Order the numbers 0.64,
2/3 , 65%, and
7/10 from least to greatest. (3 points)

Final Answer:

The equations of the tangents to the curve[tex]\(x = 9t^2 + 6, y = 6t^3 + 3\)[/tex]that pass through the point (15, 9) are [tex]\(y = 2x - 21\)[/tex] and[tex]\(y = -2x + 51\).[/tex]

Explanation:

To find the equations of the tangents, we first substitute (x = 15) and (y = 9) into the parametric equations[tex]\(x = 9t^2 + 6\)[/tex] and [tex]\(y = 6t^3 + 3\)[/tex]. Solving for (t), we get (t = 1) and (t = -1). These values of (t) correspond to the points of tangency.

Next, we find the slopes of the tangents by taking the derivatives of (x) and (y) with respect to (t), resulting in (dx/dt = 18t) and (dy/dt = 18[tex]t^2[/tex]). At (t = 1), the slope is (18), and at (t = -1), the slope is (-18).

Using the point-slope form of a linear equation [tex]\(y - y_1 = m(x - x_1)\)[/tex], where (m) is the slope and [tex]\((x_1, y_1)\)[/tex] is the point of tangency, we obtain the equations of the tangents: (y - 9 = 18(x - 15)) and (y - 9 = -18(x - 15)). Simplifying these expressions yields (y = 2x - 21) and (y = -2x + 51).

Answer:Divide 24,000 by 4 = 6,000 which = 1/4. so 3/4 = 18,000.  

1 hour = 60 minutes  

40 gallons X 60 minutes = 2,400 gallons per hour.  

18,000/2,400 = 7.5 hour to fill 3/4  

7.5 hours = 450 minutes.

Answer:

600 min  

Step-by-step explanation:

It takes 1 min per 40 gal

Time = 24 000  × 1/40

Time = 600 min

Answer:

EC = 5

GC = 7

Step-by-step explanation:

A bisector divides a segment into two equal parts. Since BE is 5 and BE = EC, EC is also 5.

All the perpendicular bisectors meet at point G. Therefore all the segments going from any vertex to point G are congruent. Since BG is 7, GC then will be 7 aswell. Hope this helped!

Answer:

90 meters/second = rate

Step-by-step explanation:

To find out how fast he ran, we use the equation

distance = rate * time

We know the distance = 270 meters

and we know the time = 3 seconds

Substitute these values in

270 meters = rate * 3 seconds

Divide both sides by 3 seconds

270 meters  / 3 seconds = rate

90 meters/second = rate

Answer:

Step-by-step explanation:

you want to find his speed  so your going to divide the distance he ran by the amount of time which is  270/3 and the answer is 90

Answer:

Correct answer is option (B)

Step-by-step explanation:

We have been given that area of Maxine's living room is 88 square feet. Further, we are given that length of the room is 3 feet longer than the width.

Let us assume that x be the width of the room, therefore, length of the room will be [tex]x+3[/tex].

We know that area of a rectangle can be found by multiply the measures of length and width, therefore, we can set:

[tex]\text{Area} = \text{length}\times \text{width}\\\text{Area} = (x+3)\times x\\\text{Area} = x^{2}+3x\\[/tex]

Now, since we are given that area is 88 square feet, therefore, we can set this expression for area equal to 88 to get the desired equation:

[tex]x^{2}+3x=88[/tex]

Therefore, correct answer is option (B)

Answer:

Motorcycle will complete the 540 mile trip in 11.25 hr.

The car will complete it 2.25 hours less, or 9 hours.

The speed of the car therefore is 540/9 = 60 mph.

60t + 48t = 540

108t = 540

t = 5

So they will meet in 5 hours, after which time the motorcycle will have traveled 48*5 = 240 miles

and the car will have traveled 60*5 = 300 miles.

Hope this help

Step-by-step explanation:

Answer:

? = 113

Step-by-step explanation:

The angles are alternate interior angles.  Alternate interior angles are equal if the lines are parallel.  Since the lines are parallel, the angles are equal.

? = 113

Answer:

6i

Step-by-step explanation:

[tex]\sqrt{-36} = \sqrt{-1}\sqrt{36}\\= 6i[/tex]

The square root of a negative 1 is I, so you just take out the negative, replace it with I, then solve the square root like normal

[tex]i=\sqrt{-1}\\\\-36=(-1)(36)\\\\\sqrt{-36}=\sqrt{(-1)(36)}=\sqrt{-1}\cdot\sqrt{36}=i\cdot6=6i\\\\Used\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\Answer:\ \boxed{\sqrt{-36}=6i}[/tex]

Answer:

0

Step-by-step explanation:

[tex]f(x)=\sqrt{x}+12  and g(x)=2\sqrt{x}[/tex]

We need to find (f-g)(144)

(f-g)(144) = f(144) - g(144)

[tex]f(x)=\sqrt{x}+12[/tex]

[tex]f(144)=\sqrt{144}+12=12+12= 24[/tex]

[tex]g(x)=2\sqrt{x}[/tex]

[tex]g(144)=2\sqrt{144}=2(12)= 24[/tex]

(f-g)(144) = f(144) - g(144)= 24-24=0

Answer:

o is correct answer

Step-by-step explanation:

f(x)=[tex]\sqrt{x}[/tex]+12

g(x)=2[tex]\sqrt{x}[/tex]

we will find

(f-g)x=[tex]\sqrt{x}[/tex]+12-2[tex]\sqrt{x}[/tex]

(f-g)x=-[tex]\sqrt{x}[/tex]+12

now we  will find

(f-g)(144)

put x=144

(f-g)(144)=- [tex]\sqrt{144}[/tex]+12

(f-g)(144)=-12+12=0

hence proved

Answer:

Emily Ruth's annual premium is $1058.50

Step-by-step explanation:

Emily Ruth is a female of 27 years age purchasing 20 year endowment insurance with face value $25000.

From the given table,

For females, the age of a male 3 years younger should be used.

So, we have to check for 24 year male for 20 year endowment.

It is 42.34 for every $1000 face value.

For a face value of $25000,

it is 25 * 42.34 = $1058.50

∴ Emily Ruth's annual premium is $1058.50

Answer:

The cell phone took 4.7 seconds to reach the ground.

Step-by-step explanation:

A hang glider dropped his cell phone from a height of 350 feet:

Initial velocity: Vo = 0 ft/s

Height: h = 350 feet = 350 ft

Time to reach the ground: t=?

Gravity's acceleration: g = 32 ft/s^2

h = Vo t + g t^2 / 2

Replacing the known values in the equation above:

350 ft = (0 ft/s) t + (32 ft/s^2) t^2 /2

350 ft = 0 + (16 ft/s^2) t^2

350 ft = (16 ft/s^2) t^2

Solving for t^2: Dividing both sides of the equation by 16 ft/s^2:

(350 ft) / (16 ft/s^2) = (16 ft/s^2) t^2 / (16 ft/s^2)

21.875 s^2 = t^2

Solving for t: Square root both sides of the equation:

sqrt(21.875 s^2) = sqrt(t^2)

4.677071733 s = t

t = 4.677071733 s

Rounding to the nearest tenth:

t = 4.7 s

The cell phone takes about 4.7 seconds to reach the ground

Acceleration is rate of change of velocity.

[tex]\large {\boxed {a = \frac{v - u}{t} } }[/tex]

[tex]\large {\boxed {d = \frac{v + u}{2}~t } }[/tex]

a = acceleration ( m/s² )

v = final velocity ( m/s )

u = initial velocity ( m/s )

t = time taken ( s )

d = distance ( m )

Let us now tackle the problem!

Given:

Height = h = 350 feet

Gravitational Acceleration = g = 32.2 feet/s²

Initial Velocity = u = 0 m/s

Unknown:

time taken to reach the ground = t = ?

Solution:

This problem is about Free Fall.

When an object experiences free fall, the acceleration experienced by the object is the same as the acceleration due to gravity which is equal to 9.8 m/s² or 32.2 feet/s²

[tex]h = ut + \frac{1}{2}gt^2[/tex]

[tex]350 = 0t + \frac{1}{2}(32.2)t^2[/tex]

[tex]350 = 0 + 16.1t^2[/tex]

[tex]t^2 = 350 \div 16.1[/tex]

[tex]t \approx 4.7 ~ \text{seconds}[/tex]

Grade: High School

Subject: Physics

Chapter: Kinematics

Keywords: Velocity , Driver , Car , Deceleration , Acceleration , Obstacle

Answer:

5

Step-by-step explanation:

because 5*5=25 and you have 1 remainder

Answer: 457.65

Step-by-step explanation:

40,731 / 89 = 457.65

Have a good day :)

The answer to the division of 89 by 40,731 is approximately 0.00218468. This number is so small because you are dividing a small number by a significantly larger one.

The question is asking for the division of 89 by 40,731. In this case, you have to divide the two numbers. Using a calculator, 89 divided into 40,731 yields a very small number, approximately 0.00218468. This is a very small number because you are dividing a smaller number by a significantly larger one.

To better conceptualize this, consider making a pie with 40,731 pieces, and you only took 89 pieces. The proportion you took (or the answer to 89 divided by 40,731) would be very small, just like the number 0.00218468.

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Answer:

Step-by-step explanation:

The ratio of the height of the building to the number of floors is 13 feet/floor, i.e., each floor of the building is approximately 13 feet tall.

Given the information that a single building with 8 floors measures 104 feet in height, we can calculate the ratio of the height of the building to the number of floors as follows:

104 feet / 8 floors = 13 feet/floor

This ratio or unit rate represents the height corresponding to one floor. In plain terms, this means each floor of the building is approximately 13 feet tall.

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Answer:

13 feet/floor

Step-by-step explanation:

Answer:

0.2655

Step-by-step explanation:

Multiply 8.85 by 3. Then Divide it by 100.

You will get the dividend of 0.2655.

Answer:

3% of 8.85 = 0.2655

Step-by-step explanation:

3% or 0.03

0.03 x 8.85 = 0.2655

hope this helped if so please mark brainlest

The system of linear equations x - y = 7 and 0.5x + y = 5 can be solved by first rearranging into y = mx + b form and graphing. Intersecting point of the two lines is the solution. In such equations, y is the dependent variable, relying on x, the independent variable.

You've been asked to solve the system of linear equations by graphing. The pair of equations you're given are: x - y = 7, and 0.5x + y = 5. Let's start by expressing these equations in the form y = b + mx.

For x - y = 7, you can rearrange it as y = x - 7 where the slope (m) is 1 and the y-intercept (b) is -7.

For 0.5x + y = 5, you can rearrange it as y = -0.5x + 5 where the slope (m) is -0.5 and the y-intercept (b) is 5.

Now you must graph these two lines on the same graph. Where these two lines intersect, that is the solution of the system of equations.

When graphing these lines, start at the y-intercept (b) and use the slope (m) to find additional points. The slope is a ratio representing the vertical change in y for each unit of horizontal change in x.

Expressing Equations Graphically in this way can help visually solve the system of equations.

Also note that, in each equation, y is the dependent variable since its value relies on the value of x, the independent variable.

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Answer:

The solution is (-5,4).

Step-by-step explanation:

We are given the equation, |x+1|=|-x-9|

Now, |x+1| = [tex]\left\{\begin{matrix}x+1 & ,x>0\\ -(x+1)& ,x<0\end{matrix}\right.[/tex]

Also, |-x-9| = [tex]\left\{\begin{matrix}-x-9 & ,x>0\\ -(-x-9)& ,x<0\end{matrix}\right.[/tex]

So, equating these two functions gives the value of x = -5. After substituting this value in any of the function term say y = x+1, we get y = 4.

Moreover, from the graph below we see that, after equating these functions, the solution is given by the points at which they intersect.

Hence, the solution is (x,y) = (-5,4).

Answer:

0.8125

Step-by-step explanation:

See picture!

Answer:

y=-5x+4

Step-by-step explanation:

y-4=-5(x-0)

y-4=-5x

y=-5x+4

Answer:

Step-by-step explanation:

For shirt :

Original cost = $54

New cost = $18

Change amount = 54 - 18 = $36

% INC/DEC = (36 /54) * 100 = 2 * 100 / 3 = 66.66%

For PS4 :

Original cost =$400

New cost = $250

Change in amount = 400- 250 =$150

% INC/DEC = (150/400) * 100 = 37.5%

For Coffee maker:

Original cost = $30

New cost = $20

Change in amount = 30 - 20 = $10

% INC/DEC = (10/30)*100 = 33.33 %

For Luggage:

Original cost = $180

New cost = $50

Change in amount = 180 - 50 = $130

% INC/DEC = (130/180)*100 = 72.22 %

Answer:

the new frame is bigger than the original frame by 10%

Step-by-step explanation:

Let the length of the original frame be l,

then it's width is (10% of l)=[tex]\frac{10}{100}[/tex]×l

                                           =[tex]\frac{l}{10}[/tex]

hence area of original frame=A=length×width

                                               =[tex]\frac{l^{2} }{10}[/tex]

now the length of frame is enlarged by 10%

new lenght of frame=l+10%×l

                                 =l+[tex]\frac{10}{100}[/tex]×l

                                  =[tex]\frac{11}{10}[/tex]×l

width of new frame==[tex]\frac{l}{10}[/tex]

area of new frame=length×width

                              =[tex]\frac{11l^{2} }{100}[/tex]

percent change=((area of new frame-area of old frame)×100)÷area of old frame

=10%

Answer:

9.09091%

Step-by-step explanation:

Since the two lines are parallel and they are both being bisected by the same line, then the resulting bisected angles are the same.

To solve for x you will set 2x - 3 = 135, since both angle measures are the same.

2x - 3 = 135

2x = 138

x = 69

Answer:

x and y do not show direct variation.  

Step-by-step explanation:

The formula for direct variation is

y = kx     Divide each side by y

k = y/x

k should have the same value for every point except, of course, (0,0)

For the first point,

k = 2/(-1) = -2

For the third point,

k = 2/1 = 2

The values of k are different, so x and y do not show direct variation.

Answer:x and y do not show direct variation.  

Step-by-step explanation:

The formula for direct variation is

y = kx     Divide each side by y

k = y/x

k should have the same value for every point except, of course, (0,0)

For the first point,

k = 2/(-1) = -2

For the third point,

k = 2/1 = 2

The values of k are different, so x and y do not show direct variation.

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Step-by-step explanation:

1. For the function f(x) = x^2 + 2x + 3:

a) f(-x) = x^2 - 2x + 3

b) -f(x) = -x^2 - 2x - 3

c) -f(-x) = -x^2 + 2x - 3

2. For the function g(x) = 55/x + 3x:

a) g(-x) = -55/x - 3x

b) -g(x) = -55/x - 3x

c) -g(-x) = 55/x + 3x

For both functions f and g, we found the values of f(-x), -f(x), -f(-x), g(-x), -g(x), and -g(-x) by substituting -x into the original functions and negating the functions where necessary.

1. For the function f defined by f(x) = x^2 + 2x + 3:

a) To find f(-x), we substitute -x into the function:

f(-x) = (-x)^2 + 2(-x) + 3 = x^2 - 2x + 3

b) To find -f(x), we negate the entire function:

-f(x) = -(x^2 + 2x + 3) = -x^2 - 2x - 3

c) To find -f(-x), we substitute -x into the negated function:

-f(-x) = -((-x)^2 + 2(-x) + 3) = -x^2 + 2x - 3

2. For the function g defined by g(x) = 55/x + 3x:

a) To find g(-x), we substitute -x into the function:

g(-x) = 55/(-x) + 3(-x) = -55/x - 3x

b) To find -g(x), we negate the entire function:

-g(x) = -(55/x + 3x) = -55/x - 3x

c) To find -g(-x), we substitute -x into the negated function:

-g(-x) = -(-(55/(-x)) + 3(-x)) = -(-55/x - 3x) = 55/x + 3x

Answer:

7.3 repeating

Step-by-step explanation:

58-14

=44

44/6

=7.3 repeating

Answer:

Amount of gas that can be hold by Joe's tank = 16 gallons.

Step-by-step explanation:

Given that Joe's gas tank is 1/4 full. After he buys 6 gallons of gas, it is 5/8 full. Now we need to find about how many gallons can Joe's tank hold.

So let's find change that happened after filling the gas.

Change = (5/8 full) - (1/4 full)

Change = (5/8 - 1/4)  full

Change = (5/8 - 2/8)  full

Change = (5 - 2)/8  full

Change = 3/8  full

So that means 3/8 full happens in 6 gallons

then 1 full will happen in 6/(3/8) gallons = 6*(8/3) gallons = 48/3 gallons = 16 gallons

So the amount of gas that can be hold by Joe's tank = 16 gallons.

Answer:

hint for next time

Step-by-step explanation:

never ask a a and b question for only 5 points