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An equation of the function in standard form is equal to 2x²/3 + 16x/3 + 8 = 0.

A quadratic function can be defined as a mathematical expression (equation) that can be used to define and represent the relationship that exists between two or more variable on a graph.

In Mathematics, the standard form of a quadratic equation is given by;

ax² + bx + c = 0

y = f(x) = ax² + bx + c

Next, we would formulate a system of equations from the data contained in the table above:

-2 = a(-3)² + b(-3) + c  ⇒ -2 = 9a - 3b + c      .......equation 1.

0 = a(-2)² + b(-2) + c  ⇒   0 = 4a - 2b + c      .......equation 2.

8 = a(0)² + b(0) + c  ⇒   8 = c                            .......equation 3.

Substituting the value of c into equation 1 and equation 2, we have:

-2 = 9a - 3b + 8    ⇒ 9a - 3b = -10    .......equation 4.

0 = 4a - 2b  + 8    ⇒ 4a - 2b = -8      .......equation 5.

Multiplying equation 5 by 1.5 and solving simultaneously, we have:

9a - 3b = -10

6a - 3b = -12

3a = 2

a = 2/3

For the value of b, we have:

4a - 2b = -8

4(2/3) - 2b = -8

8/3 - 2b = -8

2b = 8 + 8/3

2b = 32/3

b = 32/6

b = 16/3.

Substituting the values of a, b and c into the standard form of a quadratic equation:

ax² + bx + c = 0

2x²/3 + 16x/3 + 8 = 0

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When given triangles are given then the value of x and y is 5 and 14 respectively.

When BC is similar to EF.

19= 4x-1

19+1=4x

20=4x

x=5

When DE is similar to AB

y-6 =8

y=8+6

y=14

Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent.

A pair of triangles are said to be similar if two pairs of corresponding angles in those triangles are congruent. We can conclude that the third pair must also be equal if the first two angle pairs are. When all three pairs of angles are equal, the sides of the three triangles must also be proportionate.

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Answer:

this is a little much if you broke it down into single questions I would be happy to help

Step-by-step explanation:

Answer:

The answer is below!!

Step-by-step explanation:

I. Fill in each step of the problem-solving process to solve this problem.

Cadence went to the amusement park and paid $14.25 for a souvenir refill cup. Refills cost $1.25 each. If Cadence spent a total of $23, how many refills did she get? ~

Step 1: What is the unknown?

Step 2: What is the key information that can be used to solve the problem?

Step 3: What is a strategy (equation) that can be used to solve the problem?

Step 4: What is the solution to the problem?

          ↓

[tex]\sf 14.25+1.25x=23[/tex]

[tex]\sf 14.25\cdot \:100+1.25x\cdot \:100=23\cdot \:100[/tex]

[tex]\sf 1425+125x=2300[/tex]

[tex]\sf 1425+125x-1425=2300-1425[/tex]

[tex]\sf 125x=875[/tex]

[tex]\sf \cfrac{125x}{125}=\cfrac{875}{125}[/tex]

[tex]\boxed{\sf x=7}[/tex]

Step 5: Check your answer.

To check your answer, plug x = 7 in the given term

[tex]\sf 14.25+1.25(7)=23[/tex]

[tex]\sf 14.25+8.75=23[/tex]

[tex]\sf 23=23[/tex]

→ → → →

II. Solve each problem. Show your work.

Jordan’s bill for car repairs was $500. The cost for parts was $240 and the mechanic charged $65 per hour. How many hours did it take the mechanic to repair Jordan’s car?

Let the number of hours = x

[tex]\sf 65x+240=500[/tex]

[tex]\sf 65x=260[/tex]

[tex]\sf x=4[/tex]

Therefore, it took the mechanic 4 hours to repair Jordan’s car!

→ → → →

2. Marcus made 6 baskets in his first basketball game. In each of the next 4 games, he made the same number of baskets. If he made a total of 34 baskets , how many baskets did he make in each of the 4 games?

Let x = baskets Marcus made in each of the 4 games

[tex]\sf 4x+6=34[/tex]

[tex]\sf 4x=34-6[/tex]

[tex]\sf \cfrac{4x}{4}=\cfrac{28}{4}[/tex]

[tex]\sf x=7[/tex]

Therefore, Marcus made 7 baskets in each of the 4 games!

And we're done!

________________________

Hope this helps!

Have a great day!

y = -48 (1/x) is the variation equation.

A relationship between a set of values for one variable and a set of values for other variables is known as a variation.

One of the most fundamental concepts in mathematics is the idea of a function, in part because functions are a useful tool for describing and illuminating patterns.

given that

x and y vary inversely that means x = k 1/y or y = k 1/x.

so, x= k(1/y)

xy = k

from the question x=-12 when y=4

-12(4) = k

k = -48

now,

y = K (1/x)

y = -48 (1/x)

This is the variation equation.

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Answer:

3/4

Step-by-step explanation:

7x +4x = - 3x+10+6x-4

11x=-3x+6x+10-4

11x=3x+6

11x-3x=6

8x=6

X=3/4

Answer:

a) 1.999 moles He

b) 0.50 moles Cu

Step-by-step explanation:

Step-by-step explanation:

1 km = 1000 m = 0.621371 miles

so,

786.3 m = 0.7863 km (simply divide by 1000).

40 km/h = 40×0.621371 mph (as the reference of 1 hour stays the same).

= 24.8548 mph

always consider the direction of the conversion rate : are you going from a smaller to a larger unit, or from a larger to a smaller unit ?

if we would have said

1 m = 0.001 km

then we would have converted 786.3 m by multiplying it by 0.001 (also getting 0.7863 km as result, of course).

but because we defined it the other way around, we had to divide by 1000. it is clear that this is the same operation, yes ?

in the same way, if we would have said

1 mile = 1.60934 km

then we would have converted 40 km to miles by dividing 40 by 1.60934. again getting the same result, of course.

Answer:

Step-by-step explanation:

you could use multiplication or addition,

Answer:

Step-by-step explanation:

The scaling factor is 2: 1, the distance between Q and S is 3 units.

A scale factor is a number or conversion factor used to adjust the size of a figure without changing its shape. It is used to enlarge or reduce the size of an object. If the original dimensions are known, the scaling factor may be determined.

When describing a shape, you must define the amount to which it has been enlarged.

AC = 6

It signifies that the 6/3 = 2:1 scale factor has been preserved.

As a result, the total dimension of PQRS is half of ABCD.

So,

QS = 1/2 (BD)

Because BD = 6, (can be counted by graph grid)

So,

QS = 1/2 (5) = 3

Hence "Because the scale factor is 2: 1, the distance between Q and S is 3 units."

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The rational numbers are √10, √1000 and √100000 . Options A, C and D

A rational number can be defined as a  number that can be expressed as a fraction.

It also has the numerator and denominators as integers and expressed in decimal forms.

Given the values;

√10 = 3. 162

√100 = 10

√1000 = 31. 6

√100000 = 316. 22

Thus, the rational numbers are √10, √1000 and √100000 . Options A, C and D

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The coordinates of point P are ( -3.5, 2.25).

Given points L( -6, 5) and M( 4, - 6). We are to determine the coordinate of point P that lies along the directed line segment which partitions the segment in the ratio of 1 to 3.

The coordinates of the point that divides a line segment internally in the ratio m:n are given as follows:

[ (mx₂ + nx₁ ) / (m + n) , (my₂ + ny₁ ) / (m + n) ]

Now, m : n = 1 : 3

( x₁, y₁ ) = L( - 6 , 5 )

( x₂, y₂ ) = M( 4, - 6 )

Therefore,

P( x, y) =  [ ( 1 × 4 + 3 × -6 ) / 4 , ( 1 × - 6 + 3 × 5) / 4 ]

P( x, y) = [ ( 4 - 18 ) / 4 , ( - 6 + 15) / 4 ]

P( x, y ) = [ -14/4 , 9/4 ]

P( x, y) = ( - 7/2 , 9/4 )

P( x, y) = ( - 3.5, 2.25 )

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The length of the segment MN is 9.5 units

The endpoints of the line segment MN are given as

M = (-2, -2)

N = (7, -5)

The length of the segment MN is calculated as:

MN = √(x2 - x1)^2 + (y2 - y1)^2

Substitute the known values in the above equation

So, we have

MN = √(-2 - 7)^2 + (-2 + 5)^2

Evaluate the sum and the difference

So, we have

MN = √-9^2 + 3^2

Evaluate the exponents

So, we have

MN = √81 + 9

Evaluate the sum

So, we have

MN = √90

Evaluate the exponents

So, we have

MN = 9.5

Hence, the length of the segment MN is 9.5 units

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Answer:

P = 3.75x - 7

Step-by-step explanation:

the perimeter (P) is the sum of the 3 sides of the triangle

P = 1.5x - 3 + 1.5x - 3 + 0.75x - 1 ← collect like terms

  = 3.75x - 7

Answer:

B

Step-by-step explanation:

23-15=8

Answer:

Y=x³ is the parent graph I don't know if that helps.

Answer:

Cubic

Step-by-step explanation:

Answer: 6 costumes

Step-by-step explanation: 8.05 divided by 1.25 would be 6.44, but how can you make 6.44 costumes? The most costumes Tanya can make are 6 costumes for the school play.

If a certain missing number will result in the expression 20x +24 when using the distributive property, then the number that must be multiplied by (5x + 6 ) to result in the expression 20x + 24  is 4.

The distributive property is a property of multiplication, according to which if two or more values that are added together are multiplied by a number, then the result will be the same if each of these values is multiplied separately with that number and then the products are added together.

Considering y to be the number that must be multiplied by (5x + 6),

y (5x + 6) = y(5x) + y(6)

As the expression is,

20x + 24

y(5x) = 20x and y(6) = 24

6y = 24

y = 24 ÷ 6

y = 4

This can be confirmed as follows,

y(5x) = 20x

Putting y = 4 in this equation,

4(5x) = 20x

Hence the number that must be multiplied by (5x + 6) to result in the expression 20x + 24 is calculated to be 4.

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Given that angle E and angle F are supplementary, the numerical measure of angle F is 74°.

Supplementary angles are angles that sum up to 180 degrees.

Given the data in the question;

Since E and F are supplementary, it means they sum up to 180 degrees.

Measure of angle E + Measure of angle F = 180°

Plug in the given values and solve for x

( 9x - 38 ) + ( 2x + 42 ) = 180

9x + 2x - 38 + 42 = 180

11x + 4 = 180

11x = 180 - 4

11x = 176

Divide both sides by 11

11x = 176

11x/11 = 176/11

x = 16

Now, the numerical measure of angle F will be;

Measure of angle F = ( 2x + 42 )

Measure of angle F = 2( 16 ) + 42

Measure of angle F = 32 + 42

Measure of angle F = 74°

Given that angle E and angle F are supplementary, the numerical measure of angle F is 74°.

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Answer:

Step-by-step explanation:

1)Distribute. (-25a+180-20c)(25a+15b-20c). 2) Combine like terms. -625a+180+15b+400c.

Answer:

The lesser integer is 9.

Step-by-step explanation:

[tex]x + 4(x + 2) = 53[/tex]

[tex]x + 4x + 8 = 53[/tex]

[tex]5x + 8 = 53[/tex]

[tex]5x = 45[/tex]

[tex]x = 9[/tex]

Answer:

Hence,required shortest distance =102.89m

The shortest distance from A to C is 102.89 m.

Perimeter refers to the total distance around the boundary of a two-dimensional shape. It is the sum of the lengths of all the sides of the shape.

Using Pythagoras theorem

AC² = 50²+80²

AC² =8900

AC =√8900

AC = 94.33

So, the distance removing the diameter

= 94.33-15

= 79.33

Now, Circumference of semicircle = πr

= 23.56 m

So, the possible distances

A - B - C = 50 +80= 130

A-C = 23.56 + 79.33= 102.89

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The factors of equation are -4 and -5.

Rewriting the equation -

x² + 9x + 20 = 0

ax² + bx + c = 0

The mentioned equation will be factorized using the given two rules -

1. sum of the factors will be equal to numeral in middle expression b (9x in this case)

2. product of factors will be equal to product of a and c (20 in this case)

Using above rules, the appropriate factors should be 5 and 4.

Representing the factors in mentioned equation -

x² + 4x + 5x + 20 = 0

Taking common factors

x(x + 4) +5(x + 4) = 0

(x + 4) (x + 5) = 0

x = -4, -5

Hence, the two factors of given equation are -4 and -5.

To check the answer, we will keep each value of x in  the equation -

When x = -4

x² + 9x + 20 = 0

(-4)² + 9(-4) + 20 = 0

16 -36 + 20 = 0

36 - 36 = 0

0 = 0

When x = -5

x² + 9x + 20 = 0

(-5)² + 9(-5) + 20 = 0

25 - 45 + 20 = 0

45 - 45 = 0

0 = 0

As both Left Hand Side and Right Hand Side of the equation are same for both values of x, the factors are correct.

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Answer:

Step-by-step explanation:

26:45

Answer:

D

Step-by-step explanation:

The highest number that divides exactly into two or more numbers. 3 and 9 cannot be divided by anything greater than 3.

Answer: i think its D.

Step-by-step explanation:

Equation that models the potential energy of a 2 kg skateboard that is sliding down a ramp is :

U = 2gh

Gravitational acceleration can be defined as the acceleration of any object when the object is in free fall. or we can say that the gravitational acceleration is the quantity which describes the acceleration of free falling object within vacuum. It is denoted by g .

Potential energy is the stored energy of the object which is generally based on the relative position of the various parts of the object. It is also known as gravitational energy.

Formula of potential energy :

U = mgh

where, U = gravitational energy

            m = mass of object

            g = gravitational acceleration

            h = vertical height  of object

In the question given,

mass = 2kg

as, U = mgh

therefore, U = 2gh

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The complete question is :

On Earth with a gravitational acceleration g , the potential energy stored in an object varies directly with its mass m and its vertical height h .

a. What is an equation that models the potential energy of a 2 -kg skateboard that is sliding down a ramp?

b. The acceleration due to gravity is g=-9.8m/s² . What is the height of the ramp if the skateboard has a potential energy of -39.2 kg m² /s² ?

Two expressions with equal sign is called as Equation, The value of - 5xV + 512 for x=-6 and J/ = 22 is 1172.

Two expressions with equal sign is called as Equation.

- 5xV + 512 for x=-6 and J/ = 22

Plug in values of x and V in above expression.

-5(-6)22+512

negative into negative is positive.

=660+512

=1172

There The value of expression - 5xV + 512 is 1172.

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The coordinates of point b ( x, y) are ( - 5, 4 ).

The midpoint of the line ab is m( -1, -1 ).

The coordinates of the endpoints of the line are a( 3, -6) and b( x, y).

Now, the midpoint of the line with two endpoints A(x, y) and B( c, d) is given as:

m = [ ( x + c) / 2 , ( y + d) / 2 ]

Therefore,

m = [ ( 3 + x) / 2, ( - 6 + y ) / 2 ]

( -1 , - 1) = [ (3 + x / 2 ), ( -6 + y / 2 ) ]

Therefore,

(3 + x) / 2 = - 1

3 + x = - 2

x = - 2 - 3

x = - 5

And;

-6 + y / 2 = - 1

- 6 + y = - 2

y = - 2 + 6

y = 4

Therefore, ( x, y) = ( - 5, 4).

Therefore, the coordinates of point b are ( - 5, 4 ).

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