A cylindrical container has a height of 24 inches. Currently, the container is filled with water to a height of 18 inches. A leaky
faucet drips into the container, causing the height of the water in the container to increase by 2 inches per hour. The equation
below can be used to find t, the number of hours it would take to fill the container.
18 + ?t = 24
What number should be the coefficient of t?

Step-by-step explanation:

(1)

Let the numerator be x and denominator be y. A/Q x + y = 4 + 2x → - x + y = 4

(2)

multiplying each term by 2, 2x-2y= -8

(3)

Also, (x+3) / (y+3) = 2 / 3 → 3x - 2y = -3

Subtracting (2) from (3) → x = 5 and by putting this in (1) we can get y=9. Hence, the fraction is 5 / 9

Answer:

[tex]\frac{5}{9}[/tex]

Step-by-step explanation:

let the fraction be [tex]\frac{x}{y}[/tex], then

x + y = 2x + 4 ( subtract x from both sides )

y = x + 4 → (1)

If 3 is added to numerator and denominator, then

[tex]\frac{x+3}{y+3}[/tex] = [tex]\frac{2}{3}[/tex] ( cross- multiply )

3(x + 3) = 2(y + 3) ← distribute both sides

3x + 9 = 2y + 6 ← substitute y = x + 4

3x + 9 = 2(x + 4) + 6

3x + 9 = 2x + 8 + 6 = 2x + 14 ( subtract 2x from both sides )

x + 9 = 14 ( subtract 9 from both sides )

x = 5

Substitute x = 5 into (1)

y = 5 + 4 = 9

Hence the original fraction is [tex]\frac{5}{9}[/tex]

Answer:

Answer is 11+6i

Step-by-step explanation:

You just have to add imaginary part together and the real part. The answer will be 11+6i

Answer: 11+6i

Step-by-step explanation:

A relation is a function if you associate exactly one output for every input. This means that, when you choose a value for x, there must be only one correspondent value for y. This only happens in the top-right parabola.

Answer:all real number greater than 0

Step-by-step explanation:

Firstly if you input any number equal to 0 or less than 0 you will not find the defined range...

You cant use o or any negetive number as domain in the term of log or ln type math..

But if u put any value more than 0 you can find all real number as range

Such as, log(0.001)=-3

log(1)=0

log(120)=2.07

So the domain is all real number above o...but the range is all real number including 0 and negetive number..

The domain of y=logx is all real numbers greater than 0.

Hence, option b is the correct answer.

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Answer:  C

Step-by-step explanation:

20 people have a dog: 8 are yes dog/yes cat & 12 are yes dog/no cat

17 people have no dog: 10 are no dog/yes cat & 7 are no dog/no cat

[tex]\begin{array}{c|c|c|c}\underline{\qquad \qquad}&\underline{Cat}&\underline{No\ Cat}&\underline{TOTAL}\\Dog&8&12&20\\\underline{\ No\ Dog\ }&\underline{\ 10\ }&\underline{\quad 7\quad }&\underline{\quad 17\quad }\\TOTAL&18&19&37\end{array}[/tex]

Answer:

2

Step-by-step explanation:

The function is given as  [tex]f(x)=\frac{3}{(x-11)(x+4)}[/tex]

Vertical asymptotes occur when the denominator is set to 0.

Thus,

(x-11)(x+4) = 0

x = 11 or x = -4

Hence, there are 2 vertical asymptotes

Answer: 2

Step-by-step explanation:

A P E X

Answer:

3/50 or 0.06

Step-by-step explanation:

6/100=3/50

6/100=0.06

Answer:

0.06

Step-by-step explanation:

Answer: y= -3/2x

Explanation:

3x+ 2y- 6

→ 2y= -3x+ 6

→ y= -3/2x+ 3

Parallel to y= ax+ b is to have the same slope (ax) and have a different y- intercept.

For this equation, y= -3/2x + 3, it is y= -3/2x because the line has to pass through point (0,0).

Answer:

[tex](0, \infty)[/tex]

Step-by-step explanation:

By definition all the exponential functions of the form

[tex]f (x) = a (b) ^ x[/tex]

Where a is the main coefficient and b is the base they have range [tex](0, \infty)[/tex]

Whenever [tex]a> 0[/tex] and b> 0.

In this case the function is:

[tex]f (x) = 11(\frac{1}{3}) ^ x[/tex]

Note that for this function [tex]a = 11> 0[/tex] and [tex]b =\frac{1}{3}>0[/tex]

Therefor the range is: [tex](0, \infty)[/tex]

Answer:

a) y = sin x

b) y = csc x

c) y = cot x

Step-by-step explanation:

only d is even

Answer: C

Step-by-step explanation:

Binomial have only two terms.

A) 3x²-6x²-+x has three terms

B) 6x³-6x²+x-1 has four terms

C) 3x³-6x has two terms

D) 6x³ has only one term

Answer:

In graph

Step-by-step explanation:

First put it in Slope -Intercept form.

then graph the y- intercept first.

After that it's rise over run so think 1/1

up 1 over one.

Answer:

CCCCCCCCCCCCC

Step-by-step explanation:

Answer:

The maximum speed of Hal's airplane in still air is:

[tex]v= 250\ miles/h[/tex]

The speed of the wind

[tex]c = 50\ miles/h[/tex]

Step-by-step explanation:

Remember that the velocity v equals the distance d between time t.

[tex]v=\frac{d}{t}[/tex]  and [tex]t*v=d[/tex]

The distance that Hal travels when traveling with the wind is:

[tex](2\ hours)(v + c) = 600[/tex] miles

Where v is the speed of Hal and c is the wind speed.

The distance when traveling against the wind is:

[tex](3\ hours)(v-c) = 600[/tex] miles

Now we solve the first equation for v

[tex](2)(v + c) = 600[/tex]

[tex]2v + 2c = 600[/tex]

[tex]2v= 600-2c[/tex]

[tex]v= 300-c[/tex]

Now we substitute the value of v in the second equation and solve for c

[tex]3((300-c)-c) = 600[/tex]

[tex]3(300-2c) = 600[/tex]

[tex]900-6c = 600[/tex]

[tex]-6c = 600-900[/tex]

[tex]-6c = -300[/tex]

[tex]6c = 300[/tex]

[tex]c = 50\ miles/h[/tex]

Then:

[tex]v= 300-(50)[/tex]

[tex]v= 250\ miles/h[/tex]

The maximum speed of Hal's airplane in still air is:

[tex]v= 250\ miles/h[/tex]

The speed of the wind

[tex]c = 50\ miles/h[/tex]

Answer:

46°

Step-by-step explanation:

Alternate angles from 46° and alternate angles are equal

Answer:

The roots are {-3, -2, 2, 3}.

Step-by-step explanation:

The trick here is to represent y² by some other letter, such as x.  If we do that, then y^4-13y^2+36=0 becomes x² - 13x + 36 = 0.

Recognize that the factors -4 and -9 of 36 sum up to 13.  Thus,

x² - 13x + 36 = 0 is equivalent to (x - 4)(x - 9) = 0, and x = 4 or x = 9.

Recall that x = y².

When x = 4:  y² = 4, and so y = ±2.

When x = 9, y² = 9, and so y = ±3.

The roots are {-3, -2, 2, 3}.

The roots of the bi-quadratic equation y⁴ - 13y² + 36 = 0 are,

- 2, 2, -3, 3.

A polynomial is an algebraic expression.

A polynomial of degree n in variable x can be written as,

a₀xⁿ + a₁xⁿ⁻¹ + a₂xⁿ⁻² +...+ aₙ.

Given, y⁴ - 13y² + 36 = 0.

This a bi-quadratic polynomial.

Let, x = y².

Therefore,

x² - 13x + 36 = 0.

x² - 4x - 9x + 36 = 0.

x(x - 4) - 9(x - 4) = 0.

(x - 4)(x - 9) = 0.

x = 4 Or x = 9.

Now,

For x = 4 ⇒ y² = 4 ⇒ y = ± 2.

For x = 9 ⇒ y² = 9 ⇒ y = ± 3.

So, The roots of the biquadratic equation are - 2, 2, -3, 3.

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Answer:

(n+9) (2p+q)

Step-by-step explanation:

2p(n + 9) + q(n + 9) =

Factor out the term (n+9)

(n+9) (2p+q)

This is completely factor

We can either convert to standard form first or convert to a common multiplier, kinda like a common denominator.  The latter makes more sense if they wanted the result in scientific notation, but let's do it that way anyway.

a)

4.5 × 10⁴ + 3.8  × 10³ = 45 × 10³ + 3.8  × 10³ = 48.8× 10³ = 48,800

Answer:  48,800

b)

4.5 × 10⁴ - 3.8  × 10³ = 45 × 10³ - 3.8  × 10³ = 41.2× 10³ = 41,200

Answer:  41,200

c)

7.2 × 10⁻³ + 6.3  × 10⁻² = 7.2 × 10⁻³ + 63  × 10⁻³ = 70.2 × 10⁻³

       = 7.02 × 10⁻² = 0.0702

Answer: 0.0702

Answer:

y = x -1

Step-by-step explanation:

x - y = 7

We need to put this in slope intercept form to find the  slope.

Add y to each side

x-y+y =7+y

x = y+7

Subtract 7 from each side

x-7 = y+7-7

x-7 = y

The slope is 1  since it is in the form y = mx+b

We have a slope 1 and an point (1,0)

We can use point slope form to make an equation

y-y1 = m(x-x1)

y-0 = 1(x-1)

y = x -1

This is in slope intercept form

Answer:b

Step-by-step explanation: you graph each answer choice and see which one looks like the graph

Answer:  The correct option is

(B) [tex]y=\left(\dfrac{1}{2}\right)^{x-3}+1.[/tex]

Step-by-step explanation:  We are given to select the function that is shown in the graph.

From the graph, we know that

if the function is represented by y = f(x), then f(0) = 9. That is, the value of y at x = 0 is 9.

Option (A) :  Here, the given function is

[tex]y=\left(\dfrac{1}{2}\right)^{x+3}-1.[/tex]

So, at x = 0, the value of y is given by

[tex]y(x=0)=\left(\dfrac{1}{2}\right)^{0+3}-1=\dfrac{1}{8}-1=-\dfrac{7}{8}\neq 9.[/tex]

So, this option is not correct.

Option (B) :  Here, the given function is

[tex]y=\left(\dfrac{1}{2}\right)^{x-3}+1.[/tex]

So, at x = 0, the value of y is given by

[tex]y(x=0)=\left(\dfrac{1}{2}\right)^{0-3}+1=\left(\dfrac{1}{8}\right)^{-1}+1=8+1=9.[/tex]

So, this option is CORRECT.

Option (C) :  Here, the given function is

[tex]y=\left(\dfrac{1}{2}\right)^{x-1}+3.[/tex]

So, at x = 0, the value of y is given by

[tex]y(x=0)=\left(\dfrac{1}{2}\right)^{0-1}+3=2+3=5\neq 9.[/tex]

So, this option is not correct.

Option (D) :  Here, the given function is

[tex]y=\left(\dfrac{1}{2}\right)^{x+1}-3.[/tex]

So, at x = 0, the value of y is given by

[tex]y(x=0)=\left(\dfrac{1}{2}\right)^{0+1}-3=\dfrac{1}{2}-3=-\dfrac{5}{2}\neq 9.[/tex]

So, this option is not correct.

Thus, (B) is the correct option.

Answer:

19

Step-by-step explanation:

Plug in x = 3 into the function

f(x)=2x^2+1

f(x)=2(3)^2+1

f(x)=18+1

f(x)=19

The answer is:

f(3) = 19

Work/explanation:

To evaluate this function, plug in 3 for x:

[tex]\sf{f(x)=2x^2+1}[/tex]

[tex]\sf{f(3)=2(3)^2+1}[/tex]

[tex]\sf{f(3)=2\times9+1}[/tex]

Then, according to PEMDAS, we multiply:

[tex]\sf{f(3)=18+1}[/tex]

[tex]\sf{f(3)=19}[/tex]

Therefore, when x = 3, the function evaluates to 19.

Answer:

= [tex]3ab^{\frac{2}{3} }[/tex]

Step-by-step explanation:

∛(27 a³ [tex]b^{7}[/tex])

= ∛27 · ∛a³ · ∛b³ · ∛b³ · ∛b

= 3 · a · b · b ∛b

= 3ab² [tex]b^{\frac{1}{3} }[/tex]

or

= [tex]3ab^{\frac{2}{3} }[/tex]

Answer:

x=5

Step-by-step explanation:

Factoring  x2 - 2x – 15 we get

(x+3)(x-5) so x+3=0 and x-5=0 or x=-3 and x=5

Answer:

x=5

Step-by-step explanation:

x^2 - 2x – 15 = 0

Factor

What 2 numbers multiply to -15 and add to -2

-5*3 = -15

-5+3 = -2

(x-5) (x+3) = 0

Using the zero product property

(x-5) =0   x+3 =0

x-5+5 =0+5      x+3-3 = 0-3

x=5                  x=-3

Answer:

C. 6x - 7y = 21

Step-by-step explanation:

y=2/3 x - 3, y-intercept = -3

A. 2/3 x + 3y = -3

   3y = -2/3 x - 3

     y = -2x - 1; y-intercept = -1

B.-2/3 x + 3y = 6

   3y = 2/3 x + 6

     y = 2x + 2; y-intercept = 2

C. 6x-7y=21

    7y = 6x - 21

     y = 6/7 x - 3; y-intercept = -3

D. x+4y = 12

   4y = -x +12

     y = -1/4 + 3; y-intercept = 3

Answer is C. 6x - 7y = 21

Answer:

The total surface area of the solid is 702 cm² ⇒ answer B

The true statements are m∠WYX = 46° and  m∠YWX = 63° ⇒ 1st and 2nd answers

Step-by-step explanation:

* Lets explain the solid figure

- It has one rectangular base of dimensions 10 cm and 14 cm

- It has 4 rectangular side faces , two of dimensions 6 cm and 10 cm

 and another two of dimensions 6 cm and 14 cm

- It has 4 triangular faces , two of base 10 cm and height 12 cm and

 another two of base 14 cm and height 11 cm

- The total surface area of the solid is the sum of the area of the 9 faces

* Lets find the area of all the faces

# Area of the base

∵ The base is a rectangle

∵ Area of the rectangle = length × width

∵ Length = 14 cm and width = 10 cm

∴ Area of the base = 14 × 10 = 140 cm²

# Area of the four rectangular faces

∵ Length = 10 cm  and width = 6 cm

∴ The area of the face with dimensions 10 , 6 = 10 × 6 = 60 cm²

∵ Length = 14 cm  and width = 6 cm

∴ The area of the face with dimensions 14 , 6 = 14 × 6 = 84 cm²

# Area of the four triangular faces

∵ Area of a triangle = 1/2 × base × height

∵ The base = 10 cm and the height = 12 cm

∴ The area of the face = 1/2 × 10 × 12 = 60 cm²

∵ The base = 14 cm and the height = 11 cm

∴ The area of the face = 1/2 × 14 × 11 = 77 cm²

∵ The total surface area of the solid = the sum of the areas of 9 faces

∴ TSA = 140 + 2 × 60 + 2 × 84 + 2 × 60 + 2 × 77

∴ TSA = 140 + 120 + 168 + 120 + 154 = 702 cm²

* The total surface area of the solid is 702 cm²

* Lets solve the 2nd part

- WXY is a scalene triangle

- m∠WXY is 71°

- The two sides of the triangle WY and XY exceeded

- The ray WY and the ray XY intersect each other at point Y and

  formed vertically opposite angles with measure 46°

∵ Ray WY intersect ray XY at point Y

∴ m∠WYX = 46°

- In Δ WYX

∵ m∠WXY = 71° ⇒ given

∵ m∠WYX = 46° ⇒ proved

∵ The sum of the measures of the interior angles of a triangle is 180°

∴ m∠YWX + m∠WXY + m∠WYX = 180°

∴ m∠YWX + 71° + 46° = 180

∴ m∠YWX + 117° = 180° ⇒ subtract 117 from both sides

∴ m∠YWX = 63°

Lets check the true statements

# m∠WYX = 46° ⇒ true

# m∠YWX = 63° ⇒ true

# m∠WXY = 46° ⇒ not true

# m∠YWX = 46° ⇒ not true

# m∠WYX = 134° ⇒ not true

* The true statements are m∠WYX = 46° and  m∠YWX = 63°

Answer:

The correct option is D.

Step-by-step explanation:

Given information: △ABC≅△ECD.

The corresponding parts of congruent triangles are congruent.

The congruent angles are :

[tex]\angle A\cong \angle E[/tex]

[tex]\angle B\cong \angle C[/tex]

[tex]\angle C\cong \angle D[/tex]

[tex]\triangle BCA\cong \triangle CDE[/tex]

Option A is incorrect.

[tex]\triangle CAB\cong \triangle DEC[/tex]

Option B is incorrect.

The congruent sides are :

[tex]BC\cong CD[/tex]

Option C is incorrect.

[tex]AC\cong ED[/tex]

[tex]AB\cong EC[/tex]

It can also written as

[tex]AB\cong CE[/tex]             [tex][\because EC=CE,\text{Reflective Property}][/tex]

Therefore the correct option is D.

The correct statement is BC ≅ ED.

The correct statement is BC ≅ ED.

Since △ABC ≅ △ECD, the corresponding sides and angles of the triangles are congruent.

Therefore, we can conclude that BC ≅ ED.

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Answer:

Option C and option D

Step-by-step explanation:

we have that

[tex]y=x^{2}-4x+5[/tex]

This is the equation of a vertical parabola open upward

The vertex is a minimum

Convert the equation into vertex form

Complete the square

[tex]y-5=x^{2}-4x[/tex]

[tex]y-5+4=x^{2}-4x+4[/tex]

[tex]y-1=x^{2}-4x+4[/tex]

[tex]y-1=(x-2)^{2}[/tex]

[tex]y=(x-2)^{2}+1[/tex] ----> equation of the parabola in vertex form

The vertex is the point (2,1)

therefore

when the bird is 2 feet away from the first fence post, it reaches its minimum height of 1 foot

Answer: C and D

Step-by-step explanation:

Answer:

2(d - 3) is the equation. You cannot solve for d. You can only simplify it

A matching side of Polygon A measures 5 inches if it is 4 times smaller than a side of Polygon B that measures 20 inches.

If Polygon A is 4 times smaller than Polygon B, and a side of Polygon B measures 20 inches, then the matching side of Polygon A measures 5 inches. This is because when an object is said to be 'x times smaller' than another, you divide the original size by 'x' to find the new size. Therefore, the matching side length of Polygon A would be 20 inches ÷ 4 = 5 inches.

Example related to area comparison between two squares: Marta has a square with a side length of 4 inches. She has another square with side lengths that are twice as long. The side length of the larger square would be 4 inches x 2 = 8 inches. Since the area of a square is the side length squared, the area of the larger square would be 8 inches x 8 inches = 64 square inches, which is 4 times the area of the smaller square (16 square inches).

Answer:

In general, quadratic equations have two x-intercepts. But sometimes it happens that a quadratic eqution has one x-intercept or no interepts. That's why we should fully analyze this equation:

Given the following equation: y=3x^2 + 7 + m

If y=0, then:

3x^2 + 7 + m = 0 ⇒ x^2 = (-m-7)/3

Then [tex]x =[/tex]± [tex]\sqrt{\frac{-m-7}{3}}[/tex]

Given that we can take the square root of a negative number, the only way this equation has two x-intercepts is if m<-7.

Summarizing:

The equation: y=3x^2 + 7 + m has two x-intercepts only if m is less than -7. If m equals -7, the equation has only one x-intercept, and finally, if m is greater than -7, the equation has NO x-intercepts.