4 (Simple Interest and Arithmetic Sequences MC)

After hip surgery, your physical therapist tells you to slowly return to walking. The therapist suggests walking for 5 minutes each day for the first week and increasing that time by 5 minutes per day each week thereafter. How many weeks will it be before you are up to 45 minutes of walking per day?

10
11
9
13

(A). Yes, overdetermined systems can be consistent.

As, the system of equations below is consistent because it has a solution

x1 = 2 , x2 = 4 , x1 + x2 = 6.

We have,

'Over-determined system is a system of linear equations, in which there are more equations than unknowns'.

If we have m equations and n variables where m>n (more equations than variables), then system can be consistent if last m−n equations are linear combinations of previous ones.

For e.g. Let us consider the system,

x + y = 1

x - y = 1

3x + y = 3

solving these equations, we can see

The only intersection point is (1,0). Thus, x= 1 and y= 0 is the solution of this system.

Thus, over-determined system can be consistent.

According to the options,

Hence, option A is correct.

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The  required single payment is required to settle both debts in one month is $4071.26.

Simple interest is the amount of interest charged on a specific pripal amount at a specific interest rate. Compound interest, on the other hand, is the interest that is computed using both the principal and the interest that has accumulated over the preceding period.

We have,

Interest of 12 month = 6.30%

For one month = 6.30/12

= 0.525% per month

Total debt =  $2,100 +  $1,950

Total debt = $4050

Interest of one month = 0.525% of $4050

= $21.26

Net debt = $4050 + $21.26.

Thus, required single payment is required to settle both debts in one month is $4071.26.

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The solution for x is x = -2 + sqrt(17) and x = -2 - sqrt(17) will give the brainliest.

What is the quadratic equation?

A quadratic equation is a type of polynomial equation of degree 2, that can be written in the form of ax^2 + bx + c = 0 where x is the variable, a,b,c are constant and a is not equal to zero.

To solve for x in the equation 9/(x+4) = 2x, we can first clear the fractions by multiplying both sides of the equation by (x+4). This gives us:

9 = 2x*(x+4)

Then we can simplify the right side of the equation:

9 = 2x^2 + 8x

Next, we can move all the x terms to one side of the equation and all the constants to the other side:

2x^2 + 8x - 9 = 0

Now we can use the quadratic formula to solve for x:

x = (-b +/- sqrt(b^2 - 4ac)) / 2a

where a = 2, b = 8, and c = -9

So we have:

x = (-8 +/- sqrt(8^2 - 42-9)) / 2*2

x = (-8 +/- sqrt(64 + 72)) / 4

x = (-8 +/- sqrt(136)) / 4

x = (-8 +/- 4*sqrt(17)) / 4

x = (-2 +/- sqrt(17))

So the solutions for x are x = -2 + sqrt(17) and x = -2 - sqrt(17)

The solution for x is x = -2 + sqrt(17) and x = -2 - sqrt(17) will give the brainliest.

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Answer:

absolutely

Step-by-step explanation:

Needs are for survival in life like food, rent or mortgage, utilities, and other expenses.  Transportation costs, insurance coverage, and any clothing and tools you need for work are included in this part of your budget.  A want includes expenses that you can comfortably live without and is not essential for survival.

The distance between the xy, yz, and xz planes are 5, 3, and 7.

Multivariable Calculus

This question relates to multivariable calculus.

a) Distance of point (x, y, z) from the XY-plane

The |z co-ordinate of the point| = |z|

distance of the point (3, 7, -5) from xy plane

|-5|=5

b) Distance of point (x, y, z) from yz plane

The |x coordinate of the point| = |x|

Therefore, the distance of the point (3, 7, -5) from yz plane is

|3|=3

c) Distance of point (x, y, z) from xz plane

The |y coordinate of the point| = |y|.

The distance of the point (3, 7 -5) from the xz-plane is

|7|=7

d) Distance of point (x, y, z) from the x-axis

The distance of the points from the x-axis is

[tex]x^{2} =y^{2} +z^{2} \\\\x=\sqrt{y^{2} +z^{2} } \\\\x=\sqrt{7^{2}+(-5)^{2} } \\\\x=\sqrt{74}[/tex]

e) Distance of point (x, y, z) from the y-axis

[tex]y=\sqrt{x^{2} +z^{2} } \\\\y=\sqrt{3^{2}+(-5)^{2} } \\\\y=\sqrt{34}[/tex]

f) Distance of point (x, y, z) from the z-axis

[tex]z=\sqrt{x^{2} +y^{2} } \\\\z=\sqrt{3^{2}+7^{2} } \\\\z=\sqrt{58}[/tex]

From the calculations above,

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All together the number of yards of material Erin will need to sew jacket and skirt is 4 1/4 yards

From the question the following can be gotten

She needs 2 3/4 yards of material for the jacket and 1 1/2 yards of material for the skirt.

The total number of yards she will require is calculated using the addition operation

The total number of yards

Addition of fractions

= 2 3/4 + 1 1/2

= 17 / 4

= 4 1/4

The total number of yard required is 4 1/4

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According to the information, to create a rectangle polygon with a perimeter of 18 units, we must put sides of 3 units and bases of 6 units.

A polygon is a term that refers to a plane geometric figure composed of a finite sequence of consecutive line segments that enclose a region in a plane. These segments are called sides, and the points at which they intersect are called vertices.

A rectangle is a polygon with four sides and four vertices that is characterized by having two of its sides longer than the other two sides. Therefore, to draw a rectangle with a perimeter of 18 units we must distribute the measurements as follows:

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Answer:

C

Step-by-step explanation:

C. √2, √6,2√2 are not the lengths of the sides of a 30°-60°-90° triangle.

In a 30°-60°-90° triangle the ratio of the sides are always the same, the hypotenuse is twice the length of the shorter leg, and the longer leg is √3 times the length of the shorter leg.

A. 1/2, √3/2, 1 are the lengths of the sides of a 30°-60°-90° triangle. As the shorter leg is 1, the longer leg is 1√3=√3 and the hypotenuse is 12=2.

B. 5/2, 5√3/2, 10 are the lengths of the sides of a 30°-60°-90° triangle. As the shorter leg is 5/2, the longer leg is (5/2)*√3=5√3/2 and the hypotenuse is (5/2)*2=5

D. 3,3√3,6 are the lengths of the sides of a 30°-60°-90° triangle. As the shorter leg is 3, the longer leg is 3√3=3√3 and the hypotenuse is 32=6

So, option C is not the lengths of a 30°-60°-90° triangle.

The value of y and z in the equation are 31 and 7 respectively.

System of equation can be solved using different method such as elimination method, substitution method and graphical method.

Therefore, let's solve the system of equation using substitution method as follows:

y = 9 + 3z

y = 51 - 3z

Let's substitute the value of y in equation(ii)

51 - 3z = 9 + 3z

51 - 9 = 3z + 3z

42 = 6z

divide both sides of the equation by 6

z = 42 / 6

z = 7

Therefore, let's find the value of y using equation(i)

y = 9 + 3z

y = 9 + 3(7)

y = 9 + 21

y = 31

Therefore,

y = 31 and z = 7

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The integration of the expression [x / (x² + 1)³] will be - 1 / 4(x² + 1)² + c.

Integration is a way of finding the total by adding or summing the components. It's a reversal of differentiation, in which we break down functions into pieces. This approach is used to calculate the total on a large scale.

I = ∫ [x / (x² + 1)³] dx

Let x² + 1 = t, then x dx = dt / 2. Then we have

I = ∫ [1 / 2(t)³] dt

I = (1/2) ∫ [1 /(t)³] dt

I = (1/2) [-1 /2t²] + c

I = - (1/4) (1/(x² + 1)²) + c

I = - 1 / 4(x² + 1)² + c

The integration of the expression [x / (x² + 1)³] will be - 1 / 4(x² + 1)² + c.

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The flux of the vector field F is the integral of the normal component of the vector field over the surface.

The flux of the vector field F is the integral of the normal component of the vector field over the surface. In this case, the surface is the circle with radius r centered at the origin and the normal component of the vector field is just the z-component, which is equal to 2x. The integral of the normal component of the vector field over the circle is given by

Φ = ∫C 2x ds = ∫0 2π r2 2cosθ dθ

= 4πr2

This is the flux of the vector field F coming out of the circle.

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The equation of y = f(x) and the equation of the new function g(x)  under the transformation applied is Y=-3(x-1)² -1  or Y=-3x+6x-4.

What is the quadratic function opens upward or downward?

There is a simple way to identify whether the graph of a quadratic function opens upward or downward: if the leading coefficient is bigger than zero, the parabola expands upward; otherwise, the parabola opens downhill.

Y = -(3x²+2) reflects it about the x-axis. All positive y’s now become negative.

It used to be an upward-opening parabola with y-intercept = 2. Now, it’s a downward opening parabola with y-intercept = -2

Move it to the right by 2 means replace x by x-2

Move it up by 1 means replacing the y-intercept of -2 by -1, just add 1 to the y-intercept

Y=-3(x-1)² -1  or Y=-3x+6x-4

Hence, The equation of y = f(x) and the equation of the new function g(x)  under the transformation applied is Y=-3(x-1)² -1  or Y=-3x+6x-4.

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The required value of x is 3

A convex quadrilateral having exactly one set of opposite sides that are parallel to one another is called a trapezium. When drawn on a piece of paper, the trapezium is a two-dimensional shape that resembles a table. A quadrilateral is a polygon in Euclidean geometry that has four sides and four vertices. ​

Using the mid-segment theorem of trapezium.

The line segment that joins the midpoints of a trapezoid's two non-parallel sides is known as its mid segment. The average length of the bases makes up a trapezoid mid segment, which is parallel to the trapezoid's set of parallel lines. ​

[(3x + 1) + 15]/2 = 12.5

(3x + 1) + 15 = 25

3x + 1 = 10

3x = 9

x = 3

Thus, required value of x is 3.

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Answer:

Step-by-step explanation:

Consider the following four matrices:

(1000),(0010),(0100),(0001).

See what happens when you solve the equation AB=BA

for each of those four (let B

be each one of those four). To facilitate it, write A=(acbd)

You will get a set of equations for the entries of a

which are easily solved. This trick is quite general.

B must have 2n subsets since it has two corresponding subsets for each subset of A series  (S1, S2,..., Sa), one of which contains the extra element and the other of which does not.

Set B's size is |B| = |A| + 1 since it includes all of the components of set A plus an additional element. There must be two equivalent subsets in set B for each subset of A (S1, S2,..., Sa), one of which must contain the extra element and the other of which must not. This extra element must be present in at least one subset. B must therefore have a total of 2n subsets. For instance, if set A has the three subsets S1, S2, and S3, then set B will have the same three subsets plus S1 plus the extra element, S2 plus the extra element, and S3 plus the extra element, for a total of six subsets.

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So, the position vector of a point r is (1-1/3)p + (1/3)q.

The position vector of a point can be found using the following formula:

r = (1-λ)p + λq

where λ is the scalar value that represents the ratio in which the point divides the line segment.

In this case, the ratio of the point dividing the line segment is 1:2. So, λ = 1/3.

Substituting the values of p and q, we get:

r = (1-1/3)p + (1/3)q

To show that point p is the midpoint of the line segment rq, we can use the following property of midpoints:

The position vector of the midpoint of a line segment with endpoints p and q is given by (p+q)/2.

In this case, the position vector of point p is (1-1/3)p + (1/3)q, and the position vector of point q is (2/3)p + (2-2/3)q = (2/3)p + (4/3)q

So, the midpoint of the line segment rq is given by:

((1-1/3)p + (1/3)q + (2/3)p + (4/3)q)/2 = (3/3)p + (5/3)q

which is (p+q)/2, so p is the midpoint of the line segment rq

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Answer: I am Not that good In Maths But here you go

Step-by-step explanation:

Part A:

The population of a city in 2015 is 36,000 and it is increasing at 15% per year. We can model this using an exponential equation of the form:

P(z) = P0 * (1 + r)^z

Where:

P(z) is the population after z years

P0 is the initial population in 2015 (36,000)

r is the rate of growth (0.15)

z is the number of years since 2015

So the exponential equation that models the population is:

P(z) = 36,000 * (1 + 0.15)^z

Part B:

To find the population in 2020, we would substitute z = 5 (2020 - 2015) into the equation:

P(5) = 36,000 * (1 + 0.15)^5

P(5) = 36,000 * 1.15^5

Calculating this gives us a population of approximately 63,746 in 2020.

To obtain this answer, we used the exponential equation that models the population, P(z), where a represents the number of years since 2015, with the given information that population in 2015 was 36,000 and it's increasing at 15% per year and substitute the value of 5 for z.

At the same rate, a machine take 44 hours until the drill reaches its final depth of −132 feet.

Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.

We have to given that;

A machine that drills holes for wells drilled to a depth of−72 feet in one day (24 hours).

Now, Let a machine drill holes reaches its final depth of −132 feet in x hours.

Hence, By definition of proportion, we get;

⇒ 72 / 24 = 132 / x

⇒ x = 132 × 24 / 72

⇒ x = 3,168 / 72

⇒ x = 44 hours

Thus, It take 44 hours to reaches its final depth of −132 feet.

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Answer:

0.8

Step-by-step explanation:

.40 / 100x200

we can compute A=3 by 3 matrix, B= 1 by 3 matrix

C=2 by 2 matrix D= 3 by 1 matrix  and E= 1 by 1 matrix ,

We can compute only AA ,AD,BA, BD,CC,DB,EE,

[tex]We\ have \ A=\left[\begin{array}{ccc}1&0&-1\\2&1&0\\3&2&1\end{array}\right] \\\\B=[1\ 2 \ 3]\\\\C=\left[\begin{array}{ccc}1&1\\1&1&\end{array}\right] \\\\D=\left[\begin{array}{ccc}1\\1\\1\end{array}\right] \\\\E=[3][/tex]

So ,we have to produced 25 matrix -

AA,AB,AC,AD,AE

BA,BB,BC,BD,BE

CA,CB,CC,CD,CE

DA,DB,DC,DD,DE

EA,EB,EC,ED,EE

To multiply two matrix column of first matrix equal to row of second matrix.

So we can compute A=3 by 3 matrix, B= 1 by 3 matrix

C=2 by 2 matrix D= 3 by 1 matrix  and E= 1 by 1 matrix ,

We can compute only AA ,AD,BA, BD,CC,DB,EE,

[tex]AA=\left[\begin{array}{ccc}1&0&-1\\2&1&0\\3&2&1\end{array}\right] \left[\begin{array}{ccc}1&0&-1\\2&1&0\\3&2&1\end{array}\right] \\\\AA=\left[\begin{array}{ccc}-2&-2&-2\\4&1&-2\\10&4&-2\end{array}\right] \\\\AD=\left[\begin{array}{ccc}0\\1\\6\end{array}\right] \\\\CC=\left[\begin{array}{ccc}2&2\\2&2\\\end{array}\right] \\\\EE=[9][/tex]

So we can compute A=3 by 3 matrix, B= 1 by 3 matrix

C=2 by 2 matrix D= 3 by 1 matrix  and E= 1 by 1 matrix ,

We can compute only AA ,AD,BA, BD,CC,DB,EE,

The complete question is :-

Let the matrices,

[tex]A=\left[\begin{array}{ccc}1&0&-1\\2&1&0\\3&2&1\end{array}\right] \\\\B=[1\ 2 \ 3]\\\\C=\left[\begin{array}{ccc}1&1\\1&1&\end{array}\right] \\\\D=\left[\begin{array}{ccc}1\\1\\1\end{array}\right] \\\\E=[3][/tex]

Which of the 25-matrix products AA, AB, AC ......EE are defined? Compute those products that are defined.

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If Suzy orders supplies for quick stop gas station and she needs to order additional lids for the disposable soda cups. The  size that lid need to purchase from the soda cups is 9.42in.

Using this formula to find the size that lid need to purchase from the soda cups

C= πd

Where:

C = circumference = ?

π =constant pi = 3.14

d = diameter = 3

Let plug in the formula

C = 3.14 × 3

C  = 9.42 in

Therefore we can conclude that the size that lid need to purchase from the soda cups is 9.42in.

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If a 150-pound person uses 6.6 calories per minute when walking at a speed of 4 mph.  The time a person walk at this speed to use at least 160 calories is: 24minutes.

Calories that was used = 6.6 calories per minute

Total calories = 160 calories

So,

Let x represent the minutes to walk

6.6x=160

Divide both side by 6.6x

x=160/6.6

x= 24.24 minutes

x = 24 minutes ( Approximately)

Therefore we can conclude that the time a person walk at this speed to use at least 160 calories is: 24minutes.

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Answer:

y=x^3 - 10x + 16

Step-by-step explanation:

Answer:

not sure about this ......

If a balloon was originally filled to a volume of 4,400 cubic centimeters. The inequality expression of the volume of the balloon is: V < 4400.

Volume = 4,400 cubic centimeters

Since the air inside the balloon leaks out over time which implies that the air inside the balloon will reduce.

So the expression is:

V < 4400

Where:

V = Volume

< = less than

Therefore the  inequality expression is V < 4400.

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The complete question is:

A balloon was originally filled to a volume of 4,400 cubic centimeters. Air inside the balloon leaks out over time.

Write an inequality that describes V, the volume of the balloon in cubic centimeters as air leaks out.

Enter your inequality without a thousands separator.

Answer:

Step-by-step explanation:

y = kx

a. Because x and y vary directly, the equation is in the form y = kx.

FOR YOUR UNDERSTANDING WAY

The ratio of y to x would be 4/20 = 1/5. So the equation would be y=1/5x

Answer:

3000

Step-by-step explanation:

Answer:

Answer:

$1,392

Step-by-step explanation:

1,200(0.08)(2) = 192

1,200 + 192 = $1,392

Step-by-step explanation:

The linear equation of the line would be y = 7/5x. The number of loaves of bread from 85 pounds of flour would be 7/5(85) = 119 loaves.

Each term in a linear equation has an exponent of 1, and when this algebraic equation is graphed, it always produces a straight line. It is called a "linear equation" for this reason.

Slope calculation:

This line's slope would be the proportional constant.

This point (35, 49) is extremely near to the lines that would result in the linear constant 49/35 = 7/5 , the line's equation is y = (7/5)x .

Using 85 pounds of flour, Calculate the loaves of bread that may be made (7/5) * 85 = 119 loaves.

Therefore, the equation is y = (7/5)x that is used to forecast the number of loaves that could be created from 85 pounds of flour, and the result was 119 loaves.

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The complete question is:

A bakery makes small batches of bread daily. Each day, the bakery records the amount of flour used the number of loaves of bread made. All loaves are approximately the same size. The table and graph show the bakery’s data for five days.

write an equation that can be used to model the number of loaves of breast, y that can be made from x pounds flour

Use an equation to predict the number of loaves that can be made from 85 pounds of flour show your work or explain your answer