A triangle PQR has coordinates (1, 3), (5, 1) and (3, k) respectively in an
anticlockwise direction).
Find the value of k if the triangle's area is 6 units?​

Answer:

The answer is -1 / 6

Step-by-step explanation:

use the formula y2 - y1 / x2 - x1 = m

7 - 8 / 10 - 4 = -1 / 6

Answer:

9100.09

Step-by-step explanation:

i did the math so this is it

Answer:

My answer is 8

Step-by-step explanation:

I calculate the area of all the shapes and added them together

the square comes first = the formlula = a  to the power of 2  or just L x W =  2 x 2 = 4

The traingles - the formula = the height x base/2 2 x 2 /2 = 2  ( but there are two traingles so) 2 x 2 = 4

add the two shapes areas together = 4+4 = 8

Answer:

12.5- the cost, in dollars, for tile per square foot

x(x+2)- the area, in square feet, of the room

400- the flat rate, in dollars, the company charges for installation

The length and width of the rectangular room is L = x feet , W = ( x + 2 ) feet

The area of the rectangle is given by the product of the length of the rectangle and the width of the rectangle

Area of Rectangle = Length x Width

Given data ,

Let the area of the rectangular room be A

Now , the length of the room L = x feet

And , length of a certain room is 2 feet more than its width

The width of the room W = ( x + 2 ) feet

The total charge for tiling the room C = 12.5 x ( x + 2 ) + 400

Now , the area of the rectangular room A = x ( x + 2 ) feet²

So , the width, in feet, of the room = ( x + 2 ) feet

The length, in feet, of the room = x feet

The area, in square feet, of the room = x ( x + 2 ) feet²

The cost, in dollars, for tile per square foot = $ 12.50

The amount of materials needed to cover the room's floor = 12.5 x ( x + 2 )

The flat rate, in dollars, the company charges for installation = $ 400

Hence , the expressions are solved and the area of rectangle is x ( x + 2 ) feet²

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Answer:

16 laps

Since Cheyene ran 16 laps

32-16=16

Stormy ran 16 laps

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Answer:

g(-4) = 1

General Formulas and Concepts:

Algebra I

Step-by-step explanation:

What g(-4) is saying is what the output of the function g(x) when x= -4. According to the graph, when x = -4, y = 1.

∴ g(-4) = 1

Answer:

B

Step-by-step explanation:

Answer:

x = 22

Step-by-step explanation:

We need to find the value of x for the given equation.

[tex]\dfrac{\dfrac{1}{5}}{\dfrac{1}{11}}=\dfrac{x}{10}\\\\\dfrac{1}{5}\times 11=\dfrac{x}{10}[/tex]

Cross multiplying both sides,

[tex]11\times 10=5x\\\\x=\dfrac{11\times 10}{5}\\\\x=11\times 2\\\\x=22[/tex]

So, the value of x is equal to 22.

Answer:

-5

Step-by-step explanation:

4x - 1 = 6x + 9

4x = 6x + 10

-2x = 10

x = -5

Answer:

10d+16

Step-by-step explanation:

=>3(2d+2)+2(2d+5)

=>6d+6+4d+10

=>10d+16

Answer:

14

Step-by-step explanation:

so it means the opposite of negative 14 which is postive 14

Answer:

D.Since m(x) = -(x + 4)(x-7), the zeros for m(x) are -4 and 7.

Step-by-step explanation:

Answer:

Step-by-step explanation:

So first you want to take the constants of -x^2 (which would be -1) and -28 and multiply them to get the product of 28.

Since the other constant of 11x is 11, you want to find 2 numbers whose sum give you 11 and whose product give you 28. That would be 4 and 7, because 4 + 7 = 11 and 4 * 7 = 28. But since you have -x^2 you will want to put a negative sign in front of one of your x variables and in front of 4 or 7, so that you still get 11x when you factor it out.

So you would set up the equation like this (-x+4)(x-7) = 0. To make it easier to find the values of x, you could just write it out as -x+4 = 0 and x-7 = 0. Than you solve for x in botn euqations.

Then you would find out that x = 4, 7.

Does this help?

Answer:

y=25x

Step-by-step explanation:

It is a linear equation with a slope of 25

Answer:

b=2f+6

b=2*9+6

b=18+6

b=24

Step-by-step explanation:

Answer:

24

Step-by-step explanation:

2 x 9 + 6 = 24

Answer:

24 miles

Step-by-step explanation:

3 hours = 180 minutes

[tex]\frac{4}{y}: \frac{30}{180}[/tex]

y × 30 = 4 × 180

30y = 720

30y ÷ 30 = 720 ÷ 30

y = 24

Answer: y=0.25

Step-by-step explanation: 1.2 / 4.8 = 0.25

Answer:

915'000.+123=915,123

Answer:

cant answer with two equal signs

Step-by-step explanation:

but if u mean

-1/2=-5/18+h that equals h=-2/9

and if u mean

-1/2+-5/8=h it equals h= -7/9

Answer:

Probability = 0.8333...

Step-by-step explanation:

Based on the data, the probability is :

P = number of successes/number of possible outcomes

P = 35 /32 = 0.8333...

which agrees with answer D) in your list

6f+21=-15

6f+21-21=-15-21

6f=-36

6f/6=-36/6

f=-6

Answer: f=-6

Step-by-step explanation:

Answer:

[tex]Factor = 220 \%[/tex]

Step-by-step explanation:

Given

[tex]Initial = 2\frac{1}{2}[/tex]

[tex]Final = 5\frac{1}{2}[/tex]

Required

Determine the factor of increment

First, we calculate the percentage increment

[tex]\% Increment = \frac{Final - Initial}{Initial} * 100\%[/tex]

Substitute values for Final and Initial

[tex]\% Increment = \frac{5\frac{1}{2} - 2\frac{1}{2}}{2\frac{1}{2}} * 100\%[/tex]

Express fractions as decimals

[tex]\% Increment = \frac{5.5 - 2.5}{2.5} * 100\%[/tex]

[tex]\% Increment = \frac{3}{2.5} * 100\%[/tex]

[tex]\% Increment = \frac{3* 100}{2.5} \%[/tex]

[tex]\% Increment = \frac{300}{2.5} \%[/tex]

[tex]\% Increment = 120 \%[/tex]

So, the factor of increment is:

[tex]Factor = 100\% + Increment[/tex]

[tex]Factor = 100\% + 120 \%[/tex]

[tex]Factor = 220 \%[/tex]

Answer:

21/4 or 5 and 1/4 hours

Step-by-step explanation:

3/4 times 7 or 7/1

Answer:

Is there a question?

Step-by-step explanation:

Answer:

[tex]volume = 927,587.2ft^3[/tex]

Step-by-step explanation:

The equation to find the volume of a sphere is as follows:

[tex]volume = \frac{4}{3}\pi r^3[/tex]

We have a radius of 60.5ft, let's plug this into the equation and solve:

[tex]volume = \frac{4}{3} \pi (60.5)^3 \\volume = 927,587.17\\volume = 927,587.2[/tex]

Therefore, the volume of a sphere with a radius of 60.5ft is 927,587.2ft^3.

Hope this helps!!

- Kay :)

Volume of the sphere is 927587.2 cubic feet (nearest tenth).

"A sphere is a set of points in space that are a given distance r from the center. The volume of a 3 -dimensional solid is the amount of space it occupies."

Formula to find the volume of a sphere

Volume of the sphere = [tex]\frac{4}{3} \pi r^{3}[/tex]

V = [tex]\frac{4}{3} \pi (60.5)^{3}[/tex]

V = 927,587.167

Using calculator, we get

V ≅ 927587.2 cubic feet

Hence, Volume of the sphere is 927587.2 cubic feet (nearest tenth).

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Answer:

[tex]4x^2 - 8x + 15 - \frac{78}{4x+5}[/tex]

Step-by-step explanation:

To solve polynomial long division problems like these, it's helpful to build a long division table. Getting used to building these can make problems like this much simpler to solve.

Begin by looking at the first term of the cubic polynomial.

What would we have to multiply [tex]4x + 5[/tex] by to get an expression containing [tex]16x^3[/tex]? The answer is [tex]4x^2[/tex], since [tex](4x + 5) \times 4x^2 = 16x^2 + 20x[/tex].

This is the first step of our long division, and we write out the start of our long division table like this:

[tex]{ }\qquad{ }\quad{ }\quad{ }\,\,\,\,\,4x^2\\4x + 5\quad)\!\!\overline{\,\,\,16x^3 - 12x^2 + 20x - 3}\\{ }\qquad{ }\quad{ }\quad{ }\,\,16x^3 + 20x^2\\[/tex]

On the left is the divisor. On top is [tex]4x^2[/tex]. In the middle is the polynomial we are dividing, and on the bottom is the result of multiplying our divisor by

The next step is to subtract the bottom expression from the middle one, like so:

[tex]{ }\qquad{ }\quad{ }\quad{ }\,\,\,\,\,4x^2\\4x + 5\quad)\!\!\overline{\,\,\,16x^3 - 12x^2 + 20x - 3}\\{ }\qquad{ }\quad{ }\quad{ }\,\,\underline{16x^3 + 20x^2}\\{ }\qquad{ }\quad{ }\quad{ }\,\,\,\,\,0x^3 - 32x^2\\[/tex]

We are left with [tex]-32x^2[/tex]. The next thing to do is to add the next term of the polynomial we are dividing to the bottom line, like this:

[tex]{ }\qquad{ }\quad{ }\quad{ }\,\,\,\,\,4x^2\\4x + 5\quad)\!\!\overline{\,\,\,16x^3 - 12x^2 + 20x - 3}\\{ }\qquad{ }\quad{ }\quad{ }\,\,\underline{16x^3 + 20x^2}\\{ }\qquad{ }\quad{ }\quad{ }\,\,\,\,\,\,\,\,\,\,\,\,\,\, - 32x^2 + 20x\\[/tex]

Now we return to the beginning of the instructions, and repeat the process: namely, what would we have to multiply [tex]4x + 5[/tex] by to get an expression containing [tex]-32x^2[/tex]? The answer is [tex]-8x[/tex], and we fill out our long division table like so:

[tex]{ }\qquad{ }\quad{ }\quad{ }\,\,\,\,\,4x^2 - \,\,\,\,8x\\4x + 5\quad)\!\!\overline{\,\,\,16x^3 - 12x^2 + 20x - 3}\\{ }\qquad{ }\quad{ }\quad{ }\,\,\underline{16x^3 + 20x^2}\\{ }\qquad{ }\quad{ }\quad{ }\,\,\,\,\,\,\,\,\,\,\,\,\,\, - 32x^2 + 20x\\{ }\qquad{ }\quad{ }\quad{ }\,\,\,\,\,\,\,\,\,\,\,\,\,\, - 32x^2 - 40x\\[/tex]

Once again, we subtract the bottom expression from the one above it, and include the next term of the divisor, like so:

[tex]{ }\qquad{ }\qquad{ }\quad{ }4x^2 - \,\,\,\,8x \,+ 15\\4x + 5\quad)\!\!\overline{\,\,\,16x^3 - 12x^2 + 20x - 3}\\{ }\qquad{ }\quad{ }\quad{ }\,\,\underline{16x^3 + 20x^2}\\{ }\qquad{ }\quad{ }\quad{ }\,\,\,\,\,\,\,\,\,\,\,\,\,\, - 32x^2 + 20x\\{ }\qquad{ }\quad{ }\quad{ }\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\underline{- 32x^2 - 40x}\\{ }\qquad{ }\qquad{ }\qquad{ }\qquad{ }\qquad{ }\,\,\,\,\,60x - 3\\[/tex]

And repeat. What do we multiply [tex]4x + 5[/tex] by to get an expression containing [tex]60x[/tex]? The answer is 15. Our completed long division table looks like this:[tex]{ }\qquad{ }\qquad{ }\quad{ }4x^2 - \,\,\,\,8x \,+15\\4x + 5\quad)\!\!\overline{\,\,\,16x^3 - 12x^2 + 20x - 3}\\{ }\qquad{ }\quad{ }\quad{ }\,\,\underline{16x^3 + 20x^2}\\{ }\qquad{ }\quad{ }\quad{ }\,\,\,\,\,\,\,\,\,\,\,\,\,\, - 32x^2 + 20x\\{ }\qquad{ }\quad{ }\quad{ }\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\underline{- 32x^2 - 40x}\\{ }\qquad{ }\qquad{ }\qquad{ }\qquad{ }\qquad{ }\,\,\,\,\,60x - 3\\{ }\qquad{ }\hspace{3cm}\,\,\underline{60x + 75}\\{ }\hspace{4.3cm}\,\,-78[/tex]

Now, the expression at the top,

[tex]4x^2 - 8x + 20x + 15[/tex]

is our quotient, and the last number, [tex]-78[/tex], is our remainder.

Hence we arrive at the solution of

[tex]\frac{16x^3-12x^2+20x-3}{4x+5} =4x^2 - 8x + 15 - \frac{78}{4x+5}.[/tex]