justification two common tangents

Answer:

a. x = total - $5

b. x = $6

c. x = $10

Step-by-step explanation:

a. pen + book = total

Let x = book

$5 + x = total

x = total - $5

b. pen + book = total

Total = 411

$5 + x = $11

x = $11 - $5

x = $6

c. pen + book = total

Total = $15

$5 + x = $15

x = $15 - $5

x = $10

Answer:

Hello!

The manager of a cafeteria that caters only to the workers at a hospital wants to conduct a survey to determine which drink served at the cafeteria is most popular during lunch. What is the population that the manager is studying?

The correct answer would be:

C. Hospital workers who eat in the cafeteria

Hope this helps.

Model A shows the 3-D shape of the molecule, but model B does not. Then the correct option is C.

The compound can be represented in the form of 3-D shape and as well as chemical formula.

The particles are bound together, this becomes simpler to comprehend the precise structure or architecture of the compound when model A depicts the molecule in three dimensions.

Model A shows the 3-D shape of the molecule, but model B does not.

Then the correct option is C.

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The reciprocal is determined by interchanging y with 2x to have y/2x. Hence the reciprocal of 2x/y is y/2x

The reciprocal is determined by changing the numerator for denominator

Given the expression

f(x, y) = 2x/y

The reciprocal is determined by interchanging y with 2x to have y/2x. Hence the reciprocal of 2x/y is y/2x

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The reciprocal of 2x / y is equals to y / 2x

Reciprocal is simply defined as the inverse of a value or a number.

For example If x is a real number, then its reciprocal will be 1/x.

Therefore, the reciprocal of 2x / y can be calculated as follows:

Reciprocal of 2x / y =

Hence,

[tex]\frac{1}{\frac{2x}{y} } = 1 X \frac{y}{2x}[/tex]

Therefore, the reciprocal of 2x / y = y / 2x

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Answer: 5.22

Step-by-step explanation:

The apothem = 87 cm = 0.87 m.

Using the formula [tex]A=\frac{1}{2}ap[/tex] to find the area of the base, where a is the apothem and p is the perimeter, we get [tex]A=\frac{1}{2}(0.87)(6)=2.61[/tex]

So, using the formula [tex]V=Bh[/tex], we get the volume to be [tex]2.61(2)=5.22 \text{ m}^{3}[/tex]

The proportional relationship is correctly graphed by graph vs.

A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:

y = kx

In which k is the constant of proportionality.

In this problem, the relationship that gives the montant M considering the number of items sold n is:

M = 3n.

Considering that the montant is the vertical axis, the graph is composed by points (n, 3n), that is, points (100, 300), (200, 600) and so on, hence the graph is graph vs.

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Answer:

1st = [tex]A. \sf \ y = 1[/tex]

2nd = [tex]D. \ \sf y - 5 = 3(x + 2)[/tex]

PART A

Given: y = -2

This equation has a slope of 0

Equation that pass (-1, 1)

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

y = 1

PART B

[tex]\sf Given : y = -\dfrac{1}{3} x + 2[/tex]

Here slope is -1/3 and y-intercept is 2

Perpendicular lines has negatively inverse slope.

→ per. slope = -(slope)⁻¹ = -(-1/3)⁻¹ = 3

Equation in point slope form:

[tex]\sf y - y_1 = m(x - x_1)[/tex]

[tex]\sf y - 5 = 3(x - (-2))[/tex]

[tex]\sf y - 5 = 3(x + 2)[/tex]

Answer:

[tex]y = 1[/tex]

[tex]y-5=3(x+2)[/tex]

Step-by-step explanation:

The line [tex]y = -2[/tex] is a horizontal line.

Therefore, a line that is parallel to the given line and passes through point (-1, 1) is another horizontal line with the y-value of the point.

Therefore, the line is [tex]y = 1[/tex]

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Slope-intercept form of a linear equation:

 [tex]y=mx+b[/tex]

where:

Given linear equation:

[tex]y=-\dfrac{1}{3}x+2[/tex]

Therefore, the slope of this equation is -1/3.

If two lines are perpendicular to each other, the product of their slopes will be -1.   Therefore, the slope (m) of the line perpendicular to the given line is:

[tex]\implies m \cdot -\dfrac{1}{3}=-1[/tex]

[tex]\implies m=3[/tex]

Use the point-slope form of a linear equation, with the found slope and the point (-2, 5) to create the equation:

[tex]\implies y-y_1=m(x-x_1)[/tex]

[tex]\implies y-5=3(x-(-2))[/tex]

[tex]\implies y-5=3(x+2)[/tex]

Answer:

The answer is B

Step-by-step explanation:

Answer:

False

Step-by-step explanation:

y > 5x-4

This inequality is greater than, so it would be a dotted line

You would have a solid line when it is greater than or equal to ≥  or less than or equal to ≤

The graph of a function f(x) = ∛x is shown in the picture, and the domain of the function will be all real numbers.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We have a function:

f(x) = ∛x

The domain of the function will be all real numbers.

x ∈(-∞, ∞)

The graph will be curved.

Plug x = 0, y = 0

x = 1, y = 1

The graph is shown in the attached picture.

Thus, the graph of a function f(x) = ∛x is shown in the picture, and the domain of the function will be all real numbers.

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The equation x² − 10x − 11 = 0 that is equivalent to (x – 5)² = 36. Then the correct option is A.

The equivalent is the expressions that are in different forms but are equal to the same value.

The equation is given below.

x² − 10x − 11 = 0

Then the equation can be written as

x² − 10x + 25 – 25 − 11 = 0

                        (x – 5)² = 36

Then the correct option is A.

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Answer:

1 999 000

Step-by-step explanation:

Formula:

[tex]1+2+3+.\ .\ .+n=\frac{n\times \left( n+1\right) }{2}[/tex]

………………………………………

Then

[tex]1+2+3+....+1997+1998+1999=\frac{1999\times \left( 1999+1\right) }{2}[/tex]

[tex]1+2+3+....+1997+1998+1999=\frac{1999\times \left( 2000\right) }{2}[/tex]

[tex]1+2+3+....+1997+1998+1999=\frac{3998000 }{2}[/tex]

[tex]1+2+3+....+1997+1998+1999=1999000[/tex]

Answer:

5) x = 5

6) x = 8

Step-by-step explanation:

5) Since RT is 40 and RS is 15, ST = RT- RS=25

Since ST also equals 5x, 5x = 25 and x = 5.

6) Since ∠CBD and ∠DBA are supplementary, they add up to [tex]180^\circ[/tex], and because ∠CBD = [tex]90^\circ[/tex], ∠DBA = [tex]90^\circ[/tex].

Since ∠DBA - ∠DBE = ∠EBA, ∠EBA = [tex]90^\circ-40^\circ=50^\circ[/tex].

Also ∠EBA = 6x + 2, so 6x + 2 = [tex]50^\circ[/tex].

6x = 48, and x = 8.

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Answer:  [tex]\textsf{(1, 1) is NOT a solution of the inequality}[/tex]

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Given:  [tex]y \le-3x + 1[/tex]

Find:  [tex]\textsf{Determine if (1, 1) is a solution of the inequality}[/tex]

Solution:  In order to determine if (1, 1) is a solution we need to plug in 1 for the x values and 1 for the y values and see if the equation evaluated to true.

Plug in the values

Simplify

As we can see the expression states that 1 is less than or equal to -2 which is false therefore (1, 1) is NOT a solution of the inequality.

Hey there!

Algebra I

Inequality

Ordered pair

y ≤ -3x+1

1 ≤ -3(1) + 1

1 ≤ -3 + 1

1 ≤ -2

The statement is NOT true as 1 is not less than or equal to -2.

Therefore, the ordered pair is not a solution of the inequality.

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Answer:

x is 8√2.

Step-by-step explanation:

Answer:

8√2

Step-by-step explanation:

Idea 1 : (Pythagorean theorem)

2x² = 16²

then

2x² = 256

then

x² = 256/2 = 128

then

x = √128

then

x = √(64×2)

then

x = √64 × √2

then

x = 8√2

………………………………………………………

Idea 2 : (diagonal of a square)

16 is the diagonal of a square with side square of lengths x

Then

x√2 = 16

Then

[tex]x = \frac{16}{\sqrt{2} } =\frac{8\times2}{\sqrt{2} } =\frac{8\times\sqrt{2} \times \sqrt{2} }{\sqrt{2} } =8\sqrt{2}[/tex]

Answer:

55 white

Step-by-step explanation:

So ratio 5:4 is essentially saying, for each 5 white marbles, there are 4 red ones. This can be represented in the equation: 5x+4x=99. We specifically want an integer solution. Because what is 1.2 of a marble? And what is -1 marbles? So as x increases by 1, the entire thing increases by 9. This gives you the equation: 9x=99 which gives you x=11. So there are 55 white and 44 red.

The answer is P(>204.3) = 0.5000

There are an infinite number of real numbers > 204.3, but an equally infinite number of real numbers < 204.3

The chance of randomly selecting a number >204.3 is 1/2 or 50%

or for 4 decimals: 50.0000%

The probability of an event can be calculated via chance formula with the aid of truly dividing the favorable range of effects by means of the whole number of feasible effects.

Opportunity = the wide variety of ways of achieving fulfillment. The whole range of viable effects. As instance, the possibility of flipping a coin and it being head is ½, because there is 1 way of having a head and the whole range of viable effects is two (a head or tail).

Chance is the department of mathematics that research the possible outcomes of given occasions together with the outcomes' relative likelihoods and distributions.

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Answer:

isn't that the midpoint formula??

The probability of getting positive difference between the numbers 3 or greater between 1,2,3,4,5,6,7,8,9,10 if two numbers are selected is 28/45.

Given Numbers:{ 1,2,3,4,5,6,7,8,9,10}

We have to find the probability that the positive difference between the numbers selected is 3 or greater.

Probability is the likelihood of happening an event among all the events possible.

Total number of combinations when two numbers are selected from 10 numbers is 10 C 2=10!/2!(10-2)!

=10*9*8!/2*1(8!)

=10*9/2

=45 combinations

Combinations of numbers whose difference will be 3 or more are: (10,7),(10,6),(10,5),(10,4)(10,3)(10,2)(10,1)(9,6)(9,5)(9,4)(9,3)(9,2)(9,1)(8,5)(8,4)(8,3)(8,2)(8,1)(7,4)(7,3)(7,2)(7,1)(6,3)(6,2)(6,1)(5,2)(5,1)(4,1)

Total numbers =28

Probability=numbers/total combinations

=28/45

Hence the probability that two numbers selected gives difference of 3 or more is 28/45.

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Answer:

2400 miles

Step-by-step explanation:

So the first equation is pretty straight forwards, it's in the slope-intercept form y=mx+b where m is the slope, and b is y-intercept, since as x increases by 1, the value y increases by m, which by definition is what the slope is, so m is the slope. In this context the slope is how many miles in x hours. So Space Explorer B flies 400 miles per hour. The amount of miles that Space Explorer A flies per mile can be calculated by dividing the 36400 by the 13 hours it had to travel. This gives you 2800 miles. So to find how many fewer miles Space Explorer B travels than Space Explorer A you subtract the 2 slopes. 2800 - 400 = 2400. So Space Explorer B travels 2400 fewer miles than Space Explorer A

The constant of proportionality is 1/3

and three more values are

x       1        2        3        4        5        

y       3       6        9        12       15

From the question, we are to determine the constant of proportionality

The given equation is

k = x ÷ y

From the given information,

When x = 1, y = 3

∴ k = 1 ÷ 3

k = 1/3

Thus, the constant of proportionality is 1/3

Now, we will determine the values of y for the values x = 3, x = 4, and x = 5

Since

k = x ÷ y

Then,

y = x ÷ k

When x = 3

y = 3 ÷ 1/3

y = 3 × 3

y = 9

When x = 4

y = 4 ÷ 1/3

y = 4 × 3

y = 12

When x = 5

y = 5 ÷ 1/3

y = 5 × 3

y = 15

Hence, the constant of proportionality is 1/3

and three more values are

x       1        2        3        4        5        

y       3       6        9        12        15

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Answer:

c. 7x2 +18 - 4x2 – 3 + 6x

Step-by-step explanation:

3(x^2 + 2x + 5)

3x^2 + 6x + 15

a.) 7x^2 - 18 - 4x^2 – 3 + 6x

= 3x^2 - 21 + 6x

b.) 7x^2 +18 - 4x^2 – 3 + 8x

= 3x^2 + 15 + 8x

c.) 7x2 +18 - 4x2 – 3 + 6x

= 3x^2 + 15 + 6x

d.) 7x2 +18 - 3x2 – 3 + 6x

= 4x^2 + 15 + 6x

Answer:

72°

Step-by-step explanation:

Adjacent angles of a rhombus are supplementary, so

Since opposite angles of a parallelogram are congruent, angle BCD is congruent to angle BAD.

The measure of angle BAD is 3(22)+6 = 72°

The set that can represent an exponential function is the one in option c.

An exponential function is of the form:

[tex]f(x) = A*(b)^x[/tex]

So, as x increases by one unit, we multiply the previous number by b.

From the given options, the only one that can represent an exponential function is the third one:

(1, 1/2) , (2, 1/4) , (3, 1/8) ( 4, 1/16)

As you can see, as x increases, the value of y keeps being divided by 2.

This exponential function is:

[tex]f(x) = 1*(1/2)^x = (1/2)^x[/tex]

Evaluating it, we get:

[tex]f(1) = (1/2)^1 = 1/2\\\\f(2) = (1/2)^2 = 1/4\\\\f(3) = (1/2)^3 = 1/8\\\\etc...[/tex]

Then we conclude that the correct option is the third one.

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The speed of skaters was 10 km per hr.

Mathematically, the speed of an object is directly proportional to the distance traveled and inversely proportional to the time taken. In simple words, the more the speed, the distance traveled is more in a short period and vice-versa.

Let the speed of the skater be x

We know, speed = [tex]\frac{Distance}{Time}[/tex]

According to the question:

[tex]\frac{20}{x} = \frac{40}{x + 10}[/tex]

Cross multiplying both sides,

20(x+10) = 40x

20x + 200 = 40x

20x = 200

x = 10

Thus, the speed of skaters was 10 km per hr.

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Answer:

See below.

Step-by-step explanation:

Is the equation written correctly?

y = 3×2¹ +4 has no variable, unless the "3×2" is supposed to be "3x*2^1"

If so,

y = 3x*2¹ +4 for x = 1 would be

y = 3(1)2¹ +4

y = 3*2 +4

y = 10

⊰________________________________________________________⊱

Answer:

See Below.

Step-by-step explanation:

[tex]\large\begin{gathered} \sf{Start \ by \ plugging \ in \ the \ number \ that \ x \ is: 1} \\ \sf{Now, \ evaluate: y=3*1*2^1+4} \\ \sf{y=3*2+4} \\ \sf{Multiply \ 3 \times 2 \ first: y=6+4} \\ \sf{Now, \ just \ add: y=10}{ \end{gathered}[/tex]

Done!!

⊱________________________________________________________⊰

[tex]\bf{\overbrace{C}\underbrace{A}\overbrace{LL}\underbrace{I}\overbrace{G}\underbrace{R}\overbrace{A}\underbrace{P}\overbrace{H}\underbrace{Y}}[/tex]

Answer:

Step-by-step explanation:

Argument

One of the ways to recognize the domain is that it should be on the x axis of a graph. That lets out A and D. They are both describing the y axis. t = 0 has no meaning with this question.

Answer B

Answer:

Step-by-step explanation:

According to the diagram MK is the angle bisector of  ∠LMJ in the triangle LMJ.

Use angle bisector theorem, which states:

Applied to the given triangle, the ratios are:

Use segment addition postulate and substitute known values to get:

Her earnings vary directly with her number of hours worked

The hourly rate is given as:

Rate = $21.25 per hour

This means that:

She earns $21.25 each hour

This in other words means that, her earning increases as the number of hours increase.

The above is an illustration of a direct variation.

Hence, her earnings vary directly with her number of hours worked

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Sadie earns $21.25 per hour. Do her earnings vary inversely or directly with her number of hours worked?

Hello!  

To find the mass of the liquid by itself, subtract the mass of the container from the mass of the liquid and container.

⇒ 1,300 - 250

⇒ 1,050 grams

∴ The mass of the liquid by itself is 1,050 grams.

The mean is the best central tendency to measure the expected number of strokes required for the ninth hole.

What is mean?

In statistics, in addition to the mode and median, the mean is one of the measures of central tendency. Simply put, the mean is the average of the values in the given set. It indicates that values in a particular data set are distributed equally.

The three most frequently employed measures of central tendency are the mean, median, and mode. The total values provided in a datasheet must be added, and the sum must be divided by the total number of values in order to determine the mean.

Why mean is the best choice in this case?

Since it considers all of the data in relation to one another, the mean is an effective indicator of central tendency. When there are outliers (extreme values) in the data, for example, the mean is a poor measurement; in this situation, the median is preferable.

The data set is roughly symmetrical in the scenario described in the question, so the mean is the most-suited central tendency measure to employ here.

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Answer:

The mean is the best choice because the data is nearly symmetrical.