Quadratic equation. Find the value of m so that the roots of the equation (4 - m) x^2 + (2m + 4)x + (8m + 1) = 0 may be equal.

Answers

Answer 1

The quadratic has one root with multiplicity 2 if the discriminant is 0, which is

[tex](2m+4)^2-4(4-m)(8m+1)[/tex]

(That is, for a quadratic [tex]ax^2+bx+c[/tex], the discriminant is [tex]b^2-4ac[/tex].)

Set the discriminant equal to 0 and solve for [tex]m[/tex]:

[tex](2m+4)^2-4(4-m)(8m+1)=0[/tex]

[tex]4m^2+16m+16+32m^2-124m-16=0[/tex]

[tex]36m^2-108=0[/tex]

[tex]36m(m-3)=0[/tex]

[tex]\implies m=0\text{ or }m=3[/tex]


Related Questions

A scientist created a scatterplot to display the height of a plant over a 12-day period. Plant Height A graph has days on the x-axis and height (inches) on the y-axis. A trend line goes through points (5, 3) and (12, 7). Which is the equation of the trend line that is shown? y = StartFraction 1 Over 7 EndFraction x + StartFraction 4 Over 7 EndFraction y = StartFraction 1 Over 7 EndFraction x + StartFraction 16 Over 7 EndFraction y = StartFraction 4 Over 7 EndFraction x minus StartFraction 1 Over 7 EndFraction y = StartFraction 4 Over 7 EndFraction x + StartFraction 1 Over 7 EndFraction

Answers

Answer:

The correct option is (D) [tex]y=\frac{4}{7}\ x+\frac{1}{7}[/tex].

Step-by-step explanation:

The two-point form for the equation of straight line is:

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

The two points provided are:

A = (5, 3)

B = (12, 7)

Compute the equation of the trend line as follows:

[tex](y-y_{1})=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\ (x-x_{1})\\\\(y-3)=\frac{7-3}{12-5}\ (x-5)\\\\(y-3)=\frac{4}{7}\ (x-5)\\\\y-3=\frac{4}{7}\ x-\frac{20}{7} \\\\y=\frac{4}{7}\ x-\frac{20}{7}+3\\\\y=\frac{4}{7}\ x+\frac{-20+21}{7}\\\\y=\frac{4}{7}\ x+\frac{1}{7}[/tex]

Thus, the equation of the trend line is [tex]y=\frac{4}{7}\ x+\frac{1}{7}[/tex].

The correct option is (D).

Answer:

D

Step-by-step explanation:

what is a unit rate?​

Answers

Answer:

A unit rate is like a calculator or price per unit. that you will have to divide the numerator by the denominator.

Step-by-step explanation:

Example: "A motorcycle travels 230 miles on 4 gallons of gasoline." basically you will have to find the average mileage per gallon of how much that motorcycle used.

I'm not sure if this helped. sorry

PLEASE HELP I"M BEING TIMED!!!!!!!!!!!!!!!!!!!!!!!!!!!!!




Which expression is equivalent to log Subscript 12 Baseline StartFraction x Superscript 4 Baseline StartRoot x cubed minus 2 EndRoot Over (x + 1) Superscript 5 Baseline EndFraction?

4 log Subscript 12 Baseline x + one-half log Subscript 12 Baseline (x cubed minus 2) minus 5 log Subscript 12 Baseline (x times 1)

4 log Subscript 12 Baseline x + one-half log Subscript 12 Baseline StartFraction x cubed Over 2 EndFraction minus 5 log Subscript 12 Baseline 1

log Subscript 12 Baseline 4 x + one-half log Subscript 12 Baseline (x cubed minus 2) minus 5 log Subscript 12 Baseline (x) + 1

4 log Subscript 12 Baseline x + one-half log Subscript 12 Baseline (x cubed minus 2) minus 5 log Subscript 12 Baseline (x + 1)

Answers

Answer:

[tex]D)4log_{12}x+\frac{1}{2} log_{12}(x^3-2)-5log_{12}(x+1)[/tex]

(4 log Subscript 12 Baseline x + one-half log Subscript 12 Baseline (x cubed minus 2) minus 5 log Subscript 12 Baseline (x + 1)

Step-by-step explanation:

Given the expression:

[tex]log_{12}\dfrac{x^4\sqrt{x^3-2} }{(x+1)^5}[/tex]

first apply the division law of logarithm:

[tex]log_{a}x/y=log_{a}x-log_{a}y[/tex]

[tex]log_{12}\dfrac{x^4\sqrt{x^3-2} }{(x+1)^5}=log_{12}x^4\sqrt{x^3-2}-log_{12}(x+1)^5[/tex]

Next, by addition law:[tex]log_{a}xy=log_{a}x+log_{a}y[/tex]

[tex]=log_{12}x^4+log_{12}\sqrt{x^3-2}-log_{12}(x+1)^5\\\\Log a^m=mLog a, Log \sqrt{x}=log x^{1/2}\\\\ =4log_{12}x+log_{12}(x^3-2)^{1/2}-5log_{12}(x+1)\\\\=4log_{12}x+\frac{1}{2} log_{12}(x^3-2)-5log_{12}(x+1)[/tex]

Answer:

Its D on edge

Step-by-step explanation:

What is the slope-intercept form of an equation of a line perpendicular to y=2x−3 and passing through the point (5,−1)?

Answers

Answer:

y=-2x+9

Step-by-step explanation:

1. Make m value opposite of og m value.

2. Then plug in variables x and y into the equation

3. Solve for b

-1 = -2(5) + b

9 = b

4. You have the answer

factor the binomials using gcf 16p + 4

Answers

the gcf is 4. 4(4p+1)
Idkkkkkkkkkkkkkkkkkkkkk

6) Troy has a garden that is 17 feet by 14 feet. He is planning on planting some
bulbs in the garden. Each bulb requires 2 square feet of space. How many bulbs
can Troy plant in the garden? *
119

Answers

Answer:

140

Step-by-step explanation:

first multiply 17 by 14 to get 238 then dived 238 by 2 to get 140

solve |-4|/|-4| please help

Answers

Answer:

i think the answer is 1 dont take my word for it though

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

The absolute value of -4 is 4, therefore |-4|/|-4| = 4/4 = 1

The coordinates for a quadrilateral are A(3, 5), B(7, 5), C(8, 3) and D(4, 3). Determine the type of quadrilateral.
Group of answer choices

Rectangle

Parallelogram

Square

Rhombus

Answers

Answer:

Rhombus

Step-by-step explanation:

Just graph on the coordinate grid.

Answer:

Parallelogram

Step-by-step explanation:

You have to put the coordinates in a Cartesian diagram and connecting the points you will find the figure

O terreno da fazenda de Eduardo foi aumentado 2 m na horizontal e 2 m na vertical. Se antes do aumento o terreno tinha o formato de um quadrado de lado x, qual a nova área após os aumentos?

Answers

Answer:

New area of Eduardo's farm after the increase = x² + 4x + 4

Nova área da fazenda de Eduardo após o aumento = x² + 4x + 4

Step-by-step explanation:

English Translation

The land on Eduardo's farm was increased by 2 m horizontally and 2 m vertically. If before the increase the land was shaped like an x-side square, what is the new area after the increases?

Solution

The previous area of Eduardo's farm is the are of a square with side lenght of x.

Area of a square = (side length)² = x²

Then, the land on Eduardo's farm was increased by 2 m horizontally and 2 m vertically.

New horizontal length of Eduardo's farm = (x+2)

New vertical length of Eduardo's farm = (x+2)

New area of Eduardo's farm = (x+2)(x+2)

= x² + 4x + 4

In Portugese/Em português

A área anterior da fazenda de Eduardo é a de um quadrado com comprimento lateral de x.

Área de um quadrado = (comprimento lateral)² = x²

Em seguida, o terreno da fazenda de Eduardo foi aumentado 2 m na horizontal e 2 m na vertical.

Novo comprimento horizontal da fazenda de Eduardo = (x + 2)

Novo comprimento vertical da fazenda de Eduardo = (x + 2)

Nova área da fazenda de Eduardo

= (x + 2) (x + 2) = x² + 4x + 4

Hope this Helps!!!

Espero que isto ajude!!!

OVER HERE WALKER
What is the circumference of a circle with a diameter of 21 cm ?

Answers

Answer:

65.97

Step-by-step explanation:

LUI
• Chicken nuggets, burger, hot dog
Apple Juice or milk
French fries or fruit
HOOD
8
The list below shows some of the possible
outcomes. List the missing possible outcomes
below.
ter and
ps the
- only
nd a
Chicken nuggets, apple juice, French fries
Chicken nuggets, apple juice, fruit
Chicken nuggets, milk, French fries
Chicken nuggets, milk, fruit
Burger, apple juice, French fries
Burger, milk, French fries
Burger, apple juice, fruit
Hot dog, apple juice, French fries
Hot dog, milk, French fries
Hot dog, milk, fruit

Answers

Answer:

cool cool no c um hi hi hi hi hi hi hi hi hi hi hi hi hu x

63x−8≤23 OR −4x+26≥6

Answers

Answer:

63x-8<23

63x<23+8

63x < 31

63. 63

x < 0.492

Anne wants to create a data display to summarize prices of the 264 homes for sale in her
area. A sample of the data is shown below.
$72,000, $129,500, $132,000, $149,400, $152,000, $183,500, $225,000, $289,000, $348,000
She wants the display to show how many homes are available for homebuyers with various
budgets. Which data display is best for Anne's purpose?
a histogram, because the minimum and maximum values are clearly displayed
a box plot, because the median is clearly displayed
a box plot, because the data are divided into four ranges of values
a histogram, because the bars show the frequency of data points within different ranges

Answers

Answer:

The correct option is (D).

Step-by-step explanation:

The boxplot is a consistent way to exhibit the data-distribution based on, minimum, first quartile, median, third quartile and maximum.  

Therefore we can say it provides information about the location of the center, dispersion and skewness (measure of asymmetry) of the data.

The methods commonly used for depicting a frequency distribution are:

Histogram/Column graph Bar graph Frequency Polygon Pie chart

Out of these, one of the most general and extensively used devices of illustrating a frequency distribution is the histogram.

In this case it is provided that Anne wants the display of prizes to show how many homes are available for home buyers with various  budgets.

So, Anne can set range of budget values and assign the number of buyers with various  budgets.

From the provided data the range of budget values can be set as:

Less than $50,000

$50,000 - $100,000

$100,000 - $150,000

$150,000 - $200,000

$200,000 - $250,000

$250,000 - $300,000

$300,000 - $350,000

Thus, the histogram data display is best for Anne's purpose.

The correct option is (D).

This question is based on the concept of statistics. Therefore, the histogram data display is best for Anne's purpose. Hence, the correct option is D, histogram.

Given:

Anne wants to create a data display to summarize prices of the 264 homes for sale in her  area. A sample of the data is shown below.

$72,000, $129,500, $132,000, $149,400, $152,000, $183,500, $225,000, $289,000, $348,000.

According to the question,

As we know that, the boxplot is consistent way to exhibit the data distribution based on the minimum, first quartile, median, third quartile and maximum.  

Therefore, it provides information about the location of the center, dispersion and skewness (measure of asymmetry) of the data.

The following methods commonly used for depicting a frequency distribution are:

Histogram/Column graph Bar graph Frequency Polygon Pie chart

Out of these, one of the most extensively used devices of illustrating a frequency distribution is the histogram.

In this question it is provided that, Anne wants the display of prizes to show how many homes are available for home buyers with various  budgets.

Thus, Anne can set range of budget values and assign the number of buyers with various budgets.

From the given data the range of budget values can be written as:

Less than $50,000

$50,000 - $100,000  

$100,000 - $150,000

$150,000 - $200,000

$200,000 - $250,000

$250,000 - $300,000

$300,000 - $350,000

Therefore, the data display is best for Anne's purpose. Hence the correct option is D, histogram.

For more details, prefer this link:

https://brainly.com/question/23370669

Teri has a bag of colored marbles. Five marbles are red, four are green, ten are blue, and one is white. Marbles are randomly selected out of the bag.
What is the probability of selecting a red marble and then a white marble without replacement?


Answers

Answer:

1/76

Step-by-step explanation:

Five marbles are red,

four are green,

ten are blue, and

one is white.

Sample space S= 5+4+10+1= 20

Probability of selecting a red Mable

Pr(red) = 5/20= 1/4

Probability of selecting a white Mable without replacement after the first selection

Pr(white) = 1/19= 1/19

the probability of selecting a red marble and then a white marble without replacement?

= 1/4*1/19= 1/76

Donna took twice as long to drive 720 miles and Maple took to drive 200 miles. Find the rates and ties of both if Donna's speed exceeded that of Maple by 40 miles per hour

Answers

Answer:

Donna traveled for 8 hours at 90 mph

Maple traveled for 4 hours at 50 mph

Step-by-step explanation:

The velocity at which each person traveled is given by the distance traveled divided by the time spent (t). From the information given, the following expressions can be written

[tex]t_d = 2t_m\\V_d = V_m+40\\V_d = \frac{720}{t_d}\\V_m = \frac{200}{t_m}\\\\V_d = \frac{360}{t_m}\\ \frac{360}{t_m}=\frac{200}{t_m}+40\\t_m = 4\ hours\\t_d=2*4 = 8\ hours\\\\V_d = \frac{720}{8}=90\ mph\\V_m = \frac{200}{4}=50\ mph\\[/tex]

Therefore, Donna traveled for 8 hours at 90 mph and Maple traveled for 4 hours at 50 mph.

WILL CHOOSE BRAINLIEST! PLEASE HELP! 15 POINTS!
Find the area of the shaded segment of the circle.

Answers

[(81*3.14)/4] - (81/2)

Answer:

The shaded segment  = The arc area - The triangle

The arc area = pi x radius^2 x angle/360

                     = pi x 9^2 x (360-270)/360 = 63.61 (m2)

The triangle area = 9 x 9/2 = 41.5 (m2)

(because this is right triangle)

=> The shaded segment = 63.61 - 41.5 = 22.11 (m2)

Can someone please help with these 4 questions?

Answers

Answer:

Q4. 2144     Q5. -16     Q6.   Downwards     Q7.   0 seconds

Step-by-step explanation:

Q4.    h(t) = -16t² + 2400    Substitute 4 for t

h(4) = -16(4)² + 2400          Simplify the exponent

h(4) = -16(16) + 2400          Multiply

h(4) = -256 + 2400            Add

h(4) = 2144

Q5.   I graphed the equation on the graph below to find the instantaneous velocity. The instantaneous velocity is -16.

Q6.   At 4.5 seconds, the water rocket is traveling down because the highest point the rocket goes is at 2.8, so 4.5 is traveling downwards.

Q7.   0 seconds because the rocket goes 0 feet in 0 seconds.

If these answers are correct, please make me Brainliest!

Find the parallelogram.

Answers

Answer:

area - 120 cm

Step-by-step explanation:

Answer:

A = 120 cm^2

P = 54 cm

Step-by-step explanation:

Area of parallelogram: = base * height

A = 15 cm * 8 cm = 120 cm^2

Perimeter of parallelogram = sum of lengths of sides

P = 15 cm + 15 cm + 12 cm + 12 cm = 54 cm

Jason runs 440 yards in 75 seconds.at this rate,how many minutes does it take him to run a mile​

Answers

Answer:

5 minutes

Step-by-step explanation:

Do a proportion

440/75= 1760/x

cross multiply

440x=1760(75)

simplify

132000/440

The ratio of the leg opposite to an angle to the hypotenuse of a right triangle is
called the ____ of the angle.

A. sine
B. secant
C. cosine
D. cosecant

Answers

Answer:

cosine I think

Step-by-step explanation:

The ratio of the perpendicular and the hypotenuse is given by the sine of the angle. Then the correct option is A.

What is trigonometry?

Trigonometry deals with the relationship between the sides and angles of a right-angle triangle.

The ratio of the leg opposite to an angle to the hypotenuse of a right triangle is called the sine of the angle.

The sine is given as the side opposite to the angle is known as perpendicular.

The ratio of the perpendicular and the hypotenuse is given by the sine of the angle.

More about the trigonometry link is given below.

https://brainly.com/question/22698523

#SPJ2

The pot has a diameter of 10 inches a height of 12 inches. there are 120 meatballs each meatball is 2.4 inches. the sauce takes up half the pot already. determine if the sauce overflows or not. pls help its due in an hour! ):

Answers

the answer is c

Step-by-step explanation:

YALL I NEED HELP MY DUMBSELF FORGETS TO DO THESE STUFF SMH

CAN U ALSO EXPLAIN HOW U GOT THE ANSWER PLZ THXX
I need to find the area

Answers

Area=1/2 x b x h
=1/2 x 7 x 3
= 21/2
=10.5

slove the x in the digram below explain

Answers

Answer:

x= 20

Step-by-step explanation:

a flat angle is, in terms of geometry, the space between an intersection between two lines whose opening measures 180 degrees or 180º. Since the angle is 180º there is no difference between two lines or a line and we can say that the angles in a straight line always add up to 180º.

Step 1

define

according to the graph

3x+80+2x=flat angle=180°

3x+80+2x=180°

Step 2

solve for x

3x+80+2x=180°

5x+80=180

subtract 80 in each side

5x+80-80=180-80

5x=100

divide by 5

(5x)/5=100/5

x=20

happy to help:)

2/7 as a percent to the nearest whole number

Answers

29% (.285 is 29 percent rounded because u have to move two decimals to the right to get your percentage)

The chart indicates the time, speed, and velocity of five runners.

A 4-column table with 5 rows. The first column labeled runner has entries Garreth, Luigi, Elisa, Jasmine, Logan. The second column labeled total time has entries 45 minutes, 35 minutes, 40 minutes, 35 minutes, 35 minutes. The third column labeled speed has entries 6.2 miles per hour, 5.0 miles per hour, 6.2 miles per hour, 5.0 miles per hour, 5.6 miles per hour. The fourth column labeled velocity has entries 5.5 miles per hour west, 4.3 miles per hour east, 5.5 miles per hour west, 4.0 miles per hour south, 4.0 miles per hour north.
Which best describes the runners?

A.Garreth and Elisa ran the same distance but not the same displacement, Luigi and Jasmine went the same displacement, and Logan ran faster than Jasmine.
B.Garreth ran farther than Luigi, Elisa and Jasmine went the same distance, and Logan and Jasmine has the same displacement in the opposite direction.
C.Garreth and Elisa ran together, Luigi and Jasmine went the same distance, and Logan and Jasmine have the same displacement in the opposite direction.
D.Garreth ran less than Logan, Elisa and Jasmine went the same displacement, and Luigi and Garreth ran together.

Answers

Answer:

c (just took the test)

Step-by-step explanation:

Garreth and Elisa ran together, Luigi and Jasmine went the same distance, and Logan and Jasmine have the same displacement in the opposite direction.

As per the given information, in which the time, speed, and velocity of five runners, the statement that gives the best description about the runners is: “Garreth and Elisa ran ………..  in the opposite direction.” Hence, Option C is correct.

Who are called runners?

From a cardiovascular aspect, runners are highly fit athletes, but they frequently struggle with their balance, upper body strength, and glute power. Sports that use different muscles and gaits are recommended for runners.

While sprinters are taller and significantly more muscular, long-distance runners often have a shorter, lighter build. The types of workload each runner endures are a direct result of the differences between these two body types.

Logan and Jasmine moved in the opposite direction at the same speed as Jasmine, while Garreth and Elisa ran side by side. Luigi and Jasmine also covered the same distance.

Therefore, Option C is correct.

Learn more about runners from here:

https://brainly.com/question/2456125

#SPJ5

A scale drawing is shown for clubhouse. The measurements are 4“ x 8“ what will the actual clubhouse measurements be if the scale factor is 1 inch equals 2 feet

Answers

Answer:

8ft. x 16ft.

Step-by-step explanation:

If each inch is scaled to 2 ft, then you simply multiply the values by two. The new scaled dimensions would be 8 x 16 ft. Hope this helps.

Hi there! I need some help with this question, thx!


In the table, Pattern A uses the rule "add 5" and Pattern B uses the rule "add 15."

Pattern A is 0, 5, 10, 15, 20
Pattern B is 0, 15, 30, 45, 60

Which statement is true?


A. Every term in Pattern B is 3 times the corresponding term in Pattern A.

B. Every term in Pattern B is 10 more than the corresponding term in Pattern A.

C. Every term in Pattern B is 5 times the corresponding term in Pattern A.

D. Every term in Pattern B is 13 the corresponding term in Pattern A.

Answers

Answer:

sky im going with A

Step-by-step explanation:

A I took the test it is correct

The length of an arc of a circle is 9.42cm. If the diameter of the circle is 10cm, find the angle subtended by the arc at the center of the circle. (Take π = 3.142)
SHOW ALL WORKING.

Answers

Answer:

1.89 radians  or 108 degrees.

Step-by-step explanation:

Circumference of the circle = 10 * 3.142

= 31.42.

So 31.42 is equivalent to 2 pi radians, so:

Angle subtended at the center

= (9.42 / 31.42) * 2 pi

=  (9.42 / 31.42) * 2 * 3.142

= 1.89 radians  or 108 degrees..

2x-y<5
[tex]2x - y \leqslant 5[/tex]

Answers

Answer:

Step-by-step explanation:

Please be sure to include the directions when you post a question.  I will assume you want to graph this inequality 2x - y ≤ 5.  

2x - y = 5 is a linear function whose graph is that of a straight line.  Because of the ≤ sign, the solution set includes all points on this straight line PLUS all  points below it.

x - intercept:  Set y = 0 in 2x - y = 5 and solve the resulting equation for x:

2x - 0 = 5.  Then x = 5/2, and the x-intercept is (5/2, 0).

y-intercept:  Set x = 0 and solve for y:  2(0) - y = 5:  y = -5.  Then the y-intercept is (0, -5).  

Plot both points (5/2, 0) and (0, -5).  Draw a solid line through them.  Shade the area BELOW this line.

Can someone help me

Answers

Answer:C

Step-by-step explanation:

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