Beth said that g(x)=f(x)=x²-12 is a horizontal translation of f(x)=x² . Find and fix the errors and write the correct equation for a horizontal translation.

For part two using what we already know can you figure out the length of the segment?

answer D) 24

Answer:

3rd last row, 4th from the left (132) diagonally left upwards. 132, 11, 12

Step-by-step explanation:

132 ÷ 11 =12

Answer:

f(6) = 2

Step-by-step explanation:

Since y is a function of x, that is y = f(x), f(6) implies that we shall be evaluating the value of y when the value of x is 6.

To do this we shall draw a vertical line, x = 6 and check where this line intersects with the graph of the function f(x)

The vertical line x = 6 intersects with the graph of the function f(x) on the horizontal line y = 2. The function f(x) assumes the value 2 for values of x between 4 and 8. Therefore,  f(6) = 2

Answer: Last option.

Step-by-step explanation:

We know that input values of a function are the values of the variable "x" and output values of a function are the values of the variable "y".

By definition, in functions each input value have one and only one output value.

Then, find [tex]f(6)[/tex] you can see that the input value is [tex]x=6[/tex] and you need to find the corresponding ouput value (or "y")

You can observe in the figure attached that the value of "y" for  [tex]x=6[/tex] is  [tex]y=w[/tex], obtaining the point (6,2)

Therefore:

[tex]f(6)=2[/tex]

This matches with the last option.

Answer:

55

Step-by-step explanation:

20×22=440 8 ' 55

Answer:  Third option

[tex]y = |x + 1|[/tex]

Step-by-step explanation:

The main function

[tex]f (x) = | x |[/tex]

has its vertex in the point (0, 0)

The function shown in the graph has its vertex in the point (-1, 0)

The transformation made to f (x) that moves its vertex one unit to the left is:

[tex]y = f (x + 1)[/tex]

After this transformation the new function is:

[tex]f (x) = | x + 1 |[/tex]   Note that this function corresponds to the function plotted in the image.

Therefore the answer is the third option

Answer:

r = 2.5

Step-by-step explanation:

The equation given says y = r * x

So, the y value would be an unknown times the given x value.

To solve for r, all you have to do is divide.

25 ÷ 10 = 2.5

12.5 ÷ 5 = 2.5

10 ÷ 4 = 2.5

2.5 is the constant of proportionality.

Answer: THIRD OPTION

Step-by-step explanation:

We need to remember that a right angle is an angle that measures 90 degrees.

By definition, when two or more lines intersect (or cross one another ) at a 90-degree angle, then these lines are called "Perpendicular".

Therefore, in this case, we know that these two lines intersects at a right angle (angle of 90 degrees), then, we can conclude that these lines are Perpendicular.

This matches with the third option.

Answer:

Perpendicular lines

Step-by-step explanation:

Two or more lines are called intersecting lines.That point would be on each of these lines.

Answer:

f(x) = (x − 3)² − 11

Step-by-step explanation:

To convert to vertex form, complete the square.

f(x) = x² − 6x − 2

f(x) = x² − 6x + 9 − 9 − 2

f(x) = (x − 3)² − 11

We need to complete the square: if we add and subtract 11 from the expression, we have

[tex]f(x)=x^2-6x-2=x^2-6x-2+11-11=x^2-6x+9-11=(x-3)^2+11[/tex]

Answer:

(1,9),(3,7),(5,5) (7,2)

Answer with explanation:

The sum of two distinct variables is 10.

  x + y=10

It is linear equation in two variables.

To plot this graph in two dimensional plane find two distinct points satisfying the equation.

x=0, gives , y=10 or , y=0 gives , x=10.

x=1, gives ,y=10 -1,→y=9

So,two ordered pairs lying in the coordinate system are , (0, 10) and (1, 9) or (10,0) and (1,9), you will get the equation of line.

Otherwise , you can Draw the graph of this function by writing the equation in Slope Intercept form which is as:

  [tex]\frac{x}{10}+\frac{y}{10}=1[/tex]

By writing the slope intercept form of line shows that , the line passes through , (10,0) and (0,10) means cutting x axis and y axis at these two points.

Answer:

A because they are opposites.

Step-by-step explanation:

They equal the same they are just swapped the 2 set of numbers are the same but the first set of numbers are different when you add them they become the same number in the end :) hope this helps

B. Addition Property of Equality justified the statement,

"If WX=YZ, then WX+RS=YZ+RS".

Facts regarding any two or more quantities connected by the equal sign are known as properties of equality.

There are four types of properties of equality.

Addition property, when two equal quantities are increased by a common value, the equality is preserved.

Transitive property of equality, entities that are equivalent to one another are also equivalent to one another.

Subtraction property, equality is maintained when a common term is subtracted from two equal terms.

Multiplying by a common term do not alter the equality, according to the multiplication property of equality.

Given, An equation WX = YZ, Now, In this expression WX + RS = YZ + RS

We have added RS to both side of the equation to maintain the equality sign.

learn more about properties of equality here :

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It's actually very simple. Semicircle is a half of a circle. So the area and perimeter is also divided by 2. Also the radius is a half of diameter so 130.

[tex]Area=\frac{\pi130^2}{2}\approx\frac{53092.92}{2}=\boxed{26546.46ft^2}[/tex]

Hope this helps.

r3t40

Answer:

1 hour

8 min

49 sec

Step-by-step explanation:

we know that

1 m=3.281 ft

1 mi=5,280 ft

Convert 26 mi to ft

26 mi=26*5,280=137,280 ft

Convert 137,280 ft to m

137,280 ft=137,280/3.281=41,840.90 m

using proportion

9.87/100=x/41,840.90

x=41,840.90*(9.87)/100

x=4,129.70 sec

Remember that

1 hour=3,600 sec

1 hour=60 min

1 min=60 sec

4,129.70 sec=4,129.70/3,600= 1.147 h

0.147*60=8.82 min

0.82*60=49 sec

therefore

1 hour

8 min

49 sec

John could maintain his 100-m dash pace for an entire 26-mi marathon, his time would be 1 hour, 8 minutes, and approximately 50 seconds.

First, we need to convert John's 100-meter dash time into a pace that can be extrapolated over the marathon distance. Given that John ran a 100-m dash in 9.87 seconds, we need to find out how many meters he runs per second. This would be 100 m / 9.87 s = 10.13 meters per second.

Next, we convert the marathon distance from miles to meters. As there are 5280 feet in a mile and 3.281 feet in a meter, there are 5280 / 3.281 = 1609.34 meters in a mile. The marathon distance is therefore 26 miles * 1609.34 meters/mile = 41842.84 meters.

Using John's pace, we can calculate the time it would take to run the marathon: 41842.84 meters / (10.13 meters/second) = 4129.64 seconds.

Finally, we convert the total seconds to hours, minutes, and seconds. There are 3600 seconds in an hour and 60 seconds in a minute:

Therefore, if John could maintain his 100-m dash pace for an entire 26-mi marathon, his time would be 1 hour, 8 minutes, and approximately 50 seconds.

Answer:

Answer: yes.

Step-by-step explanation:

x: (x1 + x2)/2 = (-3 + 1)/2 = -2/2 = - 1 So far so good.

y: (y1 + y2)/2 = (1 - 4 )/2 = (-3/2) = -1.5

The midpoint is (-1 , - 1.5)

True

Answer:

In mathematics, the notion of permutation relates to the act of arranging all the members of a set into some sequence or order, or if the set is already ordered, rearranging (reordering) its elements, a process called permuting. These differ from combinations, which are selections of some members of a set where order is disregarded.

Step-by-step explanation:

Reason 1: Given.

Reason 2: Vertical angles

Reason 3: Angle, Side, Angle(ASA)

Answer:

.72 or .73 which ever one is on your sheet

Step-by-step explanation:

Answer:

0.72 or 0.73

Step-by-step explanation:

8/11 expressed as a decimal is 0.72 or 0.73

Answer: A) given

B) definition of congruent

C) definition of bisect

Step-by-step explanation:

Answer:

[tex]\large\boxed{D.\ 8x^2-3x+7}[/tex]

Step-by-step explanation:

[tex](2x^2-7x+5)-(-6x^2-4x-2)\\\\=2x^2-7x+5-(-6x^2)-(-4x)-(-2)\\\\=2x^2-7x+5+6x^2+4x+2\qquad\text{combine like terms}\\\\=(2x^2+6x^2)+(-7x+4x)+(5+2)\\\\=8x^2-3x+7[/tex]

Answer:

8x^2-3x+7

Step-by-step explanation:

By simplifying the expression.

Answer:

82

Step-by-step explanation:

49 - 3 + 72/2

= 46 + 36

= 82

For this case we must find the value of the following expression:

[tex]7 ^ 2[/tex]-3 + 9 * 8÷2 =

According to the PEMDAS algebraic order of operations:

P: Perform any calculation within parentheses

E: Simplify any exponential expressions.

MD: Do all the multiplications and divisions, from left to right, as they appear.

AS: Do all the addition and subtraction, from left to right, as they appear.

So:

49-3 + 9 * 8÷2 =

49-3 + 72÷2 =

49-3 + 36 =

46 + 36 =

82

ANswer:

82

Answer:

- 273

Step-by-step explanation:

The n th term of an arithmetic sequence is

• [tex]a_{n}[/tex] = a₁ + (n - 1)d ← substitute in values

[tex]a_{100}[/tex] = 222 + (99 × - 5 ) = 222 - 495 = - 273

ANSWER

[tex]( - \infty , + \infty )[/tex]

EXPLANATION

The given function is

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

This is a polynomial function.

The domain refers to all real values for which the function is defined.

Polynomial functions are defined everywhere.

The domain is all real numbers.

Or

[tex]( - \infty , + \infty )[/tex]

Answer:

Step-by-step explanation:

ax^2+bx+c

-b +- sqaure root of b^2 -4ac/2a

-2 +- square root (2)^2-4(2)(-1)/2(2)

-2 +- square root 4+8 /4

-2 +- 2 square root 3 /4

reduce

-1 +- square root 3/2

Answer:

[tex]\large\boxed{x=\dfrac{-1-\sqrt3}{2}\ or\ x=\dfrac{-1+\sqrt3}{2}}[/tex]

Step-by-step explanation:

The quadratic formula of a quadratic equation:

[tex]ax^2+bx+c=0[/tex]

Discriminant of a Quadratic is [tex]\Delta=b^2-4ac[/tex]

If Δ < 0, then an equation has no real solution (has two complex solutions)

If Δ = 0, then an equation has one real solution [tex]x=\dfrac{-b}{2a}[/tex]

If Δ >0, then an equation has two real solutions [tex]x=\dfrac{-b\pm\sqrt{\Delta}}{2a}[/tex]

==========================================

We have the equation:

[tex]2x^2+2x-1=0\\\\a=2,\ b=2,\ c=-1[/tex]

Substitute:

[tex]\Delta=2^2-4(2)(-1)=4+8=12>0\\\\\sqrt\Delta=\sqrt{12}=\sqrt{4\cdot3}=\sqrt4\cdot\sqrt3=2\sqrt3[/tex]

[tex]x=\dfrac{-2\pm2\sqrt3}{(2)(2)}=\dfrac{-2\pm2\sqrt3}{4}[/tex]    simplify by 2

[tex]x=\dfrac{-1\pm\sqrt3}{2}[/tex]

[tex]

4n-3=-2n+9n \\

6n-3=9n \\

3n=-3 \\

n=\boxed{-1}

[/tex]

2 is not a solution but -1.

ANSWER

No, n=2 is not a solution.

EXPLANATION

The given equation is

[tex]4n - 3 = - 2n + 9n[/tex]

If n=2 is a solution, then it must satisfy this equation.

We substitite n=2 into the equation to get:

[tex]4(2)- 3 = - 2(2)+ 9(2)[/tex]

[tex]8- 3 = - 4+ 18[/tex]

[tex]5 = 14[/tex]

This statement is false

Therefore n=2 us not a solution.

[tex]\bf \textit{parabola vertex form with focus point distance} \\\\ \begin{array}{llll} 4p(x- h)=(y- k)^2 \\\\ 4p(y- k)=(x- h)^2 \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ y+1=-14(x-2)^2\implies -\cfrac{1}{14}[y-(\stackrel{k}{-1})]=[x-\stackrel{h}{2}]^2~\hfill \stackrel{center}{(-2~,~-1)}[/tex]

Answer:

Step-by-step explanation:

Say that your equation is 2x+4=8, x=2

you would plug in the 2 where your x is so, 2(2) +4=8

then you'd solve regularly.

Hope my answer has helped you!

Answer:

Negatively skewed.

Step-by-step explanation:

In a negatively skewed distribution, the mode is greater then the median, and the median is greater then the mean. Overall, the majority of the data is to the right, which means that the distribution of data is skewed to the left, or negatively skewed.

Answer: Hence, Option 'C' is correct.

Step-by-step explanation:

As we know that if one tail is longer than the other, the distribution is said to be skewed.

And there are two types of skewed  distribution :

1) Negatively skewed

2) Positively skewed

It depends on the direction of the long tail.

If the long tail is to the right , then it is said to be positively skewed distribution.

If the long tail is to the left , then it is said to be negatively skewed distribution.

According to question, the distribution  here is a positively skewed distribution.

Hence, Option 'C' is correct.

Answer:

56,994

Step-by-step explanation: multiply the population by 0.02, round it to the nearest whole number, and then multiply that number by 3 and add it onto 53,768

The population of Oak Forest in three years will be approximately 57,091.

To find the population of Oak Forest in three years, we can use the formula for exponential growth. The formula is: P = P0 * (1 + r)t, where P is the final population, P0 is the initial population, r is the growth rate, and t is the number of years. In this case, P0 is 53,768, r is 0.02 (2% as a decimal), and t is 3. Plugging these values into the formula, we get:

P = 53,768 * (1 + 0.02)3

Simplifying the expression inside the parentheses:

P = 53,768 * (1.02)3

Calculating (1.02)3:

P = 53,768 * 1.0604

Calculating the final population:

P ≈ 57,091

Therefore, the population of Oak Forest in three years will be approximately 57,091.

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Answer:

y = 4x - 6.

Step-by-step explanation:

Slope-intercept form is y = mx + c where m = the slope and c = the y-intercept.

4x = y +6

Subtract 6  from both sides:

4x - 6 = y

we would write it as y = 4x - 6.

Answer:

Slope intercept form

y = 4x - 6

Step-by-step explanation:

Slope intercept form y = mx + b

In this case 4x = y +6

Re-write

y + 6 = 4x

Subtract 6 from both sides

y = 4x - 6  <-------Slope intercept form

Pages Minutes

15 1

45 3

75 5

300 20

600 40

15 x 2= 39

45x 2= 90

75x2=150

30x20=60

600 x 2 = 1,200

Answer:

[tex]\large\boxed{(x-4)^2+(y+3)^2=25}[/tex]

Step-by-step explanation:

The equation of a circle:

[tex](x-h)^2+(y-k)^2=r^2[/tex]

(h, k) - center

r - radius

We have the center (4, -3) and the point on the circle (9, -3).

The length of radius is equal to the distance between a center and an any point on a circle.

The formula of a distance between two points:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Susbtitute:

[tex]r=\sqrt{(9-4)^2+(-3-(-3))^2}=\sqrt{5^2+0^2}=\sqrt{5^2}=5[/tex]

The center (4, -3) → h = 4, k = -3.

Finally we have:

[tex](x-4)^2+(y-(-3))^2=5^2\\\\(x-4)^2+(y+3)^2=25[/tex]