Quadratic function has minimum value which is -8.
correct option: 1
What is quadratic equation?A variable with the largest power of two in a quadratic equation is called a variable. Quad, which signifies square, is the root of the term quadratic. The phrase must be two times its own strength, neither higher nor lower.
Given that they are the x values for which f(x) = 0, the roots of the function f(x) = ax² + bx + c correspond to the solutions of the quadratic equation ax² + bx + c = 0.
The term ax² is known as the quadratic term (hence the function's name), the word bx is known as the linear term, and the value c is known as the constant term.
Here, the given function,
f(x) = x² - 2x - 7 .......... (i)
now, differentiate with respect to x
d/dx {f(x)} = d/dx ( x²) - d/dx (2x) - d/dx (7)
or, f'(x) = 2x - 2 ............. (ii)
Now, put f'(x) = 0
so, 0 = 2x - 2
or, 2x - 2 = 0
or, 2x = 2
or, x = 1
From equation (ii)
f'(x) = 2x - 2
now, differentiate with respect to x
f''(x) = 2 > 0
So, it implies that, the function has minimum value at x = 1
Now, putting x = 1 in equation (i), we get -
f(1) = (1)² - 2×(1) - 7
f(1) = - 8
Function has minimum value is: - 8.
Thus, correct option is : (1)
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Which numbers could be a solution to the inequality? -6 < 3x+ 9 <21
Step-by-step explanation:
-6-9<3x<21-9
-15<3x<12
1) -15<3x
-5<x
2) 3x<12
x<4
so the range of the solution is -5<x<4
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Answer:
(-10,0)
Step-by-step explanation:
y = 3/2 x + 15
To find the x intercept let y =0 and solve for x
0 = 3/2x +15
Subtract 15 from each side
-15 = 3/2x -15+15
-15 = 3/2x
Multiply each side by 2/3
2/3 *-15 = 2/3 * 3/2x
-10 =x
The x intercept is
(-10,0)
Answer: (-10,0)
Step-by-step explanation:
30 POINTS!! PLEASE HELP
Mai created a scale model of a shoe store her company plans to build. The ratio of the model's dimensions to the dimensions of the actual shoe store to
be built is 1:20. If the volume of the model was 35 ft, what is the volume of the actual shoe store that Mai's company plans to build?
Answer:
it's 700 so last one
Step-by-step explanation:
since it's 1 to 20 you multiply 35×20 and you get 700
Which of the following could be the areas of the three squares below?
Answer:
A. 12 ft², 16 ft², and 20 ft²
Step-by-step explanation:
Do think it is A, B, C, D?
Answer:
D
Step-by-step explanation:
the 80*10=800
8 in 183= 80
8 in 4879 = 800
A book costs $1.49 and is sold in a retail store for $8.99. What is the percentage in mark up? *
Answer:
603.35%
Step-by-step explanation:
Given that a book costs $ 1.49 and is sold in a retail store for $ 8.99, to determine what is the percentage in mark up, the following calculation must be performed:
1.49 = 100
8.99 = X
8.99 x 100 / 1.49 = X
899 / 1.49 = X
603.35 = X
Thus, the mark up percentage of the book is 603.35%, which implies an increase of more than 6 times its initial value.
Use the Trig Ratios to find the Missing Side Length
Answer:
[tex] \tan(55) = \frac{x}{8} \\ x = \tan(55) \times 8[/tex]
The radius of a cylindrical water tank is 4 ft, and its height is 10 ft. What is the volume of the tank?
Answer:
502 cubic feet
Step-by-step explanation:
The Volume of the tank is 502 cubic feet.
what is the measure of m?
6
24
m
n
Answer:
m=√180
Step-by-step explanation:
n² = 6×24
n² = 144
m² = n² + 6²
m² = 144 + 36
m² = 180
m =√180
Translate the phrase into an algebraic expression. The difference of c and 6
Answer:
c - 6
Step-by-step explanation:
differnce is subtraction
so subtract.
5x≥25 help th bewbsanks
Austin’s bus arrives at 7:55am if he starts his chores at 7:30 am will he be done in time to meet his bus explain your reasoning answer key
Answer:
it depends on his chores, how many he has, and how he does them
Step-by-step explanation:
Answer:
Yes
Step-by-step explanation:
I had the same question his chores only last for 15 minutes so yes he would be done in time
If the logarithm of 5832 is 6, what is the base?
[tex] logx(5832) = 6[/tex]
Answer:
The base is 4.2426.
Step-by-step explanation:
Logarithm definition:
Suppose we have that:
[tex]\log_{a}{b} = c[/tex]
It means that;
[tex]b = a^c[/tex]
In this question:
[tex]\log_{x}{(5832)} = 6[/tex]
It means that:
[tex]x^6 = 5832[/tex]
[tex]x = \sqrt[6]{5832}[/tex]
[tex]x = (5832)^{\frac{1}{6}}[/tex]
[tex]x = 4.2626[/tex]
The base is 4.2426.
Which is the function g(x) for a restricted domain?
O g(x) = 3x-4; 2-4
O g(x) = 3x + 4; x > 0
O g(x) = 3/x+4; x 24
O g(x) = 35-4;> 0
The answer choice which correctly describe s the function g (x) for a restricted domain as required to be determined in the task content is; g (x) = ³√(x + 4) , x ≥ -4.
Which function correctly represents the function g (x) for a restricted domain?As evident in the task content, the function which correctly represents the function g (x) for a restricted domain is to be identified.
By observation of the function;
g (x) = ³√(x + 4) , x ≥ -4.
As evident in the task content; the lowest value of g(x) is; 0.
By checking; when x = -4; the corresponding value of g (x) is;
g (-4) = ³√(-4 + 4)
g (-4) = 0.
On this note, the required function is; g (x) = ³√(x + 4) , x ≥ -4.
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5/6 x 2 2/5 solve using distributive property to find the problem
Answer:
2
Step-by-step explanation:
Answer:
5/6 x 2 2/5 = 2
Step-by-step explanation:
https://www.fractioncalc.com/
This calculator link will help you with fraction equations
:))
Which graph shows a dilation?
Answer:
Step-by-step explanation:
Sorry but im struggling with this too :(
Help! Will Give Brainliest!!!!
Answer:
The answer is C or B i dont really know
Step-by-step explanation:
can i get help on this?
complete the table below to show the differences bettween algebraic expression and equation
Complete the table below to show the differences between algebraic
expression and equation.
Describe each to show their differences.
Give 3 examples of each.
Answer:
Explained below with examples
Step-by-step explanation:
1. Algebraic expression in mathematics are basically expressions that are formed from variables, integer constants, and also algebraic operations.
Examples include;
>> 2x² − xy
>> 3ab + 2b²
>> x² + y²
2. An algebraic equation is a phrase where the two sides of the equation which are the left and right hand sides are connected by the equal to sign (=).
Examples are;
>> 3y - y² = 2y² + 2
>> 3x - 4y = x + 2
>> 5a + 3b = 2b - 1
There are 17 girls and 23 boys in P.E class.Of these students,10 girls and 14 boys will try out for basketball.What percentage of the stidents will try out for basketball?
Answer:
[tex]60%[/tex]%
Step-by-step explanation:
[tex]17+23=40[/tex][tex], 40[/tex] in total.
[tex]10+14=24[/tex], 24 students trying out.
24 of 40 as a percent[tex]=60[/tex]
Answer:
60%
Step-by-step explanation:
According to formula if finding percent, given number(10+14)divide by total number(17+23) multiply 100% which is 24/40*100= 60%
7 1/2 divided by 3/4
Answer:
2 2/3
Step-by-step explanation:
Answer:
10
Step-by-step explanation:
First convert to mixed fractions 7 1/2-> 15/2
Then multiply by the reciprocal---> 15/2 x 4/3
The answer is 60/6
Then simplify---> 10/1 or 10
Determine whether the given equation has one solution, no solution, or infinitely many solutions. 2 - 3(x+ 4) = 3(3 - x) cannot be determined one solution Ono solution infinitely many solutions.
Answer:
no solution
Step-by-step explanation:
The given equation is :
2 - 3(x+ 4) = 3(3 - x)
We need to solve the equation. It can be done as follows :
2-3x-12 = 9-3x
As -3x gets canceled from both sides. It means the given equation has no solution.
x2 + 16x – 2 = 11
1) Rewrite the equation by completing the square.
Your equation should look like (x + c)2 = d or (x - c)2 = d.
I
+
utan
pls help
Answer:
(x+8)^2=77 and x=negative 8±√77
Step-by-step explanation:
After watching a video, I got it right on Khan
The equation with completing the squares is (x + 8)² = 77.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 4 = 9 is an equation.
We have,
x² + 16x - 2 = 11
We can make complete squares.
x² + 16x - 2 - 11 = 0
x² + 16x - 13 = 0
x² + 2 x 8 x (x) -8² + 8² - 13 = 0
(x² + 16x + 8²) - 64 - 13 = 0
(x + 8)² - 77 = 0
(x + 8)² = 77
Thus,
The equation is (x + 8)² = 77.
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g(r) = (r + 14)? – 49
1) What are the zeros of the function?
Write the smaller r first, and the larger T second.
Answer:
smaller r =-21
larger r =-7
The vertex of the parabola is at
(-14,-49)
A plane traveling 480 miles in 1 hour travels how far in 15 minutes
Answer:
120 Miles
Step-by-step explanation:
What is the answer for (a^2+12c)÷7b-1
34 in.
16 in.
22 in.
Lateral Surface Area =
in squared
Total Surface Area =
in squared
Volume =
in cubed
Answer:
Step-by-step explanation:
Lateral surface area of the triangular prism = Perimeter of the triangular base × Height
By applying Pythagoras theorem in ΔABC,
AC² = AB² + BC²
(34)² = (16)² + BC²
BC = [tex]\sqrt{1156-256}[/tex]
= [tex]\sqrt{900}[/tex]
= 30 in.
Perimeter of the triangular base = AB + BC + AC
= 16 + 30 + 34
= 80 in
Lateral surface area = 80 × 22
= 1760 in²
Total Surface area = Lateral surface area + 2(Surface area of the triangular base)
Surface area of the triangular base = [tex]\frac{1}{2}(\text{Base})(\text{Height})[/tex]
= [tex]\frac{1}{2}(30)(16)[/tex]
= 240 in²
Total surface area = 1760 + 2(240)
= 1760 + 480
= 2240 in²
Volume = Area of the triangular base × Height
= 240 × 20
= 4800 in³
28÷x=168
What is the value of "x"
A small bar of gold measures 20 mm by 250 mm by 2 mm. One cubic millimeter of gold weighs about
0.0005 ounces. Find the volume in cubic millimeters and the welght in ounces of this small bar of gold.
cubic millimeters and the weight of the bar is
The volume of the bar is
ounce(s).
Answer: 5 ounces
Step-by-step explanation:
volume is 20*250*2=10000 cubic mm
10,000*0.0005=5
Emily and her twin sister Erica were each given $500 for their birthday. Emily deposits her money in an account that pays 4.75% interest compounded annually. Erica deposits her money in a 5% simple annual interest account. After 10 years how much more money will Emily have in her account?
A $22.41
B $45.26
C $250.00
D $295.26
Answer:
B $45.26
Step-by-step explanation:
After 10 years
Emily will have 500 * 1.045^10 = $795.26
Erica will have 500 + 10*0.05*500 = 500 * 1.5 = 750$
Emily will have $45.26 more.