Find the quadratic function y = ax² + bx + c whose graph passes through the given points.
(-1,-5), (1,1),(-2,-2)

The equation of each line that is perpendicular to the given lines and passes through the stated points are:

20. y = -x + 2

21. y = -7/2x - 35/2

22. y = -8/3x - 7

23. y = 1/4x + 1

In slope-intercept form, y = mx + b, the slope of the equation is m, while the y-intercept of the equation is b.

If two lines are perpendicular to each other, the values of m, which is their slope, are negative reciprocals.

20. The slope of y = 3/3x - 2 is 1, the slope (m) of the line that is perpendicular to it is -1.

Substitute (x, y) = (-2, 4) and m = -1 into y = mx + b, to find the value of b:

4 = -1(-2) + b

4 = 2 + b

4 - 2 = b

2 = b

b = 2

Write the equation of the perpendicular line by substituting m = -1 and b = 2 into y = mx + b:

y = -x + 2

21. The slope of -2x + 7y = 14 is 2/7. Therefore, the slope (m) of the line that is perpendicular to it is -7/2.

Substitute (x, y) = (-3, -7) and m = -7/2 into y = mx + b, to find the value of b:

-7 = -7/2(-3) + b

-7 = 21/2 + b

-7 - 21/2 = b

-35/2 = b

b = -35/2

Write the equation of the perpendicular line by substituting m = -7/2 and b = -35/2 into y = mx + b:

y = -7/2x - 35/2

22. The slope of 3x - 8y = 16 is 3/8. Therefore, the slope (m) of the line that is perpendicular to it is -8/3.

Substitute (x, y) = (-3, 1) and m = -8/3 into y = mx + b, to find the value of b:

1 = -8/3(-3) + b

1 = 8 + b

1 - 8 = b

b = -7

Write the equation of the perpendicular line by substituting m = -8/3 and b = -7 into y = mx + b:

y = -8/3x - 7

23. The slope of 4x + y = 7 is -4. Therefore, the slope (m) of the line that is perpendicular to it is 1/4.

Substitute (x, y) = (4, 2) and m = 1/4 into y = mx + b, to find the value of b:

2 = 1/4(4) + b

2 = 1 + b

2 - 1 = b

1 = b

b = 1

Write the equation of the perpendicular line by substituting m = 1/4 and b = 1 into y = mx + b:

y = 1/4x + 1

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Answer: its answer b

Step-by-step explanation:

The solution for f(3) in the function f(x) = 7x² - 2x is 57

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

F(X) = 7x2-2x

To make the equation legible, we need to rewrite it

So, we have the following representation

f(x) = 7x² - 2x

Also from the question, we have

f(3)

This means that the value of x is 3, and we calculate f(x) when x = 3

Substitute the known values in the above equation, so, we have the following representation

f(3) = 7x² - 2x

So, we have the following equation

f(3) = 7(3)² - 2(3)

There are constants to add or subtract to both sides of the equation

So, we have the following representation

f(3) = 57

Hence, the solution is 57

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Answer: 45

Step-by-step explanation:

The total profit in all was [tex]1040-900=\$ 140[/tex].

The total profit per pizza was [tex](0.50)(8)=\$4[/tex].

This means they sold [tex]\frac{140}{4}=35[/tex] pizzas.

Adding this to the 10 pizzas held back, there were [tex]35+10=45[/tex] pizzas in the original order.

The number of pinto beans in the jar is 24

Ratio, in math, is a term that is used to compare two or more numbers. It is used to indicate how big or small a quantity is when compared to another. In a ratio, two quantities are compared using division. Here the dividend is called the 'antecedent' and the divisor is called the 'consequent

let x be the number of pinto beans

white beans = x + 36

Total beans = 2x + 36

Total share = 2 + 5, which is 7

number of pinto beans(x) = 2/7 * (2x + 36)

x = 2/7 * (2x + 36)

By cross multiplying,

7x =2(2x + 36)

7x = 4x + 72

collect like terms

7x - 4x = 72

3x = 72

x = 72/3

x = 24

In conclusion, 24 pinto beans are in the jar.

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Answer:

-10

Step-by-step explanation:

2(x+3)=x-4

2x+6=x-4

-x     -x

x+6=-4

  -6 -6

x=-10

Answer:

x = -10

Step-by-step explanation:

HOW TO SOLVE YOUR PROBLEM

1. Distribute

2(x + 3) = x - 4

2x + 6  = x - 4

2. Subtract 6 from both sides

2x + 6  = x -4

2x + 6 - 6 = x - 4 - 6

3. Simplify

Subtract the numbers:

2x + 6 - 6 = x - 4 - 6

2x = x - 4 - 6

Subtract the numbers:

2x = x - 4 - 6

2x = x - 10

4. Subtract x from both sides

2x = x - 10

2x - x = x - 10 - x

5. Simplify

Combine like terms:

2x - x = x - 10 - x

1x  = x - 10 - x

Multiply by 1:

1x = x - 10 - x

x = x - 10 - x

Combine like terms:

x = x - 10 - x

x = -10

Solution:

x = -10

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Answer:

the III quadrate the x line (horizontal line) the number there is -4 on the y line (vertical line) -6 from the right side of the III quadrate

The solution of the absolute value equation is x=1/6.

What is the solution to an equation?

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.

When |3x-1|- | 2x+5-(5-x)| = 0

When 3x-1 < 0 and 2x+5-(5-x) < 0

-(3x-1) - ( - ( 2x+5-(5-x) ) ) =0

on simplifying, variable cancels out, so no solution

When 3x-1 < 0 and 2x+5-(5-x) > 0

-(3x-1) - (  ( 2x+5-(5-x) ) ) =0

on simplifying, x=1/6

When 3x-1 >0 and 2x+5-(5-x) < 0

(3x-1) - ( - ( 2x+5-(5-x) ) ) =0

on simplifying, x=1/6

When 3x-1 >0 and 2x+5-(5-x) >0

(3x-1) - (  ( 2x+5-(5-x) ) ) =0

on simplifying, variable cancels out, so no solution

So, the solution is x=1/6

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Answer:

y - 4 = (32/3)x

Step-by-step explanation:

x-intercept: -3/8

y-intercept: 4

x-intercept: (-3/8, 0)

y-intercept: (0, 4)

slope = (y_2 - y_1)/(x_2 - x_1)

slope = (4 - 0)/(0 - (-3/8)) = 4/(3/8) = 32/3

y - y_1 = m(x - x_1)

y - 4 = (32/3)x

Answer:

so sometimes this happens to me and I get a parent or a teachers to help me and I’m sometime doing the math wrong when my answer is right so maybe double check work

Step-by-step explanation:

Answer:

y=4x+14

Answer choice 4

Step-by-step explanation:

What is the slope-intercept form of the line that passes through the points (-4,-2) and (-2, 6)?

m=(6+2)/(-2+4)

m=4

Slope-point form: (y+2)=4(x+4)

Simplify to slope-intercept form:

y+2=4x+16

y=4x+14

Answer:

1250 teenagers

Step-by-step explanation:

= 5000 * (1/4)

= 5000 * 0.25

= 1250

Answer:

[tex]\huge\boxed{\sf 1250 \ teenagers}[/tex]

Step-by-step explanation:

Total people = 5,000

= 25% of total people

Key: "of" means "to multiply" and total people = 5000

= 25% × 5000

Key: % means "out of 100"

[tex]\displaystyle =\frac{25}{100} \times 5000\\\\= 25 \times 50\\\\= 1250 \ teenagers\\\\\rule[225]{225}{2}[/tex]

The key features that f(x) and g(x) have in common are; A: Both f(x) and g(x) have the same domain of (∞, -∞).

We are given the functions as;

Polynomial function; f(x) = 2x² - 3x + 5

Exponential function; g(x) = 2ˣ - 5

In this question we must analyze the domain, range, x-intercepts and changing intervals:

The domain of both functions are a set of all real numbers with both functions continuous.

The range of both functions from the graph attached is;

Range of f(x) = (3.875, +∞)

Range of g(x) = (-5, +∞)

The x-intercepts of both functions are;

x-intercept for f(x) is non existent

x-intercept for g(x) is (2.322, 0)

From the attached graph;

f(x) increases over interval of (3.875, ∞)

g(x) increases over the interval of a set of real numbers

Looking at the given options, we can say that option A is the correct one

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The function f ( x ) = y = 2 ( x + 5 )² - 6 is a one to one function

What is one to one function?

One to one function or one to one mapping states that each element of one set, say Set (A) is mapped with a unique element of another set, say, Set (B), where A and B are two different sets. It is also written as 1-1. In terms of function, it is stated as if f(x) = f(y) implies x = y, then function f is one to one.

The function, f(x), is a one to one function when one unique element from its domain will return each element of its range. This means that for every value of x, there will be a unique value of y or f(x).

f ( x₁ ) = f ( x₂ ) if and only if x₁ = x₂

Given data ,

Let the function be f ( x )

where f ( x ) = y

So , the equation will be

y =  2 ( x + 5 )² - 6

Now , on simplifying the equation , we get

y = 2 ( x² + 10x + 25 ) - 6

y = 2x² + 20x + 50 - 6

y = 2x² + 20x + 44

Therefore , the function is f ( x ) = y = 2x² + 20x + 44

Now , replace y with x , we get

f ( y ) = x = 2y² + 20 y + 44

And f ( x₁ ) = f ( x₂ )

So , the function is one to one function

Hence , The function f ( x ) = y = 2 ( x + 5 )² - 6 is a one to one function

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The matrix formed after solving C-D is C-D = -4     8    10

                                                                              4   -12   -6

                                                                              1      2    4

What is Matrix in Mathematics?

A matrix is a rectangular array or table of numbers, symbols, or expressions that are organised in rows and columns to represent a mathematical object or an attribute of such an object in mathematics. For instance, consider a matrix with two rows and three columns.

Solution:

Given That Matrix C = 1   7   5

                                    4   -7  0

                                    2   6   7

Also, Matrix D = 5   -1   -5

                          0    5   6

                          1     4    3

To Find: C-D

Since the order of both the matrices is 3 * 3

we can solve the problem

For this we will substract each element from Matrix C from its corresponding element in Matrix D

C-D = (1-5)   (7+1)   (5+5)

         (4-0)   (-7-5)   (0-6)

         (2-1)   (6-4)   (7-3)

C-D = -4     8    10

           4   -12   -6

           1      2    4

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The probability that the weight will be between 3183 and 4022 grams is; 0.9323

The formula for z-score is;

z-score = (x – μ) / σ

where;

x is sample mean

μ is population mean

σ is standard deviation

Now, we want to find the probability that the weight will be between 3183 and 4022 grams. This is;

P(3183 < X < 4022)

When X = 3183

z = (3183 - 3637)/227

z = -2

When X = 4022

z = (4022 - 3637)/227

z = 1.696

Using online probability between two z-scores calculator, we have;

P(-2 < x < 1.696) = 0.9323

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Answer:

[tex]\huge\boxed{\sf x = 128\°}[/tex]

Step-by-step explanation:

x + 52° = 180 (Angles on a straight line add up to 180°)

Subtract 52 to both sides

x = 180 - 52

x = 128°

[tex]\rule[225]{225}{2}[/tex]

Answer:

X= 128°

Step-by-step explanation:

The angels on a straighlije add up to 180°

hence <DCA+ <BCA= <BCD

X+ 52°=180°

X=180°-53°

X=128°

Answer:  Choice A

Step-by-step explanation:

1/8 = 0.125

That is a decimal that terminates after 3 decimal places (choice A)

Answer:

375 minutes

Step-by-step explanation:

72 km = 90 mins. 32 km = 40 mins. how many mins = 300 km?

72/90 = 0.8

32/40 = 0.8

so:

300/x = 0.8

multiply both sides by x:

x(300/x) = 0.8(x)

300 = 0.8x

divide both sides by 0.8:

x = 375

The parametric equations for an object moving clockwise along the ellipse are x =  3 cos((2π/3) t) and y = 5 sin((2π/3) t)

Given: the equation of an ellipse x²/9 + y²/25 = 1

Beginning at (0,5) and requiring 3 seconds

The parametric equations representing an ellipse x²/a² + y²/b² = 1  are

x = a cos(t) and y = b sin(t)

where t is the parameter with values between [0, 2π]

If t represents time. Then, if a lap around the ellipse is completed in T seconds we have,

x = a cos((2π/T) t)

y = b sin((2π/T) t)

where 2π/T is the period of the motion.

Combining these results, therefore, we have the parametric equations:

x =  3 cos((2π/3) t)

y = 5 sin((2π/3) t)

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The inequality equation given on number line shows as.

What is number line?

In elementary arithmetic, number line could be a image of a graduated line that is visual illustration of the important numbers. each purpose of range|variety} line is assumed to correspond to a true number, and each complex number to a degree.

Main body:

The given inequality is :

y≥ -8

to represent it on the number line we need to select number which are greater than -8 .

Hence the graph on number line looks line as represented in figure.

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Here is the completed table:

                         Tuna     Cheese   Ham   Total

Brown                  21          11             8        40

White                  21           15           24       60

Total                     42        26           32           100

Number of tuna sandwiches that were on white bread : 1/2 x 42 = 21

Number of tuna sandwiches that were on brown bread : total number of tuna sandwiches - total number of tuna sandwiches on white bread: 42 - 21 = 21

Number of ham sandwiches on brown bread : 20% x 32

= 0.25 x 32 = 8

Number of ham sandwiches on white bread : number of ham sandwiches - number of ham sandwiches on brown bread

32 - 8 = 24

Number of white bread sandwiches - number of brown bread sandwiches = 20

number of white bread sandwiches = x + 20

number of brown bread sandwiches = x

x + x + 20 = 100

x + x = 100 - 20

2x = 80

x = 40

number of white bread sandwiches = 40 + 20  = 60

Number of white bread cheese sandwiches = total number of white bread sandwiches - total number of tuna and ham white bread sandwiches

Number of white bread cheese sandwiches = 60 - (21 + 24)

= 60 - 45

= 15

Number of brown bread cheese sandwiches = total number of brown bread sandwiches - total number of tuna and ham brown bread sandwiches

40 - (21 + 8)

40 - 29 = 11

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Answer:

3x+4=34

x=10

Step-by-step explanation:

Since it’s in the median it is a number in between the 2 on the shape and the number right between 28 and 40 is 34 so we can set 3x+4 equal to that to find x

3x+4=34

   -4. -4

3x=30

/3.  /3

x=10

Hopes this helps please mark brainliest

Answer:

Step-by-step explanation:

EF is the median, therefore the mean between 28 and 40

(28 + 40) : 2 =

34

3x + 4 = 34

3x = 30

x = 10

Answer:

The blue dot is -19

Step-by-step explanation:

Since every 2 ticks are worth 6 (|-10|-|-4|=6), then one tick is worth 3.

We are going backward, so we can count backward.

We have to go down 3 ticks, so -10-3=-13; -13-3=-16; -16-3=-19.

The blue dot is -19

Answer: The blue dot equals to -19.

Step-by-step explanation:

On the number line, there are the numbers -10 & -4.

-7 would fit in the middle of them. That means the number line goes by minus 3.

Count -10 , -13, -16, then you get on the the blue dot which is -19.

Therefore, -19 is the answer.

Answer: To make it very simple for ourselves, we can just divide 8 by 4.29. Our answer will then be 1.8648018648 or rounded to 1.86 servings per dollar.

Hope this helps.

He is best known in the modern day for the Pythagorean Theorem, a mathematical formula which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares on the other two sides.

Pythagoras was a Greek philosopher who made important developments in mathematics, astronomy, and the theory of music. The theorem now known as Pythagoras's theorem was known to the Babylonians 1000 years earlier but he may have been the first to prove it.

The most famous contribution for which Pythagoras is popular worldwide is the discovery of the Pythagoras Theorem which applies to all Right Angled Triangle. In the theorem, he stated that the sum of the square of both Base and Height will be equal to the square of Hypotenuse of a Right Angle Triangle.

The the smallest positive solution to the Trigonometry sin(5x)cos(9x) - cos(5x)sin(9x) = - 0.25 is x = 3.617degree

Trigonometry is a branch of mathematics that studies relationships between the sides and angles of triangles

sin(5x)cos(9x) - cos(5x)sin(9x) = -0.25

sin(5x)cos(5x + 4x) - cos(5x)sin(5x + 4x) = -0.25

-sin( 5x - 9x) = -0.25

-sin (9x -5x) = -0.25

sin ( 4x) = 0.25

Using the sine inverse

arcsin(0.25) = x = 0.25268 rad ≅ 14.47 degree

so dividing this angle by 4

x = 3.617degree

Therefore, the smallest positive solution to the Trigonometry is x = 3.617degree

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Answer:

1/3 cup

Step-by-step explanation:

A brownie recipe needs 1/2 cup of white sugar per batch if I only want to make 2/3 of a batch how much white sugar do I need?

1/2 * 2/3 = 2/6 = 1/3 cup

Answer:

-3x -12

Step-by-step explanation:

-6x +3x = -3x

-3-9 = -12

The given equation, y = -4(x-3)² + 6, rewritten in standard form is y = -4x² + 24x - 30

From the question, we are to rewrite the given equation in standard form.

The given equation is

y = -4(x-3)² + 6

The standard form of a quadratic equation is

y = ax² + bx + c  

Now, we will express the given equation in the standard form of a quadratic equation.

y = -4(x - 3)² + 6

y = -4(x - 3)(x - 3) + 6

y = -4(x(x -3) -3(x - 3)) + 6

y = -4(x² - 3x - 3x + 9) + 6

y = -4x² + 12x + 12x - 36 + 6

y = -4x² + 24x - 30

Hence, the equation is y = -4x² + 24x - 30

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