In the diagram below, AB is parallel to CD. What is the value of x?
B
459
A. 30
B. 45
C. 60
D. 135
​

The equation of f(x) is

The graph of g(x) is shifted 3 units to the left. This is a horizontal translation.

For horizontal translation, we follow the following rule >>>

Let parent function be f(x), then

• f(x+a) is the parent translated "a" units left

• f(x-a) is the parent translated "a" units right

Thus, following the rule, we can clearly say that g(x) = f(x+3)

We can write >>

The remaining Kit volume in the syringe is sufficient to correct the dose to 20 mCi.

To solve this problem, we can use the concept of radioactive decay and the decay factor. Here's how we can calculate the required volume to correct the dose:

Determine the initial activity of the kit:

Initial activity = 180 mCi

Calculate the decayed activity at 9:30 (after 1.5 hours):

Decay factor = 0.841

Decay activity = Initial activity * Decay factor

Calculate the remaining activity after withdrawing 20 mCi at 8 am:

Remaining activity = Initial activity - 20 mCi

Calculate the remaining activity at 9:30:

Remaining activity at 9:30 = Remaining activity * Decay factor

Calculate the desired activity at 9:30 (20 mCi):

Desired activity at 9:30 = 20 mCi

Calculate the volume needed to achieve the desired activity:

Volume needed = Desired activity at 9:30 / Remaining activity at 9:30 * Volume at 9:30

Calculate the remaining volume at 9:30:

Remaining volume = Volume at 8 am - Volume withdrawn - Volume accidentally discharged

Calculate the volume that needs to be added:

Volume to be added = Volume needed - Remaining volume

Let's perform the calculations step by step:

Determine the initial activity of the kit:

Initial activity = 180 mCi

Calculate the decayed activity at 9:30 (after 1.5 hours):

Decay factor = 0.841

Decay activity = 180 mCi * 0.841 = 151.38 mCi

Calculate the remaining activity after withdrawing 20 mCi at 8 am:

Remaining activity = 180 mCi - 20 mCi = 160 mCi

Calculate the remaining activity at 9:30:

Remaining activity at 9:30 = 160 mCi * 0.841 = 134.56 mCi

Calculate the desired activity at 9:30 (20 mCi):

Desired activity at 9:30 = 20 mCi

Calculate the volume needed to achieve the desired activity:

Volume needed = (Desired activity at 9:30 / Remaining activity at 9:30) * Volume at 9:30

Volume at 9:30 = Remaining volume = 30 ml - (30 ml / 2) = 15 ml

Volume needed = (20 mCi / 134.56 mCi) * 15 ml = 2.236 ml

Calculate the remaining volume at 9:30:

Remaining volume = 30 ml - (30 ml / 2) = 15 ml

Calculate the volume that needs to be added:

Volume to be added = Volume needed - Remaining volume = 2.236 ml - 15 ml = -12.764 ml

Since the calculated volume to be added is negative, it means that no additional volume is required. The remaining Kit volume in the syringe is sufficient to correct the dose to 20 mCi.

For such more questions on Kit Volume Correction

https://brainly.com/question/22971212

#SPJ8

Two figures are "congruent" if they have the same shape and size meaning they can be reflected and repositioned.

Note: They can not be resized if they are congruent.

The first option is congruent because the diagonals divides the shape into two equal parts of same sizes and angles.

The second option can not be said to be congruent because the sizes and angles of the shapes can not be determined and the shapes looks different a little.

The third option can be said to be congruent because the angles are vertical angles formed from the intersection of two lines which bisects each other

The last two shapes are not congruent because they are of different sizes.

The second and last option is correct. (Not congruent)

To find the distance between points A and B, we can use trigonometry and the given information.

Let's label the distance between A and B as "d". We know that point C is 94.4 meters away from point A. From angle A, we have the measure of 72°, and from angle C, we have the measure of 30°.

Using trigonometry, we can use the tangent function to find the value of "d".

tan(72°) = d / 94.4

To solve for "d", we can rearrange the equation:

d = tan(72°) * 94.4

Using a calculator, we can evaluate the expression:

d ≈ 4.345 * 94.4

d ≈ 408.932

Therefore, the distance between points A and B is approximately 408.932 meters.

Answer: 15

Okay, so I just kept putting in equations in my calculator so I could get 15(Someone commented the correct answer on the previous answer) so the equation is 50÷10-10 to get 15

The average cost per class if 10 classes is taken is : $15

The total cost is given as :

Initiation fee + additional cost(number of classes)

Number of classes = 10

Total cost = $50 + $10(10)

Total cost = $50 + $100

Total cost = $150

The average cost per class :

Total cost / number of classes

$150 / 10

= $15

Learn more : https://brainly.com/question/18112348

53/6, 203/10 and 73/5 rounded to the nearest whole number are 9, 20 and 15 respectively

Approximation is the process of using rounded values when presenting numerical data and making rough calculations.

The digits 1,2,3 and are rounded down and digits 5,6,7,8 and 9 are rounded up.

The numbers can be rounded to the nearest whole number as follows:

53/6 = 8.83 = 9          (round up)

203/10 = 20.3 = 20    (round down)

73/5 = 14.6 = 15           (round up)

Learn more about approximation on:

brainly.com/question/28128444

#SPJ1

Answer:

In city one, the hotel charges before taxes were $5,250.

In city two, the hotel charges before taxes were $6,750.

Step-by-step explanation:

Let the hotel charge in the first city be x and in the second city be y.

Given that the hotel charge before tax in the second city was $ 1500 higher than in the first. That can be written as:

\(y - x = \$1500\) ...[1]

The tax in the first city was 5 %, and the tax in the second city was 8.5 %.

The total hotel tax paid for the two cities was $ 836.25

5% of x + 8.5% of y = $836.25

\(0.05x+0.085y=\$836.25\)...[2]

Now putting value of y from [1] in to [2]:

\(y = \$1500+x\)

\(0.05x+0.085\times (\$1500+x)=\$836.25\)

On solving we get :

x = $5,250

Using vakue of x in [1] to find y:

\(y=\$1500+\$5,250=\$ 6,750\)

In city one, the hotel charges before taxes were $5,250.

In city two, the hotel charges before taxes were $6,750.

1. The amplitude is 3

2. The period is π

3. The phase shift is -90

4. The vertical shift is 2

5. The graph is attached

From the question, we have the following parameters that can be used in our computation:

y = 3sin[2(θ - 90)] + 2

A sinusoidal function is represented as

f(x) = Asin(B(x + C)) + D

Where

So, we have

Amplitude = 3

Period = 2π/2

Phase shift = -90

Vertical shift = 2

Evaluate

Amplitude = 3

Period = π

Phase shift = -90

Vertical shift = 2

Hence, the amplitude is 3 and the period is π

Read more about sinusoidal function at

brainly.com/question/21286958

#SPJ1

Answer:

In the third month, Becca will be walking \(7\) dogs

Step-by-step explanation:

The graph for the question is attached

Becca started her dog walking business with one dog

Additional dog she tries to walk every next month \(= 2\)

The attached graph indicates that in the third month, Becca will be walking \(7\) dogs

Answer:

Answer:(3^-6)^-5 backward

Hi there!  

»»————-　★　————-««

I believe your answer is:  

\(3^{30}\)

»»————-　★　————-««  

Here’s why:  

⸻⸻⸻⸻

\((3^5)^6\\-----------\\\rightarrow \text{Recall the power of a power rule:}} (a^x)^y=a^{xy}\\\\\rightarrow (3^5)^6\\\\\rightarrow 3^{(5*6)}\\\\\rightarrow \boxed{3^{30}}\)

⸻⸻⸻⸻

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.  

Hello!

surface area

= 2(4 x 2) + 2(12 x 4) + 2(12 x 2)

= 160cm²

Answer: 11/9

Step-by-step explanation:

you would cross out the two 4s(using butterfly method) and make them 1s. So 11 x 1 and 1 x 9 = 11/9

Answer:

11/4 times 4/9 is 11/9

Step-by-step explanation:

We have to find,

(11/4) times 4/9

\((11/4)(4/9) = (11*4/4*9)\)

We can cancel the 4s from the numeratorand denominator to get,

\((11*4/4*9) = (11*1/1*9) = 11/9\\=11/9\)

The answer is 11/9

Answer:

The solution is (>)

Step-by-step explanation:

It can be said this is bigger because the number 7 is bigger than 6. The language is simple like this, for example we ignore the 2, the number 75 and 60 is clearly bigger than 75. It's the same as 2.75 with 2.6. So the number is 2.75 bigger than 2.6

Answer:

\(Area = 153.938040026m^2\)

\(Circumference= 43.9822971503m\)

Step-by-step explanation:

Area

\(Area = \pi r^2\\Area = \pi *7^2\\Area = 49\pi\\Area = 153.938040026\)

Circumference

\(C = 2\pi r\\C = 2\pi*7\\C= 14\pi\\C=43.9822971503\)

A polynomial of degree n can pass through n + 1 points. So, if we have n + 1 points, we can construct a unique polynomial that passes through all those points.

A nonzero polynomial passing through a specific point (x, y) means that the value of the polynomial at that x-coordinate must be equal to the y-coordinate of the point. So, if the point (2, 0) is one of the points that the polynomial passes through, then we have:

\(p(2) = 0\)

We can construct a polynomial with this information. For example, one possible polynomial is:

\(p(x) = (x - 2)^2\)

This polynomial satisfies the equation p(2) = 0 since:

\(p(2) = (2 - 2)^2 = 0^2 = 0\)

Therefore, the polynomial \(p(x) = (x - 2)^2\) is a nonzero polynomial that passes through the point (2, 0) and satisfies the equation p(x). Note that there could be other polynomials that also satisfy the given conditions.

In general, a polynomial of degree n can pass through n + 1 points. So, if we have n + 1 points, we can construct a unique polynomial that passes through all those points.

Learn more about degree :

https://brainly.com/question/29182596

#SPJ4

The complete question is :

Find A Nonzero Polynomial P(\(x\)) Passing Through The Point (2,0) And Satisfying The Equation P(\(x\)) = P'(\(x^2\))?

Answer:

They should get 8 napkins

Step-by-step explanation:

4 napkins= 10 items ordered so just do 4x2=8, cause 8 napkins= 20 items.

I hope it helps you!

Bella The Bear~

Answer:

They should get 8 napkins

Step-by-step explanation:

4 napkins= 10 items ordered so just do 4x2=8, cause 8 napkins= 20 items.

I hope it helps you!

~XxBellsAloneXx~

Answer:

x=0, y=0

Step-by-step explanation:

① Label the 2 given equations.

x -2y= 0 -----(1)

3x +y= 0 -----(2)

② Make x the subject of formula in equation (1).

From (1): x= 2y -----(3)

③ Substitute equation (3) into (2):

3(2y) +y= 0

Expand:

6y +y= 0

Simplify:

7y= 0

y= 0

④ Find x.

Subst. y=0 into (3):

x= 2(0)

x= 0

Answer:

72

Step-by-step explanation:

let the unknown number be " y "

thus, 72 hundreds multipled by 7 makes 504

From the statement, we know that:

0. Maria is 62 in tall,

1. if her sister was 1.5 in taller, she would be exactly half Maria's height.

We define the variable:

• x = Eva's height in inches.

From point 2, we know that:

Replacing the data from points 1 and 2, we get the following equation:

Solving for x the last equation, we get:

We have found that Eva's height is 29.5 inches.

• The equation to solve is:

• Eva'is height is, x = 29.5 ,inches.

The answer is 29.5 inches

Answer:

0.82

Step-by-step explanation:

100 has 2 zeros so you move the decimal 2 places to the left.

82.

8.2

0.82

Answer:

0.82

Step-by-step explanation:

Decimals are out of 100, this fraction, 82/100, is also out of one hundred; this makes the question much easier to solve.  Just take the numerator and put it as a decimal, so in this case, the numerator is 82. We take that numerator and make it a decimal: 0.82.

The dimensions of the box if it is to use the minimum possible amount of metal are,

⇒ 2.714 m, 2.714 m, 1.358 m

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

A container with an open top is to have 10 m³ capacity.

Now,

Let the dimensions are x, y and z.

Since, Volume of box = 10 m³

Hence, We get;

⇒ xyz = 10

⇒ z = 10/xy

Since, A container is open in top.

Hence, The surface area = 2xz + 2yz + xy

Substitute z = 10/xy;

⇒ S.A = 2x (10/xy) + 2y (10/xy) + xy

          = 20/y + 20/x + xy

For minimum metal;

⇒ d (S.A)/ dx = 0

⇒ - 20/x² + y = 0

⇒ y = 20/x²  ..(i)

And, d (S.A) / dy = 0

⇒ - 20/y² + x = 0

⇒ x = 20/y²   ..(ii)

Divide equation (i) and ((ii);

⇒ x = y

Hence, We get;

⇒ xyz = 10

⇒ x³ = 10

⇒ x = 2.714

And, y = 2.714

So, The value of z is,

⇒ z = 10/xy

⇒ z = 10 / 2.714×2.714

⇒ z = 1.358 m

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ1

When He ate 1/7 of a sandwich at lunch and another 25% at supper, He did not finish 9 of the 14 sandwiches.

A fraction can be used to symbolise a portion of a whole or a ratio of two quantities in mathematics. It has a horizontal strip separating the numerator (top number) from the denominator (bottom number). The numerator is the overall number of equally-sized parts that the whole is divided into, and the denominator is the number of those parts that are being taken into account. For instance, the fraction 3/4 denotes three of a whole that is made up of four equal portions. The numerator, 3, indicates that we are only taking into consideration three of the four equal portions that the denominator, 4, denotes. Depending on whether or not the numerator is less than or larger than, a fraction may be proper or improper.

given

Assume that the hamburger is cut into 1 complete piece.

He consumed 1/7 of the burger for lunch, making the remaining portion as follows:

1 - 1/7 = 6/7

He consumed 25% of the remaining sandwich at supper, which is:

(25/100) x (6/7) = 6/28 = 3/14

As a result, the amount of the meal he has not yet consumed is:

6/7 - 3/14 = (12/14) - (3/14) = 9/14

When He ate 1/7 of a sandwich at lunch and another 25% at supper, He did not finish 9 of the 14 sandwiches.

To know more about fraction visit:

https://brainly.com/question/10354322

#SPJ1

Answer:

20% profit

Step-by-step explanation:

Given:

Profit:

Profit percent:

Answer:

c.p=1450

s.p=1740

profit=s.p-c.p

=1740-1450

=290

Answer:

Step-by-step explanation:

1) y = 3x -------------(I)

  y = 4x  - 5 -------------(II)

Plug in y= 3x in equation (II)

3x  =  4x - 5

3x + 5 = 4x

       5 = 4x - 3x

      5 = x

x= 5

Plug in s = 5 in equation (I)

y = 3*5 = 15

x = 5

y = 15

keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above

\(x-y=8\implies -y=-x+8\implies y=\stackrel{\stackrel{m}{\downarrow }}{1}x-8\impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill\)

\(\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{ 1 \implies \cfrac{1}{\underline{1}}} ~\hfill \stackrel{reciprocal}{\cfrac{\underline{1}}{1}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{\underline{1}}{1} \implies \text{\LARGE -1}}}\)

Answer: 13 weeks

Step-by-step explanation:

y = -24x + 379

67 = -24x + 379

24x = 379 - 67

x = 312 / 24

x = 13

Answer:

the answer is 13 weeks

Step-by-step explanation:

y = amount left

y = 67

67 = -24x+379

-312 = -24x

x = -312 / -24

x = 13

apples= 200

bad apples= 15%

how many apples are bad.

\( 200 \times \frac{15}{100} \)

\( = 30\)

therefore, there are 30 bad apples.

Answer:

No. It is not possible.

Step-by-step explanation:

No, that is not possible.

The problem lies in that \(a=b\).

Looking at your fourth line of work, \((a+b)(a-b)=b(a-b)\)

You divided by \((a-b)\).

And because \(a=b\), \(a-b=0\)

This means that when you divided by \((a-b)\) you divided by zero, which cannot happen.