Mazie Invested $4500 in an account earning 4.3% interest compounded continuously. After how many years will she have $7400 in her account

The current rate is simply equal to $175 per month, let us call this as rate A:

A = 175

The new rate is $94 plus $4.50 per devices, let us call this as rate B:

B = 94 + 4.50 x

where x is the number of devices connected to the network

The inequality equation for us to find x which the new plan is less than current plan is:

94 + 4.50 x < 175

Solving for x:

4.50 x < 81

x < 18

So the number of devices must be less than 18.

- From the graph, we can actually see that the new rate intersects the current rate at number of devices equal to 18. So it should really be below 18 devices.

The number of devices connected should be less than 18 (1 to 17 devices) so that the new charges will be less than the old charge.

Given:

The old monthly charge for internet service per household is $175.

The new charges include a fixed pay of $94 plus $4.50 per connected device.

Let x be the number of connected devices.

So, the new charges can be written mathematically as,

[tex]C=94+4.5x[/tex]

Now, the new charge should be less than the old charge. This condition can be written as,

[tex]C=94+4.5x<175\\4.5x<81\\x<18[/tex]

So, the number of devices connected should be less than 18 (1 to 17 devices) so that the new charges will be less than the old charge.

See the attached graph.

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Answer:

75°

Step-by-step explanation:

to find the hypotenuse on the given triangle

divide the given height ( 3sqrt(2) ) by the sin of the given angle (45)

 3sqrt(2) / sin 45 = 6

answer is B. 6

CR = CP = 17

PQ = QR = 15

CQ = x^2 +15^2 = 17^2 = x^2 + 225 = 289

x^2 = 289-225 = 64, sqrt(64) = 8, CQ = 8

The sides of the triangles will be 15 cm, 13 cm and 21 cm.

A closed polygon with three sides, angles and vertex is called triangle.

Given that, the first side of a triangle is 2 cm longer than the second side. the third side is 5 cm shorter than twice the second side and the perimeter is 49 cm.  

Let the second side be x, then the sides will be,

x+2, x and 2x-5

∵ Perimeter = 49 cm

∴ x + 2 + x + 2x - 5 = 49

4x-3 = 49

4x = 52

x = 13

Therefore, side will be =

Side 1 = 15 cm

Side 2 = 13 cm

Side 3 = 21 cm

Hence, the sides of the triangles will be 15 cm, 13 cm and 21 cm.

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Final answer:

The division Property of Equality is used to transform Equation 1 (35 = 5x) into Equation 2 (7 = x) by dividing both sides of the equation by 5.

Explanation:

The property of equality used to transform Equation 1 (35 = 5x) to Equation 2 (7 = x) is the division Property of Equality.

This property states that if you divide both sides of an equation by the same non-zero number, the two sides remain equal. To get from Equation 1 to Equation 2, both sides of Equation 1 are divided by 5.

Division is similar to multiplication in that it follows the same rules for signs and equality. When dividing both sides by the same number, the numerator and denominator cancel out if they are the same, leaving a value of 1.

For instance, dividing 5x by 5 will lead to x, and dividing 35 by 5 will give 7, hence 7 = x, which is Equation 2.

each little square = 1 square inch

the design takes up 21 squares so area is 21 square inches

 the perimeter = 6 +2+3+3+3+5 = 22 inches

Answer:

B

Step-by-step explanation:

If you divide x so only x and a number remains, you will get B.

[tex]f(x) = x^{3} - 8x^{2} + 16x[/tex] has multiple zero = 4; multiplicity = 2.

" A multiple zero has the multiplicity which represents the number of times linear factor of multiple zero occur in the polynomial .Zero of the polynomial is associated with multiple zero."

According to the question,

Given,

[tex]f(x) = x^{3} - 8x^{2} + 16x[/tex]

Simplify the given polynomial to get the multiple zero and multiplicity,

[tex]f(x) = x^{3} - 4x^{2}- 4x^{2} + 16x[/tex]

       [tex]\implies x^{2} (x-4) -4x(x-4)=0\\\\\implies (x^{2} -4x)(x-4) =0\\\\\\\implies (x) (x-4)(x-4)=0\\\\\implies x(x-4)^{2} =0[/tex]

Zero is associated with x =4.

(x-4) occur twice.

Hence, multiple zero = 4 and multiplicity = 2 of the given function.

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Answer:

$1.69

Step-by-step explanation:

If he wants to buy something for $6.21 but he only has $4.52, we need to find out the difference between $6.21 and $4.52.

For that, we have to subtract the smallest number from the biggest, that is

$6.21 - $4.52 = $1.69

Therefore, he would need to borrow $1.69 from his friend.

The side of the square having an area of 121 yards² is 11 yards

What is the area of a square?

A square is a 4 sided polygon where all the sides are of equal length.

The area of the square is the square of any one of its side

Let a be the side of the square

Area of the square = a²

Given data ,

Let the area of the square be Y = 121 yards²

Now , let the side of the square be = a

And the equation for the area of the square is

Area of the square = a²

where a is the side of the square

So , substituting the values in the equation , we get

a² = 121 yards²

Taking square root on both sides , we get

a = 11 yards

Therefore , the value of a is 11 yards

Hence , The side of the square having an area of 121 yards² is 11 yards

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Step 1: (ab-9)(ab+8)

Step 2: ab x ab +8 x ab -9 x ab -9 x 8

Step 3:  ab2  +8ab-9ab-72=

Step 4: ab2 -ab-72

solved!!! that how you would solve it everything will continue as normal

The answer is b, not c. I just completed the quiz and got the question wrong by answering c. :/

he hiked 4 km east in 45 minutes

45 minutes = 3/4 of an hour

4 /.75 = 5.33

 so the answer would be D. 5.3 km per hour east

The numbers cannot be uniquely determined with the given information.

Let's solve this problem step by step.

Let's assume the second number is 'x'. Since the first number is 10 more than the second number, then the first number can be represented as 'x + 10'.

Since the first number is also twice the third number, the first number can be represented as '2y', where 'y' is the third number.

Now, we can form an equation using the given information: x + (x + 10) + 2y = 45

Simplifying the equation, we get: 2x + 2y + 10 = 45

Further simplifying, we get: 2x + 2y = 35

Dividing both sides of the equation by 2, we get: x + y = 17.5

Now, we have two variables and one equation, which means we have an infinite number of possible solutions. We need more information to determine the actual values of x and y.

Therefore, the numbers cannot be uniquely determined with the given information.

Final answer:

To create a box with a volume of 9075 in3, a 61 in. by 61 in. piece of cardboard is needed after cutting out 3 in. squares from each corner and folding up the sides.

Explanation:

To determine the size of the cardboard needed to construct a box with a volume of 9075 in3 when 3 in. squares are cut from each corner and the sides are folded up, we first need to express the volume of the box in terms of the dimensions of the cardboard. Let x represent the length of one side of the original square piece of cardboard. After cutting out 3 in. squares from each corner, the length and width of the base of the box will be x - 6 inches (since 3 inches are removed from each side), and the height will be 3 inches (the size of the squares cut from the corners).

The volume V of the box can be expressed as V = (x - 6)(x - 6)(3). Given that V = 9075 in3, we can set up the equation 9075 = (x - 6)2 × 3. Solving for x will give us the size of the original cardboard piece.

To solve the equation, divide both sides by 3 to isolate (x - 6)2, which gives 3025 = (x - 6)2. Taking the square root of both sides gives x - 6 = 55, so x = 61. Therefore, a 61 in. by 61 in. piece of cardboard is needed to construct the box.

Answer:

C

Step-by-step explanation: