5x^2-8x+12=3x+10
solve quadratic by factoring

The equation of the line passing through the given points is y = -2x+1.

Given that is a line passing through two points (0, 1) and (2, -3) we need to find the equation of the line using them,

We know that the equation of a line passing through points (x₁, y₁) and (x₂, y₂) is =

y-y₁ = y₂-y₁ / x₂-x₁ (x-x₁)

Here (x₁, y₁) and (x₂, y₂) are (0, 1) and (2, -3),

Therefore, the required equation is =

y-1 = -3-1/2 (x-0)

y-1 = -2x

y = -2x+1

Hence, the equation of the line passing through the given points is y = -2x+1.

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The equation of a circle with diameter endpoints of (13, -1) and (15, 9) will be x² + y² - 28x - 8y + 186 = 0.

Given that:

Endpoints of diameter, (13, -1) and (15, 9)

The equation of the circle when endpoints of diameter are given is written as,

(x - x₁)(x - x₂) + (y - y₁)(y - y₂) = 0

The equation of the circle is calculated as,

(x - 13)(x - 15) + (y + 1)(y - 9) = 0

x² - 28x + 195 + y² - 8y - 9 = 0

x² + y² - 28x - 8y + 186 = 0

The equation of a circle with diameter endpoints of (13, -1) and (15, 9) will be x² + y² - 28x - 8y + 186 = 0.

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Answer:

-8

Step-by-step explanation:

f[f(0)]=f[3×0-2]=f(-2)=3(-2)-2=-8

The value of x is given as follows:

x = 13.1 ft.

The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:

We have that the important parameters are given as follows:

Hence the value of x is obtained as follows:

sin(57º) = 11/x

x = 11/sine of 57 degrees

x = 13.1 ft.

The triangle is given by the image presented at the end of the answer.

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Answer:

87.9646 millimeters.

Step-by-step explanation:

The circumference (C) of a circle is given by the formula:

C = πd

Where d is the diameter of the circle and π (pi) is a mathematical constant approximately equal to: 3.14159.

In this case, the diameter of the circle is given as 28 millimeters, so we can substitute this value into the formula to find the circumference:

C = πd = π(28 mm) = 87.9646 mm (rounded to 4 decimal places)

Therefore, the circumference of the circle is approximately 87.9646 millimeters.

The solution to the given system of equations is a = 6, b = 4.

The system of equations is given as follows:

a + b = 10  .....(i)

a - b = 2    .....(ii)

To solve this system of equations, we can use the method of elimination.

Adding the two equations, we get:

(a + b) + (a - b) = 10 + 2

2a = 12

a = 6

Substituting a = 6 into one of the equations, we get:

6 - b = 2

b = 4

Therefore, the solution to the system of equations is:

a = 6, b = 4.

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Answer:B

Step-by-step explanation:i did the quiz

The radius of the sphere with a volume of 10000 m³ is approximately 13.4 meters.

A sphere is simply a three-dimensional geometric object that is perfectly symmetrical in all directions.

The volume of a sphere is expressed as:

Volume =  (4/3)πr³

Where r is the radius of the sphere and π is the mathematical constant pi (approximately equal to 3.14).

Given that the volume of the sphere is 10000 m³, we can set up the equation:

Volume =  (4/3)πr³

r³ = Volume / (4/3)π

r = ∛( Volume / (4/3)π )

r = ∛( 10000/ ( (4/3) × 3.14) )

r = 13.4 m

Therefore, the radius is 13.4 m.

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Answer:

B' ( -1,-4)

C' (-6,-5)

Step-by-step explanation:

Take each point and move it one unit left and then 3 units up.

Helping in the name of Jesus.

The x and y int for the equation are x = undefined and y-int = 1

From the question, we have the following parameters that can be used in our computation:

y = 4^x

Set the variable x to 0 to calculate the y-intercept

So, we have

y-int = 4^0

y-int = 1

Set the variable y to 0 to calculate the x-intercept

So, we have

4^x = 0

So, we have

x = ln(0)/ln(4)

Evaluate

x = undefined

Hence, the x-intercept is undefined

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The height of the rectangle is approximately 15.5 inches.

Let's call the height of the rectangle "h". We know that the width is 47 inches longer than the height, so the width can be expressed as "h + 47".

We can use the Pythagorean theorem to solve for the height. The Pythagorean theorem states that for a right triangle with legs of length "a" and "b" and hypotenuse of length "c", a^2 + b^2 = c^2.

In this case, we can consider the rectangle to be a right triangle, with the height as one leg, the width as the other leg, and the diagonal as the hypotenuse. So we can write:

h^2 + (h + 47)^2 = 65^2

Simplifying this equation gives:

2h^2 + 94h - 1476 = 0

We can solve for "h" using the quadratic formula:

h = (-b ± sqrt(b^2 - 4ac)) / 2a

In this case, a = 2, b = 94, and c = -1476. Plugging these values into the quadratic formula gives:

h = (-94 ± sqrt(94^2 - 4(2)(-1476))) / 4

Simplifying this expression gives:

h = (-94 ± sqrt(10084)) / 4

h = (-94 ± 100.42) / 4

h = -48.6 or 15.42

Since the height of the rectangle cannot be negative, we can discard the negative solution. Therefore, the height of the rectangle is approximately 15.5 inches.

Check the picture below.

[tex]\tan(18^o )=\cfrac{\stackrel{opposite}{x}}{\underset{adjacent}{18}} \implies 18\tan(18^o)=x \implies 5.8\approx x[/tex]

Make sure your calculator is in Degree mode.

The distance between the areas of the two states is A = 1.727 x 10⁵ km²

Given data ,

Let the area of Nebraska = 2 x 10⁵ km²

Let the area of Massachusetts = 2.73 x 10⁴ km²

The difference between the areas of Nebraska and Massachusetts A =  the area of Nebraska - the area of Massachusetts

On simplifying the exponents , we get

A = 2 x 10⁵ km² - 2.73 x 10⁴ km²

Taking the common factor , we get

A = 10⁴ ( 20 - 2.73 )

A = 10⁴ ( 17.27 )

A = 1.727 x 10⁵ km²

Hence , the area is A = 1.727 x 10⁵ km²

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Answer:

The sample space describing all possible outcomes is:

{H1, H2, H3, H4, T1, T2, T3, T4}

The outcomes for the event that the coin toss is heads are:

{H1, H2, H3, H4}

Step-by-step explanation:

If it pertains to using the format H1 to mean that the coin toss is heads and the number chosen is 1.

Step-by-step explanation:

5 000 gm = 5 kg

784kg  - 5kg=  779 kg  more than average

Answer:

The answer is 1/5

Step-by-step explanation:

5ft:25ft=5ft/25ft=1/5

Answer:

1/2

Step-by-step explanation:

Answer:

90 children's tickets and 200 adult tickets were sold.

Step-by-step explanation:

Let's use the variables c and a to represent the number of children's and adult tickets sold, respectively.

From the problem, we know that:

The total number of tickets sold is 290: c + a = 290

The total revenue from ticket sales is $2250: 5c + 9a = 2250

We now have two equations with two unknowns. We can use substitution or elimination to solve for c and a. Here's one way to use elimination:

Multiply the first equation by 5 to get 5c + 5a = 1450

Subtract the above equation from the second equation to eliminate c: 5c + 9a - (5c + 5a) = 2250 - 1450

Simplify: 4a = 800

Solve for a: a = 200

Substitute a = 200 into the first equation to solve for c: c + 200 = 290

Simplify: c = 90

Therefore, 90 children's tickets and 200 adult tickets were sold.

The missing angle of the given image is: ∠HLI = 150°

There are different terms in this type of case when looking for missing angles and they include:

Corresponding angles

Supplementary angles

Opposite angles

Alternate angles

Now, we are given that:

∠JLI = 30°

We know that the sum  of angles on a straight line is 180°. Thus:

∠HLI = 180° - 30°

∠HLI = 150°

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Using Pythagorean's theorem we can see that the variables are:

t = 13.86

w = 12.81

Remember that for any right triangle, Pythagorean's theorem says that the sum of the squares of the legs is equal to the square of the hypotenuse, where the hypotenuse is the side opposite to the 90° angle.

Then for the first triangle we can write:

t² + 8² = 16²

Solving for t:

t = √(16² - 8²) = 13.86

For the second triangle we have:

10² + 8² = w²

Solving for w:

w = √(10² + 8²)

w = 12.81

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Yes , y varies directly with x as a proportion of k = 2.5

Given data ,

Let the values of x = { 2 , 6 , 18 }

Let the values of y = { 5 , 15 , 45 }

Now , the proportion equation is y = kx

On simplifying , we get

k = 5/2

k = 2.5

Therefore , the proportionality constant is k = 2.5

Hence , the proportion is y = 2.5 ( x )

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Because the angles add up to 180°, we conclude that the shelves are parallel.

Two adjacent angles always should add up to 180°. The top shelve and middle shelve will be parallel only if:

∠1 = ∠5

∠2 = ∠6

And we know that:

∠1 + ∠2 = 180°

Then we could rewrite this as:

∠5 + ∠2 = 180°

Replacing the measures we will get:

60° + 120° = 180°

180° = 180°

That equation is true, this, the shelves are parallel.

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The volume of the sphere is 5,575.28 ft³.

The volume of the sphere is calculated by applying the following formula as shown below;

V = ⁴/₃ πr³

where;

The radius of the sphere is calculated as follows;

r = d/2

where;

r = 22 ft / 2

r = 11 ft

The volume of the sphere is calculated as;

V = ⁴/₃ π(11)³

V = 5,575.28 ft³

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The equations that can be used to solve for y, the length of the room are y * (y - 5) = 750, y^2 - 5y = 750 and (y + 25)(y – 30) = 0

From the question, we have the following parameters that can be used in our computation:

Area = 750

Length = y

Width = y - 5

The area is the product of the length and the width

So, we have

y * (y - 5) = 750

When expanded. we have

y^2 - 5y = 750

Lastly, we have

(y + 25)(y – 30) = 0 -- when factored

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The difference in the students who chose peach pie and apple pie is 46

From the question, we have the following parameters that can be used in our computation:

From the above, we have the percentage difference to be

Difference = 38% - 15%

When the given values are substituted, we have

Difference = 23%

This means that

Students = 23% * 200

Evaluate

Students = 46

Hence, the number of students is 46

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The perimeter of the quadrilateral is  b + 2c - 2 inches

To determine the value of the perimeter, we need to know the properties of a quadrilateral.

These properties includes;

The perimeter of a quadrilateral is expressed as;

Perimeter = A + B + C + D

add the values of the sides

Substitute the values, we have;

Perimeter = b + c + b - 2 + c - b

collect the like terms

Perimeter = b + 2c - 2

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The water cooler tank has to be filled 18 times to quench the thirst of 1200 students.

We have

Number of students= 1200

Water consumption per student= 750 ml

So, Total water consumption

= Number of students × Water consumption per student

= 1200 × 750 ml

= 900000 ml

= 900 Liter

Now, the time cooler tank has to be filled to quench the thirst

= 900 / 50

= 18 times

Thus, the water cooler tank has to be filled 18 times to quench the thirst of 1200 students.

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Answer:

Step-by-step explanation:

You want the amounts in each of two accounts, one earning 8% interest, and the other, with an initial balance that is $450 greater, earning 12% interest. The total interest earned is $176.

Let x represent the initial balance in the 12% account. Then the initial balance in the 8% account is (x -450). The total interest earned is ...

  0.08(x -450) +0.12(x) = 176

  0.20x - 36 = 176 . . . . . simplify

  0.20x = 212 . . . . . . add 36

  x = 1060 . . . . . .  divide by 0.2

  x -450 = 610

The 8% account had $610 invested; the 12% account had $1060 invested.