It takes a hose 3 minutes to fill a rectangular aquarium 8 inches long, 10 inches wide, and 14 inchestall. How long will it take the same hose to fill an aquarium measuring 23 inches by 25 inches by 26inches?minutesEnter an integer or decimal number [more..]Round your answer to the nearest minuteSubmit

For the intersection operation we have to look what elements both sets have in common, in this case both E and L has the number 8. Then the second answer is:

Now, the union operation adds the all elements into a single set without repetition, in this case the first answer is:

From the triangle, we have:

c = 13

b = 7

Let's solve for a.

The triangle is a right triangle.

To find the length of the missing sides, apply Pythagorean Theorem:

We are to solve for a.

Rewrite the equation for a:

Thus, we have:

Take the square root of both sides:

ANSWER:

By definition, Inverse variation equations have the following form:

Where "k" is the Constant of variation.

Given the values shown in the table, you can find the value of "k":

- Choose a point from the table. This could be:

Notice that:

- Substitute these values into the equation and solve for "k":

Knowing the Constant of variation, you can write the following equation:

The answer is:

4) For every 1 unit that x increases, y will increase by 2 units.​

1) For the function y=5/3x +1/2

If we remember that "rise over run" mnemonics, that'll make it easier to memorize it.

2) Plotting the graph of this function. Look at point A (1,2)

Counting from bottom to up (2 units "rise" on the y-axis, point A is 1 unit to right "run". So, For every 1 unit that x increases, y will increase by 2 units.​

A negative linear relationship occurs when for increasing x values, the values of y are decreasing.

Observing the graphs, we can see a positive linear relationship for graphs A and C (x - increases, y - increases).

For Graph D, we can observe no correlation.

For graph B, we can observe a negative linear relationship (x - increases, y - decreases).

Answer: Graph B

Inconsistent

a) Given:

x + y + z = -1 . . .(1)

y - 3z = 11 . . . (2)

2x + y + 5z = -12 . . .(3)

To find:

If the solution of the system of equations is either consistent dependent solution or an inconsistent one

We need to solve the system of equations. From equation (2), we will make y the subject of formula:

y = 11 + 3z (2*)

Substitute for y with 11 + 3z in both equation (1) and (2):

For equation 1: x + 11 + 3z + z = -1

x + 11 + 4z = -1

x + 4z = -1-11

x + 4z = -12 . . . (4)

For equation 3: 2x + 11 + 3z + 5z = -12

2x + 11 + 8z = -12

2x + 8z = -12-11

2x + 8z = -23 . . .(5)

We need to solve for x and z in equations (4) and (5)

Using elimination method:

To eliminate a variable, its coefficient needs to be the same in both equations

Let's eliminate x. We will multiply equation (4) by 2:

2x + 8z = -24 . . . (4*)

Now both equations have the same coefficient of x. Subtract equation (4) from (5):

2x - 2x + 8z - 8z = -23 - (-24)

0 + 0 = -23 + 24

0 = 1

Let hand side is not the same as right hand side.

When the left hand side is not equal to right hand side, the solution is said to be inconsistent or no sloution.

Your answer is inconsistent

Let b be the number of boxes.

Since each box has 6 cards, we will have the term 6b to get the remaining boxes.

Since Jen already put 150 cards into boxes, we have the following:

for 150 cards, Jen used 25 boxes. We can check that the remaining 5 boxes can be found using the previous equation:

therefore, the equation is 150+6b=180

The solution of the equation e^(x/4) = |4x| for the x by graphical approach is 0.27 and -0.24.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.

A formula known as an equation uses the same sign to denote the equality of two expressions.

As per the given expression,

e^(x/4) = |4x|

The function e^(x/4) is an exponential function and the plot of this function has been plotted below.

The mode function |4x| has also been plotted below.

The point of intersection is the point where both will be the same or the solution meets.

The first point of intersection is (0.267,1.0691) so x = 0.267 ≈ 0.27

The second point of intersection (-0.2357,0.9428) so x = -0.2357 ≈ -0.24

Hence " The solution of the equation e^(x/4) = |4x| for the x by graphical approach is 0.27 and -0.24.".

For more about the equation,

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Answer:

Tangent to radius of a circle theorem

A tangent to a circle forms a right angle with the circle's radius, at the point of contact of the tangent.

Part A:

With the theorem above, we will have that the tangent is perpendicular to the line radius drawn from the point of tangency

Therefore,

The value of angle CBA will be

Part B:

Since the angle formed between the tangent and the radius from the point of tangency is 90°

Hence,

The final amswer is

Tangent lines are PERPENDICULAR to a radius drawn from the point of tangency

Part C:

Concept:

Three interior angles of a triangle will always have the sum of 180°

Hence,

The measure of angles in a triangle will add up to give

Part D:

Since we have the sum of angles in a triangle as

Then the formula below will be used to calculate the value of angle BCA

By substituting the values,we will have

Hence,

The measure of ∠BCA = 33°

The Volume of the suitcase is given by the formula:

Length x width x height = L X W X H

L= 2 1/3ft

W= 1/3ft

H= 1 1/2ft

Volume of the suitcase is 1 1/6 cubic feet

The blue line passes through the points

(-2.6, 1) and (-1.4, 2.5)

I will label the coordinates as follows for reference:

Step 1: Find the slope of the blue line

The slope between two points is calculated with the formula:

We substitute the values and we get that the slope of the blue line is:

The slope m of the blue line is 1.25.

step 2: With that slope, calculate b (the intercept of the blue line with the y axis).

For this we use the point - slope equation:

Where we will use the sane x1 and x2 as in the previous step, so we get

We compare this with the slope-intercept equation

And we can see that the incercept b is 4.25

step 3: Find the value of c.

to find the value of c, we need to know at which point the blue line crosses the x axis.

Since we already have the equation of the blue line y=1.25x+4.25, and the line crosses the x axis at y=0, we substitute this to find the x value that is equal to c:

The blue line crosses the x axis at (-3.4,0), thus we can conclude that

Step 4: Define the two point where the orange line passes through.

We know from the picture that the orange line passes through (c,0) and (0,-b)

Since we have the values of c = -3.4 and b=4.25, we can say that the orange line passes through (-3.4, 0) and (0, -4.25)

Step 5: Calculate the slope of the orange line.

the orange line passes through (-3.4, 0) and (0, -4.25), so we define:

The circles in option B and D has their centers in the second quadrant

Here, we want to know which of the circles have their centers in the second quadrant

Generally, the equation of a circle can be represented as;

where (h,k) represents the center of the circle

Now, let us get the center of each of the circles;

A. (4,-3)

b. (-1,7)

C.(5,6)

D. (-2,5)

The second quadrant has its coordinates in the form (-x,y)

Out of all the options, the option that fits these quadrant is the second and fourth

So the circles in option B and D has its center in the second

Option A

The graph shows an inverse proportion.

As x increases, y decreases in value.

Finding the slope of the graph:

dy / dx = (y₂ - y₁) / (x₂ - x₁)

x₁ = 5, x₂ = 9, y₁ = 40, y₂ = 30

dy / dx = (30 - 40) / (9 - 5)

dy / dx = -10 / 4

dy / dx = -2.5

This means that as x increases by 1, decreases by 2.5

A is the only correct option.

Answer:

Explanation;

Here, we want to get the length of AD

From the information given:

Thus, mathematically:

Now, we can get AD

We simply substitute for the value of x

We have that as:

Answer:

• (a)g[f(x)]=5(-3x+5)+5

• (b)No

Explanation:

Given f(x) and g(x):

(a)First, we find the composition, g[f(x)].

(b)Next, we simplify g[f(x)] obtained from part (a) above.

Given two functions, f(x) and g(x), in order for the functions to be inverses of one another, the following must hold: f[g(x)]=g[f(x)]=x.

Since g[f(x)] is not equal to x, the functions are not inverses of one another.

Firs we need to find the equation of the line

x= clothing donations (pounds)

y= Amount earned (dollars)

We have the next points

(0,0)

(100,400)

We will calculate the slope

Therefore the equation is

y=4x

then if x=2200

y=4(2200)

y=8800

To find:

Which theorem used to prove that both triangles are congruent.

Solution:

It is given that both triangles are right triangles. So, each one of the corresponding angles is 90 degrees.

angle M is given 73 degrees and angle V is given 73 degrees. So, we can see that two pairs of angles are equal in triangle.

Thus, AA similarity postulate can be use to prove that both triangles are congruent.

Thus, option C is correct.

ANSWER

P(AuB) = 0.23

STEP-BY-STEP EXPLANATION:

Given information

P(A) = 0.2

P(B) = 0.1

P(AnB) = 0.07

What is P(AUB)

The next step is to substitute the above data into the formula

Answer:

-45 is an integer

√100 = 10 is a whole number

√89 is an irrational number-root

4.919191... is a rational decimal

-2/5 is a rational number-ratio

.12112111211112... is an irrational decimal

Finnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn

Hello there. To solve this question, we need to remember some properties about quadratic functions and its key features.

Let f(x) = ax² + bx + c, for a not equal to zero.

The main key feature we can see at first glance is the leading coefficient a.

If a < 0, the parabola (the graph of the function) will have its concavity facing down.

If a > 0, the parabola will have its concavity facing up.

It also means the function will have either a maximum or a minimum point on its vertex, respectively.

Another key feature of the function is the y-intercept, i. e. the point in which the x-coordinate is equal to zero, is (0, c).

The x-intercepts of the graph (in plural), are the roots of the function.

If b² - 4ac > 0, we'll have two distinct real roots.

If b² - 4ac = 0, we'll have two equal real roots.

If b² - 4ac < 0, we'll have two conjugate complex roots (not real roots)

This b² - 4ac is the discriminant of the function.

The roots can be found by the formula:

x = (-b +- sqrt(b² - 4ac))/2a

The vertex of the graph can be found on the coordinates (xv, yv), in which xv is calculated by the arithmetic mean of the roots

xv = ((-b + sqrt(b²-4ac))/2a + (-b-sqrt(b²-4ac))/2a)/2 = -b/2a

The yv coordinate can be found by plugging in xv in the function

yv = a(-b/2a)² + b(-b/2a) + c, which will be equal to -(b²-4ac)/4a.

Since we are dealing with a right triangle, we can use the Pythagorean theorem, shown below

In our case, H=4, L_1=2, L_2=x; then,

Solving for x,

The answer is x=2sqrt(3)

Given the follow equivalence

where

old width=42.9

Old height= 32.5

New width=3.3

then

New height is 2.5 inches

Solving the equation for r:

With the first equations, we can establish some limits for V:

With the lowest value for r (r=0):

With the highest value for r (r=9.5x10^-3)

According to the radius range, velocity can be between 0 and 3.61x10^-2

It is also necessary to check the domain of the function considering it is a square root. The argument of an square root cannot be less than 0. Then:

This is the same limit for velocity obtained before. Then, we can say for velocity that:

To answer this question, we always need to take into account the reference angle in a right triangle. The reference angle here is theta, Θ, and we have that:

Then, the length of the side adjacent to theta is equal to 15.

In summary, we have that the length of the side adjacent to the angle Θ is equal to 15.

Answer:

67% decrease

Explanation:

From the given problem:

Initial number of bananas = 120

Final number of bananas = 40

Since we have a negative value, we have a 67% decrease.

Answer:

y - 4 = [tex]\frac{11}{2}[/tex] ( x - 3 )

Step-by-step explanation:

( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] )

( [tex]x_{2}[/tex] , [tex]y_{2}[/tex] )

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

y - [tex]y_{1}[/tex] = m( x - [tex]x_{1}[/tex] )

~~~~~~~~~~~~~~~

( 3 , 4 )

( 1 , - 7 )

m = [tex]\frac{-7-4}{1-3}[/tex] = [tex]\frac{-11}{-2}[/tex] = [tex]\frac{11}{2}[/tex]

y - 4 = [tex]\frac{11}{2}[/tex] ( x - 3 )

879,087.

EXPLANATION

To find the number of lawnmowers, we need to first find 70% of the number of lawnmowers that was kept in the past. Then add the to the number of lawnmowers kept in the past.

From the given question;

Number of lawnmowers kept in the past = 517, 110.

70% of lawnmowers kept in the past = 70% of 517 110

Number of lawnmowers now kept in store = number of lawnmowers kept in the past + 70% of lawnmowers kept in the past

= 517 110 + 361 977

= 879,087.

If Smith uses both medications, then its dosage is the sum of each.

The total dosage of the medication would be 49 ml if he got both medications.

5 + 8h

h= number of hours

Replace h by 5 and solve

5 + 8(5)

5 +40

45

She will charge $45