If John invests $600 in a savings account earning interest at a rate of 6% compounded semiannually how much will be in account after 8 years

Answer:

44, 46

Step-by-step explanation:

The integers are both even, so if the smaller one is x, then the larger one is x+2.

Therefore:

((x) + (x+2))² = 4048 + (x)² + (x+2)²

(2x + 2)² = 4048 + x² + x² + 4x + 4

4x² + 8x + 4 = 2x² + 4x + 4052

2x² + 4x - 4048 = 0

x² + 2x - 2024 = 0

(x + 46) (x - 44) = 0

x = -4+, 44

Since x must be positive, x = 44.  And x+2 = 46.  So the numbers are 44 and 46.

Let's check:

(44 + 46)² = 8100

4048 + 44² + 46² = 8100

Answer: I got A. 768 as the answer

547663

Step-by-step explanation:

Answer:

12 cm²

Step-by-step explanation:

To find the area of a rectangle, you multiply all of its dimensions together, which is length and width. That is A = l * w

Plug in: A = 4 cm * 3 cm

Multiply: A = 12 cm²

Answer:

Choice A. P = I² · R where

Step-by-step explanation:

Electrical power is the rate at which the electrical force does work. So what is electrical work? That's the work [tex]W[/tex] that the electrical force do when it moves charges [tex]Q[/tex] across a potential difference [tex]V[/tex]:

W = [tex]V\cdot Q[/tex].

The power is the rate at which the electrical force do the work:

[tex]\displaystyle P = \frac{W}{t} = V \cdot \frac{Q}{t}[/tex].

On the other hand, current [tex]I[/tex] is the charge through a cross-section of the circuit in unit time. By the definition of current:

[tex]\displaystyle\frac{Q}{t} = I[/tex].

[tex]\displaystyle P =V \cdot \frac{Q}{t} = V\cdot I[/tex].

Consider Ohm's Law:

[tex]V = I \cdot R[/tex].

Therefore

[tex]\displaystyle P = V\cdot I = (I \cdot R) \cdot I = I^{2}\cdot R[/tex].

Choice-A is one of several useful, correct formulas for electrical power.  It's true in AC circuits as well as DC ones.

I'm not sure about the second point you posted, but I believe the answer is (-2, 1). Here is my work:

Answer:-2,1

Step-by-step explanation:

Answer:

18 Inches total of rope

Step-by-step explanation:

9+9=18

or

9 x 2 = 18

You can do this two ways:

1. You can multiply 9 (how long the rope is) by 2 (how many ropes you have. so...

length of rope * number of ropes

9 * 2 = 18

2. Or you  can add 9 plus nine together and it will give you the same answer. so...

9 + 9 = 18

Hope this helped!

Answer:

[tex]9x^{2}+3x-20=(3x+5)(3x-4)[/tex]

Step-by-step explanation:

We need to drag the tiles and place them in boxes to form the correct pairs.

The given options are:-

1) [tex]9x^{2}+3x-20[/tex]

2) [tex](4x-3y)^{2}[/tex]

3) [tex](3x+5)(3x-4)[/tex]

4)[tex](3x+2)(9x^{2} -6x+4)[/tex]

First we simplify the all given factor and then compare with provided options

2) [tex](4x-3y)^{2}[/tex]

=[tex]16x^{2}+9y^{2}-24xy[/tex]

3) [tex](3x+5)(3x-4)[/tex]

[tex]9x^{2}-12x+15x-20[/tex]

[tex]9x^{2}+3x-20[/tex]

Here we can see equation (3) match with (1)

so, [tex]9x^{2}+3x-20=(3x+5)(3x-4)[/tex]

Hence, the correct match is shown in figure-1

The expressions that are equivalent should be matched as follows;

9x² + 3x - 20 ↔ (3x + 5)(3x - 4)

In order to match the equivalent expressions, we would have to either expand or factor each of the given expressions as follows;

9x² + 3x - 20

By applying the sum-product pattern, we have:

9x² + 15x - 12x - 20

By writing the common factor from the two pairs, we have:

(9x² + 15x) + (-12x - 20)

3x(3x + 5) - 4(3x + 5)

(3x + 5)(3x - 4)

Next, we would expand the expression (4x - 3y)²;

(4x - 3y)(4x - 3y)

16x² - 12xy - 12xy + 9y²

16x² - 24xy + 9y²

9y² - 24xy + 16x²

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Answer:

The first blank is "y", the second blank is "x", and the third blank is 1:3.

Answer:

when you move a decimal point to the left you are increasing the number

when you move a decimal to the right you are decreasing the number

Answer:

The answer is  26/100

ANSWER

c. never

EXPLANATION

When we have

[tex]\frac{a}{b}[/tex] in mathematics, we call b the divisor.

In mathematics, division by zero is not defined.

We cannot divide a function, or a number by zero and get a value.

That is why, there is the restriction, b≠0

Therefore, zero is never a divisor.

The correct answer is C

Answer:

48 cm²

Step-by-step explanation:

Let's call the width and height of the rectangle w and h.

w / h = 3 / 4

2w + 2h = 28

Solve the system of equations with substitution.

w = 3/4 h

2 (3/4 h) + 2h = 28

3/2 h + 2h = 28

7/2 h = 28

h = 8 cm

So the width is:

w = 3/4 (8)

w = 6 cm

So the area is:

A = wh

A = 48 cm²

Answer:

Rectangle

Step-by-step explanation:

The cross-section will result in a face, that looks just like the top face, since the cut + face are parallel. And because that face is rectangular, so will the cross-section.

Answer:

Rectangle

Step-by-step explanation:

Given : A prism and a plane

To Find : The intersection of the prism and the plane is a _______ cross section.

Solution:

We are given a rectangular prism

Let length be l , breadth be b and height be h

When the prism is intersected by plane , The height becomes 0 .

Length and breadth will remain same

So, the obtained figure is rectangle

So, Option B is true .

Hence The intersection of the prism and the plane is a rectangle cross section.

Answer:

Figure A sides are 1/4 the size of Figure B

The top of Figure A = 4, the top of Figure B = 1.

Divide 1 by 4 to get the scale factor, which is 1/4 as a fraction or 0.25 as a decimal.

Step-by-step explanation:

ANSWER

[tex]\frac{1}{ {x}^{10} }[/tex]

EXPLANATION

The given exponentiial expression is

[tex] {x}^{ - 8} \bullet {x}^{ - 2} [/tex]

We simplify using the rule:

[tex] {a}^{m} \times {a}^{n} = {a}^{m + n} [/tex]

We apply this property to get:

[tex]{x}^{ - 8} \bullet {x}^{ - 2} = {x}^{ - 8 + - 2}[/tex]

We simplify to get;

[tex]{x}^{ - 8} \bullet {x}^{ - 2} = {x}^{ - 10}[/tex]

We rewrite as a positive index to get;

[tex]{x}^{ - 8} \bullet {x}^{ - 2} = \frac{1}{ {x}^{10} } [/tex]

Answer:

[tex]A = 301.59\ cm^2[/tex] or [tex]A=96\pi\ cm^2[/tex]

Step-by-step explanation:

The lateral area of a cylinder is calculated by the following formula

[tex]A = 2\pi r * h.[/tex]

Where r is the radius of the right cylinder and h is the height

In this case we know that the diameter d of the cylinder is

[tex]d=2r\\\\r=\frac{d}{2}\\\\r=\frac{12}{2}\\\\r=6\ cm[/tex]

[tex]h=8\ cm[/tex]

Therefore the lateral area is:

[tex]A = 2\pi*6 * 8.[/tex]

[tex]A = 96\pi[/tex]

[tex]A = 301.59\ cm^2[/tex]

Answer:

The lateral area of a right cylinder = 96π cm²

Step-by-step explanation:

Points to remember

The lateral area of a right cylinder  = 2πrh

Where r - Radius of cone and

h - Height of cone

To find the lateral surface area

Here diameter d = 12 cm

then radius r = d/2 = 12/2 = 6 cm

And h = 8 cm

Lateral surface area =  2πrh

= 2 * π *6 * 8 = 96π cm²

Therefore the lateral area of a right cylinder = 96π cm²

Answer:

I think it's 0.30

Step-by-step explanation:

Answer:

Option 3: 300 phones

Step-by-step explanation:

Given

Phone produces each day: 1000

Number of phones that were checked = 30

Defective phones = 9

So the probability of defective phones will be calculated by dividing the number of defective phones by total number of phones checked.

So, the probability of defective phones

= 9/30

= 0.3 or 30%

So, from 1000 phones the defective phones will be:

1000*0.3

= 300 Phones ..

Answer:

Question 1: x = 3

Question 2: x = -4

Question 3: x = -2

13: x=3

14: x=-4

15: x=-2

All I did was use an calculator to find out the missing variables or u could have just put all the answer chooses in it and see which one is right.

Need the table, please include an attachment!

Answer:

(C) Y=26.9x-1.3 is the answer

Step-by-step explanation:

The greatest common factor between 14 and 24 is 2 because

The factors of 14 that divides 14 without a remainder are 1,2, and 7

The factors of 24 that divides 14 without a remainder are 1,2,3,4,6,8,and 12

Therefore 2 is the greatest factor between 14 and 24.

For this case we have that by definition, the Greatest Common Factor or GFC of two numbers is given by the biggest factor that divides both without leaving residue. We should look for the GFC of 14 and 24.

14: 1,2,7,14

24: 1,2,3,4,6,8,12,24

Thus, it is observed that the GFC of both numbers is 2.

Answer:

2

Answer: 15

Step-by-step explanation

Answer:

Step-by-step explanation:

[tex]\underline{+\left\{\begin{array}{ccc}2x+3y=9\\-2x+2y=6\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad\qquad5y=15\qquad\text{divide both sides by 5}\\.\qquad\qquad\boxed{y=3}[/tex]

The length of the edge of the bases is x = 4 and x=1.79.

The volume of a rectangular box can be calculated if you know its three dimensions: width, length, and height.

The volume of a box with a square base and a height of 2 cm is 32cm for box A and the volume of a box with a square base and a height of 10cm is 32cm.

What is the length of the edge of the bases?

The volume of the box = length × width × height

Therefore, we are going to make use of Equation (1) to determine the solution to this question, so that we have;

For Box A; We are given our volume to be equal to 32cm^3, height = 2cm, length and width = x cm.

For Box B IS;

[tex]\rm 32 = 2x^2\\\\x^2 = 16\\\\x^2=4^2\\\\x=4[/tex]

Here  Length = width.

For box B;

[tex]\rm 32 = 10x^2\\\\x^2=\dfrac{32}{10}\\\\x^2=3.2\\\\x=1.79[/tex]

Hence, the length of the edge of the bases is x = 4 and x=1.79.

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Answer:Two <‘s supplementary to equal <‘are=

I got this correct on Odyssey:)

Answer:

Option B.

Step-by-step explanation:

∠1 and ∠3 are supplementary and ∠2 and ∠4 are supplementary.

Because they are exterior sides in opposite rays.

In other words ∠1 + ∠3 = 180° and ∠2 + ∠4 = 180°

and it is given that ∠1 ≅ ∠2

So ∠3 ≅ ∠4

Since Two angles supplementary to equal angles are equal will be the reason.

Option B is the correct option.

Answer:

485 ft

Step-by-step explanation:

step 1

Find the distance from the base of the building to the base of the radio tower

Let

x -----> the distance from the base of the building to the base of the radio

we know that

tan(36°)=254/x

x=254/tan(36°)=349.60 ft

step 2

Find the distance from the base of the tree to the base of the radio tower

Let

x -----> the distance from the base of the tree to the base of the radio tower  

we know that

tan(62°)=254/x

x=254/tan(62°)=135.05 ft

step 3

Find the distance from the base of the building to the base of the tree

Adds the distances

349.60 ft+135.05 ft=484.65 ft

Round to the nearest foot

484.65 ft=485 ft

The final distance is approximately 485 feet.

Calculating the Distance from the Building to the Tree

To determine the distance from the base of the building to the base of the tree given the angles of elevation to the top of the radio tower, we can use trigonometry.

Let the height of the radio tower be 254 feet. Assume the distance from the base of the building to the base of the tower is x feet, and the distance from the base of the tree to the base of the tower is y feet.

Step-by-Step Solution:

Using the angle of elevation from the building, 36°, we can write:

tan(36°) = 254 ÷ x

Solving for x: x = 254 / tan(36°)

Using the angle of elevation from the tree, 62°, we can write:

tan(62°) = 254 ÷ y

Solving for y: y = 254 / tan(62°)

Calculate the values:

tan(36°) ≈ 0.7265

x = 254 / 0.7265 ≈ 349.6 feet.

tan(62°) ≈ 1.8807

y = 254 ÷ 1.8807 ≈ 135.1 feet.

The total distance from the base of the building to the base of the tree is x + y:

Total distance = 349.6 + 135.1 ≈ 485 feet.

Thus, the distance from the base of the building to the base of the tree is approximately 485 feet.

Answer:

The correct option is C.

Step-by-step explanation:

If a line passing through two point then the equation of line is

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]

From the given graph it is clear that the line of best fit passing through the points (0,0) and (14,45). So, the equation of line of best fit is

[tex]y-0=\frac{45-0}{14-0}(x-0)[/tex]

[tex]y=\frac{45}{14}x[/tex]

The equation of line of best fit is [tex]y=\frac{45}{14}x[/tex], therefore the correct option is C.

Answer:

The CORRECT answer is False

Step-by-step explanation:

I just took the test and got it correct!!

cos x + i sin x in the range 0 to 2pi will be unique so false.

Complex numbers exist the numbers that exist expressed in the form of a+ib where, a, and b are real numbers, and 'i' exists an imaginary number named “iota”. The value of i = (√-1).

The abbreviated polar form of a complex number exists z = rcis θ, where r = √(x2 + y2) and θ = tan-1 (y/x).

The range is the difference between the highest and lowest values in a set of numbers. To find it, subtract the lowest number in the distribution from the highest.

The range in statistics for a given data set is the difference between the highest and lowest values. For example, if the given data set is {2,5,8,10,3}, then the range will be 10 – 2 = 8. Thus, the range could also be defined as the difference between the highest observation and lowest observation.

Hence, cos x + i sin x in the range 0 to 2pi will be unique so false.

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Answer:

The value of y when x = 5 and z = 16 is 272

Step-by-step explanation:

* Lets Talk about the direct variation

- y is varies jointly (directly) as x and z, that means there are direct

  relation between y , x and z

- y increases if x increases or z increases

∴ y ∝ x × z

- To change this relation to equation we use a constant k

∴ y = k (x) (z), where k is the constant of variation

- To find the value of k we substitute the values of x , y and z in

  the equation above

∵ y = 136 when x = 5 and z = 8

∴ 136 = k × 5 × 8

∴ 136 = 40 k ⇒ divide both sides by 40

∴ k = 3.4

- Substitute this value in the equation

∴ y = 3.4 (x) (z)

∵ x = 5 , z = 16

∴ y = 3.4 (5) (16) = 272

∴ The value of y when x = 5 and z = 16 is 272

Answer:

The correct answer is B.

Step-by-step explanation:

If y varies jointly as x and z, then we can write the join variation equation.

[tex]y=kxz[/tex], where 'k' is the constant of proportionality.

If y = 136 when x = 5 and z = 8,then

[tex]136=k(5)(8)[/tex],

[tex]\implies 136=40k[/tex]

[tex]\implies \frac{136}{40}=k[/tex]

[tex]\implies \frac{17}{5}=k[/tex].

The variation equation now becomes:

[tex]y=\frac{17}{5}xz[/tex]

when x = 5 and z = 16, then

[tex]y=\frac{17}{5}(5)(16)[/tex]

[tex]y=17(16)[/tex]

[tex]y=272[/tex]

The correct answer is B.

A function of the form f(x)=ab^x is called an exponential exponential growth function, when b is greater than 1

What is an exponential function?

An exponential function is defined as a function whose value is a constant raised to the power of an argument is called an exponential function.

It is a relation of the form y = aˣ in mathematics, where x is the independent variable.

It is given the exponential function :

f(x) = abˣ  and b>1

Therefore, If the base (b) is greater than one is called an exponential growth, if it smaller than one it called an exponential decay.

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there is 1 solution of the equation represented on the graph because the line only cuts the graph at one point

Answer:

none

Step-by-step explanation:

The solutions to an equation given graphically are the points where the graph crosses the x- axis.

This graph has no points of intersection with the x- axis and therefore no solutions are shown.