What is the standard form of the equation of a quadratic function with roots of 3 and −1 that passes through (1, −10)?
y = 2.5x2 − 5x + 7.5 y = 2.5x2 − 5x − 7.5 y = −2.5x2 − 5x + 7.5 y = −2.5x2 − 5x − 7.5

Answer: To solve the inequality x^2 - 8x + 15 < 0, we first want to find the critical points, which are the points where the quadratic function changes direction (from increasing to decreasing or vice versa). To find the critical points, we need to set the quadratic equal to zero and solve for x. In this case, we have:

x^2 - 8x + 15 = 0

To solve this equation we should factor it or use the quadratic formula.

(x - 5)(x - 3) = 0

x = 5, x = 3

This means that the critical points for the inequality are x = 5 and x = 3. To find the solution set of the inequality, we test the signs of the function at the critical points and in the intervals between them.

The solution of the inequality is x < 3 or x > 5.

Step-by-step explanation:

Answer: This is evaluataion, To evaluate an algebraic expression means to find the value of the expression when the variable is replaced by a given number.

Step-by-step explanation: In this situation you are going to divide the numerator and denominator by 2. For example 2/8 makes 1/4. 1/4 is equivalent to 2/8 but not fully simplified.

Another way to solve this is to reduce to lowest terms. For example, 5/15 is reduced by dividing the numerator and denominator by 5 to get 1/3.

Divide the numerator and denominator to get a decimal form of the fraction or divide 5+2 by 3+6

The slope of this line is equal to 8/3.

The two additional points on the line are (-1, 13/3) and (1, 29/3).

Mathematically, the slope-intercept form of a line can be calculated by using this equation:

y = mx + c

Where:

Next, we would determine the slope of the data points as follows;

Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope, m = (y₂ - y₁)/(x₂ - x₁)

Slope, m = (7 - (-1))/(0 - (-3))

Slope, m = 8/3

At point (0, 7), an equation of this line can be calculated in slope-intercept form as follows:

Note: The y-intercept is equal to 7.

y = mx + c

y = 8x/3 + 7

For the additional points, when x = 1 we have:

y = 8(1)/3 + 7

y = 8/3 + 7

y = 29/3

When x = -1, the value of y is given by;

y = 8(-1)/3 + 7

y = -8/3 + 7

y = 13/3

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Answer:

A rectangle of 10.6 x 11.4 dimensions.

Step-by-step explanation:

(5.3*2)*(5.7*2)=5.3*4*5.7=10.6x11.4.

The largest snack Sasha can make while still using the correct ratio of ingredients is 555g.

An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. The numerical relationship between two values demonstrates how frequently one value contains or is contained within another.

Given that after school Sasha likes to make snacks by mixing raisins and nuts in a ratio of 3:5 when she checked the cupboard today there were only 60g of raisins and 75g of nuts left.

The largest snack Sasha can make while still using the correct ratio of ingredients is calculated as,

E = ( 60 x 3 + 75 x 5 )

E = 180 + 375

E = 555 g

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Answer:

0.857

Step-by-step explanation:

                   ----------------

               7  |   6

7 goes 0 times into 6, so we write a 0.

                       0.

                   ----------------

               7  |   6.0

Add .0 to 6 to get 6.0

7 goes 8 times into 60.

8 × 7 = 56

                       0.8

                   ----------------

               7  |   6.0

                  -    5.6

                ------------

60 - 56 = 4

Write another 0, 6.00, and bring down a zero.

                       0.8

                   ----------------

               7  |   6.00

                  -    5.6

                ------------

                           40

7 goes 5 times into 40.

                      0.85

                   ----------------

               7  |   6.00

                  -    5.6

                ------------

                           40

                      -    35

                      ---------

40 - 35 = 5

Add another 0 to 6.00 to get 6.000; bring down that zero.

Now you have 50.

                      0.857

                   ----------------

               7  |   6.000

                  -    5.6

                ------------

                           40

                      -    35

                      ---------

                              50

7 goes 7 times into 50.

7 × 7 = 49

Add a zero, bring down a zero,

                      0.857

                   ----------------

               7  |   6.0000

                  -    5.6

                ------------

                           40

                      -    35

                      ---------

                              50

                          -   49

                         -----------

                                  10

7 goes 1 time into 10.

You end up with 0.8571

                     0.8571

                   ----------------

               7  |   6.0000

                  -    5.6

                ------------

                           40

                      -    35

                      ---------

                              50

                          -   49

                         -----------

                                  10

                              -     7

                          -----------

                                    3

0.8571 rounds to 0.857

According to the given expression, the account's initial deposit is 750, the balance after one year is 845, and the balance after two years is 952.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Given, The amount of money in a savings account is modeled by A(x) = 750(1.01)^12x, where x represents number of years.

Expression for money is given

Thus, balance at x = 0

Balance A(0) = 750

Balance at x = 1

Balance A(1) = 750(1.01)^12*1

A(1) = 845.11

Balance at x = 2

Balance A(2) = 750(1.01)^12*2

A(2) = 952.43

Therefore, In the account initial deposit is 750, balance after 1 year  is 845, and balance after 2 years will be 952 as per the given expression.

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Answer:

Infinitely many solutions

Step-by-step explanation:

After calculating The perimeter of rectangle is 46.52 in the given rectangle.

What is area of rectangle?

area of rectangle can be defined as the product of length and breadth.

Given ,

A rectangle has a length 20 5 /6 and

breadth = 2 3/7

The perimeter of rectangle  = 2 (l+b)

length = (120 + 5 ) / 6 = 125/ 6

breadth = (14+3) / 7  = 17/7

perimeter  = 2 (125/6 + 17/7 )

= 2 ( (125*7 + 17 * 6) / 42 )

= 2 (875+102) / 42

= 2 * 23.26

= 46.52

Hence, after calculating The perimeter of rectangle is 46.52 in the given rectangle.

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Step-by-step explanation:

area of square=length×length

=25ft²

area of rectangle=length × breath

=2×9

18ft²

area of the figure=25 +18

=43ft²

The solution to the given linear equation is t = 14

From the question, we are to solve the given linear equation.

From the given information,

The given linear equation is

t - 5 = 9

To solve the equation, we will use the addition property of equality

Solving the equation

t - 5 = 9

Add 5 to both sides of the equation

t - 5 + 5 = 9 + 5

Simplify

t = 14

Hence, the solution is t = 14

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Answer:

  D.  5

Step-by-step explanation:

You want the constant of proportionality in the relation shown by the graph.

A proportional relation has the equation ...

  y = kx . . . . . . . . where k is the constant of proportionality

When x=1, this becomes ...

  y = k

The value of y when x=1 is marked on the graph: y = 5 at that point, so ...

  k = 5

The value of the constant of proportionality is 5.

Answer: The appropriate dosage of medicine for a 180 Ib person is 12 ounces.

Step-by-step explanation:

From the word problem, we know that:

Since we are given w (the amount the person weighs is 180 Ib), we can plug the value into the equation to solve for t.

t= 3 + 0.05 (180)

t = 3 + 9

t = 12

So the appropriate dosage of medicine for a 180 Ib person is 12 ounces.

Answer:

The inverse of a function, denoted as f^-1 (x), is a new function that "undoes" the original function. To find the inverse of a function, you need to switch the x and y variables and then solve for y. To find the inverse of f(x) = 1/3 x - 5, you need to switch the x and y variables and then solve for y:

Step-by-step explanation:

To solve for y, you need to get x alone on one side of the equation:

x + 5 = 1/3 y

3x + 15 = y

The inverse of f(x) = 1/3 x - 5 is f^-1 (x) = 3x + 15

It is important to note that not all functions have an inverse, only functions that are one-to-one or "injective" functions have inverses.

Answer: 3x + 15 = the inverse function of f(x)

Explanation:

First of all, arrange the equation and leave the "x" alone.

x/3 - 5 = y (Multiply both sides by 3)

x - 15 = 3y (Then, leave "x" alone)

x = 3y + 15 (As the final step, change x and y variables.)

y = 3x + 15 (This is the inverse function of f(x).)

Answer: I'm guessing this is addition.

Shipping 1 large box would be $51. Shipping 2 large boxes would be $54 dollars.

Step-by-step explanation: I don't know if you wanted addition or multiplication but the answer I gave is addition

Answer: To solve these simultaneous equations, we can substitute one equation into the other.

4x-3 = 3x + y.

3x+y =2y+5x-12

If we substitute the first equation into the second equation, we get:

3(4x-3) + y = 2y+5x-12

12x -9 + y = 2y+5x-12

Now we can solve the system of equations by isolating one of the variables and then substituting it back in one of the equations.

12x - 9 + y = 2y + 5x - 12

y = -9 + 2y + 5x -12

y = 2y + 5x -21

y - 2y = 5x -21 -9

-y = 5x -30

y = -5x + 30

Now we can substitute the value of y back into one of the original equations, we have:

4x-3 = 3x + (-5x + 30)

4x-3 = -2x + 30

4x-3+2x = 30

6x -3 = 30

6x = 33

x = 5.5

Now we can substitute the value of x back into one of the original equations to find the value of y:

4x -3 = 3x + y

4(5.5) -3 = 3(5.5) + y

22 - 3 = 16.5 + y

19 = 16.5 + y

y = 2.5

So the solution to the system of equations is x = 5.5 and y = 2.5.

Step-by-step explanation:

The shape of the ABCD is a rhombus. The diagonals are not equal to each other.

What is the 2-dimensional shape?

A two-dimensional shape with horizontal and vertical axes is known as a 2d shape (x-axis and y-axis). Two-dimensional shapes have only length and width. There is no thickness or height to these shapes.

Given the vertices of ABCD are  A(-3,0), B (1,5), C(-3,10) and D(-7,5).

The formula distance between points (x₁, y₁) and (x₂, y₂) is √[(x₂ - x₁)² + (y₂ - y₁)²].

The distance between A and B is √[(1 - (-3))²+(5 - 0)²] = √(4²+5²) = 6.4

The distance between B and C is √[(-3 - 1)²+(10 - 5)²] = √(4²+5²) = 6.4

The distance between C and D is √[(-7 - (-3))²+(5 - 10)²] = √(4²+5²) = 6.4

The distance between A and D is √[(-7 - (-3))²+(5 - 0)²] = √(4²+5²) = 6.4

The distance between A and C is √[(-3 - (-3))²+(10 - 0)²] = √(10²) = 10

The distance between B and D is √[(-7 - 1)²+(5 - 5)²] = √(8²) = 8

The slope of a line passes through the points (x₁, y₁) and (x₂, y₂) is (y₂ - y₁)/(x₂ - x₁).

The slope of AB is (5-0)/(1-(-3))=5/4

The slope of BC is (10-5)/(-3-1)=-5/4

The slope of CD is (5-10)/(-7-(-3))=5/4

The slope of AD is (5-0)/(-7-(-3))=-5/4

The number of vertices of the quadrilateral is 4.

Thus it is either a square or rectangle or rhombus or parallelogram.

Since the length of all sides is equal thus it is either a square or rhombus.

Since the diagonals are not equal it is a rhombus.

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There are 10 different ways to choose three products out of five.

What are permutation and combination?

Permutation and combination are mathematical concepts used to study the arrangements and selections of items.

Permutation: An arrangement of items, where order matters.

Combination: A selection of items, where order does not matter.

In this case, the manager has to choose three products out of five possibilities, which is a combination problem. To find the number of different ways to choose three products out of five, we can use the formula: nCr = n! / (r! (n - r)!).

n = 5 (number of items)

r = 3 (number of items to be chosen)

nCr = 5! / (3! (5 - 3)!) = 5! / (3! 2!) = (5 x 4) / (2 x 1) = 10.

Hence, there are 10 different ways to choose three products out of five.

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Answer: multiples of 4 are -4,8,12,16,20,24,28,32,36,40,44,48,52

Step-by-step explanation:

4x1=4

4x2=8

4x3=12

4x4=16

4x5=20

4x6=24

4x7=28

4x8=32

4x9=36

4x10=40

4x11=44

4x12=48

4x13=52

Answer:

208

Step-by-step explanation:

52×4=208

Answer: Let's call the present age of the son x and the present age of the father y.

We know that y = 3x and that six years ago, the sum of their ages was 45.

So, we can write the equation:

x + (y-6) = 45

x + (3x-6) = 45

4x = 51

x = 12.75

The present age of the son is 12.75 years.

Step-by-step explanation:

Answer:

Angle 6 = 70

Step-by-step explanation: Using vertical angles if you look across from angle 6 you would see the angle of 70 degrees which means they are equal because they're across from each other.

The intercept, b of the line is 20

It is important to note that the general equation of a line is expressed as;

y = mx + c

Given that;

From the information, we have that;

Now, substitute the values to determine the intercept

50 = 5(6) + c

expand the bracket

50 = 30 + c

collect like terms

c = 50 - 30

c = 20

Hence, the value is 20

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Answer:

Step-by-step explanation:

The company will need to hire approximately 200 freelancers in order to complete the remaining 40,000 hours of work. This is because each freelancer works 200 hours per month, so in order to complete the 40,000 hours of work in the last 4 months, the company will need to hire 200 freelancers.

The observed time cycles of five given elements are 2.1, 1.01, 3.4, 4.1, 1.5 respectively

To determine the observed time (OT),

The observed time (OT) of each cycles will be added together for each element. and divided by total number of cycles for each element.

This is done in the following ways

1) (1.2+2.0+2.2+2.1+2.1)/5 = 10.5/5 = 2.1

2) (1.1+1.0+1.2) = 3.3/3 = 1.1

3) (3.4+3.5+3.3+3.5+3.4+3.3)/6 = 20.1/6 = 3.4

4) 4.0+4.2)/2 = 8.2/2 = 4.1

5) (1.4+1.4+1.5+1.5+1.5+1.4)/6 = 8.7/6 = 1.5

therefore each elements total cycle OT is added and then it is divided with each elements relevant number of cycles and this as a result provides the answer to the question

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The shape of the ABCD is a rhombus. The diagonals are not equal to each other.

What is the 2-dimensional shape?

A 2d shape is a two-dimensional shape with horizontal and vertical axes (x-axis and y-axis). 2D shapes are flat shapes with only length and width. These shapes have no thickness or height.

Given the vertices of ABCD are  A(-3,0), B (1,5), C(-3,10) and D(-7,5).

The formula distance between points (x₁, y₁) and (x₂, y₂) is √[(x₂ - x₁)² + (y₂ - y₁)²].

The distance between A and B is √[(1 - (-3))²+(5 - 0)²] = √(4²+5²) = 6.4

The distance between B and C is √[(-3 - 1)²+(10 - 5)²] = √(4²+5²) = 6.4

The distance between C and D is √[(-7 - (-3))²+(5 - 10)²] = √(4²+5²) = 6.4

The distance between A and D is √[(-7 - (-3))²+(5 - 0)²] = √(4²+5²) = 6.4

The distance between A and C is √[(-3 - (-3))²+(10 - 0)²] = √(10²) = 10

The distance between B and D is √[(-7 - 1)²+(5 - 5)²] = √(8²) = 8

The slope of a line passes through the points (x₁, y₁) and (x₂, y₂) is (y₂ - y₁)/(x₂ - x₁).

The slope of AB is (5-0)/(1-(-3))=5/4

The slope of BC is (10-5)/(-3-1)=-5/4

The slope of CD is (5-10)/(-7-(-3))=5/4

The slope of AD is (5-0)/(-7-(-3))=-5/4

The number of vertices of the quadrilateral is 4.

Thus it is either a square or rectangle or rhombus or parallelogram.

Since the length of all sides is equal thus it is either a square or rhombus.

Since the diagonals are not equal it is a rhombus.

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Answer:

Step-by-step explanation:

Using the Law of Cosines, we can calculate the three angles of the triangle.

A = cos⁻¹((17² + 30² - 20²) / (2 x 17 x 30))

A = cos⁻¹(7 / 510)

A = cos⁻¹(0.0137254901960784)

A = 84.2°

P = cos⁻¹((20² + 30² - 17²) / (2 x 20 x 30))

P = cos⁻¹(11 / 600)

P = cos⁻¹(0.0183333333333333)

P = 70.0°

K = 180° - (84.2° + 70.0°)

K = 25.8°

Therefore, the angles of △HPK are:

Angle H = 84.2°

Angle P = 70.0°

Angle K = 25.8°

Round your final answer to the nearest tenth:

Angle H = 84.2°

Angle P = 70.0°

Angle K = 25.8°

Answer:

4. So Adrian can buy 3 more cd's at the sale price.

5. 36 km every week.

Step-by-step explanation:

Adrian has enough money to buy 3 cd's at $16 each. If the cd's are on a sale and are sold at a discount price of $12, he can buy more cd's because the price is cheaper. To find out how many more cd's he can buy, you can subtract the original cost of the cd's from the sale price of the cd's and then divide that amount by the sale price of the cd's.

3 cd's x $16 = $48

$48 - $12 = $36

$36 / $12 = 3

Rehman and his father jog to the park 3 km away from their house and back every evening except Sundays, so they jog a total of 6 km per day. To find out how many kilometres they jog per week, you need to multiply the distance they jog per day by the number of days they jog in a week (7 days - 1 Sunday).

6 km/day x 6 days/week = 36 km/week

So Rehman and his father jog 36 km every week.

The correct option is A.

"The theoretical probability, P(gold), is 25%, and the experimental probability is 27.5%."

First, let's find the theoretical probability.

We know that there are:

For a total of 40 marbles.

The theoretical probability of randomly pulling a gold marble is equal to the quotient between the total number of gold marbles and the total number of marbles, it is:

P = 10/40

P = 1/4 = 0.25

For the experimental probability, we need to take the quotient between the number of times that the outcome of the experiment was a gold marble and the total number of times that the experiment was performed.

The experiment was performed 40 times and 11 times we got the gold marble, then:

E = 11/40  = 0.275

Then the correct statement is A:

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Answer: The theoretical probability, P(brown), is 25%, and the experimental probability is 32.5%.

Step-by-step explanation:

Value of g(x) with given values of x:

                      x -5 -4 -3 -2 -1

                   g(x) 7 1 -1 1 7

Given: the functional equation:

                          g(x) = 2(x + 3)^2 – 1

Solution:

Value of g(x), when x= -5

g(x) = 2 (-5 +3)^2 – 1

      = 2 (-2)^2 – 1

      = 2* (-2)* (-2) – 1

      = 8 – 1

      = 7

Value of g(x), when x= -4

g(x) = 2 (-4 +3)^2 – 1

      = 2 (-1)^2 – 1

      = 2* (-1)* (-1) – 1

      = 2 – 1

      = 1

Value of g(x), when x= -3

g(x) = 2 (-3 +3)^2 – 1

      = 2 (0)^2 – 1

      = 2* 0  – 1

      = 0 – 1

      = - 1

Value of g(x), when x= -2

g(x) = 2 (-2 +3)^2 – 1

      = 2 (1)^2 – 1

      = 2* (1)* (1) – 1

      = 2 – 1

      = 1

Value of g(x), when x= -1

g(x) = 2 (-1 +3)^2 – 1

      = 2 (2)^2 – 1

      = 2* (2)* (2) – 1

      = 8 – 1

      = 7