The image of a figure is shown. What are the coordinates of X in the pre-image of the figure if the rule that created the image was T–5.2, 1.4(x, y)?
X =

(a) The maximum displacement of the wave is 14 cm.

(b) The time for the wave to bounce opposite directions before coming to rest  is 3.0 s.

(c) The period of the wave is 3.0 s and the amplitude is 14 cm.

(d) The graph’s frequency is 0.33 Hz

(e) The wave attained maximum displacement at time 6 s and 7.5 s.

A) The maximum displacement of the wave is the point of maximum rise of the curve = 14 cm

B) Time of motion of the wave; This is the time for the wave to bounce opposite directions before coming to rest makes a complete cycle

It takes the wave 0.75s to bounce up and the 2.25 s to bounce down, and finally it came to rest at 3.0 s.

C) The period of the wave is the time taken for the wave to make a complete cycle = 3 s

Frequency of the wave

f = 1/T

f = 1/3 = 0.33 Hz

The frequency indicates the number of cycles in a second.

D) Position of the wave at time 6 s and 7.5 s

The wave attained maximum displacement at time 6 s and 7.5 s.

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Answer:

B ∩ (¬A ∩ ¬C)

Step-by-step explanation:

You want to exclude the section C shares with A, the one C shares with B and the one it shares with both. Intersecting ¬A (not A) with ¬C (not C) you obtain the entire area except A and C, which then can be intersected with B to obtain the highlighted area.

The ordered pair which is a solution of the system of equations is; (4.9, 0).

The equations given in the task content can be solved as a system as follows, since y = y;

4x -19.4 = 0.2x -4.2

4x -0.2x = 19.4 -4.2

3.8x = 15.2

x = 15.2/3.8

x = 4.9

y = 4(4.9) -19.4

y = 0.2

Hence, the best ordered pair solution is; (4.9, 0).

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Answer: B

Step-by-step explanation:

[tex](5x^2 -x-3)(2x+6)\\\\=2x(5x^2 - x-3)+6(5x^2 - x-3)\\\\=10x^3 - 2x^2 - 6x+30x^2 - 6x-18\\\\=\boxed{10x^3 +28x^2 - 12x-18}[/tex]

Hello!

Let's solve !

⇒ (x - 3)² = 5

⇒ x² - 6x + 9 = 5

⇒ x² - 6x + 4 = 0

⇒ x = -(-6) ± √36 - 4(1)(4) / 2

⇒ x = 6 ± √20 / 2 = 6 ± 2√5 / 2

⇒ x = 3 ± √5

∴ The solutions are x = 3 + √5 and x = 3 - √5.

Answer:

p=(x−3)25

Step-by-step explanation:

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                     (x-3)^2-(5*p)=0 

STEP1:

 1.1    Evaluate :  (x-3)2   =  x2-6x+9 

Equation at the end of step1:

x2 - 6x - 5p + 9 = 0

STEP2:

Solving a Single Variable Equation:

 2.1     Solve   x2-6x-5p+9  = 0

(a) The inequality follows from the binomial theorem.

[tex](a - b)^2 = a^2 - 2ab + b^2 \ge 0 \implies a^2 + 2ab + b^2 = (a+b)^2 \ge 4ab \\\\ \implies \dfrac{(a+b)^2}4 \ge ab \\\\ \implies \dfrac{a+b}2 \ge \sqrt{ab} ~~~~~~~~ (1)[/tex]

By the same reasoning,

[tex]\dfrac{c+d}2 \ge \sqrt{cd}[/tex]

Adding these results together, we have

[tex]\dfrac{a+b}2 + \dfrac{c+d}2 = \dfrac{a+b+c+d}2 \ge \sqrt{ab} + \sqrt{cd}[/tex]

and since [tex]\sqrt{ab}[/tex] and [tex]\sqrt{cd}[/tex] are both positive, they also satisfy the AM-GM inequality,

[tex]\dfrac{\sqrt{ab} + \sqrt{cd}}2 \ge \sqrt{\sqrt{ab}\times\sqrt{cd}} = \sqrt[4]{abcd}[/tex]

and the 4-variable result follows,

[tex]\dfrac{a+b+c+d}2 \ge 2\times\dfrac{\sqrt{ab}+\sqrt{cd}}2 \ge 2 \sqrt[4]{abcd} \\\\ \implies \dfrac{a+b+c+d}4 \ge \sqrt[4]{abcd} ~~~~~~~~ (2)[/tex]

(b.i) With [tex]m=\frac{a+b+c}3[/tex], we have

[tex]\dfrac{3m}4 = \dfrac{a+b+c}4 \implies m - \dfrac m4 = \dfrac{a+b+c}4 \\\\ \implies m = \dfrac{a+b+c+m}4[/tex]

(b.ii) From (2) it follows that

[tex]\dfrac{a+b+c+m}4 \ge \sqrt[4]{abcm} = \sqrt[4]{abc\times\dfrac{a+b+c+m}4}[/tex]

Using the result from (b.i), this is equivalent to

[tex]\dfrac{a+b+c}3 \ge \sqrt[4]{abc\times\dfrac{a+b+c}3}[/tex]

Take 4th powers on both sides.

[tex]\left(\dfrac{a+b+c}3\right)^4 \ge abc \times \dfrac{a+b+c}3[/tex]

Divide both sides by [tex]\frac{a+b+c}3[/tex].

[tex]\left(\dfrac{a+b+c}3\right)^3 \ge abc[/tex]

Finally, take the cube root of both sides.

[tex]\dfrac{a+b+c}3 \ge \sqrt[3]{abc}[/tex]

as required.

Answer:

Step-by-step explanation:

find 2^-6 as a fraction​

2^-6 = 0.015625

0.015625 as a fraction

(0.015625/1) × (1000000/1000000) =

15625/1000000

simplified = 1/64.

[tex]\frak{Hi!}[/tex]

[tex]\orange\hspace{300pt}\above2[/tex]

                  Let's find [tex]\boldsymbol{\sf{2^{-6}}}[/tex] as a fraction

                  Did you know that if we have a number with negative

                  exponents, we flop it over? This is how it's done-:

                  [tex]\boldsymbol{\sf{2^{-6}=\displaystyle\frac{1}{2^6}}}[/tex]. And Now we need to evaluate

                 [tex]\boldsymbol{\sf{\displaystyle\frac{1}{64}}}[/tex].

done!!

[tex]\orange\hspace{300pt}\above3[/tex]

Answer:

kkrg=u/d

-678/09

=12 ans

Using equations of linear model function, the number of hours Jeremy wants to skate is calculated as 3.

The equation that can represent a linear model function is, y = mx + b, where m is the unit rate and b is the initial value.

Equation for Rink A:

Unit rate (m) = (35 - 19)/(5 - 1) = 16/4 = 4

Substitute (x, y) = (1, 19) and m = 4 into y = mx + b to find b:

19 = 4(1) + b

19 - 4 = b

b = 15

Substitute m = 4 and b = 15 into y = mx + b:

y = 4x + 15 [equation for Rink A]

Equation for Rink B:

Unit rate (m) = (39 - 15)/(5 - 1) = 24/4 = 6

Substitute (x, y) = (1, 15) and m = 6 into y = mx + b to find b:

15 = 6(1) + b

15 - 6 = b

b = 9

Substitute m = 6 and b = 9 into y = mx + b:

y = 6x + 9 [equation for Rink B]

To find how many hours (x) both would cost the same (y), make both equation equal to each other

4x + 15 = 6x + 9

4x - 6x = -15 + 9

-2x = -6

x = 3

The hours Jeremy wants to skate is 3.

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Answer:

[tex]sin(\frac{143.13}{2} )=0.9487\\\\cos(\frac{143.13}{2} )=0.3162\\\\tan(\frac{143.13}{2} )=2.9999=3\\[/tex]

Step-by-step explanation:

angles in II quadrant are found by solvig 180- ∅ where ∅ is the acute angle

Let us then find the acute angle: in[tex]cos^{-} (\frac{4}{5}) = 36.86^{0} \\\\so \ x \ the \ angle \ in \ the \ second \ quadrant \ is \ 180-36.86=143.13^{0} \\\\sin(\frac{143.13}{2} )=0.9487\\\\cos(\frac{143.13}{2} )=0.3162\\\\tan(\frac{143.13}{2} )=2.9999=3\\[/tex]

The statement that describes a key feature of g if g(x) = f(x + 4) and f(x) = 10ˣ is "horizontal asymptote of y = 0". (Correct choice: B)

According to the statement, we have an original function f(x) = 10ˣ and a transformation rule for horizontal translation g(x) = f(x + 4). By applying this rule, we have that g(x) = 10ˣ ⁺ ⁴, which have these features:

Therefore, the statement that describes a key feature of g if g(x) = f(x + 4) and f(x) = 10ˣ is "horizontal asymptote of y = 0". (Correct choice: B)

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As the intervals moves from left to right on the graph, the average rate of change increases

The function is an exponential growth function.

This is known because it has an initial value at (0, 2), and the value increases to the right

The average rate of change of exponential growth functions increases towards the right.

This means that:

The initial statement is "as the intervals moves from left to right on the graph, the average rate of change increases

Because the average rate of change keeps changing, the final statement is:

Since the average rate of change is also changing, the function is changing and approaches infinity

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Answer: [tex](x+3)^2 + (y-4)^2 = 9[/tex]

Step-by-step explanation:

See attached image, this is straight formula substitution.

Answer:

2.99 x 10⁸ meters per second

Step-by-step explanation:

Scientific notation (also called "Standard form") is written in the form of [tex]a \times 10^n[/tex], where  [tex]1\leq a < 10[/tex]  and  [tex]n[/tex] is any positive or negative whole number.

To convert a number into scientific notation, move the decimal point to the left or right until there is one digit before the decimal point.

The number of times you have moved the decimal point is the power of 10 ([tex]n[/tex]).

If the decimal point has moved to the left, the power is positive.

If the decimal point has moved to the right, the power is negative.

To convert the given number to scientific notation

The decimal point for the given number 299000000 is after the last zero:

⇒  299000000.

Move the decimal point 8 places to the left:  

⇒ 2.99000000

Get rid of the redundant zeros:

⇒ 2.99

Multiply by 10 to the power of the number of decimal places moved:  

⇒ 2.99 x 10⁸

Therefore, the speed of light using scientific notation is:

Answer: I am not so sure but I think it’s asking for the median so that would be ANSWER 9.2

Step-by-step explanation:

The solution to the equations 3x - 4y=12 and 2x+y=8 are x = 4 and y = 0

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

We have two equations:

3x - 4y=12 and

2x+y=8

Multiplu by 4 on both side in equation  2x+y=8

8x + 4y = 32

Add the equaton 8x + 4y = 32 and 3x - 4y=12

3x - 4y=12

8x + 4y = 32

11x = 44

x = 4

Similarly, we can find the value of y:

y = 0

Thus, the solution to the equations 3x - 4y=12 and 2x+y=8 are x = 4 and y = 0

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Answer: [tex]T=\frac{2}{F-5}[/tex]

Step-by-step explanation:

[tex]F=\frac{2}{T}+5\\\\F-5=\frac{2}{T}\\\\\frac{1}{F-5}=\frac{T}{2}\\\\T=\frac{2}{F-5}[/tex]

a) The amount of meal reimbursement (in $) you expect to receive from the NSLP for last month is $146,205.

b) The total amount of milk reimbursement (in $) you expect for last month is $103,950.

c) The total amount of reimbursement (in $) your district will receive for last month is $250,155 ($146,205 + $103,950).

d) The average reimbursement (in $) per meal for both lunch and milk combined last month is $2.53 ($250,155/99,000).

Reimbursement is a process by which an entity is compensated for the expenses it incurs under a stated program.

Examples of expenses under the reimbursement policy include  business expenses, insurance costs, and overpaid taxes.

Annual NSLP lunches = 31.2 million

Lunches                        Free         Reduced Price     Full-Price       Total

National Quantity     16.1 million       3.2 million      11.9 million    31.2 million

District Lunches            27,000             18,000            54,000          99,000

Reimbursement rate      $2.68               $2.28              $0.25           $0.195

Reimbursement         $72,360           $41,040          $13,500         $19,305

Total reimbursement = $146,205 ($72,360 + $41,040 + $13,500 + $19,305)

Amount for milk reimbursement = $103,950 ($0.35 x 1.5 x 2 x 99,000)

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After solving the algebraic expression a(b-c)-b(a+c)-c(a-b) we get the equivalent answer as  ₋2(ab ₊ ac).

What is equivalent of algebraic expression?

Expressions that are equivalent do the same thing even when they have distinct appearances. When we enter the same value(s) for the variable, two algebraic expressions that are equivalent have the same value (s).

Given the expression is a(b₋c)₋b(a₊c)₋c(a₋b)

The first step is to multiply the terms.

⇒(a×b ₋ a×c) ₋ (b×a ₊ b×c) ₋ (c×a - c×b)

= (ab ₋ ac) ₋ (ba ₊ bc) ₋ (ca ₋ cb)

Now open the brackets.

= ab ₋ ac ₋ ba ₋ bc ₋ ca ₊ cb

Now comes main step of combining the like terms.

Put similar terms together on both sides of the equation.The two phrases are equal if each of the terms in both of them is the equivalent.

= ab ₋ ba ₋ ac ₋ ca ₋ bc ₊bc

Since, bc is a  like term with opposite sign, therefore bc  gets cancelled.

= ab ₋ ba ₋ ac ₋ ca

= ₋2ab ₋ 2ac

Take 2 as a common term from both the terms.

= ₋2(ab ₊ ac)

Hence we get the required equivalent of a(b-c)-b(a+c)-c(a-b) as

₋2(ab ₊ ac)

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Answer:

x = 15

y = 60

Step-by-step explanation:

Angles (x + 50) and (3x + 20) follows corresponding angle theorem.

-----

⇒ x + 50 = 3x + 20

⇒ x - 3x = 20 - 50

⇒ -2x = -30

⇒ x = 15

The angles (x + 50) and (2y - 5) lies on a straight line which sum ups to 180°

⇒ (x + 50) + (2y - 5) = 180

⇒ 2y + x + 45 = 180

⇒ 2y + 15 + 45 = 180

⇒ 2y + 60 = 180

⇒ 2y = 120

⇒ y = 60

Answer:

Please see the attached picture ! :D

-------- HappY LearninG <3 ----------

The first missing number in the sequence is 35, and the last missing number is 77.

The two missing numbers in the given sequence is calculated as follows;

= ?    49     63    ?

The given sequence is factor 7 which increases by 2

= 7 x 5      7 x 7       7 x 9     7 x 11

= 35         49          63          77

Thus, the first missing number in the sequence is 35, and the last missing number is 77.

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The sequence's initial missing number is 35, and its last missing number is 77.

The following number in the list is

The two missing numbers are determined as follows for the given sequence:

= ? 49 63 ?

The sequence is factor 7, which rises by 2 in the specified order.

= 7 x 5      7 x 7       7 x 9     7 x 11

= 35         49          63          77

Thus, the first missing number in the sequence is 35, and the last missing number is 77.

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The equation of the function is f"(x) = 2x^2 - 3

The parent function is given as:

f(x) = x^4

When it is stretched vertically by a factor of 2, the rule is

f'(x) = 2f(x)

So, we have

f'(x) = 2x^2

When shifted down 3 spaces, the rule is

f"(x) = f'(x) - 3

So, we have:

f"(x) = 2x^2 - 3

Hence, the equation of the function is f"(x) = 2x^2 - 3

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Answer:

Jesse will need about 89.5 square inches of gift wrap.

Step-by-step explanation:

We need to find the amount of wrapping paper that will cover the entire outside surface of the cylindrical gift. This means that we need to find its surface area, which is the total area an object's surface occupies.

The formula for cylinder surface area is as follows:

[tex]A=2\pi rh+2\pi r^{2}[/tex] (where r = radius and h = height)

In this case, the radius, or r, is 1.5 in, and the height, or h, is 8 in. Plugging these values into our formula, we get a total surface area of:

[tex]A=2\pi rh+2\pi r^{2}\\= 2\pi *1.5*8+2\pi * 1.5^{2} \\= 24\pi +4.5\pi \\=28.5\pi \\ \approx \text{\bf 89.5 \bf $in^{2}$ }[/tex]

Hope this helps!

Answer:

28.5 pi square inches

Step-by-step explanation:

The surface area of a cylinder is the lateral area plus two times the area of the base circle. The lateral area is the perimeter of the base circle times the height, and the perimeter of a circle is 2*pi*r.

Therefore the lateral area is:

LA = Perimeter*Height

     = 2*pi*r*h

     = 2*pi*1.5*8

     = 24pi

The base area would be A = pi*r*r since the bases of cylinders are circles.

BA = pi*r*r

     = pi*1.5*1.5

     = 2.25 pi

Since there are two circles (top AND bottom) in a cylinder, the final surface area of the cylinder would be:

SA = LA + 2BA

     = 24pi + 2*2.25pi

     = 24pi + 4.5pi

     = 28.5 pi

Answer:

[tex]\sqrt{269}[/tex] is ≈ 14.01

Step-by-step explanation:

If the table top is a square, to find the area, you would multiply one side times itself.

If you are given the area, and need to find the sides, you will take the square root of the area to find the side length.

Your question doesn't say to round, but 269 is not a perfect square.

[tex]\sqrt{269}[/tex] is ≈ 14.01

If the area of the base was 169, that is a perfect square. [tex]\sqrt{169}[/tex] = 13

The number of students from the math club that went to the soap box derby.

From the question, we see that there are two vans and 6 students in each van.

Thus, to get the number of students from the math club that went to the soap box derby, we will solve as follows;

Number of students that went to derby = 2 × 6 = 12

Complete question is;

The entire school 250 students went to the soap box derby. The math club went in 2 vans and each van held 6 students how many students from the math club went to the soap box derby

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Answer:

-31 degrees

Step-by-step explanation:

-4-27=-31

Answer:

6

Step-by-step explanation:

most of them are rectangles

The type of follow-up questions that can be asked to obtain the data needed to make a decision about the validity of that statement are:

This refers to the type of questions that are asked to a person in order to get extra information about a topic.

Hence, we can see that from the complete question, there is the need to perform tests to get results which would involve the procurement of data, controlled experiments, etc, and the follow-up questions that can be used are given above.

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