write a quadratic function in standard form containing the point (5,-6) and x-intercepts -7 and 3

Answers

Answer 1

The quadratic equation in standard form that contains the points (5, - 6), (- 7, 0) and (3, 0) is y = - (1 / 4) · x² - x + 21 / 4.

How to determine a quadratic function in standard form from a point and two x-intercepts

Herein we find the equation of a parabola that contains a points and its x-intercepts (two real roots). According to fundamental theorem of algebra, we can derive a quadratic function with real coefficients if we know three points of the parabola. The procedure is shown below.

First, use the quadratic function in product form and substitute on all known variables to determine the lead coefficient:

y = a · (x + 7) · (x - 3)

- 6 = a · (5 + 7) · (5 - 3)

- 6 = a · 12 · 2

- 6 = 24 · a

a = - 6 / 24

a = - 1 / 4

Second, expand the quadratic function into its standard form:

y = - (1 / 4) · (x + 7) · (x - 3)

y = - (1 / 4) · (x² + 4 · x - 21)

y = - (1 / 4) · x² - x + 21 / 4

The quadratic equation in standard form is y = - (1 / 4) · x² - x + 21 / 4.

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Write A Quadratic Function In Standard Form Containing The Point (5,-6) And X-intercepts -7 And 3

Related Questions

PLEASE HELP ME I NEED 4 ANSWERS !!!!!!!!!! a) Fill in the gaps to factorise the expression below.
3x² + 16x + 5 = (3x + −)(x + −)
b) Use your answer to part a) to solve 3x² + 16x + 5 = 0

Answers

The roots the the given quadratic equation, will be -1/3 and -5 so the factors will be (3x+1)(x+5). As the value of roots is known, so the value of quadratic equation will be zero (0) for both the roots.

As per the question statement, we are supposed to fill the gaps to factorize the quadratic equation given :

3x² + 16x + 5 = (3x + _)(x + _)

We need to solve the expression for finding out its factors.

y = 3x² + 16x + 5

y = 3x² + 15x + x + 5

y = 3x(x + 5) + 1(x + 5)

y = (3x + 1)(x + 5)

Therefore, the roots the the given quadratic equation, will be -1/3 and -5 so the factors will be (3x+1)(x+5). As the value of roots is known, so the value of quadratic equation will be zero (0) for both the roots.

Quadratic equation: Any equation where there is just one term that squares the unknown and none that raises it to a higher power.Roots: Roots of any quadratic equation / expression is the value of the variable at which the complete value of the expression becomes zero (0). Number of roots = highest degree.

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Constructing a Confidence Interval for a Population Proportion
If n = 130 and p= 0.69, construct a 99% confidence interval.

Answers

The Confidence Interval for a Population Proportion is 0.69 ± 1.13

(-0.44 to 1.82)

Confidence Interval:

Confidence Interval means a range of values that is determined through the use of observed data, calculated at a desired confidence level that may contain the true value of the parameter being studied.

Given,

n = 130 and

p= 0.69,

construct a 99% confidence interval.

Here we need to find the confidence interval.

According to the formula, the confidence interval is,

We know that,

Sample Size: 130

Sample Mean: 0.69

Confidence Level: 99%

99% Confidence Interval: 0.69 ± 1.13

(-0.44 to 1.82)

"With 99% confidence the population mean is between -0.44 and 1.82, based on 130 samples."

Margin of Error: 1.13

(to more digits: 1.13)

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A rectangular dog pen is constructed using a barn wall as one side and 120m of fencing for the other three sides. a) give a sketch of the situation. b) express the area in terms of x. c) sketch the graph. d) find the value of x that gives the greatest area. e) find the dimensions of the pen. f) state the domain.

Answers

The solutions to the question are

The area of the pen in terms of x is A = x(120 - 2x)The x value that gives the highest area is 30The dimensions is 30 by 60The domain is 0 <= x <= 60

a) How to determine the sketch

The given parameters are:

Sides = 3

Fourth side = barn wall

Perimeter = 120 m

Next, we sketch the dog pen using the above parameters (see attachment)

b) The area of the pen

Here, we have

P = 120m

Also, we have

P = 2x + y

This gives

2x + y = 120

Make y the subject

y = 120 - 2x

The area is calculated as

A = xy

So, we have

A = x(120 - 2x)

Hence, the area is A = x(120 - 2x)

The sketch of the graph

See attachment for the graph of A = x(120 - 2x)

The value of x that gives the greatest area

We have

A = x(120 - 2x)

Expand

A = 120x - 2x^2

Differentiate

120 - 4x= 0

So, we have

4x = 120

This gives

x = 30

Hence, the value of x that gives maximum area is 30

The dimensions of the pen

Recall that

y = 120 - 2x

So, we have

y = 120 - 2 * 30

Evaluate

y = 60

Hence, the dimensions is 30 by 60

The domain of the function

From the graph, we have

x = 0 to 60

Hence, the domain of the function is 0 <= x <= 60

Answers

The base of the parallelogram is 3

The height of the parallelogram is 8

How to calculate the base and height of the parallelogram ?

Let the base be represented as (x+2)

Let the height be represented as (x-2)

The area of the parallelogram is 24

The first step is to get two numbers that can be multiplied together to get 24

= 3 × 8

The two numbers are 3 and 8

Hence the base is 3 and the height is 8

Answers

The most appropriate choice for for linear equation will be given by -

Gain in weight of Max = 7.69 pounds

What is linear equation?

At first it is important to know about equation

Equation shows the equality between two algebraic expressions by connecting the two algerbraic expressions by an equal to sign.

A one degree equation is known as linear equation.

Let the gain in weight be x pounds

Weight of Max in the month of September = 3.04 pounds

Weight of Max today = 10.73 pounds

By the problem,

3.04 + x = 10.73

x = 10.73 - 3.04

x = 7.69

Gain in weight of Max = 7.69 pounds

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which graph represents the inequality 2.5 greater than the product of -0.5 and a number?

Answers

The graph of the inequaity expression is added as an attachment

What are inequality expressions?

Inequality expressions are mathematical statements that are represented by variables, coefficients and operators where the opposite sides are not equal

How to plot the graph of the inequaity expression?

The mathematical statement is given as

"2.5 greater than the product of -0.5 and a number"

Product means times

So, we have the following representation

"2.5 greater than the product of -0.5 and a number" ⇒ 2.5 greater than -0.5 * a number

Let the number be x

So, we have

"2.5 greater than the product of -0.5 and a number" ⇒ 2.5 greater than -0.5x

Greater than is represented by >

So, we have

"2.5 greater than the product of -0.5 and a number" ⇒ 2.5 > -0.5x

Next, we plot the graph of the inequality expression

See attachment for the graph of the inequality expression

Answers

Explanation

to find the area of the stove that does not include the area of the burnes ( yellow area), we can subtract the area of the 4 circles from the area of the full rectangle

Step 1

[tex]\begin{gathered} \text{Area}=\text{rectangle-}4\text{ circles} \\ Area=(length\cdot width)-4(\pi\text{ }\frac{diameter^2}{4}) \\ A\text{rea}=(length\cdot width)-(\pi\text{ }\cdot diameter^2) \end{gathered}[/tex]

then, Let

for circle:

diameter= 6 in

for rectangle

length= 24 in

width= 22 in

Step 2

replace,

[tex]undefined[/tex]

Write an equation of the line passing through the point A(6,-1) that is perpendicular to the line y=-2x+8

Answers

Answer:

[tex]y+1=\frac{1}{2}(x-6)[/tex]

Step-by-step explanation:

Perpendicular lines have slopes that are negative reciprocals, so the slope of the line to be found is 1/2.

Substituting into point-slope form, the equation is

[tex]y+1=\frac{1}{2}(x-6)[/tex]

The freezing point of seawater is −2 °C. The freezing point of nitric acid is −42 °C.

A photo of frozen seawater is shown.

How much greater is the freezing point of seawater than the freezing point of nitric acid?

Answers

The difference between the freezing point of seawater and the freezing point of nitric acid is 40 °C.

As per the question, we can write

The freezing point of seawater = −2 °C.

The freezing point of nitric acid = −42 °C.

We were asked to calculate the difference between the freezing point of seawater and the freezing point of nitric acid. We can find the difference between the freezing point of seawater and the freezing point of nitric acid by following the steps mentioned below;

The difference between the freezing point of seawater and the freezing point of nitric acid = Freezing point of Seawater - Freezing point of nitric acid

The difference between the freezing point of seawater and the freezing point of nitric acid = -2 - (-42) = 40 °C.

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which expression would be easier to simplify if you use the associative property to change the grouping A: [-14+(-26)]+67B: (2/5+3/5) +7/3C: (43 + 60) + 40D: (50+50)+63

Answers

The associative property let us associate different terms or factors in order to solve some expression.

We have to find the expression in which this property is more useful.

The only expression where the associative may be helpful is C, as we can associate this way:

(43 + 60) + 40 = 43 + (60 + 40) = 43 + 100 = 143

In the other expression there is no advantage in applying this property.

Answer: C

How can you use the Power of a Quotient, Quotient of Powers, Zero Exponent Laws Identity Exponent and to evaluate numerical expressions with whole-number exponents?

Answers

Calculate identity exponents using the exponent of the quotient, degree of exponent, and the law of zero exponent equations and evaluate numerical equations with integer exponents.

The following is an equivalent numeric expression with an integer exponent that uses the quotient, the quotient, zero-degree rule, and the identity exponent, and evaluates the numeric expression.

[tex]2^{5} \\[/tex] × [tex]2^{6}[/tex] = [tex]2^{11}[/tex], using the product of powers.

2² × 2³ = (2×3)² = 6², using the power of a product.

[tex](2^{2})^{6}[/tex] = [tex]2^{12}[/tex], using the power of a power.

The seven laws of exponents are the power rule, the power ratio rule, the power rule, the power rule, the power quotient rule, the power zero rule, and the negative exponent rule. Arithmetic questions, as well as how to multiply, divide and add powers.

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Toby picks a 5-digit number. It is larger than 49,999 and it is a multiple of 5. How many different numbers could he have picked?

Answers

The total number of different numbers which Toby could have picked according to the task content as given is; 1,000.

How many different numbers could Toby have picked?

It follows from the task content that the number of different numbers which Toby could have picked given the conditions is to be determined.

On this note, since the required number is to be greater than 49,999 and must be a 5-digit number, the numbers which he could pick would range from;

49,999 - 99,999.

Hence, there are 5000 numbers in between.

Additionally, since the number must be a multiple of 5, the total number of multiples of 5 from 5,000 consecutive numbers is;

= 5,000/5

= 1000 different numbers.

Therefore, Toby could pick any of 1000 different numbers.

Answers

The coordinates of the point that at 7/8 from a to b are (5, -5/8)

How to determine the coordinate of the point on the line segment?

On the segment, we have the following endpoints

A = (-2, 2)

B = (6, -1)

Also, we have the line ratio to be

Ratio, m : n = 7/8

Express the ratio as a ratio

So, we have

m : n = 7 : 8 - 7

Evaluate the difference

So, we have

m : n = 7 : 1

The coordinate of the point at the given distance is then calculated as

Point = 1/(m + n) * (mx2 + nx1, my2 + ny1)

So, we have

Point = 1/(7 + 1) * (7 * 6 + 1 * -2, 7 * -1 + 1 * 2)

Evaluate the products

So, we have

Point = 1/8 * (42 -2, -7 + 2)

Evaluate the sum and the difference

So, we have

Point = 1/8 * (40, -5)

Evaluate the products

So, we have

Point = (5, -5/8)

Hence, the coordinates of the point that is 7/8 of the distance from a to b are (5, -5/8)

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The U.S. Energy Information Administration (US EIA) reported that the average price for a gallon of regular gasoline is 3.91. The US EIA updates its estimates of average gas prices on a weekly basis. Assume the standard deviation is .24 for the price of a gallon of regular gasoline and recommend the appropriate sample size for the US EIA to use if they wish to report each of the following margins of error at confidence. Round up to the next whole number.

a. The desired margin of error is .11 The appropriate sample size is
.

b. The desired margin of error is .07 . The appropriate sample size is
.

c. The desired margin of error is .04. The appropriate sample size is

Answers

Answer:

Step-by-step explanation:

1 = 1

A bag of flour has a mass of 4.5 kilograms. How many grams are in 4.5 kilograms?

Answers

The first thing we have to know is that 1 kilogram is equal to 1000 grams

[tex]\begin{gathered} 1\operatorname{kg}\to1000gr \\ \frac{1000gr}{1\operatorname{kg}} \end{gathered}[/tex]

if we have 5.4 kilograms

[tex]\begin{gathered} 4.5\operatorname{kg}\cdot\frac{1000gr}{1\operatorname{kg}}=(4.5)(1000gr) \\ \end{gathered}[/tex][tex]4.5kg=4500gr[/tex]

What is the value of x?
6x-2(x+4)=12

Answers

Answer:

Step-by-step explanation:

6x-2x-8=12

4x-8=12 (add 6x and -2x)

4x=20 (8+12=20)

x=5 (4 divide by 20 =5)

6x-2(x+4)=12
6x-2x-8=12
+8 +8

4x = 20
/4 /4

X=5

Find 3/4 divided by 2/3 then draw a picture and write an explanation describing how to get the answer.

Answers

The outcome of the quotient between the two fractions 3/4 and 2/3 is 9/8

How to find the quotient between the two fractions?

So let's define two fractions as:

a/b and c/d.

The quotient between the fractions a/b and c/d can be written as:

(a/b)÷(c/d).

Now, the quotient is equal to the product with the inverse, so we can rewrite this as:

(a/b)÷(c/d) = (a/b)*(d/c)

Now, in this case, we want to find 3/4 divided by 2/3, this will be:

(3/4)÷(2/3) = (3/4)*(3/2) = 9/8

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What is f^-1(-7) plus f(-7)? I need help answering this question

Answers

Answer:

Step-by-step explanation:

You want the sum of f^-1(-7) and f(-7) given the function definition in the table.

Inverse function

The inverse function f^-1(x) consists of ordered pairs that are the reverse of the ordered pairs (x, f(x)). That is ...

(x, f^-1(x)) ≡ (f(x), x)

Another way to describe f^-1(x) is "the value of z that gives f(z) = x". This means f^-1(-7) is the value of x that gives f(x) = -7. That x-value is 6:

f^-1(-7) = 6 . . . . . from the 4th column of the table

Function value

We can read the function value directly from the table:

f(-7) = 7 . . . . . . the first column of the table

Sum

Then the sum of interest is ...

f^(-1)(-7) +f(-7) = (6) +(7)

f^(-1)(-7) +f(-7) = 13

Additional comment

The inverse function ordered pairs are ...

(x, f^-1(x)) = {(7, -7), (12, 11), (8, -13), (-7, 6), (13, 5)}

Exploring Sample Space

In the given sample spaces, which has the largest sample space?

M-{1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
A {10, 20, 30, 40, 50, 60, 70, 80, 90}
T{20, 25, 30, 35, 40, 45, 50, 55, 60}
H-{2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22}
????

Answers

I think is option A because is adding 10+10 while the other options are adding +1 or +5

Find the slope between the following points (8,-4) and (2, -4)

Answers

Let:

[tex]\begin{gathered} (x1,y1)=(8,-4) \\ (x2,y2)=(2,-4) \end{gathered}[/tex]

We can find the slope m, using the following formula:

[tex]m=\frac{y2-y1}{x2-x1}=\frac{-4-(-4)}{2-8}=\frac{0}{-6}=0[/tex]

Answer:

someone please help me!!!!

Answers

Answer:

First Choice:

(1.4)(0.18)²

Step-by-step explanation:

Using the negative exponent rule

[tex]\left(\dfrac{a}{b}\right)^{-1} = \dfrac{b}{a}[/tex]

we get

[tex]\left(\dfrac{5}{7}\right)^{-1} = \dfrac{7}{5}[/tex]

[tex]\dfrac{7}{5} = 1.4\\\\[/tex]

Therefore
[tex]\left(\dfrac{5}{7}\right)^{-1}\left(0.18\right)^2\\\\= (1.4)(0.18)^2[/tex]

what is the answer of that

Answers

40° is the value of the angle ∠QPR.

What are angles?When two straight lines or rays intersect at a single endpoint, an angle is created. The vertex of an angle is the location where two points come together. The Latin word "angulus," which means "corner," is where the word "angle" originates. The names of fundamental angles include acute, obtuse, right, straight, reflex, and full rotation.

So, PQ ⊥ PS then, ∠QPS = 90°.

According to the given figure: ∠QPR + ∠RPS = ∠QPS

Then,

7x - 9 + 4x + 22 = 9011x + 13 = 9011x = 90 - 1311x = 77x = 7

So, ∠QPR = 7x - 9°

Substitute x = 7 as:

7(7) - 9°49 - 9°40°

Therefore, 40° is the value of the angle ∠QPR.

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12/4= x/5
can someone help me. i need a step-by-step answer!

Answers

12/4= x/5

Multiply both sides of the equation by 20, the lowest common denominator of 4,5.

5×12=4x

Multiply 5 and 12 to get 60.

60=4x

Swap the sides so that all the terms of the variables are on the left side.

4x=60

Divide both sides by 4.

x = 60/4

Divide 60 by 4 to get 15.

x=15

Question
Solve the formula C = πd for л.

Answers

Two or more expressions with an Equal sign is called as Equation.π= C/d for equation C = πd

What is Equation?

Two or more expressions with an Equal sign is called as Equation.

The given equation is C = πd

c equal to pi times of d

We need to solve it for π

To solve for π we have to separate π from d. To make this We have to divide both sides by d.

So C/d= π

Hence π= C/d for equation C = πd

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[x+(1/3)] + [x+(1/5)] = 1, where [x] is the whole part of x.

Answers

[tex](x + \frac{1}{3} ) + (x + \frac{1}{5} ) = 1 \\ x + x + \frac{1}{3} + \frac{1}{5} = 1 \\ 2x(15) + \frac{1}{3} (15) + \frac{1}{5} (15) = 1(15) \\ 30x + 5 + 3 = 15 \\ 30x = 15 - 5 - 3 \\ 30x = 7 \\ \frac{30x}{30} = \frac{7}{30} \\ x = \frac{7}{30} [/tex]

ATTACHED IS THE SOLUTION

Find the values of x and z

Answers

z = 104
The angle opposite z is 104, so therefore z must be equal to the opposite angle.

x = 2
We know angles on a straight line add up to 180. We already know that there are two angles, one of which is 104.
180-104 is 76.
Next, we put this value into an equation:
76 = 13x + 50
76 -50 = 13x
26 = 13x
2 = x

??????????????????/?

Answers

iven

adiius of circle = 3 ft

ind

rea and circumference of a circle

xplnanation

Circumference of a circle is given by

[tex]\begin{gathered} C=2\pi r \\ C=2\times3.14\times3 \\ C=18.84ft \end{gathered}[/tex]

Area of circle =

[tex]\begin{gathered} A=\pi r^2 \\ A=3.14\times3\times3 \\ A=28.26ft^2 \end{gathered}[/tex]

inal ANnswer

ircumference =

[tex]18.84ft[/tex]

Area =

[tex]28.26ft^2[/tex]

Florence wants to invest money abroad. Florence is aware that France generally has a recession every 6 years and America generally has a recession every 8. in the year 2005, both France and America were in recession. Florence needs to work out the next time they will both be in recession. When will this be?

Answers

The most appropriate choice for LCM will be given by

After the year 2005, France and America will be in recession in the year 2029

What is LCM?

Suppose a and b are two numbers. LCM of a and b is the lowest common multiple of a and b. LCM of a and b is the lowest number that is divisible by both a and b.

Here,

France has a recession every 6 years.

America has a recession every 8 years.

Florence works out when France and America will both be in recession.

It will be possible in the year which is a common multiple of 6 and 8

In the year 2005, both France and America were in recession

France and America will both be in recession again after (LCM of 6 and 8) years

Now,

6 = 2 x 3

8 = 2 x 2 x 2

LCM of 6 and 8 = 2 x 2 x 2 x3

= 24

France and America will both be in recession again after 24 years

After the year 2005, France and America will be in recession in the year (2005 + 24) = 2029

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Mark's football team has scored about 24 points each game. They played 12 games this season.
What is the best estimate for the total number of points they scored in the season?
Ο Α. 150
B. 250
OC. 20
OD. 360

Answers

Answer:

250

Step-by-step explanation:

Answer : about 300 points

Step by Step- explains 24 x 12 = 288 rounded up to 300

There are 4 triangles and 8 squares. What is the simplest ratio of triangles to squares?

Answers

Answer:

1:2

Step-by-step explanation:

For every triangle there are two squares.

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