Given g(x)=x^2-7x+1/4 show that the least possible value of g(x) is -12

Answers

Answer 1
The least vale of the function would be the vertex. To find the vertex first find the x value by using x= -b/2a
x=7/2 or 3.5
Now plug this in for x to find the y value.
y = (7/2)^2 -7(7/2) + (1/4)
y = (49/4) -(49/2) + (1/4)
y = (49/4) -(98/4) + (1/4)
y = (-48/4)
y = -12
The vertex is (3.5,-12)
The minimum (or max) of a function is the y value of the vertex so the min value is -12

Related Questions

Joel earns $1,500 per month. If he spends $375 on rent each month, what percent of his income does he spend on rent? A. 20% B. 40% C. 331/3% D. 25%

Answers

the rent percent each month is D
D 25% joel spends:D hopes this helped

Rewrite 11/15 as a decimal number. Round to the nearest thousandth. 1.363 1.364 0.733 0.734

Answers

The answer would be C) 0.733 because divide 11 and 15 and you get 0.733333 and since you wanted it rounded to nearest thousandth, its going to be 3 decimal spaces so remove the last three number 3's from the right and you end up with 0.733.

the expression 13x+5 represents the number of marbles you have after purchasing 13 bags of marbles. a. what does the term 13x represent b. what does 5 represent c. what does x represent

Answers

a. 13x can mean the number of bags of marbles times the number of marbles in each bag (the total number of marbles in 13 bags)

b. 5 can represent the initial numbers of marbles one has. For example, even before purchasing 13 bags of marbles you already had 5 marbles from before (they are like 5 extra marbles)

c. x can stand for the number of marbles in each bag 

At how many points does the graph of the function below intersect the x-axis?
y = 2x2 - 3x + 1
A.2
B.1
C.0

Answers

A.2 I did graph on my calculator finds out the function intersect both x-axis and y-axis(Hope it help:)
The discriminant, b^2 - 4ac, will tell you how many and what type of solutions you have in a quadratic equation.
a= 2 b= -3 c= 1
(-3)^2 -4*2*1
9-8=1
Since the discriminant is a positive real number, there will be two real solutions,
So the graph will cross the x axis in two places. The answer is A

round 2.36 to 1 significant figure

Answers

Final answer:

Rounding 2.36 to 1 significant figure results in 2, as the first non-zero digit remains unchanged when the subsequent digit is less than 5.

Explanation:

To round 2.36 to 1 significant figure, you look at the first non-zero digit, which is 2. Since the digit following it (3) is less than 5, the number 2 remains unchanged, and any digits after the 3 are dropped. Therefore, the number 2.36 rounded to 1 significant figure is simply 2.

To round 2.36 to 1 significant figure, we look at the digit after the first significant figure. If this digit is less than 5, we round down. If it is 5 or greater, we round up. In this case, the digit after the first significant figure is 6, which is greater than 5, so we round up. The rounded number to 1 significant figure is 2.4.

A conical paper cup has dimensions as shown in the diagram. How much water can the cup hold when full?

Answers

94.2 cm divided by pi which is 3.14 equals to 30 evenly hoped this helped yall out

The volume of the conical cup is approximately 94.25 cm³. This is the amount of water it can hold when full.

To find the volume of the conical paper cup, we'll use the formula for the volume of a cone:

[tex]\[ V = \frac{1}{3} \times \pi \times r^2 \times h \][/tex]

Where:

- ( V ) is the volume of the cone

- ( pi ) is a constant (approximately 3.14159)

- ( r ) is the radius of the circular base of the cone

- ( h ) is the height of the cone

Given:

- ( r = 3 ) cm (half the diameter)

- ( h = 10 ) cm

Substituting the given values into the formula:

[tex]\[ V = \frac{1}{3} \times \pi \times (3^2) \times 10 \][/tex]

[tex]\[ V = \frac{1}{3} \times \pi \times 9 \times 10 \][/tex]

[tex]\[ V = \frac{1}{3} \times 90\pi \][/tex]

[tex]\[ V = 30\pi \][/tex]

Now, let's calculate the approximate value of [tex]\( \pi \)[/tex] which is 3.14159:

[tex]\[ V \approx 30 \times 3.14159 \][/tex]

V≈94.2477

So, the volume of the conical paper cup is approximately [tex]\( 94.2477 \, \text{cm}^3 \) or \( 94.25 \, \text{cm}^3 \)[/tex] rounded to two decimal places. This is the amount of water the cup can hold when full.

How to graph x>4 on the number line

Answers

You draw a circle on top of 4, but don't fill it in, and then an arrow coming out of it and going to the right until the end of the number line. At least, that's how I'd do it, if this answer doesn't add up with what you've been doing in class then it's probably the wrong one

The length of a rectangle is 6 yards longer than its width. If the perimeter of the rectangle is 32 yd, find its area in square yards.

Answers

Let, width = x
Length = x + 6

Now, perimeter, 2(l+b) = 2(x+6+x)
2(2x+6) = 32
4x + 12 = 32
4x = 20
x = 5 &
x+6 = 5+6 = 11

As rectangle's dimensions are 11*5, it's area would be: 11 * 5 = 55 yards²

So, your final answer is 55 Yd²

Hope this helps!
Final answer:

First, find the width by using the perimeter formula for a rectangle, solve the equation, and then calculate the length by adding 6 yards. With both widths, calculate the area. The rectangle's area is 55 square yards.

Explanation:

To solve for the area of the rectangle, we must find its length and width first. The given condition is that the length is 6 yards longer than the width. If we denote the width as w yards, then the length would be w + 6 yards.

Since the perimeter is the sum of all sides, for a rectangle, it can be calculated by the formula P = 2l + 2w, where P is the perimeter, l is the length and w is the width. Substituting the given perimeter (32 yd) and the expressions for length and width, we have:

32 yd = 2(w + 6 yd) + 2w32 yd = 2w + 12 yd + 2w32 yd = 4w + 12 yd32 yd - 12 yd = 4w20 yd = 4ww = 5 yd (width)l = w + 6 yd = 5 yd + 6 yd = 11 yd (length)

Now that we have both dimensions, the area of the rectangle can be calculated using the formula A = l × w. Substituting the found values:

Area = 11 yd × 5 yd = 55 yd²

Therefore, the area of the rectangle is 55 square yards.

When the nth root of a is written, it is the positive value that is shown

Answers

The nth root of a is always positive unless, a < 0 and "n" is an odd number. Also if a < 0 and "n" is an even number, then it's an imaginary number. I hope this helps a lot

Jackie deposited $315 into a bank account that earned 1.5% simple interest each year.If no money was deposited into or withdrawn from the account, how much money was in the account after ​3​ years?Round your answer to the nearest cent.Enter your answer in the box.$

Answers

It would probably be $329.20

pens cost 20p each and pencils cost 12p each

if I want to buy 6 pens and 5 pencils

what will be the total ?

Answers

6pens cost=20p×6=120p 
5pencils cost=12p×5=60p
total =6pens+5pencils
        =120p+60p
        =180p
        ⇒1rupee 80p

i don't know the answer can you help me

In the Numbers Game, a state lottery, four numbers are drawn with replacement from an urn containing balls numbered 0-9, inclusive. Find the probability that a ticket holder has the indicated winning ticket. (Put your answer to three decimal places.)
Three digits in exact order.

Answers

P(first number correct) = 1/10
P(second number correct) = 1/10
P(third number correct) = 1/10
P(fourth number correct) = 1/10

P(all four numbers correct) = 1/10 x 1/10 x 1/10 x 1/10
= 1/10000
= 0.0001

In a circle, a 90 degree sector has area of 64pi ftsqd. what is the radius of the circle? ...?

Answers

Area = 64π x 4
A = πr2.
r = √(A/π) 

radius = 16

Answer:

16

Step-by-step explanation:

If 7 is added to the square of a postitive integer, the result is 43. Find the positive integer.

Answers

subtract 7 from 43. which equals 36. then find the square which is 6.

Suppose that a "code" consists of 4 digits, none of which are repeated. (a digit is one of the 10 numbers 0,1,2,3,4,5,6,7,8,9) how many codes are possible?

Answers

The answer is 5040.

This is permutation without the repetition:
P = n!/(n - r)!

n - the number of choices
r - the number of chosen

We have:
n = 10
r = 4

P = 10!/(10 - 4)!
   = 10!/6!
   = (10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1) / (6 * 5 * 4 * 3 * 2 * 1)
   = 10 * 9 * 8 * 7
   = 5040

What is the value of x in 5(2x - 7)=15x-10?

Answers

Step  1  :Equation at the end of step  1  : 5 • (2x - 7) - (15x - 10) = 0 Step  2  :Step  3  :Pulling out like terms :

 3.1     Pull out like factors :

   -5x - 25  =   -5 • (x + 5) 

Equation at the end of step  3  : -5 • (x + 5) = 0 Step  4  :Equations which are never true :

 4.1      Solve :    -5   =  0

This equation has no solution.
A a non-zero constant never equals zero.

Solving a Single Variable Equation :

 4.2      Solve  :    x+5 = 0 

 Subtract  5  from both sides of the equation : 
                      x = -5 

One solution was found :                   x = -5

The value of x in 5(2x - 7)=15x-10 is 5

What is Algebraic expression ?

Algebraic expressions are the idea of expressing numbers using letters or alphabets without specifying their actual values. The basics of algebra taught us how to express an unknown value using letters such as x, y, z, etc. These letters are called here as variables. An algebraic expression can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is a coefficient.  

Here, the Algebraic expressions with variable in x is given :

5(2x - 7)=15x-10

which is solved using properties of multiplication and solving for value x by arranging variables and constant separately aside:

5(2x - 7)=15x-10  

20x - 35 = 15x -10

20x -15x = 35-10

5x = 25

x= 5

Therefore, the value of x in 5(2x - 7)=15x-10 is 5

more on algebraic expression at :

brainly.com/question/20660076

#SPJ2

Find the secant of both angle A and angle B.

A. sec A = 13/5; sec B = 13/12
B. sec A = 13/12; sec B = 13/5
C. sec A = 12/13; sec B = 5/13
D. sec A = 24/10; sec B = 10/24

Answers

Final answer:

The secant of angle A is 13/5 and the secant of angle B is 13/12. Option A is correct.

Explanation:

To find the secant of angle A and angle B, we need to use the reciprocal function of cosine which is secant. The secant of an angle is equal to the reciprocal of the cosine of that angle.

So, if sec A = 13/5, it means that the cosine of angle A is equal to 5/13. Similarly, if sec B = 13/12, it means that the cosine of angle B is equal to 12/13.

the price of an item has been reduced by 65% . the original price was $41 .

Answers

If you're asking for the price now it's been reduced, then this is how you work it out.
41 ÷ 2 = 20.5. = 50%
41 ÷ 10 = 4.1 = 10%
4.1 ÷ 2 = 2.05 = 5%.
20.5 + 4.1 + 2.05 = 26.65 = 65%
41 - 26.65 = $14.35 (the answer)

a radius is a segment that connects any point on the circle to any point inside of that circle

true or false?

Answers

False.

The radius is a line that connects any point on the circle to center. Radius is a constant size line and not line that changes its size therefore it cannot connect any point on circle to any point inside of that circle. 

Answer:

If the question is to the center of that circle instead of "any point inside of that circle" then the answer is true.

Step-by-step explanation:

I got it wrong because I didn't read it all but it is true if it is to any point inside of that circle.

which of the numbers listed below are solutions to the equation?
Check all that apply.
x^2 = 7
A. None of these.
B. square root of 7
C. 49
D. 14
E. negative sqr root of seven
F. -49

Answers

The solution for the given equation is square root of 7. Therefore, option B is the correct answer.

What is an equation?

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The given equation is x²=7.

The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.

For the given equation x²=7, square root on both the sides.

That is, x=±√7

Therefore, the solution of the equation is x=±√7.

To learn more about an equation visit:

https://brainly.com/question/14686792.

#SPJ2

help plz asap the question in the picture

Answers

MAY i ASK where is the picture my good kind sir?

Choose the correct simplification of the expression (5xy5)2(y3)4.

Answers

I hope this helps you

Answer:

[tex]25x^{2}y^{22}[/tex] is the answer.

Step-by-step explanation:

The given expression is [tex](5xy^{5})^{2}(y^{3})^{4}[/tex].

Now we have to simplify the expression given in the question.

[tex](5xy^{5})^{2}(y^{3})^{4}=(5)^{2}(x)^{2}(y^{5})^{2}(y^{3})^{4}=25x^{2}y^{10}y^{12}=25x^{2}y^{10+12}=25x^{2}y^{22}[/tex]

Therefore the simplified form of the expression will be [tex]25x^{2}y^{22}[/tex]

What is 50/100 in its simplest form as a fraction?

Answers

In simplest form it would be 1/2 since 50 and 100 are divisible by 50.  

Answer: 1/2

Step-by-step explanation: 1/2 bc 50 and 50 is like 1/2 and 1/2

Hope this helped ya! :}

Edit: js realized this was 7 years ago-

Determine whether the infinite geometric series is convergent or divergent. If it is convergent, find its sum. (If the series is divergent, enter DIVERGENT.)

(1)-(1/6)+(1/36)-(1/216)+... ...?

Answers

The geometric series can be rewritten as
1 + (-1/6) + (-1/6)^2 + (-1/6)^3 + ...
Since the magnitude of the common ratio is less than 1. The series is then convergent and it has a sum.
S = a/(1-r) = 1/(1+1/6) = 6/7

I hope my answer has come to your help.

2280÷60 how to work it out

Answers

you could do 228/6 = 38 

2280/60 = 38

hope this helps you

Metrics are based on the british system of weights and measures. true false

Answers

I looked it up, and it said false.

Answer: it is false :)


What percent us 28 of 70?

Answers

   
[tex]\displaystyle\\ \frac{28}{70} ^{(7} = \frac{4}{10} = \frac{40}{100} = \boxed{40\%}[/tex]



I feel like I am asking so my questions but I dont really care its a Sunday xD
Solve:
-2x - 1 + 3x =7

Answers

you would add like terms so it would be 1x then you add 1 to 7 so you would get 8.. the you divide both sides by 1x and you'd get 8=x

Answer:  x = 8

−2x − 1 + 3x =7

−2x + −1 + 3x =7

(−2x+3x) + (−1) =7 (Combine Like Terms)

x+ −1 =7

x−1=7

Step 2: Add 1 to both sides.

x−1+1=7+1

x=8

How do you number 3 and can you explain everything for detail please

Answers

-y = x + 3   . . . . this is the sides for the double lines

2y + 24 = x + 9 . . . . this is the sides for the single lines

To solve you need to substitute one equation into the other

-y = x + 3
y = -x - 3  . . . place this equation into the other equation where (Y) is

2y + 24 = x + 9
2 ( -x - 3) + 4 = x +9
-2x - 6 + 24 = x + 9
-2x +18= x+9
-3x = -9
x = 3  . . . substitute this answer into the equation and solve for (Y)

-y = x + 3
- y = 3 +3
-y = 3 + 3
 y= -6





{(3,2), (-6,2), (7,3), (8,4)}

What is the range of this function?

A) {2, 3, 4}

B) {7, 3, 8, 4}

C) {3, -6, 7, 8}

D) {3, 2, -6, 2}

Answers

the range of a function is all the y values.
So ur range is { 2,3,4}...if they repeat more then once, u only have to write them once
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