Write the point-slope form of an equation of the line through the points (-4, 7) and (5,-3).
0
A. Y+4= -1; (1 – 7)
B.Y-5 = = 10 (x+3)
OC. y +3 = = 10 (2+5)
D. y - 7= -5° (x+4)

Answer:

the speed of the boat is 6.67 ft/s

Step-by-step explanation:

Given;

height of the winch, h = 12 ft

the rate at which the winch pulls, the rope, = 4 ft/s

This form a right triangle problem;

let the height of the right triangle = h

let the base of the triangle = b (this corresponds to the horizontal displacement of the boat)

let the hypotenuse side = c

c² = b² + h²

[tex]2c\frac{dc}{dt} = 2b\frac{db}{dt} + 2h \frac{dh}{dt}\\\\The \ height \ of \ the \ winch \ is \ not \ changing \\\\2c\frac{dc}{dt} = 2b\frac{db}{dt} + 2h (0)\\\\2c\frac{dc}{dt} = 2b\frac{db}{dt} \\\\c\frac{dc}{dt} = b\frac{db}{dt} ----(*) \\\\when;\\\\the\ hypotenuse \ c = 15 \ ft\\\\the \ the \ the \ height, h = 12 \ ft\\\\the \ base, b \ becomes ;\\\\b^2 = c^2 -h^2\\\\b^2 = 15^2 - 12^2\\\\b^2 = 81\\\\b = \sqrt{81} \\\\b = 9 \ ft\\\\\\from \ the \ equation (*) \ above;\\\\[/tex]

[tex]c\frac{dc}{dt} = b \frac{db}{dt} \\\\dc/dt = 4 \ ft/s, \ \ c = 15 \ ft, \ \ b = 9 \ ft\\\\15 (4) = 9\frac{db}{dt} \\\\60 = 9 \frac{db}{dt} \\\\\frac{db}{dt} = \frac{60}{9} = 6.67 \ ft/s[/tex]

Therefore, the speed of the boat is 6.67 ft/s

Answer: A)  4√2 units

Step-by-step explanation:

Use the distance formula to find the distance(d) between Point D and Point C:

[tex]d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}[/tex]

[tex]d=\sqrt{(8-4)^{2}+(2-(-2))^{2}}=\sqrt{(4)^{2}+(4)^{2}}=\sqrt{16+16} =\sqrt{32} =4\sqrt{2}[/tex]

Answer:

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

Step-by-step explanation:

In order for two lines to be parallel they must have the same slope. In other words the m constant in the line equation needs to match

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

This means for the equation we're trying to find, we already know m. It's just -1/2 since that's the slope of the line it needs to be parallel to.

Next, let's find the constant b. We know the slope, and we know it goes through points (-4, 1), so let's plug this into our equation

[tex]y = -\frac{1}{2}x + b\\1 = - \frac{1}{2}\times{-4} + b\\1 = 2 + b\\b = -1[/tex]

Now that we have both constants, we know the equation of the line.

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

To convince yourself this is correct, let's plot these two lines.

Given:

The function is:

[tex]g(x)=f(x+2)-3[/tex]

To find:

The statement that best compares the graph of g(x) with the graph of f(x).

Solution:

The transformation is defined as

[tex]g(x)=f(x+a)+b[/tex]                .... (i)

Where, a is horizontal shift and b is vertical shift.

If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.

If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.

We have,

[tex]g(x)=f(x+2)-3[/tex]               ...(ii)

On comparing (i) and (ii), we get

[tex]a=2[/tex]

[tex]b=-3[/tex]

Therefore, the graph of g(x) is shifted 2 units left and 3 units down.

Hence, the correct option is C.

Answer:

so 3 people both read their books and watched films.

Step-by-step explanation:

n(U) = 50

n(A) = 18 ( read books)

n(B) = 28 ( watched films)

n(A U B) with a line at the top = 7

so

Finding n(AUB)

n( A U B) with a line at the top = n(A) + n(B) - n( A n B)

7 = 50-n(A U B)

or, n( A U B) = 50 - 7

so, n(A U B) = 43

Then

n( A U B) = n(A)+n(B)-n(A n B)

43 = 18 + 28 - n( A n B)

or, 43 = 46 - n(A n B)

or, n(A n B) = 46 - 43

so, n(A n B) = 3

Answer:

Please what is the first value there?

x is the same as 1x or 1

√5 = 2.2360679775

(2)1/2 is the same as 5/2 or 2.5

√7 = 2.64575131106

√11 = 3.31662479036

3.5

least to greatest:

x < √5 < (2)1/2 < √7 < √11 < 3.5

Answer:

I say Its letter d

Step-by-step explanation:

I hope this help

Answer:

More nurses with a baccalaureate degree is estimated to pass the exam but this was not a significant difference.

Step-by-step explanation:

Answer:

D. [tex]3x\sqrt{2x}[/tex]

Step-by-step explanation:

The problem gives on the following equation:

[tex]\sqrt{32x^3}+-\sqrt{16x^3}+4\sqrt{x^3}-2\sqrt{x^3}[/tex]

Alongside the information that ([tex]x\geq0[/tex]).

One must bear in mind that the operation ([tex]\sqrt[/tex]) indicates that one has to find the number that when multiplied by itself will yield the number underneath the radical. The easiest way to find such a number is to factor the term underneath the radical. Rewrite the terms under the radical as the product of prime numbers,

[tex]\sqrt{2*2*2*2*2*x*x*x}-\sqrt{2*2*2*2*x*x*x}+4\sqrt{x*x*x}-\sqrt{2*x*x*x}[/tex]

Now remove the duplicate factors from underneath the radical,

[tex]2*2*x\sqrt{2x}-2*2*x\sqrt{x}+4x\sqrt{x}-2x\sqrt{x}[/tex]

Simplify,

[tex]4x\sqrt{2x}-4x\sqrt{x}+4x\sqrt{x}-x\sqrt{2x}[/tex]

[tex]3x\sqrt{2x}[/tex]

Answer:

first: there is a problem in the question in de mentioned quantity u mentioned 10k instead of (10kg).

Step-by-step explanation:

add all your 1uantity afteru divide by 8

Answer:

one fertilizer bag from weight of two kilograms

Step-by-step explanation:

Grams of fertilizer needed = Length in meters * Width in meters * 25

                                            = 8 * 8 * 25

                                            = 1600 grams

Kilograms of fertilizer needed = 1600 / 1000

                                                 = 1.6 kilograms

Therefore, gardener can order 1 fertilizer bag with weight of 2kilpgrams.

9514 1404 393

Answer:

Step-by-step explanation:

Let s represent the number of sodas sold. Then the number of hot dogs sold is (s-50) and the total is ...

  s +(s -50) = 218

  2s = 268 . . . . . . . . . add 50

  s = 134 . . . . . . . divide by 2

134 sodas were sold; 84 hot dogs were sold.

Answer:

81

Step-by-step explanation:

180-41-58=81

angles in a triangle add up to 180 :)

Answer:

9.42 meters

Step-by-step explanation:

diameter = 8 m

radius = 4 m

Length of arc = radius * central angle in radians

= 4 * 3[tex]\pi[/tex] / 4

= 12[tex]\pi[/tex] / 4

= 3[tex]\pi[/tex]

= 66 / 7

= 9.42 m

The length of the arc of a circle of diameter 8 meters subtended by a central angle of 3pi/4 radians is 9.42 meters.

The arc period of a circle can be calculated with the radius and relevant perspective using the arc period method.

expalination:

⇒angle= arc/radius

= 3pi/4 radians

diameter = 8 m

radius = 4 m

Length of arc = radius * central angle in radians

⇒4 * 3 / 4

⇒12 / 4 = 3

⇒66 / 7

⇒9.42 m

Hence the arc of a circle is 9.42 m.

Learn more about arc of a circle here:-https://brainly.com/question/2005046

#SPJ2

Step-by-step explanation:

[tex](4x^2-x+6)-(3x^2+5x-8)=4x^2-x+6-3x^2-5x+8[/tex]

By simplifying the right side of the equation, we come up with

[tex]x^2+6x-14[/tex], or D

Answer:

7 / 17 ;

10 / 17 ;

5 / 17

Step-by-step explanation:

Guests :

Mother = 1

Aunts = 3

Uncles = 3

Brothers = 4

Male cousin = 1

Female cousin = 5

_________________

Total guests = 17

Since each of the guests have an equal probability of arrival :

Probability that first guest to arrive :

Brother or uncle :

Number of brothers =4

Number of uncles = 3

P(brother or uncle) = required outcome / Total possible outcomes

Required outcome (number of brothers + uncles) = (4 + 3) = 7

Total possible outcomes = total guests = 17

P(brother or uncle) = 7 / 17

2.)

P(brother or cousin) :

Required outcome = (number of brothers + cousins) = (4 + 1 + 5) = 10

Total possible outcomes = total guests = 17

P(brother or cousin) = 10/17

3.)

P(brother or mother) ;

Required outcome = (number of brothers + mother) = (4+1) = 5

Total possible outcomes = total guests = 17

P(brother or mother) = required outcome / Total possible outcomes = 5 / 17

Answer:

C. rotation 180º about the origin

Step-by-step explanation:

Given

Quadrilaterals GWVY and G'W'V'Y'

Required

Describe the transformation rule

Pick points Y and Y'

[tex]Y = (5,-4)[/tex]

[tex]Y' = (-5,4)[/tex]

The above obeys the following rule:

[tex](x,y) \to (-x,-y)[/tex]

When a point is rotated by 180 degrees, the rule is:

[tex](x,y) \to (-x,-y)[/tex]

Hence, (c) is correct

No question?

Why not add one!

Answer:

61.42 units

Step-by-step explanation:

Perimeter = sum of all sides of surrounding the figure = circumference of a circle + 2(length of the rectangle)

Note: two semicircles = 1 full circle

Perimeter = πd + 2(L)

Where,

Diameter of the circle (d) = 10

Length of rectangle (L) = 15

Plug in the values

Perimeter = π*10 + 2(15)

Perimeter = 10π + 30

≈ 61.42 units (approximated to nearest tenths)

Answer:

As x increases, the rate of change of g exceeds the rate of change of f.  

Step-by-step explanation:

Given

[tex]f(x) = 90x^2 + 180x + 92[/tex]

[tex]\begin{array}{ccccccc}x & {0} & {1} & {2} & {3} & {4} & {5} & f(x) & {92} & {362} & {812} & {1442} & {2252} & {3242} \ \end{array}[/tex]

[tex]g(x) = 6^x[/tex]

[tex]\begin{array}{ccccccc}x & {0} & {1} & {2} & {3} & {4} & {5} & g(x) & {1} & {6} & {36} & {216} & {1296} & {7776} \ \end{array}[/tex]

Required

Which of the options is true?

A. At [tex]x \approx 4.39[/tex], f(x) has the same rate of change as g(x)

Rate of change is calculated as:

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

For f(x)

[tex]f(x) = 90x^2 + 180x + 92[/tex]

[tex]f(4.39) = 90*4.39^2 + 180*4.39 + 92 = 2616.689[/tex]

So, the rate of change is:

[tex]m = \frac{2616.689}{4.39} = 596.06[/tex]

For g(x)

[tex]g(x) = 6^x[/tex]

[tex]g(4.39) = 6^{4.39} = 2606.66[/tex]

So, the rate of change is:

[tex]m = \frac{2606.66}{4.39} = 593.77[/tex]

The rate of change of both functions are not equal at x = 4.39. Hence, (a) is false.

B. Rate of change of g(x) is greater than f(x) with increment in x

Using the formula in (a), we have:

[tex]\begin{array}{ccccccc}x & {0} & {1} & {2} & {3} & {4} & {5} & f(x) & {92} & {362} & {812} & {1442} & {2252} & {3242} & m &\infty & 362 & 406 & 480 & 563 &648.4\ \end{array}[/tex]

[tex]\begin{array}{ccccccc}x & {0} & {1} & {2} & {3} & {4} & {5} & g(x) & {1} & {6} & {36} & {216} & {1296} & {7776} & m & \infty & 6 & 18 & 72 & 324 & 1555 \ \end{array}[/tex]

From x = 1 to 4, the rate of change of f is greater than the rate of g.

However, from x = 5, the rate of change of g is greater than the rate of f.

This means that (b) is true.

The above table further shows that (c) and (d) are false.

Answer:

Step-by-step explanation:

C

Answer:

C

Step-by-step explanation:

Answer:

a) 675 b) 1050 c) 675 d)455 e) 120

Step-by-step explanation:

Answer:a, 0,293

Step-by-step explanatThe number of ways to get any 3 students from 25 given students is :

25C3 = 2300

Let A be the event that has 1 Male and 2 Female

15C1*10C2=675

The probability of having 1 Male and 2 Female is

675/2300=0.293 ion:

Answer:

sorry in dont know the ans

Answer:

c = 3.00 + .50b

Step-by-step explanation:

The cost is the flat fee plus the cost per book times the number of books

c = 3.00 + .50b

Answer:

CAD = 25°

Step-by-step explanation:

The angles are shown to be equal in the figure so BAC = CAD.

Answer:

"Type II error" is the right answer.

Step-by-step explanation:

Thus the above is the right answer.

Answer:

5/12

Step-by-step explanation:

5/12 , 2/3, 5/6,3/4

Get a common denominator of 12

5/12, 2/3 *4/4, 5/6*2/2, 3/4 *3/3

5/12, 8/12, 10/12, 9/12

The numerator closest to 0 is the fraction closest to 0

5/12

Answer:

15.924 feets

Step-by-step explanation:

The height I'd the flagpole can be obtained using trigonometry ;

Solution triangle has been attached below,

The height, h of flagpole

Tan θ = opposite / Adjacent = h / 12

Tan 53 = h / 12

h = 12 * tan 53

h = 15.924