g(6) must be greater than 21 which is 22 only.
What is function?In mathematics, a function is an expression, rule, or law that establishes the relationship between an independent variable and a dependent variable.
Since g'(x) > 0 for all x and we know that g(x) is an increasing function.
Additionally, since g"(x) > 0 for all x, we know that g(x) is a concave-up function.
Since g(x) is increasing, we know that g(6) > g(5) = 18.
Now, we can use the fact that g(x) is concave-up to find a lower bound on g(6).
By the definition of concave-up, we know that the slope of the tangent line to g(x) is increasing.
This means that the slope of the line connecting (3,g(3)) to (5,g(5)) is less than the slope of the line connecting (5,g(5)) to (6,g(6)).
Using this information, we can find a lower bound on g(6):
g(5)- g(3) / (5-3) < g(6)- g(5)/ (6-5)
18- 12/2 < g(6)- 18
3 < g(6) - 18
g(6) > 21
Therefore, g(6) must be greater than 21.
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Given a prime $p$ and an integer $a$, we say that $a$ is a primitive root $\pmod p$ if the set $\{a,a^2,a^3,\ldots,a^{p-1}\}$ contains exactly one element congruent to each of $1,2,3,\ldots,p-1\pmod p$.For example, $2$ is a primitive root $\pmod 5$ because $\{2,2^2,2^3,2^4\}\equiv \{2,4,3,1\}\pmod 5$, and this list contains every residue from $1$ to $4$ exactly once.However, $4$ is not a primitive root $\pmod 5$ because $\{4,4^2,4^3,4^4\}\equiv\{4,1,4,1\}\pmod 5$, and this list does not contain every residue from $1$ to $4$ exactly once.What is the sum of all integers in the set $\{1,2,3,4,5,6\}$ that are primitive roots $\pmod 7$
Only 3 & 5 from the set {1,2,3,4,5,6} are primitive root (mod7), therefore, sum of integers is 3 + 5 = 8.
What is primitive root?A number g is a primitive root modulo n if every number a coprime to n is congruent to a power of g modulo n in modular arithmetic. That is, g is a primitive root modulo n if for every integer a coprime to n, some integer k for which gk ≡ a (mod n).
The index or discrete logarithm of a to the base g modulo n is a value k like this. So, if and only if g is a generator of the multiplicative group of integers modulo n, g is a primitive root modulo n.
In Article 57 of his Disquisitiones Arithmeticae (1801), Gauss defined primitive roots and credited Euler with coining the term.
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(x - 7)2 + (y + 5)2 = 4
what’s the center and radius
Answer:
(7, - 5 ) and r = 2
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
(x - 7)² + (y + 5)² = 4 ← is in standard form
with centre = (h, k ) = (7, - 5 ) and r = [tex]\sqrt{4}[/tex] = 2
Craig won first prize in Mrs. Short's class
so he gets to pick a prize from the treasure
box. He doesn't know what he wants, so
he is going to chose randomly. There are 7
different gift card prizes: fast food, ice cream,
CD's, DVD's, movies, the mall and Carowinds.
If there is an equal number of each card in
the box, what is the probability he will pull out
the gift card for Carowinds?
Group of answer choices
0/7
6/7
1/7
1/2
Answer:
[tex] \frac{1}{7}[/tex]
Answer:
1/7
Step-by-step explanation:
there is seen prizes and he pulls seven times so the odds would be 1/7
state if the function is a growth or decay and the factor
y=2x
Answer:
the function shows growth of a factor of 2
Step-by-step explanation:
In the diagram below, transversal t intersects parallel lines I and m.
What is the value of x?
Step-by-step explanation:
x+10=116
x=116-110
=106
x=106
253 x 804 =
Solve by using standard algorithms
Answer:
203412
Step-by-step explanation:
253
*804
___
16
40
32
20
12
______
203412
This is a Vedic Math trick you can use to multiply fast, called the criss-cross method.
PLS FIND X ASAP PLS PLS
Answer:
1- the figure doesn't provide enough information from what I'm aware of
2- x= 17.78
3- x=12
4- x=19
Step-by-step explanation:
Bru.h I suck at doing this and mostly like DECIMALS I don’t like that- someone pl help me
Answer:
D
Step-by-step explanation:
Answer:
5,006.04
Step-by-step explanation:
Hope it Helps!
:)
Convert the improper fractions to mixed numbers
Answer:
28.1 7/8
29.3
30.18/8=9/4=2 1/4
Step-by-step explanation:
Answer:
28. 1 [tex]\frac{7}{8}[/tex]
29. 3
30. 2[tex]\frac{2}{8}[/tex]
Manchu has drawn a
rectangle with a base of
24 cm and an area of
336 cm². He cuts the
rectangle as shown to make two triangles.
What are the height and area of each
triangle?
Answer:
Height of each triangle: 14cm
Area of each triangle: 168cm²
Step-by-step explanation:
So we know that the base of the area is 24. Lets find the height.
336 ÷ 24 = 14
If he makes two triangles out of the rectangle that just means he cuts it in half.
To find the area of one triangle lets do:
336 ÷ 2 = 168
Let's double check our answer:
(14 × 24) ÷ 2 = 168
Seems great!
Amelia made a line plot of her scores on 25-point math quizzes. What is the difference between the total of her most frequent number of points per quiz and the total of her greatest number of points scored per quiz? A. 0 points B. 6 points C. 18 points D. 22 points
Answer:
I think it B.
Step-by-step explanation:
I NEED HELP ASAP!!! PLEASE HELP ME!!!!!!!
A cubical box has each edge 10 cm and another cuboidal box is 12.5 cm long, 10 cm wide and 8 cm high. Which box has the greater lateral surface area and by how much
On solving the provided question, we can say that So, the total surface area of cuboid is larger by (610 — 600 = IO) cm2
what is cuboid?A cuboid is a solid or three-dimensional form in geometry. A cuboid is a convex polyhedron having 8 vertices, 12 sides, and 6 rectangular faces. Another name for a cuboid is a cuboid. A cube is a cuboid with six square faces. Boxes include things like books and bricks. The following are the key variations between cubic and cubic: In contrast to a cube, which has rectangular faces, a cube has six equally sized square faces. Even though the cube and cuboid structures have a similar appearance, they differ in some ways in terms of side length, diagonal, and area.
(Lateral surface area of cube = 4edge2
lateral surface area of cuboid =2h (l + b)
[tex]2 x 8(12.5+ 10)\\= 16 x 22.5\\= 360\\[/tex]
lateral surface area of the cube is larger by (400
- 360
= 40)cm2
Total surface area of cube = 6edge2
= 600
lateral surface area of cuboid
[tex]=2 (lb + bh + hl)\\2(12.5 x 10+ x 8+8 x 12.5)\\= 2 (125 + 80 + 100)\\= 610[/tex]
So, the total surface area of cuboid is larger by (610 — 600 = IO) cm2
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A $1,200 bond earns 3% simple interest per year on its purchase price. What is the amount of interest earned after 15 MONTHS?
Select one:
$1245
$3
$36
$45
Answer:
45$
Step-by-step explanation:
Answer:
$45
Step-by-step explanation:
$1,200 x 0.03% = $36 yearly
$36/12 = $3 per month
$3 x 15 months = $45
What is the greatest possible quotient of any two distinct members of the set $\left\{\frac{2}{5}, \frac{1}{2},5,10\right\}$? Specifically, we wish to maximize $\frac{x}{y}$, where $x$ and $y$ are chosen from the previous set.
The greatest possible quotient of any two distinct members of the set; { 2 / 5, 1 / 2, 5, 10 } as required to be determined is; 25.
What is the maximum possible quotient of any pair of numbers from the set?It is evident from the task content that the set from which the two numbers whose quotient is to be maximised is; { 2 / 5, 1 / 2, 5, 10 }.
On this note, since the quotient which is to be maximised is hypothetically; x / y;
Therefore, in a bid to maximize the result of the quotient; it follows that the numerator, x must be as great as possible and the denominator, y must be as less as possible.
On this note, since the maximum number in the set is 10 and the minimum is 2 / 5; we have that;
10 / (2 / 5)
= ( 10 × 5 ) / 2
= 25.
Ultimately, it can be inferred that the greatest possible quotient as required is; 25.
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Need help answering this question!!!!
What are the 3 algorithms?
Sequencing, selection, and iteration are the three fundamental building blocks that make up an algorithm.
What is algorithm?An algorithm in mathematics is a process, a description of a series of steps that can be used to solve a mathematical computation, but they are now much more prevalent than that. The long division algorithm is perhaps the most well-known application of algorithms in science (and in daily life, for that matter).
Algorithms are all about figuring out the most effective ways to perform the math, despite the fact that the above explanation might sound a little fussy and detailed. Mathematicians are known for being lazy, so they frequently seek out shortcuts, as the anonymous mathematician puts it. For locating these short cuts, algorithms are used.
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Pls help me to do this
Answer:
1. 2 more children
2. 13 centimeters
3. Can't determine without ruler
Step-by-step explanation:
1. 5-3 = 2
2. 22-9 = 13
Please help me answer this math question !
Answer:
y=-3x+6
Step-by-step explanation:
Which is the product of [tex]\frac{7}{9\\}[/tex] and 6?
( 100 POINTS )
Answer:
[tex] \sf \: \frac{14}{3} [/tex]
Step-by-step explanation:
Given problem,
[tex] \sf \rightarrow \: \frac{7}{9} \times 6[/tex]
Let's solve the problem,
[tex] \sf \rightarrow \: \frac{7}{9} \times 6[/tex]
[tex] \sf \rightarrow \: \frac{(7 \times 6)}{9} [/tex]
[tex] \sf \rightarrow \: \frac{42}{9} [/tex]
[tex] \sf \rightarrow \: \frac{14}{3} [/tex]
Hence, the product is 14/3.
can you find the proportion pwease :)
Answer:
15 cookies, 10 brownies.
Step-by-step explanation:
I'm assuming that she is selling the same amount of cookies and brownies per hour. If that is the case...
Multiply it by 5. If 3 cookies were sold in one hour, and there's 5 hours, just multiply 3 by 5. Total number is 15 cookies.
Same goes for brownies. Multiple 2 brownies by 5. That makes 10 brownies.
Is the area of an equilateral triangle is 9 root 3 cm square then the semi perimeter of the triangle is?
The equilateral triangle has a 9 root 3 cm square area, and its semi-perimeter is 9 cm.
what is triangle ?A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric forms. The name given to a triangle with the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.
given
area of equilateral triangle = [tex]9\sqrt{3}cm^{2}[/tex]
formula of area of equilateral triangle = [tex]\frac{\sqrt{3}a^{2} }{4} sq.units[/tex]
a = side of triangle
[tex]\frac{\sqrt{3}a^{2} }{4} sq.units[/tex] = [tex]9\sqrt{3}cm^{2}[/tex]
[tex]a^{2} = \frac{4* 9\sqrt{3} }{\sqrt{3} }[/tex]
[tex]a^{2} = 36\\ a = 6 cm[/tex]
since equilateral triangle all sides are equal
perimeter of triangle = 6 + 6 + 6
= 18cm
the semi perimeter of the triangle = 18 /2 = 9 cm
The equilateral triangle has a 9 root 3 cm square area, and its semi-perimeter is 9 cm.
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how do i answer this question
The constant of variation for the given data is 1/4.
What is the constant of proportionality?If the corresponding elements of two sequences of numbers, frequently experimental data, have a constant ratio, known as the coefficient of proportionality or proportionality constant, then the two sequences of numbers are proportional or directly proportional.
Given that the data in the table is,
x f(x)
-8 -2
-4 -1
0 0
4 1
8 2
The constant of proportionality will be calculated as,
F(x) = kx
-2 = k x -8
k = -2 / -8
k = 1 / 4
Here, the proportionality constant will be 1/4.
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what is the distance between (-3,5) and (4,5)
Answer: 7
Step-by-step explanation:
Distance (d) = √(4 - -3)2 + (5 - 5)2
= √(7)2 + (0)2
= √49
= 7
ΔX = 4 – -3 = 7
ΔY = 5 – 5 = 0
y = 0x + 5
When x=0, y = 5
Answer:
Step-by-step explanation:
D = SQRT(x 2 - x 1) 2 + (y 2 - y 1) 2
X2 Y2
(-3,5)
X1 Y1
(4,5)
D= SQRT (-3-4)^2 + (5-5)^2
D= SQRT 49
D=7
which fraction is greater? a)3/18,2/6
Answer:
2/6
Step-by-step explanation:
The LCD of 18 and 6, so when you multiply 2/6, it will be 5/18. So 5/18 is greater than 3/18
Answer:
3/18 is smaller than 2/6
Step-by-step explanation:
8. The price of a hoodie on sale increased from $25 to $45. By what percentage was the price of the hoodie increased?
Answer:
44.44%
Step-by-step explanation:
L) simplify
sin²x ( cot²x + 1 )
Answer: 1.
Step-by-step explanation:
[tex]\displaystyle\\sin^2x(cot^2x+1)=\\\\sin^2x(\frac{cos^2x}{sin^2x}+1)=\\\\\frac{sin^2xcos^2x}{sin^2x}+sin^2x=\\\\cos^2x+sin^2x=\\\\1.[/tex]
ILL GIVE BRAINLIEST
Answer:
I can't read the question it's too blurry
Need help ASAP. Question in photo. Will mark brainliest if correct
Answer:
C
Step-by-step explanation:
I did this question today, pls lmk if u get it right
Factor the algebraic expression 24a + 20
Answer:
Step-by-step explanation:
Take the GCF of 24 and 20.
4 (6a+5)
The simplified expression is 4(6a+5).
What is meant by expression?An expression is a sentence with a minimum of two numbers or variables and at least one math operation.
The given algebraic expression is 24a + 20.
By taking 4 as common factor, the expression become like 4(6a + 5).
Hence, 4(a+5) is the simplified expression.
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