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Answer:

y=30x+55

Step-by-step explanation:

$55 is constant because for each trip he will take $55 dollars so that gives you your y-intercept and m=$30 and x is the amount of hours worked. every time x increases he will be making more money

Answer:

which didi you pick , but if you pitted the sixeth one is correct

Step-by-step explanation:

because I hope this helps

Answer:

20-12=8 the answer is 8 I did the math

Answer:

8 is right

Step-by-step explanation:

because 20-12=8

SOLUTION:

=) x² - 15² = 121

=) x² - 225 = 121

=) x² = 121 + 225

=) x = root 346

=) x = 18.6

Answer:

\(x = 26\) , \(x = 4\)

solving steps:

\((x - 15)^2 = 121\)

\(\sqrt{(x - 15)^2} = \pm \sqrt{121}\)

\(x- 15= \pm 11\)

\(x = 11 + 15\) , \(x = -11 +15\)

\(x = 26\) , \(x = 4\)

Answer:

9.8

Step-by-step explanation:

The endpoints of the longer diagonal have coordinates (-3, 1) and (6, 5).

To find the length of the longer diagonal, we use the distance formula and the coordinates of the endpoints.

\( d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \)

\( d = \sqrt{(-3 - 6)^2 + (1 - 5)^2} \)

\( d = \sqrt{(-9)^2 + (-4)^2} \)

\( d = \sqrt{81 + 16} \)

\( d = \sqrt{97} \)

\( d = 9.8 \)

Answer:

x = 400

Step-by-step explanation:

Let 15% of x is equal to 60.

We can find it as follows :

\(15\%\ of\ x=60\\\\\dfrac{15x}{100}=60\\\\x=\dfrac{60\times 100}{15}\\\\x=400\)

So, 15% of 400 is equal to 60.

Answer:

C and D

Step-by-step explanation:

Let's solve for x to see what range the answer has to be in:

-2x - 3 ≤ -1

-2x ≤ 2

x ≥ -1

So the value of x must be larger than or equal to -1. So the answers would be 1 and 0

Answer:

- 5/6

- 1/3

Step-by-step explanation:

Answer:

A and F

Step-by-step explanation:

5/6 and 1/3

Using the information in the given diagram, the value of the missing angle is: m∠1 = 75°

The transverse line theorem states that If two parallel lines are cut by a transversal, then corresponding angles are congruent. Two lines cut by a transversal are parallel IF AND ONLY IF corresponding angles are congruent.

Now, when we draw a horizontal line parallel to lines a and b and directly cutting across the vertex of angle 1, we can see that angle 1 will be composed of two angles.

Now, for the transverse line theorem we can say that:

Angle 1 will be composed of two angles namely:

48 degrees and (180 - 153) degrees.

Thus:

m∠1 = 48° + 27°

m∠1 = 75°

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Answer:

f(x) = x³ - 4x + 6

f'(x) = 3x² - 4

a) f'(2) = 3(2²) - 4 = 12 - 4 = 8

6 = 8(2) + b

6 = 16 + b

b = -10

y = 8x - 10

b) 3x² - 4 = 0

3x² = 4, so x = ±2/√3 = ±(2/3)√3

= ±1.1547

f(-(2/3)√3) = 9.0792

f((2/3)√3) = 2.9208

c) 3x² - 4 = 8

3x² = 12

x² = 4, so x = ±2

f(-2) = (-2)³ - 4(-2) + 6 = -8 + 8 + 6 = 6

6 = -2(8) + b

6 = -16 + b

b = 22

y = 8x + 22

f(2) = 6

y = 8x - 10

The equation perpendicular to the tangent is y = -1/8x + 25/4

-The smallest slope on the curve is 2.92

The curve has the smallest slope at the point (1.15, 2.92)

The equations at tangent points are y = 8x + 16 and  y = 8x - 16

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

y = x³ - 4x + 6

Differentiate

So, we have

f'(x) = 3x² - 4

The point is (2, 6)

So, we have

f'(2) = 3(2)² - 4

f'(2) = 8

The slope of the perpendicular line is

Slope = -1/8

So, we have

y = -1/8(x - 2) + 6

y = -1/8x + 25/4

We have

f'(x) = 3x² - 4

Set to 0

3x² - 4 = 0

Solve for x

x = √[4/3]

x = 1.15

So, we have

Smallest slope = (√[4/3])³ - 4(√[4/3]) + 6

Smallest slope = 2.92

So, the smallest slope is 2.92 at (1.15, 2.92)

Here, we set f'(x) to 8

3x² - 4 = 8

Solve for x

x = ±2

Calculate y at x = ±2

y = (-2)³ - 4(-2) + 6 = 6: (-2, 0)

y = (2)³ - 4(2) + 6 = 6: (2, 0)

The equations at these points are

y = 8x + 16

y = 8x - 16

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Answer:

42

Step-by-step explanation:

Rectangle: A = 6 x 5 = 30

Triangle: A = 1/2(6 x 4) = 12

Area of figure: 30 + 12 = 42

Answer:

(-2)

Step-by-step explanation:

just do -2 x-3 x than + 13 and than you will get - 2

When writing a proof, you should construct the first statement by copying the “prove” statement(s) from the original problem. The Option B is correct.

When constructing the first statement in a proof, it is important to begin with copying the “prove” statement(s) from the original problem. This involves writing the next statement based on the given or previously proven statements.

It is not helpful to write a justification for the first statement in the right column without considering its logical connection to the problem. By beginning with a logically connected statement, the proof can proceed in a clear and organized manner which leads to a valid conclusion.

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The area of a circle with a diameter of radius 14 inches is given as follows:

A = 153.86 inches².

The area of a circle of radius r is given by π multiplied by the radius squared, as follows:

A = πr².

The radius, representing the distance between the center and a point on the circumference of the circle, has the measure defined as half the diameter, hence it is given as follows:

r = 7 inches.

Hence the area of the circle with radius of 7 inches is given as follows:

A = 3.19 x 7²

A = 153.86 inches².

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Here is the two column proof:

    Statement                                        Reason                                              

Answer: The trip should take 3.5 hours.

Step-by-step explanation: To find the time, divide the distance by the rate. In this case, 210/60 = 3.5.

Answer:

3.5 hours or specifically, 3 hours and 30 minutes

Step-by-step explanation:

We know that the car can be driven 60 miles per hour. The goal is 210 miles. If you divide 210 miles by 60, the result is 3.5. The whole number 3 in 3.5 will represent the hours taken which means 3 hours. The 0.5 will also represent the minutes. 0.5 = 1/2, 1/2 of an hour = 30 minutes.

Subtracting the initial amount of water from the amount used, the remaining amount of water is given by:

1.) 3.075 gallons.

To find the remaining amount of water in the barrel, we have to subtract the initial amount by the amount used.

We have that:

Hence the remaining amount is:

15 - 11.925 = 3.075 gallons.

Which means that option 1 is correct.

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Answer: 3.075 gallons

Step-by-step explanation:

Answer:

The worst-case probability is 0.05

Step-by-step explanation:

The given significance level (\(\alpha\)) = 0.05

since Probability of a type I error is \(\alpha\)

∴ P (type I error) = 0.05

0.05 will be the worst-case probability of a type I error in at least one of the tests.

Answer:

the answer is d i believe.

Answer:

The answer is D I took the test the other person is right!

Step-by-step explanation:

The total path length covered in 5 second will be 69.45 meter.

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

Given is a train going at 70 km/h must reduce its speed to 30 km/h when passing over a bridge. It performs the operation in five seconds.

Using the first equation of motion -

v = u + at

(30 x 5/18) = (70 x 5/18) + 5a

(30 x 5/18) - (70 x 5/18)  = 5a

- (5/18) x 40 = 5a

- (200/18) = 5a

a = - (40/18)

a = - 2.22 m/s²

S = 19.44 x 5 + 0.5 x (- 2.22) x 25

S = 97.2 - 27.75

S = 69.45 meter

Therefore, the total path length covered in 5 second will be 69.45 meter.

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[Question translation in english -

A train going at 70 km/h must reduce its speed to 30 km/h when passing over a bridge if it performs the operation in five seconds what total path has been traveled in that time.]

A possible vector function that represents the curve of intersection of the two surfaces is r(t) = (5 cos(t), 5 sin(t), 5 cos(t) sin(t))

The cylinder x^2 + y^2 = 25 represents the set of points in 3D space where the distance from the origin to the point (x, y, z) is equal to 5. The surface z = xy represents the set of points in 3D space where the height of the point (x, y, z) is equal to its x-y coordinate.

The curve of intersection of the two surfaces is given by the set of points in 3D space that are simultaneously on the cylinder and on the surface z = xy. This means that for any point on the curve of intersection, the distance from the origin to the point must be equal to 5, and the height of the point must be equal to its x-y coordinate.

We can find a vector function that represents the curve of intersection by parameterising the points on the curve in terms of a scalar parameter t. For example, a possible parameterization of the curve of intersection is:

r(t) = (5 cos(t), 5 sin(t), 5 cos(t) sin(t))

where t is a scalar parameter that ranges over all values between 0 and 2π. The values of x, y, and z are given by 5 cos(t), 5 sin(t), and 5 cos(t) sin(t), respectively, and represent a point on the curve of intersection for each value of t.

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Answer: 5 inspections in 4 hours, because if its 8 hours it would be 10 inspections

Step-by-step explanation:

Answer:

1.25

Step-by-step explanation:

10 ÷ 8 = 1.25

The highest point for the quadratic function for the height of the object, h(t) = -16·t² + 224·t + 816, indicates that the interval over which the height of the object is increasing is; (-∞, 7]

The shape of the graph of a quadratic function is a parabola.

The function for the height of the object in question 3 is; h(t) = -16·t² + 224·t + 816

Where;

t = The time in seconds

The height of the object is increasing in the interval to the left of the highest point, which can be found as follows;

The x-coordinate of the highest point of the quadratic function, f(x) = a·x² + b·x + c is; x = -b/(2·a)

Therefore, the x-coordinates of the highest point of the object is; -224/(2 × (-16)) = 7

Therefore, the height of the object is increasing in the interval; -∞ < t ≤ 7

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Answer:

91% of the time the auto will get less than 26 mpg

Step-by-step explanation:

Think of (or draw) the standard normal curve.  Mark the mean (22.0).  Then one standard deviation above the mean would be 22.0 + 3.0, or 25.0.  Two would be 22.0 + 2(3.0), or 28.0.  Finallyl, draw a vertical line at 26.0.

Our task is to determine the area under the curve to the left of 26.0.

Using a basic calculator with built-in statistical functions, we find this area as follows:

normcdf(-100, 26.0, 22.0, 3.0) = 0.9088, which is the desired probability:  91% of the time the auto will get less than 26 mpg.

Answer:

800 fish per day is the initial growth rate of the fish population

Step-by-step explanation:

The growth rate is the derivative of the population function with respect to time (t). Therefore, we need to calculate the derivative of P(t) and evaluate it at t=0:

\(\frac{d\,P(t)}{dt} =800-2\,t\\\)

which evaluated at t = 0 becomes:

\(800-2\,(0)=800\)

To establish trust with Martina, the nurse should show respect, use non-verbal communication, incorporate play, involve the parent, and individualize the approach.

To establish a trusting relationship with Martina, the nurse can employ several approaches:

Respect and empathy: The nurse should approach Martina with genuine respect and empathy, recognizing her unique needs and individuality. This can be conveyed through a calm and patient demeanor.

Non-verbal communication: Since Martina may not be responsive to verbal cues, the nurse can utilize non-verbal communication to establish connection and trust. This can include maintaining eye contact, using gentle touch, and respecting Martina's personal space.

Play and familiar objects: Given Martina's engagement with the blue stuffed dog, the nurse can incorporate play into their interactions. Bringing familiar objects or toys that Martina finds comforting can help create a sense of familiarity and security.

Parental involvement: Involving Martina's mother in the care process can be beneficial. The nurse can communicate with the mother, seek her input, and involve her in the administration of medications. This helps build trust not only with Martina but also with her caregiver.

Individualized approach: Recognizing Martina's autistic disorder, the nurse should tailor their approach to her specific needs. Understanding her sensory sensitivities and preferences can help create a safe and comfortable environment.

By implementing these strategies, the nurse can foster trust and a positive therapeutic relationship with Martina, promoting her overall well-being and care.

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Complete Question:

What approach would help the nurse establish a trusting relationship with Martina, a 3-year-old with bronchitis and autistic disorder, who is intensely occupied with a blue stuffed dog and does not seem responsive to the nurse's presence in the room, while the mother is also present?

9514 1404 393

Answer:

  a) (-7, -2)

  b) 15 square units

Step-by-step explanation:

The slope at x is given by the derivative:

  y' = 3x^2 -10x +3

The slope of the normal is the negative reciprocal of this.

at a(4, -3) the slope of the normal is ...

  ma = -1/y' = -1/((3(4) -10)(4) +3) = -1/11

Then the point-slope equation of the line is ...

  y +3 = -1/11(x -4)

__

at b(1, 0) the slope of the normal is ...

  mb = -1/y' = -1/((3(1) -10)(1) +3) = -1/-4 = 1/4

Then the point-slope equation of the line is ...

  y = 1/4(x -1)

Solving these two equations will give the coordinates of point C.

  (1/4(x -1) +3) = -1/11(x -4)

  11(x -1) +132 = -4(x -4)

  15x = -105

  x = -7

  y = 1/4(-7 -1) = -2

The coordinates of point C are (-7, -2).

__

There are a few ways to find the area of a triangle that is specified by its vertex coordinates. I like the method that involves finding the determinants of pairs of coordinates around the figure. The area is half the absolute value of their sum. This can be made a little easier by listing the coordinates, repeating the first pair:

  a(4, -3)

  b(1, 0)

  c(-7, -2)

  a(4, -3)

Working down the list, the area will be ...

  A = 1/2|(4(0) -1(-3)) +(1(-2) -(-7)(0)) +((-7)(-3) -4(-2))| = 1/2|(0 +3) +(-2 +0) +(21 +8)|

  A = 1/2|30| = 15 . . . . square units

_____

The attached graph finds the intersection of the normals quite easily. The attached spreadsheet does the area calculation from the triangle coordinates. These tools are very handy for problems like this.

Answer:

Step-by-step explanation:

\(Curve:\ y=x^3-5x^2+3x+1\\\\y'(x)=3x^2-10x+3\\A=(4,-3)\\B=(1,0)\\y'(4)=3*4^2-10*4+3=11\\slope\ of\ the\ normal\ in \ A: -\frac{1}{11} \\Equation\ normal\ in \ A:\\y+3= -\frac{1}{11}*(x-4)\ or\ -x-11*y=29\ (1)\\\\y'(1)=3*1^2-10*1+3=-4\\slope\ of\ the\ normal\ in \ B: \frac{1}{4} \\Equation\ normal\ in \ B:\\y-0=\frac{1}{4} (x-1)\ or\ -x+4y=-1\ (2)\\\\Coordinates\ of\ C:\\(1)-(2) ==> y=-2\\(2) ==> x=-7\\\\C=(-7,-2)\\\)

Area of the  triangle ABC:

\(S=\dfrac{|CB|*|CA|*sin(\widehat{ACB})}{2}\\A=(4,-3),B=(1,0),C=(-7,-2)\\AB^2=(4-1)^2+(-3-0)^2=9+9=18\\AC^2=122\\BC^2=68\\\\Using\ Al'Kashi\ theorem:\\AB^2=CB^2+CA^2-2|CB||CA|*cos(\widehat{ACB})\\\\cos(\widehat{ACB})=\dfrac{68+122-18}{2\sqrt{68*122} } =\dfrac{86}{\sqrt{68*122} } \\\\sin^2(\widehat{ACB})=1-cos^2(\widehat{ACB})=1-\dfrac{86^2}{68*122} \\\\S=\dfrac{\sqrt{68} *\sqrt{122}*\sqrt{\dfrac{900}{68*122} }}{2}=15\\\)

Answer:

15*w+1.5(15)*y

15w+22.5y

Week=7 days.

7(15w+22.5y)

105y+157.5y hours

Step-by-step explanation:

Answer:

5 ;7

explantion:

-1+2=1

1+2=3

3+2=5

5+2=7

the pattern is +2