Solve the rational equation x divided by 6 equals x squared divided by quantity x minus 1 end quantity, and check for extraneous solutions.

Answer:

The correct answer is 17 weeks.

Step-by-step explanation:

First, write an equation:

total cost = (30)weekly + deposit

Let's solve:

1004.51 = 30w + 500

504.51 = 30w                          Subtract 500 from both sides

16.817 = w                                Divide both sides by 30

17 = w                                      Round up (money always rounds up)

Hope this helps,

♥A,W,E,S.W.A.N.♥

Answer:

Step-by-step explanation:

4/(x+23)

The quotient of four and a number increased by 23 will be (x/4) + 23.

The divisor and the number being divided by it are referred to as the dividend and the number being divided by it, respectively. The result of division is the quotient.

Mathematical operations, such as number addition, subtraction, multiplication, and division, must be applied. It has the fundamental operators +, -, ×, and ÷.

It is given that the quotient of four and a number increased by 23.

Let the number be x.

The quotient indicates division as x/4.Further, it increases by 23 as,

(x/4) + 23.

Thus, the quotient of four and a number increased by 23 will be (x/4) + 23.

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Answer:

75

Step-by-step explanation:

Since x+3 is the factor of the function f(x) .

So, -3 should satisfy f(x),

Thus putting -3 in f(x) we get

                       3×[tex](-3)^{3}[/tex]-2×(-3)+k = 0

                       -81+6+k = 0

                         k = 75.

So , k should be equal to 75.

Answer:

[tex]f(x)=-\left(\dfrac{1}{2}\right)^x+4[/tex]

The exponential function is increasing and is concave down

Step-by-step explanation:

Let the equation of exponential function be

[tex]f(x)=a\cdot b^x+c,\ ,\ b>0[/tex]

1. Exponential function f(x) has a y intercept of 3, so the graph of f(x) passes through the point (0,3). Thus,

[tex]3=a\cdot b^0+c\\ \\3=a+c[/tex]

2. Exponential function f(x) has an x intercept of -2, so the graph of f(x) passes through the point (-2,0). Thus,

[tex]0=a\cdot b^{-2}+c\\ \\0=\dfrac{a}{b^2}+c[/tex]

3. Function is always increasing as the value of x increases, but the function never reaches y=4, so

[tex]c=4[/tex]

Hence,

[tex]\left\{\begin{array}{l}a+4=3\\ \\\dfrac{a}{b^2}+4=0\end{array}\right.\Rightarrow \left\{\begin{array}{l}a=-1\\ \\\dfrac{-1}{b^2}+4=0\end{array}\right.\Rightarrow \left\{\begin{array}{l}a=-1\\ \\b^2=\dfrac{1}{4}\end{array}\right.[/tex]

So,

[tex]a=-1,\\ \\b=\dfrac{1}{2},\\ \\c=4,\\ \\f(x)=-\left(\dfrac{1}{2}\right)^x+4[/tex]

Answer:

The answer is 11

Step-by-step explanation:

Final answer:

The distance between the top of the escalator and the ground floor is approximately 12 feet.

Explanation:

To find the distance between the top of the escalator and the ground floor, we can use trigonometry. We have the length of the escalator (16 feet) and the angle of depression (42.51 degrees). The distance we need to find is the opposite side of the right triangle formed by the top of the escalator, the floor, and the length of the escalator. We can use the sine function to find this distance.

The formula is sin(angle) = opposite/hypotenuse. Plugging in the values, we get sin(42.51) = opposite/16. Solving for opposite, we have opposite = sin(42.51) * 16.

Using a calculator, we find that opposite ≈ 12.014 feet. Rounding to the nearest foot, the distance between the top of the escalator and the ground floor is approximately 12 feet.

Answer:

B) 2/11

Step-by-step explanation:

(4/2a)(a/11)

4/2a=2/a

(2/a)(a/11)=2/11

Answer:

D.6x-7

Step-by-step explanation:

Answer:

B. 6x-49

Step-by-step explanation:

36x2-49

36x2=72

72-49=23

18%-7= (-6.82)

6x-49=(-43)

18% - 49=(-50.26)

23-(-6.82)=16.18

23-(-43)=66

23-(-50.26)=73.26

Answer:

5 blue tiles

Step-by-step explanation:

Answer: 5 blue tiles are in each row

Step-by-step explanation:

If Gia has 80 tiles and puts them in all in 8 equal rows there would be 10 rows because 80÷8=10. So considering the fact that there is a equal number of blue and white tiles I divided 10 by 2 and I got 5 so I came to the conclusion that there is 5 blue tiles in each row and there is 5 white tiles in each row.

Answer:

x = -7

Step-by-step explanation:

(x-1)/4-(x+2)/5=-1

[5(x-1) - 4(x+2)]/20 = -1

5x-5-4x-8 = -20

x-13= -20

x= -20 +13

x= -7

Answer:

x = 20°

Step-by-step explanation:

See the attached diagram.

Given that B and C are the two centers of two equal circles.

Now, ∠ ECD = 80° also given.

Now, Δ BCE is an isosceles triangle as BC = CE = Radius of the circle.

So, ∠ EBC = ∠ CEB.

Now, ∠ ECD = ∠ EBC + ∠ CEB = 80°

⇒ 2 ∠ EBC = 80°

⇒ ∠ EBC = 40°

Again, the triangle Δ ABF is an isosceles triangle as AB = BF = Radius

So, ∠ BAF = ∠ BFA = x°

Now, ∠ EBC = ∠ BAF + ∠ BFA = 40°

⇒ x° + x° = 40°

⇒ 2x = 40

⇒ x = 20° (Answer)

Answer:

-3

Step-by-step explanation:

-3-3=-6

Answer:

-3

Step-by-step explanation:

ok so -6 +3

-6 is negative and when you add the 3 you move to the left closer to the 0

you end up with -3

Answer: The height of hill is 125 feet.

Step-by-step explanation:

Given that velocity of the rollercoaster is [tex]v= \sqrt{(v_\limit{0}^{2} )+64h}[/tex]

Where, [tex]v_\limit{0}[/tex] is initial velocity and h is height from top of hill.

and v is velocity at height h.

Initial Velocity [tex]v_\limit{0}[/tex] is 10feet/sec at top of hill.

Also, Velocity at bottom of the hill is 90feet/sec.

Therefore, the value of h at top of the hill is h=0 and value of h at bottom of the hill is h=h

[tex]v= \sqrt{(v_\limit{0}^{2} )+64h}[/tex]

[tex]90= \sqrt{(10)^{2} +64h}[/tex]

[tex]90^{2}= 10^{2} +64h[/tex]

8100=100+64h

8000=64h

h=125 feets.

Thus, The height of hill is 125 feet.

Answer:

[tex]Angle\ b= 70\°[/tex]

Step-by-step explanation:

The correct question is

Angle a and angle b are vertical angles

Angle a =8x+6

Angle b= 4x+38

Solve for x and find the measure of angle b

we know that

Vertical Angles are the angles opposite each other when two lines cross. They are always congruent.

m∠a=m∠b -----> by vertical angles

substitute the given values

[tex](8x+6)\°=(4x+38)\°[/tex]

solve for x

[tex]8x-4x=38-6[/tex]

[tex]4x=32[/tex]

[tex]x=8[/tex]

Find the measure of angle b

[tex]Angle\ b= (4x+38)\°[/tex]

substitute the value of x

[tex]Angle\ b= (4(8)+38)\°[/tex]

[tex]Angle\ b= 70\°[/tex]

Where the above parameters are given, the measure of angle b is 70°.

Given:

Angle a = 8x + 6

Angle b = 4x + 38

Since angle a and angle b are vertical angles, they are equal:

8x + 6 = 4x + 38

Now, let's solve for x:

8x - 4x = 38 - 6

4x = 32

x = 32 / 4

x = 8

Now that we've found x, we can substitute it back into the equation for angle b to find its measure:

Angle b = 4x + 38

= 4 * 8 + 38

= 32 + 38

= 70

So, the measure of angle b is 70°.

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Answer:

y = - [tex]\frac{1}{2}[/tex] x + [tex]\frac{5}{2}[/tex]

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = - [tex]\frac{1}{2}[/tex], thus

y = - [tex]\frac{1}{2}[/tex] x + c ← is the partial equation

To find c substitute (- 3, 4) into the partial equation

4 = [tex]\frac{3}{2}[/tex] + c ⇒ c = 4 - [tex]\frac{3}{2}[/tex] = [tex]\frac{5}{2}[/tex]

y = - [tex]\frac{1}{2}[/tex] x + [tex]\frac{5}{2}[/tex] ← equation of line

Answer:The equation of the line is;

Step-by-step explanation:

Answer:

98.75%.

Step-by-step explanation:

On March 20, 2011, a $1000 bond had a selling price of $987.50.

We are asked what will be the quoted price for the bond.

Now, the quoted price of a bond is the price at which the bond was last traded and it is expressed as the percentage of the original bond value.

So, in our case the quoted price will be [tex]\frac{987.50}{1000} \times 100 = 98.75[/tex] %. (Answer)

Solution of system of linear equation y = 2x – 4 and 3x - 2y = 8 is x = 0 and y = -4

Need to determine solution of following system of linear equation

y = 2x – 4    ------(1)

3x - 2y = 8   ------(2)

If we observe the equation (1), we can say that we are having value of y in terms of x. so substitution method is the best approach to solve the above system of linear equation.

In substitution method, we will substitute value of y in equation (2) in terms of variable x from equation (1)  

On substituting y = 2x – 4 in equation (2) , we get equation in one variable that is x which is as follows

3x – 2 (2x – 4 )   = 8    

=> 3x – 4x + 8 = 8

=> -x = 8 – 8  

=> x = 0

On substituting x = 0 in equation (1), we get  

y = 2 x 0 – 4

=> y = -4

Hence solution of system of linear equation y = 2x – 4 and 3x - 2y = 8 is x = 0 and y = -4

Answer:

The time taken by smaller pipe to fill the tank alone is 74.2 min

Step-by-step explanation:

Given as :

The time taken by two pipes to fill tank = 19 min

Let the time taken by larger pipe to fill tank = y

And the time taken by smaller pipe to fill tank = x

According to question

The smaller pipe takes 49 minutes longer than larger pipe

I.e x = y + 49

Now,

[tex]\dfrac{1}{x}[/tex] + [tex]\dfrac{1}{y}[/tex] = [tex]\dfrac{1}{49}[/tex]

Or, [tex]\dfrac{1}{y + 49}[/tex] + [tex]\dfrac{1}{y}[/tex] = [tex]\dfrac{1}{49}[/tex]

Or, [tex]\dfrac{y + 49 + y}{y^{2} + 49 y }[/tex] = [tex]\dfrac{1}{49}[/tex]

Or, 2 y + 49 = [tex]\dfrac{y^{2}+49y }{19}[/tex]

Or, 19 × ( 2 y + 49 ) = y² + 49 y

Or, 38 y + 931 = y² + 49 y

Or, y² + 49 y - 38 y - 931 = 0

or, y² + 11 y - 931 = 0

Or, Applying quadratic equation method to calculate the value of y

so, y = [tex]\frac{- b \pm \sqrt{b^{2}-4\times a\times c}}{2\times a}[/tex]

Or,  y = [tex]\frac{- 11 \pm \sqrt{11^{2}-4\times 1\times (-931)}}{2\times 1}[/tex]

Or, y = [tex]\frac{- 1 \pm \sqrt{121+3724}}{2}[/tex]

or, y = [tex]\frac{- 1 \pm \sqrt{3845}}{2}[/tex]

or, y = [tex]\frac{- 1 \pm 62.008}{2}[/tex]

∴   y = 25.2 , - 36.5

So, The time taken by larger pipe = y = 25.2 min

and the time taken by smaller pipe to fill the tank = y + 49 = 25.2 + 49 = 74.2 min

Hence The time taken by smaller pipe to fill the tank alone is 74.2 min answer

The equation written by Elliot, which was not included in the question, is:

[tex]0.10(7-x)+0.5(x)+0.25(0.5x)=5.90[/tex]

The statements from which you have to identify the errors are:

a) He should have written the expression for the number of dimes as x – 7.

b) He should have written the coin values as 5, 10, and 25 and not as 0.5, 0.10, and 0.25.

c) He should have written the coin value for the nickel as 0.05.

d) He should have translated the scenario as the value of all dimes = value of all nickels and value of all quarters = value of all nickels.

e) He should have written the expression for the number of nickels as 2x.

Answer:

There two errors:

Explanation:

I will start by writing the correct expression following the statements step-by-step:

1) He has half as many quarters as nickels

2) He has 7 fewer dimes than nickels.

3) Mulitiply each number of coins by its value in dollars:

4) Add he values of all the coins:

5) Equal to the total value of $ 5.90:

6) Compare with the equation written by Elliot:

7) Conclusion:

There are two errors:

Answer:

for the people on edgen the answer is the first and the third options

Step-by-step explanation:

uhhh

Answer:

[tex]x=12[/tex]

Step-by-step explanation:

we have

[tex]-8(8-x)=\frac{4}{5}(x+28)[/tex]

solve for x

Applying distributive property both sides

[tex]-8(8)-8(-x)=\frac{4}{5}(x)+\frac{4}{5}(28)[/tex]

[tex]-64+8x=\frac{4}{5}(x)+\frac{112}{5}[/tex]

Multiply by 5 both sides to remove the fractions

[tex]-64(5)+8x(5)=4x+112[/tex]

[tex]-320+40x=4x+112[/tex]

subtract 4x both sides

[tex]-320+40x-4x=4x+112-4x[/tex]

[tex]-320+36x=112[/tex]

Adds 320 both sides

[tex]-320+36x+320=112+320[/tex]

[tex]36x=432[/tex]

divide by 36 both sides

[tex]x=12[/tex]

Answer:

Charlie used 4 20-cent stamps and 8 32-cent stamps.

Step-by-step explanation:

Let the number of 20 cents stamps be [tex]x[/tex]. Then, as per question, Chalie used twice as many 32-сent stamps as 20 cent stamps.

Therefore, number of 32-cent stamps is [tex]2x[/tex].

Now, total cost of the stamps is $ 3.36 = 336 cents

Cost of 1 20-cent stamp is 20 cents. So, cost of [tex]x[/tex] 20-cent stamps is [tex]20x[/tex]. Similarly, cost of [tex]2x[/tex] 32-cent stamps is [tex]32(2x)=64x[/tex]

Total cost = [tex]20x+64x=84x[/tex]

As per question,

[tex]84x=336\\x=\frac{336}{84}=4[/tex]

Number of 20-cent stamps = [tex]x = 4[/tex]

Number of 32-cent stamps = [tex]2x=2\times 4=8[/tex]

So, Charlie used 4 20-cent stamps and 8 32-cent stamps.

Answer:

No. of 32 cent stamps = 8

and that of 20 cent stamps = 4

Explanation:

Let no. of 32 cent stamps used be x and the number of 20 cent stamps used be y.

We are given that total postage on a package put by Charlie by using only 32 and 20 cent stamps is equal to $3.36.

So, since 100 cents make one dollar, $3.36 = 336 cents.

So,

32x + 20y = 336

Also we are given that Charlie used twice as many 32 cent stamps as 20 cent stamps which can be written as,

x = 2y

Substituting this equation in previous equation we get

32 [tex]\times[/tex]2y + 20y = 336

=> 64y + 20y = 336

=> 84y = 336

=>y = 4

Putting the value of y in x = 2y we get x = 2*4 = 8

So, no. of 32 cent stamps = 8 and that of 20 cent stamps = 4

Answer:

24000

Step-by-step explanation:

2000 * 12

= 2 * 12 *(1000)

=24*1000

If we want to multiply by 1000 we "tack" three zeros onto the end.

24000.

Answer: 24,000

Step-by-step explanation: if 2,000 multiplied by 10 = 20,000, and 2,000 multiplied by 2 = 4,000, then if you add those together you get 24,000

Monica makes $550 and Phil makes $275 per week

Step-by-step explanation:

Monica and Phil each have part-time jobs

We need to find how much each person make​s

Assume that Phil makes $x in a week

∵ Phil makes $x per week

∵ Monica makes twice as much money in a week as Phil

∴ Monica makes = $2x per week

∵ The total of their weekly earnings is 825

- Add their weekly earnings

∴ x + 2x = 825

- Add the like terms

∴ 3x = 825

- Divide both sides by 3

∴ x = 275

- Find 2x

∴ 2x = 2(275) = 550

Monica makes $550 and Phil makes $275 per week

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Answer:

Step-by-step explanation:

If given figures are similar, then corresponding sides are in proportion.

Therefore we have the equation:

[tex]\dfrac{x}{3}=\dfrac{56}{14}[/tex]           cross multiply

[tex](14)(x)=(3)(56)[/tex]

[tex]14x=168[/tex]            divide both sides by 14

[tex]\dfrac{14x}{14}=\dfrac{168}{14}[/tex]

[tex]x=12[/tex]

Two figures are known as similar figures if there the corresponding angles are equal and the corresponding sider is in ratio. The length of the missing side is 12 units.

Two figures are known as similar figures if there the corresponding angles are equal and the corresponding sider is in ratio. It is denoted by the symbol "~".

For two similar figures, the ratio of any two corresponding sides is in ratio, therefore, the length of the unknown side can be written as,

(10/40) = (14/56) = (14/56) = (3/x)

1/4=3/x

x = 12

Hence, the length of the missing side is 12 units.

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Answer:

The arrangement of the given equation in the slope - intercept form are

1. [tex]y = 1x +82[/tex]  

Step-by-step explanation:

Given:

Let  A ≡ ( x1 , y1 )   ≡ (-12 , 70)

       B ≡ ( x2 , y2 ) ≡ (-4 , 78)

Slope - intercept form :

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

Where,

m is the slope of the line.

c is the y-intercept.

When two points are given say ( x1 , y1 )  and ( x2 , y2)  we can remove slope by  

Slope,

[tex]m=\frac{y_{2}- y_{1}}{x_{2}- x_{1}}[/tex]

∴ [tex]m =\frac{78-70}{-4--12}\\m =\frac{8}{-4+12}\\m =\frac{8}{8}\\ m= 1[/tex]

Now equation of a line  for a point ( x1 , y1 )  and having slope m is given as,

[tex](y-y_{1})=m(x- x_{1})\\ \textrm{substituting ( x1 , y1 ) and m we get}\\y-70=1(x-(-12))\\y= x+12+70\\y=x+82[/tex]

Which is in the required form

y = 1x + 82

Intercepts: Where the line cut X axis called X- intercept and where cut Y axis is called Y- intercept.

Answer:

Step-by-step explanation:

Area of side walk = (106 * 81) - (100 * 75)

Area of side walk = 8586 - 7500 = 1086 square foot.

Answer:

OPTION B

Step-by-step explanation:

3 and 'a' are multiplied and 5 is subtracted from the result.

OPTION B says 5 less than 3 times a number would fit perfectly.

Other options talk about adding or taking ratios and clearly do not fit the case.

Hence, the right answer is Option B.

Answer:

The guy wire is 7.2111 ft long

Step-by-step explanation:

Notice that we are in the presence of a right angle triangle formed by: the height (the standing 6 ft pole), the base (the distance from the pole to the anchoring point on the ground), and the actual guy wire. See attached image for reference.

Notice that since pole and ground are perpendicular to each other (at 90 degrees) , the guy wire forms what is called the "hypotenuse" (longest side) of the right angle triangle. We can therefore use the Pythagorean Theorem to solve this problem with the formula for the hypotenuse:

[tex]Hypotenuse=\sqrt{side1^2 +side2^2} \\Hypotenuse= \sqrt{6^2+4^2}\\Hypotenuse=\sqrt{36+16} \\Hypotenuse=\sqrt{52} \\Hypotenuse=7.2111\, ft[/tex]

The coordinates of point P are: (1/5 , -12/5)

Step-by-step explanation:

Here

R(-3,-4) = (x1,y1)

S(5,0) = (x2,y2)

The ratio is: 2:3

The coordinates of a point that divides the line in ratio m:n are given by:

Let P be the point then

[tex](x_P, y_P) = (\frac{mx_2+nx_1}{m+n},\frac{my_2+ny_1}{m+n})[/tex]

Putting values

[tex](x_P, y_P) = (\frac{(2)(5)+(3)(-3)}{2+3},\frac{(2)(0)+(3)(-4)}{2+3})\\= (\frac{10-9}{5},\frac{0-12}{5})\\=(\frac{1}{5},\frac{-12}{5})[/tex]

Hence,

The coordinates of point P are: (1/5 , -12/5)

Keywords: Coordinate geometry

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Answer:

The total amounts of petrol used up by his car is 3.235 gallons.

Step-by-step explanation:

Tony drives his car and drives the first 13 miles in 13 minutes.

So, the average speed was [tex]\frac{13}{13} \times 60 = 60[/tex] mph.

which is less than 65 miles per hour, and the miles traveled per gallon is 50.

So, 50 miles of travel is done by 1 gallon of petrol.

Hence, 13 miles travel is done by [tex]\frac{13}{50} = 0.26[/tex] gallons of petrol.

Now, Tony then drives at an average speed of 68 mph > 65 mph for 1 hour and 24 minutes i.e. 1.75 hours.

Then he travels (68 × 1.75) = 119 miles and the miles traveled per gallon is 40.

So, 40 miles of travel is done by 1 gallon of petrol.

Hence, 119 miles travel is done by [tex]\frac{119}{40} = 2.975[/tex] gallons of petrol.

Therefore, the total amount of petrol used up by his car is (0.26 + 2.975) = 3.235 gallons. (Answer)

Answer:

50.8 centimeters

Step-by-step explanation:

So, if Shannon's chair is 20 inches tall, you would multiply that by 2.54 in order to get the length in centimeters.

20 x 2.54 = 50.8.

So Shannon's char is 50.8 centimeters tall.