what is the value of t(-4) when f(x)= -x-2

Answer:

Observe the attached image

Step-by-step explanation:

We have the graph of a line that passes through the points (0,5) and (2, 1).

The equation of the line that passes through these points is found in the following way:

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

Where

m = slope

[tex]m = \frac {y_2-y_1}{x_2-x_1}\\\\m = \frac{1-5}{2-0}\\\\m = -2\\\\b = y_2-mx_2\\\\b = 1 -(-2)(2)\\\\b = 5[/tex]

So

[tex]y = -2x + 5[/tex]

We must apply to this function the transformation[tex]f (x-4)[/tex].

We know that a transformation of the form

[tex]y = f (x + h)[/tex] shifts the graph of the function f(x) h units to the right if [tex]h <0[/tex], or shifts the function f(x) h units towards the left if [tex]h> 0[/tex].

In this case [tex]h = -4 <0[/tex] then the transformation [tex]f(x-4)[/tex] displaces the graph 4 units to the right.

Therefore if f(x) passes through the points (0,5) and (2,1) then [tex]f (x-4)[/tex] passes through the points (4, 5) (6, 1)

And its equation is:

[tex]y = -2(x-4) +5\\\\y = -2x +13[/tex]

Observe the attached image

For this case we must find the inverse of the following function:

[tex]f (x) = x ^ 2 + 7[/tex]

For this we follow the steps below:

Replace f(x) with y:

[tex]y = x ^ 2 + 7[/tex]

We exchange the variables:

[tex]x = y ^ 2 + 7[/tex]

We solve the equation for "y", that is, we clear "y":

[tex]y^ 2 + 7 = x[/tex]

We subtract 7 on both sides of the equation:

[tex]y ^ 2 = x-7[/tex]

We apply square root on both sides of the equation to eliminate the exponent:

[tex]y = \pm\sqrt {x-7}[/tex]

We change y by[tex]f ^ {- 1} (x):[/tex]

[tex]f ^ {- 1} (x) =\pm\sqrt {x-7}[/tex]

Answer;

Option A

Answer:

To sum consecutive numbers we use the formula:

n * (n+1) / 2

1 through 55 = (55 * 56) / 2 = 1,540

1 through 9 = (9 * 10) / 2 = 45

10 through 55 = 1,540 -45 = 1,495

********************************************************

EDITED

Gee, it seems I added ALL numbers from 10 through 55

ALL ODD numbers from 10 through 55 sum to

759

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Let x be the number of packages of paper towels.

Each package of paper towels costs $2.79.

Then x packages of paper towels cost $2.79x.

Hence, a function f(x) is

[tex]f(x)=2.79x[/tex]

Practically, you can buy 0 packages, 1 package, 2 packages and so on, only whole numbers of packages, so practical domain is all whole numbers.

Answer:

If x is greater than 1 it is growth, if it less than it is decay

Step-by-step explanation:

Answer: option c

Step-by-step explanation:

You can use these identities:

[tex]sin\alpha=\frac{opposite}{hypotenuse}\\\\tan\alpha=\frac{opposite}{adjacent}[/tex]

Then, using the angle that measures 30 degrees, you know that:

[tex]\alpha=30\°\\opposite=8\\adjacent=b[/tex]

Substituting:

[tex]tan(30\°)=\frac{8}{b}[/tex]

Now you must solve for b:

[tex]b=\frac{8}{tan(30\°)}\\\\b=8\sqrt{3}[/tex]

Using the angle that measures 30 degrees, you know that:

[tex]\alpha=30\°\\opposite=8\\hypotenuse=c[/tex]

Substituting:

[tex]sin(30\°)=\frac{8}{c}[/tex]

Now you must solve for c:

[tex]c=\frac{8}{sin(30\°)}\\\\c=16[/tex]

ANSWER

The correct answer is C

EXPLANATION

The side adjacent to the 60° angle is 8 units.

The hypotenuse is c.

Using the cosine ratio, we have

[tex] \cos(60 \degree) = \frac{adjacent}{hypotenuse} [/tex]

[tex]\cos(60 \degree) = \frac{8}{c} [/tex]

[tex] \frac{1}{2}= \frac{8}{c} [/tex]

Cross multiply

[tex]c = 8 \times 2 = 16[/tex]

Also

[tex]\cos(30 \degree) = \frac{b}{c} [/tex]

[tex]\cos(30 \degree) = \frac{b}{16} [/tex]

[tex] \frac{ \sqrt{3} }{2} = \frac{b}{16} [/tex]

Multiply both sides by 16

[tex]b = 16 \times \frac{ \sqrt{3} }{2} [/tex]

[tex]b = 8 \sqrt{3} [/tex]

The correct answer is C

Answer:

8/45

Step-by-step explanation:

Write 4 5/8 as an improper fraction:  45/8.

Then invert this result, obtaining:

 .  This is the "reciprocal" of 4 5/8.

Answer:

37/8

Step-by-step explanation:

attachement ---

Answer:

r = 1.3 meters  

Step-by-step explanation:

A python curls up to touch the tip of its own tail with its nose, forming the shape of a circle.

A python curls up to touch the tip of its own tail with its nose, forming the shape of a circle.  

The python is 2.6 pi (2.6π) meters long.

What is the radius r of the circle that the python forms?

Now we have: C = π d, or (with d = 2 r):  C = 2 π r.

Changing that around: r = C / 2 π

So with our value of C = 2.6π meters, that gives us:

r = 2.6π/2π = 2.6/2, so r = 1.3 meters  

Answer:

The answer is 1.3

Step-by-step explanation:

Because it is half of the diameter which was 2.6

If a local city collects 8% sales tax if the total purchase was $216 then $17.28 is collected for sales tax.

A relative value indicating hundredth parts of any quantity is known as Percentage.

Given that a  local city collects 8% sales tax

The total purchase was $216.

We need to find the amount collected for sales tax.

To find this we have to find 8% of 216.

Convert 8% to the decimal value.

8/100=0.08

Now multiply 0.08 with 216

0.08×216

$17.28

Hence, if a local city collects 8% sales tax if the total purchase was $216 then $17.28 is collected for sales tax.

To learn more on Percentage click:

https://brainly.com/question/28269290

#SPJ3

The amount collected for sales tax is $16.

Step 1: Understand the Problem

The total purchase amount ($216) includes the sales tax. We need to find how much of this amount is the sales tax itself.

Step 2: Convert the Percentage to a Decimal

Convert the sales tax rate from a percentage to a decimal.

[tex]\[ \text{Sales Tax Rate} = \frac{8}{100} = 0.08 \][/tex]

Step 3: Set Up the Equation

Let ( P ) be the pre-tax purchase amount and ( T ) be the total amount including tax. The relationship can be written as:

[tex]\[ T = P + \text{Sales Tax} \][/tex]

Since the sales tax is 8% of the pre-tax amount,

[tex]\[ \text{Sales Tax} = 0.08 \times P \][/tex]

Thus, the total amount is:

[tex]\[ T = P + 0.08P = 1.08P \][/tex]

Step 4: Solve for the Pre-Tax Amount

We know the total amount ( T ) is $216.

[tex]\[ 216 = 1.08P \][/tex]

To find ( P ):

[tex]\[ P = \frac{216}{1.08} \][/tex]

[tex]\[ P \approx 200 \][/tex]

Step 5: Calculate the Sales Tax

Now, find the sales tax:

[tex]\[ \text{Sales Tax} = 0.08 \times P \][/tex]

[tex]\[ \text{Sales Tax} = 0.08 \times 200 \][/tex]

[tex]\[ \text{Sales Tax} = 16 \][/tex]

Therefore the amount collected for sales tax is $16.

The answer is C: the average reading speed of the science fiction novel.

If x is her reading speed for the historical fiction novel, and her reading speed for the sci-fi novel is just two pages more than that of the historical fiction novel, then the equation to find out how fast she reads the science fiction novel would be x + 2, as you’re adding 2 to the reading speed of the historical fiction book (x)

Answer:

The answer to this question is correct but on PLATO the answer choice is actually A.

Step-by-step explanation:

PLATO

Answer:

298

Step-by-step explanation:

Given

(8 - (- 9))² + (-3 - (- 6))² ← evaluate the parenthesis before squaring

= (8 + 9)² + (- 3 + 6)²

= 17² + 3²

= 289 + 9

= 298

Answer: (8+9)^2 + (-3 + 6)^2

= 17^2 + 3^2

= 289 + 9

= 298. ANS.

Answer:I THINK 89.3 in.

You can solve this problem with the Pythagorean Theorem. The base is a square. So half way across the middle will the right under the tip of the pyramid.

ANSWER

A) For all x > 0 the graph will be higher.

EXPLANATION

Jack's graph has equation

y=2x

This graph passes through the origin and has slope 2.

Nina's graph is y=5x.

This graph also passes through the origin and has slope 5.

Since 5 is greater than 2, for all x>0, Nina's graph will be higher.

Answer: A

Step-by-step explanation: Changing the 2 to a 5 makes an exponential growth function increase at a faster rate. Therefore, for all x > 0 the graph will be higher. At x = 0 the graphs will have the same value and for all x < 0, Nina's graph will be lower.

Answer:

[tex]\large\boxed{\left(\dfrac{2b}{3}\right)^4=\dfrac{16b^4}{81}}[/tex]

Step-by-step explanation:

[tex]\left(\dfrac{2b}{3}\right)^4\qquad\text{use}\ \left(\dfrac{a}{b}\right)^n=\dfrac{a^n}{b^n}\ \text{and}\ (ab)^n=a^nb^n\\\\=\dfrac{2^4b^4}{3^4}=\dfrac{16b^4}{81}[/tex]

Answer:

16b^4/81

Step-by-step explanation:

ANSWER

[tex]x = \frac{5}{4} - \frac{ \sqrt{ 17} }{4} [/tex]

or

[tex]x = \frac{5}{4} + \frac{ \sqrt{ 17} }{4} [/tex]

EXPLANATION

The given equation is:

[tex]2 {x}^{2} - 5x + 1= 0[/tex]

Comparing this to

[tex]a {x}^{2} + bx + c = 0[/tex]

we have a=2, b=-5, c=1

The quadratic formula is given by

[tex]x = \frac{ - b \pm \sqrt{ {b}^{2} - 4ac} }{2a} [/tex]

We substitute the values to get,

[tex]x = \frac{ - - 5 \pm \sqrt{ {( - 5)}^{2} - 4(1)(2)} }{2(2)} [/tex]

[tex]x = \frac{ 5 \pm \sqrt{ 17} }{4} [/tex]

[tex]x = \frac{5}{4} - \frac{ \sqrt{ 17} }{4} [/tex]

or

[tex]x = \frac{5}{4} + \frac{ \sqrt{ 17} }{4} [/tex]

Answer:

A

Step-by-step explanation:

Substitute the values of n into the recursive formula and check result against values in table

A

[tex]a_{2}[/tex] = 3 + 5 = 8 ← correct

[tex]a_{3}[/tex] = 8 + 5 = 13 ← correct

[tex]a_{4}[/tex] = 13 + 5 = 18 ← correct

[tex]a_{5}[/tex] = 18 + 5 = 23 ← correct

Answer:

the answer is A

Step-by-step explanation:

Answer:

-19000

Step-by-step explanation:

1000-20000=-19000

Answer:

C -19000

Step-by-step explanation:

          1,000

     - 20,000

----------------------=

        -19000

Answer:

y=x-8 and y=-x+4

Step-by-step explanation:

The slopes of the lines can be anything, as long as they are the opposite reciprocals of each other. Then you can plug in the point for x and y to solve for b in both lines (for y=mx+b where m is the slope)

Answer:

[tex]\large\boxed{y=\dfrac{8}{37}}[/tex]

Step-by-step explanation:

[tex]Domain:\ 2+2y\neq0\to y\neq-1\\\\\dfrac{-30+15y}{2+2y}=-11\\\\\dfrac{-30+15y}{2+2y}=\dfrac{-11}{1}\qquad\text{cross multiply}\\\\(-30+15y)(1)=(-11)(2+2y)\qquad\text{use the distributive property}\\\\-30+15y=(-11)(2)+(-11)(2y)\\\\-30+15y=-22-22y\qquad\text{add 30 to both sides}\\\\15y=8-22y\qquad\text{add}\ 22y\ \text{to both sides}\\\\37y=8\qquad\text{divide both sides by 37}\\\\y=\dfrac{8}{37}[/tex]

How many classes could Anna take so that the total cost for the month would be the same?

5 classes

What is the total monthly cost when it is the same for both gyms?

$37.50

Step-by-step explanation:

The number of classes Anna could take so the total cost for the month would be the same is 5.

The total monthly cost when it is the same for both gyms would be $37.50.

When the total cost is the same, both equations for the gym would be equal to each other.

7.5x = 5.5x + 10

In order to determine the value of x, take the following steps:

Combine similar terms

7.5x - 5.5x = 10

Add similar terms together

2x = 10

Divide both sides by 2

x = 5

Total cost = 7.5 x 5 = $37.50

To learn more about total cost, please check: https://brainly.com/question/25879561

#SPJ2

Answer:

Option C is correct

Step-by-step explanation:

The relationship between Roberts age and Julia’s age is given by:

r = j+3            ....[1]

where,

r is the Robert's age and j represents the Julia's age in years

We have to find the table of values represents the relationship between Roberts age and Julia’s age

if r = 9 years

then;

[tex]9 = j+3[/tex]

Subtract 3 from both sides we have;

6 = j

or

j = 3 years

Similarly:

if r = 15 years

then;

[tex]15= j+3[/tex]

Subtract 3 from both sides we have;

12 = j

or

j = 12 years

If r = 21 years

then;

[tex]21= j+3[/tex]

Subtract 3 from both sides we have;

18 = j

or

j = 18 years

Therefore, the table of values represents the relationship between Roberts age and Julia’s age is, Table C

option c is the right answer

Answer:

Step-by-step explanation:

6,18,8,4,18,20,10,10,21,6,17,18

Arrange the data in ascending order

4,6,6,8,10,10,17,18,18,18,20,21

Part A

Mean = 156/12 = 13 is correct

Median = 15 is incorrect because the data is not arranged. Median when there are even numbers will be: 10+17/2 = 13.5

Mode = 10 is incorrect, because mode is most repeating value and in the data set it is 18 so, Mode = 18

Part B

10,12 and 52 should be added in data set in ascending order

4,6,6,8,10,10,10,12,17,18,18,18,20,21,52

Mean = 230/15 = 15

Median = Middle term as odd numbers = 8th term = 12

Mode = 10 and 18

Part C

Both median and mean are used to measure central tendency.

The best measure of central tendency is considered median because the mean is affected by the presence of outliers while median is not affected by outliers.

Answer:

He is correct.

Step-by-step explanation:

I got 100% on my paper

Final answer:

The next time a museum tour and video both start at the same time after 10:00 a.m. is at 11:00 a.m., as that is when their intervals (every 20 minutes for tours and every 15 minutes for videos) have their Least Common Multiple.

Explanation:

The question is about finding the next time a museum tour and a video both start at the same time after 10:00 a.m. The tours start every 20 minutes and the videos start every 15 minutes. To find the next common start time, we need to calculate the Least Common Multiple (LCM) of 20 and 15 which is the smallest number that both 20 and 15 can divide into without leaving a remainder.

Multiples of 20 are 20, 40, 60, 80, 100, ...

Multiples of 15 are 15, 30, 45, 60, 75, ...

The first common multiple of the two intervals is 60 minutes. Therefore, since both the tour and the video start at the same time (10:00 a.m.), the next time they will both start together will be 60 minutes later, which is at 11:00 a.m.

Answer:

(6,-5)

Step-by-step explanation:

As the point is 4 units to the left of X=2, the reflection must be 4 units to the right of X=2

Peter will be 75 years old in 47 years.

Answer:

In 47 years Peter will be 75 years old

Step-by-step explanation:

If Peter will be 54 years old in 26 years then subtract 26 from 54

54-26=28

This means that Peter is 28 right now, if you want to double check that work then add 26 to 28 implying that in 26 years Peter with be 54 years old

28+26=54

This shows that your calculations are correct! Now you have to figure out how many years from now will Peter be when he turns 75 years old, so you subtract his current age which is 28 from 75

75-28=47

Now to double check this add 47 to his current age which is 28

28+47= 75

This shows that your calculations are correct and it will take 47 years for Peter to be 75 years old!

Answer:

Option D.

[tex]A =96\pi\ cm^2[/tex]

Step-by-step explanation:

The area of the circular bases is:

[tex]A_c = 2\pi(a) ^ 2[/tex]

Where

[tex]a=4\ cm[/tex] is the radius of the circle

Then

[tex]A = 2\pi(4) ^ 2[/tex]

[tex]A = 32\pi\ cm^2[/tex]

The area of the rectangle is:

[tex]A_r=b * 2\pi r[/tex]

Where

[tex]b=8\ cm[/tex]

b is the width of the rectangle and [tex]2\pi r[/tex] is the length

Then the area of the rectangle is:

[tex]A_r=8 * 2\pi (4)[/tex]

[tex]A_r=64\pi\ cm^2[/tex]

Finally the total area is:

[tex]A = A_c + A_r\\\\A = 32\pi\ cm^2 + 64\pi\ cm^2\\\\[/tex]

[tex]A =96\pi\ cm^2[/tex]

Answer:

The correct answer is option B.  96π

Step-by-step explanation:

Points to remember

Surface area of cylinder = 2πr(r + h)

Where r is the radius of cylinder and h is the height of cylinder.

From the figure we get r = 4 cm and h = 8 cm

To find the surface area of cylinder

Surface area = 2πr(r + h)

 = 2π * 4(4 + 8)

 = 96π

The correct answer is option B.  96π

y = 7x +3 slope is rise over run with would be 7/1 and y intercept is 3

The equation in the slope-intercept form is y=7x+3.

Given:

Find:

Solution:

We will use y = mx+b where m = slope and b = y-intercept.

y = mx+b

Now, putting (1,10) in the place of x and y and slope as 7, we get;

10 = 7*1 + b

b = 10-7

b=3

So, the y-intercept is 3.

Now, putting the y-intercept in the slope-intercept equation, we get;

y = 7x+3

Hence, the equation in slope-intercept form is y=7x+3.

To learn more about slope-intercept, refer to:

https://brainly.com/question/1884491

#SPJ2

ANSWER

C)

[tex] {x}^{2} + {y}^{2} = 10[/tex]

EXPLANATION

The center of the circle is (0,0).

The circle passes through (-1,-3).

The radius can be obtained using the distance formula:

[tex]r = \sqrt{(0 - 1)^{2} + {(0 - - 3)}^{2} } = \sqrt{10} [/tex]

The equation is given as:

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

Where (h,k) is the center and r is the radius.

This implies that;

[tex]( {x - 0)}^{2} + ( {y - 0)}^{2}= {( \sqrt{10)} }^{2} [/tex]

[tex] {x}^{2} + {y}^{2} = 10[/tex]

Answer:

12.A.) Heptagon

Step-by-step explanation:

I will say 1 block is 1 something okay cause I don’t have a key mini has an area of 2 (2x2=4/2=2) And the giant has an area of 32 (8x8=64/2=32) I don’t know if the small one became big or the big one became small so if the small to big is 16 big to small is 0.0625 or the numbers the other way around

Answer:

Area of left triangle = 2 * 2 / 2 = 2

Area of triangle on the right = 8 * 8 / 2 =32

32 / 2 = 16

Therefore the triangle on the right has 16 times the area than the triangle on the left.

Step-by-step explanation: