Complete the equation of the line through (-6,5) and (-3,-3) Use exact numbers. y=

Let the required positive number is x.

The square of the number is [tex]x^2[/tex]

Now, we have been given that square of a positive number decreased by twice the number. It means we have

[tex]x^2-2x[/tex]

Now, it is equal to 48. Hence, we have

[tex]x^2-2x=48\\ x^2-2x-48=0\\ x^2-8x+6x-48=0\\ x(x-8)+6(x-8)\\ (x-8)(x+6)=0\\ x=8,-6[/tex]

The number is positive, Hence, we have [tex]x=8[/tex]

Therefore, the required number is 8

Answer: 40

What we all know is that there is only one way to breath (inhaling and exhaling) For the ancient Chinese, as cited on ancient proverb there are forty (40) ways.  These different ways promote relaxation thru breathing on the lower stomach. 

The equation of the given line is y=2x+4. Therefore, option A is the correct answer.

From the given graph coordinates on the line are (-2, 0) and (0, 4).

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

Slope of a line, m= 4/2 = 2

Put m=2 and (-2, 0) in y=mx+b

0=2(-2)+b

b=4

Substitute m=2 and b=4 in y=mx+b

That is, y=2x+4

The equation of the given line is y=2x+4. Therefore, option A is the correct answer.

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To find the height of the new cone with a larger radius that maintains the same volume, we calculate the volume of the original cone and solve for the new height using the cone volume formula.

The student wants to find out the new height of the cone with a larger radius while maintaining the same volume as the original cone. The volume of a cone is given by the formula V = 1/3 πr²h. To find the height of the new cone, we'll use the volume of the original cone as the constant value.

Let's first calculate the volume of the original cone:

Now, let's set up an equation with the new radius to solve for the new height (h_new):

By substituting the V_original from step 1 into step 3, we can solve for h_new. The result will be the height of the new cone with a radius of 444 inches that has the same volume as the original cone.

Image option 2 will produce the magnetic field in the electromagnetism.

The portion of space near a magnetic body or a current-carrying body in which the magnetic forces due to the body or current can be detected.

Given that figures,

In figure option 2 there are wires given and as we know when there is current flowing in a body or wire it will create an electric field as well as magnetic field.

Hence, image option 2 is the correct option.

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Assuming the order of selection doesn't matter:

[tex] \displaystyle
\binom{9}{3}=\dfrac{9!}{3!6!}=\dfrac{7\cdot8\cdot9}{2\cdot3}=84 [/tex]

Answer:

Sound waves travel through iron at 11,427,840 km/h.

Step-by-step explanation:

A kilometer is equal to 0.62 miles. An hour is equal to 3600 seconds. Therefore, if a sound wave travels through iron at a rate of 5120 m/s, it would be equal to (5120 x 0.62) km/s. This is equal to 3174.4 km/s which, multiplied by 3600 (the number of seconds that make an hour), would determine the speed in which a sound wave travels through iron. So, as 3174.4 x 3600 is 11,427,840, so sound waves travel at 11,427,840 km/h.

The system of the equations representing the situation is a+b = 243 and

a-b = 109 and values of a and b are 176 and 67 respectively.

A system of equations is a collection of two or more equations with a same set of unknowns.

Given that, A total of 243 adults and children are at a movie theater. There are 109 more adults than children in the theatre. If a represents the number of adults and b represents the number of children,

Establishing the equations according to the given situation,

a+b = 243......(i)

a-b = 109.......(ii)

Adding the equations, we get,

2a = 352

a = 176

Therefore, b = 67

Hence, The system of the equations representing the situation is a+b = 243 and  a-b = 109 and values of a and b are 176 and 67 respectively.

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Answer:

5 x n, where n is any natural number.

Step-by-step explanation:

If A is a 6 x 5 matrix, it means that A has 6 rows and 5 columns, this means that if a matrix B can be multiplied by A, then each one of its columns must have 5 entries. Therefore, B has to be a matrix with 5 rows and it might have any arbitrary number of columns, in other words B is a 5 x n matrix, where n must be a natural number bigger than 1.

Final answer:

The current value of the guitar after depreciating by 13% per year over 6 years is calculated using the exponential decay formula  [tex]V = P(1 - r)^t[/tex], which gives us an approximate current value of $173.45

Explanation:

The given formula represents depreciation, where the value of an asset decreases over time. Applying this to the provided scenario, with an original price of $400 and a 13% annual depreciation rate, we calculate the value after 6 years. Substituting these values into the formula, we find: Value =  [tex]400 \times (1 - 0.13)^6 = 400 \times 0.87^6 = \$173.45.[/tex]Therefore, after 6 years, the asset's value is approximately $173.45. Depreciation formulas like this one help assess the declining worth of assets over time due to various factors.

Answer:

The coordinates of the center of the lake are [tex](\frac{-1}{3},\frac{-4}{3})[/tex].

Step-by-step explanation:

It is given that Hillman Peak, Garfield Peak, and Cloudcap are three mountain peaks on the rim of the lake. The peaks are located in a coordinate plane at H(-4,1), G(-2,-3), and C(5,-2).

If we joint these points, then we get a triangle and the center of a triangle is known as centroid.

The formula for centroid of a triangle is

[tex]Centroid=(\frac{x_1+x_2+x_3}{3},\frac{y_1+y_2+y_3}{3})[/tex]

The centroid of the triangle H(-4,1), G(-2,-3), and C(5,-2) is

[tex]Centroid=(\frac{-4-2+5}{3},\frac{1-3-2}{3})[/tex]

[tex]Centroid=(\frac{-1}{3},\frac{-4}{3})[/tex]

Therefore the coordinates of the center of the lake are [tex](\frac{-1}{3},\frac{-4}{3})[/tex].

Answer:

280

Step-by-step explanation:

i n e e d p o i n t s

The percentage of respondents from the 46-55 age group who rated the film excellent is 20 %.

To determine the percentage of respondents from the 46-55 age group who rated the film excellent, you need two pieces of information: the number of respondents in that age group who rated the film excellent and the total number of respondents in that age group. The formula for calculating the percentage is:

[tex]\[ \text{Percentage} = \left( \frac{\text{Number of respondents who rated excellent}}{\text{Total number of respondents in the age group}} \right) \times 100 \][/tex]

Assuming you have these numbers, let's denote the number of respondents who rated the film excellent in the 46-55 age group as X and the total number of respondents in that age group as Y. The formula becomes:

[tex]\[ \text{Percentage} = \left( \frac{X}{Y} \right) \times 100 \][/tex]

For example, if 20 respondents in the 46-55 age group rated the film excellent out of a total of 100 respondents in that age group, the calculation would be:

[tex]\[ \text{Percentage} = \left( \frac{20}{100} \right) \times 100 = 20\% \][/tex]

Therefore, replace X and Y with the actual numbers from your data to find the specific percentage.

Answer:

Step-by-step explanation:

Alright lets get started.

We have given the area of each circle as 196 pi square units.

since the area of the circle =[tex]\pi*radius^2[/tex]

so,the radius of the circle :

[tex]196\pi =\pi r^2[/tex]

[tex]r^2=196[/tex]

[tex]r=14[/tex]

therefore the diameter of the circle will be [tex]2*radius=2*14=28[/tex]

the perimeter of the rectangle=[tex]2*(length+ width)[/tex]

the length of the rectangle will be addition of diameters of the circle=[tex]28+28=56[/tex]

breadth of the rectangle is equal of the diameter =28

Perimeter of the rectangle =[tex]2*(56+28)=168[/tex]

Answer  168 units.

The perimeter of the given rectangle is 168 units

Given that area of each of the circles are [tex] 196 \pi [/tex] sq units and we know that the area of circle [tex]=\pi r^{2}[/tex] using this radius of the circle will be

[tex]\pi r^{2} =196\pi\\ r^{2} = 196\\ \\ r=14[/tex]

So, the diameter of the circle is twice the radius which is

[tex]2\times r\\ 2\times 14 =28 [/tex]

Here we can see that length of rectangle is equal to twice the diameter of the circle and breadth is equals to twice the radius

[tex]length= 28+28=56[/tex]

[tex]breadth = 2\cdot14=28[/tex]

How to find the perimeter of the given rectangle ?

To find the perimeter we use the formula

Perimeter of rectangle = [tex]2\cdot(length + breadth)[/tex]

On solving we get ,

[tex]2\cdot(56 +28)\\ 168 units[/tex]

Therefore, The perimeter of the given rectangle is 168 units

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We found the width at ground level to be approximately 19.6 meters.

We start by assuming the equation of the parabola to be of the form y = ax² + bx + c.

Since the vertex of the parabolic arch is at (0, 12), we know that c = 12. Next, we use the condition that at y = 10 meters, the width is 8 meters, meaning the points (4, 10) and (-4, 10) lie on the parabola. Plugging these into the equation:

Solving for the same with (-4,10) is unnecessary as it results in the same equation. Next, we use the vertex form y = a(x - h)² + k ⇨ y = a(x - 0)² + 12 ⇨ y = ax² + 12.

From equation (1), we have 16a + 4b = -2. Since the vertex form tells us there is no 'b' term in the simplest form, 'b' must be 0. Thus, 16a = -2 ⇨ a = -1/8.

The equation of the parabola is therefore y = -(1/8)x² + 12.

To find the width at ground level (y = 0):

Thus, the total width of the arch at ground level is approximately 2 × 9.8 = 19.6 meters.

Answer:

Total amount earned after 25 years=$27,897.16

Step-by-step explanation:

Step 1: Express formula for calculating total amount

The total amount after 25 years can be expressed as;

A=P(1+r)^n

where;

A=total amount after 25 years

P=principal amount

r=annual interest rate

n=number of years

Step 2: Substitute values in the expression

In our case;

P=$6,500

r=6%=6/100=0.06

n=25 years

replacing in the original expression;

A=6,500(1+0.06)^25

A=27,897.16

Total amount earned after 25 years=$27,897.16

Final answer:

The total amount after 25 years will be $27,897.16, and the amount of interest earned on a $6,500 investment at a 6% annual interest rate will be $21,397.16.

Explanation:

To calculate the total amount and interest earned on $6,500 at 6% for 25 years, we'll assume that the interest is compounded annually. The formula to calculate the total amount with compound interest is:

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

Where:

Let's plug the values into the formula:

A = $6,500(1 + 0.06/1)^(1*25)

A = $6,500(1 + 0.06)^25

A = $6,500(1.06)^25

A = $6,500 * 4.29187072

A = $27,897.16

The total amount after 25 years will be $27,897.16.

To find the interest earned, subtract the principal from the total amount:

Interest = A - P

Interest = $27,897.16 - $6,500

Interest = $21,397.16

The amount of interest earned will be $21,397.16.