If two points are given, then exactly one line can be drawn through those two points. Which geometry term does the statement represent?

Answer:

f(9,6) = 2

Step-by-step explanation:

We know df = (df/dx)dx + (df/dy)dy

From the question, df/dx = fx(8,5) = 2 and df/dy = fy(8,5) = 2

Since we need to find f(9,6) and f(8,5) = -2

dx = 9 - 8 = 1 and dy = 6 - 5 = 1

f(9,6) = f(8,5) + df

df = (df/dx)dx + (df/dy)dy

df = fx(8,5)dx + fy(8,5)dy

Substituting the values of fx(8,5) = 2, fy(8,5) = 2, dx = 1 and dy = 1

df = 2 × 1 + 2 × 1

df = 2 + 2

df = 4

f(9,6) = f(8,5) + df

substituting the value of df  and f(8,5) into the equation, we have

f(9,6) = -2 + 4

f(9,4) = 2

The value of f(9,6) = 2

Answer: C)  tan(pi/56)

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

Explanation:

I recommend using a trig identity reference sheet. The specific identity we will be using is [tex]\frac{\tan(A)-\tan(B)}{1+\tan(A)\tan(B)} = \tan(A-B)[/tex]

What we are given is in the form [tex]\frac{\tan(A)-\tan(B)}{1+\tan(A)\tan(B)}[/tex] with A = pi/7 and B = pi/8

A-B = (pi/7)-(pi/8)

A-B = pi(1/7-1/8)

A-B = pi(8/56 - 7/56)

A-B = pi*(1/56)

A-B = pi/56

Therefore,

[tex]\frac{\tan\left(\pi/7\right)-\tan(\pi/8)}{1+\tan(\pi/7)\tan(\pi/8)} = \tan\left(\pi/56\right)[/tex]

Answer:

1. Average Number of Steps of

= Total of the different steps /  divided by 3

= 6,943/3

= 2,314.3 steps

2. Weighted Average Number of Steps of 3, 58-inch, 5, 64-inc, and 2, 76-inch people

= Total steps by the 10 people divided by 10

= 23,558/10

= 2,355.8 steps

3. The difference is not much.

4. The weighted average (2,355.8 steps) is a more accurate representation of the data.  The calculation of the ordinary average steps is more confusing than the weighted average steps.

Step-by-step explanation:

1. Calculation of the Weighted Average Number of Steps of:

3, 58-inch people = 3 x 2,601 =   7,803

5, 64-inch people = 5 x 2,357 = 11,785

2, 76-inch people = 2 x 1,985 =  3,970

10 persons' total steps = 23,558

2. Calculation of the ordinary average:

58-inch people =  2,601

64-inch people =  2,357

76-inch people =  1,985

Total steps           6,943

Answer:

36y² - 1

Factorize

We have the final answer as

[tex](y - \frac{1}{6} )(36y + 6)[/tex]

Hope this helps you

Answer: (A) .                                                                                                          

because if you travel 60 miles per hour and i takes 2 hours yto get there you have to double 60 miles so 120 miles per 2 hours

The relationship between Sara's speed and the time it takes her to get to her parent's house will be s = 120/t so option (A) will be correct.

Work is the completion of any task for example if you have done your homework in 5 hours then you have done 5 hours.

Another illustration of labor is when you finish your meal in an hour, which means that you finished your work in an hour. In essence, work is the length of time it took you to complete any task.

Given that Sara drives 60 miles in 2 hours.

Distance covered by sara is = 60(2) = 120 miles.

We know that

speed = distance/time

Let's say speed is S time is t then

⇒ S = 120/t so the correct equation of the given question will be this.

For more information about the work and time relation

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Answer: A(3, -5)

B(6, -2)

C(9, -2)

Step-by-step explanation:

If we have a point (x, y), and we do a reflection over the axis y = a, then the only thing that will change in our point is the value of x.

Now, the distance between x and a must remain constant before and after the reflection.

so if x - a = d

then the new position of the point will be:

(a - d, y) = (2a - x, y).

I will use that relationship for the 3 points

A)

We start with the point (1, -5)

The reflection over y = -1 leaves.

The distance between 1 and -1 is = 1 - (-1) = 2.

Then the new point is (-1 - 2, -5) = (-3, -5)

Now we do a reflection over y = 1, so D = -3 - 1 = -2

Then the new point is:

A = (1 -(-2), -5) = (3, -5)

B) (2, -2)

Reflection over y = -1.

distance, d = 2 - (-1) = 3

the point is (-1 - 3, -2) = (-4, -2)

Now, a reflection over y = 1.

The distance is D = -4 - 1 = -5

The new point is (1 - (-5), 2) = (6, -2)

C) (5, -2)

reflection over y = -1

Distance: D = 5 - ( - 1) = 6

New point: (-1 - 6, -2) = (-7, -2)

Reflection over y = 1.

Distance D = -7 - 1 = -8

New point ( 1 - (-8), -2) = (9, -2)

Answer:

C. 1/16

Step-by-step explanation:

[tex]16 * 4^{-4}[/tex]

16 can be written as a power of 4.

[tex]4^2 * 4^{-4}[/tex]

The bases are same, add exponents.

[tex]4^{2+-4}[/tex]

[tex]4^{-2}[/tex]

Simplify negative exponent.

[tex]\frac{1}{4^2 }[/tex]

[tex]\frac{1}{16}[/tex]

Answer:

8192

Step-by-step explanation:

2 ¹²= 4096

4096 x 2 = 8192

Answer:

36 tickets

Step-by-step explanation:

At a city museum, child tickets are sold for $5.30, and adult tickets are sold for $9.40

The total sales that were made are $1206

Let x represent the number of child tickets that were sold

Let y represent the number of adult tickets that was sold

5.30x +9.40y= 1206

The number of adult tickets sold was three times greater than the child tickets

y= 3x

Substitute 3x for y in the equation

5.30x + 9.40y= 1206

5.30x + 9.40(3x)= 1206

5.30x + 28.2x= 1206

33.5x= 1206

Divide both sides by the coefficient of x which is 33.5

33.5x/33.5= 1206/33.5

x = 36

Hence the number of child tickets that were sold that day is 36 tickets

Answer:

the answer is y= 2/3x - 5

Answer:

Option C.

Step-by-step explanation:

In the given figure we have two parallel lines AB and CD.

A transversal line FB intersect the parallel lines at point B and C.

We know that the if a transversal line intersect two parallel lines, then corresponding angles are congruent.

[tex]\angle ABC=\anle ECF[/tex]

[tex]x=y[/tex]

To prove this by translation, we need a translation along the directed line segment CB maps ine CD onto line AB and angle y onto angle x.

Therefore, the correct option is C.

Answer:

There is sufficient evidence to conclude that women make less money than men doing the same job.

Step-by-step explanation:

The hypothesis for the test can be explained as follows:

H₀: Women does not make less money than men doing the same job, i.e. [tex]\mu\geq \$1343[/tex].

Hₐ: Women make less money than men doing the same job, i.e. [tex]\mu<\$1343[/tex].

From the provided data compute the sample mean and standard deviation:

[tex]\bar x=\frac{1}{n}\sum X=\frac{1}{18}[1811+728+...+1170]=1125.11\\\\s=\sqrt{\frac{1}{n-1}\sum (X-\bar x)^{2}}=\sqrt{\frac{1}{18-1}\times 1322541.86}=278.92[/tex]

Compute the test statistic as follows:

[tex]t=\frac{\bar x-\mu}[\s/\sqrt{n}}=\frac{1125.11-1343}{278.92/\sqrt{18}}=-3.143[/tex]

The test statistic value is -3.143.

Compute the p-value as follows:

[tex]p-value=P(t_{n-1}<-3.143)=P(t_{17}<-3.143)=0.003[/tex]

*Use a t-table.

The p-value of the test is 0.003.

The p-value of the test is very small for all the commonly used significance level. The null hypothesis will be rejected.

Conclusion:

There is sufficient evidence to conclude that women make less money than men doing the same job.

Answer:

6x + y = -18

Step-by-step explanation:

The given equation is,

y - 6 = -6(x + 4)

We have to rewrite this equation in the form of Ax + By = C

Where A, B and C are the integers.

By solving the given equation,

y - 6 = -6x - 24 [Distributive property]

y - 6 + 6 = -6x - 24 + 6 [By adding 6 on both the sides of the equation]

y = -6x - 18

y + 6x = -6x + 6x - 18

6x + y = -18

Here A = 6, B = 1 and C = -18.

Therefore, 6x + y = -18 will be the equation.

Answer:

x=5

Step-by-step explanation:

35 = 7x

Divide each side by 7

35/7 = 7x/7

5 = x

Answer:

Chain rule: [tex]\frac{d}{dx} [f[u(x)]] = \frac{df}{du} \cdot \frac{du}{dx}[/tex], u-Substitution: [tex]f\left[u(x)\right] = \int {\frac{df }{du} } \, du[/tex]

Step-by-step explanation:

Differentiation and integration are reciprocal to each other. The chain rule indicate that a composite function must be differentiated, describing an inductive approach, whereas u-substitution allows integration by simplifying the expression in a deductive manner. That is:

[tex]\frac{d}{dx} [f[u(x)]] = \frac{df}{du} \cdot \frac{du}{dx}[/tex]

Let integrate both sides in terms of x:

[tex]f[u(x)] = \int {\frac{df}{du} \frac{du}{dx} } \, dx[/tex]

[tex]f\left[u(x)\right] = \int {\frac{df }{du} } \, du[/tex]

This result indicates that f must be rewritten in terms of u and after that first derivative needs to be found before integration.

Answer:

2nd option. this provides an unbiased way to choose the clients surveyed.

Answer:

Yes

Step-by-step explanation:

They are congruent by the AAS postulate.

∠A corresponds to and is congruent to ∠D

Side BC corresponds to and is congruent to side EC

∠C is congruent to ∠C by the Vertical Angles Theorem.

So, ΔABC ≅ ΔDEC

Answer:

a) percentage of the employees that will experience lost-time accidents in both years = 1.2%

b) percentage of the employees that will suffer at least one lost-time accident over the two-year period = 10.8%

Step-by-step explanation:

given

percentage of lost time accident last year

P(L) = 8% = 0.08 of the employees

percentage of lost time accident current year

P(C) = 4% = 0.04 of the employees

P(C/L) = 15% = 0.15

using the probability

P(L ∩ C) = P(C/L) × P(L)

= 0.08 × 0.15 = 0.012 = 1.2%

percentage of the employees will experience lost-time accidents in both years = 1.2%

b) Using the probability of the event

P(L ∪ C) = P(L) + P(C) - P(L ∩ C)

= 0.08 + 0.04 -0.012 = 0.108 = 10.8%

percentage of the employees will suffer at least one lost-time accident over the two-year period = 10.8%

Answer:

-3

Step-by-step explanation:

Easy way:

Between the two marked points, you can count that you need to go down 6 and over 2. That means the rise/run is -6/2, or -3.

Full way:

Starting Point: (-1,3)

Ending Point: (1,-3)

Slope is given by (y₂-y₁)/(x₂-x₁)

To calculate this, (-3-(3))/(1-(-1))

Clean up the double negatives to get (-3-3)/(1+1), AKA -6/2

-6/2 = -3.

Answer:  8x³ + 12x² - 16x - 16

Step-by-step explanation:

  (4x² - 2x - 4)(2x + 4)

= (2x + 4)(4x² - 2x - 4)

= 2x(4x² - 2x - 4)  +  4(4x² - 2x - 4)

=   8x³ - 4x² - 8x   +  16x² - 8x - 16

=   8x³ + (-4x² + 16x²) + (-8x - 8x) - 16

=   8x³ + 12x² - 16x - 16

Answer:

18

Step-by-step explanation:

Given the above table of the data set, the number of values less than or equal to 6 would be the sum of the frequencies of all values that is equal to or less than 6.

From the table above, we would add up the frequencies of the values of 6 and below, which is:

2 + 3 + 6 + 4 + 3 = 18

Answer = 18

The number of values less than or equal to 6 is 18

Here the number of values should be less than or equivalent to 6 represent the sum of the frequencies i.e. equal or less than 6

So, here the number of values should be

= 2 + 3 + 6 + 4 + 3

= 18

Hence, we can conclude that  The number of values less than or equal to 6 is 18

Learn more about frequency here: https://brainly.com/question/20875379

Answer:

X+y = 20... equation 1

3.2x + 2y = 54.4...equation 2

X= 12

12 of $3.2 grade is needed

Step-by-step explanation:

Let x = grade containing$ 3.2 per pound

Let y = grade containing $2.00 per pound

X+y = 20... equation 1

X3.2 +2y = 20(2.72)

3.2x + 2y = 54.4...equation 2

Multiplying equation 1 by 2

2x +2y = 40

3.2x + 2y = 54.4

1.2x = 14.4

X= 12

If x= 12

2x +2y = 40

2(12) + 2y = 40

2y = 40-24

2y = 16

Y= 8

Answer:

-1

Step-by-step explanation:

since m=4

we substitute in eqn which is 2(5-(1/2m))

2(5-(1/2(4)))

2(5-2)-7

=-1

Answer:

f(x) = (x + 6)² - 29

Step-by-step explanation:

Given

f(x) = x² + 12x + 7

To complete the square

add/subtract ( half the coefficient of the x- term )² to x² + 12x

x² + 2(6)x + 36 - 36 + 7

= (x + 6)² - 29, thus

f(x) = (x + 6)² - 29

answers are 6, and -29

[tex]y^2 = 9(9+3)\\\\y^2 = 9(12)\\\\y^2 =3^2\cdot3\cdot2^2\\\\y = 6\sqrt{2}[/tex]

Answer:

The least common multiple of $6!$ and $(4!)^2.$

is 6×4! or 144

Answer:

g(x) = -2x - 5

2x becomes -2x as a reflection across the y-axis

add on -5 to shift the function 5 units down

Answer:

Less than 4/10

Step-by-step explanation:

First lets convert both fractions to a common denominator:

16 and 10 can both go into 80 equally.

Now lets convert the fractions so they have a denominator of 80:

(6/16)    *5  = 30/80

(4/10)    *8 = 32/80

we can multiply the fractions to get just the numerator   (*80)

Now compare 30 to 32.  As you can see 32 is greater meaning that 6/16 is less that 4/10.

Answer:

15

Step-by-step explanation:

Answer:

30

Step-by-step explanation:

30 hcchxfifififififfud7dd7d

Answer:

a=11/5 OR 5.5

Step-by-step explanation: