What is the smallest possible real value of x^2+8x?

Answers

Answer 1
Answer:   -16

========================================================

Explanation:

Let's complete the square

y = x^2 + 8x

y + 16 = x^2 + 8x + 16 .... adding 16 to both sides

y + 16 = (x+4)^2

y = 1(x+4)^2 - 16

We added 16 to both sides to allow the right hand side to factor into a perfect square.

The last line shown above is in the form y = a(x - h)^2 + k where

a = 1

h = -4

k = -16

Note the positive 'a' value indicates we have a minimum.

The vertex is (h,k) = (-4, -16)

The lowest y value possible is at the vertex.

So the smallest y value is y = -16.

This means the smallest possible value of x^2+8x is -16.


Related Questions

15 kg equals how many grams

Answers

Answer:

15,000g

Step-by-step explanation:

Answer: 15000 grams

Step-by-step explanation: To convert Kilograms to Grams, you'll need to multiply the mass value by 1000.

Answer the two questions below. THANKS!!

Answers

Problem 1

We're given that angle A = angle B. Also that angle B = angle C.

By the transitive property, we can say angle A = angle C.

So basically all three angles are equal to one another. Let's call that unknown angle x.

For any triangle, the three angles always add to 180, so,

x+x+x = 180

3x = 180

x = 180/3

x = 60

That proves angles A,B, and C are each 60 degrees. This triangle is considered equiangular since all angles are the same. Furthermore, the triangle is also considered equilateral meaning all sides are the same. The term equilateral is more widely used, so I'd go with that term if you could only pick one.

==========================================================

Problem 2

As mentioned in problem 1, the three angles of a triangle add to 180

A+B+C = 180

A+B+90 = 180

A+B+90-90 = 180-90

A+B = 90

This shows A and B are complementary angles. Complementary angles by definition add to 90 degrees.

Which fact helps you prove the isosceles triangle theorem, which states that the base angles of any isosceles triangle have equal measure? The base angles of an equilateral triangle have equal measure. If two sides of a triangle are equal, the third side must be equal to the others. If a triangle is equiangular, then it is equilateral. If one angle of a triangle is larger than another angle, then the side opposite the larger angle is longer than the side opposite the smaller angle.

Answers

Answer:

If one angle of a triangle is larger than another angle, then the side opposite the larger angle is longer than the side opposite the smaller angle.

The fact which helps to prove the isosceles theorem is; The base angles of an equilateral triangle have equal measure.

Isoscelles triangle

Isoscelles triangles in plane shape concept are characterized by two equal sides.

On this note, similarly in equilateral triangles, 2 sides are equal ( although, all sides of an equilateral triangle are equal).

Ultimately, the statement which helps to prove the isosceles triangle theorem is therefore; The base angles of an equilateral triangle have equal measure since all the two sides are equal as in isoscelles triangles too.

Read more on isoscelles triangle;

https://brainly.com/question/11884412

Write the slope-intercept form of the equation of the line described. Through (-2, -2) parallel to y = -2/7x -5

Answers

Answer: y= -2/7x-2

Step-by-step explanation:

To be parrell they have to have the same slope but different y intercepts.

so just put -2 so it will cross that point

A large bottle of orange juice contains 400 mL of juice. A medium size bottle contains 60% as much. Find how many millilters are in the medium bottle using the double number line.

Answers

Answer:

240 mL

Step-by-step explanation:

60% of 400 is 240 mL! Your Welcome!

Answer:

the answer would be 240

Step-by-step explanation:

you have to take the percentage and turn it into a decimal by dividing by 100 and that gets you .6 and then you have to time 400 by .6 and then you get your answer

what is the answer of CGF of 9 and 12​

Answers

Answer:

The answer of CGF is 3.................

Answer:

3

Step-by-step explanation:

List the factors of each number

factors of 9 are 1, 3, 9

factors of 12 are 1, 2, 3, 4, 6, 12

The common factors are 1 and 3

GCF = 3

.............llllllllllllllllwwwwwwww

Answers

Answer:

wwwwwwwwwwwwwwwwwww

1 3/4 divided by 1/2-1 1/2 to the 3rd

Answers

Answer:

-7/4

1/8

Step-by-step explanation:

1. If the problem is; (1 3/4) / (1/2 - 1 1/2)^(3)

(a). Convert to improper fractions;

(7/4) / (1/2 - 3/2)^3

(b). Simplify;

(7/4) / (-2/2)^3

(7/4) / (-1)^3

(7/4) / (-1)

-7/4

2. If the problem is; ((1 3/4) / (1/2)) - (1 1/2)^3

(a). Convert to improper fractions;

((7/4)/ (1/2)) - (3/2)^3

(b). Simplify;

((7/4)/ (1/2)) - (3/2)^3

((7/4)*(2/1)) - (27/8)

(7/2) - (27/8)

(28/8) - (27/8)

1/8

johnny invests $9000 in two mutual funds

Answers

Answer:

$4500 each if he splits it eqaully

Step-by-step explanation:

9000÷2=4500

hope this helped (~‾▿‾)~

A total of $5000 is invested: part at 5% and the remainder at 15%. How much is invested at each rate if the annual interest is $720?

Answers

Answer:

At 5% , $300 was invested

At 15%, $4,700 was invested

Step-by-step explanation:

Let the amount invested at 5% be $x and the amount invested at 15% be $y

x + y = 5000 ••••••(i)

Let’s work with the interest;

5% of x + 15% of y = 720

0.05x + 0.15y = 720 •••••(ii)

From i;

x = 5000-y

Insert this into ii

0.05(5000-y) + 0.15y = 720

= 250 - 0.05y + 0.15y = 720

250 + 0.1y = 720

0.1y = 720-250

0.1y = 470

y = 470/0.1

y = $4700

x = 5000-y

x = 5000-4700 = $300

arrangement the following in ascending order ; -5/7, -3/14, 4/7, -6/7​

Answers

Answer:

-4/7-5/7-6/7-3/14 ascending order

Answer:

The sorted inputs in order from least to greatest is:

-6/7 < -5/7 < -3/14 < 4/7

Step-by-step explanation:

Given

-5/7, -3/14, 4/7, -6/7​

The least common denominator (LCD) is: 14

Rewriting as equivalent fractions with the LCD:

-5/7            -3/14            4/7          -6/7

-10/14          -3/14           8/14          -12/14

Sorting this table by the numerators of the equivalent fractions in order from least to greatest:

-6/7                -5/7              -3/14              4/7

-12/14     <      -10/14     <      -3/14        <   8/14

Therefore, the sorted inputs in order from least to greatest is:

-6/7 < -5/7 < -3/14 < 4/7

List or circle the possible values that satisfy each inequality.

Answers

First question: 5, 10

Second question: 2, 3, 5

To solve this, plug each of the numbers into the inequality and circle the numbers that make the inequality true.

Give the factors for the numerator [n] and denominator [d] after reducing.

Answers

Answer:

The factors for the numerator [n] and denominator [d] after reducing will be:

[tex]\frac{x^2-25}{x^2-4x}\div \:\frac{2x^2+2x-40}{x^3-x}=\frac{\left(x-5\right)\left(x+1\right)\left(x-1\right)}{2\left(x-4\right)^2}[/tex]

Step-by-step explanation:

Given the expression

[tex]\frac{x^2-25}{x^2-4x}\div \frac{2x^2+2x-40}{x^3-x}[/tex]

[tex]\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{a}{b}\div \frac{c}{d}=\frac{a}{b}\times \frac{d}{c}[/tex]

[tex]=\frac{x^2-25}{x^2-4x}\times \frac{x^3-x}{2x^2+2x-40}[/tex]

[tex]\mathrm{Multiply\:fractions}:\quad \frac{a}{b}\times \frac{c}{d}=\frac{a\:\times \:c}{b\:\times \:d}[/tex]

[tex]=\frac{\left(x^2-25\right)\left(x^3-x\right)}{\left(x^2-4x\right)\left(2x^2+2x-40\right)}[/tex]

[tex]=\frac{\left(x^2-25\right)x\left(x^2-1\right)}{\left(x^2-4x\right)\left(2x^2+2x-40\right)}[/tex]

[tex]\mathrm{Cancel\:the\:common\:factor:}\:x[/tex]

[tex]=\frac{\left(x^2-25\right)\left(x^2-1\right)}{2\left(x-4\right)\left(x^2+x-20\right)}[/tex]

∵ As factor  [tex]\left(x^2-25\right)\left(x^2-1\right)=\left(x+5\right)\left(x-5\right)\left(x+1\right)\left(x-1\right)[/tex]

so the expression becomes

[tex]=\frac{\left(x+5\right)\left(x-5\right)\left(x+1\right)\left(x-1\right)}{2\left(x-4\right)\left(x^2+x-20\right)}[/tex]

∵ As factor [tex]2\left(x-4\right)\left(x^2+x-20\right)=2\left(x-4\right)^2\left(x+5\right)[/tex]

so the expression becomes

[tex]=\frac{\left(x+5\right)\left(x-5\right)\left(x+1\right)\left(x-1\right)}{2\left(x-4\right)^2\left(x+5\right)}[/tex]

[tex]\mathrm{Cancel\:the\:common\:factor:}\:x+5[/tex]

[tex]=\frac{\left(x-5\right)\left(x+1\right)\left(x-1\right)}{2\left(x-4\right)^2}[/tex]

Therefore, the factors for the numerator [n] and denominator [d] after reducing will be:

[tex]\frac{x^2-25}{x^2-4x}\div \:\frac{2x^2+2x-40}{x^3-x}=\frac{\left(x-5\right)\left(x+1\right)\left(x-1\right)}{2\left(x-4\right)^2}[/tex]

A recipe for biscuits says to mix 6 cups of flour with 2 cups of milk. How many cups of flour would you need for 3 cups of milk?​

Answers

Answer:

9 cups of flour

Step-by-step explanation:

6 / 2 = 3

3 • 3 = 9

a=4, b = 5, A = 16
Solve the Triangle

Answers

Triangle has two solutions: a=4; b=5; c=1.051 and a=4; b=5; c=8.561.

Extra: #1 Obtuse scalene triangle.

Sides: a = 4   b = 5   c = 1.051

Area: T = 0.724

Perimeter: p = 10.051

Semiperimeter: s = 5.026

Angle ∠ A = α = 16° = 0.279 rad

Angle ∠ B = β = 159.846° = 159°50'45″ = 2.79 rad

Angle ∠ C = γ = 4.154° = 4°9'15″ = 0.073 rad

Height: ha = 0.362

Height: hb = 0.29

Height: hc = 1.378

Median: ma = 3.009

Median: mb = 1.517

Median: mc = 4.497

Inradius: r = 0.144

Circumradius: R = 7.256

Vertex coordinates: A[1.051; 0] B[0; 0] C[-3.755; 1.378]

Centroid: CG[-0.901; 0.459]

Coordinates of the circumscribed circle: U[0.526; 7.237]

Coordinates of the inscribed circle: I[0.026; 0.144]

Exterior (or external, outer) angles of the triangle:

∠ A' = α' = 164° = 0.279 rad

∠ B' = β' = 20.154° = 20°9'15″ = 2.79 rad

∠ C' = γ' = 175.846° = 175°50'45″ = 0.073 rad

the perimeter of a triangle is

88 centimeters. If two sides are equally long and the third side is

7 centimeters longer than the​ others, find the lengths of the three sides.

Answers

Side lengths are: 27,27, and 34.

Match each equation on the left to the mathematical property it uses on the right.

Answers

Answer: 1,d 2,e 3,c 4,b 5,a

Step-by-step explanation:

Number is from top to bottom on left and letters are same way on right.

Which graph shows different numbers of gold coins that colin can find go win more than 200 points?

Answers

Answer:

Step-by-step explanation:

Its the closed dot on 9. i just did the quiz. Your welcome.

Answer: the closed dots on 9 10 11 12 13 14

15

1. Eight people work in an office. They are paid hourly rates of 12£,15£,15£,14£,14£,13£,14£,13£

(a) Find: (i) the mean (ii) the median (iii) the mode.

Answers

12,13,13,14,14,14,15,15
mean: 13,75
median: 14
mode: 14
hope it helps! :)

1 point
The weights of laboratory cockroaches follow a Normal distribution with
mean 80 grams and standard deviation 2 grams. Use the figure from above.
About what percent of the cockroaches have weights less than 78 grams?
16%
none of these
32%
34%
O 2.5%

Answers

Answer:

16% of the cockroaches have weights less than 78 grams.

Option A is correct.

Step-by-step explanation:

Mean = 80 g

Standard Deviation = 2

We need to find percent of the cockroaches have weights less than 78 grams so, x=78

First we will find z using formula:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

Putting values of x, mean and Standard Deviation to find z

[tex]z=\frac{x-\mu}{\sigma}\\z=\frac{78-80}{2}\\z=-1[/tex]

We need to find P(z<-1)

Looking in the normal distribution table

[tex]P(z<-1)=0.15866\\P(z<-1)\approx 0.16\\Converting \ into \ percentage\\P(z<-1)=16\%[/tex]

So, 16% of the cockroaches have weights less than 78 grams.

Option A is correct.

Find the area of the figure shown below. Use 3.14 for π and round your answer to the nearest hundredth.

Answers

Answer:

ans: 111.54

Step-by-step explanation:

u can simple do by multiple

Answer:

38.24

Step-by-step explanation:

A middle school took all of its 6th grade students on a field trip to see a symphony at a theater that has 2500 seats. The students filled 66% of the seats in the theater. How many 6th graders went on the trip?​

Answers

Answer:

1650

Step-by-step explanation:

66% = 66/100

66/100 times 2500 = 0.66 times 2500 = 1650

There were 1650 students

1,650 students went
0.66*2500=1650

If a farmer is able to get 120 eggs from 20 chickens, how many eggs is the farmer able to get per chicken?

Answers

Answer:

6 eggs per chicken

Step-by-step explanation:

hdjdjidbdudbddjow0s

Answer:

6

Step-by-step explanation:

change the fraction 2/5 to a percent

A. 25%
B. 40%
C. 7%
D. none none of these choices are correct​

Answers

2/5 make denominator 100
2/5 = 40/100 = 40%

Answer: B

Step-by-step explanation:

If X equals -5 which number line shows the value of X

Answers

Answer:

There is no picture or graph, if you put a graph or picture ill be able to answer it.

Step-by-step explanation:

Pam drivers 14,735 miles in one year. The next year she drivers 13,869 miles. How many miles did she Drive in all?

Answers

Answer:28604 in total

Step-by-step explanation:

just copy and paste hope this helps

Answer:

28604 miles

Step-by-step explanation:

Just add the two numbers to get the total number of miles:

  14735

+ 13869=

  28604



Ben is planning to sell cookies and popcorn for a school bake sale. He is selling cookies, c, for $0.75 each and popcorn, p, for $1.00 per

bag. Interpret the expression 0.75c+p

Answers

The expression 0.75c + p represents the cost for the consumer for purchasing c cookies and p popcorn.

The coefficient 0.75 represents the cost of 75 cents per cookie and the coefficient of 1 before p represents the cost of $1.00 per bag of popcorn.

Which of these is equivalent to 3/8 x 5/6 Answer Correctly Or Dont Answer
A. 15/4
B. 16/5
C. 8/14
D. 8/48

Answers

A is the correct answer

complete the statements,extra points!!! please don't answer if you don't know ​

Answers

Answer:

1. 0.08703 killograms

2. Decameters

3. Liters

Step-by-step explanation:

convert.

plz help................

Answers

Answer:

Step-by-step explanation:

1,2222

2,3333

3,4444

4,5555

5,6666

6,7777

7,8888

8,9999

9,10101010

Other Questions
Does technology make you more intelligent or less so? If you look at recent scientific studies, you might be surprised to learn that while tech-savvy humans may be smarter about some things, were dumber about others. Certainly, the importance of technology in our everyday lives cant be disputed. It allows us to connect and work with people around the world, and it helps us keep track of our busy lives. On a broader scale, technology has improved the safety of transportation, productivity in the business world, andespecially in some parts of the worldaccess to higher levels of education. However, scientists now say there are some good reasons for using advanced technology in moderation. Recent studies show that technology has caused a loss of short- and long-term memory, a decrease in our ability to take in concepts and make connections, and a loss of creative drive.To understand one of the key impacts of living in such a connected world, ask yourself this question: How often do you have to look up a familiar phone numbersay, for your best friend or one of your children? Information that humans once stored in our minds is now delegated to smart phones. And according to an article in the online publication Futurism, 90 percent us can no longer remember numbers when we want towe suffer from digital amnesia. Chelsea Pullano, the author of Is Technology Making Us Dumb? explains that while modern humans know many more ways to find information, we no longer store that information in our brains. Perhaps more troubling, the trend applies not only to information stored1. How does the evidence in this second paragraph relate to the claim?2. What kind of reasoning does Simmons use in the second paragraph? Is her reasoning sound? Find the values of x and y in the equation below. Twenty percent of the 7th grade students like football. If there are 340 students in the 7th grade, how many like football?? Can someone plz help with 7-8 plz ASAP will give 10 points and mark brainliest why education and training important in professional I am give reason WILL MARK BRAINLIEST PLEASE HELP During project initiation, priorities and procedures are often most important, but as the project proceeds ____________ issues become the predominant source of conflict. someone please make a story for me idk A ball is kicked horizontally at 4.6 m/s off of a cliff 12.4 m high. How far from the cliff will it land? A) 2.5 mB) 1.6 mC) 7.4 m D) 4.1 m Besides opinions and the specific details included by the writer, what else should you look for in science articles to determine the author's perspective?tonethemespurposesignal words Native people in the Amazon rainforest use a toxin to help them catfish the toxin interferes with the gas exchange in the fish which makes them slow and easy to catch? An empty shipping box weighs 250 grams. The box is then filled with T-shirts. Each T-shirt weighs 132.5 grams. The equation W = 250 + 132.5T represents the relationship between the quantities in this situation, where W is the weight, in grams, of the filled box and T the number of shirts in the box. Select two possible solutions to the equation W = 250 + 132.5T . Which statement describes a physical property related to the particles thatmake up a material?A. Carbon is flammable because its atoms combine easily withoxygen atoms in the presence of heat.B. Fluorine is highly reactive with other elements because its atomshave 7 valence electrons.C. Neon is not reactive with other elements, because its atoms have8 valence electrons.D. Gold is a relatively dense metal because its atoms have moreprotons than atoms of many other metals. California, the most populous state, has approximately 4 x 107 people living in it. The population of the entire United States is approximately 3 x 108 . About how many times greater is the population of States than the population of California PLEASE HELP!!Which is the simplified form of the expression1 - StartFraction 1 Over q Superscript 30 Baseline EndFraction2 - q Superscript 303 - StartFraction p Superscript 12 Baseline Over q Superscript 60 Baseline EndFraction4 - p Superscript 12 Baseline q Superscript 60 26. (02.08)Which of the following represents the area of a rectangle whose length is x + 4 and whose width is x - 9? x2-36x2+ 5x - 36x-5x - 36x2+ 36x- 5 A cart is rolling along at a steady 6.6 m/s when it meets a slope. The cart accelerates at 2.0 m/s^2 as it rolls down the hill. How far from the top of the hill will the cart move in 5.5 s What is Velocity?*O The measurement of an object's speed and directionThe measurement of an object's tendency to remain at restHow fast an object travelsO Where an object travels during geography class students listed the number of the states they had visited.the responses were 12,9,17,7,5,4,2,1,8,5what is the Mean for the data set?A 3.2 statesB 2.8 states C7 states D not here Plz help me answer this!!!