What is the equation of the line that passes through the point (6,8) and has a slope of 1/2

Answer:

line c

Step-by-step explanation:

Answer:

1 : 4 and 6 : 24

Step-by-step explanation:

We can generate equivalent ratios by dividing or multiplying each part of the ratio by the same value

Divide both parts by 3 , then

3 : 12 = 1 : 4 ← in simplest form

Multiply both parts by 2

3 : 12 = 6 : 24

answer: 828$

Step-by-step explanation:

step 1

Find out the total cost of the land

Multiply the total area in acres by $1,863 per acre

step 2

we know that

To determine the selling price of each lot to reach break even, divide the total cost by the number of lots.

Answer:

55

Step-by-step explanation:

Volume of a rectangular prism is width time length times height.

V = WLH

The volume of each brick is:

V = (6 in) (10 in) (4 in)

V = 240 in³

The total volume is 13,200 in³, so the number of bricks is:

13,200 in³ / 240 in³ = 55

Skippy should invest $ 7500 in account offering 4 % interest and $ 2500 in account offering 8 % simple interest

Solution:

Given that Skippy has a total of $10,000 to split between two investments

One account offers 4% simple interest, and the other account offers 8% simple interest

Total interest earned = 500

Number of years = 1

Let the principal with rate of interest 4 % is x

So the principal for rate of interest 8 % is 10000 - x

Total interest earned = simple interest for 4 % interest + simple interest for 8 % interest

Simple interest is given as:

[tex]S.I = \frac{pnr}{100}[/tex]

Where "p" is the principal and "r" is the rate of interest and "n" is the number of years

Therefore,

[tex]\text{ Total interest earned } = \frac{x \times 1 \times 4}{100} + \frac{10000-x \times 1 \times 8}{100}[/tex]

[tex]500 = 0.04x + (10000 - x)0.08\\\\500 = 0.04x + 800 - 0.08x\\\\-300 = -0.04x\\\\x = 7500[/tex]

Therefore skippy should invest $ 7500 in account offering 4 % interest

And skippy should invest (10000 - x) = (10000 - 7500) = $ 2500 in account offering 8 % interest

Answer:

[tex]x=-2\sqrt5\ and\ x=2\sqrt5[/tex]

Step-by-step explanation:

Given:

The given equation to solve is:

[tex]x^2=20[/tex]

In order to solve the above equation, we take square root on both the sides.

While taking square root on both sides, we must consider both positive and negative values. So, this gives:

[tex]\sqrt{x^2}=\pm\sqrt{20}[/tex]

From the definition of square root function, we have

[tex]\sqrt{a^2}=a[/tex]

Therefore,

[tex]x=\pm\sqrt{20}[/tex]

Now, writing 20 into the product of its prime factors, we have

[tex]20=2^2\times 5[/tex]

Therefore, [tex]x=\pm\sqrt{2^2\times 5}[/tex]

We also know, [tex]\sqrt{a\times b}=\sqrt{a}\times\sqrt{b}[/tex]

So, [tex]\sqrt{2^2\times 5}=\sqrt{2^2}\times \sqrt{5}=2\sqrt5[/tex]

Therefore, [tex]x=\pm2\sqrt5[/tex]

So, there are two values of 'x'. They are:

[tex]x=-2\sqrt5\ and\ x=2\sqrt5[/tex]

Answer:

Please see the detailed answers below:

Step-by-step explanation:

Solution 1:

Sandwich = $9.25

Salad = $4.35

Tax = 7.5%  

=> ($9.25 + $4.35) x 7.5 / 100 = 13.6 x 0.075 = $1.02

The amount of Tax on Veena's meal is $1.02

Solution 2:

Book read by Christian = (1/4) / (2/3) = (1/4) x (3/2) = 3/8

Christian will read 3/8 books per week.

Solution 3:

Sale Price = (100 - Discount Rate) x Cost Price

Let Y = Sale Price

By Putting the values in above equation:

Y = (100 - 45) x $650

Y = 0.55 x $650

Y = $357.5

Hence the Sale Price of the bicycle will be $357.5

Solution 4:

Percent error = [(Experimental Value - Accepted Value) / Accepted Value] x 100

Percent error = [(15.5 - 14.5) / 14.5] x 100

Percent error = [1 / 14.5] x 100

Percent error = 2.2%

Hence the percent error in Mark's estimate is 2.2%

Answer:

[tex]61\%[/tex]

Step-by-step explanation:

Cost in December[tex]=\$159[/tex]

Cost in January[tex]=\$62[/tex]

Total decrease in the cost[tex]=159-62=\$97[/tex]

[tex]Percentage\ decrease=\frac{97}{159}\times100\\\\=61.006\approx 61\%[/tex]

The basketball player's mass is approximately 46.2857 kilograms.

To solve for the player's mass, we can rearrange the equation to isolate the mass variable. The equation can be rewritten as m = 36S/h.

Plugging in the given values, we get m = 36 * 2.7 / 2.1.

Solving this expression gives us a mass of approximately 46.2857 kilograms.

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Answer:

  $2.50

Step-by-step explanation:

The total fee is the fee per share multiplied by the number of shares:

  $0.025 × 100 = $2.50 . . . . Erin's brokerage fee

Answer:

2.50

Step-by-step explanation:

Which polynomial is equal to  (-3x^2 + 2x - 3) subtracted from  (x^3 - x^2 + 3x)?

The polynomial equal to (-3x^2 + 2x - 3) subtracted from  (x^3 - x^2 + 3x) is [tex]x^3 + 2x^2 + x + 3[/tex]

Given that two polynomials are: [tex](-3x^2 + 2x - 3)[/tex] and [tex](x^3 - x^2 + 3x)[/tex]

We have to find the result when [tex](-3x^2 + 2x - 3)[/tex] is subtracted from  [tex](x^3 - x^2 + 3x)[/tex]

In basic arithmetic operations,

when "a" is subtracted from "b" , the result is b - a

Similarly,

When [tex](-3x^2 + 2x - 3)[/tex] is subtracted from  [tex](x^3 - x^2 + 3x)[/tex] , the result is:

[tex]\rightarrow (x^3 - x^2 + 3x) - (-3x^2 + 2x - 3)[/tex]

Let us solve the above expression

There are two simple rules to remember:

So the above expression becomes:

[tex]\rightarrow (x^3 - x^2 + 3x) + 3x^2 -2x + 3[/tex]

Removing the brackets we get,

[tex]\rightarrow x^3 - x^2 + 3x + 3x^2 -2x + 3[/tex]

Combining the like terms,

[tex]\rightarrow x^3 -x^2 + 3x^2 + 3x - 2x + 3[/tex]

[tex]\rightarrow x^3 + 2x^2 + x + 3[/tex]

Thus the resulting polynomial is found

The value of [tex]x_2 = 1[/tex]

Solution:

Given that a approximate solution to the equation [tex]x^2 +6x - 2=0[/tex] can be calculated using the iterative formula shown below

[tex]x_{n+1} = \frac{2-(x_n)^3}{6}[/tex]

Also given that [tex]x_1 =2[/tex]

To find: value of [tex]x_2[/tex]

To find value of [tex]x_2[/tex] , substitute n = 1 in given iterative formula

[tex]x_{1+1} = \frac{2-(x_1)^3}{6}[/tex]

Solve the above expression by substituting [tex]x_1 = 2[/tex]

[tex]x_2 = \frac{2-(2)^3}{6}[/tex]

[tex]x_2 = \frac{2-8}{6}\\\\x_2 = \frac{-6}{6}\\\\x_2 = -1[/tex]

Thus value of [tex]x_2 = 1[/tex]

HERE'S YOUR ANSWER:

Let number of girls be- x

and number of boys be- 2x(boys are 2 times NO. of girls)

therefore

x + 2x = 24

3x = 24

x = 24/3

x = 8

hence number of girls = 8

boys are 2 times more than girls = 16

HOPE IT HELPS...

Answer:

x - 0.8y

Step-by-step explanation:

5.20/6.5 = $0.80 per pound

x = total cost of potatoes

y = number of potatoes

x = 0.8y

Answer: 138

Step-by-step explanation:

Let the first number be x , the second number be x + 2 and the third number be x + 4 since they are consecutive even numbers.

Their sum implies:

x + x + 2 + x + 4 = 408

3x + 6 = 408

subtract 6 from both sides

3x + 6 - 6 = 408 - 6

3x = 402

divide through by 3

3x/3 = 402/3

Therefore x = 134.

The numbers are :

134 , 136 and 138 , this means that the largest number is 138

Answer:

Step-by-step explanation:

x = small box and y = large box

30x + 40y = 330

y = 2x

30x + 40(2x) = 330

30x + 80x = 330

110x = 330

x = 330/110

x = 3 <===== 3 small boxes

y = 2x

y = 2(3)

y = 6 <=== 6 large boxes

check...

30x + 40y = 330

30(3) + 40(6) = 330

90 + 240 = 330

330 = 330 (correct)

Answer:

5/2

Step-by-step explanation:

It would have a greater slope and perhaps start higher on the y axis.

Step-by-step explanation:

I assume you can choose your own numbers as long as they are higher than the current. This means the numbers on your y axis will change but not the numbers on your x axis because that determines the time. So let's change the y axis numbers from going by 20 and make them go by 25. You could technically keep the dots in the same place as long as you change the y axis numbers because you are still earning more money.

Answer:

Dolphin is 3 feet above the surface of the water.

Step-by-step explanation:

Dolphin is 30 feet below the surface of the water, then its position on the vertical number line is -30.

Thus,

[tex]-30+23-17+27\\ \\=(-30-17)+(23+27)\\ \\=-47+50\\ \\=3[/tex]

Dolphin is 3 feet above the surface of the water.

Final answer:

After a series of movements, the calculated final position of the dolphin is 3 feet above the surface of the water, which is a reasonable result for a dolphin.

Explanation:

The question involves calculating the final position of a dolphin relative to the water surface after a series of vertical movements (rising and sinking). Initially, the dolphin is 30 feet below the surface. Then, the following movements occur:

The dolphin rises 23 feet.

The dolphin sinks 17 feet.

The dolphin rises another 27 feet.

To find out where the dolphin is relative to the surface after these movements, we can sum the changes in position:

Initial position: -30 feet (below the surface is considered negative)

+ Rise 23 feet: -30 + 23 = -7 feet

+ Sink 17 feet: -7 - 17 = -24 feet

+ Rise 27 feet: -24 + 27 = +3 feet

After calculating these movements, the dolphin is 3 feet above the surface of the water. Dolphins are known to be able to jump several times their length out of the water, and considering they measure about 2 meters long, this result of the dolphin being 3 feet above the water is reasonable.

Answer:

The maximum rate of change is between second 15 and second 19.

Step-by-step explanation:

See the attached table.

The table shows the total distance a spider traveled after a light was turned on.

Now, the average rate of change between two consecutive times in the table is given by  

= [tex]\frac{\textrm {Total change in Distance in feet}}{\textrm {Total change in Time in seconds }}[/tex]

Therefore, between second 5 and second 11, the average rate of change = [tex]\frac{7 - 4}{11 - 5} = 0.5[/tex]

Between second 11 and second 15, the average rate of change = [tex]\frac{13 - 7}{15 - 11} = 1.5[/tex]

Between second 15 and second 19, the average rate of change = [tex]\frac{20 - 13}{19 - 15} = 1.75[/tex]

Between second 19 and second 28, the average rate of change = [tex]\frac{24 - 20}{28 - 19} = 0.44[/tex]

Therefore, the maximum rate of change is between second 15 and second 19. (Answer)

Answer:

Option C -> None of the above.

Step-by-step explanation:

Given-

2 r + ( t + r )

⇒ 2 r + t + r

⇒ 2 r + r + t

⇒ 3 r + t

∵ 2 r + ( t + r ) = 3 r + t.

∴ The given expression is equivalent to Option C : None of the above.

Answer:

C. None of the above

Step-by-step explanation:

Answer:

increase is 37.5%

Step-by-step explanation:

3000/8000 *100= 37.5%

WAR is given as 57 degrees.

If you draw a line from W to R, the angle WRA would also be 57 degrees.

57 + 57 = 114

The measure of AR = 180 -114 = 66 degrees.

Answer:

66.

Step-by-step explanation:

If You See W.And R., They Are The Same Angle's, So If They Are Little And Big At The Same Time, You Can Notice It Will Be 66* :)

Tell Me If You Have Any Problomes With These!!!!

Hope This Information Helps!!!

Answer:

Option A) x=4,12 is correct.

The solution of the given quadratic equation is x=4,12

Step-by-step explanation:

Given equation is in quadratic form

Given quadratic equation is

[tex]0=4x^2-64x+192[/tex]

Rewriting the above equation

[tex]4x^2-64x+192=0[/tex]

Now dividing the equation by 4 we get

[tex]\frac{1}{4}(4x^2-64x+192)=\frac{0}{4}[/tex]

[tex]x^2-16x+48=0[/tex]

For quadratic equation [tex]ax^2+bx+c=0[/tex]

solution [tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

where a and b are coefficients of [tex]x^2[/tex] and x respectively, c is a constant

Here a=1, b=-16, c=48

[tex]x=-\frac{(-16)\pm\sqrt{(-16)^2-4(1)(48)}}{2(1)}[/tex]

[tex]=\frac{16\pm\sqrt{16^2-192}}{2}[/tex]

[tex]=\frac{16\pm\sqrt{256-192}}{2}[/tex]

[tex]=\frac{16\pm\sqrt{64}}{2}[/tex]

[tex]x=\frac{16\pm 8}{2}[/tex]

Therefore

[tex]x=\frac{16+8}{2}[/tex] and [tex]x=\frac{16-8}{2}[/tex]

[tex]x=\frac{24}{2}[/tex] and [tex]x=\frac{8}{2}[/tex]

[tex]x=12[/tex] and [tex]x=4[/tex]

Therefore the solution of the given quadratic equation is x=4,12

Option A) x=4,12 is correct.

Answer:

B. Investors will have to pay tax on the interest income received from the bonds.

Step-by-step explanation:

Investors will have to pay tax on the interest income received from the bonds because it is a taxable income.

The interest earned from a corporate bond is subject to taxation by both the federal and state governments.

Again, the maturity of the bond is determined at the time they are issued. Creditworthiness will only affect the bond price but not its maturity period.

Answer: x = 6

Step-by-step explanation: To solve for x, we must first isolate the term containing x which in this problem is -3x.

Since 28 is being added to -3x, we subtract 28 from both sides of the equation to isolate the -3x. On the left, the +28 and -28 cancel out and on the right 10 - 28 is -18 so we have -3x = -18.

Now we can finish things off by just dividing both sides of the equation by -3. On the left the -3's cancel and we have x. On the right, -18 divided by -3 is 6 so we have x = 6 which is the solution to our equation.

The volume of the solid generated by rotating triangle ABC around AB is 24π cubic units.

To find the volume of the solid generated by rotating triangle ABC around side AB, you can use the method of cylindrical shells. The volume of the solid generated by rotating a region bounded by a curve around an axis is given by the formula:

[tex]\[ V = \int_{a}^{b} 2\pi x \cdot h(x) \, dx \][/tex]

Where:

[tex]\( a \) and \( b \) are the limits of integration along the x-axis (in this case, from 0 to the length of side AB),[/tex]

[tex]\( h(x) \) is the height of the curve at the position x, and[/tex]

[tex]\( 2\pi x \) represents the circumference of the cylindrical shell with radius x and height \( h(x) \).[/tex]

In this case, triangle ABC is a right triangle, so rotating it around AB will generate a cone with height AB and base radius AC.

Given that AB = 2 and AC = 6, the radius of the base of the cone formed by rotating the triangle will be [tex]\( r = AC = 6 \)[/tex]. The height of the cone will be the same as the length of side AB, so [tex]\( h = AB = 2 \).[/tex]

Now, we can calculate the volume:

[tex]\[ V = \int_{0}^{2} 2\pi x \cdot 6 \, dx \][/tex]

[tex]\[ = 12\pi \int_{0}^{2} x \, dx \][/tex]

[tex]\[ = 12\pi \left[\frac{x^2}{2}\right]_{0}^{2} \][/tex]

[tex]\[ = 12\pi \left(\frac{2^2}{2} - \frac{0^2}{2}\right) \][/tex]

[tex]\[ = 12\pi \left(\frac{4}{2}\right) \][/tex]

[tex]\[ = 12\pi \cdot 2 \][/tex]

[tex]\[ = 24\pi \][/tex]

So, the volume of the solid generated by rotating triangle ABC around side AB is [tex]\( 24\pi \)[/tex] cubic units.

The solid formed by rotating triangle ABC around side AB is a cone. The volume of this cone is calculated using the formula V = (1/3)πr^2h where r is the radius of the base and h is the height, resulting in approximately 57.91 cubic units.

The question asks for the volume of the solid generated by rotating a triangle around one of its sides. In this case, rotating triangle ABC with AB = 2, BC = 5, and AC = 6 around side AB will generate a conical surface. Since side AB will be the axis of rotation, the other two sides will act as generating lines of the cone, where side AC becomes the slant height (l) and side BC becomes the base's radius (r).

To calculate the volume of the cone, we use the formula V = (1/3)\u03c0r^2h, where r is the radius of the base, and h is the height of the cone. Here the height (h) of the cone is not directly provided, but with the Pythagorean theorem, we can find it since we know the slant height and radius: h = \\/(l^2 - r^2) = \\/(6^2 - 5^2) = \\/(36 - 25) = \\/11. Finally, the volume can be calculated: V = (1/3)\\(3.1415)\(5)^2\\/11\approx 57.91 cubic units.

The theorem of Pappus is a useful approach to solving this problem, but it requires knowing the centroid's distance from the axis of rotation, which is not provided, so we are not using that method here.

Answer:

The given numbers from smallest to largest is

[tex]0.012, \frac{1}{10}, 32\%, 65\%, \frac{7}{10}, 0.721, 0.721, \frac{652}{900}[/tex]

Step-by-step explanation:

Given numbers are

[tex]\frac{652}{900}, 0.012,\frac{7}{10}, 32\%,\frac{1}{10}, 0.721, 65\%[/tex]

We have to arrange the given numbers from smallest to largest

That is to write in ascending order.

Rewritting the given numbers are

[tex]\frac{652}{900}, 0.012,\frac{7}{10}, \frac{32}{100},\frac{1}{10}, 0.721, \frac{65}{100}[/tex]

[tex]\frac{652}{900}, 0.012,0.7, 0.32, 0.1, 0.721, 0.65[/tex]

[tex]0.724, 0.012, 0.7, 0.32, 0.1, 0.721, 0.65[/tex]

Now arranging the above numbers from smallest to largest

[tex]0.012, 0.1, 0.32, 0.65, 0.7, 0.721, 0.724[/tex]

ie, 0.12, [tex]\frac{1}{10}, 32\%, 65\%, \frac{7}{10}, 0.721, 0.721, \frac{652}{900}[/tex]

The given numbers in ascending order is

[tex]0.012, \frac{1}{10}, 32\%, 65\%, \frac{7}{10}, 0.721, 0.721, \frac{652}{900}[/tex]

Answer:

the answer is C) 12

Step-by-step explanation:

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