A full pond containing 625 gallons of water begins losing its water at a rate of 20% per week. If the pond now contains 320 gallons of water, how many weeks has it been since the pond was at full capacity?

(Use the digits 0 – 9 to enter a number. Use a decimal point only if necessary.)

Answer:

Part a
[tex]m = \dfrac{280-\boxed{140}}{\boxed{4} - 2} = \dfrac{\boxed{140}}{\boxed{2}}[/tex]

[tex]y = \boxed{70}x[/tex]

Part b.
The heart's resting rate is [tex]\boxed{70}[/tex] beats each minute

Step-by-step explanation:

Q6

Part a

The slope-intercept form of an equation is y = mx + b

where m is the slope and b the y-intercept ie the value of y when x is 0

Here we see when x = 0, y = 0 so the value of b is 0 and the equation is simply

y = mx

To compute m, all we have to do is take 2 points on the graph, find the difference in y values(called rise) and divide by the difference in x values(called run)

This would be [tex]\dfrac{y2-y1}{x2-x1}[/tex]

We are given y2 as 280(on the numerator). The corresponding x2 value from the graph is 4

We are given x1(on the denominator) as 2. The corresponding y1 value is 140 from the graph

So just fill in the missing values to get

[tex]m = \dfrac{280-\boxed{140}}{\boxed{4} - 2} = \dfrac{\boxed{140}}{\boxed{2}}[/tex]

The above simplifies to 70

So the equation is

[tex]y = \boxed{70}x[/tex]

Part b
The interpretation is:

The heart's resting rate is [tex]\boxed{70}[/tex] beats each minute

If the volume of a cube decreases at a rate of 10 m/sec, then the  rate at which the side of the cube changes when the side of the cube is 2 m is -0.83 meter per second

The rate of  volume of the the cube decreasing = 10 meter per second

Consider the side of the cube is x

The volume of the cube = x^3

The rate of change of volume with respect to time

dV / dt = 3x^2 dx/dt

dV / dt = -10 meter per second

The dx / dt = (dV / dt) / 3x^2

We haver to find the rate at which side of the cube changes when the side of the cube is 2 meter

Then x = 2

dx / dt = -10 / (3 × 2^2)

= -10 / 12

= -0.83 meter per second

Therefore, the rate at which side of the cube changes when the side of the cubes is 2 meter is -0.83 meter per second

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The answer is No because one x-value corresponds to two different

y-values.

What is the function?

Each element of X is given exactly one element of Y by a function from a set X to a set Y. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between two varying quantities.

Here the given function is,

           x     y

           3     4

           4     4

           5     2

           5     5

From the table we can see that there are 2 values of x having same

y - value.

Hence, the given table does not represents a function.

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Answer: A linear equation in the form y = mx + b can be determined by examining the values in the table. To find the value of m, we can use the formula for the slope of a line, which is (y2 - y1) / (x2 - x1). Using the first and last values in the table, we can compute the slope as (7 - 15) / (4 - 0) = -1/4.

Therefore, the equation that represents the table is:

y = (-1/4) * x + b

We can use any of the given points to find the value of b. For example, using the point (1, 13), we can solve the equation to find b:

13 = (-1/4) * 1 + b

b = 14 - 1/4 = 13 3/4

Therefore, the final equation that represents the table is:

y = (-1/4) * x + 13 3/4

The required number of seconds would it take to travel the the length of the building is 91.

The equation for speed is basic like distance partitioned by time. You take the distance voyaged (for instance 3 meters) and gap it when (three seconds) to get the speed (one meter each second) Thus, we can characterize Speed as the pace of progress of position of an article toward any path.

We have,

length of the building = 455 meter

speed of elevator = 5 m/s

We know,

speed = distance/time

5 = 455/time

Time = 455/5

Time = 91 seconds.

Thus,time take to travel the the length of the building is 91 seconds.

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Answer:

The percent decrease is 70%.

Step-by-step explanation:

Answer:

70%

Step-by-step explanation:

Axillary is 3 skulls.The remainder goes to the appendix.

The bones could potentially represent up to 22 different people.This is due to the possibility that each bone comes from a different person.

There were only 3 skulls, leading some to first believe there would only be 3 persons. However, there were 4 right femurs, indicating that there is a missing skull to correspond with one of the right femurs.

In light of this, you can only conclude, until further proof, that each bone belongs to a different person.

Axillary =3 skulls.

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Answer:

[tex]x=64, y=72[/tex]

Step-by-step explanation:

Using the angle sum of a triangle, [tex]x=180-57-59=64[/tex].

Thus, the left hand triangle has angles of 42°, 64° (using vertical angles), and y°. It follows that [tex]y=180-42-64=74[/tex].

The required possible lengths of the parking lot is 300.

The  perimeter of a shape is characterized as the complete length of its limit. The border of a not entirely set in stone by adding the length of the relative multitude of sides and edges encasing the shape.

The area of a shape is the "space encased inside the border or the limit" of the given shape. We compute the region for various shapes utilizing math equations.

Perimeter = 520 feet, area = 12000 feet

We know that,

Perimeter = 2(L + B)

2(L + B) = 520

(L + B) = 260--------(1)

And

Area = L×B = 12000

From equation(1),we get

L(L - 260) = 12000

L^2 - 260L = 12000

L^2 - 260L - 12000 = 0

On solving above quadratic equation

L = 300 or L = -40

Thus, possible value of length is 300.

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Answer:

-6.5y - 1.1x

Step-by-step explanation:

Rearrange the problem to where like terms are closer together:

11.7y+5.2y + 1.2x + x - 3.3x

Simplify by adding the like terms and your final answer will be -6.5y -1.1x

The values of the variables x, y, z in the parallelogram are x=31, y=153, z=96.

In Euclidean geometry, a parallelogram is a simple (non-self-intersecting) quadrilateral with two sets of parallel sides. Both the congruence of opposite sides and the congruence of opposite angles require the Euclidean parallel postulate, or one of its equivalent formulations, and neither condition can be proved without it.

The values of the three supplied variables x, y, and z in the parallelogram are given to us.

Let's abbreviate the parallelogram, which is depicted in the attached image, ABCD.

Here,

m∠CAB = 31°,  m∠ABC =96°.

Since CD and AB are parallel, AC is a transversal now. So,

m∠CAB =m∠ACD

m∠ACD=31°

x=31

From the ΔABC we have,

m∠ABC +m∠ACB+m∠BAC=180°

96°+Y+31°=180°

y+127°=180°

y=153°

y=153

And also we know that the measure of opposite angles in a parallelogram are always equal.

So, m∠ADC=m∠ABC

z=96°

z=96

Therefore, the required values of x, y, z are 31, 153, 96.

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The measure of length of side p is 33 ft  .

What is measure of length?

Some of the commonly used units for measuring length are centimeters, millimeters, meters, inches, feet, yards, feet, etc. Some of the units to measure mass are pounds, ounces, kilograms, grams, centigrams, milligrams, etc.

Given as the length of the swimming pool measured by drawing similar triangle :

I.e The smaller Triangle similar to larger Triangle

Let o is the points of meeting of two triangles

And OAB is smaller triangle having sides OA , AB , BO

The measure of side OA = 8 ft

The measure of side AB = 12 ft

Again, OPQ is larger triangle having sides OP , PQ , QO

The measure of side OP = 22 ft

The measure of side PQ = p ft

∵ both Δ OAB    and  ΔOPQ  are similar

The from similarity property  

[tex]\begin{aligned}& \frac{P Q}{A B}=\frac{O P}{O A} \\& \text { l.e } \frac{p}{12}=\frac{22}{8} \\& \text { Or, } \frac{p}{12}=\frac{11}{4} \\& \therefore \mathrm{p}=\frac{11}{4} \times 12 \\& \text { or. } \mathrm{p}=11 \times 3 \\& \text { l.e } \mathrm{p}=33 \mathrm{ft}\end{aligned}[/tex]

Hence, the measure of length of side p is 33 ft  .

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Answer:

See Picture

Step-by-step explanation:

The equation of the line that is parallel to y = -1/2x - 3 and passes through the point (4, -1) is y + 1 = -1/2x + 2 written in slope-intercept form.

What is the slope of the equation?

The slope of a line is a measure of its steepness. Mathematically, the slope is calculated as "rise over run" (change in y divided by change in x).

To find the equation of a line that is parallel to y = -1/2x - 3 and passes through the point (4, -1), we can use the point-slope form:

y - y1 = m(x - x1)

where (x1, y1) is the given point, and m is the slope of the line.

Since the given line is parallel to y = -1/2x - 3, it has the same slope, which is -1/2. Substituting this value for m and the coordinates of the given point into the point-slope form, we get:

y - (-1) = (-1/2)(x - 4)

Combining like terms and multiplying through the parentheses, we get:

y + 1 = -1/2x + 2

Hence, the equation of the line that is parallel to y = -1/2x - 3 and passes through the point (4, -1) is y + 1 = -1/2x + 2 written in slope-intercept form.

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Answer:

B

Step-by-step explanation:

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

The x-coordinate of the point is 9.

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

The equation of a line y = (2/3)x - 6 ______(1)

Now,

The line passes through a point (x, 0).

(x, 0) = (x, y) ______(2)

Now,

Putting (2) in (1) we get,

0 = (2/3)x - 6

6 = (2/3)x

x = 6 x 3 / 2

x = 9

Thus,

The x-coordinate of the point is 9.

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Answer:

Q: How much are 5 small greeting cards?

A: $6

Q: How much are 4 large greeting cards?

A:$17

How much is it altogether? $23.

Step-by-step explanation:

Small greeting card cost: $1.20

Large greeting card cost: $4.25

Let's solve how much it would cost to get 5 small greeting cards.

5 (1.20)=6

So $6 for 5 small greeting cards

Let's solve how much it would cost for 4 large greeting cards

4 (4.25)= 17

So $17 for 4 large greeting cards.

I hope this helps!!! I didn't understand the question completely, so hopefully I added everything that you needed.

Let x represent the number of people coming on the trip.

The 3-day ticket rate per person plus the total rental cost is 299 + 872.50 = $<<299+872.50=1171.50>>1171.50.

The total amount paid per person for the trip, assuming Marissa and Mykuria are able to get enough friends to come on the trip so that the vacation rental house will be at maximum capacity, is 361.25. This can be represented as an expression as follows:

(299 + 872.50)/x = 361.25

This equation can be rearranged to solve for the value of x, which represents the number of people coming on the trip.

Answer:

x = 3; y = -1

Step-by-step explanation:

2x - 3y = 9

x = 4 + y

Since the second equation is already solved for x, use the substitution method. Substitute 4 + y for x in the first equation and solve for y.

2x - 3y = 9

2(4 + y) - 3y = 9

8 + 2y - 3y = 9

-y = 1

y = -1

Now substitute -1 for y in the second original equation, and solve for x.

x = 4 + y

x = 4 + (-1)

x = 3

Answer: x = 3; y = -1

Answer:

y = 2/3x + 3

Step-by-step explanation:

(-1,-1) (3,5)

5+1/3+1

6/4

2/3

y = 2/3x + b

5 = (2/3)(3) + b

5 = 2 + b

b = 3

y = 2/3x + 3

The value of the unknowns are w = 5 , x = 12 , y = 1 and z = 15

What is a Matrix?

In mathematics, a matrix (plural matrices) is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object

A+B = B+A  Commutative Law of Addition.

A+B+C = A +(B+C) = (A+B)+C  Associative law of addition.

ABC = A(BC) = (AB)C  Associative law of multiplication.

A(B+C) = AB + AC  Distributive law of matrix algebra.

R(A+B) = RA + RB

Given data ,

Let the Matrix be A

Now , the given matrices are

[tex]2\left[\begin{array}{ccc}w&2\\5&z\\\end{array}\right] + 3\left[\begin{array}{ccc}2&x\\-2&-6\\\end{array}\right] =4\left[\begin{array}{ccc}4&7\\y&3\\\end{array}\right][/tex]

On simplifying the matrices , we get

[tex]\left[\begin{array}{ccc}2w&4\\10&2z\\\end{array}\right] + \left[\begin{array}{ccc}6&2x\\-6&-18\\\end{array}\right] =\left[\begin{array}{ccc}16&28\\4y&12\\\end{array}\right][/tex]

Now , from the distributive law of matrices ,

2w + 6 = 16   be equation (1)

4 + 2x = 28   be equation (2)

10 - 6 = 4y     be equation (3)

2z - 18 = 12    be equation (4)

So on simplifying the equation , we get

2w + 6 = 16   be equation (1)

Subtracting 6 on both sides , we get

2w = 10

Divide by 2 on both sides , we get

w = 5

So on simplifying the equation , we get

4 + 2x = 28   be equation (2)

Subtracting 4 on both sides , we get

2x = 24

Divide by 2 on both sides , we get

x = 12

So on simplifying the equation , we get

10 - 6 = 4y     be equation (3)

4y = 4

Divide by 4 on both sides , we get

y = 1

So on simplifying the equation , we get

2z - 18 = 12    be equation (4)

Adding 18 on both sides , we get

2z = 30

Divide by 2 on both sides , we get

z = 15

Therefore , the values are w = 5 , x = 12 , y = 1 and z = 15

Hence , The value of the unknowns are w = 5 , x = 12 , y = 1 and z = 15

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Check the picture below.

the name of the line is both XY and YX

Answer:

Not enough context

Step-by-step explanation:

We need the bar graph/information for the amount child and adult tickets cost.

Answer:

No, 9 is not a solution to 12 [tex]\leq[/tex] a

Step-by-step explanation:

 The expression 12 [tex]\leq[/tex] a states " 12 is less or equal to a."  If a were 9, the statement would not be true, since 9 is less than 12.  This contradicts the expression.

The equation represents a circle that has a diameter of 12 units will be x² + (y - 3)² = 36. Hence, option A is correct.

Equations are mathematical expressions that have two algebras on either side of an equal (=) sign. The expressions on the left and right are shown to be equal to one another, demonstrating this relationship. L.H.S. = R.H.S. (left-hand side = right side) is a fundamental simple equation.

As per the provided information in the question,

Use the equation of a circle,

(x -a)² + (y - b)² = r²

Here, a and b represent the center of the circle and r is the radius of the circle.

A center can be anywhere along the y-axis if it is (0, 3).

(x -0)² + (y - 3)² = 6²

x² + (y - 3)² = 36

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Answer: x = 1.3125

Step-by-step explanation:

−4.75+0.8x=−3.7

First, add 4.75 to both sides

0.8x = 1.05

Then divide by 0.8 on both sides

x = 1.3125

Answer:

x = 1.3125

Step-by-step explanation:

The function that has the greater initial​ value is function A

From the question, we have the following parameters that can be used in our computation:

Function A: table

Function B: y = 3x + 6

The initial value of a function is when the input value is 0

i.e. when x = 0

From the table, we have

x = 0 when y = 8

From the equation, we have

y = 3(0) + 6

y = 6

8 is greater than 6

Hence. function A has the greater initial value

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