How would I solve 5(x -2) =2x +16?

Answer:

16

Step-by-step explanation:

Since Dean bought 8 postcards during 2 days of vacation, then after 4 days, that would be 16 because multiply by 2.

Answer:

16 postcards

Step-by-step explanation:

So Dean's rate of buying is:

8 postcards/2 days = 4 postcards per day.

Thus, we can find out how many postcards he gets after 4 days by multiplying

4 postcards × 4 days, which equals to 16 postcards.

Hope this is helpful!

Answer:

y=-5x+4

Step-by-step explanation:

y-4=-5(x-0)

y-4=-5x

y=-5x+4

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:

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:

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:

Domain of y=[tex]\sqrt[4]{x-1}[/tex]: is x>=1

Interval notation: [1,∞)

Step-by-step explanation:

We have y=[tex]\sqrt[4]{x-1}[/tex]

1) The domain of a function is the set of x values for which the function is real and defined.

2) So, x-1 should be positive means x-1>=0, because fourth root of any negative value would be a complex number and not a real number.

3) Now we solve the inequality x-1>=0

4) Adding 1 to both sides of the inequality we get,

x-1+1 > = 0+1

5) Cancel out -1 and +1 from the left side

6) We get x>=1

It concludes that for the domain of the given function, the x value must be greater than or equal to 1

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:

x=2

Step-by-step explanation:

-2(1 - 4x) = 3x + 8

The first step is to distribute the -2

-2*1 -2(-4x) = 3x+8

-2+8x = 3x+8

Subtract 3x from each side.

-2+8x-3x = 3x-3x+8

-2+5x=8

Add 2 to each side

-2+2 +5x=8+2

5x=10

Divide by 5

5x/5 = 10/5

x=2

Answer:

2

Step-by-step explanation:

Final answer:

Assuming a square garden with each side being 8 feet, 50% of the space allocated to daisies would be 32 square feet.

Explanation:

Mr. King is dividing his garden evenly for tulips and daisies, meaning each flower type will occupy 50% of the garden's area. The length of the garden is given as 8 feet, but the width is not mentioned. To determine the actual area for daisies, we need both dimensions of the garden. However, if we assume that the width is also provided or the garden is square (8 feet by 8 feet), then the total area of the garden is 64 square feet (8 feet * 8 feet).

Now, to find the space filled with daisies, we calculate 50% of the total area:

0.50 * 64 square feet = 32 square feet.

Therefore, if the garden is a square and the other dimension equals the given length, the space filled with daisies will be 32 square feet.

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).

[tex]Use\ \dfrac{a^n}{a^m}=a^{n-m}\\\\\dfrac{14ab^2x^3}{2abx^2}=\dfrac{14}{2}\cdot\dfrac{a}{a}\cdot\dfrac{b^2}{b}\cdot\dfrac{x^3}{x^2}=7\cdot1\cdot b^{2-1}\cdot x^{3-2}=\boxed{7bx}[/tex]

Answer:

[tex]7bx[/tex]

Step-by-step explanation:

[tex]\mathrm{Divide\:the\:numbers:}\:\frac{14}{2}=7 =\frac{7ab^2x^3}{abx^2}[/tex]

[tex]\mathrm{Cancel\:the\:common\:factor:}\:a =\frac{7b^2x^3}{bx^2}[/tex]

[tex]\mathrm{Cancel\:the\:common\:factor:}\:b =\frac{7bx^3}{x^2}[/tex]

[tex]\mathrm{Apply\:exponent\:rule}:\quad \frac{x^a}{x^b}\:=\:x^{a-b}[/tex][tex]\frac{x^3}{x^2}=x^{3-2}=x[/tex]

[tex]=7bx[/tex]

Hope this helps!!!

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:

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:

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

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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:

0.8125

Step-by-step explanation:

See picture!

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

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: 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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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

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:

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:

5

Step-by-step explanation:

because 5*5=25 and you have 1 remainder

Answer:

We have $440 to spend on fliers

Step-by-step explanation:

Budget = supplies + fliers

555 = 115 + fliers

Subtract 115 from each side

555-115 = 115-115 + fliers

440 = fliers

We have $440 to spend on fliers

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:

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: