find the equation of each line from the given information. write the equation in standard Form. show your work for. The line contains the points (3.0) and (4,6)​

Answer:

y = (-5/4)x + 12.25

Step-by-step explanation:

Slope intercept form:

y = mx + b

Slope form:

m = (y₂ - y₁)/(x₂ - x₁)

Let:

(x₁ , y₁) = (9 , 1)

(x₂ , y₂) = (5 , 6)

Plug in the corresponding numbers to the corresponding variables.

m = (6 - 1)/(5 - 9)

Simplify.

m = (5)/(-4)

Your slope is -5/4

Plug in -5/4 for m in the slope-intercept form equation, and use a point to solve for b. For example, we will use (9, 1):

y = mx + b

y = (-5/4)x + b

(1) = (-5/4)(9) + b

Simplify.

1 = (-11.25) + b

Isolate the variable, b. Note the equal sign, what you do to one side, you do to the other. Add 11.25 to both sides.

1 + (11.25) = -11.25 (+11.25) + b

1 + 11.25 = b

b = 12.25

your y-intercept is 12.25

Plug in the corresponding numbers to the corresponding variables.

y = mx + b

m = -5/4

b = 12.25

y = (-5/4)x + 12.25 is your answer.

~

Answer:

8.717 both the sides

Step-by-step explanation:

Given:

Let ABC be the given triangle with

angle A= 55

angle B=55

angle C= 70

side across angle C, c= 10 inches

side across angle B, b =?

aide across angle A,a=?

Now using the law of sin to find a and b:

                a/sinA=c/sinC

                a= (c/sinC)(sinA)

Putting the values:

                a= (10/sin70)(sin55)

                a= 8.717

As the given triangle is isosceles so side a=b

hence a=b= 8.717 inches !

Answer:

5x + 2y + z

Step-by-step explanation:

The perimeter of a polygon is the sum of the lengths of all the sides of the polygon. This polygons has 8 sides. Their lengths are:

x, x, x, x, x, y, y, z

The perimeter of the polygon is the sum of the lengths shown above.

perimeter = x + x + x + x + x + y + y + z

The expression above can be simplified by combining like terms.

perimeter = 5x + 2y + z

Answer:

x^2+6x+9

(x+3)^2

Step-by-step explanation:

Answer:

3(2b+3)^2=36

(2b+3)^2=12

2b+3=+2 radical3

2b+3= 2 radical 3

b=- radical 3 -3 over 2

b= radical 3- 3 over 2

b=- radical 3 - 3 over 2

Answer:

The answer is A

Step-by-step explanation:

What is segment ab? is there a picture that is supposed to go with it?

Answer:  The required co-ordinates of point M are (8, 9).

Step-by-step explanation:  Given that the point M divides segment AB into a ratio of 2 : 3, where A is at (0, 15) and B is at (20, 0).

We are to find the co-ordinates of point M.

We know that

the co-ordinates of a point that divides the line segment joining the points (a, b) and (c, d) are given by

[tex]\left(\dfrac{mc+na}{m+n},\dfrac{md+nb}{m+n}\right).[/tex]

For the given division, (a, b) = (0, 15), (c, d) = (20, 0) and m : n = 2 : 3.

Therefore, the co-ordinates of point M are given by

[tex]\left(\dfrac{2\times20+3\times0}{2+3},\dfrac{2\times0+3\times15}{2+3}\right)\\\\\\=\left(\dfrac{40}{5},\dfrac{45}{5}\right)\\\\\\=\left(8,9).[/tex]

Thus, the required co-ordinates of point M are (8, 9).

Step-by-step explanation:

[tex](x^2+5x+4)\div(x+2)^2=(x^2+4x+4+x)\div(x+2)^2\\\\=(x^2+2(x)(2)+2^2+x)\div(x+2)^2\qquad\text{use}\ (a+b)^2=a^2+2ab+b^2\\\\=\bigg((x+2)^2+x\bigg)\div(x+2)^2=\dfrac{(x+2)^2+x}{(x+2)^2}=\dfrac{(x+2)^2}{(x+2)^2}+\dfrac{x}{(x+2)^2}\\\\=1+\dfrac{x}{(x+2)^2}[/tex]

Answer:

0.5r

Step-by-step explanation:

If Jerry took half the time Macy did then that means Macy took twice as long as Jerry. If Jerry’s speed was r then Macy’s speed is 0.5r or half the speed of Jerry. This will mean Macy goes half as slow and takes twice as long to get there.

The average speed of Marcy in miles per hour is 0.5r.

If Jerry took half the time Marcy did then that means Marcy took twice as long as Jerry. If Jerry’s speed was r then Macy’s speed is 0.5r or half the speed of Jerry. This will mean Marcy goes half as slow and takes twice as long to get there.

Hence, The average speed of Marcy in miles per hour is 0.5r.

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Answer:

I think it's C, sorry if I'm wrong

Answer:

Step-by-step explanation:

(3x²+1)(4x-3) = 12x^3-9x²+4x-3.....answer 1

If circle with center O has a radius of 18 centimeters. If the length of arc AB = 6π centimeters then measure of x is 60°

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

Given,

Circle with centre O,

Radius of circle=18 centimeters

length of arc AB = 6π centimeters

We need to find the measure  θ  of x

We have a formula to find the length of arc.

Length of an Arc = θ × (π/180) × r

Apply the given values in formula

6π=θ × (π/180) × 18

π gets cancelled on both the sides

6=θ/10

θ=60°

Hence if circle with center O has a radius of 18 centimeters. If the length of arc AB = 6π centimeters then measure of x is 60°

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Answer: The answer is 12.6 Meters Squared

You get that from multiplying 120 to 3.5 and 2.5 . After doing that you will get 420 cm and 300 cm. Knowing that a meter is 100 cm you will get 4.2 meters and 3 meters. To find the area of the kitchen space you will multiple 4.2 and 3 meters together and get 12.6 Meters, therefore 12.6 meters squared is the area of the kitchen floor.

To solve the problem, set up two equations: X + Y = 12 and X = 2Y. Using the substitution method, replace X with 2Y in the first equation to find Y = 4, and subsequently find X = 8.

The problem given to us involves finding two numbers, X and Y, given that the sum of these two numbers is 12 and the first number, X, is twice the second number, Y. To solve for X and Y, we can set up a system of two linear equations.

The first equation comes from the sum of the two numbers:

X + Y = 12

The second equation comes from the statement that X is twice Y:

X = 2Y

Now we have a system of equations:

One method to find solutions for X and Y is by substitution. We can substitute 2Y in place of X in the first equation:

Now that we know Y is 4, we can find X using the second equation:

The two numbers are X = 8 and Y = 4.

Take out the 3 , to make the vertex form easier;)

Your answer ish c. 2

A slope is also known as the gradient of a line. The correct option is B.

A slope also known as the gradient of a line is a number that helps to know both the direction and the steepness of the line.

slope = (y₂-y₁)/(x₂-x₁)

The slope of the line that is passing through (-2, 6) and (4, 6) can be calculated as,

Slope = (6-6)/(-2-4) = 0/(-6)

Hence, there exists no slope between the two of the given points.

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Answer:

25

Step-by-step explanation:

15 * 15 = 225

3 * 3 = 9

225 / 9 = 25

Answer:

the answer is 25

Step-by-step explanation:

So you multiple 15x15 which equals 225 then you multiply 3x3 which is 9

the you take 225 and divide it by 9 wich would then be 25................hope i helped

Final answer:

To find w from the equation 3w - 4z = 8, add 4z to both sides, and then divide by 3 to isolate w, giving w = (4z + 8) / 3.

Explanation:

The equation 3w - 4z = 8 is a linear equation in two variables (w and z). To find w in terms of z, you need to isolate w on one side of the equation. Here is the process step by step:

Add 4z to both sides of the equation: 3w - 4z + 4z = 8 + 4z.

Simplify the equation: 3w = 4z + 8.

Divide every term by 3 to solve for w: w = (4z + 8) / 3.

So, w is equal to (4z + 8) / 3 when isolated from the given equation.

B. Parallelogram

Explanation: both have parallel sides

The two of the given figures are parallelogram. The correct option is B.

In parallelogram  the opposite sides are equals and it is not formed 90 degree angle between two sides.

In the two of the given figures, it can be observed that the two figures have opposite sides parallel and equal. Therefore, the two of the given figures are a parallelogram.

Hence, the two of the given figures are parallelogram.

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Answer:

[tex]\large\boxed{Q6.\ \sin X\approx0.778}\\\boxed{Q7.\ x\approx5.9}[/tex]

Step-by-step explanation:

Q6.

[tex]\sin\theta=\dfrac{opposite}{hypotenuse}[/tex]

We have

[tex]opposite=14\\\\hypotenuse=18[/tex]

Substitute:

[tex]\sin X=\dfrac{14}{18}=\dfrac{14:2}{18:2}=\dfrac{7}{9}=0.777...\approx0.778[/tex]

Q7.

Use sine.

We have

[tex]opposite=x\\\\hypotenuse=8\\\\\alpha=48^o\\\\\sin48^o\approx0.7431[/tex]

Substitute:

[tex]\dfrac{x}{8}=0.7431[/tex]               multiply both sides by 8

[tex]x=5.9448\to x\approx5.9[/tex]

Answer:

the correct answer would be C sorry if I'm wrong but that's how I know how to do it

The answer is 103 because it’s in the “middle”

Median means the middle number.

The answer : 103

Absolutely down graph is true!!

because, certainly 2<y<3

and we know 2^y=5 ==> log5 with base 2 =y

so it concludes we must have a node between 2<y<3 in x=5

Answer: C

Since all the answers have (-6), it means that you multiply the whole equation on both sides by 6, which makes a (2/3)x become a 4x and a (1/2) become 3

Answer:

C

Step-by-step explanation:

Start by multiplying through by 3. That is the first of 2 possible steps.

3[2/3 x - 1  = 1/2]

2x - 3 = 3/2              

Now multiply by 2

2 [ 2x - 3 = 3/2]

4x - 6 = 3

That makes C the only possible answer.

Answer:

1) [tex]\frac{13}{4}[/tex]

2) [tex]\frac{11}{2}[/tex]

3) [tex]\frac{5}{3}[/tex]

4) [tex]\frac{35}{8}[/tex]

Step-by-step explanation:

we know that

A mixed number is the sum of a whole number  and a fraction number

case 1) we have

[tex]3\frac{1}{4}[/tex]

so

[tex]3\frac{1}{4}=3+\frac{1}{4}=\frac{3*4+1}{4}=\frac{13}{4}[/tex]

case 2) we have

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

so

[tex]5\frac{1}{2}=5+\frac{1}{2}=\frac{5*2+1}{2}=\frac{11}{2}[/tex]

case 3) we have

[tex]1\frac{2}{3}[/tex]

so

[tex]1\frac{2}{3}=1+\frac{2}{3}=\frac{1*3+2}{3}=\frac{5}{3}[/tex]

case 4) we have

[tex]4\frac{3}{8}[/tex]

so

[tex]4\frac{3}{8}=4+\frac{3}{8}=\frac{4*8+3}{8}=\frac{35}{8}[/tex]

Answer:

y < 3

Step-by-step explanation:

Given

15y - 9 < 36 ( Isolate 15y by adding 9 to both sides )

15y < 45 ( divide both sides by 15 )

y < 3

Answer:

y < 3

Step-by-step explanation:

on edge 2020

Answer:

The area of the shaded sector is [tex]51.2\pi \ units^{2}[/tex]

Step-by-step explanation:

I assume that the problem is

Find the area of the shaded sector of the circle with radius equal to 16 units

step 1

Find the value of x

we know that

[tex]8x+2x=360\°[/tex]-----> by complete circle

[tex]10x=360\°[/tex]

[tex]x=36\°[/tex]

The central angle of the shaded sector is 2x

[tex]2(36\°)=72\°[/tex]

step 2

Find the area of the circle

The area of the circle is equal to

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

we have

[tex]r=16\ units[/tex]

substitute

[tex]A=\pi (16)^{2}[/tex]

[tex]A=256\pi\ units^{2}[/tex]

step 3

Find the area of the shaded sector

we know that

A central angle of 360 degrees subtends an area of circle equal to [tex]256\pi\ units^{2}[/tex]

so

by proportion

Find the area of the shaded sector by a central angle of 72 degrees

[tex]\frac{256\pi}{360}=\frac{x}{72} \\ \\ x=256\pi *(72)/360\\ \\x=51.2\pi \ units^{2}[/tex]

Answer:

Part a) The total length of the circular portions is [tex]12\pi\ in[/tex]

Part b) The total length of wire needed is tex]53.7\ in[/tex]

Part c) The total weight of the ornament is [tex]97\ g[/tex]

Step-by-step explanation:

Part a) Find the total length of the circular portions in terms of pi

we know that

The diameter of the circle is equal to the length side of the square

[tex]D=4\ in[/tex]

The total length of the circular portions is equal to the circumference of three complete circle

Because each circular portion is equal to 3/4 of circle

so

[tex](3/4)*4=3[/tex]

The circumference of four three quarter circles is equal to

[tex]C=3(\pi D)[/tex]

substitute the diameter

[tex]C=3(\pi (4))[/tex]

[tex]C=12\pi\ in[/tex]

Part b) Find the total length of wire needed

The total length of the circular portions is [tex]12\pi\ in[/tex]

assume

[tex]\pi =3.14[/tex]

[tex]12(3.14)=37.68\ in[/tex]

The total length of the square portion is equal to

[tex]4b=4(4)=16\ in[/tex] -----> perimeter of a square

Adds the lengths

[tex]37.68+16=53.68\ in[/tex]

Round to the nearest tenth

[tex]53.68=53.7\ in[/tex]

Part c) Find the total weight of the ornament

we know that the ornament weights 1.8 grams per inch

so

Multiply the total length by 1.8 to obtain the total weight

[tex]53.7(1.8)=96.66\ g[/tex]

Round to the nearest gram

[tex]96.66=97\ g[/tex]

Answer:

Step-by-step explanation:

The formula of a volume of a cube:

V = s³

s - side length

We have s = 1/4 ft. Substitute:

V = (1/4)³ = 1/64 ft³

We have four cubes.

4V = 4 · 1/64 = 1/16 ft³

Answer:

A

Step-by-step explanation:

If you plug them in you get 2≥-1

Answer:

determine the periods in the problem, which is the number of periods per year

Step-by-step explanation:

Answer:

determine the periods, which is the number of periods per year

Step-by-step explanation:

n/a

____________________________________________________

Answer:

Your answer would be C). y = 100 - 5x

____________________________________________________

Step-by-step explanation:

Let's break down the question so it would be more easier to figure out the answer.

We would be making a y = mx + b equation

Important information:

With the information above, we can use that to make our equations.

We know that the place has a 100 gallon fish tank. in the question, it says that for the equation, the tank was full, so that would be our "beginning point" or "starting value. From the equation, it would represent our "B" value.

Our equation should look like this now:

y = mx + 100

Now we need to find the rate of change.

In the question, it says that the tank DRAINS at around 5 gallons per minute, meaning that we would have to subtract 5 (-5). That would represent your "m" value on the equation. Your equations should now look like this:

y = -5x + 100

F.Y.I: y = 100 - 5x is the same that as -5x + 100, it's just flipped, and y = 100 - 5x is the answer choice that looks close to the one we made.

Answer choice C). y = 100 - 5x would be your FINAL answer.

____________________________________________________

The equation that describes the situation where a 100-gallon tank is drained at a rate of 5 gallons per minute is y = 100 - 5x. This because each minute, the volume decreases by 5 gallons from the starting amount of 100 gallons.

The question is about how to represent a process which decreases at a constant rate in terms of mathematical expression. In this case, Patti's Pet Palace is draining a 100-gallon fish tank at a rate of 5 gallons per minute. The total amount of water in the tank decreases as time progresses and the tank drains.

This process can be represented using a negative slope linear equation. If y represents the amount of water in the tank after x minutes, the initial amount is 100 gallons and it decreases by 5 gallons each minute.

Therefore, the equation to represent this process is y = 100 - 5x. That means option C is the correct answer. For each minute that passes (represented as 'x'), 5 gallons are subtracted from the initial 100 gallons.

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