Which of the following graphs is described by the function given below?
y = 2x2 + 6x + 3
5
101
10
10
-20
20
- 10
10
-10
20-
101
A.
B.
C.
D.
A. Graph A
B. Graph B
O C. Graph C
D. Graph D
Answers
Answer:
Which of the following graphs is described by the function given below?
y = 2x2 + 6x + 3
-A. Graph A
The function y = 2x^2 + 6x + 3 is a quadratic function that has a vertex of (-1.5,-1.5)
How to determine the graph of the function?The equation of the function is given as:
y = 2x^2 + 6x + 3
Differentiate
y' = 4x + 6
Set to 0
4x + 6 = 0
This gives
4x = -6
Divide by 4
x = -1.5
Substitute x = -1.5 in y = 2x^2 + 6x + 3
y = 2(-1.5)^2 + 6(-1.5) + 3
Evaluate
y = -1.5
This means that the function y = 2x^2 + 6x + 3 has a vertex of (-1.5,-1.5)
See attachment for the graph of y = 2x^2 + 6x + 3
Read more about quadratic graphs at:
https://brainly.com/question/18797214
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Answer:
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A sequence of patterns is made from circular tiles and square tiles. Here are the first three patterns in the sequence:
a) How many square tiles are needed to make Pattern Number 7? [2 MARKS]
b) How many circular tiles are needed to make Pattern Number 20? [2 MARKS]
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Answers
Answer:
a) 49
b) 84
c) (B) -- always odd
Step-by-step explanation:
We observe that the number of square tiles is the square of the pattern number. The number of circular tiles is 1 more than the pattern number on each side of the square.
square tiles = n²
circular tiles = 4(n +1)
__
a)7² = 49 square tiles are needed for pattern number 7.
__
b)4(20+1) = 84 circular tiles are needed for pattern number 20.
__
c)The parity of the number of square tiles matches the parity of the pattern number. (The square of a number has the same parity as the number.) Since 4 is a factor in the number of circular tiles, its parity is always even. The parity of the total number of tiles will match the parity of the pattern number.
When the pattern number is odd, the total number of tiles will always be odd. (B)
Hello, would be very nice if someone could help me ! :)
A finite geometric series is the sum of a sequence of numbers. Take the sequence
1, 2, 4, 8, ..., for example. Notice that each number is twice the value of the
previous number. So, a number in the sequence can be represented by the
function f(n) = 2^n-1. One way to write the sum of the sequence through the 5th
number in the sequence is ∑^5 n-1 2^n-1.
This equation can also be written as S5 = 2^0+2^1+ 2^2+ 2^3+ 2^4. If we multiply this equation by 2. the equation becomes 2(S5) = 2^1+ 2^2+ 2^3+ 2^4+ 2^5
What happens if you subtract the two equations and solve for S5? Can you use this information to come up with a way to find any geometric series Sn in the
form ∑^a n-1 b^n-1 ?
Answers
Answer:
Step-by-step explanation:
2S₅ - S₅ = 2⁵ - 2⁰
S₅ = 2⁵ - 1
Sₙ = (bᵃ - 1) / (b - 1)
Simplify the ratio:
42 : 28 : 21
Please explain step by step to get marked as brainliest!
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Answer:
6:4:3
Step-by-step explanation:
Use 7 to simplify
ChallengE
See attachment and answer :)
Answers
[tex]\displaystyle{\sf\:4\:\sqrt{48}\:-\:\dfrac{5}{2}\:\sqrt{\dfrac{1}{3}}\:+\:6\:\sqrt{3}}[/tex]
Answer :[tex]\displaystyle{\boxed{\red{\sf\:4\:\sqrt{48}\:-\:\dfrac{5}{2}\:\sqrt{\dfrac{1}{3}}\:+\:6\:\sqrt{3}\:=\:\dfrac{127\:\sqrt{3}}{6}}}}[/tex]
Step-by-step-explanation:
We have given an expression.
We have to simplify the expression.
The given expression is
[tex]\displaystyle{\sf\:4\:\sqrt{48}\:-\:\dfrac{5}{2}\:\sqrt{\dfrac{1}{3}}\:+\:6\:\sqrt{3}}[/tex]
[tex]\displaystyle{\implies\sf\:4\:\sqrt{16\:\times\:3}\:-\:\dfrac{5}{2}\:\sqrt{\dfrac{1}{3}}\:+\:6\:\sqrt{3}}[/tex]
We know that,[tex]\displaystyle{\boxed{\pink{\sf\:\sqrt{a\:\times\:b}\:=\:\sqrt{a}\:\times\:\sqrt{b}\:}}\:\cdots\sf\:a\:,\:b\:\geq\:0}[/tex]
[tex]\displaystyle{\implies\sf\:4\:\sqrt{16}\:\times\:\sqrt{3}\:-\:\dfrac{5}{2}\:\sqrt{\dfrac{1}{3}}\:+\:6\:\sqrt{3}}[/tex]
[tex]\displaystyle{\implies\sf\:4\:\times\:4\:\sqrt{3}\:-\:\dfrac{5}{2}\:\sqrt{\dfrac{1}{3}}\:+\:6\:\sqrt{3}}[/tex]
We know that,[tex]\displaystyle{\boxed{\blue{\sf\:\sqrt{\dfrac{a}{b}}\:=\:\dfrac{\sqrt{a}}{\sqrt{b}}\:}}\:\cdots\sf\:b\: > \:0}[/tex]
[tex]\displaystyle{\implies\sf\:16\:\sqrt{3}\:-\:\dfrac{5}{2}\:\times\:\dfrac{\sqrt{1}}{\sqrt{3}}\:+\:6\:\sqrt{3}}[/tex]
[tex]\displaystyle{\implies\sf\:16\:\sqrt{3}\:-\:\dfrac{5}{2}\:\times\:\dfrac{1}{\sqrt{3}}\:+\:6\:\sqrt{3}}[/tex]
[tex]\displaystyle{\implies\sf\:\dfrac{16\:\sqrt{3}\:\times\:2\:\sqrt{3}\:-\:5}{2\:\sqrt{3}}\:+\:6\:\sqrt{3}}[/tex]
[tex]\displaystyle{\implies\sf\:\dfrac{16\:\times\:2\:\sqrt{3}\:\times\:\sqrt{3}\:-\:5}{2\:\sqrt{3}}\:+\:6\:\sqrt{3}} \\ \\\displaystyle{\implies\sf\:\dfrac{32\:\times\:3\:-\:5}{2\:\sqrt{3}}\:+\:6\:\sqrt{3}}[/tex]
[tex]\displaystyle{\implies\sf\:\dfrac{8\:\times\:4\:\times\:3\:-\:5\:+\:(\:6\:\sqrt{3}\:\times\:2\:\sqrt{3}\:)}{2\:\sqrt{3}}} \\ \\ \\\displaystyle{\implies\sf\:\dfrac{8\:\times\:12\:-\:5\:+\:(\:6\:\times\:2\:\times\:\sqrt{3}\:\times\:\sqrt{3}\:)}{2\:\sqrt{3}}} \\ \\ \\\displaystyle{\implies\sf\:\dfrac{8\:\times\:12\:-\:5\:+\:(\:12\:\times\:3\:)}{2\:\sqrt{3}}} \\ \\ \\\displaystyle{\implies\sf\:\dfrac{8\:\times\:12\:-\:5\:+\:12\:\times\:3}{2\:\sqrt{3}}} \\ \\ \\ \displaystyle{\implies\sf\:\dfrac{8\:\times\:12\:+\:12\:\times\:3\:-\:5}{2\:\sqrt{3}}} \\ \\ \\\displaystyle{\implies\sf\:\dfrac{12\:(\:8\:+\:3\:)\:-\:5}{2\:\sqrt{3}}} \\ \\ \\\displaystyle{\implies\sf\:\dfrac{12\:\times\:11\:-\:5}{2\:\sqrt{3}}} \\ \\ \\\displaystyle{\implies\sf\:\dfrac{132\:-\:5}{2\:\sqrt{3}}} \\ \\ \\\displaystyle{\implies\sf\:\dfrac{127}{2\:\sqrt{3}}} \\ \\ \\ \displaystyle{\implies\sf\:\dfrac{127}{2\:\sqrt{3}}\:\times\:\dfrac{\sqrt{3}}{\sqrt{3}}} \\ \\ \\\displaystyle{\implies\sf\:\dfrac{127\:\sqrt{3}}{2\:\times\:3}} \\ \\ \\\displaystyle{\implies\sf\:\dfrac{127\:\sqrt{3}}{6}} \\ \\ \\ \displaystyle{\therefore\:\underline{\boxed{\red{\sf\:4\:\sqrt{48}\:-\:\dfrac{5}{2}\:\sqrt{\dfrac{1}{3}}\:+\:6\:\sqrt{3}\:=\:\dfrac{127\:\sqrt{3}}{6}}}}}[/tex]
In the number 777.77 how does the value of 7 in the tenths place compare to the value of 7 in the hundredths place
Answers
Answer:
630
Step-by-step explanation:
the value of 7 in the tenths place is 70
the value of 7 in the hundredths place is 700
compare 700 and 70
So 700-70 = 630
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Answers
Answer:
5 sqrt(6) = x
Step-by-step explanation:
The pythagorean theorem states
a^2 + b^2 = c^2
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7^2 + (sqrt(101))^2 = x^2
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150 = x^2
Take the square root of each side
sqrt(150) = sqrt(x^2)
sqrt(25*6) = x
5 sqrt(6) = x
Rewrite this equation in Slope-intercept form
(PLEASE SHOW ALL WORK)
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have a great day :)
1. What is the value of x that satisfies the equation? Must show all proper work/steps!
32^2x = 16^2x+8
Student's Work
Student's Answer
A. x = 4
B. x =- 4
C. x = 16
D. x = 1
Please explain all steps
Answers
[tex] {32}^{2x} = 16 ^{2x + 8} \\ = > {2}^{5(2x)} = {2}^{4(2x + 8)} \\ = > {2}^{10x} = {2}^{8x + 32} \\ = > 10x = 8x + 32 \\ = > 10x - 8x = 32 \\ = > 2x = 32 \\ = > x = \frac{32}{2} \\ = > x = 16[/tex]
Answer:
x = 16
Hope you could get an idea from here.
Doubt clarification - use comment section.
What is the slope of the linear equation that has the values shown in the table
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Answer:We noted above that a linear function has the form f(x)= mx+b, f ( x) = m x + b, where m m is the slope of the line, and b b is the y y -intercept. Since m m and b b can take on various values
Step-by-step explanation:
what is an equation of the line that passes through points (4,-8) (-4,2)?
Answers
Answer:The equation of the line that passes through the points (–12, –8) and (–17, –16) is y + 16 = 8/5(x + 17). slope = (-16 + 8)/(-17 + 12) = -8/-5 = 8/5 y + 16 = 8/5(x + 17)
Step-by-step explanation:
How is 8/15 written as a mixed number?
Answers
Answer:
8/15 is already a proper fraction, therefore it cannot be converted to a mixed number. Hope this helps!
Step-by-step explanation:
Graph the system. Use the graph to approximate
the solution of the equation.
Answers
Answer:
2.09
Step-by-step explanation:
And set them up as a function. We could set y equals to each side of it. So if we set y equals to the left-hand. Side we get Y is equal to three has to the X power.
Answer:
Plot a graph of the function y = log (x) and move it by 1 unit to the left.
Plot the graph of the function y = x ^ 2, reflect over the x-axis, and move it 10 units up.
The coordinates of the intersection of the graphs are the solution.
Solution: x=3
I think this your answer you did not really say your answer?????
Help help help math math help
Answers
Hope this helps!!!
Given: Triangle ABC Prove: m∠A=64°
By the triangle sum theorem, the sum of the angles in a triangle is equal to . Therefore, m∠A+m∠B+m∠C=180°. Using the Substitution Property, (4x)°+90°+(x+10)°=180°. To solve for x, first combine like terms to get 5x + 100 = 180. Using the Response area, 5x = 80. Then, using the division property of equality, x = 16. To find the measure of angle A, use the Response area to get m∠A=4(16)°. Finally, simplifying the expression gets m∠A=64°.
Answers
Answer:
Given: Triangle ABC Prove: m∠A=64°
By the triangle sum theorem, the sum of the angles in a triangle is equal to . Therefore, m∠A+m∠B+m∠C=180°. Using the Substitution Property, (4x)°+90°+(x+10)°=180°. To solve for x, first combine like terms to get 5x + 100 = 180. Using the Response area, 5x = 80. Then, using the division property of equality, x = 16. To find the measure of angle A, use the Response area to get m∠A=4(16)°. Finally, simplifying the expression gets m∠A=150
Determine which of the values is a solution of 4t+6 is less than or equal to 10.
Values:
1, -8, -4, 3, 0, 7
Answers
Answer:
1, 3, 7
Step-by-step explanation:
4t + 6≤10
4t≤4
t≤1
Therefore, t can either be equal to or greater than 1.
__________________________________________________________
Hope this helps!!
If I am wrong, please tell me, I enjoy learning from my mistakes:)
Examine the figure. What is the measure of angle a?
Answers
Answer:
59Step-by-step explanation:
90+31=121
180-121=59
Answer:
a=59
basic fact:
angles on a straight line add up to 180
Step-by-step explanation:
we can ignore b for a start
31+90+a=180
121+a=180
121+59=180
a=59
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Please!!!!!!!!!!!!!!!!!!
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Answer:
i know it is C last year i took that quiz and well i studied /j
Step-by-step explanation:
A calf weighs 18 lbs. when it is 2 months old, and after 8 months it weighs 36 lbs.
Let x be the calf's age and y be the weight.
a. Write an equation in slope-intercept form that represents the situation.
Answers
The equation in slope-intercept form that represents the situation is y = 3x + 12
A linear equation is on the form:
y = mx + b
where y, x are variables, m is the rate of change and b is the initial value of y.
Let x be the calf's age in month and y be the weight.
A calf weighs 18 lbs. when it is 2 months old, and after 8 months it weighs 36 lbs. Hence it can be represented by:
(2, 18) and (8, 36). The equation is given by:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-18=\frac{36-18}{8-2}(x-2) \\\\y=3x+12[/tex]
The equation in slope-intercept form that represents the situation is y = 3x + 12
Find out more on linear equation at: brainly.com/question/14323743
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Answers
Answer:
10^3
Step-by-step explanation:
Answer:
10³
Step-by-step explanation:
10 × 10 × 10 = 10³
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Answer:
D
Step-by-step explanation:
:)
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Answer:
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B. 2/3
C. 1/3
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a
long. What is the length in feet of the actual house?
Answers
Answer:
30/5=68x6=48 feet
Step-by-step explanation:
divide the demesions
What kind of taxes are likely to pay for universities and police?
а
local taxes
b. state taxes
C federal taxes
d income taxes
Answers
Answer: I'd say the best answer is b.
Step-by-step explanation:
14.9 x 100 PLS HELP
Answers
Answer:
just move the decimal to the right two place, for two zeroes. The answer is 1490.
Step-by-step explanation: Just simply multiply 14.9 by 100.
Answer:
1490.Step-by-step explanation:multiply 14.9 by 100
Define the following sequence recursively: 96, 48, 24, 12, ....
Select one:
a. f(1)=12 f(n−1)=2⋅f(n) n≥2
b. f(1)=12 f(n−1)=−12⋅f(n) n≥2
c. f(1)=96 f(n)=12⋅f(n−1) n≥2
d. f(1)=96 f(n)=2⋅f(n−1) n≥2
Answers
Answer:
I do not see that any of your options will work.
Step-by-step explanation:
a) and b) have a false first statement because f(1) = 96, not 12
c) would create the sequence 96, 1152, 13824
d.) would create the sequence 96, 192, 384. 768...
I believe the correct answer would be
f(1) = 96 f(n) = ½f(n-1) n ≥ 2
which could be either c) or d) if taking potential typographic errors into account. Recording a "2" or "12" where a "½" ought to be.