What is the standard form of the equation of a quadratic function with roots of 4 and −1 that passes through (1, −9)?

y = 1.5x2 − 4.5x − 6
y = 1.5x2 − 4.5x + 6
y = −1.5x2 − 4.5x − 6
y = −1.5x2 − 4.5x + 6

Answer:

Step-by-step explanation:

A contrapositive statement changes "if not p then not q" to "if not q to then, not p." The converse of the conditional statement is “If Q then P.” The contrapositive of the conditional statement is “If not Q then not P.” The inverse of the conditional statement is “If not P then not Q.” if p → q, p → q, then, ∼ q →∼ p ∼ q →∼ p

A Note about Notation: Be careful with the notation  a|b

. This does not represent the rational number  ab

. The notation  a|b

 represents a relationship between the integers  a

 and  b

 and is simply a shorthand for “ a

 divides  b

.”   "Divides" as in  a|b

 is a relation (true or false), while "divided by" as in  ab

 or   a/b

 is an operation (results in a number).

The definition for “divides” can be written in symbolic form using appropriate quantifiers as follows: A nonzero integer  m

 divides an integer  n

 provided that  (∃q∈Z)(n=m⋅q).

Answer:

w = -20

"The beautiful thing about learning is that no one can take it away from you." :)

The height of the trapezoid is 7 mm.

A quadrilateral with one set of parallel opposite sides is referred to as a trapezium.

To find the height of a trapezoid when the area and the lengths of the parallel bases are given, we can use the formula:

h = 2A / ([tex]b_1 + b_2[/tex])

where

h is the height,

A is the area,

[tex]b_1[/tex] and [tex]b_2[/tex] are the lengths of the parallel bases.

As per given information in the question.

Using the given area of 35 mm² and the lengths of the parallel bases,

For [tex]b_1[/tex] = 8 mm and [tex]b_2[/tex] = 6 mm

we get:

h = 2 x 35 / (8 + 6) = 7 mm

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Answer:

A monthly budget worksheet cause it shows your income and expenditure, so you are able to spend within your budget and it helps you know your disposable income

Answer:

Solving 8x ÷ 4 = 100, we have:

2x = 100

x = 50

So the value of x is 50.

Answer:

x = 50

Step-by-step explanation:

To answer this question, we have to isolate the x. To do this, we have to get rid of any other numbers around it by doing the inverse of the operation.

1)

2)

This means that x is 50!

To check our answer is correct we can substitute 50 to x in the question...

It is correct!

Hope this helps, have a lovely day! :)

Answer:

This problem can be solved using the method of Lagrange multipliers. Let's define the Lagrangian function as: L(K, L, λ) = Q - λ(K + 4L - 16) Taking partial derivatives with respect to K, L, and λ, we get: dL/dK = 0 => 1 - λ = 0 => λ = 1 dL/dL = 0 => 1 - 4λ = 0 => λ = 1/4 dL/dλ = K + 4L - 16 = 0 Solving the last equation for K, we get: K = 16 - 4L Substituting this into the Lagrangian function, we get: L = Q - λ(16 - 4L + 4

Below 10 in.*6 in.*14 in., the triangular prism's volume is 420 cubic inches.

The area of the base must be multiplied by the prism's height in order to determine the volume of a triangular prism.

The base of this triangular prism is a triangle with a base of 6 inches and a height of 10 inches, so its area is:

Area of base = (1/2) × base × height = (1/2) × 6 in × 10 in = 30 in²

The height of the triangular prism is given as 14 inches.

Hence, the triangular prism's volume is:

Volume = Area of base × height = 30 in² × 14 in = 420 cubic inches.

So, the volume of the triangular prism is 420 cubic inches.

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Answer: -8x +10

Step-by-step explanation:

-2(2x -5) -4x

1. simplify parthentheses

-4x +10 -4x

add like terms

-8x +10

Answer:

H

Step-by-step explanation:

% of 11 year olds is 24

% of 12 year olds is 16

then ratio of

11 year olds : 12 year olds

= 24 : 16 ( divide both parts by 8 )

= 3 : 2

the solutions to the quadratic equation 1 = 2x^2 + 7x are:

[tex]x= \frac{(-7+\sqrt{51} )}{4}[/tex] and [tex]x= \frac{(-7-\sqrt{51})}{4}[/tex]

ToToToToToToToToToToToToToToToToToToToToToToToToToToToToToToToTo solve this quadratic equation by completing the square, we need to rewrite the equation in the form of (x + p)^2 + q = 0, where p and q are constants. This will allow us to solve for x.

First, we can factor out the coefficient of the x^2 term, which is 2:

[tex]2x^2 + 7x - 1 = 0[/tex]

Next, we can isolate the x^2 and x terms on one side of the equation by subtracting 1 from both sides:

[tex]2x^2 + 7x = 1[/tex]

Now, we need to add and subtract a constant term inside the parentheses to create a perfect square trinomial. To determine this constant term, we take half of the coefficient of the x term (which is 7/2) and square it:

[tex](\frac{7}{2} )^{2} = \frac{49}{4}[/tex]

So we add and subtract 49/4 inside the parentheses:

[tex]2x^2 + 7x + \frac{49}{4} - \frac{49}{4} = 1[/tex]

We can simplify the left side by factoring the perfect square trinomial:

[tex]2(x + \frac{7}{4} )^2 - \frac{51}{8} = 0[/tex]

Now, we can solve for x by isolating the perfect square term and taking the square root of both sides:

[tex]2(x + \frac{7}{4} )^2 = \frac{51}{8}[/tex]

[tex](x + \frac{7}{4} )^2 = \frac{51}{16}[/tex]

[tex]x + \frac{7}{4}=±\sqrt{\frac{51}{16} }[/tex]

[tex]x = -\frac{7}{4} ± \sqrt{\frac{51}{16} } /2[/tex]

Simplifying this expression, we get:

[tex]x = (-7 ±\sqrt{51} )/4[/tex]

Therefore, the solutions to the quadratic equation 1 = 2x^2 + 7x are:

[tex]x = (-7 + \sqrt{51} )/4 and x = (-7 -\sqrt{51} )/4.[/tex]

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Thus, remaining seats on the school bus that are empty is found as: 6 seats.

The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.

Given data:

Total seats in bus = Total rows of seats * Number of seats in each row

Total seats in bus = 22 * 4

Total seats in bus = 88

Filled seats = 19 * 4 = 76

Left seats = 88 - 76 = 12

Now, 1/2 of the 12 seats is filled = 6 seats.

remaining seats = 6

Thus, remaining seats on the school bus that are empty is found as: 6 seats.

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the expression would be used as follows:

Number of boxes of donuts (N) = 6 x Number of donuts (D)

Ling bought 108 boxes of donuts.

This expression is a mathematical equation that uses multiplication to calculate the number of boxes of donuts Ling bought.

Equations are used to solve problems involving unknowns, such as how much a person owes for groceries or how many people are required to complete a certain task.

The expression that would show how many boxes of donuts Ling bought is:

Number of boxes of donuts (N) = 6 x Number of donuts (D)

In this expression, N represents the number of boxes of donuts Ling bought and D represents the number of donuts. This expression can be used to calculate the number of boxes of donuts Ling bought when the number of donuts is known.

For example, if Ling bought 18 donuts, the expression would be used as follows:

Number of boxes of donuts (N) = 6 x Number of donuts (D)

N = 6 x 18

N = 108

Therefore, Ling bought 108 boxes of donuts.

This expression is a mathematical equation that uses multiplication to calculate the number of boxes of donuts Ling bought. The expression can be used whenever the number of donuts is known and can be used to calculate the number of boxes of donuts Ling bought.

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Answer

15.71 cm

Explanation

Answer:

1400 - 2.5t =  1200 + 1.5t

t = 50

Step-by-step explanation:

There are no children in the class who have no sisters. This is because the mean number of children is 1, and some children have more than one sibling to Balance out those who have only one.

To solve this problem, we need to use some basic principles of statistics and probability. Let's start by identifying the key information provided in the problem. We know that there are 20 children in the class, and that some of them have sisters. Specifically, 8 children have one sister and 6 children have two sisters. We also know that the mean (average) number of children is 1, which means that on average, each child has one sibling.

To find out how many children had no sisters, we can use the following formula:

Total number of children - (number of children with one sister x 1) - (number of children with two sisters x 2) = number of children with no sisters

Using the values from the problem, we get:

20 - (8 x 1) - (6 x 2) = 0

This means that there are no children in the class who have no sisters. While this may seem counterintuitive, it's important to remember that the mean number of children is 1, which means that some children must have more than one sibling in order to balance out the others who have only one.

In summary, the answer to the question is that there are no children in the class who have no sisters. This is because the mean number of children is 1, and some children have more than one sibling to balance out those who have only one.

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Thus, the mean and standard deviation for the randomly selected individuals is found as: mean = 80.1 and standard derivation = 7.66.

The standard deviation is a measurement of how widely spaced out a set of data is from the mean. The bigger the dispersion or variability, the higher the standard deviation and the greater the magnitude of the value's divergence from its mean. It represents the absolute variability of a distribution.

Given data:

Number of population n = 300

probability p = 0.267

Mean is given as np:

np = 300*0.267

np = 80.1

standard derivation: √np(1 - p)

√np(1 - p) =  √80.1(1 - 0.267)

√np(1 - p) =  √58.7133

√np(1 - p) =  7.66

Thus, the mean and standard deviation for the randomly selected individuals is found as: mean = 80.1 and standard derivation = 7.66.

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Correct question:

According to a study done by Nick Wilson of Otago University Wellington, the probability a randomly selected individual will not cover his or her mouth when sneezing is 0.267. Suppose you sit on a bench in a mall and observe 300 randomly selected individuals’ habits as they sneeze.

What are the mean and standard deviation?

Answer: 50 mph

Step-by-step explanation:  

To find (f-g)(1), we first need to find f(1) and g(1): f(1) = -(1)^2 - 1 - 3 = -5 g(1) = -1 Now we can substitute these values into (f-g)(x) = f(x) - g(x) and simplify: (f-g)(1) = f(1) - g(1) = (-5) - (-1) = -4 Therefore, (f-g)(1) = -4.

Answer: x = [tex]\frac{1}{2}[/tex] , y= [tex]\frac{3}{2}[/tex]

Step-by-step explanation:

Answer:

Calculation:

Total Amount: $227

Down Payment: $47

Interest Rate: 9.6% (0.096)

Number of Payments: 12

Remaining Balance: $227 - $47 = $180

Remaining Balance with Interest: $180 + (9.6/100 * $180) = $197.68

Amount of Payment: $197.68 / 12 = $16.47

Answer: The amount of each payment is $16.47.

Product A is priced at Ksh 55,000, while Product B is priced at Ksh 32,000.

Assume that the selling price for both the two items A and B is "S" and the cost price for both is "C". Using this knowledge, we can create two equations that relate the costs and revenues of the two items, one for Tom and one for John:

Tom: 5C - 2(5S) = [tex]P_1[/tex]

John: 3(5C) - 13C = [tex]P_2[/tex]

where [tex]P_1[/tex] and [tex]P_2[/tex] represent Tom's and John's respective profits.

We are aware that John deposits Ksh. 110,000 while Tom deposits Ksh. 230,000 at the end of the business day. Thus, we can say:

[tex]P_1[/tex] = 230,000 - 5C

[tex]P_2[/tex] = 110,000 - 18C

These values are what we obtain when we enter them into the equations for Tom and John:

5C - 2(5S) = 230.000 - 5C

When we simplify these equations, we obtain:

10C - 10S = 230,000

2C = 110,000

Solving for C, we get:

C = 55,000

We may determine S by adding this value back into the original equation:

10(55,000) - 10S = 230,000

Simplifying this equation, we get:

S = 32,000

Therefore, the price for product A is Ksh 55,000 and the price for product B is Ksh 32,000.

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Comparing the box plots, the statements which are not true are Class A has greater variability and over half of the students in Class A have two or more siblings.

Based on the given box plots, we can make the following observations:

a) Class B has a higher median: True. We can see from the plot that the median line for Class B (represented by the orange line inside the box) is higher than the median line for Class A (represented by the blue line inside the box).

b) Class A has greater variability: False. We can see from the plot that the boxes for both classes have similar lengths, indicating similar variability. However, Class A has a few more outliers compared to Class B, which indicates some extreme values that are far from the median.

c) Both A and B have students who are only children: True. We can see from the plot that both classes have a box plot labelled "0" indicating that some students in each class are only children.

d) Over half of the students in class A have two or more siblings: False. We can see from the plot that the box labelled "2+" in Class A only covers about a third of the box, indicating that less than a third of the students have two or more siblings. Therefore, the statement is not true.

Therefore, the answer is b) Class A has greater variability and d) Over half of the students in Class A have two or more siblings.

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The simplified expression would be 11a + 2.

In order to simplify the given expression, we first need to combine like terms.

The terms can be combined by adding their coefficients:

Now we can substitute these combined terms back into the original expression:

(7a + 9) + (4a - 7) = 7a + 4a + 9 - 7

And then simplify further:

= 11a + 2

Therefore, the simplified form of the expression (7a + 9) + (4a - 7) is 11a + 2.

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Step-by-step explanation:

what did you ask the question? ask it clearly please?? if you ask clearly the question. we also give answer

Answer:

x = -2,  y = 6

Step-by-step explanation:

First, find the opposite of 10 by multiplying 5x+3y=8 by -2 to eliminate 10x.

10x+10y=40

-2(5x+3y=8)

10x+10y=40

-10x-6y=-16       (Subtract 10y - 6y)   (Subtract 40 - 16)

      4y = 24      (Divide by 4 on both sides)

       y = 6

Substitute 6 in the y value in any of the equations.

 10x+10(6)=40       (Replaced 10y with 10(6) )

 10x+60=40

      -60 = -60     (Subtract 60 from both sides)

10x     = -20        (Divide by 10 on both sides)

10           10

x = -2

Option A "Reject the hypothesis" is the appropriate conclusion in this case.

As per the question,

Based on the results from the simulation trials, Peter should conclude that his hypothesis should be rejected.

The simulation showed that finches are a guaranteed bird type for only 80% of the birds, which is lower than the observed percentage of 75% finches at Peter's bird feeder.

This indicates that the predicted percentage of finches continuing at the same rate is not supported by the simulation results.

Therefore, option A "Reject the hypothesis" is the appropriate conclusion in this case.

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Answer:

Two events are said to be independent if one event occurring does not affect the probability that the other event will occur. However, if one event occurring or not does, in fact, affect the probability that the other event will occur, the two events are said to be dependent.

If one event occurs or not, it does, in fact, affect the probability that the other event will occur, and then the two events are said to be dependent.

Answer:

  $1.53

Step-by-step explanation:

You want to know the total tax on purchases of $4.56, 12.45, and 2.13 if the tax rate is the sum of 6.5% and 1.5%.

The tax is the product of the tax rate and the total of purchases. The tax rate will be the sum of the state and county tax rates:

  6.5% +1.5% = 8% = 8/100

The attached calculation shows the tax is $1.53 after rounding to cents.

The tax rate on Mary Lou Mason's purchases is $1.53.

What is meant by rate?

In mathematics, rate usually refers to the ratio of two quantities that have different units of measurement.

To calculate the total tax on Mary Lou Mason's purchases, we need to first calculate the total cost of her purchases, including both the prices of the items and the sales tax.

The total cost of Mary Lou Mason's purchases before taxes is:

$4.56 + $12.45 + $2.13 = $19.14

To calculate the sales tax, we need to multiply the total cost of the purchases by the sum of the state and county tax rates:

6.5% + 1.5% = 8%

So the sales tax rate is 8%.

To calculate the total tax on Mary Lou Mason's purchases, we multiply the total cost of the purchases by the sales tax rate:

$19.14 x 8% = $1.53

Therefore, the tax on Mary Lou Mason's purchases is $1.53.

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