A charge of $8.99 is automatically deducted from Ari's bank account each
month for a live TV streaming service. What is the change in Ari's bank
account after 6 months for this service? Lesson 1-3 7.NSO.2.2, 7.NSO.

We have shown that the product of two rational numbers is rational.

A number system is defined as a system of writing to express numbers.

Let a and b be two rational numbers, such that:

a = p/q

b = r/s

where p, q, r, and s are integers and q, s are non-zero.

We need to show that the product ab is also a rational number.

We have:

ab = (p/q) x (r/s)

= (p x r) / (q x s)

Since p, q, r, and s are all integers,

ab = m/n

where m = p x r and n = q x s.

Since both m and n are integers and n is non-zero ,we can conclude that ab is a rational number.

Therefore, we have shown that the product of two rational numbers is rational.

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In a directly proportional relationship, increasing one variable will increase another. The weight of the roof whose depth is 1.75 inches is 6,300 pounds.

In a directly proportional relationship, increasing one variable will increase another. This directly proportional relationship between p and q is written as p∝q where that middle sign is the sign of proportionality.

Let there are two variables p and q. Then, p and q are said to be directly proportional to each other if p = kq, where k is some constant number called the constant of proportionality.

Given the hail's weight varies directly with its depth. Therefore, the relation can be written as,

Weight ∝ Depth

W∝D

Introducing the constant to remove the proportionality we will get the equation as,

W = kD

1800pounds = k × 0.5 inches

3600ponds/inches = k

Now, the weight of the roof whose depth is 1.75 inches can be written as,

W = kD

W = 3600 × 1.75

W = 6,300 pounds

Hence, the weight of the roof whose depth is 1.75 inches is 6,300 pounds.

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The final answer in scientific notation with the correct number of significant digits, and label with the correct units is 4.1 * 10^6 square ft

The dimensions of the field are given as

Length = 3.3 * 10^3

Width = 2.5 * 10^3

From the question, we have

Half of the field is used to grow crops

This means that the area of the portion of the field that has crops growing is

Area = 1/2 * Length * Width

So, we have

Area = 1/2 * 3.3 * 10^3 * 2.5 * 10^3

Evaluate the product

Area = 4.125 * 10^6

In (a), we have

Area = 4.125 * 10^6

The units are 2 significant digits

So, the result must also have 2 significant digits

This means that

Area = 4.1 * 10^6 square ft (when approximated)

The units are 2 significant digits

So, the result must also have 2 significant digits

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We want to find a polynomial

f(x) = a x³ + b x² + c x + d

such that the roots of f are x = -3, x = -1, and x = 4, and f(x) takes on a value of -24 when x = -2.

The factor theorem for polynomials tells us that we can factorize f(x) as

a x³ + b x² + c x + d = a (x + 3) (x + 1) (x - 4)

Expand the right side:

(x + 3) (x + 1) (x - 4) = x³ - 13x - 12

So we have

a x³ + b x² + c x + d = a x³ - 13a x - 12a

In order for both sides to be equal, the coefficients of both polynomials on terms of the same degree must be equal. This means

a = a (of course)

b = 0 (there is no x² term on the right)

c = -13a

d = -12a

We also have that f (-2) = -24, which means

f (-2) = a (-2 + 3) (-2 + 1) (-2 - 4)

-24 = 6a

a = -4

which in turn tells us that c = 52 and d = 48.

So we found

f(x) = -4x³ + 52x + 48

The value of the current assets is $44500.

Plants asset = $27000

Equity = $81000

The value of the current asset will be:

Cash $7,500

Prepaid Rent $12,000

Accounts Receivable $6,000

Merchandise Inventory $19,000,

Current asset = $44500

Plant assets will be:

Land $16,000

Building $11,000.

Plant asset = $16000 + $11000 = $27000

Stockholders equity will be:

Common stock = $30000

Retained earnings = $51000

Equity = $81000

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Answer:

11,260

Step-by-step explanation:

im pretty sure that the formula were were using was

A=Pe^rt.

That means, we have to plug it in the formula.

P= 7500

r= 0.029

t= 14

you calculate it and then to the nearest ten dollars, your answer will be

$11,260. :)

Using Exponential Function, the amount of money to the nearest $10 would be in the account after 14 years is $11,260.

Exponential function is "a function whose value is constant raised to the power of an argument, especially the function whose constant is e".

According to the question,

Ariana invested $7500 in an account paying interest rate 2.9% compounded continuously assuming no deposits or withdrawals are made.

In order to find amount of money after 14 years only if we use exponential function.

Formula to find amount of money after 14 years = P .\(e^(rt)\)    where 'r' is the rate of interest and 't' is time period and 'P' is the Principal.

Amount of money after 14 years = P .\(e^(rt)\)

= (7500)\(e^(0.029)(14)\)    [2.9% = \(\frac{2.9}{100}\) = 0.029]

= 7500\(e^(0.406)\)

= 7500 (1.5008)           [The value of \(e^(0.406)\)  = 1.5008]

= 11,256.

Hence, using Exponential Function, the amount of money to the nearest $10 would be in the account after 14 years is $11,260.

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1) Note the the linearization of th function f(X) at a =1 is l(x) = 2x-3
2) since l(x) = 2x-3, f(1.01) is = - 0.98

Linearization is the process of converting a nonlinear function's gradient with respect to all variables into a linear representation at that moment.

for the  above prompt , we have to use the formula:

l (x) =  f(a) + f' (a) (x-a)

where  (a) is the value fo the function at point a

and f' (a)  is the derivative of the function evaluated at point  a.


Using a =  1, f(a) becomes:


f(1)  = 2 (1) ⁵ - 8 (1) + 5

f (1) =-1


f(x) = 10x⁴ -8

So f' (1 ) when evalutated will give us the slope of the tangent line at x =1

Thus,

f (1 ) = 10 (1)⁴ -8

= 2

Hence substituting all the values into th e linearization formula we get:

l(x) = f( 1) + f '(1) (x-1)

= -1 + 2 *( x-1 )
= -1 + 2x - 2
= 2x -3

This means that the linearization of the function f(x ) at a= 1 is l(x) = 2x-3


b) Given the l(x) above, f(1.01) gives us:

l(x) = 2x -3
= 2 (1.01) -3
= - 0.98

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Astronomers can use geometry to measure the distance of objects in space and describe ttheir relationship.

It should be noted that astronomers study stars, planets, and other celestial bodies. It should be noted that they use ground-based equipment, like optical telescopes, and space-based equipment. Some astronomers study distant galaxies and phenomena such as black holes and neutron stars.

In this case, astronomers can use geometry to measure the distance of objects in space and describe ttheir relationship.

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Answer:

distance between, motion

Step-by-step explanation:

plato, I got it right

Answer:

The literary magazine must pay $ 10 if poem is written by Gil, $ 20 if poem is written by Holly and $ 30 if poem is written by Ivan.

Step-by-step explanation:

The wage indicate the amount of money earned in hour for production of poems. If a literary magazine needs just one poem, then the cost will be the wage multiplied by time taken for the creation of the poem. There are three possibilities:

Gil

\(C = \left(10\,\frac{USD}{h})\cdot (1\,h)\)

\(C = 10\,USD\)

Holly

\(C = \left(10\,\frac{USD}{h}\right)\cdot (2\,h)\)

\(C = 20\,USD\)

Ivan

\(C = \left(10\,\frac{USD}{h}\right)\cdot (3\,h)\)

\(C = 30\,USD\)

The literary magazine must pay $ 10 if poem is written by Gil, $ 20 if poem is written by Holly and $ 30 if poem is written by Ivan.

Answer:

45

Step-by-step explanation:

21 + 2w

21 + 2(12)

21 + 24

45

answer:

58

step-by-step explanation:

for this plug in,

2(17) + 2(12)

34 + 24 = 58

The solution is, the percent of error, rounded to the nearest percent is 25%.

A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.

here, we have,

given that,

While viewing a herd of cattle on a ranch, Herbert estimated that there were 750 cattle in the herd.

The actual number of cattle in the herd was 600.

now, we have to find the percent of error, rounded to the nearest percent.

so, we get,

Herbert estimated that there were 750 cattle in the herd.

The actual number of cattle in the herd was 600.

so, error = 750 - 600

              = 150

so, we get,

the percent of error = 150 * 100 / 600

                                 = 25%

Hence, The solution is, the percent of error, rounded to the nearest percent is 25%.

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Since function f gives the vertical distance of each town from sea level, then when we have the following:

it means that at certain elevation, the two towns have the same vertical distance from sea level, that is the reason why they produce the same output.

The function f(e) is given by the following expression:

Then, since two towns have different elevations, but their inputs produce the same output on f, we have that the elevations of the towns are 25 and -25

The measure of distance RS, if The sides QU = 140 m, US = 115 m, TU = 104.55 m, rounding to the nearest hundredth of a meter, is 200 m.

Triangles are basic three-sided polygons with three internal angles. It is one of the basic geometric shapes, symbolized by the symbol, and has three vertex connections.

Given:

The sides QU = 140 m, US = 115 m, TU = 104.55 m

As you can see, the triangle QRS and triangle QTU are similar, thus the ratio of their sides will be equal,

QU / QS = TU / RS

140 / 140 + 115 = 104.55 / RS

140 / 255 = 104.55 \ RS

RS = 104.55 × 255 / 140

RS = 190.43 or 200 m

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Answer: 190.43m

Step-by-step explanation:

In Photo

Answer:

The answer is C. 168 in^2

Step-by-step explanation:

(Area = Base x Height)

21 * 8 = 168

Answer:

\(y\ge 14-x\) and \(y \leq 24 - \frac{11}{5} x\)

6 cupcakes and 10 brownies

Step-by-step explanation:

From the graph (6, 8) solution of system of inequalities graphically.

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

Let the number of cupcakes be c and the number of brownies be b.

Bakery sell cupcakes for $2.75 each and brownies for $1.25 each. Mia has $30 to spend and must buy at least 14 cupcakes and brownies altogether.

c+b≥14 -----------(I)

2.75c+1.25b<30 -----------(II)

Solve each inequality and then find the intersection.

14-b≤c<10.90-0.45b

Therefore, from the graph (6, 8) solution of system of inequalities graphically.

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Answer:

-Below.

Step-by-step explanation:

4) When the carton is unopened the number of servings x = 0.

So there are 64-4(0) = 64 ounces in an unopened carton.

5) When all the milk has been poured out no. ounces left (y)  = 0 so

64 - 4x = 0

4x = 64

x = 16

So each serving contains 16 ounces of milk.

If the total price of the trip per student was $7.00, approximately the percentage of the trip that would go towards the price of the bus is 71.43%.

The percentage is the ratio of a variable or value to another.

Percentages are fractional values, computed as the quotient of a numerator over a denominator multiplied by 100.

The bus roundtrip charge per student = $5.00

The trip price per student = $7.00

Percentage of the trip going towards the price of the bus = 71.43% ($5/$7 x 100).

Thus, we expect that 71.43% of the trip amount will be consumed for the bus charter.

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Answer:

Cylinder + Rectangular Prism

Step-by-step explanation:

On the sides we can see 2 half-cylinders. 2 half-cylinders make up 1 whole cylinder. In between the half-cylinders, a rectangular prism is squashed.

Think of this as a sandwich, the 2 buns are half cylinders, and the meat is the prism.

Therefore the answer is a cylinder and a rectangular prism.

The expression x^2 + 2x - a is divisible by x + 4 when a = 6x.

A long division polynomial is an algorithm for dividing polynomial by another polynomial of the same or a lower degree.

By using the long division method:

x + 4 | x^2 + 2x - a

-x^2 - 2x + 4x    

-------------------

      -a + 6x    

-x^2 - a + 6x    

-------------------

        2x - a

-x^2 - 2x + 4x    

-------------------

          0

The remainder is 0 a = 6x.

Hence, the expression x^2 + 2x - a is divisible by x + 4 when a = 6x.

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The time taken to grow to $8000 is 17 years and 4 months.

The formula used to find the time compounded continuously.

t = ln(A/P) / r

It is the interest we earned on the interest.

The formula for the amount earned with compound interest after n years is given as:

A = P \((1 + r/n)^{nt}\)

P = principal

R = rate

t = time in years

n = number of times compounded in a year.

We have,

P = $4000

A = $8000

r = 4%

The formula used:

t = ln(A/P) / r

t = ln(8,000/4,000) / 0.04

t = 17.329 years

This means,

= 17 years 4 months

Thus,

The time taken to grow to $8000 is 17 years 4 months.

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\(~~~~~\sin 30^{\circ} = \dfrac{\text{Perpendicular}}{\text{Hypotenuse} }\\\\\\\implies \dfrac 12 = \dfrac{8}x\\\\\\\implies x = 8\cdot2\\\\\\\implies x = 16 ~ \text{cm.}\)

The measure of the side length is 16 cm after applying the sin ratio which is the side opposite to the angle/hypotenuse.

It is a triangle in which one of the angles is 90 degrees and the other two are sharp angles. The sides of a right-angled triangle are known as the hypotenuse, perpendicular, and base.

It is given that:

A right-angle triangle is shown in the picture.

To find the side length of the hypotenuse apply the sin ratio

sin30 = side opposite to the angle/hypotenuse

1/2 = 8/x

x = 8(2)

x = 16 cm

Thus, the measure of the side length is 16 cm after applying the sin ratio which is the side opposite to the angle/hypotenuse.

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By the property of parallelograms that diagonals are equal in length and they bisect each other we have determined the values of x and y.

A basic quadrilateral with two sets of parallel sides is known as a parallelogram. In a parallelogram, the opposing or confronting sides are of equal length, and the opposing angles are of equal size.

The area of a parallelogram is base multiples by height as two triangles form a parallelogram.

We know the diagonals of a parallelogram are equal and they bisect each other, From this property, we can write,

OA = OC.

x + 23 = 31.

x = 31 - 23.

x = 8 units.

XZ = 2(OX).

26 = 2(- 44 + x).

26 = - 88 + 2x.

2x = 114.

x = 57 units.

OL = OJ

8x - 56 = 24.

8x = 80.

x = 10.

OM = OK.

36 = 4y + 20.

4y = 16.

y = 4.

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To find the slope of the line, we can use the formula:

m = (y2 - y1) / (x2 - x1)

Let's choose two points from the table to calculate the slope:

Using points (1, 4) and (2, 7):

m = (7 - 4) / (2 - 1) = 3

Using points (2, 7) and (3, 10):

m = (10 - 7) / (3 - 2) = 3

Using points (3, 10) and (4, 13):

m = (13 - 10) / (4 - 3) = 3

Since the slope of the line is the same for all pairs of points, we can conclude that the relationship is proportional.

What is slop?

Slope is the measure of the steepness of a line, defined as the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line.

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\( \sqrt{147} \\ = \sqrt{3 \times 7 \times 7} \\ = 7 \sqrt{3} \)

Answer:

12.

Step-by-step explanation:

if to re-write the given condition, then

\(\frac{3}{0.25} =\frac{18}{1.5} =\frac{30}{2.5} =\frac{36}{3} ;\)

it is clear, the required constant is 12 (12 per hour).

Answer:

4

Step-by-step explanation:

t + s - r

where,

r=13

s=10

t=7

u=15

substituting

7+10-13 =17-13 =4

Hey there!

t + s - r

= 7 + 10 - 13

= 17 - 13

= 4

Therefore, your answer might be:

Option B. 4

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:

3,0,-6,0

Step-by-step explanation:

x1=3 because 3+0+0=3

since x2 and s2=0.

Notice that we can make an intermediate step between both graphs by moving the green graph three units to the left:

Notice that the horizontal lengths of the red graph and the blue graph are the same, but all the vertical lengths seem to have been multiplied by 2.

Since the blue graph (black, in the text) is called f and the transformation that takes the graph of f to the red graph is "multiplying by 2", then, the red graph is given by the expression:

Since the green graph is a three-units shift to the right of the red graph, then it is given by the expression:

Since the function whose graph is the green graph is called g, then:

Therefore:

1) The sequence of transformation that takes f to g is:

1.- A stretching in the y-direction by a factor of 2.

2.- A 3-units shift to the right.

2) In function notation, g is given in terms of f by: g(x) = 2f(x-3).

Answer:

6.2

Step-by-step explanation:

hope it helpes you in the long run