Explain the steps necessary to convert a quadratic function in standard form to vertex form

[tex]\bf \sqrt{x+11}-x=-1\implies \sqrt{x+11}=x-1\implies \stackrel{\textit{squaring both sides}}{(\sqrt{x+11})^2=(x-1)^2} \\\\\\ x+11=\stackrel{\mathbb{F~O~I~L}}{x^2-2x+1}\implies 11=x^2-3x+1\implies 0=x^2-3x-10 \\\\\\ 0=(x-5)(x+2)\implies x= \begin{cases} 5\\ -2 \end{cases}[/tex]

Gives x = -5 or x = 2.

Learn how to solve radical equations step by step by isolating terms and squaring, resulting in solutions to the given equation.

To solve the equation (square root of x+11)-x=-1, follow these steps:

Answer:

(f-g)(x) = x-3

Step-by-step explanation:

Given

f(x) = 3x-2

and

g(x) = 2x+1

We have to find (f-g)(x)

So,

(f-g)(x) = f(x)-g(x)

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

= 3x-2-2x-1

=x-3

Hence,

(f-g)(x) = x-3

Answer:

( f - g ) ( x ) = x - 3

Step-by-step explanation:

We are to find [tex] ( f - g ) ( x ) [/tex] given that [tex] f ( x ) = 3 x - 2 [/tex] and [tex] g ( x ) = 2 x + 1 [/tex].

So basically we have to subtract the function g from function f.

[tex] ( f - g ) ( x ) = f(x) - g(x) [/tex]

Substituting the given functions in the above equation to get:

[tex] ( f - g ) ( x ) = (3x - 2) - (2 x + 1 ) [/tex]

[tex] ( f - g ) ( x ) = 3x - 2 - 2 x - 1  [/tex]

[tex] ( f - g ) ( x ) = 3x - 2 x - 2 - 1  [/tex]

[tex] ( f - g ) ( x ) = x - 3 [/tex]

Answer:

C. The domain is all real numbers, and the range is non-negative real numbers( [tex]y\ge0[/tex])

Step-by-step explanation:

The absolute value parent function is [tex]y=|x|[/tex]

The domain of a function refers to all values of x for which the function is defined.

The parent absolute value function is defined for all values of x.

Therefore the domain is all real numbers.

The range refers to the y-values for which x is defined.

The parent has a v-shape and its vertex is at the origin.

Therefore the least y-value is 0 and there is no maximum y-value.

The range is [tex]y\ge0[/tex]

See attachment.

Answer: B. 36

Step-by-step explanation: Round each number.

11.72 -> 12

3.01 -> 3

Multiply the rounded numbers.

12 x 3 = 36

The answer would be 36.

Answer:

[tex]\large\boxed{f^{-1}(x)=\dfrac{x+4}{3}=\dfrac{1}{3}x+\dfrac{4}{3}}[/tex]

Step-by-step explanation:

[tex]f(x)=3x-4\to y=3x-4\\\\\text{exchange x to y and vice versa}\\\\x=3y-4\\\\\text{solve for y}\\\\3y-4=x\qquad\text{add 4 to both sides}\\\\3y=x+4\qquad\text{divide both sides by 3}\\\\y=\dfrac{x+4}{3}[/tex]

Answer:

Step-by-step explanation:

Look at the picture.

We know: the sum of the angles measure in the triangle is 180°. Therefore we have the equation:

[tex]35^o+35^o+\alpha=180^o[/tex]

Solve it:

[tex]70^o+\alpha=180^o\qquad\text{subtract}\ 70^o\ \text{from both sides}\\\\\alpha=110^o[/tex]

Angle α and β = x are the supplementary angles. Supplementary angles add up to 180°. Therefore:

[tex]\alpha+\beta=180^o[/tex]

[tex]110^o+\beta=180^o\qquad\text{subtract}\ 110^o\ \text{from both sides}\\\\\beta=70^o[/tex]

[tex]\beta+\gamma+\gamma=180^o[/tex]

[tex]70^o+2\gamma=180^o\qquad\text{subtract}\ 70^o\ \text{from both sides}\\\\2\gamma=110^o\qquad\text{divide both sides by 2}\\\\\gamma=55^o[/tex]

Answer:

[tex]x=\sqrt[3]{10}-2[/tex]

Step-by-step explanation:

The composite function (f(x+1)) is moved in the x-axis by -1, you know this by solving x+1=0.

The equivalent expresion for f(x+1) is

[tex]f(x+1)= (x-1+3)^{3}+4[/tex]

[tex]f(x+1)=(x+2)^{3}+ 4[/tex]

Eval the above expression in g(x)

[tex]g(x)=(x+2)^{3}+4-2[/tex]

We must find x that gives g(x)=12

The equation is the following

[tex]12=(x+2)^{3}+2[/tex]

Grouping terms>

[tex](x+2)^{3} =10[/tex]

To solve for x, must apply cubic root in both sides of equation:

[tex]\sqrt[3]{(x+2)^{3} } =\sqrt[3]{10}[/tex]

it then turns in the following>

[tex]x+2=\sqrt[3]{10}\\[/tex]

Giving the stated answer

[tex]\huge{\boxed{\text{No.}}}[/tex]

Unless the points are both the same point, there is only one straight line to connect them both. Any other line would either only touch one point or touch neither of the points.

Answer: 0.999548

Step-by-step explanation:

If the probability that a person will die next year is 425/1,000,000

The the probability of them not dying is:

(1,000,000-425)/1,000,000=999548/1,000,000

Next let’s move the decimal 6 spots to the left.

The answer would be 0.999548

Answer:

Step-by-step explanation:

We know: the angles measures in a triangle add up to 180°.

(look at the picture)

z + 50 + 60 = 180

z + 110 = 180    subtract 110 from both sides

z = 70°

x + 50 + 70 = 180

x + 120 = 180         subtract 120 from both sides

x = 60°

Angles x, y and z are on one side of a straight line. Therefore they add to 180°.

x + y + z = 180

60 + y + 70 = 180

y + 130 = 180         subtract 130 from both sides

y = 50°

Answer:

x = 60°, y = 50°

Step-by-step explanation:

We know: the angles measures in a triangle add up to 180°.

z + 50 + 60 = 180

z + 110 = 180    subtract 110 from both sides

z = 70°

x + 50 + 70 = 180

x + 120 = 180         subtract 120 from both sides

x = 60°

Angles x, y and z are on one side of a straight line. Therefore they add to 180°.

x + y + z = 180

60 + y + 70 = 180

y + 130 = 180         subtract 130 from both sides

y = 50°

Answer:

Front section tickets: $40

Back section tickets: $25

Step-by-step explanation:

If x is the price of back section tickets, and x + 15 is the price of front section tickets, then:

275 (x + 15) + 325 x = 19125

275 x + 4125 + 325 x = 19125

600 x = 15000

x = 25

So back section tickets are $25, meaning front section tickets are $40.

Answer:

A. Parabola

Step-by-step explanation:

Parabola best describes the locust of points equidistant from a given directrix and focus.

Parabola is the curve that best describes the locus of points equidistant from a given directrix and focus. This can be obtained by understanding what a parabola is.

The equation is y² = 4ax, when directrix is parallel to the y-axis, a is distance from origin to focus.

Hence parabola is the curve that best describes the locus of points equidistant from a given directrix and focus.

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Answer:

Osvoldo does not meet his goal

He had to have eaten at least 66 grams of whole grains to meet his goal.

Step-by-step explanation:

step 1

Find out the 30% of the grams of carbohydrates that Osvoldo ate today

Remember that

30%=30/100=0.30

so

0.30(220)=66 grams

step 2

Compare the 30% of the grams of carbohydrates that Osvoldo ate today with the 55 grams of whole grains

we know that

To Osvoldo meet his goal the 55 grams of whole grain must be greater than or equal to the 30% of the grams of carbohydrates that Osvoldo ate today

55 < 66

therefore

Osvoldo does not meet his goal

He had to have eaten at least 66 grams of whole grains to meet his goal.

Answer:

y  ≥ 14.

Step-by-step explanation:

y - 27 ≥ -13 Add 27 to both sides:

y  ≥ 14 (answer).

For this case we must find the solution of the following inequality:

[tex]y-27 \geq-13[/tex]

We must add 27 to both sides of the inequality:

[tex]y \geq-13 + 27[/tex]

We know that different signs are subtracted and the sign of the major is placed.[tex]y \geq14[/tex]

So, the solution is [tex]y \geq14[/tex]

Answer:

Option C

Step-by-step explanation:

rearrange the equations first

y=-3x-2---eq(1)

y=-3x+1-4

y=-3x-3---eq(2)

In first eq slope is -3x and y-intercept is -2

In second equation, the slope is -3x and y-intercept is -3

the slopes are the same in both equations but the y-intercepts are different

so the lines are parallel. The system is inconsistent

For this case we have the following system of equations:

[tex]3x = -2-y\\4 + y = -3x + 1[/tex]

By clearing "y" from both equations we have:

Equation 1:

[tex]3x + 2 = -y\\y = -3x-2[/tex]

Equation 2:

[tex]y = -3x + 1-4\\y = -3x-3[/tex]

It is observed that the slopes of both equations are equal. Recall that the equation of a line in the slope-intersection form is given by:

[tex]y = mx + b[/tex]

Where "m" is the slope.

If the slopes are equal, then the lines are parallel.

Answer:

Parallel

The answer is 84 degrees because d and f both are 48 degrees so that adds up to 96. So that means you add 84 plus 96 which is 180 so the answer is 84 degrees.

Answer. The answer is 84

Answer:

Step-by-step explanation:

[tex]A=\left[\begin{array}{ccc}a&b\\c&d\end{array}\right] \\\\\det A=\left|\begin{array}{ccc}a&b\\c&d\end{array}\right|=ad-bc[/tex]

[tex]\left\{\begin{array}{ccc}x+2y=5\\x-3y=7\end{array}\right\\\\A=\left[\begin{array}{ccc}1&2\\1&-3\end{array}\right] \\\\\det A=A=\left|\begin{array}{ccc}1&2\\1&-3\end{array}\right|=(1)(-3)-(1)(2)=-3-2=-5[/tex]

Answer:

-5

Step-by-step explanation:

Answer:

C (2, -5/2)

Step-by-step explanation:

To find the midpoint of two points

mid = (x1+x2)/2, (y1+y2)/2

       = (2+2)/2, (4+-9)/2

       = 4/2, -5/2

       =2,-5/2

Answer: 3p+5=11

Step-by-step explanation:

3p+5=11

-5 -5

3p=6

3p/3=6/3

P=2

$2

The cost of each pencil is $2.

A word problem is a verbal description of a problem situation. It consists of few sentences describing a 'real-life' scenario where a problem needs to be solved by way of a mathematical calculation.

For the given situation,

Number of pencils = 3

Number of notebook = 1

Cost of a notebook = $5

Total cost = $11

Let number of pencil be p.

Lela purchased three mechanical pencils and a notebook is

⇒ [tex]3p+5=11[/tex]

⇒ [tex]3p=11-5[/tex]

⇒ [tex]3p=6[/tex]

⇒ [tex]p=\frac{6}{3}[/tex]

⇒ [tex]p=2[/tex]

Hence we can conclude that the cost of each pencil is $2.

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5x^4

Step-by-step explanation:

simply we take 5x^4 bec. it can be divided by 40 and 135

So you're asking to evaluate this equation?

mk/m+k for m = 6 and k = 2

Answer:

[tex]\frac{2x-y}{x(x-y)}[/tex]

Step-by-step explanation:

To express as a single fraction

multiply numerator/denominator of [tex]\frac{1}{x}[/tex] by (x - y) and

multiply numerator/ denominator of [tex]\frac{1}{x=y}[/tex] by x

= [tex]\frac{x-y}{x(x-y)}[/tex] + [tex]\frac{x}{x(x-y)}[/tex]

Add the numerators leaving the denominator

= [tex]\frac{2x-y}{x(x-y)}[/tex]

Answer:

36x² + 24x + 4

Step-by-step explanation:

Given

(6x + 2)² = (6x + 2)(6x + 2)

Each term in the second factor is multiplied by each term in the first factor, that is

6x(6x + 2) + 2(6x + 2) ← distribute both parenthesis

= 36x² + 12x + 12x + 4 ← collect like terms

= 36x² + 24x + 4

Hii!

__________________________________________________________

Answer:

Step-by-step explanation:

Note that both terms, 4x and -16, have something in common.

In math, this "something" is known as the greatest common factor (g.c.f.).

The g.c.f. of 4x and -16 is 4, so that's what we factor out.

First, we divide both 4x and -16 by 4.

We obtain.

x-4

Put parentheses around x-4

(x-4)

Now put 4 outside the parentheses

4(x-4)

--

Hope that this helped! Best wishes,

--

The factored form of the expression 4x - 16 is 4(x - 4).

To factor the expression 4x - 16, we can look for the greatest common factor (GCF) of the terms. In this case, both terms have a common factor of 4.

We can factor out the GCF of 4 from each term:

4x - 16 = 4(x - 4)

Therefore, the factored form of the expression 4x - 16 is 4(x - 4).

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Answer:

b

becasue to find his current weight you would use what you know and the amount of lbs he added (represented as x)

96 + x

Step-by-step explanation:

Answer:

x=7

Step-by-step explanation:

The given equation is:

[tex]\frac{x}{3}+\frac{x}{6} = \frac{7}{2}[/tex]

Multiplying both sides by LCM of 3 and 6

So,

[tex]\frac{x}{3}*6+\frac{x}{6}*6 = \frac{7}{2}*6\\2x+x=7*3\\3x=21\\\frac{3x}{3} =\frac{2}{3}\\ x=7[/tex]

Hence, the solution of the equation is x=7 ..

Answer: x = 7

Step-by-step explanation:

(x/3)+(x/6)=7/2

add variables

(2x+x)/6=7/2

combine like terms

3x/6=7/2

simplify

x/2=7/2

multiply denominators by 2

x=7

Answer:

Step-by-step explanation:

Y/1 = 2x + 5

Y = 2x + 5

Y = 2x + 5

When x = 1

Y = 2 ×1 +5

Y = 2 + 5

Y = 7

When x =0

Y = 2 × 0 + 5

Y = 5

When x = -2

X = 2 × -2 + 5

X = 1

( Make a table in the side of the page)

X | 1 0 -2

_ _______

Y 7 5 1

The graph for the coordinate points (0, 5), (1, 5.5), (2, 6), (3, 6.5) and (4, 7) is plotted below.

The general equation of a straight line is y=mx+c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis.

The given equation of a line is y=1/2x+5.

Substitute x=0, 1, 2, 3, 4, 5,....in a equation y=1/2x+5, we get

When x=0, y=5

When x=1, y=5.5

When x=2, y=6

When x=3, y=6.5

When x=4, y=7

So, the coordinate points are (0, 5), (1, 5.5), (2, 6), (3, 6.5) and (4, 7)

Therefore, the graph for the coordinate points (0, 5), (1, 5.5), (2, 6), (3, 6.5) and (4, 7) is plotted below.

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Answer:

D. I, II, III

Step-by-step explanation:

Let us look at the definition of set:

A set is a collection of well-defined and distinct objects

I: The collection of all the days in a week.

The set will consist of seven elements.

II: The collection of all teachers in a school.

Also a set.

III: The collection of all integers more than -5.

This is a set.

Therefore, Option D is correct ..

Answer: 245 [tex]in^{2}[/tex]

Step-by-step explanation:

You can find the Surface Area of a figure by adding up the areas of each shape.

First you have to find the area of the base.

7×7 = 49

Then you can find the area of the 4 triangles that complete the pyramid.

Formula for area of a triangle: [tex]\frac{1}{2} bh[/tex] (one half of base times height)

[tex]\frac{1}{2} (14*7) = x\\\frac{1}{2} 98 = x\\x = 49[/tex]

Since all the triangles are the same, you only have to calculate that once.

Now you just add everything together, and that's your surface area.

[tex]49+49+49+49+49= 245[/tex]

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Answer:  245

Step-by-step explanation:

first you have to 7 for the square which = 14

then after that you do 1/2 b x h = 1/2  7 x 14= 3.5 x 14= 49 but then you have 4 triangles so 49 x 4=196.     Then  49 + 196= 245  

For this case we have that a percentage equivalent to[tex]\frac {1} {8}[/tex]is given by:

[tex]x = \frac {1} {8} * 100 =[/tex] 12.5%

Then, according to the steps, it is observed that Harriet made an incorrect division, deboa multiply. So, the second step is the wrong one.

Answer:

Option B