tex]

[tex]477=800-19w[/tex]

[tex]-323=-19w[/tex]

[tex]w=17[/tex]

Pablo has been saving for 17 weeks if he still needs $477.

Answer:

Pablo wants to save $800 to buy a TV.

He saves $19 each week.

The amount, A (in dollars), that he still needs after  weeks is given by the following function.

[tex]A(w)= 800-19w[/tex]

(a) How much money does Pablo still need after 6 weeks?

Putting w = 6 in the equation;

[tex]A(6)= 800-19(6)[/tex]

= $686

(b) If Pablo still needs $477, how many weeks has he been saving?

This means Pablo has already saved [tex]800-477=323[/tex] dollars

Means he has saved for [tex]\frac{323}{19}=17[/tex] weeks.

He has been saving for 17 weeks now.

Answer:

x = 4 (extraneous solution)

Step-by-step explanation:

[tex] \frac { 4 } { x - 4 } = \frac { x } { x - 4 } - \frac { 4 } { 3 } \\ \frac { 4 } { x - 4 } - \frac { x } { x - 4 } = - \frac { 4 } { 3 } \\ \frac { 4 - x } { x - 4 } = - \frac { 4 } { 3 } \\ 3 ( 4 - x ) = - 4 ( x - 4 ) \\ 1 2 - 3 x = - 4 x + 1 6 \\ 4 x - 3 x = 1 6 - 1 2 \\ x = 4 \\[/tex]

This solution is extraneous. Reason being that even if it can be solved algebraically, it is still not a valid solution because if we substitute back [tex]x=4[/tex], we will get two fractions with zero denominator which would be undefined.

Answer:

A = 28 units ^2

Step-by-step explanation:

The area of a triangle is

A = 1/2 bh

The base is 14 and the height is 4

A = 1/2 (4) * 14

A = 28 units ^2

Answer:

6√2

Step-by-step explanation:

A 45 45 90 right triangle, so ratio of leg : leg: hypotenuse = a: a : a√2 (a = value of leg)

Given: leg = 6

So the ratio of leg : leg: hypotenuse = 6 : 6 : 6 √2

Answer:

x = 6√2

Answer:

B

Step-by-step explanation:

Since the triangle is right use the sine ratio to solve for x

and the exact value for sin45° = [tex]\frac{1}{\sqrt{2} }[/tex], then

sin45° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{6}{x}[/tex]

Multiply both sides by x

x × sin45° = 6 ( divide both sides by sin45° )

x = [tex]\frac{6}{sin45}[/tex] = [tex]\frac{6}{\frac{1}{\sqrt{2} } }[/tex] = 6[tex]\sqrt{2}[/tex]

Answer:

So value of x = -1 and value of y = 1

Solution Set (-1,1)

Step-by-step explanation:

x+y =0

x-y +2 =0

We need to solve these equations to find value of x and y

x+y =0 eq(1)

Add -2 on both sides

x-y = -2 eq(2)

Add equation 1 and 2

x+y = 0

x-y =-2

______

2x = -2

x = -2/2

x = -1

Now, put value of x = -1 in equation 1

x+y = 0

-1 +y =0

Adding +1 on both sides

-1+1+y = 0+1

y = 1

So value of x = -1 and value of y = 1

Solution Set (-1,1)

We would plot the values of x= -1 and y = 1 on the graph.

Graph is attached in the figure below.

Answer:

13

Step-by-step explanation:

                                                                   x    y

y=1/2x+3 and passes through the point (10,-5) 10 = x and -5 =y    1/2(10) - this mean times

-5 = 1/2(10) +3

1/2(10/1) = 1 x 10 and 2 x 1 = 10/2 = 5

-5 = 5 + 3 = 7

-5 = 7          + 5 + 7

+5  +5

= 13

(I wish You'll understand)