a) The quadratic 3x^2-12x-11 can be written in the form 3(x+a)^2+b. Find the values of a and b. b) Given that the solutions of the equation 3x^2-12x-11=0 can be written as c ± √d, where c and d are rational numbers. Find the values of c and d answer for d as a fraction in it's simplest form

Answers

Answer 1

Answer:

Step-by-step explanation:

a) 3x^2-12x-11=3*x^2-3*2*2*x+3*4-23=3*(x^2-2*2x+2^2)-23=3*(x-2)^2-23

so  a= -2 ,b= -23

b) x1=[12+V(12^2-4*3* -11)]/6=12/6+V(144+132)/6=2+2/6V69=2+1/3V69=

2+V69/9=2+V23/3

c=2, d= 23/3

Answer 2

a) The value of a and b from the expression are -2 and -23 respectively.

b) The value of c and d are 2 and 23/3 respectively'

a) Given the quadratic function [tex]3x^2-12x-11[/tex], writing the equation in the form [tex]3(x+a)^2+b[/tex] using the completing the square method.

[tex]3x^2-12x-11=0\\x^2-\frac{12}{3}x-\frac{11}{3} =0\\x^2-4x-\frac{11}{3} =0\\(x^2-4x+4)-4-\frac{11}{3}=0\\(x-2)^2-\frac{23}{3} =0\\3(x-2)^2-23=0[/tex]

Compare the result with [tex]3(x+a)^2+b[/tex];

a = -2

b = -23

Hence the value of a and b from the expression are -2 and -23 respectively.

b) Given the quadratic equation [tex]3x^2-12x-11=0[/tex] using the general formula to factorize the equation;

[tex]x=\frac{-b\pm \sqrt{b^2-4ac} }{2a} \\x=\frac{-(-12)\pm \sqrt{(-12)^2-4(3)(-11)} }{2(3)} \\x=\frac{12\pm \sqrt{144+132} }{6} \\x=\frac{12\pm\sqrt{276} }{6} \\x=2\pm\sqrt{\frac{276}{36} }\\x=2\pm\sqrt{\frac{23}{3} } }[/tex]

Compared with c ± √d, the value of c and d are 2 and 23/3 respectively.

Learn more on quadratic functions here: https://brainly.com/question/17895228


Related Questions

Hi can any one please help me I really need help please help me I need help

Answers

Answer:

1(a)1,030,000+0.13x

(b)$1,030,026

2. (a)Base and Index

(b)See Explanation

Ste-by-Step Explanation

(a)Total Amount to be paid to the four actors

=500,000+(300,000+0.02x)+(150,000+0.03x)+(80,000+0.08x)

Collect like terms

=500,000+300,000+150,000+80,000+0.02x+0.03x+0.08x

[tex]\text{Total Amount Paid= }1,030,000+0.13x[/tex]

(b)When x=200

[tex]\text{Total Amount Paid= }1,030,000+0.13(200)\\=1,030,000+26\\=$1,030,026[/tex]

Question 2

(a)The two parts of a power are the base and index.

Take, for example, the expression: [tex]a^b\\[/tex]

[tex]a$ is the base\\b is the index[/tex]

Another example using numbers is: [tex]10^3[/tex]

In this case:

[tex]10$ is the base\\3 is the index[/tex]

(b)Like terms are terms that have the same letter/variable attached to them.

For example, the following pairs are like terms

8x and 3x4y and -9y6pq and pq3 and 3

These, however, are not like terms

3 and 3y4x and 4y

The U.S. Census reports Native Americans by Group of answer choices one tribe only or in combination with another tribe plus in combination with any other race. one tribe only, one tribe only or in combination with another tribe, and one tribe only or in combination with another tribe plus in combination with any other race. one tribe only. one tribe only or in combination with another tribe. one tribe only and one tribe only or in combination with another tribe

Answers

Answer:

one tribe only or in combination with another tribe plus in combination with any other race.

Step-by-step explanation:

United States Census Bureau (USCB) is the governmental agency saddled with the responsibility of providing data about the citizens of America and her economy. The Census Bureau was founded on the 1st of July, 1902 and has its headquarter in Suitland, Maryland, United States of America.

The U.S. Census reports Native Americans by one tribe only or in combination with another tribe plus in combination with any other race.

Native Americans are the indigenous people (citizens) of the United States of America and they are also known as the American Indians. The Census Bureau reports them by one tribe only such as Cherokee, Apache, Hopi, Chinook etc or in combination with another tribe such as Aleuts, Tlingit, Chenega, etc plus in combination with any other race such as Black Americans, Asian Americans, White Americans, Native Hawaiian etc.

2 Points
What is the measure of ZE, in degrees?

Answers

Answer:

B. 84 deg

Step-by-step explanation:

Sides DE and FE are congruent since they both have the same length.

That makes angles D and F congruent.

m<D = m<F = 48

The sum of the measures of the angles of a triangle equals 180 deg.

m<E + m<D + m<F = 180

m<E + 48 + 48 = 180

m<E = 84

If f(x) = X over 2+8, what is f(x) when X equals 10?

Answers

f(x) = x/(2+8)

x = 10

f(x) = 10/(2+8)
f(x) = 10/10
f(x) = 1

Answer:

[tex] \boxed{\huge{\sf f(x) = 1}} [/tex]

Given:

[tex] \sf f(x) = \frac{x}{2 + 8} [/tex]

To Find:

[tex] \sf f(x) \: when \: \bold{x} = 10[/tex]

Step-by-step explanation:

[tex] \sf Evaluate \: f(x) = \frac{x}{2 + 8} \: where \: \bold{x} = 10 : \\ \sf \implies f(x) = \frac{x}{2 + 8} = \frac{10}{2 + 8} \\ \\ \sf 2 + 8 = 10 : \\ \sf \implies f(x) = \frac{10}{ \boxed{\sf 10}} \\ \\ \sf \frac{ \cancel{\sf 10}}{ \cancel{\sf 10}} = 1 : \\ \sf \implies f(x) = 1[/tex]

Find the median, divide it by 3 20, 82, 39, 23, 20, 60, 64.

Answers

Answer:

by using formula of median you can do it.

Answer:

put the numbers in order

20,20,23,39,60,64,82

Find the number in the middle

39 is in the middle because there is 3 numbers on each side so it is the median.

Divide by 3.

39 / 3 = 13

Hope this helps

Step-by-step explanation:

The expression (1/23) ^1000 is closest to what integer?

HELP QUICK PLS

Answers

Answer:

The expression is close to 0

Step-by-step explanation:

Given the expression [tex](\frac{1}{23} )^{1000} \\[/tex], for us to know the closest integer, the following step must be carried out;

[tex](\frac{1}{23} )^{1000} \\=\frac{1^{1000} }{23^{1000} } \\= \frac{1}{23^{1000}} \\= \frac{1}{5.34 * 10^{1361} }} \\= 1.87*10^{-1362}[/tex]

The value gotten is a very small value which is close to 0

Melinda sold packages of gourmet coffee, x, and pastries, y, at a school fundraiser. The packages of coffee sold for $6 each and pastries sold for $4 each. At the end of the fundraiser, she had sold 2 more packages of coffee than pastries and made $72 in total sales for the fundraiser. Create and graph system of linear equations that model this situation.

Answers

Answer:

Please find the attached graph

Melinda sold 8 packages of coffee and 6 packages of pastries

Step-by-step explanation:

The parameters given are;

Number of Packages of coffee = x

Number of Packages of pastries = y

Price of each package of coffee = $6

Price of each package of coffee = $4

Number of packages of packages of coffee sold = 2 more than packages of packages pastries sold

x = 2 + y

y = x - 2................(1)

Sum of money made in the fundraiser = $72

∴ x × $6 + y × $4 = $72

y = ($72 - x × $6)/$4 = 18 - 3/2·x

y = 18 - 3/2·x.........(2)

The solution is

x - 2 = 18 - 3/2·x

x + 3/2 = 18 + 2 = 20

5/2·x = 20

x = 2/5×20 = 8

y = x - 2 = 8 - 2 = 6

This is the answer from plato/edmentum.

The equation of a circle is given below. ( x + 8 3 ) 2 + y 2 = 1 (x+ 3 8 ​ ) 2 +y 2 =1left parenthesis, x, plus, start fraction, 8, divided by, 3, end fraction, right parenthesis, squared, plus, y, squared, equals, 1 What is its center? ( (left parenthesis , ,comma ) )right parenthesis What is its radius? If necessary, round your answer to two decimal places. units

Answers

Answer:

The center  is (-8/3,0) and the radius is 1

Step-by-step explanation:

(x+8/3)^2 + y^2 = 1

We know the equation of a circle is given by

(x-h)^2 + (y-k)^2 = r^2 where (h,k) is the center and r is the radius

Rewriting

(x- -8/3)^2 + (y-0)^2 = 1^2

The center  is (-8/3,0) and the radius is 1

NEED HELP ASAP!! RESPOND AS QUICK AS POSSIBLE!!!

Answers

Answer:

d

Step-by-step explanation:

google

Write as an expression: Twice the product of the squares of x and y Thanks! -Jamie

Answers

Answer: [tex]2(xy )^{2}[/tex]  the same thing as 2([tex]x^{2} y^{2}[/tex])

Step-by-step explanation:

You multiply 2 by x times y squared.

John is filling a bathtub that is 12 inches deep. He notices that it takes two minutes to fill the tub with three inches of water. He estimates it will take 10 more minutes for the water to reach the top of the tub if it continues at the same rate. Is he correct?

Answers

Answer:

No

Step-by-step explanation:

2 = 3 inches

2x5=10

10 = 3x5 of 15 inches

so no and it would take 8 minutes to fill up the tub

Find the volume of the cylinder

Answers

Answer:

see below

Step-by-step explanation:

The volume of a cylinder is given by

V = pi r^2 h

We know the radius is 9 and the height is 20

V = pi  ( 9)^2 ( 20)

V = 1620 pi

If we approximate pi by 3.14

V =5086.80 cm^3

If we approximate pi by pi button

V =5089.3800099 cm^3

Answer:

V=5089.380099cm^3

Step-by-step explanation:

V=πr^2h

V=π(9)^2(20)

V=π(9)^2(20)

V=5089.380099cm^3

According to the Insurance Institute of America, a family of four spends between $400 and $3,800 per year on all types of insurance. Suppose the money spent is uniformly distributed between these amounts. If we select a family at random, what is the probability they spend less than $2,000 per year on insurance per year? (Round your answer to 4 decimal places.)

Answers

Answer:

0.471

Step-by-step explanation:

Calculation for the probability that they spend less than $2,000 per year on insurance per year

First step is to find the base

Base =$2,000-$400

=$1,600

Second step is to find the probability using this formula

P=1/b+a×base

Where,

b represents $3,800

a represents $400

base represents $1,600

Let plug in the formula

P=1/$3,800-$400×$1,600

Hence,

P=1×$1,600/$3,800-$400

P=$1,600/$3,400

P=0.471

Therefore the probability that they spend less than $2,000 per year on insurance per year will be 0.471

Write the equation of the line that passes through (1,5) and (-2, 14) in slope-intercept form

Answers

Answer:

y = -3x + 8

Step-by-step explanation:

(1, 5)  ; (-2, 14)

[tex]Slope=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\=\frac{14-5}{-2-1}\\\\=\frac{9}{-3}\\\\=-3[/tex]

m = -3   ; (1 , 5)

Equation: [tex]y-y_{1}=m(x-x_{1})[/tex]

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

y - 5 = -3x + 3

y = -3x + 3 + 5

y = -3x + 8

In this activity, you will use equations to represent this proportional relationship: Olivia is making bead bracelets for her friends. She can make 3 bracelets in 15 minutes. Find the constant of proportionality in terms of minutes per bracelet.

Answers

Answer:

If she makes 3 bracelets in 15 minutes the constant of proportionality is 15/3 = 5 minutes per bracelet.

Answer:

5 minutes

Step-by-step explanation:

Did she can make 3 bracelets in 15 minutes then you have to divide 15/3 to get the number of minutes she can make one bracket. Therefore your answer would be 5 minutes per bracelet.

Hope this helps!

H(x)=4x-2;find h(-9)

Answers

Answer: h(-9)=4*(-9)-2=-36-2=-38

-38 is ur answer

Answer:-38

Step-by-step explanation:h(x) =4x -2

H(-9)

substitute for x using -9

H(-9) =4x -2

4(-9) -2

-36-2

H(-9) =-38

Solve each system by the addition method.
x + 2y = -1
5x - 4y = 16
Put your answer in ordered pair (x, y) DECIMAL form.

Answers

Answer:

(x, y) = (2, -1.5)

Step-by-step explanation:

x + 2y = -1

5x - 4y = 16

<=>

(2)x + (2)2y = (2)(-1)

5x - 4y = 16

<=>

2x + 4y = -2

5x - 4y = 16

<=>

7x = 14

<=>

x = 2

(*)x + 2y = -1

=> 2 + 2y = -1

=> 2y = -3

=> y = -1.5

=> (x, y) = (2, -1.5)

Divide a24 − a18 + a12 by a6. What is the quotient? A. a4 − a3 + a2 B. a18 − a12 + a6 C. a18 + a12 − a6 D. a30 − a24 + a18

Answers

Answer:

A

Step-by-step explanation:

Find the point-slope equation for the line that passes through the points (-8,-32) and (3,1). Use the first point in your equation.

Answers

Hey there! :)

Answer:

y + 32 = 3(x + 8)

Step-by-step explanation:

Begin by finding the slope of the line using the slope formula:

[tex]m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Plug in the coordinates of the points into the equation:

[tex]m = \frac{1 - (-32)}{3 - (-8)}[/tex]

Simplify:

[tex]m = \frac{33}{11}[/tex]

m = 3.

Point-slope form is:

y-y₁=m(x-x₁)

Plug in the coordinates of the first point, as well as the slope:

y - (-32) = 3(x - (-8)

y + 32 = 3(x + 8)

Answer:    y+32=3(x+8)

Step-by-step explanation:

First  you need to find the slope.The slope is the change in y divided by the change in x values.

-32 - 1 = -33

-8 - 3 =    -11  

-33/-11 = 3   the slope is 3  

and in point-slope form is  like y-b= m(x-a) where b is a y coordinate and a is the x coordinate.

it could be like   y-1=3(x-3) or y+32= 3(x+8)

Jon recently drove to visit his parents who live 528 miles away. On his way there his average speed was 14 miles per hour faster than on his way home (he ran into some bad weather). If Jon spent a total of 22 hours driving, find the two rates.

Answers

Answer:

speed while going = 42, while returning home = 28

Step-by-step explanation:

let his speed on the way to his parents house is (x)

then his speed while returning is x - 14

Time = Distance / speed

528 / x + 528 / x -14 = 22

multiplying the denominator ...

528x + 528x +7392 = 22x^2 +14x

1056x + 7392 = 22x^2 + 308x

0 = 22x^2 -748x -7392

"dividing by 22"

0 = x^2 -34x-336

0 = (x+8) (x-42)

x must be 42

finally jon's speed while back home is  42 - 14 = 28

Find the surface area of the prism.
Help please

Answers

Answer:

256 in ^2

Step-by-step explanation:

The area of the base B = 12*5 = 60 in ^2

The height is 14 inches

The perimeter of the base is

2 ( l+w) =2 ( 12+5) = 2 ( 17) = 34

The surface area  is  = 2B + Ph = 2 * 60 + 34*4

                                                    = 120 + 136

                                                    =256

What is true about the domain and range of the function?
The graph of the function f(x) = (x +2)(x + 6) is shown
below.
у
6
The domain is all real numbers, and the range is all
real numbers greater than or equal to 4.
O The domain is all real numbers greater than or equal to
4, and the range is all real numbers.
O The domain is all real numbers such that -65x3-2,
and the range is all real numbers greater than or equal
to-4.
The domain is all real numbers greater than or equal to
4, and the range is all real numbers such that -63x3
-2.
4
N
-6 -4 +2
4
6
х
N
-2-
-4
6t

Answers

Answer:

The correct option is;

The domain is all real numbers and the range is all real numbers greater than or equal to -4

Step-by-step explanation:

A function defines an output given an input and the set of all the possible inputs to a function is the domain of a function such that there is an output, such that the domain is the set of x values which are points on the curve of the function

The set of outputs that are produced from a given input is the range of a function

The given function is f(x) = (x + 2)(x + 6)

From the curve we see that the minimum y-coordinate, f(x), value is at -4, which is the lower bound of the range, while the x-coordinate values, the domain can be seen extending past the graph sheet which from the expression for the function also (f(x) = (x + 2)(x + 6)) indicates that the x values is the set of all real numbers (on the number line)

Therefore, the correct option is;

The domain is all real numbers and the range is all real numbers greater than or equal to -4.

Answer:

The domain is all real numbers and the range is all real numbers greater than or equal to -4

Step-by-step explanation:

what is the solution to this equation x/5=30

Answers

Answer:

x= 150

Step-by-step explanation:

X/5 = 30

x = 5×30

x= 150

Answer:

150

Step-by-step explanation:

[tex]\frac{x}{5}[/tex] = 30

→ Multiply both sides by 5 to isolate x

x = 150

The temperatures of Charleston, South Carolina on May 3rd are recorded in the table below. Determine the equation that models this data.

Answers

Answer:

Ok, the first step to see the behavior of this data is doing a graph of it,

So we can see that it looks like an reversed V. (at the bottom of the answer you can see the graph)

Then, we can model this with a piecewise function like:

For the first part we can take the two pairs:

if 11 am is our t = 0h

(0, 85) and (6, 93)

then the linear equation

y = a*t + b

a = (93 - 85)/(6 -0) = 8/6.

and b = 85.

then the linear equation is:

y = (8/6)*t + 85. for 0h ≤ t ≤ 6h

The second part of this equation can be modeled with the points

(6, 93) and (11, 84)

then we have:

y = s*t + c

s = (84 - 93)/(11 - 6) = -7/5

and we can find the value of c as:

93 = (-7/5)*6 + c

93 + (7/5)*6 = 101.4

then this second part is:

y = (-7/5)*t + 101.4 for 6  ≤ t ≤ 11h

then, in conclusion we have:

         y = (8/6)*t + 85. for 0h ≤ t ≤ 6h

f(x) =

         y = (-7/5)*t + 101.4 for 6  ≤ t ≤ 11h

Answer:

y=7.496sin(0.3243x+0.315)+73.489

Step-by-step explanation:

simply put the data into a graph and graph each equation to see if its matched

what is the method and answer for brainliest

Answers

Equal steps mean each number is the same distance from the previous one

From -2 to 28 is 28 units

There are 4 spaces between the numbers

28/4 = 7

Each number is in increase of 7

-2 + 7 = 5

5+7 = 12

12+7 = 19

19+7 = 26

The third number would be 12

What is the result of substituting for y in the bottom equation?

y = x + 3

y= x2 + 2x-4

A. x+ 3 = x2 + 2x - 4

B. X+ 3 = x2

C. y= (x+3)2 + 2(x + 3) - 4

D. y= x2 + 2x - 4 - (x+3)

Answers

Answer:

(A)[tex]x + 3= x^2 + 2x-4[/tex]

Step-by-step explanation:

Given the equations:

[tex]y = x + 3\\y= x^2 + 2x-4[/tex]

Substitution simply means replacing the variable y in the second equation with its equivalent x+3 from the first equation.

Substitution of y into [tex]y=x^2 + 2x-4[/tex] gives us:

[tex]x + 3= x^2 + 2x-4[/tex]

The correct option is A.

The numbers -1/5 and -5 are 'negative reciprocals.' True or False?

Answers

Answer:

False

Step-by-step explanation:

The negative reciprocal of -1/5 would be 5, and the negative reciprocal of -5 is 1/5. A way to double-check is all negative reciprocals add to -1.

-1/5 + -5= -5 1/5

Hope this helps and you understand negative reciprocals more for future problems ahead.

Given: In ΔBLU, LE ⟂ BU , and BL ≅ UL Prove: ΔBEL ≅ ΔUEL STATEMENT REASON 1. LE⟂ BU and BL ≅ UL 1. Given 2. LE ≅ LE 2. Reflexive Property 3. ΔBEL ≅ ΔUEL 3. _______________ Which of the following choices will complete the reasoning for statement #3? A SSA B AAA C HL D None of these choices are correct.

Answers

Answer:

I think it is C

Step-by-step explanation:

You own a comic book store. When you order comic books for your store to sell, you get 18 comic books per bundle. How many comic books would you have to sell if you ordered 7 bundles?

Answers

Answer:

the answer is 126

Step-by-step explanation:

beacuse if you sell 7 bundles for every one you get 18 so 18+18+18+18+18+18+18=126

Answer:

126 books

Step-by-step explanation:

There are 18 books per bundle and 7 bundles

So you would multiply 7 with 18 and get your answer of 126 books to sell

Trey is running for president of the chess club, and he received 8 votes. There are 80 members in the club. What percentage of the club members voted for Trey?

Answers

Answer:10

Step-by-step explanation:

8/80=1/10*100=10

Other Questions
If a quadratic function has two solutions, what would you expect to see on the graph of its parabola? The parabola crosses the x-axis twice. The parabola touches the x-axis once. The parabola does not touch or cross the x-axis. The parabola has an infinite number of solutions. Read the lines from Act II, scene iii of Romeo and Juliet. Enter Nurse and PETER. Mercutio: A sail, a sail! Benvolio: Two, two; a shirt and a smock. Nurse: Peter! Peter: Anon! Nurse: My fan, Peter. Mercutio: Good Peter, to hide her face; for her fans the fairer face. Which is true about the scene? I need answer ASAP Annie wrote the following steps to solve a pair of equations: Step 1: y = x 5 y = 2x + 2 Step 2: 2y = 2x 10 y = 2x + 2 Which of the following shows the correct next step to solve the equations by eliminating x? A. 3y = 5 B. 3y = 8 C. 3y = 12D. 3y = 20 Garcel, Inc. held unfinished inventory at a cost of $85,000 with a sales value of $125,000. The inventory will cost $10,500 to complete. The normal profit margin is 30% of sales. The replacement cost of the inventory was $75,000. If Garcel uses the last-in, first-out method to determine inventory cost, what amount should Garcel report as inventory on its balance sheet M is the midpoint of PQ and N is the midpoint of PR, and O is the intersection of QN and RM, as shown. If QN is perpendicular PR, QN = 12, and PR = 14, then find OR. What is the answer to this? HEEELLLPPP!!! plssss Which is true about the solution to the system of inequalities shown?y 3x + 1y 3x - 3Only values that satisfy y 3x + 1 are solutionsOnly values that satisfy y 3x3 are solutionsValues that satisfy either y a 3x + 1 orys 3x - 3 are solutionsThere are no solutions Please answer this question now in two minutes In Shakespeares plays, lower class characters often speak in It takes to break an carbon-chlorine single bond. Calculate the maximum wavelength of light for which an carbon-chlorine single bond could be broken by absorbing a single photon. Round your answer to significant digits. Please Help Me ASAP!!! Factor completely. x^2 + 5x + 6 Enter your answer in the box. Help me on this question please (view attachment) How successful were Europeans in converting the Native people of the Americas to Christianity? help me please and double check yo answer if u send me the wrong answer u better not send it u won't like meLook at these details from a paragraph about the same topic: Slow down and pronounce words clearly when speaking in front of a group. When speaking to a group of people, take deep breaths to stay calm. Stand up straight and smile often if you're speaking in front of a group.Choose the main idea that ties all the details together.A. Breathe deeply when speaking in front of a group.B. Public speaking skills can be improved by following some helpful tips.C. Look up from your notes when speaking in front of a group.D. There are many reasons you may need to speak in front of a group. what is 1 1/5 subtracted by 3 1/10whoever gets it right I will choose as the brainliest When a dog is sleeping and does not react to the sound of a person walking around the house, that is most likely an example of____? The sum of the internal angles of a convex polygon is 1080. Calculate the number of diagonals of this polygon.a) 30b) 10c) 20d) 24e) 22portugueseA soma dos ngulos internos de um polgono convexo 1080. Calcule o nmero de diagonais desse polgono. a)30 b)10 c)20 d)24 e)22 EL Ratoncito Prez left this note for Betito. Read the note and answer the question. Betito, los dientes no estn limpios y estn amarillos. Visita al dentista para blanquear los dientes. What suggestion does El Ratoncito Prez have for Betito? Floss daily. Get braces. Go to the dentist. Whiten your teeth. Por que usas el presente perfecto para hablar sobre la experiencia